Release studies on mesoporous microcapsules for new corrosion

R
ELEASE STUDIES ON
MESOPOROUS MICROCAPSULES
FOR NEW CORROSION PROTECTION SYSTEMS
Dissertation
zur
Erlangung des Grades
Doktoringenieur (Dr.-Ing.)
der
Fakultät für Maschinenbau der
Ruhr-Universität Bochum
Vorgelegt von
Magdalena Walczak
aus Breslau
Bochum 2007
Die vorliegende Arbeit entstand in der Zeit von Juli 2004 bis Mai 2007 am MaxPlanck-Institut für Kohlenforschung, Mülheim an der Ruhr, und am Max-PlanckInstitut für Eisenforschung, Düsseldorf, im Rahmen von International Max-Planck
Research School for Surface and Interface Engineering in Advanced Materials
(SurMat).
Die Protokolle aller Experimente sind im Laborjournal No 2501 (Siegel SPZ-MA)
des Max-Planck-Instituts für Kohlenforschung aufbewahrt. Teile dieser Arbeit
wurden bereits publiziert (s. Appendix L).
Dissertation eingereicht am:
Tag der mündlichen Prüfung:
Erster Referent:
Zweiter Referent:
22. August 2007
13. November 2007
Prof. Dr. rer. nat. Martin Stratmann
PD Dr. Frank Marlow
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FOREWORD
Completing a dissertation takes time. Most of it is spent rather intensively navigating
the intricacies of the investigated subject. As result, there is quite a chance that this
period of time will leave its mark on the author’s character. Obviously, a significant
piece of the fascinating world of science is assimilated, which alone suffice to
change one’s perception. Sometimes, however, it tends to go beyond the fixed frame
of what, eventually, touches down a paper or even the dissertation.
“Nature is independent from our thinking” once I was told by Dr. Frank Marlow. That day I thought of it as just a nice phrase,
still unaware of how painfully true it can turn out to be. In point of fact, while
working on this dissertation my thinking often had to rely on for-practical-reasonslimited sets of data suffering from for-technical-reasons-limited accuracy. Needless
to mention, that in such situations there is a natural tendency to engage in
oversimplifications, or even mis-simplifications, in understanding of the involved
processes. Especially, that intuition as trained in everyday life is not always
applicable to the lower length-scales. Washing with water, for instance, is nothing
but a mundane act of cleaning, whereas, down at the scale of a mesoporous particle,
it is already an act of modification. I admit that considering each and every aspect of
a doctoral work is a sure way of not proceeding toward the dissertation at all;
nevertheless, caution in drawing conclusions is a certainly healthy habit.
Thinking and rethinking is my lesson, for not always the first idea is the correct one.
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ACKNOWLEDGEMENT
This work would not have come into being, not in this form, if the chain of preceding
events had taken another course. One of the most decisive moments was accepting
me as a SurMat-student by my supervisors and the coordinator of the SurMatProgramme, Dr. Angela Büttner.
My work has been supervised by Dr. Frank Marlow in MPI Kohlenforschung and by
Dr. Michael Rohwerder in MPI Eisenforschung. I am truly indebted to them for
granting me a great portion of trust and freedom yet being always watchful and ready
to help. It is their supportive attitude that practically catalyzed this work, however,
each in a slightly different way. I could never get tired of the sometimes long
discussions with Dr. Marlow – he has always managed to keep my interest on. His
commitment to science, being so much in-line with his expertise, is simply adorable!
To Dr. Rohwerder I owe the debt of gratitude for the guide toward practicability,
which is doubtlessly, and particularly for me, equally important.
I would like to acknowledge the director of MPI Eisenforschung, Prof. Martin
Stratmann, and the director of MPI Kohlenforschung, Prof. Ferdi Schüth, for the
flexible organization of the institutes which greatly facilitated my work as well as for
the their constructive critics during the seminars. To Prof. Stratmann I am
additionally grateful for accepting the duty of referring this thesis.
Many thanks to those with whom I could collaborate: Dr. Florin Turcu and Mrs.
Diana Turcu (MPIE) for their committed support and inspiring discussions; Dr.
Pablo Arnal and Mr. Piotr Bazula (MPIK) for chemical paraphrasing; Mrs. Grazyna
Paliwoda-Porebska (MPIE) for the introduction into the world of corrosion inhibitors.
A very special thank to Mr. Ahmed Khalil (MPIK), soon ‘Dr.’ himself, for the
fruitful cooperation and constructive arguments.
My thanks to those who personally contributed some of the experiments: Mr. HansJoseph Bongard at MPIK and Mrs. Else-Marie Müller-Lorenz at MPIE for SEM, Mr.
Berd Spliethoff at MPIK for TEM and Mrs. Monica Nellessen at MPIE for the
skillfull SEM-FIB. Mr. Rainer Brinkmann and Mrs. Ulla Wilczok form MPIK are
acknowledged for their invaluable advice and patience in chemical laboratory. A
special thank I owe Nicolass Guettet who made his student practice in MPIE in
summer 2005 – he has a great share on testing the different coating formulations.
-8-
Also the young Mr. Christoph Schröter is acknowledged for his laboratory activities
at MPIK.
I shall not omit my colleagues whose presence made my stay in both institutes not
just a worth-while but a truly pleasant and enriching period of time.
To Dr. Iulian Popa I am grateful for his never-ceasing humor and his support in
struggling with English language. I’d also like to acknowledge Mr. Denan
Konjhodzic for occasional interaction.
The most intimate thank belongs to my dear Emmanoel – without his unconditional
companionship and all-dimensional support it wouldn’t have been possible to
succeed this way.
The International Max-Planck Research School SurMat is kindly acknowledged for
financial support.
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CONTENTS
FOREWORD
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ACKNOWLEDGEMENT
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CONTENTS
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SUMMARY
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1
- 15 -
INTRODUCTION AND OBJECTIVES
2
STATE OF THE ART
2.1
The concept of self-healing corrosion protection at the cut-edge
2.2
Release from mesoporous microcapsules
2.2.1 The material and structure of microcapsules
2.2.2 Mesoporous silica particles
2.2.3 SBA-3-like fibers and cone-like particles
2.2.4 Release from mesoporous silica
2.3
Diffusion and diffusion barriers in porous materials
2.3.1 Diffusion basics
2.3.2 Diffusion release models
2.3.3 Release functions
2.4
Corrosion inhibitors and model molecules
2.4.1 General aspects
2.4.2 Chromates
2.4.3 Molybdates
2.4.4 The model molecule
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3
METHODS
3.1
Microphotometric measurement of release
3.1.1 Capture of raw data
3.1.2 Construction of release curves
3.1.3 Accuracy of the method
3.2
Spectroscopic measurement of release
3.2.1 Capture of data and principle of the method
3.2.2 Construction of release curves
3.2.3 Accuracy of the method
3.3
Additional characterization methods
3.3.1 X-ray diffraction
3.3.2 Scanning electron microscopy (SEM)
3.3.3 Transmission electron microscopy (TEM)
- 40 - 41 - 41 - 43 - 45 - 46 - 46 - 48 - 51 - 52 - 52 - 53 - 54 -
4
PREPARATION OF MESOPOROUS MICROCAPSULES
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4.1
SBA-3-like mesoporous fibers
4.2
Mesoporous spherical particles
4.3
Preparation of mesoporous particles on support
4.4
Loading with guest molecules
4.4.1 Loading during synthesis
4.4.2 Post-synthetic loading
4.5
Modification of mesoporous particles
4.5.1 Soft treatments
4.5.2 Surface coating (waterglass treatment)
4.5.3 Microsurgery of the particles
- 55 - 56 - 57 - 58 - 58 - 59 - 59 - 59 - 60 - 61 -
5
STUDY OF RELEASE
5.1
Microscopic observation of release
5.1.1 SBA-3-like fibers
5.1.2 Discussion of release geometry
5.1.3 Cone-like particles
5.2
Interpretation of release curves
5.3
Diffusion data from the microphotometric method
5.3.1 SBA-3-like fibers
5.3.2 Cone-like particles
5.3.3 Anisotropy of diffusion in SBA-3-like particles
5.4
Diffusion data from spectroscopic method
5.4.1 Transformed release curves
5.4.2 SBA-3-like fibers
5.4.3 Spherical mesoporous particles
5.5
Importance of cross-wall transport and surface diffusion barriers
5.5.1 Cross-wall transport
5.5.2 Surface diffusion barrier
- 61 - 61 - 61 - 63 - 64 - 66 - 67 - 67 - 68 - 70 - 75 - 75 - 76 - 80 - 81 - 81 - 82 -
6
MODIFICATION OF RELEASE
6.1
Phenomenological treatment of modified release
6.1.1 Structure of modified particles
6.1.2 Release from modified particles (model-free analysis)
6.2
Modification of the surface diffusion barrier
6.2.1 Soft modifications by water
6.2.2 Soft modification by other solutions
6.2.3 Modification of mesopore openings
6.2.4 FIB and surface diffusion barriers
6.3
Modification by surface coating
6.3.1 Variation of pH during coating
6.3.2 Variation of temperature during coating
6.4
Release from calcined particles
- 83 - 83 - 83 - 85 - 89 - 90 - 92 - 94 - 96 - 96 - 97 - 99 - 102 -
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6.4.1
6.4.2
Release from calcined and loaded SBA-3-like fibers
Release from calcined and loaded mesoporous spheres
- 102 - 104 -
7
LOADING AND RELEASE OF SELECTED CORROSION INHIBITORS
7.1
Loading and release of chromates
7.1.1 Chromate species
7.1.2 Particles loaded from water solutions
7.1.3 Particles loaded from acidic solutions
7.2
Loading and release of molybdates
7.2.1 Molybdate species
7.2.2 Release fom loaded particles
7.2.3 Coated particles
7.2.4 pH-dependent release
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8
CONCLUSIONS
8.1
Measurement and characterization of release
8.2
Diffusion in mesoporous materials
8.2.1 Cross-wall transport
8.2.2 Surface diffusion barrier
8.2.3 Diffusion anisotropy
8.3
Relevance for corrosion protection
- 117 - 117 - 118 - 118 - 118 - 119 - 119 -
APPENDIX A: TABLES OF RELEASE FUNCTIONS
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APPENDIX B: ESTIMATION OF SCATTERING EXTINCTION ( ESCA )
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APPENDIX C: CONSTRUCTION OF RELEASE CURVES
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APPENDIX D: EXTINCTION COEFFICIENT OF RHODAMINE 6G
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APPENDIX E: EXTINCTION COEFFICIENT OF MOLYBDATES
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APPENDIX F: EFFECT OF PARTICLE SIZE DISTRIBUTION
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APPENDIX G: SIGNIFICANCE OF THE BARRIER PARAMETER
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APPENDIX H: MODIFICATION OF SYNTHESIS CONDITIONS
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APPENDIX I: ESTIMATION OF THE FIB-AFFECTED ZONE
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APPENDIX J: ABBREVIATIONS AND IMPORTANT SYMBOLS
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APPENDIX K: LIST OF CHEMICALS
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APPENDIX L: LIST OF PUBLICATIONS
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REFERENCES
- 142 -
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SUMMARY
The idea for “Release studies on mesoporous microcapsules for new corrosion
protection systems” has been motivated by a concept of corrosion protection, yet, it
addresses a more general issue of applicability of mesoporous silica for the storage
and delivery of functional molecules.
Coatings for corrosion protection usually contain pigments which constantly release
substances actively inhibiting corrosion (corrosion inhibitors). As most powerful
inhibitors are under discussion to be toxic to men and/or environment (chromates
already have been banned) this constant leaching poses a considerable problem.
Hence, intelligent coatings are requested, where the inhibitor is safely stored and
only released when needed. One of the most important properties of such a system is
the rate at which the inhibitor can be delivered.
In this work mesoporous silica particles have been employed as a carrier of the
functional molecules. Fibers and cone-like particles with coiled mesopores (SBA-3
type) and rhodamine 6G were investigated as a model system. The processes
governing release have been studied in detail. Two methods of release measurement
have been developed: microphotometric – suited for individual particles, and
spectroscopic – measuring release in a suspension of particles releasing the stored
molecules. Diffusion has been identified as the rate-limiting factor for the release.
It has been found that release from the studied SBA-3-like structures is dominated by
cross-wall transport and influenced by a surface diffusion barrier. The strong
tortuosity of the mesopores and transverse concentration gradients lead to
preferential transport of the guest molecules across silica walls. The outermost silica
wall is easily modified by external influences, e.g. drying, resulting in the formation
of a diffusion barrier. Further, transport along the mesopores is not restricted and
diffusion anisotropy occurs. The diffusion coefficient associated with cross-wall
transport differs by at least one order of magnitude from that associated with
transport parallel to the pores.
Soft treatments, commonly thought to have no effect on silica, have been shown to
modify release times by a factor of up to 3. A further retardation of release has been
achieved by deposition of thin silica coating on particle’s surface. The variation of
- 14 -
coating condition allows tuning of the release time between several minutes and a
few hours.
Preliminary investigations of incorporation and release of selected corrosion
inhibitors have been carried out.
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1 INTRODUCTION AND OBJECTIVES
Galvanized steel sheet is nowadays the third most produced form of flat steel in the
world [ 1 ], after non-galvanized hot- and cold-rolled strip. It finds versatile
applications in which the corrosion resistance plays a decisive role alongside the
classical engineering properties, such as strength or formability. Especially,
corrosion protection of the so-called cut-edge is of special importance as it is
inherent to many finishing processes; cut-to-length, drilling or clinching to name the
most common. One particular concept of corrosion protection at the cut-edge has
motivated this thesis.
The key idea is the localized delivery of a corrosion inhibiting substance, realized
exclusively at the cut-edge and only in case of acute corrosion. Such targeted
delivery is often described as smart or being capable of self-healing. In contrast to
the classical solutions its functionality is spatially selective. Also, no unwanted
uncontrolled release of inhibitors in the environment occurs.
The realization of a self-healing corrosion protection requires a system for storage
and release of functional substances. One possibility is the incorporation of
microcapsules into the galvanic layer (or the topcoat) that are gradually released as
the coating deteriorates. The microcapsules are then free to deliver the stored
substance with corrosion inhibiting property. Ideally, the rate of delivery is
proportional to the actual rate of corrosion. The design and release performance of
such microcapsules is essential for the entire concept. In practice, it is advantageous
to use microcapsules with porous cores rather than shell-like objects as they are in
principle mechanically more stable and have the capacity of sustained release. In
addition, they are more flexible due to the possibility of post-synthetic loading from
an arbitrary solution.
This thesis investigates both the abilities and the limitations of silica-based
mesoporous microcapsules as a delivery system. Specifically, the following aspects
are addressed:
1) Identification of a model system and an application-oriented prototype. A suitable
type of mesoporous particles had to be chosen from the variety of available
mesoporous materials.
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2) Loading with guest molecules. All pores of a single particle represent a usable
volume for storage of the functional molecules (guest molecules) but realization of
the filling is not trivial. An optimal procedure is sought for.
3) Characterization of release. There are no commercial methods available for
measuring release from disperse systems. The measurement and interpretation of
release requires the development of suitable techniques.
4) Prevention of leakage. In order to assure the maximum efficacy for corrosion
protection the loss of guest molecules during manufacturing (galvanic bath) should
be prevented. A method for preventing or significantly inhibiting release is required.
5) Modification of release kinetics. A tight encapsulation would disable any further
release (following of 4). A compromise is sought where an initial delay is followed
by an efficient delivery.
The investigation of the above-listed aspects can be conducted at a purely
phenomenological way. Both, try-and-error as well as a systematic variation of
process parameters would likely lead to a successfully working system. It is
conceivable to produce a self-healing system for corrosion protection without
understanding the underlying phenomena. However, the systematic approach is
advantageous as some of the phenomena are also of current interest for the science of
mesoporous materials and their knowledge enables systematic adaptation of the
system under changed condition. Especially the study of release kinetics offers a
unique opportunity to investigate the aspects of diffusion.
6) Release rate-limiting factors. In a diffusion-controlled release system it can be the
effective diffusion coefficient or a surface diffusion barrier. These two parameters
are to be determined.
7) Anisotropy of diffusion. Systems with ordered porosity are inevitably bound to
anisotropy of their properties. This also applies to diffusion; however, it has not been
studied on mesoporous silica particles so far.
This thesis embraces all of the aspects –1) to 7); however the most attention is given
to the measurement and characterization of release, because of their central meaning
for the self-healing corrosion as well as the fact that the obtained information can be
generalized for other applications.
- 17 -
2 STATE OF THE ART
2.1
THE CONCEPT OF SELF-HEALING CORROSION PROTECTION AT THE CUT-EDGE
The manufacture of flat steel products typically concludes with a cut-to-length or a
cut-to-shape of coil coated sheets. The ultimate cut generates a so-called cut-edge
where the uncoated steel substrate is exposed and so subjected to a usually unfriendly
environment. The sheets are coated with a metallic layer further covered with a
topcoat (paint, lacquer, etc.). The metallic layer – typically zinc or Zn-alloy in case
of steel, protects the workpiece relaying on the difference in corrosion potentials of
the two metals. The ratio of anode to cathode surface area is equal to the ratio of the
thickness of the zinc coating to that of the steel substrate; for the majority of
galvanized steel products it is 1/100 [2]. The applied amount of zinc is, however,
insufficient to assure the cathodic protection for an extended time period. The
accelerated sacrifice of Zn, besides the undesired corruption of the steel substrate,
leads also to unaesthetic detachment of the topcoat.
Since the inherent nature of cut-edge makes the cut-edge corrosion inevitable,
preventive solutions have been ever sought for [3]. The increase of the coating
thickness seems to be the simplest but uneconomic. Effective protection abstaining
from the costly increase of coating’s mass is only possible by means of advanced
techniques taking providing additional corrosion protection.
There is no official or commonly accepted definition of corrosion self-healing and
generally an intuitive description of the term is practiced in literature. The idea as
such seems to appear in mid 90s of the last century [4]; however, the first mention of
self-healing ability in the corrosion context dates back twenty years earlier [5]. Since
then a number of coating concepts has emerged, claiming that the function of
corrosion protection is active only in the case of on-going corrosion or that the
coating regenerates after its corrosion-related damage. Principally, extended in time
corrosion protection is indispensable but insufficient for a protection system to be
regarded as self-healing. Some composite coatings may provide such protection but
exclusively owing to the improved barrier properties, e.g. [6]. Improved barrier will
provide no advantage at the cut-edge: the zinc will corrode beneath it.
The problem of cut-edge corrosion is not limited to steel. Although on a different
basis, aluminum alloys are also affected. This is worth noting because an intense
- 18 -
investigation of self-healing corrosion protection for aluminum alloys is apparent in
literature [7,8,9,10,11,12,13]. Concerning the protection of steel the essential ideas
include:
a) Dispersion of corrosion inhibitor in the organic coating [14];
b) Precipitation of corrosion products, e.g. that of Zn [15], or Zn/Mg [16];
c) Incorporation of oxide colloidal particles into the zinc coating [17];
d) Enrichment of the polymer/metal interlayer with organic microcapsules [18] or
oxide nanocontainers [19];
e) Composite sol-gel coating with incorporated polyelectrolyte nanocontainers [20].
In all of the above-listed concepts, the storage and on-demand release of active
substances play the key-role. It seems to be the most universally fulfilled by some
kind of microcapsules. The name ‘microcapsules’ rather than ‘nanocontainers’ is
preferred because the physical size of the further investigated particles is in the µmrange. The universality of the microcapsule-based protection system is ensued by the
range of available microcapsules and corrosion inhibiting substances (or other
functional molecules). The possible types of microcapsules are discussed in chapter
2.2. A brief overview of the available corrosion inhibitors is provided in chapter 2.4.
The mechanism triggering the release is another indispensable element of a selfhealing coating. Even the most effective substance released in insufficient amount, or
at insufficient rate, cannot prevent a corrosion failure. Mechanical damage of the
coating is the most straight-forward option and has been regarded as the trigger in
literature, e.g. [18]. However, to rely exclusively on mechanical damage limits the
self-healing functionality to a single event. This single event very likely leads to
corrosion but itself does not make the case. Also, enhanced corrosion rate induced by
causes other than mechanical damage would not be covered. Therefore, the
triggering mechanism should better rely on the corrosion itself.
Under normal conditions of pH and temperature the corrosion of coated steel
proceeds by anodic metal dissolution:
Me ( s )
º
+
Me (naq)
+ ne −
and is accompanied by the cathodic oxygen reaction:
(Eq. 2.1-1)
2 STATE OF THE ART
O 2 ( g ) + 2 H 2 O( l ) + 4 e −
- 19 -
º 4OH
−
( aq )
(Eq. 2.1-2)
where mass transport of oxygen to the metal surface is the rate limiting factor [21].
An advantage can be taken from each of the two reactions if the microcapsules are
stored in the metallic coating. Dissolution of metal obviously results in release of the
microcapsules exactly at the location of corrosion. The capsules are then free to
release their contents. Optimally, the rate of this release is adjusted by local increase
of pH induced by the cathodic reaction (Eq. 2.1-2). The rise of pH on the steel part of
a corroding Zn/steel couple has been reported to reach 11.5 [22].
In summary, microcapsules incorporated into the metallic part of a regular steel
coating are a prospective system for corrosion protection at the cut-edge (Fig. 2.1-1).
The efficacy of the system depends on the rate at which the substance can be released
and how well the actual pH on the corroding surface is able to trigger this release.
Fig. 2.1-1. The prospective
concept
of
self-healing
corrosion protection at the cutedge: sacrificial dissolution of
Zn releases microcapsules,
which are then free to deliver
their contents – a corrosion
inhibiting substance – leading to
reduction of corrosion rate.
2.2
2.2.1
RELEASE FROM MESOPOROUS MICROCAPSULES
THE MATERIAL AND STRUCTURE OF MICROCAPSULES
An intuitive thought of a microcapsule is that of a shell-like object, possibly small,
whose main function is to safely store the active agents it contains (reservoir).
Release from such a microcapsule is typically realized by its rupture and a prompt
liberation of the carried substance. Meanwhile, a peak-like delivery is not necessarily
desired because it centers the efficiency of delivery to one spot in time only. It is
- 20 -
naturally thinkable to produce a shell-like capsule in which release is controlled by
permeation through the shell material; however, it would be hard to ensure the
mechanical stability of the coating as whole, due to the eventual collapse of the
capsule [18].
A prolonged in time delivery, so-called sustained release, can be achieved without
the loss of mechanical stability when a porous particle instead of a shell-like capsule
is used. Release of molecules stored in a porous matrix takes more time than those
stored in a shell-like particle owing to the diffusion through the porous matrix (Fig.
2.2-1). Since the readiness of diffusion is determined by the parameters of the porous
matrix, the rate of delivery could be additionally tuned. The use of a porous support
has one inconvenience - some of the capsule’s volume is occupied by the matrix,
lowering the usable volume, i.e. the loading capacity as compared with a shell-like
capsule of the same volume. However, there is a more flexible choice of material for
porous capsules and enhanced loading may be adjusted by matrix-substance
interactions.
Fig. 2.2-1. Destruction of a shell-like
capsule liberates the contents at once,
whereas diffusion through a porous
matrix extends the delivery in time
(scheme). The arrow indicates
initiation of release.
There are two principal types of material available for the synthesis of microcapsules:
1) Organic microcapsules. The fabrication of organic microcapsules can be realized
by coacervation of polymer precursor [ 23 ] layer-by-layer deposition of
polyelectrolyte [20] or entrapment in polymer matrix [24]. All the solutions have one
thing in common – they are very system-specific. The prescription that works for one
inhibitor is not necessarily operative with another one. This is a serious disadvantage
considering that there is no definite substance to act as “the” corrosion inhibitor
(chapter 2.4). Also problematic is the typically opposite pH response. Enhanced
release at low pH and impeded release at higher pH is typically due to polymer
2 STATE OF THE ART
- 21 -
ionization [ 25 ]. Further, organic materials are typically instable towards UV
radiation which could be a problem in out-door service. In conclusion, the
application of organic microcapsules is feasible but connected with additional
research effort.
2) Inorganic microcapsules. The combination of inorganic material with high
porosity is represented by mesoporous materials [26]. They are defined as materials
having pores in the size range between 2 and 50 nm [27]. Since the first reports on
ordered mesoporous silica in 1992 [28] quite an abundance in available shapes, sizes,
types of porosities and surface chemistries has been achieved. The pore volume
fraction is typically around 60% and the material can be synthesized virtually
independent from the later application, i.e. independent from the type of the
functional molecule to be stored. Especially interesting are silica-based mesoporous
particles as they retain their solid properties as long as pH of the surrounding
medium is not exceeding ~10.5 [29].
There are additional aspects that should be taken into account when designing
microcapsules for a self-healing coating. A good compatibility to the other coating
components and the ability to up-take and release the functional substance are the
most obvious. The microcapsules should also be of a suitable size. Microcapsules too
large could have a negative effect on the mechanical properties of the metallic
coating. Microcapsules too little, in turn, perform too fast delivery and are also
difficult to handle. The diversity of syntheses of mesoporous silica offers sufficient
flexibility in all these aspects.
2.2.2
MESOPOROUS SILICA PARTICLES
The synthesis of ordered mesoporous materials has been described by a patent filed
in 1969 [30,31], but the key-properties were not recognized by then. The work of
researchers from Mobil Company in 1992 [28] is customarily regarded as the birth
date of mesoporous materials. Since then a multitude of synthetic approaches has
been also developed by other groups. The most common codes associated with these
materials are: MCM - Mobil Company, SBA – University of Santa Barbara, MSU –
Michigan State University, KIT - Korea Advanced Institute of Science and
Technology, and FDU – Fudan University. The common characteristics are:
-
Pores of 2 – 50 nm with narrow size distribution
- 22 -
-
The matrix is made of amorphous silica
Specific surface area ~ 1000 m2/g
Pore volume ~ 1 cm3/g
Pores are often ordered (examples in Fig. 2.2-2)
Fig. 2.2-2. The X-ray diffraction patterns and the assigned pore structures of A)
MCM-41 (hexagonal), B) MCM-48 (cubic) and C) MCM-50 (stabilized lamellar).
Figure adapted from ref. [32].
In the most general view, mesoporous materials are fabricated by precipitation of a
precursor in the presence of surfactant, serving as a template. The template is then
removed depending on the further application. The detailed description of the
formation process is still deficient. The two regarded alternatives include liquid
crystal templating, with the surfactant forming an LC-phase prior to the precipitation
[33] and cooperative formation with no distinct LC-phase [34] (Fig. 2.2-3). Removal
of the template is in principle considered independent.
Fig. 2.2-3. Formation of mesoporous silica on the example of MCM-41 [35].
The ordered silica is formed by either (1) true liquid crystal templating [33]
or (2) cooperative surfactant/inorganic self-assembly [34].
The precipitation of silica is realized by condensation of silicon alcoxides, e.g.,
tetraethoxysilane. The precursor is first hydrolyzed:
2 STATE OF THE ART
≡ Si − OR + H 2 O
- 23 -
⎯
⎯→ ≡ Si − OH + ROH
(Eq. 2.2-1)
which is typically catalyzed by an acid (e.g., HCl) or a base (e.g., NH3). The rate of
hydrolysis may vary between minutes and days depending on the type of the
precursor. Subsequently, the silicic acid undergoes condensation after:
≡ Si − OH + HO - Si ≡
⎯
⎯→ ≡ Si − O - Si ≡ + H 2 O
(Eq. 2.2-2)
which results in formation of oligomeric species that are further free to form chains,
rings or branched structures and, in doing so, build a polymeric silicate. Eventually,
the polysilcates link together to form a 3D network around the template. At this point
the mesoporous material acquires its mesopore structure and also individual particles
are formed. Once the mesoporous material reached a sufficient degree of
condensation the templating molecules can be removed. The most common method
of removal is by calcination, which removes the template by thermal decomposition.
The silica framework stays nearly unchanged, however, its surface gets
dehydroxylated [29] and some shrinkage of the structure might occur [36].
There are many synthetic routes leading to mesoporous materials. They mostly differ
by the used tamplate, silica precursor and synthetic conditions (pH, temperature).
The code names do not imply any specific structure or synthetic route and are used
only by custom. For instance MCM-41 has long hexagonally ordered pores (Fig.
2.2-2 A) and is synthesized at high pH. The same type of structure can be achieved at
low pH using SBA-15 prescription. Besides the diversity of microstructures there is
also a considerable number of morphologies. The morphology can be (but need not
be) related to the crystallographic ordering (Fig. 2.2-4).
Fig. 2.2-4. Examples of mesoporous particles with hexagonal mesopore
ordering with different morphologies: A) spheres [37], B) helical fibers [38].
- 24 -
For the application as mesoporous microcapsules for the self-healing corrosion
protection, the choice of one of the spherical options, e.g., [37,39,40,41], seems to be
straight-forward. Such round morphology minimizes the danger of crack formation
around particle’s edges, when the particles are a part of the composite coating.
However, for the preliminary study of loading and release non-spherical particles of
SBA-3-type have been used. The leitmotiv is the exact knowledge of their structure
and feasibility of inspecting the outermost surface with TEM. Laborious and perilous
preparation of microtome slices can be avoided because the outermost mesopores are
visible in transmission.
2.2.3
SBA-3-LIKE FIBERS AND CONE-LIKE PARTICLES
The synthesis class SBA-3 has been described for the first time by Huo et al. in 1994
[42]. It delivers a broad range of pore structures and particle morphologies. The
structures of SBA-3 type have a common type of local pore ordering but depending
on the synthesis conditions they may take the form of fibers [43], curve shaped
particles [44], tubes [45], ribbons [46], or spheres [47]. All SBA-3-like particles
show strong structural anisotropy which can be derived from the fact of being
hierarchically structured [52].
The two types of SBA-3-like particles studied in this thesis are fibers and cone-like
particles. They are obtained from virtually the same synthesis except that the conelike particles can be exclusively grown on a support [48]. The common feature of
these particles is their rotational symmetry, related to a specific pore ordering. The
tubular mesopores are packed in a lattice, but unlike other mesoporous particles there
is no fully translational symmetry because the pores are coiled. The cross-section of
an SBA-3-like fiber produces circles in TEM [49], whereas hexagonal ordering is
seen in the perpendicular direction. The central axis about which coiling is realized is
a disturbance of the 3D translational periodicity, acting throughout the whole particle
(Fig. 2.2-5 A). For this reason it is called a ‘global singularity’ rather than just a
defect [50]. The particles possessing such a global singularity are sometimes called
‘circulites’.
Usually, one type of synthesis is associated with one type of local pore ordering;
however, one type of local pore ordering can lead to different particle morphologies.
Although coiling of tubular micelles has been proposed as a mechanism of circulate
formation [51], particles with coiled pores are not the only outcome of SBA-3
2 STATE OF THE ART
- 25 -
synthesis. Also among circulates there is a duality. Two types of circulates can be
realized by different embedding of the global singularity into the local hexagonal
ordering [52]. In a fiber, the unit vector of the local order is parallel to the singularity,
whereas perpendicular orientation is the case of a cone-like particle (Fig. 2.2-6). This
fact implies that the two types of particles are equivalent on the meso-scale and
therefore equal transport properties can be expected. The overall release behavior can
be however additionally influenced by the particle shape.
Fig. 2.2-5. A) Structure of an SBA-3-like fiber (scheme): mesopores are coiled around
the global singularity, the local pore ordering is hexagonal. B) X-ray diffraction pattern
of SBA-3-like fibers from ref. [ 53 ]: a) reflection geometry, b) and c) transmission
geometry.
The cone-like particles can be additionally synthesized in an array [48]. Such
ordering facilitates addressing and manipulation of individual particles. Also, the
coordinate system is well defined since the particles are fixed on a surface.
Whereas the model study on SBA-3-like particles is useful for detailed investigation
of diffusion and surface modifications it becomes impractical when bigger amounts
of particles are required. Long synthesis time and unfeasible scaling of the synthesis
are the critical aspects. For the systematic study of release modifications (e.g.,
surface coating) mesoporous silica spheres are preferred. They are derived from acid
synthesis using the same surfactant as SBA-3 [39]. For this reason they can be
regarded as a type of SBA particles. However, the structure of the spheres is not well
- 26 -
studied in literature. Especially, the mesopore ordering and particle surface are not
known with detail. They are therefore not a good model for the study of diffusion.
Fig. 2.2-6. A) Scheme of the structure of cone-like particles and fibers produced
in SBA-3-type synthesis with specified details at different levels of hierarchical
organization. The capital letters indicate the levels: P-primary, S-secondary, Tternary and Q-quaternary, which are associated with a specific length scale.
Adapted from Ref. [52]. B) SEM of the particle array shown in A). C) SEM of
fibers amid other SBA-3-like particles.
2.2.4
RELEASE FROM MESOPOROUS SILICA
The application of mesoporous silica as a device for storage and delivery of
functional molecules appeared soon after the recognition of the up-taking ability of
the material. It has immediately acquired attention in the field of drug delivery [54].
The problem of drug delivery has been a subject of pharmaceutical science since
long and many basic concepts of release have been derived from this field of
research.
2 STATE OF THE ART
- 27 -
The most fundamental aspect of drug delivery is the delivery rate, or, depending on
the point of view – the rate at which the functional molecules are released. The
meaning of the rate, as well as the rate limiting factors, is thoroughly discussed in the
classical textbooks [55,56]. The overall release kinetics is a result of simultaneously
occurring processes, which can generally be classified as diffusion, erosion/chemical
reaction, swelling or osmosis [55]. However, only one of them is typically the rate
limiting and therefore priming the construction of a release model (chapter 2.3.2).
Mesoporous silica has extended the functionality of drug delivery by additional
possibilities of controlling release rates [57]. The following strategies have been
described in literature: (1) Tuning the native properties of pore surface: Controlled
release of selected drugs has been reported as due to sylilation [58] or other type of
hydrophobization [59]. (2) Grafting the silica pore walls with stimuli responsive
species: Temperature controlled and pH-controlled release has been shown for
mesoporous silica grafted with PNIPAAm (poly-N-isopropylacrylamide) [60] and
polyelectrolyte [61], respectively. The pH-response of these particles is however
reverse to that required for corrosion self-healing (opening at low pH). (3) Capping
the pore mouths: Covalently bonded CdS caps enable release only after cleaving with
disulfide reducing agents [ 62 ]. Similarly, iron oxide caps can be cleaved with
antioxidants [63]. Also photoactivation and dimerization of coumarin tethered at the
pore entrance has been reported [64]. Valve-like behavior of pore mouths has been
reported after capping with redox-switchable rotaxanes [65].
Coating of mesoporous silica particles has not been explicitly regarded as means for
tuning the release rates so far. For the corrosion application coating with a thin layer
of silica seems to be the most interesting due to its pH-dependence (Fig. 2.2-7). Thin
coatings of several nm are typically produced by concentration of undersaturated
silicate solution or condensation of silica precursor [66,67]. However, the reaction
times are long in this case (hours) which disqualifies these approaches for coating of
porous particles. Precipitation from a silicate solution by either cooling of hot
saturated solution or lowering the pH of an aqueous solution seem to be more
appropriate.
- 28 -
Fig. 2.2-7. Distribution of aqueous silicate species at 25°C in A) 0.01M
Si(IV) and B) 10-5M Si(IV). Ionic strength I = 3m [29].
An independent question in the study of release is the release measurement. Any
method indicating the amount of released (or remaining) molecules, e.g.
chromatography or NMR, is in principle suitable. In the pharmaceutical science
typically a pellet is pressed and the concentration of functional molecules measured
in the liquid phase, e.g.,[58]; or a portion of the suspension filtered at relevant time
intervals, e.g., [59]. These two approaches are not applicable for fast releasing
disperse systems. Therefore, due to the lack of alternatives, development of
experimental techniques is a requisite of this thesis.
2.3
2.3.1
DIFFUSION AND DIFFUSION BARRIERS IN POROUS MATERIALS
DIFFUSION BASICS
The phenomenon of diffusion plays the key-role in interpretation of release data from
the mesoporous microcapsules. Experimentally, two kinds of diffusion problems can
be considered, the so-called transport diffusion, where the particles diffuse in a nonequilibrium situation from one side of the system to the opposite side, and the self(or tracer-) diffusion under equilibrium conditions. The problems are described by
the transport diffusion coefficients Dt and the self-(or tracer) diffusion coefficient Ds,
respectively. Each of them is derived from a different fundamental approach.
The molecular-kinetic theory of heat applied to Brownian motion by Einstein [68]
and Smoluchowski [69] leads to the definition of Ds through what became to be
known as Einstein-Smoluchowski equation of diffusion [70]:
x 2 (t ) = 2 Ds t
(Eq. 2.3-1)
2 STATE OF THE ART
- 29 -
where x 2 (t ) represents the mean square distance covered by a diffusant during the
observation time t. For spherical particles of radius R suspended in a liquid of known
viscosity η the coefficient can be further expressed by Einstein-Stokes equation [71]:
Ds =
kT
6πRN Aη
(Eq. 2.3-2)
where k, T and NA are Boltzmann constant, absolute temperature and Avogadro
number, respectively.
The phenomenological treatment of Fick describes diffusion in analogy to Ohm’s
law of electric current and Fourier’s law of heat conduction as the proportionality
between flux of matter Φ and the gradient of its concentration c [72]:
Φ = − Dt
∂c
∂x
(Eq. 2.3-3)
This relation is also known as Fick’s first law of diffusion. When the movements of
the diffusing molecules is fully uncorrelated and the system is thermodynamically
ideal then Ds = Dt . However, from the view-point of thermodynamics the “true”
driving force for diffusion is the gradient of chemical potential rather than the
gradient of concentration leading to corrected diffusion coefficient [73]:
Dt = BRT
∂ ln a
∂ ln c
(Eq. 2.3-4)
where B, R and a are mobility, gas constant and activity, respectively. Since the
driving force for any transport process is the gradient of chemical potential, rather
than the gradient of concentration, ideal Fickean behavior in which the diffusivity is
independent of sorbate concentration is realized only when the system is
thermodynamically ideal. In practice, it has become a custom to deal with “effective”
or “net” diffusivities [74,75]. The effective coefficient is specific not only for one
type of molecule but, principally, for the whole system. It is strongly dependent on
the spatial averaging introduced by the assumed flux direction, which is essential in
the case of anisotropic media.
Description of transport in porous bodies requires a further broadening. The reason
of changed diffusion behavior is the confinement of free space and the consequential
interaction with pore walls. Obviously porosity, pore size and geometry as well as
- 30 -
concentration and other conditions should be taken into account in a proper
description. But such detailed information on the porous system is rarely available
and the common practice is to use another effective coefficient in place of the
transient diffusion coefficient in the Fickean approach (Eq. 2.3-3). This effective
coefficient is expressed by:
Deff,t =
εp
Dt
τ
(Eq. 2.3-5)
where τ and εp represent tortuosity and porosity, respectively. Tortuosity τ is the key
parameter for describing the enhancement of molecular trajectories in porous media
as compared with the free fluid. In case of small pores, collisions between the
diffusing molecules and pore walls become significant, leading to concentration
independent flux (Knudsen diffusion) [ 76 ]. In the limiting case of very strong
molecule-wall interactions and small pores, mass flow is limited by surface diffusion
[77]. The three types of diffusion in porous medium are depicted schematically in
Fig. 2.3-1.
Because diffusion of fluids inside a porous matrix is particularly relevant for such
vital research fields as catalysis, adsorption and membrane separation, the subject is
relatively well described [78]. Of special importance is diffusion in zeolites [79] –
microporous crystalline aluminosilicates, distinct for their fine (< 2 nm) and ordered
pores. The consequences ascribed to this specific structure are anisotropy of
diffusion [80] and single-file diffusion [81]. Another peculiarity of diffusion in
zeolites is a strong discrepancy between diffusion coefficients determined by
microscopic and macroscopic methods. Microscopic methods, such as pulsed-field
gradient nuclear magnetic resonance (PFG NMR) or quasi-elastic neutron scattering
(QENS) deliver coefficients typically several orders of magnitude higher than those
delivered by macroscopic methods, e.g., gravimetric measurement of up-take rate. A
valid explanation of this fact is so-called surface diffusion barrier [82] – transport
resistance located at the zeolite surface. The existence of the barrier has been
reported for NaCaA zeolites [83], for ZSM-5 [84] and later for MFI zeolites [85].
2 STATE OF THE ART
- 31 -
Fig. 2.3-1. The three distinct mechanisms by which guest molecules get
transported within a porous matrix: A) bulk diffusion (molecular diffusion),
when molecule-molecule collisions are dominant, B) Knudsen diffusion,
when molecule-wall collisions are dominant, C) surface diffusion via
adsorption sites.
The nature of the surface diffusion barrier on zeolites has been speculated to have
various origins: i) “evaporation barrier” arising from the discrepancy between the
energy of desorption and the activation energy required to leave a crystal surface [86];
ii) structural defects at the surface induced during zeolite synthesis [ 87 ]; iii)
deposition of impenetrable material at the outside of individual crystals [88]; iv)
changes in the crystal structure due to chemical reaction during the process of cation
exchange and hydrothermal treatment [ 89 ]; v) inhomogeneity of the zeolites
potential field at crystallite surface [90]; vi) steric repulsion at the entrance to small
pores [91]; vii) reorientation of the molecules from their gas phase geometry to the
adsorbed state [92]; viii) other peculiarities of adsorption at pore mouth [93].
The studies on zeolites can be used as an inspiration but the analytical tools do not
fully apply to mesoporous materials because the bigger mesopores do not restrict the
molecular mobility to the Knudsen regime. The literature data on diffusion in
mesoporous materials is limited to determination of effective diffusion coefficients
using chromatography (e.g., [ 94 ]), gas sorption (e.g., [ 95 ]), or fluorescence
microscopy (e.g. [96]). The only work that addresses diffusion anisotropy of MCM41 by means of PFG-NMR is [97]. There are no data on eventual surface diffusion
phenomena.
2.3.2
DIFFUSION RELEASE MODELS
Each release curve measured for a mesoporous particle is a statistical output of
several processes. In the case of single particle measurement diffusion through the
particle pores, diffusion through the matrix, diffusion across interfaces, surface
adsorption/desorption, surface or bulk erosion are the most relevant. In case of
release from a particle population the effects of particle size and shape distributions
- 32 -
additionally modify the release behavior. Due to the complexity and interference of
the process, certain assumptions are necessary in order to construct a release model.
For mesoporous silica diffusion through the particle is assumed to be the most
relevant process. Swelling and erosion can be excluded on the basis of aqueous
stability of the silica matrix [98,99,100]. Osmosis is neglected because the flow of
solvent molecules is much faster than that of the guest molecules. The contribution
of osmosis would only affect the initial stages of release, which are not covered by
the release experiment. The most dangerous influence of osmosis would be cracking
of the silica structure. Such cracks have been, however, not observed on the studied
particles. There is also no literature data on osmosis in mesoporous silica.
Consequently, the release models are constructed by solution of the diffusion
equation (second Fick’s law):
∂c
= ∇( Deff ∇c)
∂t
(Eq. 2.3-6)
where c and Deff are concentration and the effective diffusion coefficient,
respectively. This is a partial differential equation of second order requiring
additional conditions for its solution. A comprehensive set of solving methods in
simple symmetries is provided by Crank [101]. However, most of the real systems
are more sophisticated than the simple solutions of Eq. 2.3-6 allow. Extended models
have been therefore studied in literature. Release into limited volume of liquid has
been described by Jo et al. [102]. The effect of morphology of a coating film and the
related drug diffusivity were studied by Chen and Lee [ 103 ]. Partially coated
matrices are described analytically by a semi-empirical model of Grassi et al. [104].
The mutual influence of many releasing particles has been studied by Wu et al. [105].
However, most of the models are at least partially numerically solved. A general,
analytical solution of the diffusion problem with irregular boundaries, boundaries of
second and third kind (defined by gradient) as well as composite bodies is a rather
complicated task [ 106 ]. Both numerical solutions and complicated analytical
functions are impractical for fitting the experimental data due to the required
computational effort.
The other extreme of solving diffusion problems there are the special cases of
approximated solutions. First order kinetics, or membrane model, can be applied
when constant flux at the releasing surface is present. This is usually the case at
2 STATE OF THE ART
- 33 -
steady state or in the presence of a strong diffusion barrier. The release from
mesoporous particles studied in this thesis cannot be described by the first order
kinetics. A symmetrical solution of the diffusion problem is applied.
The solution requires the choice of a boundary condition. Let us consider the
boundary x = X, where x is a relevant dimension and X defines the position of the
boundary along that dimension. In the case of a plane-sheet this correspond with the
thickness (X = L) and in the case of a sphere or a cylinder with the respective radius
(X = R). X is sometimes referred to as the characteristic diffusion length. The two
types of boundary conditions are expressed by either concentration or flux at the
boundary (Fig. 2.3-2):
Fig. 2.3-2. Ilustration of the two types of
boundary conditions used for the solution
of diffusion equation: A) perfect sink
boundary - concentration at the boundary
is always equal the concentration outside;
B) boundary hindrance – flux through the
boundary proportional to the actual
concentration difference through the
boundary.
1) Perfect sink boundary: the concentration c at the boundary x = X, is always equal
the actual concentration in the up-taking solvent, csol:
c( x = X , t ) = csol
(Eq. 2.3-7)
For a virtually infinite volume of the up-taking solvent the increase of concentration
is negligible, which simplifies the condition to:
c( x = X , t ) = 0
(Eq. 2.3-8)
2) Boundary hindrance (surface diffusion barrier): the flux through the boundary is
related to the actual concentration difference through the boundary. For a thin
boundary such relation can be assumed to have a linear form:
- 34 -
− Deff
∂c
= β (c − csol )
∂r
(Eq. 2.3-9)
where β is the proportionality constant. The physical units of β let is associate with a
mass transfer coefficient. In practice it is, however, convenient to introduce a
dimensionless parameter, hereafter referred to as the barrier parameter:
α=X
β
Deff
(Eq. 2.3-10)
It is worth noting that Eq. 2.3-7 is a special case of the more general Eq. 2.3-9, for a
large barrier parameter α. It means that solution of the diffusion problem with the
condition (2) will also be more general and can always fit the data. However, such fit
is very likely unstable because α tends to be an ever greater number. It is therefore
reasonable to consider a physical reason for the use of condition (2).
2.3.3
RELEASE FUNCTIONS
By a release function a mathematical expression is understood that is used for fitting
experimental data in order to determine the diffusion coefficient associated with the
assumed release model. All release functions are based on the general form of the
solution of the diffusion problem:
∞
c( x, t ) = c max ∑ a n ( x) exp(− Β n Deff t )
(Eq. 2.3-11)
n =1
where x is the geometry specific coordinate and the functions a n (x) and coefficients
B n vary depending on the geometry and the boundary condition (Appendix A, Tab.
A-1 ).
The numbers obtained in a release experiment are rather extinctions than
concentrations, it is therefore convenient to express the release functions in terms of
extinctions. Because absorption extinction is proportional to concentration (LambertBeer’s law) it can be exchanged with concentration without influence on the
diffusion coefficient. The total released amount is obtained by integration of Eq.
2.3-11 and has the general form:
∞
⎛
⎞
E abs (t ) = E max ⎜1 − ∑ Α n exp(− Β n Deff t )⎟
⎝ n =1
⎠
(Eq. 2.3-12)
2 STATE OF THE ART
- 35 -
The corresponding coefficients A n and B n are given in Tab. A-2 (Appendix A).
Alternatively, Eq. 2.3-12 can rewritten to describe the total remaining amount:
∞
E abs (t ) = E max ∑ Α n exp(− Β n Deff t )
(Eq. 2.3-13)
n =1
All the above release functions have the form of a sum of exponential functions;
however, with different weights ( A n ) and time constants ( B n ) of the individual
exponents. This is the fundamental reason why each of the function would fit any
regular release curve.
The general form of the time dependence is determined by the product of B n and the
effective diffusion coefficient. Although B n are defined by the roots of the
characteristic equation they are generally time-independent. This has the practical
consequence that it is numerically justified to fit only one parameter being a product
of two numbers rather than the individual factors. Otherwise a fatal fit instability
may occur. It is convenient to separate the roots of the characteristic equation from
the characteristic diffusion length in B n , and treat Deff / X 2 as an individual fit
parameter. It should be noted that the derived parameter has a quadratic dependence
on X. The precision of X is therefore essential for the determination of Deff.
The extinction data obtained from the microphotometric method are described by Eq.
2.3-13 only if the extinction is integrated over the whole particle. In case of smaller
sampling the measured extinctions correspond with average concentration in the
particle volume transilluminated by the light beam (Fig. A-1, Appendix A). The light
beam can be approximated by a cylinder of radius ρ and the due extinctions are
proportional to the average:
c (t ) =
1
X
∫
c( x, t ) y dy
(Eq. 2.3-14)
where X = 2R in case of fiber or sphere and X = L in case of a plane-sheet. For the
approximation of thin light beam (ρ → 0 ) the integration of Eq. 2.3-11 delivers
release functions of the form of Eq. 2.3-13; however, with different coefficients A n
and B n (Tab. A-3, Appendix A).
The number of summands in release functions can be reduced in order to accelerate
the fitting. The reduction is justified by the converging character of A n diminishing
- 36 -
the importance of higher n-components (Tab. A-4, Appendix A). In practice nmax =
50 is used.
2.4
2.4.1
CORROSION INHIBITORS AND MODEL MOLECULES
GENERAL ASPECTS
Corrosion inhibitors are generally defined as substances that, when brought into
electrolyte with a corroding metal, diminish the rate of corrosion. Particularly
important are substances that accumulate at the metal/electrolyte interface by either
adsorption at the metal surface or formation of a thin film at the interface. In practice,
only substances that do so already at low concentrations, i.e. lower than few
mmol/kg, are technically considered corrosion inhibitors. They are customarily
classified as:
a) anodic inhibitors; cause a large anodic shift of the corrosion potential forcing the
metallic surface into passivation range (e.g., chromates, molybdates, phosphates),
b) cathodic inhibitors; either decrease the cathodic reaction itself or precipitate on
the cathodic areas (e.g., sodium sulfite, calcium, zinc oxide),
c) organic inhibitors; typically form a hydrophobic film at the metal surface (e.g.,
sodium benzoate),
d) precipitation inhibitors; form a protective film blocking both anodic and
cathodic sites (e.g. silicates),
e) volatile inhibitors; deposited from vapor phase (e.g., morpholine, hydrazine).
The current state of the theory of metal corrosion inhibition is reviewed by
Kuznetsov in [107]. The adsorption and formation of protective layers on the metal
surface depends on the charge the inhibitor species carry and their ability to form
chemical bonds between each other. As a rule, cation-active corrosion inhibitors
hinder the cathodic reactions or the active dissolution of the metal, whereas anionactive inhibitors are more efficient in the protection against localized corrosion.
Generally, all kinetically active corrosion inhibitor pigments of technical significance
are inorganic salts Amn + Bnm − or basic salts Amn + Bnm−−z OH z− [108], where n,m = 2 or 3 and
the ions are listed in Tab. 2.4-1. Also some rare earth element such as cerium(III),
lanthanum(III) or yttrium(III) have recently been recognized as inhibitors of the
oxygen reduction [109,110,111].
2 STATE OF THE ART
- 37 -
Chromates are by far the most effective inhibitors of Fe, Al, Cu and Zn corrosion.
CrO42− is a typical oxidant passivator of the anodic and cathodic type, functioning
independent from the presence of dissolved oxygen. Unfortunately, chromates are
very toxic and serious restrictions in their use are being introduced [112]. There is,
however, no generally accepted replacement for chromates. Many substances are
being tested but up to now no equivalently good successor has been found.
Molybdates are currently considered but still not established. Owing to this fact, the
study of release in this thesis is preferentially conducted on a suitable model
molecule (chapter 2.4.4).
Amn +
Bnm −
Zn 2+
Ca 2+
Sr 2+
Al 3+
Ba 2+
CrO 24PO 34MoO 24BO -2
HPO 32-
Mg 2+
NCN 2-
Tab. 2.4-1. Possible constituents
of a corrosion inhibitor pigment of
the general form Amn + Bnm − or
Amn + Bnm−−z OH z− .
CO 32-
The two inhibitors selected for the study are chromates and molybdates. Chromates
are quite harmful to the environment but their application at the very corrosion site in
only the absolutely necessary amounts seems to be purposeful (controlled release).
Such environmentally minimized danger provides the motivation for considering
chromates as candidate for the self-healing coating. Molybdates are studied as an
alternative. The molybdate ion, MoO42-, and chromate ion, CrO42−, are isoelectronic
and similar electrochemical behavior is intuitively expected. Yet, the efficacy of
molybdate is limited, mostly due to the oxygen dependency of the action mechanism
[113]. Molybdates are established as anodic type, oxygen dependent and non-toxic
inhibitors of Fe and Al corrosion [108]. Although with lower efficacy molybdate ions
have been reported the corrosion rate when incorporated into the polymer coating
[114].
A synergy effect in corrosion inhibition could be expected from the silica of the
mesoporous particles. Soluble silica species have been reported to exhibit a corrosion
- 38 -
inhibiting effect on iron [115]. Although the effect is limited to high concentrations
and possibly related to local change of pH [116], it could be efficient due to the
localized nature of the delivery.
2.4.2
CHROMATES
The general term “chromate” applies to both chromates and dichromates being salts
of chromic and dichromic acid, respectively. The chromate ion, CrO42-, and
dichromate ion, Cr2O72-, bear a haxavalent chromium. In an aqueous solution,
chromate and dichromate anions are in equilibrium:
2CrO42− + 2H3O+
º Cr O
2
7
2−
+ 3H2O
(Eq. 2.4-1)
which can be pushed in either direction by adjusting pH [117]. The two chromate
species can be distinguished spectroscopically by the different wavelength and
different extinction coefficients of the absorption peak [118]. A hydrochromate ion,
HCrO4-, of similar to Cr2O72- extinction spectrum may also be formed [ 119 ];
however, its molar extinction coefficient is very low so that it can be neglected in the
course of this study. Further condensation to polychromates occurs in very strong
acids [117]:
2CrnO3n+12- + 2H+
º Cr
mO3m+1
2-
+ H2O
(Eq. 2.4-2)
where m = 2n are integers. The so formed polychromates can be associated with
larger molecule sizes [120]. There is, however, no literature data available on the size
of polychromates in the function of pH.
2.4.3
MOLYBDATES
Some molybdates have been already
commercialized as corrosion inhibitor pigments;
mostly in the form of zinc-, calcium-, and
phosphomolybdate. Phosphomolybdate seems to
be especially interesting because of the
additional presence of phosphate promising a
synergetic inhibition [121].
Molybdates are compounds containing the
molybdate ion, MoO42-, where Mo is hexavalent.
Fig. 2.4-1. Structure of the largest
known polymolybdate ion with
Mo36.[122]
2 STATE OF THE ART
- 39 -
The condensation reaction is analogous to that of chromate [117]:
2MonO3n+12- + 2H+
º Mo
mO3m+1
2-
+ H2O
(Eq. 2.4-3)
but the equilibrium constants are different. In fact, molybdates have such a strong
tendency to condensation that the pure monomolybdate ions exist only in alkaline
solutions. In very strong acids molybdic acid, MoO3.2H2O, precipitates, which
converts into monohydrates when warmed. Between these two extremes polymeric
anions are formed (Fig. 2.4-2). The largest known isopolyanion is that of
[Mo36O116(H2O)16]8- and was obtained in nitric acid of pH = 0.4 (Fig. 2.4-1) [122].
The exact distribution of the molybdate species in the function of pH, temperature
and concentration has been intensively studied in the past decades; yet, the picture is
still not complete and current research ongoing [123,124,125].
Fig. 2.4-2. Occurrence of phosphomolybdate species in the function of pH: A)
obtained with ESI-TOF-MS [123] and B) obtained from 31P NMR [126].
2.4.4
THE MODEL MOLECULE
The model molecule applied in the study of release is rhodamine 6G, denoted as
Rh6G for short. It belongs to the family of cationic red dyes [ 127 ] and its
characteristic UV-Vis spectrum as well as molecule structure are shown in Fig. 2.4-3.
No corrosion inhibiting properties are associated with rhodamine and yet there are
some reasons for using it as model molecule. (i) It can be easily included into the
SBA-3 synthesis [42], which greatly shortens the time of particles preparation.
Especially, modifications of the external surface can be studied on as-synthesized
particles. (ii) Unlike most of the inhibitors it is easily detectable. Release of already
- 40 -
small amounts can be followed with a regular spectrometer. (iii) The relatively large
size of the Rh6G molecule makes possible the discrimination of cross-wall transport.
(iv) The doped particles have a very characteristic and intense color, which improves
security at the working place as they are well visible.
Fig. 2.4-3. The characteristic
UV-Vis
spectrum
of
rhodamine 6G (Rh6G) and
the molecule structure (inset)
[127].
3 METHODS
The characterization of a disperse release system involves several parameters whose
determination requires the application of several methods.
Evidently, the most important characteristic is the kinetics of release. It signifies the
efficiency of delivery both in total delivered amount and the delivery time. The
determination of release kinetics is principally based on monitoring the actual
released or remaining amount. Although there are many conventional methods for
measuring the quantity of desired molecules, they mostly work on solutions or bulk
materials, and there is no standard method applicable to a disperse system. For this
reason, two experimental methods have been developed in the scope of this work.
The two methods aim the characterization of release from a single particle of the
dispersion and release from a whole particle population. Owing to the main detection
principle, employing either a light microscope equipped with a recording device or a
UV-Vis spectrometer, the methods are named microphotometric and spectroscopic,
3 METHODS
- 41 -
respectively. In this chapter a detailed description of the essential facets of both
methods is due.
However, the measured release kinetics is intimately bond to specific particle
characteristics. Particle size, particle shape, pore size, and their distributions as well
as the stability of the release system are usually regarded the most important. For
their characterization, standard techniques were used: X-ray diffraction, scanning and
transmission electron microcopy and static light scattering. These are treated with
fewer details and only the most relevant aspects are introduced.
3.1
MICROPHOTOMETRIC MEASUREMENT OF RELEASE
The microphotometric measurement of release is a method designed for studying the
kinetics of release from single particles. It has the advantage of providing the size
and geometry of the particle under study precisely. This fact facilitates the
interpretation of the release data, since the two factors have great influence on the
later derived diffusion data. The method is generally applicable to any kind of
particle visible under microscope (here Leitz, Orthoplan was used). However, the
types of guest molecules that can be measured are limited. Release curves are
constructed based on the apparent changes in the particle’s color recorded by an
ordinary digital camera (here Ulead Eyepiece, 640x480 pixel, was used). Thus, only
guest molecules absorbing in the visible part of light spectrum can be detected.
3.1.1
CAPTURE OF RAW DATA
Raw data consist of a series of pictures acquired under a microscope at relevant times,
while a particle is loosing its guest molecules. The release experiment is prepared as
shown schematically in Fig. 3.1-1 for particles grown on a glass support. Because the
release cell, constructed later, provides only small volume of the up-taking solvent it
is reasonable to include as few particles as possible. When particles grown on
support are used, the excess can be removed with a paper tissue leaving only the area
containing the particle of interest (Fig. 3.1-1A). When loose particles are to be
investigated, e.g. fibers, a small portion is laid down on an objective glass and the
unwanted excess removed with a skewer. It should be noted that in the case of the
non-supported particles there is a danger of particle drift during the experiment. Such
particle shifts are not a problem per se, however, they make the automatic data
evaluation difficult.
- 42 -
Fig. 3.1-1 Preparation of microscopic
release experiment on the example of
particles grown on a glass support: A)
removal of excess particles, B)
attachment of cover glass using silicon
paste, C) application of water begins the
release experiment, D) microscopic
record of chosen particles
The selected area, or a powder portion, is covered with a cover glass fixed by silicon
paste (Fig. 3.1-1B). One side of the cover glass should be left open for application of
the up-taking liquid. The void between the glasses screened by the silicon paste
makes a release cell and, thus, defines the up-taking volume. The release experiment
starts with addition of the up-taking liquid, typically water. This is done by bringing
2-3 water drops at the open edge of the release cell. The liquid is immediately sucked
under the cover glass (capillary effect). The presence of the liquid changes the
position of focus plane, thus, the position of the microscope table should be
immediately re-adjusted. At this moment acquisition of the photographs follows.
The photographs are collected manually at relevant times. In case of fast releasing
particles, i.e., when the significant loss of dye occurs in the first 2 minutes a movie is
recorded. It is recommended to start the acquisition before activation of the release
cell. This will help gain data at the early times and additionally it helps define the
exact starting time (t0), which is marked by the loss of focus.
Because acquisition of the digital movie produces considerable amount of data,* after
the initial times regular photographs are collected at relevant times, initially each 5
min then each 10 minutes. The collection continues until no more loss of dye is
observed, typically 2.5 h. From the experimental set of data, release curves are
constructed.
*
A movie of 2 min recorded in a relevant format with the resolution of 648x728 pixels produces ca. 1
GB of data
3 METHODS
3.1.2
- 43 -
CONSTRUCTION OF RELEASE CURVES
The following algorithm has been developed for the construction of release curves:
1) From the movie showing the initial stage of release, frames are selected that
correspond with arbitrary chosen time interval, e.g., each 10 s. The frame selection
can be done with any kind of processing program accepting non-compressed .avi
files, e.g. VirtualDub – a freeware available at http://www.virtualdub/doorgwnload.
2) The selected frames as well as the pictures representing longer release times are
decomposed from the original RGB-pictures into its red (R), green (G) and blue (B)
components. For further image analysis, only the component showing the strongest
absorption is used. In case of a red dye, for instance, the green channel is the most
relevant, since transmission in the red part of spectrum corresponds to absorption in
the green range.
3) From the pictures of single color component, a chronological stack is constructed.
This can be done with any relevant graphical program, e.g., ImageJ: a freeware
available at http://rsb.info.nih.gov/ij, which has been used here. Working with stacks
simplifies the data processing because pictures representing all times are analyzed at
once.
4) At any of the stack pictures, a region of interest (ROI) is selected, e.g., central part
of a round particle. For the selected ROI, the mean pixel values (grey values) are
measured at each of the stack picture. The obtained values represent mean intensities
transmitted in the green range of light spectrum within the ROI. In case of particle
drift during release the position of ROI is not constant through the stack, therefore,
values obtained for the affected frames should not be used. Manual shift of ROI to
the actual particle position provides the corrected data.
5) From the mean grey values absorbencies are calculated using the formula:
E (t , x ) = − log 10
I (t , x ) − I 0
I 100% (t ) − I 0
(Eq. 3.1-1)
where I(t,x), I100%(t) and I0 are the transmission at the location x, the reference
intensity (intensity of assumed 100% transmission) at given time and the dark current
- 44 -
correction, respectively. The dark current intensity is the response of the camera to
virtually no intensity. It was estimated using a thin steel wire* as a test object (Fig.
3.1-2). Because it is impractical to include a piece of wire to each experiment the
value was estimated for a set of camera parameters and used later for all data
collected with the same set, I0 = 45.† The values of I100%(t) are obtained analogously
to the transmission data, using the same ROI, but shifted to an area outside the
particle. Location of the reference ROI should be selected at a position horizontally
shifted with respect to the particle. This helps to avoid the influence of horizontal
stripes, which seem to be inherent to an eyepiece camera.
Fig. 3.1-2. An RGB view of an
SBA-3-like fiber accompanied by
a thin steel wire used for
estimation of the dark current
intensity I0. The value of I0 is
determined in the green channel
for the area marked by a white
circle.
6) The obtained absorbencies are
combined with a manually constructed time vector. The time vector is made of the
times corresponding with the acquisition of individual photographs with respect to t0.
An example of so constructed release curve is shown in Fig. 3.1-3.
Fig. 3.1-3. An example of release curve
constructed for a cone-like particle: A) region
of interest (ROI) for measurement of intensity
I(t,x); B) corresponding ROI for measurement
of intensity I100%(t); C) Release curve: corrected
absorbencies in the function of time.
*
†
Extracted from a 500 µA-fuse
The number depends on the format of picture file, throughout this work 8-bit grayscale was used
3 METHODS
- 45 -
All microphotometric release curves show different from zero absorbance at the
equilibrium (Econst ≠ 0). This fact is due to incomplete background correction and
limited volume of the up-taking solvent. The background correction introduced by
the reference intensity in Eq. 3.1-1 is insufficient, because it cannot be measured at
the exact location of the particle. The limited volume does not satisfy the
requirement of perfect sink condition (Eq. 2.3-8) throughout the experiment and
leads to a remnant amount of dye at the equilibrium. In the study of release it could
be considered by derivation of release function with a boundary condition taking into
account the volume ratio of the releasing particle to the up-taking solvent (χ).
However, such additional fitting parameter would lead to instable fits because the
values of Econst are rather small. Also, the experimental determination of χ is not
well-founded as the size of the release cell as well as the number of co-releasing
particles is not constant. A rough estimation of χ is Vparticles / Vsol = 10-9. It is
calculated assuming 1mm slit of the release cell (Fig. 3.1-1 C) and 3 co-releasing
fibers of L = 100 µm and R = 5 µm.
3.1.3
ACCURACY OF THE METHOD
There are few sources of error contributing to the so-obtained release curves. These
are the inaccuracy of the focus position with respect to the particle plane and
corrections of the measured intensities. The first originates from the variation of the
measured intensity with the position of the focus plane. The amount of absorbed light
is proportional to both dye concentration and the path over which absorption takes
place. Depending on the position of the focus plane the light passing through the
particle changes, resulting in a corresponding modulation of recorded intensity. This
fact is important because the focus plane changes during the measurement. At the
initial stage of release the release cell is deformed by capillary forces, and at long
release times, evaporation at the open edge is very likely. Accuracy of the re-adjusted
focus is limited by visual assessment of particle contours. By the horizontal choice of
the reference intensity, influence of the horizontal stripes can be smoothed but not
excluded.
Based on the variation of the experimental data at the long release times, the
inaccuracy was estimated to ∆E = 0.03 ( ∆E / E = 15 %). However, this is the worst
case - the typical inaccuracy is about 7 %.
- 46 -
3.2
SPECTROSCOPIC MEASUREMENT OF RELEASE
The spectroscopic method aims on measuring the amount of guest molecules
released by particles in suspension (disperse delivery system). The method utilizes a
UV-Vis spectrometer as a detection device, hence the name. It has the advantage of
providing accurate spectroscopic data, which is further automatically processed for
the construction of a release curve.
3.2.1
CAPTURE OF DATA AND PRINCIPLE OF THE METHOD
The release experiment is realized in a spectroscopic cuvette (Fig. 3.2-1 A)
monitored by a regular spectrometer. In this study three spectrometers were used:
Cary 5G (Varian), Cary 100 (Varian) and Lambda 800 (Perkin Elmer). In each case a
two beam mode was used. For measurements in the UV-range quarz cuvettes were
used (QS) and for measurements in the Vis-range disposable plastic cuvettes (CVDVis, Ocean Optics). The cuvette is stirred (magnetic mini-stirrer) during the
experiment in order to ensure homogeneity of the suspension and avoid
concentration gradients.
Fig. 3.2-1. The principle of spectroscopic measurement of release: A)
schematic depiction of spectroscopic cuvette with a suspension of scattering
particles and measured light intensities; B) decomposition of the lost intensity
into absorption in the liquid defining Eabs, scattering on the particles defining
Esca and absorption on the particles defining Eerr.
3 METHODS
- 47 -
The extinction data delivered by a UV-Vis spectrometer represent the loss of
incoming light intensity as a function of wavelength. Because for release,
additionally the time dependence is relevant:*
E (λ , t ) = − log10
I (λ , t ) − I ref (λ )
I 0 (λ )
(Eq. 3.2-1)
where E (λ , t ) , I (λ , t ) , I ref (λ ) , I 0 (λ ) are the total extinction, the actual intensity,
the reference intensity and the baseline, respectively. The actual intensity is the
intensity transmitted through the sample cuvette. The reference intensity is the
analogous intensity transmitted through the reference cuvette, i.e., identical cuvette
filled with the up-taking solvent only. The baseline is a spectrum of zero absorption
measured before the actual experiment (two identical cuvettes filled with the uptaking solvent). The measurement of a baseline is recommended by the
manufacturer* in order to normalize the measured values. It is measured each time
the spectrometer is switched on or when the spectral range is changed.
There are principally three processes taking place in the cuvette depicted in Fig.
3.2-1 A: absorption in the liquid phase, scattering on the particles and absorption on
the particles. For reasonably low concentration of particles (no multiple scattering)
the intensity transmitted through the cuvette can be considered as the sum of
extinctions of three virtual cuvettes representing the three processes independently
(Fig. 3.2-1 B). Such additivity can be derived from the principle of energy
conservation [128].
The total measured extinction is, therefore, written as a corrected sum of absorption
extinction E abs (λ , t ) and scattering extinction Esca (λ ) :
E (λ , t ) = E abs (λ , t ) + Esca (λ , t ) + E err (λ , t )
(Eq. 3.2-2)
where E err (λ , t ) represents the part of scattering extinction that is not included in
Esca (λ , t ) due to: (i) light scattered in the forward direction and (ii) physical size of
the detector accepting some of the scattered light, not only that propagated in the
forward direction. Because the scattering particles contain the same absorbent as the
liquid phase the wavelength dependence of E err (λ , t ) is the same as that of E abs (λ , t ) .
*
User’s manual (Varian)
- 48 -
Since the task is to extract the absorption extinction of the liquid phase, E err (λ , t ) has
the meaning of an error. The magnitude of the error contribution is treated with detail
in chapter 3.2.3.
The absorption extinction of the liquid phase follows Lambert-Beer’s law:
E abs (λ , t ) = c(t )ε (λ )d
(Eq. 3.2-3)
where c(t ) , ε (λ ) , and d are concentration, wavelength dependent molar extinction
coefficient, and the path at which absorption takes place (thickness of the cuvette),
respectively.
The scattering extinction is a generally complicated function of wavelength and
parameters of a particle. It is also proportional to the number of scattering particles,
as long as multiple scattering is negligible. For a constant number of particles and
their invariant geometry (stable particles) it could be assumed that Esca does not
change in time. But this is insufficient because, due to release, the composition of the
particles changes and consequently, the changed refractive index modifies Esca .
However, the timescale of release is much longer than that of collecting a single
extinction curve. The time dependence is therefore not significant for a single curve
but for the long range detection. The wavelength-dependence of Esca is complicated
at long wavelength range but can be approximated by a linear function for a
reasonably narrow λ-range (see Appendix B). Corroborating, for acquisitions much
times faster than release time and a narrow spectral range of the measured extinction
it is sufficient to approximate Esca (λ , t ) by a linear function of λ. This approximation
greatly facilitates fitting of the measured extinction during the construction of a
release curve.
3.2.2
CONSTRUCTION OF RELEASE CURVES
The use of a commercial spectrometer excludes a continuous measurement of the
time-dependence at all wavelengths. Typically, the wavelength-dependent extinction
curves are collected at chosen time intervals. The raw data consist of a set of total
extinction curves in-line with a time vector. From each extinction curve only the
absorption extinction is then to be extracted numerically. Since the time needed to
acquire a single curve is much shorter (~10 s) than a typical release time (> 10 min)
the time dependence within a single extinction curve is negligible.
3 METHODS
- 49 -
Each of the total extinction curves can be described by a sum of Gaussian functions
shifted in the extinction scale by a linear contribution:
⎛ ⎛λ −b
i
E (λ ) = ∑ ai exp⎜ − ⎜⎜
⎜
c
i =1
⎝ ⎝ i
N
⎞
⎟⎟
⎠
2
⎞
⎟+a λ +b
0
⎟ 0
⎠
(Eq. 3.2-4)
where N, a1..N, b1..N and c1..N are the number of Gaussian peaks, amplitude,
wavelength and full width at half maximum of the individual Gaussian peak,
respectively. The constants a0 and b0 correspond with the linear approximation of
scattering contribution. The number of used Gaussian functions is specific for the
considered absorbent (examined guest molecule) and defined by the shape of the
molar extinction function, ε (λ ) . In case of rhodamine 6G, for instance, two peaks
are needed. For chromates, in turn, one Gaussian is sufficient.
The function defined by Eq. 3.2-4 is fit automatically to each experimental extinction
curve and the absorption extinction required for the construction of release curve is
calculated as:
E abs = E (λ max ) − E lin (λ max )
(Eq. 3.2-5)
where E (λ max ) and E lin (λ max ) are the maximum total extinction and the linear
contribution at the corresponding wavelength, respectively. An example of such fit
for Rh6G release from mesoporous spheres is pictured in Fig. 3.2-2.
Fig. 3.2-2. The principle of evaluation of
the spectroscopic data: each extinction
curve is fit by an appropriate number of
Gaussian functions and a linear function
representing the scattering contribution.
Absorption extinction Eabs is calculated by
subtraction of the scattering contribution
Elin from the total extinction E(λ,t) at the
maximum.
- 50 -
It should be noted that fitting of Eq. 3.2-4 is not a trivial task because of the many
fitting parameters. Even in the simplest case of one Gaussian these are 5 parameters.
This constitute a difficult problem at the initial states of release, when the peaks are
weak, i.e., hardly distinguishable; especially when automatic fitting is applied. In an
automatic procedure it is not possible to influence the fitted parameters once the
procedure is run. Without reasonable restrictions this usually leads to irrelevant
results. However, the positions of the Gaussians do not change during release and
their widths also do no vary much. It is therefore reasonable to restrict them based on
the pure absorption of the absorbent measured a priori.
From the absorption extinctions obtained using Eq. 3.2-5, release curves are
constructed directly by combining the values with the corresponding times. An
example of a so-constructed release curve is shown in Fig. 3.2-3. The whole
procedure has been automated by a MatLab-programmed function. An example of
the function suited for rhodamine 6G is included in Appendix C.
Fig. 3.2-3. An example of release
curve constructed from absorption
extinctions obtained from Eq. 2.2-5
plotted against the relevant time
vector.
The fact that release is measured directly in a spectroscopic cuvette and the
construction of release curves is automated minimizes the experimental effort. In
contrast to the procedures practiced in pharmacokinetics, e.g. [59], the toilsome
filtering at desired release times is not necessary.
3 METHODS
3.2.3
- 51 -
ACCURACY OF THE METHOD
The possible sources of errors and uncertainties* in the determination of Eabs:
a) Partial contribution of scattering extinction to the total extinction captured by the
acceptance angle of the detector (see Appendix B for definition)
b) Partial contribution of scattering extinction to the absorption extinction due to
absorption by guest molecules in the scattering particles (Fig. 3.2-1 B)
d) Particle movement during release (stirring) introducing noise to E(λ)
c) Instability of the automatic fitting procedure
d) Spectrometric accuracy of the spectrometer
It is, however, difficult to analyze the errors as a sum of its sources. The total error of
the method can be measured easier. The items a) and b) are considered as the by far
most significant sources of error. They can be determined by comparing the
calculated absorption extinctions with their values obtained on a sample free from
the scattering particles. For this purpose, a release experiment has been conducted on
a suspension of particles releasing at a slow rate. In parallel, the same experiment
was conducted on a bigger volume outside the spectrometer. At given times, a
portion of the suspension has been removed and filtered. Absorption of the drainedoff solvent was then measured. The results were then compared (Fig. 3.2-4). The
error is then calculated as:
∆E (t ) = E abs (t ) − E ' abs (t )
(Eq. 3.2-6)
where E abs (t ) and E ' abs (t ) are the absorption extinction obtained from the suspension
and the absorbance obtained from the filtrate, respectively.
*
Error – difference between the result of the measurement and the true value, uncertainty – dispersion
of the value attributed to the measurement (after „Guide to the expression of uncertainty in
measurement“ ISO 1993, ISBN 92-67-10188-9)
- 52 -
Fig. 3.2-4. Experimental determination of the
error in spectroscopic measurement of release
casued by partial contribution of scattering
extinction to the total extinction: A) release
curve constructed after Eq. 3.2-5; B) absorption
spectrum of the liquid phase measured on
filtered sample at the three indicated time points.
The error is the biggest at the initial stages of release, when the majority of the guest
molecules are inside the scattering particles. This maximum error defines the
sensitivity of the method. In case of rhodamine 6G and mesoporous spheres, this
systematic error is ∆E < 0.015.
Fitting procedure and particle movement during release are sources of statistical error.
The movement of the particles is induced by stirring, which is necessary to ensure
homogeneity of the suspension. Fitting may result in errors due to over- or
underestimation of the scattering extinction. These two contributions are visible as
noise of the calculated release curve and are estimated to be ∆E = 0.002.
3.3
3.3.1
ADDITIONAL CHARACTERIZATION METHODS
X-RAY DIFFRACTION
X-ray diffraction is a general method used for the characterization of periodic
structures with periodicities comparable with the wavelength of X-rays. The method
is based on the fact that an X-ray diffraction pattern of the periodic structure is
closely related to its Fourier transformation.
3 METHODS
- 53 -
The peaks in a diffraction pattern result from a constructive interference of the
electromagnetic radiation scattered by the lattice. The positions of the peaks appear
according to the Bragg’s equation:
nλ = 2d hkl sin ϑ
(Eq. 3.3-1)
where n, λ , d hkl and ϑ are the order of diffraction, the wavelength, the lattice
spacing and the incident angle, respectively. Since a specific symmetry of the
periodic structure gives a specific set of d hkl , the set of peak positions can be used
for identification of the structure’s symmetry.
The usefulness of X-ray diffraction in the study of mesoporous materials lies in the
identification of symmetry, degree of ordering and characteristic periodicity. In case
of peak scarcity only the characteristic spacing can be measured. This spacing is an
estimation of pore size. Since typically a powder sample is used the information is
averaged for all particles.
In this work, powder samples were analyzed in transmission geometry using a STOE
STADI P diffractometer operating with Cu-Kα1 radiation (MPI für Kohlenforschung/
Mülheim a.d. Ruhr). The diffractometer was equipped with a linear position sensitive
detector having its bottom angular limit of 2 ϑ at 0.6°.
3.3.2
SCANNING ELECTRON MICROSCOPY (SEM)
In scanning electron microscope (SEM), a focused beam of electrons is used to
examine fine structures on the sample surface. A beam of electrons is scanned across
the sample, and for each point, backscattered (BSE) and secondary electrons (SE) are
collected. These electrons are products of primary and secondary interaction effects,
e.g., surface ionization. An SEM image is then produced as a sequence of intensities
collected for each scanning point. In the case of well conducting surfaces, the
resolution of SEM is limited by the size of scanning beam, scanning step, energy of
the beam and it reaches 10-20 Å for high performance equipments. Because the
ability of the sample surface to produce BSE and SE is the primary image forming
phenomenon, the quality of the image is usually bad for non-conducting samples. In
this case, a thin conducting layer, typically of gold or carbon, is deposited.
The primary information delivered by SEM is particle size and shape. Depending on
the resolution, surface features, like texture or defects, are also visible.
- 54 -
In this work particles were analyzed mostly with a Hitachi S-3500N scanning
electron microscope operated by Mr. Hans-Joseph Bongard (MPI für
Kohlenforschung). The microscope was operated at 5 or 25 keV and the samples
were coated by a 10 nm layer of gold.
A part of the samples was subject to focused ion beam (FIB) – a novel technique of
sample manipulation [129]. The techniques exploit sputtering, i.e., ejection of atoms
from a solid surface induced by bombardment with energetic ions. Typically, an ion
gun is included to the standard SEM set-up so that the sputtered sample can be
observed during sputtering (Fig. 3.3-1).
Fig. 3.3-1. Set-up of scanning
electron microscope equipped with
focus ion beam (FIB) and electron
back scattered detector (EBSD, not
used in this work). Figure by
courtesy of Dr. Stephan Zaefferer
(MPI
für
Eisenforschung,
Düsseldorf).
Sample manipulation using FIB was carried out at Max-Planck-Institut für
Eisenforschung, Düsseldorf, with Zeiss 1540 XB operated by Ms. Monika Nellessen.
The gallium ion gun was operated at 30 keV and the gun current varied between 5
and 500 pA corresponding with exposure times of app. 2 hours and 1 min,
respectively.
3.3.3
TRANSMISSION ELECTRON MICROSCOPY (TEM)
In transmission electron microscopy, a typically thin slice of a material is observed in
transmission by an electron beam. Although it is a similar beam as in case of SEM,
images are formed based on different principle.
The TEM image is formed at once (no scanning) and the contrast is principally due
to scattering and diffraction on the sample. Electrons deflected from the initial
3 METHODS
- 55 -
trajectory do not contribute to the image. In other words, the TEM-image
corresponds to a map of projected electrostatic potentials for electrons along the
direction of incidence of the beam. There are both fundamental and practical
difficulties in interpretation of TEM images but the typical resolution is the range of
few Å. Truly atomic resolution can be achieved only using special techniques
(HRTEM) also applicable to mesoporous materials [130].
In this work, TEM investigation were carried out on Hitachi HF 2000 operated by Mr.
Bernd Spliethoff (MPI für Kohlenforschung, Mülheim an der Ruhr). The microscope
was equipped with a cold field emission source working at 200 keV. Calcined
samples have been used. The samples were mounted on carbon films, fixed on
copper grids.
4 PREPARATION OF MESOPOROUS MICROCAPSULES
4.1
SBA-3-LIKE MESOPOROUS FIBERS
The fibers of SBA-3-type were synthesized based on a literature prescription [50].
The surfactant, cetyltrimethylammonium bromide (CTAB), was dissolved in
hydrochloric acid together with rhodamine 6G (Rh6G) to form mother liquor. The
composition of the liquor in molar ratios was: H2O : HCl : CTAB : Rh6G = 100 :
1.78 : 0.0241 : 6.10-4. The amount of rhodamine could be varied (e.g., Tab. ). The
synthesis was conducted in batches of
10 g mother liquor using snap-cap
glasses of 10 mL (VWR)*. On top of the
mother
liquor
90
µL
of
tetrabutoxysilane (TBOS) were spread
(Fig. 4.1-1). The tightly closed glasses
were incubated under quiescent
conditions at 20°C (thermostatic control)
Fig. 4.1-1. Schematic representation of the
synthetic procedure for SBA-3-like fibers.
for 8 days. The synthesis products were
*
Attempts of using larger batches resulted in undesired change in morphology of the products
- 56 -
collected using a Pasteur pipette and dried at 50°C for 2 h. Optionally, the products
were calcined at 500°C with temperature rise for 8 h and kept for 8 h.
The calcined particles float easily in air. Due to their small size they represent a
potential health hazard when inhaled [131]. Working with a face filter-mask (3M)
was therefore practiced.
The products of the synthesis are dominated by fibers accompanied by some other,
rotationally symmetric particles (Fig. 4.1-2 A). The other particles are typically much
smaller and their volume ratio rarely exceeds 15%. The hexagonal pore ordering is
visible in both TEM (Fig. 4.1-2 B). Due to pore coiling the structure in TEM is
visible only at a specific angle.
Fig. 4.1-2. A) Typical appearance of SBA-3-like fibers under light microscope.
The fibers are accompanied by small rotationally symmetric particles. B) TEM of
an as-synthesized and calcined fibers revealing the hexagonal pore ordering.
4.2
MESOPOROUS SPHERICAL PARTICLES
There are many types of mesoporous spheres available in the family of mesoporous
materials, e.g. [37,40]. Here a specific kind was chosen from the work of Chen et al.
[39]. The mother liquor is prepared by the composition (in molar ratios) H2O : HCl :
CTAB : Rh6G = 100 : 7.50 : 0.110 : 6.10-4. The synthesis was conducted in 60 g of
mother liquor in a round glass with thread (Shott Duran, 100 mL). Under vigorous
stirring (900 rpm) 1.4 mL of silica precursor was added. The precursor was prepared
beforehand mixing tetraethoxysilane with triethoxymethylsilane in molar ratio of
TEOS : MTES = 2 : 0.25. Stirring was continued for 45 s. During this time a
precipitate appeared. The batch was then aged for 18 h under quiescent conditions at
20°C (thermostatic control). The products were filtered on a funnel-filter using a
4 PREPARATION OF MESOPOROUS MICROCAPSULES
- 57 -
vacuum pump and then dried for 2 h at 50 °C. Optionally, the particles were calcined
at 500°C with temperature rise for 8 h and kept for 8 h.
Fig. 4.2-1. A) Typical appearance of mesoporous spherical particles under an
optical microscope. B) TEM of an individual particle. The mesostructure is not
visible due to lack of long range ordering.
The resulting particles are round and have a moderate size distribution (Fig. 4.2-1 A).
There are no pores seen in TEM at any incidence angle (Fig. 4.2-1 B). X-ray
diffraction pattern indicates an ordering of the mesostructure (Fig. 4.2-2); however, it
cannot be ascribed to a particular space group due to insufficient number of peaks.
The characteristic length is d = 3.98 nm and shrinks to d = 3.29 nm after the
calcination.
Fig. 4.2-2. X-ray diffraction patterns of
as-synthesized and calcined mesoporous
spherical particles. The shift of the peak
after calcinations corresponds to a
shrinkage of the mesoporous structure.
4.3
PREPARATION OF MESOPOROUS PARTICLES ON SUPPORT
The particles on glass support were prepared in-line with the SBA-3-type synthesis
as described in ref. [48]. An increased amount of rhodamine was used in order to
enhance the dye loading. Synthetic procedure is analogous to that described in
chapter 4.1. The synthesis was conducted in glass bottles with a broad neck (20 mL,
- 58 -
NeoLab) using 20 g of mother liquor. Before the addition of silica source a glass
support was placed vertically in each bottle. The glass supports were prepared
previously from an objective glass (cut-to-width: 17 mm) and cleaning with Kuvettol
according to the manufacturer’s prescription. Tightly closed bottles were incubated
for 3 days at 20 °C (thermostatic control). The collected glass supports were rinsed
twice with 2 mL of mother liquor and once with distilled water. The water-rinse is
necessary to remove the excess particles and the Rh6G-reach mother liquor. Then the
supports were dried in air stream.
The preparation of an array of the cone-like particles requires application of
additional techniques for modification of the support, e.g. micro-contact printing [48].
The particle arrays used in this work were provided by Mr. Ahmed Khalil (currently
PhD-student of IMPRS Surmat, MPI Kohlenforschung).
The particles grown on a clean and modified supports are shown in Fig. 4.3-1.
Fig. 4.3-1. SBA-3-like particles synthesized on glass support (optical
microscopy): A) clean support, B) modified support (sample provided
by Mr. A. Khalil).
4.4
4.4.1
LOADING WITH GUEST MOLECULES
LOADING DURING SYNTHESIS
The most convenient way of loading mesoporous silica with guest molecules is by
direct incorporation during synthesis. The desired molecules are simply added to the
mother liquor. This works very well with rhodamine 6G in concentrations of up to
0.83 mmol/L.*
*
Higher concentrations were not tested.
4 PREPARATION OF MESOPOROUS MICROCAPSULES
- 59 -
The attempts to incorporate chromate or molybdate during synthesis resulted in
particles of very irregular morphology and broad size distribution instead of regular
fibers. Such fatal deformation is associated with the corruption of the mesoporous
ordering and disqualifies the method for incorporation of corrosion inhibitors.
4.4.2
POST-SYNTHETIC LOADING
The post-synthetic loading of guest molecules was realized by impregnation, i.e.,
dipping the material in a solution containing the molecules. All impregnations were
conducted on calcined particles using aqueous solutions of given concentrations.
Impregnation proceeded at room temperature under mild stirring for at least 12 h
(typically 16 h). Then the loaded particles were collected by filtering the liquid phase
off. Alternatively, impregnation under quiescent conditions was performed, i.e.
without stirring. In this case the suspension was initially dispersed using ultrasound
bath for ca. 10 s. After filtering the samples were dried for 2 h at 50 °C.
In case of rhodamine the impregnated particles show homogenous coloration,
analogous to particles loaded during synthesis. In case of chromates and molybdates
no change is visible.
Although the post-synthetic loading of particles requires additional steps in sample
preparation it has also advantages. The pore volume occupied by surfactant in an assynthesized particle is inaccessible for the storage of guest molecules. During
calcination this volume is vacated enhancing the loading capacity. It is also possible
to up-take species insoluble in the synthesis solution but soluble in other solvents,
e.g., alcohols. For molecules that corrupt the formation of the mesoporous matrix
there is barely an alternative. In addition, calcined silica is regarded as generally
more stable [36] offering durability in service.
4.5
4.5.1
MODIFICATION OF MESOPOROUS PARTICLES
SOFT TREATMENTS
The term ‘soft modification’ is introduced in this work to describe those treatments
of mesoporous particles in which no chemical reaction is expected. The treatments
consist of rinsing with a solution followed by drying. In contrast to treatments with a
film-forming solution (coating), soft treatments do not use any precursor that could
be deposited on the surface.
- 60 -
The soft treatments were
realized by rinsing a portion of
mesoporous particles with either:
(a) distilled water (H2Otreatment),
(b)
sodium
hydroxide of pH = 10.7 (NaOHtreatment) or (c) respective
Fig. 4.5-1. Experimental
set-up for modifications of
mother liquor free from guest
mesoporous particles.
molecules (ML-treatment). A
portion of particles was mixed
with the liquor at a low volume ratio (~1/1000). The suspension was then
homogenized in ultrasonic bath for max. 2 s. The sample was then immediately
drained-off on a beforehand prepared filter (Fig. 4.5-1) connected to a vacuum pump.
It is crucial to perform the treatment as fast as possible in order to minimize the loss
of the loaded guest molecules. In a typical treatment the time of contact with the
liquid did not exceed 10 s. For small particles (< 500 nm) a membrane filter had to
be added. The additional membrane leads to prolongation of the treatment time due
to the capillary action in the membrane pores. To complete the treatment the sample
was dried for 2 h at 50 °C.
4.5.2
SURFACE COATING (WATERGLASS TREATMENT)
The procedure of surface coating is analogous to that of the soft treatments with the
difference that here a film-forming solution is used. A silicate coating is precipitated
from a solution of waterglass.
The solutions of waterglass were prepared by adding commercial grade sodium
silicate into water or acid under continuous control of pH. To avoid silica
precipitation in the solution, waterglass should be added drop-wise until the desired
pH is reached.*
Following solutions were used:
(a) waterglass solution in distilled water; various pH, various temperatures
(b) waterglass solution in 0.1M HCl (pH = 1); various pH, various temperatures
*
Too fast addition of waterglass may result in deposition of silica on the pH electrode.
4 PREPARATION OF MESOPOROUS MICROCAPSULES
- 61 -
(c) waterglass solution in 0.01M HCl (pH = 2); various pH
In case of the treatments at elevated temperature, solution of given pH was heated
before the treatment and its pH not measured at the elevated temperature.
4.5.3
MICROSURGERY OF THE PARTICLES
Some of the particles synthesized on glass support were subject to microsurgery –
localized particle manipulation, by either mechanical damage or focused ion beam
(FIB).
Mechanical damage was induced using a razor-blade. The operation is quite
imprecise and cannot be controlled under a typical microscope. At reasonable
magnifications the distance between the objective and the sample is too small for
positioning of the blade. Typically, whole particles are removed or destroyed and
only rarely the desired partial destruction results. Despite these difficulties it was
possible to obtain few particles damaged in the desired way, i.e. violating the
continuity of most of the coiled pores.
Particle manipulation using FIB is much better controlled. Trimming along the axis
of symmetry can be conducted with high precision.
5 STUDY OF RELEASE
5.1 MICROSCOPIC OBSERVATION OF RELEASE
5.1.1
SBA-3-LIKE FIBERS
The microscopic appearance of an SBA-3-like fiber during release is shown in (Fig.
5.1-1 A). The loss of color is homogenous and there is no gradient visible in the axial
direction at any time. In some cases fast depletion of local zones is observed on
broken or cracked fibers (Fig. 5.1-1 B).
- 62 -
Fig. 5.1-1. Optical observation of the dye loss from SBA-3-like fibers:
A) chronological series for a typical fiber; B) selected frames for some
broken and cracked fibers. The scale bar in A) applies to all pictures.
The homogenous loss of color in Fig. 5.1-1 A indicates that the dye molecules are
transported perpendicular to the fiber axis rather than parallel to it. This deduction is
also in agreement with the lack of depletion in the vicinity of the fiber axis.
Transport along mesopores coiled around the axis of symmetry would result in such
depletion because the rate of transport along the mesopores is a function of the
coiling radius. Combining these observations with the structural information (Fig.
2.2-5) leads to the conclusion that the molecules have to be transported across the
pore walls. Such transport can be mediated by channel-to-channel connections whose
existence has been shown in literature based on the formation of stable carbon
replicas [132]. Also the calcination behavior speaks for at the possible channel-tochannel diffusion. Fibers, which can be up to few millimeters long, are calcined
easily (faster that 1h) and no dependence on the fiber length is observed [134].
Because the nature of the channel-to-channel connection is not fully explained until
now, transport mediated by these connections is thereafter referred to as cross-wall
transport [133].
A further indication provided by the homogenous loss of dye is the existence of
surface diffusion barrier. If there were no transport resistance at the surface of the
fiber, concentration of the dye across the fiber would have a Gaussian-like shape. But
there is no clear concentration gradient in that direction. This seems certain, although
the focusing effects at the edge of the fiber make the measurement of the
concentration profile difficult.
The fast depletion of local zones is an argument for the dominance of cross-wall
transport. The zones are often symmetrical with respect to the fiber axis. Because
5 STUDY OF RELEASE
- 63 -
fracture presumably opens the mesopores, the fast depleting zones of limited volume
(typically ~ 1 µm) suggest that the mesoporous system does not form an entity along
the whole fiber. If each coiled mesopore continued along the whole fiber smooth
release, with no sharp concentration gradients, would follow in case of damage. But
it is not the case and the fast depleting zones at the initial release times are
interpreted as due to casual blocking of the mesopores.
As a consequence of these findings a cylinder of infinite length can be taken as a
model for the description of diffusion in SBA-3-like fibers.
5.1.2
DISCUSSION OF RELEASE GEOMETRY
The release geometry is defined by the direction(s) of the flux (Eq. 2.3-3). In case of
spherical particles the choice is trivial because of the obvious symmetry. Radial flux
in all direction is described by spherical geometry.* In case of fibers the geometry of
release is not obvious. Due to their high anisotropy both plane-sheet geometry (axial
transport) and cylinder geometry (radial transport) is plausible (Fig. 5.1-2). The
coiled pores enable screw-like paths corresponding with a plane-parallel mass
transport. However, at the same time cross-wall transport enables radial symmetric
mass transport.
Fig. 5.1-2. Two possible release geometries of SBA-3-like fibers: A)
diffusion along the coiled mesopores (dot line) associated with planeparallel mass transport described by plane-sheet geometry; B) diffusion
with radial symmetry described by cylinder geometry
The choice of release geometry is essential for the corresponding release model and,
thereby, for the derived effective diffusion coefficients. An example of how
significant the choice is can be demonstrated by fitting one set of experimental data
*
Isotropy of the flux must be assumed.
- 64 -
with different models. Fig. 5.1-3 shows uptake of ethylene into SBA-3-like fibers
taken from literature [95] and fit with release models derived in three different
release geometries. The cylinder and plane-sheet geometries are in accordance with
Fig. 5.1-2, whereas the spherical geometry is fully irrelevant. Although there are
some systematic deviations all three models fit the data quite well. Therefore, any of
the models can be selected based on the quality of the fit. But although all models
deliver similar uptake curves the corresponding diffusion coefficients differ by
several orders of magnitude [134]:
cylinder geometry:
cyl
= 6.17⋅10-9 cm2/s
Deff
plane-sheet geometry:
Deffps = 3.28⋅10-6 cm2/s
Fig. 5.1-3. Experimental data of
ethylene uptake on SBA-3-like
fibers fit with solutions of
diffusion problem in the three
indicated geometries.
To avoid such ambiguities in interpretation of release data it is imperative to seek for
additional premises justifying the choice of release geometry. In fact, for SBA-3-like
fibers both plane-sheet and cylinder geometries are possible. However, transport
realized by only one of them is the release rate-limiting. The microscopic observation
of release advocates the choice of cylinder geometry. It should be noted that such a
choice fully neglects the axial transport, which is also present. This can be, however,
justified by the small diameter-to-length ratio of a typical fiber (L/R ~ 40) which
implies much lower axial gradients.
5.1.3
CONE-LIKE PARTICLES
Release from cone-like particles observed under a microscope appears very similar to
that of the fibers – homogenous loss of dye (Fig. 5.1-4 A). There are no radial
gradients and the time scale of the process is similar to that of an intact SBA-3-like
5 STUDY OF RELEASE
- 65 -
fiber. There are also fast releasing local zones in some mechanically damaged
particles (Fig. 5.1-4 B ). Here, the particle homogenously filled with dye at the
beginning shows a fast decoloring ring. The rest of the particle releases at the same
rate as an intact particle.
Fig. 5.1-4. Loss of dye from a cone-like particles observed under an optical
microscope: A) chronological series for a typical cone-like particle; B)
chronological series for a damaged particle; C) the particle in B) before release
(dry).
The homogeneity of release and similar
time scale of the processes indicate that
also in cone-like particles it is cross-wall
transport that dominates the release.
However, the release geometry is not
straight-forward. The particle is not-fully
Fig. 5.1-5. Two possible release
geometries anticipated for a conesymmetric and so is the flux direction
like particles: A) plane-sheet
also not-fully symmetric. There is more
geometry associated with axial
transport, and B) cylinder geometry
than one direction realizing cross-wall
asociated with the radial transport.
transport. When the sink condition is
applied equally over the particle’s
surface, the resulting flux is defined by the direction of greatest concentration
gradient. The description of the total flux requires then solution of diffusion equation
with a relatively difficult geometry (cylinder of gradual radius or a plane-sheet of
gradual thickness). However, owing to the axial-symmetry of the problem each flux
direction can be decomposed in a radial and axial component, corresponding with
cylinder and plane-sheet geometries of release, respectively (Fig. 5.1-5). Both
components are relevant when none of the particle dimensions is distinctive.
- 66 -
The fast depleting zone in Fig. 5.1-4 B is of a ring form. This appearance is in-line
with the fast depleting zone observed on the fibers. In case of the cone-like particle
the axis of symmetry is perpendicular to the observer so that radial symmetric zone
appears as a circle or a ring. This observation indicates that there are ring-like
channels in which the molecules can move faster than in any other direction.
5.2 INTERPRETATION OF RELEASE CURVES
Release curves are direct experimental results of release measurements. They can be
interpreted as-measured or analyzed by means of a release model. The modeldependent analyses require discussion of premises and lead to consequent
conclusions. They are treated in further chapters (5.3 and 5.4).
Release curves measured for as-synthesized SBA-3-like fibers measured with the
spectroscopic- and microphotometric methods are shown in (Fig. 5.2-1). The
immediate information provided by each curve is the time scale of the process and
the maximum value of Eabs.
In case of the spectroscopic curve the Emax corresponds with the total released, i.e.
deliverable, amount. The value in grams of moles can be then obtained using Eq.
3.2-3 (Lambert-Beer law) with an appropriate extinction coefficient. The calibration
of the coefficient for rhodamine 6G is shown in Appendix D. In case of the
microphotometric curve Emax represents the initial loading. The deliverable amount
can be calculated by the subtraction of Econsts, defined as Eabs at the equilibrium.
Fig. 5.2-1. Release curves of SBA-3-like fibers measured with different
methods: A) spectroscopic and B) microphotometric. The direct information
provided by the curves are the maximum deliverable amount, Emax, and the
release time, t1/2.. The spectroscopic method delivers additionally the scattering
extinction, Esca, which indicates stability of the system.
5 STUDY OF RELEASE
- 67 -
The time scale of release is quantified in terms of release time, t1/2 – the time at
which the dye content increases or drops by half of its maximum.
Additional experimental information is provided from the spectroscopic method in
the form of the scattering extinction. Independent from which factor dominates its
magnitude (Appendix B), scattering extinction is a qualitative indication of how
stable the releasing suspension is. Depending on the time behavior of Esca
sedimentation, agglomeration or dissolution of the particles can be suggested.
The release time and Emax are useful for the estimation of release efficiency. They
can be used to calculate the amount of particles needed to provide the required
amount of functional molecules.
5.3
5.3.1
DIFFUSION DATA FROM THE MICROPHOTOMETRIC METHOD
SBA-3-LIKE FIBERS
Diffusion data for SBA-3-like fibers is obtained by fitting the measured release curve
with a release function (see Fig. 5.3-1). The function describes the average dye
content probed by the light beam (chapter 2.3.3) modified by the addition of Econst:
∞
∞
E (t ) = E const + E max 4∑
n =1
∑J
m =0
2 m +1
(q n )
q n2 J 1 (q n )
exp(−
⊥
Deff
q n2 t
)
R2
(Eq. 5.3-1)
where qn are roots of J 0 (q) = 0 . The effective diffusion coefficient associated with
⊥
radial transport is Deff ,r = Deff
. This assignment is justified by the microscopic
observation of release demonstrating that release from the fiber is dominated by
cross-wall transport (chapter 5.2).
Fig. 5.3-1. A) Microscopic release
curve obtained for an as-made
SBA-3-like fiber and fit by Eq.
5.3-1; B) the measured fiber with
specified area from which the
extinctions E(t) were obtained; C)
position of reference intensity.
The depicted effective diffusion
coefficient is assigned to crosswall transport.
- 68 -
The effective diffusion coefficient determined for an as-made fiber amounts to:
⊥
= (3.5 ± 0.5)⋅10-11 cm2s-1
Deff
(Eq. 5.3-2)
The error is estimated based on the individual sources of error: pixel size in the eyepiece image, ∆R = 0.1 µm, and the accuracy of the extinction, ∆E = 0.03. It should be
noted that although existence of a surface diffusion barrier has been previously
suggested, the effective diffusion coefficient is derived from a barrier-free model.
The reason for not including surface barrier is that Eq. 5.3-1 is already describing the
curve quite well so that introduction of additional fitting parameter is of little
⊥
numerical advantage. In such a case the value of Deff
is slightly lower from that
which would result from a barrier-containing model.
5.3.2
CONE-LIKE PARTICLES
Diffusion data for cone-like particles can be obtained by using a release function
derived in either plane-sheet geometry (Eq. 5.3-3) or cylinder geometry (Eq. 5.3-4):
E (t ) = E const + E max
⊥
⎛ Deff
(2n + 1) 2 π 2 t ⎞
1
⎜
⎟
exp
−
∑
⎜
⎟
4 L2
π 2 n =0 (2n + 1) 2
⎝
⎠
8
∞
∞
∞
E (t ) = E const + E max 4∑
n =1
∑J
(q n )
⊥
⎛ Deff
q n2 t ⎞
⎟
⎜
exp
−
⎜
q n2 J 1 (q n )
R 2 ⎟⎠
⎝
m =0
2 m +1
(Eq. 5.3-3)
(Eq. 5.3-4)
where qn are roots of J 0 (q) = 0 . The application of both functions to the same
release curve is shown in Fig. 5.3-2. The curve belongs to the particle in Fig. 5.1-4 A
Obviously, both the functions fit the data with a similar quality. In the presented
example they also deliver similar effective diffusion coefficients. However, for the
further numerical analyses the plane-sheet geometry is favored. The flatter a particle,
the more relevant the plane-sheet geometry becomes and since most of the measured
particles are rather flatter than broader (L < R), the choice is legitimate. It is also
supported by the apparent homogeneity of the dye loss observed in optical
microscope (Fig. 5.1-4). Were the cylinder geometry of release dominant, the radial
gradient would have to be more pronounced. However, the assumption of only one
flux component fully neglects the other one. The measured flux is therefore
5 STUDY OF RELEASE
- 69 -
underestimated, which leads to an according underestimation of the associated
diffusion coefficient.
Fig. 5.3-2. Release from a cone-like particle of R = 3.5 µm and L = 2 µm
described by release function in either A) cylinder geometry (Eq. 5.3-3)
or B) plane-sheet geometry (Eq. 5.3-4). The effective diffusion
coefficient is in each case associated with cross-wall transport.
The effective diffusion coefficient derived for as-made cone-like particles using the
release function in plane-sheet geometry (Eq. 5.3-3) amounts to:
⊥
= (2.0 ± 0.6)⋅10-11 cm2s-1
Deff
(Eq. 5.3-5)
The error is the standard deviation of 9 independent measurements (Tab. 5.3-1). The
magnitude of the statistically-derived error is comparable with that of the estimation
based on error sources (mostly due to the inaccuracy of particle size determination).
For the lateral dimension (radius) this error is defined by pixel size of the digital
photograph, ∆R = 0.1 µm. The particle thickness is measured by depth of focus,
whose accuracy is determined by the least unit of the micrometer screw moving the
object table, ∆L = 0.1 µm, and the sensitivity of the eye toward sharpness of the
image [135].
⊥
The determined value of Deff
is comparable with that of a fiber; although
systematically lower. This could be explained by modification of surface taking
place during rinsing the cone-like particles with water. The rinsing is a necessary
step during sample preparation but it is connected with certain modification of
release (chapter 6.2.1).
- 70 -
Tab. 5.3-1. Statistics of the
effective diffusion coefficient
associated with cross-wall
transport in cone-like particles
mean
deviation
5.3.3
L /cm
⊥
/cm2s-1
Deff
2.3⋅10-4
2.2⋅10-4
2.2⋅10-4
2.0⋅10-4
2.3⋅10-4
2.2⋅10-4
2.0⋅10-4
2.2⋅10-4
2.2⋅10-4
3.01⋅10-11
2.80⋅10-11
2.11⋅10-11
2.54⋅10-11
1.36⋅10-11
1.18⋅10-11
1.59⋅10-11
1.76⋅10-11
1.90⋅10-11
2.17⋅10-4
0.11⋅10-4
2.03⋅10-11
0.64⋅10-11
ANISOTROPY OF DIFFUSION IN SBA-3-LIKE PARTICLES
The observation of fast releasing local zones in SBA-3-like particles (fibers in Fig.
5.1-1 B and cone-like particles in Fig. 5.1-4 B) has indicated that the stored
molecules can use more than one path during release. The effective diffusion
coefficients associated with those paths are likely very different, as can be concluded
by the different time scales of the two releases. The local zones seem to empty within
tens of seconds, while the release utilizing cross-wall transport takes tens of minutes.
This means that diffusion in SBA-3-like particles is strongly anisotropic.
⊥
5.3.3.1 DEFINITION OF Deff
AND
||
Deff
SBA-3-like particles with coiled pores have no strict translational symmetry [50],
thus it is inconvenient to work with Cartesian coordinates. The effective diffusion
coefficients are better attributed to the particles structure. However, since the
particles are hierarchically structured the coefficients can be considered at different
length scales [52]. The different coefficients are explained on the example of a conelike particle.
The different effective coefficients are on principle specified by the flux. In the
macroscopic view, at the level of particle morphology, the flux is conveniently
described by its polar components: axial, radial and tangential (Fig. 5.3-3 A). The
individual components are associated with Deff ,a , Deff ,r and Deff , t , respectively.
5 STUDY OF RELEASE
- 71 -
Fig. 5.3-3. Definition of different effective
diffusion coefficients in a cone-like particle of
SBA-3-type: A) radial, axial and tangential flux
components associated with Deff ,a , Deff , r and
Deff , t , respectively; B) transport parallel and
perpendicular with respect to pore walls
||
⊥
and Deff
; D)
associated; C) definition of Deff
adsorption/desorption equilibrium where cp and
cw are concentrations in the pore and at the wall
respectively, and K is an adsorption constant.
At the length scale at which pore ordering is essential (nanostructure), two flux
directions are relevant. One, Φ ||eff , describes diffusion parallel to the elongated pores,
⊥
and the other, Φ eff
, diffusion perpendicular to the pores (Fig. 5.3-3 B). They are
||
⊥
associated with the effective coefficients Deff
and Deff
, respectively (Fig. 5.3-3 B).
The perpendicular coefficient corresponds with cross-wall transport.
Owing to the characteristic embedding of the pore structure into the particle
morphology the following relations are straight-forward:
⊥
⊥
||
Deff ,a ≈ Deff
+ (1 / τ ) Deff
≈ Deff
(Eq. 5.3-6)
⊥
Deff ,r = Deff
(Eq. 5.3-7)
||
Deff , t = Deff
(Eq. 5.3-8)
- 72 -
where τ is the tortuosity factor describing the fraction of axial transport mediated by
diffusion along the coiled mesopores. The tortuosity factor is related to the pitch
vector of the coil, p, by: 1/τ = max(1, |p|/ 2πr ) with r being the coiling radius. For
most r the factor 1/τ is rather small, especially that p is typically comparable with
pore size, justifying the approximation in Eq. 5.3-6. The mesopore-mediated
mechanism of axial diffusion is therefore of negligible meaning as has already been
suggested by the lack of axial gradients in releasing fibers in chapter 5.1.1 (Fig.
5.1-1).
In fact, the parallel and perpendicular coefficients originate from the primary
processes of pore and wall diffusions. These processes are associated with the
interaction of guest molecules with pore walls [52] (Fig. 5.3-3 D).
⊥
5.3.3.2 DETERMINATION OF Deff
AND
||
Deff
The perpendicular diffusion coefficient has been measured in chapter 5.3.2 (Eq.
5.3-5). In the following the parallel coefficient is determined.
The ring-wise emptying of the damaged cone-like particle (Fig. 5.1-4 B) allows to
assume that the fast depletion of local zones is associated with the parallel transport.
Because of the different release times it follows that:
⊥
||
< Deff
Deff
(Eq. 5.3-9)
What more, the difference must be at least one order of magnitude.
The quantitative determination of the coefficients is best conducted on particles fully
dominated by either parallel or perpendicular transport. The release from assynthesized particles is fully dominated by cross-wall transport. The parallel
transport can be enabled by violation of mesopore continuity. When all pores are
||
violated then, on the basis of Eq. 5.3-9, the release is determined by Deff
.
Two methods of localized damage, hereafter called microsurgery, have been used in
order to enable the parallel transport: mechanical damage (Fig. 5.3-4 A) and focused
ion beam (Fig. 5.3-5). The FIB-microsurgery has a higher precision than the
mechanical one.
5 STUDY OF RELEASE
- 73 -
Fig. 5.3-4. SEM of SBA3-like particles: A) conelike particle exposed to
mechanical microsurgery;
B) an intact particle on
the same support. The
pictures were collected
after secondary release
(chapter 6.2.3)
Fig. 5.3-5. SEM of SBA-3-like particles exposed to FIB-microsurgery: A)
before the exposure (top view) and B) after the exposure (tilted view).
The release curves measured for an intact and the halved particles are presented in
Fig. 5.3-6. The deduced release times confirm the visually observed fast release in
case of mechanical microsurgery. There is, however, no clearly accelerated release
observed in the case of FIB-microsurgery. This fact indicates that the parallel
transport has not been enabled (most likely because of the blockage at the cut) and
||
disqualifies the use of FIB for the determination of Deff
.
Fig. 5.3-6. Microphotometric release curves measured for A) an intact cone-like particle,
B) particle exposed to mechanical microsurgery and C) particle exposed to FIBmicrosurgery. The release time are indicated. The included schemes represent the relevant
release directions.
- 74 -
The geometry of release from the mechanically
damaged particle is different than that of an
intact particle. In the halved particle the flux
follows the curved mesopores by the arc-like
paths ξ (Fig. 5.3-7). Although the flux
Fig. 5.3-7. Schematic view of release
geometry from a halved cone-like in
A) side-view and B) top-view; with
indicated flux directions.
geometry is not fully symmetric it is confined
to one plane and, what more, it is uniaxial along
ξ . Also, the flux at the releasing surface has a
plane-parallel character. The total flux can be
therefore approximated by a plane-sheet
geometry with the characteristic length ξ . This
approximation rules out the radial symmetric cross-wall transport and the effective
||
diffusion coefficient can be associated with Deff
. The average characteristic length
can be expressed by:
ξ =
π
4
R
(Eq. 5.3-10)
where R is the mean radius of the particle. For a reasonably small area at which the
absorbance is measured the release function can be described by the actual
concentration in a plane-sheet at its origin:
E (t ) = E const + E max
||
⎛ Deff
(2n + 1) 2 π 2 t ⎞
(−1) n
⎜
⎟
exp −
∑
⎟
π n =0 2n + 1 ⎜⎝
4ξ 2
⎠
4
∞
(Eq. 5.3-11)
It should be mentioned again that the release functions for the intact cone-like
particle (Eq. 5.3-3) and the release function for the halved particle (Eq. 5.3-11) are
mathematically very similar. It means that both the functions would fit equally well
to any experimental set. However, they are associated with different diffusion
coefficients and different characteristic lengths. The similarity of release functions
also implies that in a mixed case, i.e. when both parallel and perpendicular transports
||
⊥
are relevant, it is impossible to assign the fit number to either Deff
or Deff
. Such
mixing might occur when the mesopores at the cut surface are only partially opened
or not at all.
The effective diffusion coefficient derived for a mechanically halved cone-like
particle (Fig. 5.3-6 B) amounts to:
||
= (3.5 ± 0.5)⋅10-10 cm2s-1
Deff
(Eq. 5.3-12)
5 STUDY OF RELEASE
- 75 -
The error is estimated from the inaccuracy of radius determination, analogously to
||
the estimation for a fiber (chapter 5.3.1). It should be noted that the value of Deff
was derived assuming a fully irrelevant cross-wall transport and using a release
function based on approximations (plane-parallel release geometry for arc-like
release paths, average characteristic length).
5.4
DIFFUSION DATA FROM SPECTROSCOPIC METHOD
The derivation of diffusion data from a spectroscopic release curve differs from the
microphotometric case in that the flux direction, i.e., release geometry, is principally
not known. In order to apply an appropriate release function this information has to
be provided or assumed. The characteristic diffusion length needs to be likewise
provided. Also, the measured values represent a cumulative amount of guest
molecules released by all particles involved in the experiment. This fact has to be
taken into account in case of inhomogeneous particle size distribution, e.g., presence
of outstanding particles or particle parts.
5.4.1
TRANSFORMED RELEASE CURVES
In order to deal with the inhomogeneous size distributions, transformation of release
into logarithmic scale is introduced:
⎛
E (t ) ⎞
⎟⎟
Λ (t ) = log10 ⎜⎜1 −
⎝ E max ⎠
(Eq. 5.4-1)
where E(t) and Emax denote the measured release curve and the total released amount,
respectively. The use of decimal logarithm has the advantage that the visualization of
the curve is more intuitive. The value of Emax is estimated numerically by fitting the
measured curve with:
N
⎛
⎛ t
E (t ) = E max ⎜⎜1 − ∑ a n exp⎜⎜ −
⎝ τn
⎝ n =1
⎞⎞
⎟⎟ ⎟
⎟
⎠⎠
(Eq. 5.4-2)
where N, a n and τ n are an integer depending on the shape of the release curve and
the fitting parameters, respectively. The use of Eq. 5.4-2 is justified by the fact that
all spectroscopic release curves have the general form described by Eq. 2.3-12,
which is a special case of Eq. 5.4-2. The precision in determination of Emax (large N)
is essential because it influences the shape of Eq. 5.4-1. For this reason experimental
- 76 -
quantification is not recommended. The release curves are rarely measured long
enough. Evaporation of the solvent at the long release time becomes a risk at longer
times, anyway.
During fitting of the transformed release curves, the contribution of small particles or
fast releasing particle parts is suppressed. Small particles have generally faster
release kinetics, which is particularly true for the case of equal diffusion coefficients.
The influence of the fast releasing objects is therefore significant for the shape of the
curve only at the initial times. After the transformation more weight is naturally put
on the long release times. The effect of the fast releasing objects is therefore reduced.
5.4.2
SBA-3-LIKE FIBERS
5.4.2.1 DETERMINATION OF DIFFUSION DATA
The release curve measured for as-synthesized SBA-3-like fibers is shown in Fig.
5.4-1. The curve is fit by a release function derived in cylinder geometry with a
perfect sink condition:
E (t ) = E const
⊥
∞
⎛
⎞⎞
⎛ Deff
4
⎜
⎜
+ E ' max 1 − ∑ 2 exp − 2 q n2 t ⎟ ⎟
⎟⎟
⎜ R
⎜ n =1 q n
⎠⎠
⎝
⎝
(Eq. 5.4-3)
where q n are positive roots of J 0 (q n ) = 0 . Here, the constant E const represents the
amount delivered by the fast releasing fraction and E ' max is the total amount delivered
by the rest of the sample. This fast initial release can be associated with the so-called
initial burst introduced in the science of drug delivery [136]. In the transformed
function it is convenient to introduce:
A=
E ' max − E const
E ' max
(Eq. 5.4-4)
The transformed parameter can be then interpreted as the fraction of sample
described by the exponential part of Eq. 5.4-3. In a perfect case of A = 1 ( E const = 0)
⊥
all of the release is realized by diffusion with Deff
and then E ' max = E max .
5 STUDY OF RELEASE
- 77 -
Fig. 5.4-1. Release from as-synthesized SBA-3-like fibers: A) as-measured release
curve fit by diffusion in cylinder (Eq. 5.4-3) and B) fit in the transformed form. The
obtained fit parameters are indicated.
None of the experimental data could be satisfactorily fit by diffusion in cylinder with
a perfect sink condition. The deviation of the best fit is different than what could be
expected from even a broad size distribution (Appendix F). Therefore the function
derived with a perfect sink condition is wrong.
There are some arguments for the introduction of surface diffusion barrier:
1) Bad quality of the fit by diffusion with a perfect sink condition (as shown above).
Whereas a well fitting function does not imply that the assumed model is correct, a
bad fitting function allows rejecting the model as fault.
2) Indication of transport resistance by homogeneous loss of dye observed under
optical microscope. However, this indication could not be investigated quantitatively
with the mircrophotometric method due to low data quality and other experimental
limitations.
3) Fibers from different batches, as well as fibers of one batch subject to
modifications, show clearly different release kinetics. Because there is little variation
in the bulk properties of the various fibers (chapter 6.1.1) a surface-localized cause is
likely.
4) Accumulation of release in one characteristic release time, typical for a barrierlimited release (chapter 6.1.2).
The release function describing diffusion in a fiber with transport resistance at its
surface (Eq. 2.3-9) is:
- 78 -
E (t ) = E const
⊥
∞
⎛
⎞⎞
⎛ Deff
4α 2
2 ⎟⎟
⎜
⎜
exp
q
t
+ E ' max 1 − ∑ 2 2
−
n
2
⎟⎟
⎜ R2
⎜
i =1 q n ( q n + α )
⎠⎠
⎝
⎝
(Eq. 5.4-5)
where α and q n are the barrier parameter and the roots of characteristic equation
q n J 1 (q) − αJ 0 (q n ) = 0 , respectively. The fit for as-synthesized SBA-3-like fibers is
shown in Fig. 5.4-2.
Fig. 5.4-2. Release from assynthesized SBA-3-like fibers
fit by by diffusion in cylinder
with surface diffusion barrier
(Eq. 5.4-5).
None of the experimental data could be fit satisfactorily with Eq. 5.4-5. Only when
initial times are excluded from the fit the long time release seems to be well
described. However, the determined parameters are very strongly dependent on their
initial values.* The most unstable in this sense is the barrier parameter α , which
always tends toward values lower than the initial guess. In conclusion, the simple
introduction of surface diffusion barrier is insufficient for the description of release
from SBA-3-like fibers. For a function to be reliable the full time range has to be
taken into account.
Inhomogeneity of surface diffusion barrier. An extended model, availing the full time
scale, can be constructed by introducing a second releasing population. Assuming
that this second population has the same release geometry and the same effective
diffusion coefficient as that described by the simple barrier model (Eq. 5.4-5), the
model can be expanded to be accompanied by a barrier-less fraction. This view is
supported by the fact that the surface is very likely inhomogeneous due to
mechanical damage during sample manipulation and uneven effects of the sample
*
In the employed procedure of least-square fitting with large-scale algorithm an initial guess of the fit
parameter is required
5 STUDY OF RELEASE
- 79 -
treatments. Drying, for instance, cannot proceed evenly because the particles touch
each other.
The extended release function, including inhomogeneity of the barrier, is:
⊥
∞
⎛
⎛ Deff
4α 2
2 ⎞
⎜
⎜
−
E (t ) = E max 1 − A∑ 2 2
exp
q
t ⎟⎟ −
n
2
⎜ R2
⎜
+
q
(
q
)
α
=
1
n
n
n
⎝
⎠
⎝
⊥
⎛ Deff
⎞⎞
4
⎜
− (1 − A)∑ 2 exp − 2 s n2 t ⎟ ⎟
⎜ R
⎟⎟
n =1 s n
⎝
⎠⎠
∞
(Eq. 5.4-6)
where q n and s n are the roots of characteristic equations q n J 1 (q) − αJ 0 (q n ) = 0 and
J 0 ( s n ) = 0 , respectively. The fit for as-synthesized SBA-3-like fibers is shown in
Fig. 5.4-3.
Fig. 5.4-3. Release from assynthesized SBA-3-like fibers fit
by diffusion in cylinder with
inhomogeneous surface diffusion
barrier (Eq. 5.4-6).
The fit shows a good agreement with the experimental data and the obtained
parameters are insensitive toward the initial guess.
The effective diffusion coefficient determined for as-made fibers from the
spectroscopic method amounts to:
⊥
= (6.7 ± 1.6)⋅10-11 cm2s-1
Deff
(Eq. 5.4-7)
and is accompanied by a surface diffusion barrier α = 0.43 present on 16% of the
releasing surface. The accuracy of the derived coefficient is strongly dependent on
the representative radius, R . Here R = 4 µm was used and the indicated error
corresponds with the assumed value of ∆R = 0.5 µm. The obtained diffusion
coefficient seems to be greater than that determined from the microscopic method
(Eq. 5.3-2).
- 80 -
The significance of the barrier parameter is discussed in Appendix G.
5.4.3
SPHERICAL MESOPOROUS PARTICLES
In case of spherical particles, with no special texture of the mesoporous system, the
release geometry is clear. However, it is also not possible to find a satisfactory fit
using a release function describing barrier-less diffusion or homogeneous transport
resistance. The surface condition of inhomogeneous diffusion barrier is therefore
introduced.
The release function describing release from a sphere with inhomogeneous surface
diffusion barrier is:
sph
∞
⎛
⎛ Deff
⎞
6
⎜
⎜
E (t ) = E max 1 − A∑ 2 2
exp⎜ − 2 q n2 t ⎟⎟ −
⎜
n =1 q n q n + α (α − 1)
⎝ R
⎠
⎝
(
)
sph
⎛ Deff
⎞⎞
6
⎜
− (1 − A)∑ 2 exp − 2 s n2 t ⎟ ⎟
⎜ R
⎟⎟
n =1 s n
⎝
⎠⎠
∞
(Eq. 5.4-8)
where q n and s n are the roots of the characteristic equations q n cot q n + α = 1 and
s n = nπ , respectively. The fit for as-made mesoporous spheres is shown in Fig.
5.4-4. The obtained parameters are stable toward the initial guess.
The effective diffusion coefficient determined for as-made mesoporous spheres is:
sph
= (4.1 ± 0.8)⋅10-11 cm2s-1
Deff
(Eq. 5.4-9)
and is accompanied by surface diffusion barrier α = 0.31 present at 13% of the
releasing surface. Here Here R = 1.5 µm was used and the indicated error
corresponds with ∆R = 0.2 µm.
Fig. 5.4-4. Release from assynthesized mesoporous spheres fit
by diffusion in sphere with
inhomogenous diffusion barrier at
the surface (Eq. 5.4-8).
5 STUDY OF RELEASE
- 81 -
The obtained value is lower than that obtained for SBA-3-like fibers (Eq. 5.4-7). This
fact can be related to smaller pore size and to a possibly different structure of the
pore walls. Further explanation possibilities are discussed in chapter 5.5.1.
5.5
IMPORTANCE OF CROSS-WALL TRANSPORT AND SURFACE DIFFUSION
BARRIERS
Both cross-wall transport and surface diffusion barrier have been shown to have their
share in defining the kinetics of release. Because mesoporous silica is considered for
storage and delivery of functional molecules the possible implications of cross-wall
transport and surface diffusion barrier for this application are discussed.
5.5.1
CROSS-WALL TRANSPORT
As shown on the example of SBA-3-like fibers, cross-wall transport can be the
release-rate limiting factor. This implies that large pores can be combined with low
release rates. This conclusion seems counterintuitive because slower release is
usually associated with smaller pore sizes [137]. With decreasing pore size the
interaction energy between guest molecules and pore walls increases, lowering the
effective diffusion coefficient [138]. However, in SBA-3-like structures, transport
along the mesopores does not define the release time due to pore coiling and pore
blocking. The system behaves as effectively having only the pores enabling crosswall transport.
The feature of cross-wall transport is also relevant for other types of mesoporous
particles. Whenever mesopores are not fully or not directly connected with the
outside environment, the phenomenon of cross-wall transport has to be considered.
An extreme example are structures with so-called cage-like porosity [139], where the
mesopores are basically regular voids connected with each other by well-defined and
regular passages. In the common mesoporous materials, MCM-41 or SBA-15, the
mesopores are rather elongated, parallel to each other, and possibly opened. The
continuity of such mesopores is, however, not decisive for the effective diffusion
coefficient when the particle is not a single domain. In order to make a spherical
particle the mesopores ordering must be violated. Such violation can be realized by
local occurrence of a worm-like structure [140]. In such a case the tortuosity of
mesopores is enhanced and in the presence of a concentration gradient the ‘pressure’
- 82 -
on pore walls is increased. Whenever permeability of the walls is provided, e.g.
micropores in SBA-15 [141], cross-wall transport becomes significant.
In conclusion, cross-wall transport enables combination of large pores with long
release times and is not limited to structures with coiled pores.
5.5.2
SURFACE DIFFUSION BARRIER
The significance of surface diffusion barrier in as-synthesized SBA-3-like particles is
rather small as compared with the estimations for zeolites. For instance, in a ZSM-5
zeolite the presence of surface diffusion barrier changes the effective diffusion
coefficient by two orders of magnitude [84]. However, the barrier can be further
manipulated (chapter 6.2), becoming an important and well controllable design factor
for release systems based on mesoporous silica.
Tailoring of release times can be achieved by modification of the mesoporous system
(size and ordering of pores) or the particle’s surface. The first option provides little
flexibility. Change of pore size by say 10% is usually connected with the use of
different synthetic prescription, typically leading to different particle morphology.
Modification of the particle’s surface, on the other hand, is more reliable in this
respect.
- 83 -
6 MODIFICATION OF RELEASE
6.1 PHENOMENOLOGICAL TREATMENT OF MODIFIED RELEASE
Modification of release has been realized by either soft modification or surface
coating. Soft modifications include treatments with distilled water (H2O), sodium
hydroxide (NaOH) and mother liquor (ML). Surface coating refers to treatments with
a solution of waterglass (WG).
6.1.1
STRUCTURE OF MODIFIED PARTICLES
Examples of the effects of soft treatments on the surface of SBA-3-like fibers are
shown in Fig. 6.1-1.
All the treated fibers appear similar to the non-modified (parent) ones. There are no
distinct features visible and the number of defects, e.g. characteristic circular crack,
also does not change. The surface is in each case equally smooth.
Complementing the series of SEM pictures (Fig. 6.1-1) is the series of TEM pictures
in Fig. 6.1-2 obtained for the same samples.
Fig. 6.1-1. SEM image of SBA-3-like fibers: A) parent surface (no
modification), B) after ML-treatment, C) after H2O-treatment, D) after NaOHtreatment. There is no significant difference in the appearance of the surface.
- 84 -
Fig. 6.1-2. Surface of SBA-3-like fibers seen under TEM: A) parent surface
(no modification), B) after modification with mother liquid (ML), C) after
modification with water, D) after modification with sodium hydroxide (pH =
10.7). The structure of mesopores seems to be similar in each case.
In TEM the mesopore ordering is visible. However, the pattern seems not to be
particularly affected by any of the treatments – the different appearance is mostly due
to the different diffraction condition. Only the fiber’s rim is changed. The surface
appears ragged or etched, which is the most evident in case of the NaOH-treatment.
In case of H2O- and ML treatments the effect is not so clear but the fiber’s edge is
not as smooth as that of a of parent sample. The length-scale associated with the
effect is in the range of nm, which explains why no modification could be seen in
SEM.
Treatments with waterglass bring profoundly different effects. In SEM the modified
surface is clearly rough (Fig. 6.1-3 A). The tiny cracks are not visible anymore and
the steps of few nm, sparsely distributed over a parent sample (e.g., upper right
corner in Fig. 6.1-1 A), seem lower. These observations indicate deposition of a film.
In TEM the modification proves to be a porous coating of approximately 10 nm (Fig.
6.1-3 B). The pore structure beneath the coating appears to be unaffected. There is no
evident penetration of waterglass into the pores and no prominent destruction of the
porous matrix.
6 MODIFICATION OF RELEASE
- 85 -
Fig. 6.1-3. SBA-3-like fibers after treatment with solution of waterglass (WG)
seen in A) SEM and B) TEM. The treatment results in deposition of a thin
coating layer.
X-ray diffraction patterns of all the modified particles show similar background,
peak intensities and peak broadenings (Fig. 6.1-4). This fact confirms that the
mesopores structure is preserved. However, a slight shrinkage of the hexagonal
lattice is indicated by the corresponding lattice constants (d100). This slight volume
effect has likely no significant influence on the release kinetics. This view is
supported by literature data on the dependence of the effective diffusion coefficient
on pore size in mesoporous silicas [142,143].
Fig. 6.1-4. X-ray diffraction
patterns of modified SBA-3like fibers. The derived lattice
constants are indicated by d100.
6.1.2
RELEASE FROM MODIFIED PARTICLES (MODEL-FREE ANALYSIS)
The release curves measured for the modified particles are shown in Fig. 6.1-5. All
the modifications result in slower release times with the order (Tab. 6.1-1):
t 1parent < t 1ML < t 1H 2O < t 1NaOH < t 1WG
2
2
2
2
2
(Eq. 6.1-1)
- 86 -
In order to analyze possible changes in the shape of the curves, they were fit using
the general function Eq. 5.4-2. To avoid instability of fitting, the used N was taken as
the minimum number of exponentials needed to describe the experimental data with
given accuracy, usually N = 1, 2 or 3. The fit parameters are shown in Tab. 6.1-1.
Fig. 6.1-5. Release from modified SBA-3-like fibers: A) fit with the model-free
release function (Eq. 5.4-2), B) normalized by the respective Emax (Tab. 6.1-1)
Tab. 6.1-1. Release from modified SBA-3-like fibers: release times and
parameters fit by the model-free release function (Eq. 5.4-2). Only the strongest
contributions are shown. The particles were treated for 10 s in each case.
sample
t 1 /min
E max
a1
τ 1 /min
N
parent
7
0.176
0.65
13
3
ML-modified
16
0.170
0.68
22
3
H2O-modified
24
0.160
0.76
30
2
NaOH-modified
39
0.188
0.82
45
2
WG-modified
203
0.168
1.00
560
1
2
The used function can be interpreted as a model-free release function when:
N
∑a
n =1
n
=1
(Eq. 6.1-2)
This condition is justified by the fact that the intensity of all exponentials must
converge to E max , as the sum of the weights A n in any diffusion-based release
6 MODIFICATION OF RELEASE
- 87 -
function converges to 1. The time parameters τ n have the meaning of time constants
but should not be mistaken with the release time denoted by t 1 . The parameters a n
2
have no physical meaning but they may indicate the rate limiting factor. The more
weight is concentrated in a single exponential the more likely is that it will be a
barrier controlled release (Appendix G). The first weights of A n , i.e. A 1 , in a
barrier-free case are 0.81, 0.77 and 0.71 for a plane-sheet, a cylinder and a sphere
respectively. It can be therefore assumed that a 1 > 0.82 is indicative for the existence
of surface diffusion barrier. It should be noted that this condition is sufficient but not
necessary for the barrier-dominated release. A surface diffusion barrier can be
therefore expected on the fibers treated with water or the sodium hydroxide.
The number of exponential functions, N, needed to fit the data sufficiently well, is
not equal for all fits. It seems that the bigger a 1 the smaller N is needed. This trend
goes along with the increase of τ 1 . In case of WG-treatment a 1 reaches almost 1,
which indicates release fully controlled by the barrier. The time constant shows that
the release is slower by more than an order of magnitude, which complies with the
physical character of surface modification observed in TEM (Fig. 6.1-3 B). In case of
soft treatments the changed values of a 1 and τ 1 can be interpreted as an indication of
a weak barrier. This view is supported by the fact that the modifications have just a
slight effect on the bulk, which is very unlikely the cause of the changed release
kinetics (Appendix H).
Mesoporous silica spheres show analogous behavior upon modifications. There is no
difference visible in SEM after soft treatments. Modification by waterglass-treatment
results in rough surface (Fig. 6.1-6 B), which is interpreted as surface coating by
analogy to the fibers. The bulk effects seen in XRD are also similar (Fig. 6.1-7).
The measured and fit release curves are shown in Fig. 6.1-8. The corresponding
parameters are collected in Tab. 6.1-2. In case of the WG-treatment the fit is not
working well. Possible reasons are complex structure or dissolution of the coating,
both difficult to model.
- 88 -
Fig. 6.1-6. SEM of mesoporous silica spheres modified by a WG-treatment: A)
before the modification, B) after modification. The rough surface is ascribed
to a thin coating in analogy to SBA-3-like fibers.
Fig. 6.1-7. X-ray diffraction patterns of
modified mesoporous spheres. The derived
periodicity constant (d) is estimated from
the maximum intensity.
In conclusion, soft treatments corroborate the existence of surface diffusion barrier.
The effect of the modification on the bulk is negligible, there is no strong
modification visible in electron microscopy but the release is clearly modified. The
release times are longer and tend to accumulate in one exponential.
Mesoporous particles are usually considered immune to treatments with distilled
water or mother liquor. Washing with distilled water is often applied to freshly
synthesized particles “only to” remove the excess mother liqour, e.g. [144]. Although
treatments with boiling water can be drastic [99], they are mostly attributed to the
effect of temperature [145]. The obviously changed release kinetics indicates that
already brief washing with water at room temperature has an effect on the particles.
The particles are therefore not immune to such treatments, or in other words, the
structure of as-synthesized particles is not at equilibrium with water. The extent and
possible origin of the surface diffusion barrier is further studied in chapter 6.2.
6 MODIFICATION OF RELEASE
- 89 -
Fig. 6.1-8. Release from modified mesoporous silica spheres: A) fit with the modelfree release function (Eq. 5.4-2), B) normalized by the respective Emax (Tab. 6.1-2)
Tab. 6.1-2. Release from modified mesoporous silica spheres: release times and
parameters fit by the model-free release function (Eq. 5.4-2). Only the strongest
contributions are shown.
t 1 /min
E max
a1
τ 1 /min
N
parent
1
0.391
0.60
2
3
H2O-modified
7
0.309
0.62
40
2
WG-modified
114
0.323
1.00
180
1
sample
2
The treatment with waterglass results in deposition of a thin coating and a profound
modification of release. However, by a coating of 10 nm an even slower release
could be expected. Permeability of silica for such big organic molecules as
rhodamine is not high and if the coating were forming a dense film, a complete
inhibition of release would very likely be the case. But the coating is rather porous
and this fact offers a possibility of tailoring the release times in a broader time-range
by varying the coating parameters (chapter 6.3).
6.2
MODIFICATION OF THE SURFACE DIFFUSION BARRIER
Different treatment solutions and modification sequences are used to identify at
which point the modification happens and if it is accompanied by a consequent bulk
effect.
- 90 -
6.2.1
SOFT MODIFICATIONS BY WATER
Each of the soft treatments can be interpreted as an interrupted release experiment.
This is particularly true in case of water. During the treatment particles are in direct
contact with the modifying solution, which also will take up molecules released from
the particles. A better understanding of the decisive effect can be gained from
variation of the treatment conditions.
As-synthesized SBA-3-like fibers were subject to recurrent H2O-treatments of
different treatment times. The resulting release curves are shown in Fig. 6.2-1. The
corresponding parameters of a model-free analysis are collected Tab. 6.2-1.
Fig. 6.2-1. Release from SBA-3-like fibers subject to the indicated H2Otreatments: A) as-measured and fit with the sum of exponential functions (Eq.
5.4-2); B) normalized by Emax (Tab. 6.2-1).
Tab. 6.2-1. H2O-treatments of SBA-3-like fibers (Fig. 6.2-1): applied modifications
and corresponding release parameters from the model-free analysis (Eq. 5.4-2).
t 1 /min
E max
a1
τ 1 /min
N
parent
2
0.395
0.60
14
3
H2O-modified (1 x 1 min)
21
0.387
0.68
36
2
H2O-modified (2 x 1 min)
83
0.352
0.91
108
2
H2O –modified (1 x 2 min)
63
0.298
0.81
79
2
sample
2
6 MODIFICATION OF RELEASE
- 91 -
The time constant τ 1 seems to be positively correlated with the time the particles
stay in contact with water. This statement is based on three treatment times: 10 s
(Tab. 6.1-1), 1 min and 2 min (Tab. 6.2-1). However, the treatment of 2 min divided
into two steps results in considerably longer τ 1 than that of one-step.
Release from SBA-3-like fibers subject to recurrent H2O-treatments, together with
corresponding XRD data is shown in Fig. 6.2-2.
Fig. 6.2-2. Recurrent H2O-treatment of SBA-3-like fibers: A) X-ray diffraction
patterns, B) Normalized release curves. Obtained lattice constants and release
parameters in Tab. 6.2-2.
Tab. 6.2-2. Recurrent H2O-treatments of SBA-3-like fibers: applied modifications, release
parameters from the model-free analysis (Eq. 5.4-2) and lattice constants d100 from XRD. The
time of modification tmodif is a sum of individual steps.
tmodif /min
t 1 /min
E max
a1
τ1
/min
N
-
2
0.264
0.56
6
3
4.82
H2O-modif
0.17
4
0.306
0.67
17
2
4.60
H2O-modif
0.17 + 1
12
0.267
0.72
31
2
4.43
H2O-modif
0.17 + 1 + 1
36
0.285
0.79
49
1
4.32
H2O–modif
0.17 + 1 + 1 + 1
58
0.340
0.81
65
1
4.29
sample
parent
2
d100
/nm
The time constant of each subsequent step in the recurrent modification is longer
than the preceding one. It is also accompanied by shrinkage of the lattice constant.
- 92 -
However, the shrinkage is not proportional to the elongation of τ 1 . Similar
experiments with mesoporous spherical particles give analogous results (data not
shown).
The dependence of τ 1 on the cumulative treatment time indicates a possible
correlation of the modified release with bulk effects indicated by XRD. It could be
the changed amount of dye or other modification taking place while the sample is in
contact with the treating solvent (leaching). However, the disproportional increase of
τ 1 in case of the interrupted treatment indicates that rather drying than leaching is the
decisive step. This conclusion is in agreement with the observation of possible
different release times from samples prepared by different experimenters using the
same composition (Appendix H).
In conclusion, although the time of H2O-treatment is positively correlated with the
release time the decisive step for modification takes place during drying.
6.2.2
SOFT MODIFICATION BY OTHER SOLUTIONS
The effects of soft modifications by water, mother liquor and sodium hydroxide were
shown in chapter 6.1.2, where the existence of surface diffusion barrier was indicated.
Here, the same release curves are analyzed using the release function that described
diffusion with a surface diffusion barrier and its inhomogeneity (Eq. 5.4-6). The
results of respective fits are shown in in Fig. 6.2-3 and Tab. 6.2-3.
Fig. 6.2-3. Analysis of soft
modification by a release function
allowing for surface diffusion barrier
and its inhomogeneity (Eq. 5.4-6).
The obtained parameters are shown
in Tab. 6.2-3. The phenomenological
analysis of these curves is shown in
Fig. 6.1-5.
6 MODIFICATION OF RELEASE
- 93 -
Despite the fact that the modified particles have very different release times the
magnitude of the barrier parameter α is comparable in each case. The different
⊥
release kinetics seem to be due to the different values of A and Deff
/ R 2 instead. It
should be noted that all fits are very stable, i.e. independent from the initial guess.
⊥
There is also no unique Deff
/ R 2 that when fixed could be compensated by the other
fitting parameters. The numbers are therefore reliable.
Tab. 6.2-3. Release parameters obtained from the two population model allowing
surface diffusion barrier and its inhomogeneity (Eq. 5.4-6). The effective diffusion
coefficients are calculated for R = 4 µm.
sample
t 1 /min
α
⊥
Deff
/ R 2 [ s-1]
⊥
[ cm2s-1]
Deff
A
parent
7
0.43
4.2⋅10-4
6.7⋅10-11
0.16
ML-modified
16
0.54
2.8⋅10-4
3.3⋅10-11
0.17
H2O-modified
24
0.67
1.1⋅10-4
1.8⋅10-11
0.17
NaOH-modified
39
0.49
1.1⋅10-4
1.7⋅10-11
0.27
2
The fact that the barrier parameter has a similar value for all samples can be
interpreted as an indication of one blocking mechanism that applies to all samples.
This statement relies on the fact that release from SBA-3-like fibers is dominated by
cross-wall transport (chapter 5.1.1). Since there is no physical barrier seen in TEM
(Fig. 6.1-2) it seems logical to associate the effective barrier in release with the
outermost silica wall. Then, the barrier can be interpreted as blocking of the
outermost wall passages. The soft modification of release is then expressed by both
modification of the density of the outer most silica wall ( α ) as well as the number of
blocked passages (A). Unfortunately, the resolution of the structural data (TEM) is
insufficient for the experimental evidence and the physical nature of the barrier
remains a speculation.
In conclusion, soft modifications achieved with different liquors indicate that surface
diffusion barrier could be associated with blocking of the wall passages through the
outer most silica wall. There is, however, no definite evidence.
- 94 -
6.2.3
MODIFICATION OF MESOPORE OPENINGS
The soft modifications discussed above regard release dominated by cross-wall
transport. Although the slight shrinkage of the mesoporous lattice has been observed
in XRD no conclusion about the influence of the soft treatment on the mesopores
could be made. This influence can be studied on cone-like particles with enabled
parallel transport [146].
Fig. 6.2-4. Modification of release from cone-like particles of SBA-3-type: A)
Primary release from an intact particle, B) secondary release from the particles
in A). C) Primary release from mechanically damaged particle, D) secondary
release from the particle in C). The shown fits are associated with the indicated
release models. Diffusion coefficients derived from the fits are collected in Tab.
6.2-4.
Release measured for as-synthesized and modified cone-like particles are shown in
Fig. 6.2-4. The modification has been realized on particles emptied in a release
experiment, which allows focus on a particular particle. After release the particles
were loaded from aqueous solution of rhodamine 6G. The release measured on such
re-loaded particles is hereafter referred to as secondary release (in contrast to the
primary release measured before the modification). The modification is expected to
occur during drying.
6 MODIFICATION OF RELEASE
- 95 -
Both the intact and the damaged particle show longer release times in the secondary
release. However, the difference in release times observed for the intact and the
damaged particles in primary release, is reduced in the secondary release. Fitting
with a release function delivers diffusion coefficients (Tab. 6.2 4).
Tab. 6.2-4. Diffusion coefficients determined for parent and mechanically
damaged particles from both primary and secondary releases. The
geometry of the used model is indicated by an icon. The results in brackets
are the disfavored option (chapter 5.3.2).
The effective coefficients found for an intact particle differ by a factor of app. 2.5
before and after the modification. Whereas, the analogous difference for a
mechanically damaged particle is about 40. This fact indicates a possible change of
the release path as the applied modification is the same in each case. Such a change
could be connected with the contraction of the opened mesopores. Then, release
would have to be realized by cross-wall transport. Application of the release function
considering such an alternative indeed delivers diffusion coefficient comparable with
that of the particle fully controlled by cross-wall transport. Hence, the change of
release kinetics could be interpreted as due to formation of diffusion barrier at the cut
surface.
Although the quality of the microphotometric data does not provide conclusive
evidence for a discussion of surface diffusion barrier, it seems that the modification
with water is sufficient to affect mesopore openings.
- 96 -
6.2.4
FIB AND SURFACE DIFFUSION BARRIERS
Application of FIB for enabling the parallel transport in cone-like particles does not
bring the desired effect. The loss of dye is rather homogenous, without any radiusdependence (Fig. 6.2-5) and the release time is comparable with that of an intact
particle (chapter 5.3.3.2).
Fig. 6.2-5. Loss of dye
from FIB-trimmed conelike particle observed under
an optical microscope.
Fitting the release curve (Fig. 5.3-6 C) with a release model assuming parallel
FIB
⊥
= 3.0⋅10-11 cm2s-1, which is very similar to Deff
= 2.0⋅10-11
transport delivers Deff
cm2s-1 determined for the cross-wall dominated release. This result can be interpreted
as a sealing of mesopores at the trimmed surface induced by interaction with Ga ions.
This view is supported by the estimation of FIB-affected zone (Appendix I).
The high precision of trimming the particles by FIB could be used for preparation of
TEM samples. However, the modification of mesopores induced by the ion beam is
very likely connected with strong artifacts.
Similar sealing effects are known and sometimes desired. For instance, plasma
etching of silica has been studied for processing of low-k dielectric films [147].
However, successful sealing of pores at the meso-length scale has not been reported
so far [148].
6.3
MODIFICATION BY SURFACE COATING
The treatment of SBA-3-like fibers with a solution of waterglass leads to a
significant slow down of release (chapter 6.1.2). This effect is ascribed to a thin
silicate layer deposited on particle’s surface during the treatment. Here, the influence
of the coating conditions on the resulting release kinetics is studied. For practical
reasons, exclusively mesoporous silica spheres were used.
6 MODIFICATION OF RELEASE
6.3.1
- 97 -
VARIATION OF PH DURING COATING
Release from mesoporous spheres modified by WG-treatment using various pH is
shown in Fig. 6.3-1. The corresponding release times are collected in Tab. 6.3-1.
Although the variation of pH is relatively small, it has a strong influence on the
resulting release time. Especially the difference between pH = 10.50 and pH = 10.6
is striking as it results in release times different by a factor of 7. For pH > 10.60 a
gradual shortening of the release time is observed.
Fig. 6.3-1. Release from mesoporous silica
spheres subjected to treatment with
waterglass (WG) of the indicated pH. The
corresponding release times are shown in
Tab. 6.3-1.
Tab. 6.3-1. Release times (in min and h) measured for mesoporous silica spheres
subject to WG-treatment of various pH at room temperature (Fig. 6.3-1).
pH
-
10.50
10.60
10.68
10.80
t 1 /min
9
50
467
342
253
0.15
0.83
7.78
5.70
4.21
2
t 1 /h
2
To explain this behavior it is useful to interpret the process of coating in terms of solgel chemistry. Solution of waterglass in the used range of pH is a sol, where the
individual particles interact with each other. The higher the pH the smaller is the size
of individual sol particles [149]. It can be expected that a film formed by smaller
particles will be less porous and thus less permeable. This could explain the faster
release at lower pH as the bigger sol particles cannot block the surface efficiently.
Following the same line of arguments the decreasing release times for pH > 10.60
can be associated with thinner coatings formed by smaller particles. The time of
- 98 -
treatment is equal in each case whereas formation of equal thickness would require
longer times (for the higher pH). The compactness of the coating would be therefore
connected with thinner film.
Besides the different release times the release curves in Fig. 6.3-1 show different
shapes. The most distinct is the slowest curve (for pH = 10.60) with a relatively flat
beginning. The rate of release is essentially different throughout the curve. An almost
hold-up at the initial times is followed by a typical release. Because no such shape
can be possibly described by any of the release functions it likely indicates that the
coating or the particles are changing during the release. An instability of the particles
can be excluded based on the stability of scattering contribution during release
measured for non-coated particles (Fig. 6.3-2 A). The scattering contribution after
WG treatment shows a different behavior (Fig. 6.3-2 B). The distinct decrease of Esca
during this initial period could be interpreted as an indication of coating instability,
e.g. dissolution of the coating.*
Fig. 6.3-2. Typical release curves and their scattering corrections for
mesoporous silica spheres: A) non-modified spheres; B) WG-coated sphere.
How a possible dissolution of the coating would influence the shape of release curve
can be estimated by solving the diffusion equation with a boundary condition taking
into account the time dependence of the barrier parameter. In the simplest case a
linear dependence can be assumed. The boundary condition can be then used with a
time-dependent barrier parameter (Fig. 6.3-3 A):
*
Alternative: absorption effects of the particles and the solution due to changing composition
6 MODIFICATION OF RELEASE
α − α ini
⎧
t for t 0 < t < t diss
⎪α ini + ∞
α (t ) = ⎨
t diss
⎪⎩ α ∞
for
t > t diss
- 99 -
(Eq. 6.3-1)
where α ini , α ∞ and t diss are the value of the barrier parameter at the beginning of
release, the value describing no resistance and the time at which α ∞ is achieved,
respectively. However, it is very difficult to solve such diffusion problem
analytically. An example of numerical solution for selected values of t diss is shown in
Fig. 6.3-3.*
The shape of the curves calculated for larger t diss resembles that of the measured for
pH = 10.60 (Fig. 6.3-1). This provides a possible explanation which also seems quite
likely but is no definite proof for the existence of such a dissolving barrier. The
possible dissolution could be, however, interesting for corrosion protection. Sodium
silicate, has been shown to have corrosion inhibiting properties [115,116].
Fig. 6.3-3. Effect of barrier dissolution on the shape of release curve
calculated by numerical solution of diffusion problem with time-dependent
barrier parameter (Eq. 6.3-1): A) time-dependence of the barrier parameter; B)
release curves calculated for a sphere with the indicated parameters of
boundary condition for Deff = 5.10-11 cm2s-1 and R = 1µm.
6.3.2
VARIATION OF TEMPERATURE DURING COATING
Release from mesoporous silica spheres treated by the same solutions as described in
chapter 6.3.1 but at different temperatures is shown in Fig. 6.3-4. The corresponding
*
Computed with MatLab (R14), solver from Partial Differential Equation Toolbox 1.04
- 100 -
release times are collected in Tab. 6.3-2 and Tab. 6.3-3. For a better overview all
release curves are re-plotted as temperature series in Fig. 6.3-5.
The tendencies in release behavior seem to be more or less the same as described in
the previous chapter. However, the shape of the release curves seems to have
additional features and it is hard to grasp the general tendencies. In addition to the
initial retention some curves may show shoulders. These features are extremely
difficult to explain and, considering the number of parameters needed to describe a
porous coating, the construction of a relevant release model is rather unreasonable.
Especially, the experimental determination of such parameters would be most
strenuous. It can only be speculated that the structure of the coating is highly
inhomogeneous.
Fig. 6.3-4. Release from mesoporous silica spheres after WG-treatment at: A)
50°C; B) 75°C. The corresponding release times in Tab. 6.3-2 and Tab. 6.3-3.
Tab. 6.3-2. Release times (in min and h) measured for mesoporous silica
spheres subject to WG-treatment of various pH at 50°C (Fig. 6.3-4 A).
pH
-
10.50
10.60
10.68
10.80
t 1 /min
9
-
358
543
367
0.15
-
5.97
9.05
6.12
2
t 1 /h
2
6 MODIFICATION OF RELEASE
- 101 -
Tab. 6.3-3. Release times (in min and h) measured for mesoporous silica
spheres subject to WG-treatment of various pH at 75°C (Fig. 6.3-4 B).
pH
-
10.50
10.60
10.68
10.80
t 1 /min
9
68
449
190
325
0.15
1.13
7.49
3.17
5.42
2
t 1 /h
2
Apart from the difficulties in explaining the release behavior, the above survey
shows how flexible the silicate coating actually is – the release times can be tuned.
The silicate coatings are deposited using a rather fast and cheap technique. The
involved chemicals are very common and no special device is required. Unlike the
advanced techniques of CVD or spray drying, here, regular laboratory equipment is
sufficient. The method is very likely scalable to an industrial scale.
Fig. 6.3-5. Variation of release behavior with the indicated coating conditions (redrawn from Fig. 6.3-1 and Fig. 6.3-4).
- 102 -
For the application in corrosion protection the most interesting coating formulation
seems to be that of pH = 10.60 at room temperature. It has the slowest release at
initial times, which is of special interested for electrophoretic deposition with Zn. In
fact, this slow initial release could be expected to last longer in a galvanic bath (pH =
2) because of the stability of silica at low pH. It should also be noted that release
from the coated particles already occurs at the intermediate pH (water), which
implies that no pH peak is required to activate the delivery.
6.4
RELEASE FROM CALCINED PARTICLES
Calcination of as-synthesized mesoporous particles is a common means for removal
of the template. The emptied mesopores offer more volume for the storage of guest
molecules. However, calcination is not indifferent to the mesoporous system
(shrinkage [36], dehydroxylation [29]) hence change of release kinetics can be
expected. Since calcination implies that guest molecules are loaded after the process,
it is not a modification sensu stricto. The leitmotiv for the study of calcined particles
is the understanding of the phenomena governing incorporation and release of guest
molecules.
6.4.1
RELEASE FROM CALCINED AND LOADED SBA-3-LIKE FIBERS
SBA-3-like fibers were calcined and loaded with rhodamine from acidic solution of
rhodamine 6G (0.01 M HCl). Some of the fibers were additionally subject to the
H2O-treatment. The resulting release curves and XRD patterns are shown in Fig.
6.4-1. The results of fitting by diffusion in cylinder with inhomogeneous surface
diffusion barrier (Eq. 5.4-6) are collected in Tab. 6.4-1.
The loaded particles have an intensive color indicating higher loading capacity. The
amounts delivered in release are generally higher. Release from the calcined and
loaded fibers is much slower than from analogous fiber synthesized with the dye.
This slow-down could be associated with the shrinkage indicated by XRD. Such a
strong shrinkage possibly affects the wall passages that enable cross-wall transport.
6 MODIFICATION OF RELEASE
- 103 -
Fig. 6.4-1. A) Release from calcined and loaded SBA-3-like fibers fit by diffusion
with a surface diffusion barrier (Tab. 6.4-1). B) X-ray diffraction patterns of SBA-3like fibers: as-synthesized, calcined, calcined and impregnated.
Tab. 6.4-1. Parameters fit to the curves in Fig. 6.4-1 A by diffusion in
cylinder with surface diffusion barrier (Eq. 5.4-6). The effective
diffusion coefficient is calculated for R = 4 µm.
sample
t 1 /min
α
⊥
[ cm2s-1]
Deff
A
loaded from acid
8
0.15
2.5⋅10-11
0.19
loaded from acid and
H2O-treated
50
0.47
9.4⋅10-11
0.43
2
In case of the loaded fibers the slower release times are related to both lower
diffusion coefficient and stronger barrier, which are ca. 3 times smaller as compared
⊥
= 6.7⋅10-11 cm2s-1, α
with the as-synthesized fibers reported in chapter 5.4.2.1 ( Deff
= 0.43). The different values corroborate that calcined and loaded mesoporous silica
represents a system different from the as-synthesized.
The influence of the H2O-treatment on the loaded fibers is also different. The soft
treatment is very efficient in this case. Although the barrier parameter rises (weaker
barrier) the percentage of blocked pores increases essentially (efficient barrier). The
change of diffusion coefficient is difficult to understand. Its value after the treatment
rises and is even higher than that of as-synthesized fibers. It could be connected with
formation of microcracks or an effect on the silica matrix. Since the fibers were
loaded from acidic solution (pH =1) rinsing with water represents a change of pH.
- 104 -
6.4.2
RELEASE FROM CALCINED AND LOADED MESOPOROUS SPHERES
Mesoporous silica spheres were calcined and loaded from either acidic or water
solutions of rhodamine. The resulting release curves are shown in Fig. 6.4-2 and the
corresponding XRD patterns in Fig. 6.4-3. The curves were analyses by the modelfree release function (Eq. 5.4-2).
Fig. 6.4-2. Release from calcined mesoporous silica spheres loaded with rhodamine
from A) acidic solution (pH = 1) and B) from water solution. The applied treatments
are indicated. The curves were normalized by Emax obtained by fitting a model-free
release function (Tab. 6.4-2).
Tab. 6.4-2. Fit parameters obtained from a model-free release function (Eq. 5.4-2)
for calcined and loaded mesoporous spheres.
loading
modification
t 1 /min
E max
a1
τ 1 /min
N
as-synth
-
1
0.045
0.60
9
3
from water
-
2
0.267
0.72
12
2
from water
H2O-treatement
5
0.268
0.81
47
2
from water
WG-treatment
608
0.152
0.98
720
1
from acid
-
3
0.147
0.63
10
2
from acid
H2O-treatement
19
0.109
0.69
26
2
from acid
WG-treatment
493
0.421
0.89
830
1
2
6 MODIFICATION OF RELEASE
- 105 -
The mesoporous silica spheres loaded from acidic solution show release behavior
similar to that of SBA-3-like fibers. The release time is longer as compared with the
as-synthesized spheres, and also accompanied by similar shrinkage of the structure.
The additional treatments result in further prolongation of the release time.
Loading from the water solution is connected with similar shrinkage of the structure
but has little effect on the release time. This is surprising because the XRD pattern
indicates certain disordering of the structure. H2O-treatment of the water-loaded
particles results in longer release time. This supports the view that the decisive step
of soft modification occurs during drying. After immersion in water for 16 h, rinsing
with water should not produce a pH effect.
Fig. 6.4-3. X-ray diffraction
patterns of mesoporous spherical
particle subject to the indicated
treatments. Corresponding release
curves in Fig. 6.4-2.
The different release behavior of acid- and water-loaded particles could be related
with the pH-dependent interaction between the dye and silica wall. The effective
diffusion coefficient depends on the diffusion coefficients associated with pore and
surface transports [52]. The charge on silica is different in acid and in water [153]. In
the absence of surfactant the influence of the dye/silica interaction on the diffusion
coefficient is likely higher. In addition this interaction is concentration dependant,
which could explain the change after H2O-treatment.
In conclusion, the calcined mesoporous particles can be modified similarly to their
as-synthesized counterparts. The obtained release times lie in the same time-scale.
However, they offer more loading capacity, which makes them especially interesting
for the delivery application.
- 106 -
7 LOADING AND RELEASE OF SELECTED CORROSION
INHIBITORS
A decisive step in the study of mesoporous capsules as an element of corrosion
protection system is the compatibility of the capsules with corrosion inhibitors. In
this chapter loading and release of selected inhibitors is studied (chromates and
molybdates). Although both capabilities as well as limitations are brought into
discussion, the presented results have a preliminary character and should not be
treated as determinative for a real system.
There are several differences when working with chromates and molybdates in place
of rhodamine. Unlike rhodamine, the selected corrosion inhibitors cannot be
incorporated into mesoporous particles during synthesis (see chapter 4.4.2), and a
post-synthetic loading has to be used instead. The incorporation of corrosion
inhibitors is not visually obvious due to the low extinction coefficients of the
inhibitors as compared with Rh6G. Spectroscopy in the UV range is the only reliable
method to check the incorporation.
7.1
7.1.1
LOADING AND RELEASE OF CHROMATES
CHROMATE SPECIES
Solutions of lithium chromate and potassium chromate were used for loading
calcined mesoporous spheres. Depending on the pH and concentration of the
respective chromate, the solutions have different visual appearance (Fig. 7.1-1 A).
Typically yellow solutions become orange with rising chromate concentration and
decreasing pH. The UV-Vis spectra of two extreme cases, i.e., pure yellow and pure
orange are shown in Fig. 7.1-1 B. Based on the literature data [118,119]
predominance of CrO42- in the yellow solutions and predominance of Cr2O72- in the
orange solutions are identified. The molar extinction coefficients used for the
calculations are taken from literature [119]:
chromate ion:
ε CrO
dichromate ion:
ε Cr O
2
4
2−
7
2−
= 4500 cm-1mol-1 (at λ = 372 nm)
(Eq. 7.1-1)
= 1600 cm-1mol-1 (at λ = 351 nm)
(Eq. 7.1-2)
7 LOADING AND RELEASE OF SELECTED CORROSION INHIBITORS
- 107 -
Fig. 7.1-1. A) Different visual appearance of lithium chromate solutions of various pH and
concentrations. The appearance of potassium chromate is analogous. B) Absorption
spectra of the indicated solutions. The chromate species are identified based on literature
data [118,119].
7.1.2
PARTICLES LOADED FROM WATER SOLUTIONS
Results. Solutions of lithium chromate and potassium chromate in distilled water
were used for loading of calcined mesoporous silica spheres in the concentration of
either 0.01 M (mol/L) or 0.1 M. In case of particles loaded from the lower
concentration (0.01 M) a visible change of the release solution can be observed but
typical chromate bands are missing. Therefore, there is no chromate detected during
release (Fig. 7.1-2).
Fig. 7.1-2. Spectra of the leaching solution in the chromate-specific spectral
range measured during release experiment at the indicated times. Mesoporous
spheres were loaded from 0.01 M solution of K2CrO4 in distilled water.
In case of mesoporous spheres loaded from the more concentrated solution of
chromates (0.1 M), chromate specific absorption was measured (Fig. 7.1-3 A). The
release curve shows an almost constant characteristic (Fig. 7.1-3 B). The release time
is shorter that the detectable range. The chromate concentration at the end of the
max
release curve, denoted by c CrO
2 − , is calculated using Eq. 7.1-1. The total delivered
4
- 108 -
amount is estimated to be 4.45 µg of CrO42-, which corresponds with the loading
capacity of:*
m CrO 2 - / m particles ~ 2%.
4
(Eq. 7.1-3)
The results for lithium chromate are fully analogous.
Discussion. The presence of chromates in Fig. 7.1-3A indicates that delivery of the
corrosion inhibitor from mesoporous silica spheres has taken place. However, the
release time is shorter than the detection limit, i.e., t 1min ~ 3 min.† It is also thinkable
2
that the measured chromate is a remnant amount deposited at the external particle
surface during drying. Such superficially deposited chromate is not incorporated into
the mesoporous system and would dissolve readily appearing as an ‘immediate’
release.
Fig. 7.1-3. A) Spectra of the leaching solution analogous to that of Fig. 7.1-2
for mesoporous spheres loaded from 0.1 M solution of K2CrO4 in distilled
water. B) Constructed release curve with indicated total released amount.
The difference in concentrations of the two loading solutions is not reflected in the
delivered amount. The loading solutions differ by the factor of 10, whereas the
delivered amount changes by a much larger factor. This effect could be related to
dimerization of chromate (Eq. 2.4-1) occurring at higher concentrations.
*
Conditions: 0.2 mg of mesoporous particles, leaching volume = 3 mL
The detection limit of release time is defined by the time between initiation of leaching and
collection of the first spectrum, typically 12 sec, as well as the speed at which subsequent spectra can
be measured (for chromate typically 25 s).
†
7 LOADING AND RELEASE OF SELECTED CORROSION INHIBITORS
- 109 -
Incorporation of dimers rather than monomers seems to be the preferred process. The
measured spectra show the characteristic monomer peak (λmax = 372 nm) at all times,
which indicates that the possible conversion of dichromate into chromate is a prompt
process (< 1 min).
7.1.3
PARTICLES LOADED FROM ACIDIC SOLUTIONS
Calcined mesoporous silica spheres were loaded with acid solutions of either lithium
chromate or potassium chromate using the concentration of either 0.01 M (mol/L) or
0.1 M. Various pHs were used (pH = 1, 1.5, 2 and 3). The loaded particles were
measured in a release experiment. At the completion of release (no significant
increase of the released amount) 3 drops of NaOH (1 M) were added to the cuvette in
order to promote conversion of dichromate into chromate.
Results. Similarly to the results for particles loaded from water solutions (Fig. 7.1-2)
there is no chromate measured in case of particles loaded from the 0.01 M solutions
(e.g., Fig. 7.1-4).
Fig. 7.1-4. Spectra of the leaching solution in the chromate-specific spectral range
measured during release experiment at A) 2 min and B) 80 min. Mesoporous
spheres were loaded from 0.01 M solution of K2CrO4 at pH = 1.5.
In case of particles loaded from the higher concentration (0.1 M) there is chromate
absorption measured at any times during release (Fig. 7.1-5 A). At the initial times
dichromate is predominant (λmax ~ 352 nm) and after addition of NaOH only
chromate monomer (λmax = 372 nm) is present. The release characteristic before
addition of NaOH is constant (Fig. 7.1-5 B). The total delivered amount of
dichromate is m Cr O 2- = 38 µg, and stays almost the same after conversion in
2 7
chromate, m CrO 2- = 36 µg (the enhanced solvent volume, after addition of sodium
4
hydroxide, has been taken into account). The delivered amount corresponds with the
loading capacity of:
- 110 -
m CrO 2 - / m particles ~ 16%
4
(Eq. 7.1-4)
Discussion. The loading capacity of chromate is enhanced for particles loaded from
acid solution as compared with particles loaded from water solution. The obtained
value is relatively high and points out toward incorporation of chromate into the
mesoporous system. Deposition of such an amount exclusively at the external
particle surface is rather improbable.
The induced conversion of dichromate into chromate after addition of NaOH shows
that in presence of species with very different extinction coefficients, the release
curve should be first translated into released amount (in grams or moles) before any
analysis of release. In case the time of conversion lays in the detectable range, a
release artifact may result.
Fig. 7.1-5. Release from mesoporous spheres loaded from 0.1 M solution of
K2CrO4 at pH = 1. A) Spectra of the leaching solution collected at the indicated
release times. B) Release curve with Emax denoting scattering-corrected
extinction. At the time indicated by the arrow, pH of the leaching solution was
raised by addition of 3 drops of 1M NaOH. Note the corresponding change of
peak positions in A).
An additional aspect of the addition of NaOH is the dissolution of silica particles. In
the absence of particles no scattering extinction contributes the total extinction and
the measured amount has a minimal error. The total deliverable amount can be
therefore measured very accurately.
None of the acid loading solutions resulted in release times that could be measured.
However, very short release times might be justified theoretically. The literature data
7 LOADING AND RELEASE OF SELECTED CORROSION INHIBITORS
- 111 -
on diffusion coefficient in the system potassium chromate/water at 25°C provides
H 2O
Deff
= 1.3⋅10-5 cm2s-1 [ 150 ], which is already larger than of rhodamine in
H 2O
= 5.6⋅10-6 cm2s-1 [143]. These values are furthermore changed when a
water, Deff
porous medium instead of pure water is considered. In case of rhodamine the
coefficient is lower by few orders of magnitude depending on the regarded mode of
⊥
||
= 2.0⋅10-11 cm2s-1 and Deff
= 3.5⋅10-10 cm2s-1 (chapter 5.3.3.2).
diffusion: Deff
Diffusion of CrO42- can also be expected to be slower; however, to a lower degree.
This view is supported by literature data on diffusion of chromate through a glass
membr
= 9⋅10-7 cm2s-1 [151]. Hence, the small
membrane with a pore size of 4.5 nm, Deff
chromate molecule diffuses quickly out of the particle. Although lowering of pH
during loading obviously promotes formation of dichromate, further polymerization,
which might slow down diffusion after Eq. 2.4-2 is very likely negligible in the
tested range of pH and concentration.
The short release times disable the methods of release modification (chapter 6) that
could possibly slow down the release, as the chromate would leach out during the
process.
7.2
7.2.1
LOADING AND RELEASE OF MOLYBDATES
MOLYBDATE SPECIES
Solutions of lithium molybdate, sodium molybdate and sodium phosphomolybdate
were used for loading calcined mesoporous spheres. The solutions always appear
lemon yellow. UV spectra of selected solutions for various pH and concentrations are
shown in Fig. 7.2-1. Depending on pH, position and shape of the molybdate peak
changes. For low concentrations in water there is only one characteristic absorption
measured, with maximum absorption at λ = 208 nm.
- 112 -
Fig. 7.2-1. A) UV spectra of phosphomolybdate in HCl of various pH. The different peak
positions indicate different molybdate species. The dotted lines are guides for the eyes. B)
UV spectra of sodium molybdate in water at various concentrations.
The UV-Vis spectroscopic identification of the different molybdate species is not
facile because a mixture of different species coexists at the same time [123] and their
molar extinction coefficients may differ by an order of magnitude [152].
For lithium molybdate and sodium molybdate in water, background corrected molar
extinction coefficients have been determined (see Appendix E):
for sodium molybdate:
for lithium molybdate:
ε Na MoO = 8878 cm-1mol-1(λ = 208 nm)
ε Li MoO = 8253 cm-1mol-1(λ = 208 nm)
2
2
4
4
(Eq. 7.2-1)
(Eq. 7.2-2)
The values are slightly different from the ε = 9870 cm-1mol-1 reported for MoO42- in
literature [152]. This lowering of the coefficient is due to the subtraction of the peak
background, which is necessary for the determination of molybdate in the presence
of scattering particles.
In case of phosphomolybdate determination of the molar extinction coefficient is
difficult due to the presence of molybdate complexes also absorbing in the UV range
[152]. However, for the concentrations of phosphomolybdate larger than 2 µmol/L
the presence of MoO42- in water can be assumed. This view is supported by the
dominance of single molybdate tetrahedrae at pH > 6 and positions of the UVabsorption peaks analogous to those of sodium molybdate (Fig. E-2 in Appendix E).
Under this assumption the amount of molybdate delivered into water by particles
loaded from solutions of phosphomolybdate, can be estimated using extinction
coefficient of sodium molybdate ( ε PMo ≈ 8878 cm-1mol-1).
7.2.2
RELEASE FOM LOADED PARTICLES
Phosphomolybdate dissolved in distilled water or in hydrochloric acid of pH = 1, pH
= 1.9 or pH = 3.5 were used for loading calcined mesoporous spheres. In each case a
saturated solution was used.
Results. The measured release curves are shown in Fig. 7.2-2. In each case the UVSpectra have a maximum at 208 nm and there are only molybdate specific peaks of
the type shown in Fig. 7.2-1 B. The curves seem to show a two-step release, with
immediate delivery of E ~ 0.02 followed by a slower step. Very likely it is an artifact
7 LOADING AND RELEASE OF SELECTED CORROSION INHIBITORS
- 113 -
related to high Eerr at the initial release times (fitting effects of weak peaks,
absorption by the particles).
Loading from solutions of pH = 1.9 and pH = 3.5 result in a release-like behavior
with release times t 1 = 27 min and t 1 = 38 min, respectively. In case of lower pH
2
2
and water the resulting release curves have a rather flat characteristic. The loading
efficiency is estimated analogously to chromates (chapter 7.1.2) using Eq. 7.2-1:
pH = 1:
pH = 1.9:
pH = 3.5:
H2O:
m MoO 2 - / m particles ~ 1.9 %
4
m MoO 2 - / m particles ~ 3.1 %
4
m MoO 2 - / m particles ~ 3.0 %
4
m MoO 2 - / m particles ~ 1.6 %
4
(Eq. 7.2-3)
(Eq. 7.2-4)
(Eq. 7.2-5)
(Eq. 7.2-6)
Fig. 7.2-2. Release curves for mesoporous spherical particles loaded with
phosphomolybdate dissolved in A) HCl pH = 1, B) HCl pH = 1.9, C) H2O. The uptaking solvent is in each case distilled water.
Discussion. It appears that the higher loading capacity is obtained only for a specific
range of pH, but the two curves showing release of molybdate have different shape.
Taking into account the tendency of molybdates to form polyanions in acid solvents
[117] these observations could be interpreted as follows: at very low pH the size of
- 114 -
the polyanions is too big to infiltrate the mesopores. The molecules are stopped at the
pore mouths and only these, or other molecules adsorbed at the external surface,
contribute to the delivery. In water, where only individual MoO42- tetrahedrae are
present [123], the penetration of the mesoporous system is more likely. However, the
fact that both silica and molybdate bear the same charge disfavors high loading
efficiency. Only at the optimal pH are the polyanions small enough to enter the pores
and the electrostatic repulsion of silica minimized (vicinity of the point of zero
charge pHPZC = 2 [153]).
The limiting factor for improving the loading efficiency is the solubility of
molybdates. The amount of loadable molybdate is defined by the concentration in the
pores. The concentration in pores is defined by the concentration of the loading
solution, which cannot be greater than the saturation concentration. The saturation
concentration of molybdates is marked by the precipitation of MoO3 and is very
strongly pH dependent [117]. Eventual improvement of the loading efficiency could
be achieved by chemical modification of the pore walls, e.g., anchoring of functional
groups.
The limited loading efficiency of molybdates could be a problem for application in
corrosion protection. The less inhibitor can be delivered by a mesoporous particle the
more particles are needed to provide the functional amount.
The loading efficiency estimated for chromates (Eq. 7.1-4 ) is higher than those
obtained for molybdates. But unlike for chromates, release times of several minutes
are achievable. This fact facilitates modifications of the loaded particles, e.g., coating.
7.2.3
COATED PARTICLES
Results. Calcined mesoporous silica particles loaded with phosphomolybdate were
treated by a solution of waterglass (pH = 10.7, room temperature). At no time during
release of such modified particles there is a detectable MoO42- measured that could
be used for the construction of a release curve (Fig. 7.2-3). The shape of the
absorption spectra changes as the release proceeds. The high extinction at λ < 200
nm visible in the initial times disappears later.
Discussion. The absence of MoO42- in this case is surprising because it is unlikely for
a sample having release time of t 1 = 27 min (Fig. 7.2-2 B) to lose most of the
2
loading during a 1-min treatment. A possible explanation would be a chemical
7 LOADING AND RELEASE OF SELECTED CORROSION INHIBITORS
- 115 -
reaction of molybdate with silicate to build a silicomolybdate complex (e.g., [154]),
which does not absorb in the measured UV-range [155]. Such reaction is very likely
considering the presence of dissolved silicate, both during coating and during release.
The initial absorption at λ < 200 nm could be ascribed to a phosphomolybdate
complex [152], which is ‘consumed’ by the silicate upon dissolution. Whether the
release of molybdate took place remains an opened question.
Fig. 7.2-3. Absorption spectra of the up-taking solvent during release from
mesoporous spheres loaded with phophomolybdate and coated via waterglass
treatment at the indicated release times. The up-taking solvent is distilled
water. The experimental points are connected for visual clarity.
7.2.4
PH-DEPENDENT RELEASE
Leaching of molybdate into solvents of various pH was additionally investigated.
Calcined mesoporous spheres loaded with phosphomolybdate (pH of the loading
solution 1.9) were used. Three solvents were used: hydrochloric acid (pH = 1.45),
distilled water and sodium hydroxide (pH = 11).
Release of into hydrochloric acid (pH = 1.45). Similarly to the release from WGcoated particles there is no detectable MoO42- that could be used for the construction
of release curves. However, the absorption at λ < 200 nm does not disappear (Fig.
7.2-4).
- 116 -
Release of into distilled water (pH = 7). Release into water results in release time t 1
2
= 27 min (see chapter 7.2.2, Fig. 7.2-2 B).
Fig. 7.2-4. Absorption spectra of the up-taking solvent (HCl pH = 1.45) during
release from mesoporous spheres loaded with phosphomolybdate. The experimental
points are connected for visual clarity.
Release into sodium hydroxide (pH = 11). The UV-absorption spectra during release
indicate the presence of MoO42-. The release curve is shown in (Fig. 7.2-5), and the
measured release time is t 1 = 35 min.
2
Fig. 7.2-5. Release from calcined
mesoporous spheres loaded with
phosphate molybdate. Release into
sodium hydroxide of pH = 11
(compare with Fig. 7.2-2 B).
Discussion. The construction of a release curve in case of release into acid was not
possible but the presence of molybdate polyanions can be concluded from the
absorption at λ < 200 nm. In contrast to the WG-treated particles this characteristic
absorption does not change indicating that the molybdate is in equilibrium. It is not
clear if all the molybdate is released or possibly trapped in the mesopores as result of
acid condensation (Eq. 2.4-3). Based on the discussion of diffusion coefficient in
chapter 7.1.3 it is thinkable that large polyanions could have release times long
7 LOADING AND RELEASE OF SELECTED CORROSION INHIBITORS
- 117 -
enough to prevent release of inhibitor in the measured time-scale. Such trapping
would be an interesting option for storing the molybdate without an additional
surface modification.
Release into the basic solution has a slightly longer release time as that of water. This
is a little surprising, because an accelerated release could be expected as silica is
known to dissolve at pH > 10 [29]. However, for this to affect the release rate the
kinetics of dissolution would have to be faster than the kinetics of release. Also the
products of dissolution would have to be removed instantly from the releasing
surface, otherwise permeation through these products have to be taken into account.
The acid and basic solvents can be regarded as simulation of two technically
important processes: galvanic bath and corrosion case, respectively. In a galvanic
bath (1 < pH < 3) no release is desired. The present results show no release of
MoO42-, but the release of other forms of molybdates could not fully be excluded
based on the measurements. The basic solvent has a pH corresponding with that of a
corroding Zn-steel couple [22]. The delivery of the inhibitor in this case has been
shown.
8 CONCLUSIONS
8.1
MEASUREMENT AND CHARACTERIZATION OF RELEASE
The measurement of release requires monitoring of the released or remaining amount
of the stored molecules. The deficiencies of the existing experimental methodology
led to the development of two complementary methods: the microphotometric and
the spectroscopic one. The microphotometric method relies on the visualization of
actual concentration under an optical microscope and is suited for the study of
individual particles. The spectroscopic method relies on the separation of absorption
and scattering extinctions and applies to particles in a suspension. Both methods are
applicable to micron-sized mesoporous particles and allow the measurement of
release times between tens of seconds and several hours.
The characterization of release has been carried out using either phenomenological or
model-based approaches. In the phenomenological approach release curves are
- 118 -
quantified in terms of the total deliverable amount and release times ( t 1 , τ 1 ). Since
2
the other parameters have no direct physical meaning any kind of release data can be
analyzed in this way. The model-based characterization relies on diffusion in a
relevant frame and delivers effective diffusion coefficients and, when applicable, a
barrier parameter. The derived values are in principle dependent on the choice of the
model. Hence, the premises have to be based on reliable facts.
8.2
DIFFUSION IN MESOPOROUS MATERIALS
Three fundamental features of diffusion have been revealed: the cross-wall transport,
the surface diffusion barrier, and the anisotropy of the effective diffusion coefficient.
Such in-depth characterization of diffusion has not been carried out before for
mesoporous silica.
8.2.1
CROSS-WALL TRANSPORT
Cross-wall transport refers to the transport of guest molecules in the direction
perpendicular to mesopore walls, seemingly across the wall. This has been associated
with tiny pore connections, possibly micropores, with sizes similar to that of the
rhodamine molecule. Cross-wall transport dominates in particles with coiled
mesopores, where it becomes the rate-limiting factor for release. The associated
effective diffusion coefficient is comparable with that of some microporous materials,
e.g. zeolites with app. 3 times smaller pores. This fact allows the combination of
relatively long release times with relatively large pores (mesopores).
Due to the complex pore structure of mesoporous silica spheres cross-wall transport
is also relevant in this case.
8.2.2
SURFACE DIFFUSION BARRIER
The existence of surface diffusion barriers have been shown for mesoporous silica
particles. This refers to a transport resistance located at the external particle surface
and has been associated with blocking of the outermost pore passages. Already assynthesized particles were shown to have a barrier and drying has been identified as
the crucial process in its formation. The barrier influences the release kinetics and
can be used as means for its modification. Prolongation of release times by a factor
of 1.5 to 40 has been shown.
8 CONCLUSIONS
8.2.3
- 119 -
DIFFUSION ANISOTROPY
Anisotropy of the effective diffusion coefficient has been studied on the particles
with coiled mesopores. In order to enable transport in the direction parallel to the
mesopores, the continuity of the coiling has been violated by mechanical damage.
The parallel transport has been shown to be at least one order of magnitude faster
than that in the perpendicular direction (cross-wall transport).
8.3
RELEVANCE FOR CORROSION PROTECTION
The mesoporous particles studied here are promising candidates to serve as
microcapsules for a composite coating with a self-healing ability. The investigation
of the model system has shown that guest molecules can be loaded into the particles
and their release adjusted by a surface modification.
The up-take of two relevant corrosion inhibitors, chromates and molybdates, has
been shown. Chromates can be loaded up to 16 wt.%. but the release times are faster
than 3 min. The fast release is ascribed to the small size of the chromate ion and
makes the application of surface modifications impossible. The reached loading of
molybdates was lower (< 3 wt.%) but the release time was longer (~30 min). The
long release times have been achieved only for a specific pHs of the loading solution,
which is ascribed to the property of molybdate to build large polyanions at low pH.
The loading capacity of molybdates was limited by their solubility. It has been
shown that release of molybdate at neutral and slightly alkaline pHs is moderate, and,
therefore, useful in corrosion protection.
- 120 -
APPENDIX A: TABLES OF RELEASE FUNCTIONS
Tab. A-1. Summary of parameters defining the general solution of diffusion problem:
∞
c( x, t ) = c max ∑ An ( x) exp(− Β n Deff t )
(Eq. 2.3-11)
n =1
An
Bn
characteristic equation
plane-sheet of L
perfect sink
2
(− 1)n−1 cos⎛⎜ q n x ⎞⎟
qn
⎝ L ⎠
q n2
L2
1
q n = (n − )π
2
surface
barrier
2α
⎛q ⎞
cos⎜ n x ⎟
2
2
q n + α + α cos(q n ) ⎝ L ⎠
q n2
L2
q n tan q n = α
perfect sink
2
cylinder of R
for a specific release geometry obtained with either perfect sink condition (Eq. 2.3-8)
or surface diffusion barrier (Eq. 2.3-9), where Jk is Bessel function of first kind and
kth order and qn are roots of characteristic equation [101]. The characteristic diffusion
lengths: L – thickness of the plane-sheet, R – radius of the cylinder or sphere.
⎛r ⎞
J 0 ⎜ qn ⎟
q n J 1 (q n ) ⎝ R ⎠
q n2
R2
J 0 (q n ) = 0
2α
⎛r ⎞
J 0 ⎜ qn ⎟
2
2
q n + α J 1 (q n ) ⎝ R ⎠
q n2
R2
q n J 1 ( q n ) = αJ 0 ( q n )
perfect sink
2R
(− 1)n sin⎛⎜ r q n ⎞⎟
qn
⎝R ⎠
q n2
R2
q n = nπ
surface
barrier
2 Rα
⎛r ⎞
sin ⎜ q n ⎟
2
2
rq n q n + α (α − 1) sin (q n ) ⎝ R ⎠
q n2
R2
q n cot q n + α = 1
sphere of R
case
(
)
surface
barrier
(
(
)
)
APPENDIX A: TABLES OF RELEASE FUNCTIONS
- 121 -
Tab. A-2. Summary of parameters defining the release functions:
∞
⎛
⎞
E abs (t ) = E max ⎜1 − ∑ Α n exp(− Β n Deff t )⎟
⎝ n =1
⎠
and
∞
E abs (t ) = E max ∑ Α n exp(− Β n Deff t )
(Eq. 2.3-12)
(Eq. 2.3-13)
n =1
sphere of R
cylinder of R
plane-sheet of L
for a specific release geometry and either perfect sink condition (Eq. 2.3-8) or
surface diffusion barrier (Eq. 2.3-9); where Jk is Bessel function of first kind and kth
order and qn are roots of characteristic equation. The characteristic diffusion lengths:
L – thickness of the plane-sheet, R – radius of the cylinder or sphere.
case
An
Bn
characteristic equation
perfect sink
2
q n2
q n2
L2
1
q n = (n − )π
2
2α 2
q n2 (q n2 + α 2 + α )
q n2
L2
q n tan q n = α
4
q n2
q n2
R2
J 0 (q n ) = 0
4α 2
q n2 (q n2 + α 2 )
q n2
R2
q n J 1 ( q n ) = αJ 0 ( q n )
6
q n2
q n2
R2
q n = nπ
6
q n2
R2
q n cot q n + α = 1
surface barrier
perfect sink
surface barrier
perfect sink
surface barrier
(
q q + α (α − 1)
2
n
2
n
)
- 122 -
cylinder of R
plane-sheet of L
Tab. A-3. Summary of parameters defining the release function Eq. 2.3-13 for a
microphotometric release curve measured on a selected area (Fig. A-1); where Jk is
Bessel function of first kind and kth order and qn are roots of characteristic equation.
The characteristic diffusion lengths: L – thickness of the plane-sheet, R – radius of
the cylinder.
case
An
Bn
characteristic equation
perfect sink
2
q n2
q n2
L2
1
q n = (n − )π
2
2α 2
q n2 (q n2 + α 2 + α )
q n2
L2
q n tan q n = α
∞
4
1
∑ J 2m+1 (q n )
q n2 J 1 (q n ) m =0
q n2
R2
J 0 (q n ) = 0
q n2
R2
q n J 1 ( q n ) = αJ 0 ( q n )
surface barrier
perfect sink
surface barrier
∞
4α
1
∑ J 2m+1
q n2 (q n2 + α ) J 1 (q n ) m =0
Fig. A-1. Coordinate system used for derivation of the release functions
applicable for the microphotometric release curves. The measured
extinction is an average value in the volume of A) cylinder and B) cone-like
particle penetrated by a light beam. In case the cone-like particle both axial
and radial flux directions are relevant.
APPENDIX A: TABLES OF RELEASE FUNCTIONS
- 123 -
Tab. A-4. Diffusion in cylinder with a perfect sink condition (Eq. 2.3-12): roots of
the characteristic equation and the corresponding weights of subsequent exponentials.
n
qn
An
n
qn
An
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
2.4048
5.5201
8.6537
11.7915
14.9309
18.0711
21.2116
24.3525
27.4935
30.6346
33.7758
36.9171
40.0584
43.1998
46.3412
0.6917
0.1313
0.0534
0.0288
0.0179
0.0122
0.0089
0.0067
0.0053
0.0043
0.0035
0.0029
0.0025
0.0021
0.0019
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
49.4826
52.6241
55.7655
58.9070
62.0485
65.1900
68.3315
71.4730
74.6145
77.7560
80.8976
84.0391
87.1806
90.3222
93.4637
0.0016
0.0014
0.0013
0.0012
0.0010
0.0009
0.0009
0.0008
0.0007
0.0007
0.0006
0.0006
0.0005
0.0005
0.0004
- 124 -
APPENDIX B: ESTIMATION OF SCATTERING EXTINCTION ( E
SCA
)
The amount of scattered light that determines scattering extinction in Eq. 3.2-2 is
only theoretically equal to the total amount scattered on the particles. In practice, the
part of scattered intensity out of the acceptance angle of the detector, θ A (see Fig. B1), makes the measured scattered intensity:
Esca = N
2π −θ A
∫θ I
[r ]
(θ ) sin θdθ
(Eq. B-1)
A
where N, θ and I [r ] are respectively: the number of scattering particles, scattering
angle and intensity of the light scattered on individual particle as a function of its
geometry parameters [r]. In the case of a sphere there is only one geometry
parameter – the sphere’s radius. In the case of a cylinder additionally the cylinder’s
length has to be usually considered. The expression for I[r] is not trivial because of
the complicated nature of the function describing scattering.
Fig. B-1. The detector of an UV-Vis
spectrometer collects intensities within
the acceptance angle θA.
Scattering on spheres can be characterized by the Mie theory. The theory describes
how the propagation of electromagnetic radiation, considered in terms of wave
equation (derived from the Maxwell formulae), is disturbed by interaction with a
spherical boundary, e.g., [128]. A similar calculation for non-spherical particles
becomes difficult because there is no general way of solving partial differential
equations with complicated boundary conditions. For such non-spherical particles,
the solution to the scattering problem can be sought by an approximated theory or the
numerical method of the T-matrix.* In case of regular particles, such as spheres or
*
M. Mishchenko (Ed.) „Light scattering by nonspherical particles“ Academic Press Inc, 1999
APPENDIX C: CONSTRUCTION OF RELEASE CURVES
- 125 -
fibers, the approximation of Rayleigh-Gans (also known as Rayleigh-Debye-Gans
approximation) provides sufficiently accurate results.
In the Rayleigh-Gans-approximation the intensity of light scattered on a particle is
described as a product of so-called scattering matrix and the incoming light [128]:
E s = SE i
(Eq. B-2)
where E s , S and E i are total scattered field, scattering matrix and incident field. By
appropriate choice of the coordinate system the elements of the scattering matrix can
be represented as:
ik 3
S1 = −
(n − 1)υf (θ , φ )
2π
S1 = −
(Eq. B-3)
ik 3
(n − 1)υf (θ , φ ) cos θ
2π
2π
where k, n, υ and f (θ , φ ) are wave vector ( k = k =
), relative refractive index,
λ
volume particle volume and form factor as a function of scattering angle θ and
particle orientation φ , respectively. The form factor is the most important
contribution for the angular distribution of the scattered intensity.
The form factor for a sphere of radius R is:
f sph =
3
(sin qR − qR cos qR )
(qR) 3
where q is the scattering vector related to scattering angle θ by q =
(Eq. B-4)
4π
λ
sin
θ
2
.
The form factor for a cylinder of radius R and length H integrated for all cylinder
orientations with respect to the incoming beam is:
2π
f cyl = 4 ∫
0
J 1 (qR sin ϑ ) sin( qH cos ϑ )
sin ϑdϑ
qR sin ϑ
qH cos ϑ
(Eq. 8.3-1)
For an infinite cylinder the formula simplifies to:
f cyl =
J 1 (qR)
qR
(Eq. 8.3-2)
- 126 -
A comparison of scattering form factors calculated for spheres and cylinders of
various radii and lengths is presented in Fig. B-2. The plots are normalized to the
intensity scattered in forward direction in order to emphasize the angular dependence.
Obviously, the smaller the particles the more intensity is scattered out of the
acceptance angle. In the case of fibers the shorter they are, the more effectively they
scatter.
Fig. B-2. Scattering form factors in the function of scattering angle calculated for A)
sphere of various radii, B) cylinder of various radii and length of 1µm, C) cylinder of
various radii and length of 100µm. The legend in C) applies to all plots. All plots are
normalized to the intensity scattered in forward direction, θ = 0°.
The wavelength dependence of the scattered intensity is indirectly given by Eq. B-2.
Fig. B-3 shows an example calculation for a representative sphere and three different
scattering angles obtained from the Mie theory.* The chosen angles are the direction
of forward scattering, the edge of acceptance angle and the double of it. The
wavelength variation at these angles has a long range character, i.e. there are no
specific peaks or sharp edges present. This justifies the approximation of Esca (λ ) in
Eq. 3.2-2 by a linear function.
*
The calculation was conducted using MiePlot – a software calculating scattering on spherical
particles, the program is a freeware available at http://www.philiplaven.com/mieplot.htm
APPENDIX C: CONSTRUCTION OF RELEASE CURVES
- 127 -
Fig.B-3. Wavelength dependence of
scattered intensity calculated from
Mie’s theory for a mesoporous
silica sphere of radius R = 300 nm
with neff = 1.4. For the indicated
scattering angles θ the scattering
extinction in a narrow wavelength
range can be approximated by a
linear function. All plots are
normalized to the incident intensity.
The dependence of the scattered intensity on the number and size of the scattering
particles can be used for the estimation of the system’s stability. Particle dissolution
and agglomeration as well as sedimentation of the suspension are clearly reflected in
the time evolution of the scattering contribution. However, the quantitative analysis
of such effects is rather difficult because they might occur in parallel. A further
difficulty is caused by particle size distribution and change of particles’ refractive
index during release. Particle size distribution leads in general to smoothing of the
function described by Fig. B-1, which in consequence diminishes its sensitivity to the
other parameters. The change of refractive index is related to the change of particles’
composition, e.g. due to the release of surfactant, and it is generally unknown.
Analysis of the scattering extinction delivers a very important indication of the
factors limiting applicability of the spectroscopic method of release measurement.
The bigger the particles the lower the intensity scattered out of the acceptance angle
and the more scattered intensity enters the detector the bigger the error.
- 128 -
APPENDIX C: CONSTRUCTION OF RELEASE CURVES
(MATLAB SCRIPT)
% Importing data
[filename, pathname] = uigetfile('*.txt', 'Select Data File');
data=csvread(fullfile(pathname,filename));
%data=data(:,1:1400);
TimeStart = input('To (time delay): ');
TimeDelta = input('dT (inteval): ');
sizeD=size(data)
timeScale=[TimeStart:TimeDelta:TimeDelta.*sizeD(1,2)/2+TimeStart];
waveLocal=[510:0.1:545];
% Initial values and limits of fit parameters
ftype = fittype('a1*exp(-((x-b1)/c1).^2)+a2*exp(-((xb2)/c2).^2)+a3.*x+b3','coeff',{'a1','a2','a3','b1','b2','b3','c1','c2'});
opts=fitoptions(ftype);
opts.Lower=[0 0 -1 527.5 498.5 -1 16.4 23.8];
opts.Upper=[1 1 1 528.5 499.5 1 17.3 26.4];
opts.StartPoint=[0.1 0.1 0.0001 527 498.8 0.001 17 25];
opts.Robust='on';
%figure(5); hold;
for i=1:sizeD(1,2)/2
Results(i,1)=timeScale(i);
end
for i=1:sizeD(1,2)/2
i
DataX=data(:,i*2-1);
DataY=data(:,i*2);
fresult=fit(DataX,DataY,ftype,opts);
coef=coeffvalues(fresult);
[Max,I]=max(coef(1)*exp(-((waveLocal-coef(4))/coef(7)).^2)+coef(2)*exp(-((waveLocalcoef(5))/coef(8)).^2)+coef(3).*waveLocal+coef(6)');
Results(i,2)=Max-(coef(3).*waveLocal(I)+coef(6));
for k=3:10
Results(i,k)=coef(k-2);
end
APPENDIX C: CONSTRUCTION OF RELEASE CURVES
- 129 -
if i==3 | i==30 | i==100
figure(i); hold
plot(DataX,DataY,'ko');
plot(DataX,DataX.*coef(3)+coef(6),'b');
plot(DataX,coef(1)*exp(-((DataX-coef(4))/coef(7)).^2)+coef(2)*exp(-((DataXcoef(5))/coef(8)).^2)+coef(3).*DataX+coef(6),'r');
end
end
figure(1000);
plot(Results(:,1),Results(:,2),'ko');
figure(1001);hold;
plot(Results(:,1),Results(:,9),'r.');
plot(Results(:,1),Results(:,10),'b.');
legend('FWHM Gauss1','FWHM Gauss2');
proposed=fullfile(pathname,'spzma.dat');
[savefile,pathname] = uiputfile(proposed,'Save Fit Results');
save(fullfile(pathname,savefile),'Results','-ascii') ;
clear Max I coef ftype waveLocal DataX DataY DataYBgrCorr TimeDelta TimeStart a b
fresult i k opts result sizeD sizeX x1 x2 y1 y2 Results timeScale proposed filename
pathname savefile textdata data
%Structure of the Result file
%
% time,maxAbs,a1,a2,a3,b1,b2,b3,c1,c2
% time,maxAbs,a1,a2,a3,b1,b2,b3,c1,c2
% ...
% time,maxAbs,a1,a2,a3,b1,b2,b3,c1,c2
%
% where maxAbs is a maximum of the fitted function corrected by the fitted
% linear contribution
% a1= maximum of the 1st Gaussian
% a2= maximum of the 2nd Gaussian
% a3= linear coefficient
% b1= argument of the 1st Gaussian maximum
% b2= argument of the 2nd Gaussian maximum
% b3= linear constant
% c1= FWHM of 1st Gaussian
% c2= FWHM of 2nd Gaussian
- 130 -
APPENDIX D: EXTINCTION COEFFICIENT OF RHODAMINE 6G
Fig. E-1. A) Absorption spectrum of rhodamine 6G in water with indicated peak
components (Eq. D-1). B) Calibration curve: corrected maximum absorption in the
function of concentration (Eq. D-3).
Peak function:
⎛ ⎛λ −b
i
E (λ ) = ∑ ai exp⎜ − ⎜⎜
⎜
c
i =1
⎝ ⎝ i
2
⎞
⎟⎟
⎠
2
⎞
⎟+a λ +b
0
⎟ 0
⎠
(Eq. D-1)
Absorption due to rhodamine at the maximum (λmax = 529 nm):
E max = E (λ max ) − a 0 λ max − b0
(Eq. E-2)
Correction of the linear background is included to account for the Esca correction in
the construction of release curve.
Calibration curve:
E max = ε c + ε 0
Fit parameters of the calibration curve:
ε Rh6G = 74820 cm-1mol-1
ε 0 = -0.0031
(Eq. D-3)
APPENDIX E: EXTINCTION COEFFICIENT OF MOLYBDATES
- 131 -
APPENDIX E: EXTINCTION COEFFICIENT OF MOLYBDATES
Fig. E-1. A) UV absorption spectrum of lithium molybdate in water with indicated
peak components (Eq. E-1). B) Calibration curve: corrected maximum absorption in
the function of concentration (Eq. E-3).
Peak function:
⎛ ⎛λ −b
i
E (λ ) = ∑ ai exp⎜ − ⎜⎜
⎜
c
i =1
⎝ ⎝ i
2
⎞
⎟⎟
⎠
2
⎞
⎟+a λ +b
0
⎟ 0
⎠
(Eq. E-1)
Absorption due to molybdate at the maximum:
E max = E (λ max ) − a 0 λ max − b0
(Eq. E-2)
Correction of the linear background is included to account for the Esca correction in
the construction of release curve.
Calibration curve:
E max = ε c + ε 0
(Eq. E-3)
Parameters of the calibration curve fit for:
sodium molybdate (λmax = 208 nm):
nm):
lithium molybdate (λmax = 208
ε Na MoO
ε0
ε Li MoO
ε0
2
4
= 8878 cm-1mol-1
= -0.0051
2
4
= 8253 cm-1mol-1
= -0.0072
- 132 -
Fig. E-2. UV absorption spectra of natrium phosphomolybdate in
water at various concentrations. The peak at 270 nm and strong
absorption at λ < 200 nm are ascribed to phosphomolybdate complex
[126,152].
- 133 -
APPENDIX F: EFFECT OF PARTICLE SIZE DISTRIBUTION
The influence of particle size distribution on the shape of release curve is shown by
calculation of the release function derived in cylinder geometry with a perfect sink
condition (Eq. 5.4-3) for a normal distribution of particle cylinder radii.
Normal distribution function:
⎛ (r − R )2
h ( r , R, σ ) =
exp⎜⎜ −
2σ 2
σ 2π
⎝
1
⎞
⎟
⎟
⎠
(Eq. F-1)
where r, R and σ are radius, mean radius and standard deviation, respectively.
Fig. F-1. A) Calculated release curves for a monodisperse and
polydisperse populations of fibers; B) Particle size distribution
h(r) used for the calculation of the polydisperse release.
There are some reasons not to include the particle size distribution in the release
functions: (i) the influence of size distribution on the shape of release curve is not big;
(ii) any distribution function introduces at least two additional parameters, which are
hard to determine experimentally and would have to be treated as fitting parameters;
and finally (iii) the distribution of SBA-3-like fibers’ radii (e.g., Fig. 4.1-2) seems to
be narrower that that used for the calculation in Fig. F-1.
- 134 -
APPENDIX G: SIGNIFICANCE OF THE BARRIER PARAMETER
The barrier parameter α defined by Eq. 2.3-10 quantifies the surface diffusion
barrier; however, its influence on the release function is not straight-forward. The
shape of a release curve is modified by the weights and time constants of the
individual exponential functions. These are related to the dimensionless barrier
parameter mostly by the roots of a characteristic equation. It is not obvious which
values correspond with the barrier-controlled release, i.e. when the rate of release is
no more defined exclusively by the diffusion coefficient.
Release curves calculated for various barrier parameters are compared in Fig. G-1.
For stronger barrier (lower values of α ) the rate of release is obviously lower, which
appears as slower rise of the release curve in Fig. G-1 A and as slighter slope in Fig.
G-1 B. Also the shape of the curve changes becoming straighter with decreasing α .
This effect is related to the increasing weights of initial An. The more weight is put
on the first exponential the straighter the curve appears in the logarithmic
representation. The shape of a release curve can be therefore regarded as a kind of
indication of a surface diffusion barrier.
The time constants Bn are also dependent on the barrier parameter. Smaller α results
in smaller qn and therefore bigger Bn (slower release). However, the effect is not as
straightforwardly related to the barrier as in the case of An because it can be also
affected by different diffusion coefficient.
Fig. G-1.Influence of the barrier parameter α on the shape of release
curve (Eq. 2.3-13) in A) linear scale and B) logarithmic scale calculated
for a sphere with the indicated Deff/R2 ratio.
APPENDIX G: SIGNIFICANCE OF THE BARRIER PARAMETER
- 135 -
The observation that the first summand, A1, approaches unity in the strong barrier
limit can be utilized for the estimation of the barrier parameter. Assuming that the
barrier is effective when 98% of the release is ‘grasped’ by a single exponential, it
can be stated that effective barriers are those associated with α < 1. Interestingly,
release from a sphere and from a cylinder, become equally shaped in the strong
barrier case. This conclusion is based on the weights of A1 in the function of α
calculated for the two cases (Fig. G-2).
Fig. G-2. Weights of the first
exponential, A1, in the function
of
barrier
parameter α
calculated for a sphere and
cylinder.
It follows that in the limiting case of a very strong barrier, when the diffusion
through the particle becomes irrelevant and release is fully controlled by the surface
flux, release curve can be reduced to a single exponential:
E (t ) = E max (1 − Α exp(− ΒDeff t ))
This case is known as first order kinetics release or a membrane model.
(Eq. 8.3-1)
- 136 -
APPENDIX H: MODIFICATION OF SYNTHESIS CONDITIONS
Release from SBA-3-like fibers prepared by different experimenters and from fibers
prepared from different mother liquors is compared. The obtained release curves are
shown in Fig. H-1, X-ray diffraction patterns in Fig. H-2, and the corresponding
parameters in Tab. H-1. Samples prepared by different experimenters are designated
as follows:
BKN-RAMLW-WASPZ-MA-
: Mr. Rainer Brinkmann (MPIK)
: Mrs. Ulla Wilczok (MPIK)
: the author
Fig. H-1. A) Release from SBA-3-like fibers produced by different experimenters
using the same prescription, B) Release curves from SBA-3-like fibers produced
from mother liquors of different composition (Tab. H-1)
Although the samples provided by the other experimenters were prepared using the
same prescription the variation of the resulting release kinetics is considerable. The
influence of release conditions is excluded as all curves were collected using the
same spectrometer, stirring speed etc. Careful analysis of larger amount of data (not
shown here) revealed that there are four distinct types of release kinetics, each with a
characteristic τ 1 . This observation suggests that systematic variations in the synthesis
rather than random mistakes are causing the difference. The influence of mistakes in
the composition of mother liquor could be eliminated by its intentional modification.
Neither strongly changed pH nor concentration of rhodamine was found to influence
release curves determinedly, whereat the bulk seems to be somewhat affected (XRD).
Very likely, the different release behavior originates from some post-synthetic
APPENDIX H: MODIFICATION OF SYNTHESIS CONDITIONS
- 137 -
condition, not described in the lab journals (such as drying, ets., which was identified
as crucial in this work ).
This is supported by the fact that the fibers synthesized from various mother liquors
have different lattice constants (Fig. H-2). Although the change in d100 is only about
35% of that caused by WG-coating (Fig. 6.1-4) the corresponding time constants are
not affected. Shrinkage of the mesoporous matrix is therefore not fully responsible
for the modification release kinetics. In addition, the apparent independence of the
time constant on the lattice parameter indicates that diffusion through the
mesoporous channels of as-synthesized SBA-3-like fibers is the governing regime of
diffusion. Should it be Knudsen regime, the increased interaction with pore walls as
the pores get smaller would have lead to lowering of the effective diffusion
coefficient.
Tab. H-1. Composition of mother liquors and fit parameters of release shown in (Fig. H-1).
H2O:HCl:CTAB:TBOS:Rh6G
E max
a1
τ 1 /min
N
SPZ-MA-035-02
100:1.78:0.0241:0.0736:6.3.10-4
0.33
0.50
3.0
3
SPZ-MA-036-02
100:2.92:0.0241:0.0736:6.3.10-4
0.43
0.48
3.2
3
SPZ-MA-037-02
100:4.02:0.0241:0.0736:6.3.10-4
0.26
0.57
3.4
3
SPZ-MA-038-02
100:2.92:0.0241:0.0736:1.6.10-3
0.30
0.52
3.7
3
SPZ-MA-039-02
100:2.92:0.0241:0.0736:1.8.10-4
0.16
0.53
4.1
3
BKN-RA-022-05
100:1.78:0.0241:0.0736:4.2.10-4
0.15
0.90
1.5
3
MLW-WA-011-03
100:1.78:0.0241:0.0736:2.2.10-4
0.14
0.60
10.5
3
MLW-WA-079
100:1.78:0.0241:0.0736:unknown
0.35
0.55
5.1
3
sample code
Fig. H-2. X-ray diffraction patterns
for SBA-3-like fibers obtained from
mother
liquors
of
various
compositions (Tab. ).
- 138 -
In conclusion, soft modifications of release are not related to the intrinsic properties
of the particles.
APPENDIX I: ESTIMATION OF THE FIB-AFFECTED ZONE
The possible microscopic damage to mesoporous silica induced by ion bombardment
can be estimated by calculating the energy transferred by the impinging ions to the
silica matrix. For this purpose the SRIM software was used. * The matrix is
approximated by a boro-silicate glass and the calculation run for 500 ions. The
resulting ion trajectories and differential sputtering yield (atoms/ion/eV), calculated
for gallium ions accelerated by 30 keV are shown inFig. I-1. The affected zone
spreads to the depth of ~ 40 nm which is a multitude of the pore size. In fact, the
affected zone is possibly even larger in case of mesoporous silica as its density is
lower than that of the assumed silicate glass. Because the energy required for
sputtering of glass is as low as 3.4 eV, there is virtually no chance to obtain a sharp
cut with an affected zone smaller than a pore size.
Fig. I-1. A) Ion trajectories and B) differential sputtering yield
calculated with SRIM-software for 30 keV gallium ions impinging a
boro-silicate glass.*
*
Group of programs which calculate the stopping of ions and their range into matter using a quantum
mechanical treatment of ion-atom collisions, freeware available at www.srim.org
- 139 -
APPENDIX J: ABBREVIATIONS AND IMPORTANT SYMBOLS
CTAB:
cetyltrimethylammonium bromide
FIB:
focused ion beam
MTES:
triethoxymethylsilane
Rh6G:
rhodamine 6G
TBOS:
tetrabutoxysilane
TEOS:
tetraethoxysilane
α
- barrier parameter (see p. 34 for definition)
⊥
Deff
- effective diffusion coefficient for flux perpendicular to silica walls
||
Deff
- effective diffusion coefficient for flux parallel to silica walls
E abs - absorption extinction
Esca - scattering extinction
E
- extinction
- 140 -
APPENDIX K: LIST OF CHEMICALS
Cetyltrimethylammonium bromide (CTAB):
CAS 57-09-0
(purum, Fluka)
Lithium molybdate:
CAS 13568-40-6 (Aldrich)
Lithium chromate:
CAS 7789-01-7 (Aldrich)
Phosphomolybdic acid:
CAS 1313-30-0 (Aldrich)
Potassium chromate:
CAS 7789-00-6 (Aldrich)
Rhodamine 6G (Rh6G):
CAS 989-38-8
Sodium molybdate:
CAS 7631-95-0 (Aldrich)
Sodium silicate:
CAS 1344-09-8 (purum, Riedel-de Haën)
Sodium hydroxide:
CAS 1310-73-2 (pellets, Aldrich)
Tetrabutoxysilane (TBOS):
CAS 4766-57-8 (purum, Fluka)
Tetraethoxysilane (TEOS):
CAS 78-10-4
Triethoxymethylsilane (MTES):
CAS 2031-67-6 (purum, Fluka)
(standard, Fluka)
(purum, Fluka)
- 141 -
APPENDIX L: LIST OF PUBLICATIONS
M. Stempniewicz, A.S.G. Khalil, M. Rohwerder, F. Marlow
J. Amer. Chem. Soc. 2007 (in press)
“Diffusion in coiled pores – learning from microrelease and microsurgery”
F. Marlow, A.S.G. Khalil, M. Stempniewicz
J. Mater. Chem. 17 (2007) 2168–2182
“Circular mesostructures: Solids with novel symmetry properties” (Feature article)
M. Stempniewicz, M. Rohwerder, F. Marlow
Chemphyschem 8 (2007) 188-194
„Release from silica SBA-3-like mesoporous fibers: Cross-wall transport and
external diffusion barrier“
M. Stempniewicz, M. Rohwerder, F. Marlow
Surf. Sci. Cat. 2007 (in press)
„Release of Guest Molecules from Modified Mesoporous Silica“
F. Marlow, M. Stempniewicz
J. Phys. Chem. B 110 (2006) 11604-11605
„Comment On: Gas Diffusion and Microstructural Properties of Ordered
Mesoporous Silica Fibers“
F. Marlow, A.S.G. Khalil, R. Brinkmann, M. Stempniewicz
“Hierarchische Silica-Strukturen: Wachstumssteurung, Beschreibung und
Eigenschaften” in Irreversible Prozesse und Selbstorganization, T. Pöschel, H.
Malchow, L. Schimansky-Geier Eds., Logos Verlag 2006
- 142 -
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