Measuring and Engineering Microscale Mechanical Responses and

Measuring and Engineering Microscale Mechanical Responses and
Properties of Bio-relevant Materials
a thesis presented by Vernita Diane Gordon
to the Department of Physics in partial fulfillment of the requirements for
the degree Doctor of Philosophy in the subject of Physics
Harvard University
Cambridge, Massachusetts
iii
© 2003 - Vernita Diane Gordon
All rights reserved
iv
v
Measuring and Engineering Microscale Mechanical Responses and
Properties of Bio-relevant Materials
Advisor: David A. Weitz
Author: Vernita Diane Gordon
ABSTRACT
Techniques and processes for analyzing bulk mechanical responses,
for volumes of a few mL and more, are well-developed and have been
successfully used for characterizing traditional ‘hard’ condensed matter and
materials as well as viscoelastic ‘soft’ condensed matter. However, studies
of soft condensed matter, especially biological systems and systems with
size scales compatible with biological and biomedical application, often
require characterization on much smaller size scales. This may be the case,
for example, in bulk materials displaying small heterogeneities in structure
or response, or for small discrete structures. Such microscale
characterization is often not achievable via more well-developed bulk
techniques. This thesis presents several such techniques used for
characterizing mechanical responses and properties of different biological
and bio-relevant systems. Such characterization often prepares the way for
further exploitation or engineering of the system. Chapter I examines the
influence of a dynamically growing and invading multicellular tumor system
on its environment in vitro by using multiparticle tracking techniques in
combination with bulk rheology. Chapters II and III use microcantilever
iv
deformation and finite element modeling to characterize two different types
of colloidosomes, self-assembled structures templated on emulsions.
Chapter IV studies self-assembled polymer vesicles and other structures
from the same copolymer system using micropipette aspiration and a variety
of imaging techniques.
Selected work representative of molecular spectroscopy performed in
the laboratory of Patrick Thaddeus, not included in the primary thesis body,
is found in Appendices A - D. Appendix E [M. F. Hsu et al., manuscript in
preparation] discusses different methods of colloidosome fabrication and
stabilization and is included to provide context for Chapters II and III.
v
Contents
Chapter I, “Measuring the mechanical stress induced by an expanding
multicellular tumor system: a case study”
Chapter II,
“Colloidosomes:
page 1
Self-assembled polymer capsules with
colloidal crosslinkers and environmentally sensitive release triggers”
page 50
Chapter III, “Microcantilevered deformation and breaking of sintered
colloidosomes, with finite element analysis”
page 78
Chapter IV, “Engineering the formation of complex structures from
diblock copolymers”
page 109
Molecular Spectroscopy
Appendix A
page 133
Appendix B
page 144
Appendix C
page 151
Appendix D
page 159
Shell Fabrication and Stabilization
Appendix E
page 167
vi
Chapter I
Copyright 2003 Elsevier Science (USA)
To be published in Experimental Cell Research
Used by permission.
Measuring the Mechanical Stress Induced by an Expanding
Multicellular Tumor System: A Case Study
V. D. Gordon 1,2, M. T. Valentine 1,2, M. L. Gardel 1,2,
D. Andor-Ardó 1, S. Dennison 2, A. A. Bogdanov 3,
D. A. Weitz 1,2,* and T. S. Deisboeck 1,4,5
1
Division of Engineering and Applied Sciences and 2 Department of Physics,
Harvard University, Cambridge, MA 02138; 3 Center for Molecular Imaging
Research, Massachusetts General Hospital, Harvard Medical School,
Charlestown, MA 02129;
4
Complex Biosystems Modeling Laboratory,
Harvard-MIT (HST) Athinoula A. Martinos Center for Biomedical Imaging,
HST-Biomedical
Engineering
Center,
Technology, Cambridge, MA 02139;
Massachusetts
5
Institute
of
Molecular Neuro-Oncology
Laboratory, Massachusetts General Hospital, Harvard Medical School,
Charlestown, MA 02129.
1
ABSTRACT
Rapid volumetric growth and extensive invasion into brain parenchyma are
hallmarks of malignant neuroepithelial tumors in vivo. Little is known,
however, about the mechanical impact of the growing brain tumor on its
microenvironment. To better understand the environmental mechanical
response, we used multi-particle tracking and microrheological methods to
probe the environment of a dynamically expanding, multicellular brain
tumor spheroid that grew for six days in a three-dimensional Matrigel-based
in vitro assay containing 1.0 µm latex beads. These beads act as reference
markers for the gel, allowing us to image the spatial displacement of the
tumor environment using high-resolution timelapse video-microscopy. The
results show that the volumetrically expanding tumor spheroid pushes the
gel outward and that this tumor-generated pressure propagates to a distance
greater than the initial radius of the tumor spheroid. Intriguingly, beads near
the tips of invasive cells are displaced inward, towards the advancing
invasive cells. Furthermore, this localized cell traction correlates with a
marked increase in total invasion area over the observation period. This case
study presents evidence that an expanding microscopic tumor system exerts
both significant mechanical pressure and significant traction on its
microenvironment.
2
INTRODUCTION
The outcome for patients suffering from highly malignant brain tumors
remains dismal in spite of all therapeutic efforts. The most malignant form,
glioblastoma, which accounts for 23% of all primary brain tumor cases, has
a mean patient age at diagnosis of 65 years and, in the age group of 45 and
older, a 5-year relative survival rate of below 2.1 %1. The reasons for the
almost inevitable treatment failure include rapid volumetric growth, early
development of treatment resistance and, most importantly, extensive tissue
infiltration, which leaves these neoplasms surgically incurable.
A better understanding of the structural remodeling of brain
parenchyma by tumor proliferation and invasion is essential to
understanding the processes that facilitate diffuse infiltration and tumor
recurrence. However, the mechanical relationship between an expanding
tumor system and its microenvironment is still poorly understood. By
placing multicellular tumor spheroids in increasing concentrations of an
1
2002-2003, CBTRUS, Central Brain Tumor Registry of the United States,
Statistical Report, 1995-1999 (years data collected).
3
agarose gel, Helmlinger et al.2 found that such spheroids can overcome a
mechanical stress of up to 45 mmHg (6 kPa) before they become growthinhibited at stresses between 45 and 120 mmHg (6 and 16 kPa).
Furthermore, in addition to withstanding pressure, neoplastic cells much like
normal cells may also exert traction. The traction forces generated by skin
fibroblasts have been measured by Delvoye et al.3 via strain-gauge
measurements. Using distortable sheets of silicone rubber, Harris et al.4
established a method by which traction forces exerted by individual cells can
be visualized. In fact, they distinguish “compression wrinkles,” directly
beneath the traction-generating cell, from “tension wrinkles,” which radiate
outwards. Interestingly, in their follow-up paper5 the authors compare
various cell types and observe that glia cells from dorsal root ganglia exert
very strong traction forces. Since then, a variety of methods and several
2
Helmlinger, G., Netti, P. A., Lichtenbeld, H. C., Melder, R. J., and Jain, R.
K. (1997). Solid stress inhibits the growth of multicellular tumor spheroids.
Nat. Biotechnol. 15, 778.
3
Delvoye, P., Wiliquet, P., Leveque, J.-L., Nusgens, B. V., and Lapiere, C.
M. (1991). Measurement of mechanical forces generated by skin fibroblasts
embedded in a three-dimensional collagen gel. J. Invest. Dermatol. 97, 898.
4
Harris, A. K., Wild, P., and Stopak, D. (1980). Silicon rubber substrata: a
new wrinkle in the study of cell locomotion. Science 208, 177.
5
Harris, A. K., Stopak, D., and Wild, P. (1981). Fibroblast traction as a
mechanism for collagen morphogenesis. Nature 290, 249.
4
other gels, including polyacrylamide gels, collagen gels, and basement
membrane gels, have been used to study mechanical stresses at the cellsubstrate interface6,7. For instance, reorganization of basement membrane
matrices has been studied extensively with endothelial cells and fibroblasts.
Using Matrigel, a commercial basement membrane gel, Vernon et al.8
reported that cellular traction leads to extracellular matrix (ECM) alignment,
in which matrix filaments form lines or tracks; this alignment promotes
cellular elongation and directs migration. This leads ultimately to the
formation of multicellular cords and tubelike structures, characteristic of
endothelial cells. Moreover, a quantitative correlation of “contact guidance”
with collagen fibril orientation has been described for human fibroblasts9.
These traction forces can have significance for remodeling connective tissue
6
Dembo, M., and Wang, Y.-L. (1999). Stresses at the cell-to-substrate
interface during locomotion of fibroblasts. Biophys. J. 76, 2307.
7
Jenkins, G., Redwood, K. L., Meadows, L., and Green, M. R. (1999).
Effect of gel re-organization and tensional forces on α2β1integrin levels in
dermal fibroblasts. Eur. J. Biochem. 263, 93.
8
Vernon, R. B., Angello, J. C., Iruela-Arispe, M. L., Lane, T. F., and Sage,
E. H. (1992). Reorganization of basement membrane matrices by cellular
traction promotes the formation of cellular networks in vitro. Lab. Invest.
66, 536.
9
Guido, S., and Tranquillo, R. T. (1993). A methodology for the systematic
and quantitative study of cell contact guidance in oriented collagen gels.
Correlation of fibroblast orientation and gel birefringence. J. Cell Sci. 105,
317.
5
by tumors as well. In fact, contraction of collagen fibrils has been linked to
the metastatic potential of melanoma cells10 and may also be important for
cell locomotion in other cancers, including malignant brain tumors.
Tumor tissue invasion itself is a multistep process, however, including
cell attachment, degradation of ECM components, and active cell motility.
ECM-degradation in turn requires the expression of proteolytic enzymes by
the tumor cells, which has been shown to occur in gliomas in vitro and in
vivo11,12. Interestingly, the parental (high-grade glioma) cell line of the one
used in our experiment, U87MG, has been shown to release gelatinase A,
known also as metalloproteinase 2 (MMP-2)12,13. As Chintala et al.14 have
reported, MMP-2 can degrade a variety of extracellular matrix (ECM)
components, including collagen IV, which is a major (30%) ECMcomponent of the bio-gel used in our assay. A rather complex interplay
between mechanical forces and proteolytic enzymes is supported by the
work of Vernon and Sage15, who studied the remodeling of collagen type I
gels by bovine aortic endothelial (BAE) cells. Using zymography to detect
enzymatic activity, the authors found that BAE cells that had contracted
10
Klein, C. E., Dressel, D., Steinmayer, T., Mauch, C., Eckes, B., Krieg, T.,
Bankert, R. B., and Weber, L. (1991). Integrin α2β1is upregulated in
fibroblasts and highly aggressive melanoma cells in three-dimensional
collagen lattices and mediates the reorganization of collagen I fibrils. J. Cell
Biol. 115, 1427.
6
collagen gels also had secreted MMP-2. They conclude that both cellular
traction and proteolysis are important for endothelial cell invasion in the
process of angiogenesis.
To elucidate the role of and potential interplay between compression
and traction in the dynamic expansion of a micro-tumor system, we
implanted a growing multicellular (brain) tumor spheroid (MTS) in a gel
matrix and investigated the tumor’s impact on its ECM-gel
microenvironment with methods from microrheology. Specifically, we used
1.0 µm beads as reference markers for the gel and monitored their spatial
displacement with high-resolution timelapse video-microscopy. In addition,
11
Apodaca, G., Rutka, J. T., Bouhana, K., Berens, M. E., Giblin, J. R.,
Rosenblum, M. L., McKerrow, J. H., and Banda, M. J. (1990). Expression
of metalloproteinases and metalloproteinase inhibitors by fetal astrocytes
and glioma cells. Cancer Res. 50, 2322.
12
Nakano, A., Tani, E., Miyazaki, K., Yamamoto, Y., and Furuyama, J. I.
(1995). Matrix metalloproteinases and tissue inhibitors of metalloproteinases
in human gliomas. J. Neurosurg. 83, 298.
13
Uhm, J. H., Dooley, N. P., Villemure, J. G., and Yong, V. W. (1996).
Glioma invasion in vitro: regulation by matrix metalloprotease-2 and protein
kinase C. Clin. Exp. Metastasis 14, 421.
14
Chintala, S. K., Tonn, J. C., Rao, J. S. (1999). Matrix metalloproteinases
and their biological function in human gliomas. Int. J. Devl. Neurosciences
17, 495.
15
Vernon, R. B., and Sage, E. H. (1996). Contraction of fibrillar type I
collagen by endothelial cells: a study in vitro. J. Cell Biochem. 60, 185.
7
videorate imaging and particle tracking were employed to study the
thermally-driven Brownian motions of these tracer beads. In the vicinity of
invasive tips, such position fluctuations remain constant in size throughout
the observation period. The results show not only that the volumetrically
expanding spheroid pushes the gel outward but also that beads near the tips
of advancing invasive cells are displaced inward, towards these tips. This is
consistent with cell traction producing tension in the gel. In addition,
significant localized gel strain towards invasive cell tips correlates well with
a marked increase in overall gel invasion throughout the observation period,
indicating that cell traction and invasion are linked. To our knowledge this is
the first study presenting evidence that a growing microscopic tumor system
can exert both significant pressure and traction on its microenvironment.
MATERIALS and METHODS
1. Multicellular Tumor Spheroid and Morphometric Measurements:
8
The human U87MGmEGFR glioblastoma cell line* was used to generate the
multicellular tumor spheroids (MTS)16. We cultured this cell line in DMEM
medium (GIBCO BRL, Life Technologies, Grand Island, NY)
supplemented with 10% heat inactivated cosmic bovine serum (HyClone,
Logan, UT) and 400 µg/ml G418 (Life Technologies) in a humidified
atmosphere (at 37°C and 5% CO2). These cells co-express both wild-type
epidermal growth factor receptor and its mutant variant, mEGF-R17.
U87MGmEGFR cells tend to form spheroids in culture after reaching
monolayer confluence. Once detached, these spheroids can be collected from
the medium with Pasteur pipettes. A variation of the assay used in here is
described in Deisboeck et al.18.
*
Kindly provided by Dr. W. K. Cavenee (Ludwig Institute for Cancer
Research, San Diego, CA).
16
Sutherland, R. M. (1988). Cell and environment interactions in tumor
microregions: the multicell spheroid model. Science 240, 177.
17
Nishikawa, R., Ji, X. D., Harmon, R. C., Lazar, C. S., Gill, G. N.,
Cavenee, W. K., and Huang, H. J. (1994). A mutant epidermal growth
factor receptor common in human glioma confers enhanced tumorigenicity.
Cancer Res. 91, 7727.
18
Deisboeck, T. S., Berens, M. E., Kansal, A. R., Torquato, S., StemmerRachamimov, A. O., and Chiocca, E. A. (2001). Pattern of self-organization
in tumour systems: complex growth dynamics in a novel brain tumour
spheroid model. Cell Proliferation 34, 115.
9
In the present case study, we used a rather small spheroid, less than
200 µm in diameter, which we placed in a novel 1×1×1 cm plexiglass cube
filled with a 3:1 mixture of growth factor reduced (GFR) matrix, Matrigel
(BIOCAT, Becton Dickinson, Franklin Lakes, NJ) and (non-serum
supplemented) OPTI-MEM medium at 4 °C, at which temperature the
mixture remains fluid. The spheroid settled to lie close to the bottom of the
cube and several hundred microns from vertical walls (while the gel mixture
was still fluid), and it remained at this location after the medium gelled.
When raised to room temperature, this mixture gels to form a reconstituted
basement membrane. Because the liquid matrix gelled in situ about the
spheroid, there should be no stress in the matrix associated with the
introduction of the spheroid. Latex beads, 1 µm in diameter, were dispersed
in this assay mixture at 4 °C while it was still liquid, before the tumor
spheroid was inoculated, so that they are incorporated into the gel matrix
surrounding the MTS. Maintaining the assay at 37°C and 5% CO2, tumor
growth and invasion as well as the bead-containing microenvironment were
imaged at both timelapse (1 frame per 30 seconds) and videorates (30 frames
per second), allowing particle tracking and analysis of bead motions. The
gelled sample, including tumor spheroid and beads, remained in the
plexiglass cube for the six-day observation period. Figure 1.1 shows part of
10
the tumor approximately 48 hours after implantation. The dark gray area is
part of the central MTS; lighter invasive branches, consisting of mobile
tumor cells following each other in chainlike migration, are also depicted.
11
Figure 1.1: Multicellular Tumor Spheroid (MTS) with invasive
branches. Taken on Day 3, the image displays a part of the main tumor
(dark gray) and shows invasive branches originating from the surface of the
MTS. Forming these branches, invasive cells advance in a chain-like pattern.
(Original Magnification: 10×).
12
The maximum orthogonal diameters of the MTS were measured at an
original magnification of 10× and the average diameter, DMTS, determined
with an uncertainty of less than 5 µm, was used to calculate the volume,
VMTS, of the MTS core:
V
MTS
=
π
D
3
(1)
MTS
6
The average diameter of the entire tumor system, DSYS, which includes the
proliferative MTS core and invasive branches, was determined from
measurements of orthogonal diameters of the tips of the invasive chains with
an uncertainty of less than 10 µm. From this, the cross-sectional area ASYS
was calculated using:
A
SYS
 D SYS 

2


2
=π 
(2)
13
The annular cross-sectional area of the invasive region only, AINV, excluding
the MTS cross-sectional area AMTS, can then be calculated with:
A
INV
=
A
SYS
− AMTS
(3)
2. Multiparticle Tracking:
Particle tracking techniques, already well-developed for studying soft
materials, have the advantage in the present case of allowing nondestructive
in situ measurements over several days to examine the effects of a growing,
invading tumor on its local and extended environments. To act as reference
markers, latex beads, 1 µm in diameter, were mixed with the liquid Matrigel
solution at 4 °C so that the beads were evenly dispersed before the tumor
spheroid was added and gelation induced.
Carboxylated beads were purchased from Interfacial Dynamics
Corporation (Portland, OR) and their surfaces coated with amine-terminated
PEG chains, MW = 750 Da, which were covalently coupled to the surface
carboxyl groups. The empirical observation that PEG-coated materials resist
nonspecific protein adsorption has led to the widespread use of PEG in
14
biomedical applications19, and we have observed that beads coated with PEG
using this protocol are much more resistant to protein adsorption than
untreated beads20. PEG-coating was found to prevent the beads from
aggregating together in the gel, allowing more even dispersion and better
tracking accuracy. Resistance to protein adsorption also allows the beads to
diffuse thermally within the confines imposed by the Matrigel
microenvironments.
During tumor growth, the strain field induced in the gel matrix was
mapped, via these probe beads, using timelapsed images acquired using a
Hamamatsu CCD camera controlled by Metamorph imaging software
(Universal Imaging Corporation, Downingtown, PA). In-house IDL particle
tracking routines21 were used to analyze the images and Adobe Photoshop
6.0 was used for further image processing. In Figures 1.4-1.7, the color
superimposed at a position along a bead track indicates the time elapsed
19
Harris, J. M., and Zalipsky, S. (1997). “Poly(ethylene glycol): Chemistry
and Biological Applications,” American Chemical Society, Washington, D.
C.
20
Valentine, M. T., Perlman, Z., Gardel, M. L., Shin, J., Matsudaira, P. T.,
Mahadevan, L., Mitchison, T., and Weitz, D. A. (in preparation). Effect of
surface chemistry on microrheology experiments: Comparison of BSAblocks, PEG-coated, and Carboxylated beads.
21
Crocker, J. C., and Grier, D. G. (1996). Methods of digital video
microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298.
15
from the beginning of the timelapse sequence until the bead was at that
position: for each timelapse sequence, each frame has been assigned an
unique color value based on its order within the sequence, starting at indigoblue for early times and shading along the spectrum to red at late times. The
increment in color value per frame is adjusted according to the number of
frames in the sequence, so that the scaling of color with elapsed time is
different for each timelapse sequence.
Furthermore, videorate images of the same field of view were taken
using a Sony SVO-9500MD videocassette recorder immediately before
beginning and immediately after completing most timelapse sequences; this
allowed analysis of the beads’ thermal motions. We were able, over the
course of the study, to examine Brownian bead position fluctuations near
and far from the growing tumor and at the tips of invasive branches. The
Brownian position fluctuations of embedded beads have been used to study
the microrheology22 as well as the local microenvironments23 of
inhomogeneous soft materials.
22
Mason, T. G., and Weitz, D. A. (1995). Optical Measurements of
Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids. Phys.
Rev. Lett. 74, 1250.
23
Valentine, M. T., Kaplan, P. D., Thota, D., Crocker, J. C., Gisler, T.,
Prud’homme, R. K., Beck, M., and Weitz, D. A. (2001). Investigating the
16
We measured the bulk elastic modulus, G’, of the Matrigel-based
assay, using a temperature-controlled strain-controlled rheometer (C-VOR
rheometer, Bohlin Instruments, East Brunswick, NJ), to be 20-40 Pa for
frequencies from 0.05 to 100 rad/s. The viscous modulus was an order of
magnitude smaller than the elastic modulus for most of the frequency range
examined, indicating that the gel is predominantly a solid.
RESULTS
1. Morphometric Measurements:
Over the six-day observation period the MTS volume grows from 0.004
mm3 to 0.009 mm3 (Figure 1.2) in three phases: initial growth, phase I (Day
1-3); plateaued volume, phase II (Day 3-4); rapid secondary growth, phase
III (Day 4-6). The invasion cross-section area increases from 0 to 0.10 mm2
(Figure 1.3) over these six days, showing its most rapid expansion between
Days 3 and 4. This marked increase in invasion area precedes the secondary
volumetric growth (III); similarly, the invasion area plateau (Day 2-3)
precedes the MTS volume plateau (II).
microenvironments of inhomogeneous soft materials with multiple particle
tracking. Phys. Rev. E 64, 061506.
17
Figure 1.2: MTS Volume. Volume of the tumor spheroid over 6 days of
observation is shown. The gray shading and Roman numerals indicate the
three growth phases described in the text.
18
Figure 1.3: MTS Invasion Area. Total invasion cross-section area,
exclusive of the central MTS core, over the 6 days of observation is shown.
19
2. Timelapse Multiparticle Tracking:
As the tumor system grows volumetrically and invades the surrounding gel
matrix, timelapse image sequences show the displacements of beads,
embedded in the gel, following local gel motion. These reference markers
allow the gel’s time-dependent strain field induced by the tumor to be
mapped, at a variety of locations, over the period of observation.
Four hours after implantation (Day 1), bead tracks in Figure 1.4
depict gel movement radially inward toward the tumor. Tracks show
movement with a circumferential component, along a line tangential to the
tumor surface, as well as a radial component (upper center of image) at a
location where an early invasive cell is later seen to emerge. Significant
tumor growth begins about 6 hours after implantation. The increase in MTS
volume (see Figure 1.2) displaces the gel radially outward (Figure 1.5).
Tracks show more circumferential movement (middle right of image) at a
location where a cluster of invasion pathways has appeared by the end of
this 21-hour timelapse sequence. Twenty-four hours after implantation, MTS
growth continues to displace gel radially outward (Figure 1.6). However, an
emergent invasion pathway (center of image) is associated with a local gel
strain with a significant component radially inward, toward the tip of the
20
invading cell and opposite to the bulk gel movement. In Figure 1.7, three
days after implantation of the MTS (Day 4) and approximately 65 µm from
the spheroid edge, gel near the tip of an invasive branch moves a significant
distance in, toward the leading invasive cell. Meanwhile, the bulk
surrounding gel is only slightly displaced outward.
21
Figure 1.4: Timelapse Multiparticle Tracking (Day 1). Tracks are drawn
to trace the paths of moving beads as color is used to timestamp bead
positions: early times are indigo-blue and colors shade along the spectrum to
red at late times. The tracks have been superimposed on the first frame in the
timelapse sequence. Note darkened multicellular tumor spheroid top, right.
Ticks indicate acquired image dimensions, ten pixels per tick mark. (Bar =
10 µm; Original Magnification: 40×; Timelapse duration: 110 min).
22
Figure 1.5: Timelapse Multiparticle Tracking (Day 1). For orientation,
note darkened MTS bottom, right. The MTS radius, determined from the
colored arcs tracing the outgrowing spheroid edge, increased by more than
10 µm while this sequence was acquired. (Bar = 10 µm; Original
Magnification: 40×; Timelapse duration: 832 min).
23
Figure 1.6: Timelapse Multiparticle Tracking (Day 4). Note the elongated
single cell at the tip of the cell branch invading from top, right, indicated by
the arrow. Beads 7-14 µm from the cell tip (tracks 2 and 3) are displaced
about 8 µm in toward the tip over this timelapse observation. A bead
(center, right) about 30 µm from the cell tip (track 1) is displaced about 5
µm, while beads 46 µm and more distant from the tip do not show
significant displacement inward. A bead located along a line almost
orthogonal to the line of invasion (track 4) shows displacement toward the
tip much greater than would be expected to result from a true point force
producing the displacements observed for beads located along the line of
invasion (tracks 1-3). Beads very far from the invasive tip show a slight
displacement outward. (Bar = 10 µm; Original Magnification: 40×;
Timelapse duration: 165 min).
24
Figure 1.6 (continued)
25
Figure 1.7: Timelapse Multiparticle Tracking (Day 4). Note the elongated
single cell at the tip of the cell branch invading from top, right, indicated by
the arrow. Beads 7-14 µm from the cell tip (tracks 2 and 3) are displaced
about 8 µm in toward the tip over this timelapse observation. A bead
(center, right) about 30 µm from the cell tip (track 1) is displaced about 5
µm, while beads 46 µm and more distant from the tip do not show
significant displacement inward. A bead located along a line almost
orthogonal to the line of invasion (track 4) shows displacement toward the
tip much greater than would be expected to result from a true point force
producing the displacements observed for beads located along the line of
invasion (tracks 1-3). Beads very far from the invasive tip show a slight
displacement outward. (Bar = 10 µm; Original Magnification: 40×;
Timelapse duration: 165 min).
26
Figure 1.7 (continued)
27
The magnitude and spatial extent of inward strain associated with the
invasion is highly directional and not isotropic about the cell tip. The
movements of beads more than 30 µm from the leading tip of the invasive
cell indicate that the gel here is significantly strained in towards the tip. Gel
strain inward toward invasive cell tips is consistently observed throughout
this study. Established invasion pathways close to the MTS seem to induce
gel strain outward, along the direction of invasion.
3. Mean Square Displacement (MSD) of Beads:
Throughout the period of observation, the bead-averaged mean square
displacement (MSD) for groups of Brownian beads near invasive tips, at a
lag time of 0.3 seconds averaged over 3 to 6 minutes, remained within the
range 0.012-0.022 µm,2 showing displacements much less than the 1 µm
bead diameter.
Observed MSD plateau values were at least 102 times larger than
those which should be shown for 1 µm Brownian beads probing a continuum
medium with an elastic modulus of 30 Pa, our gel’s modulus as measured by
bulk rheology. Such large MSDs are observed for 1 µm beads in tumor-free
as well as tumor-bearing gel matrices. Furthermore, beads with diameters
28
0.1, 0.2, 0.5, and 1 µm, in tumor-free assays, show plateaued MSD values
independent of bead size; bead motions constrained by an elastic modulus
should have saturated MSD values depending inversely on bead size. This
suggests that the particles are not probing the gel’s elastic modulus but
rather the microvolume defined by constraining gel fibers.
DISCUSSION
The combination of this 3D-ECM gel assay with analytical methods from
microrheology and soft condensed matter science yields novel and important
insights into the dynamic interaction between tumor and microenvironment.
The timelapsed imaging of tracer beads embedded in the gel matrix allows
direct mapping of the displacement field induced by the tumor within its
microenvironment and clearly shows that the volumetrically expanding
tumor spheroid displaces the bulk matrix radially outward while gel near the
tips of invasive cells is pulled inward toward those tips. Since such gel
reportedly consists of interconnected sheets of proteins24, these phenomena
24
Kleinman, H. K., McGarvey, M. L., Hassell, J. R., Star, V. L., Cannon, F.
B., Laurie, G. W., and Martin, G. R. (1986). Basement membrane
complexes with biological activity. Biochemistry 25, 312.
29
should be attributed to stress propagation, i.e. movement of distant beads
results from transmission of the local mechanical effect exerted by the
expanding tumor or by the tip of an invasive branch. In the following, we
will discuss observations of the microtumor system expanding within the 3D
environment, on both single-cell and multicellular scales, as well as
implications of the material properties found in our investigation of the
tumor-free Matrigel-based gel mixture.
Qualitative observations of gel displacement and cell traction are not
all that can be obtained from these timelapse sequences. Equipped with
knowledge of the gel’s bulk viscoelastic properties, we can quantitatively
estimate the traction exerted by invasive cells. Figure 1.7, depicting the
result of a timelapse sequence acquired for 165 minutes during a period of
rapid invasion and negligible volumetric growth, shows that beads 7-14 µm
from the leading invasive cell tip (tracks 2 and 3) are displaced about 8 µm
in toward the tip. One bead about 30 µm from the tip (track 1) is displaced
about 5 µm. Gel 46 µm from the cell tip is effectively motionless, probably
as a result of the superposition of the invasive tip’s inward pull and the
growing spheroid’s outward displacement, as shown in Figure 1.7 by the
beads most distant from the invasive cell. We therefore treat the matrix at a
distance of 46 µm from the cell tip as fixed and can approximate the
30
unstrained length of gel at a distance r from the cell tip as L = 46 µm – r.
From this, we find the strain ∆L/L induced in the gel by the cell tip is
approximately 8µm/(46µm -14µm) ≈ 5µm/(46µm -30µm) ≈ 0.3. This
indicates that the gel is behaving approximately as a continuum elastic
medium25. If we now treat the traction-induced bead displacements as the
result of a point force, applied at the invasive cell tip in a direction
determined by averaging displacement vectors, we can estimate the
magnitude of this force using the equation of equilibrium for a threedimensional elastic solid. A displacement u will have the form
r r r r
r
1 +ν
(3 − 4ν ) F + n (n ⋅ F )
u=
8πE (1 − ν )
r
(4)
where r = (x2+z2)1/2 is the distance from the origin, where the force is
applied, E is the elastic modulus, and ν is Poisson’s ratio26. For a true point
force, equation (4) should be valid at all locations where r is large compared
to the dimension of the region where the force is applied – in this case, at
25
Timoshenko, S. P., and Goodier, J. N. (1987). “Theory of Elasticity,” 3rd
ed., McGraw-Hill, New York.
26
Landau, L. D., and Lifshitz, E. M. (1986). “Theory of Elasticity,” 3rd
edition. Pergamon Books Ltd., New York.
31
distances more than a few microns from the invasive tip. If we choose
coordinate axes such that F = Fz, the orthogonal components of u = wz + vx
can be simplified to yield
F (1 + ν )
z2
w=
(3 − 4ν + 2 )
8πE (1 − ν )r
r
(5)
and
v=
F (1 + ν ) xz
8πE (1 − ν ) r 3
(6)
Setting ν, Poisson’s ratio, to ½, and thus approximating the matrix as an
incompressible medium, the magnitude of the point force F applied over the
timelapse period can be approximated from observed displacements. From
w and v components of the four bead tracks (1-4) indicated in Figure 1.7, we
estimate that, over the 165 minutes shown in this timelapse, this invading
cell tip pulls nearby gel inward with a force in the range 10-100 nN. The
forces thus estimated are significantly less than those reported for fibroblasts
32
as measured on elastic substrates, ~2 µN6,27, but only about 2-10 times less
than those measured at the front of a migrating fibroblast28 and comparable
to the force, up to 30 nN, applied at a single focal adhesion by human
foreskin and cardiac fibroblasts29. By superposing the displacement field
resulting from such a point force with the displacement field caused by a
distant, pressurized sphere26, representing the MTS, we can better
approximate the displacement field observed in Figure 1.7. In spherical
coordinates, the radial and angular strains of a hollow, pressurized sphere
with internal and external radii RMTS and R are
u rr = a −
2b
r '3
(7)
uθθ = a +
2b
r '3
(8),
and
27
Wrobel, L. K., Fray, T. R., Molloy, J. E., Adams, J. J., Armitage, M. P.,
Sparrow, J. C. (2002). Contractility of single human dermal myofibroblasts
and fibroblasts. Cell Motil. Cytoskeleton 52, 82.
28
Galbraith, C. G., and Sheetz, M. P. (1997). A micromachined device
provides a new bend on fibroblast traction forces. Proc. Natl. Acad. Sci.
USA, 94, 9114.
29
Balaban, N. Q., Schwarz, U. S., Riveline, D., Goichberg, P., Tzur, G.,
Sabanay, I., Mahalu, D., Safran, S., Bershadsky, A., Addadi, L. and Geiger,
B. (2001). Force and focal adhesion assembly: a close relationship studied
using elastic micropatterned substrates. Nature Cell Biol. 3, 466.
33
where r ' is the distance from the center of the sphere and a and b are
constants determined by boundary conditions:
a=
pRMTS
3
R − RMTS
3
3
 1 − 2ν 


 E 
(9)
and
pRMTS R 3  1 + ν 
b= 3

3 
R − RMTS  2 E 
3
(10),
for a sphere with internal pressure p and no external pressure. At the time
and location shown in Figure 1.7, the MTS center is about 260 µm distant
from the field of view and the MTS radius is about 130 µm. We take R to be
1 cm, the linear dimension of our sample cube. While the plexiglass cube, if
completely filled with gel, might be expected to provide a confining,
external, pressure, by Day 4 the gel had lost a slight amount of fluid and
there was an air-filled gap at the top of the sample cube, which implies that
gel expansion should not be constrained by the cube. By superposing these
two displacement fields and varying the parameters p and F, we can adjust
the resultant field to resemble the observation. An internal pressure of 50 Pa
and a point force of 55 nN reproduces bead displacements at many locations
to within about 20 percent. This pressure is much less than the limiting
growth pressures2, which is not surprising since the Figure 1.7 timelapse
sequence was taken on Day 4, when volumetric growth was very low. We
34
note, however, that a growing tumor and an invading cell likely consume
some of the surrounding medium, so that gel volume is not conserved and
the system is not truly Hookean. Furthermore, the way in which proteolytic
enzymes may change the gel’s elastic properties has not been examined
here. Better characterizations of the effects, if any, of enzymatic proteolysis
on gel viscoelastic properties and of the rate and spatial distribution of gel
consumption by invasive cells will allow refinement of these traction and
force estimations, as will measurement of the gel’s true Poisson ratio.
Moreover, as the cell invades the gel, the point at which the inward force is
applied, which we have taken as the origin of our coordinate system above,
should move outward with the cell as well. Indeed, this cell-ward force does
not seem to be, in fact, a true point force. A more sophisticated treatment,
incorporating multiple, moving force origins as well as a model of cell
adhesion to and exertion of traction on gel filaments, might significantly
improve interpretation of these observations.
On a larger length and longer time scale, observation of the tumor
system shows that both spheroid volume and invasion area increase over the
observation period. However, these increases are neither monotonic nor
synchronized; rather, a marked increase in invasion area (Day 3-4) trails a
rapid gain in volume (Day 1-3) and precedes a second rapid volumetric
35
expansion (Day 4-6), as shown in Figures 1.2 and 1.3. A similar pattern has
been described previously by Deisboeck et al.18, and present observations are
in agreement with the notion that a feedback mechanism may link
volumetric growth and invasive expansion. As indicated by timelapsed
observation of bead displacement far from the MTS, the mechanical impact
of the microscopic tumor on its environment reaches well beyond a distance,
measured from the MTS edge, greater than twice the initial radius of the
MTS. Since the clinically relevant, macroscopic situation presents tumor
radii of several centimeters30 and since tumor cells have been found in vivo
at a distance greater than 4 cm from the gross tumor31, a cautious
extrapolation of these findings to the clinical situation suggests that the
tumor’s mechanical impact may be exerted throughout, and perhaps even
beyond, the entire ipsilateral brain hemisphere. Interestingly, this notion is
already supported by preliminary results from a brain tumor patient, found
30
Kansal, A. R., Torquato, S., Harsh IV, G. R., Chiocca, E. A., and
Deisboeck, T. S. (2000). Simulated brain tumor growth dynamics using a
three-dimensional cellular automaton. J. Theor. Biol. 203, 367.
31
Silbergeld, D. L., and Chicoine, M. R., (1997). Isolation and
characterization of human malignant glioma cells from histologically normal
brain. J. Neurosurg. 86, 525.
36
using specific diffusion-tensor MR-imaging, showing tumor-related changes
in the diffusion anisotropy of water throughout the brain32.
Furthermore, we find that marked ECM-gel invasion appears to be
correlated with tumor cell traction. This corresponds well with the findings
of Klein et al.10, who report that two highly aggressive melanoma cell lines
efficiently contract 3D collagen type I gels and that their synthesis of α2β1
integrins is upregulated. The upregulation of such cell adhesion receptors is
important in this context since integrins mediate also in malignant brain
tumor cells both interaction with ECM components and invasiveness33.
However, the identity of specific mechanism(s) used by tumor cellgenerated traction to facilitate directed movement is still unclear. Vernon
and Sage15, for example, propose that traction-mediated alignment of an
ECM may produce specific pathways that other cells follow. Davis and
Camarillo34 suggest a similar concept drawn from their studies of endothelial
32
Zhang, S., Laidlaw, D. H., Bastin, M. E., Sinha, S., and Deisboeck, T. S.
(submitted). Computational visualization and analysis of structural
heterogeneity in a diffusion tensor MRI-data set from a brain tumor patient.
33
Paulus, W., and Tonn, J. C. (1994). Basement membrane invasion of
glioma cells is mediated by integrin receptors. J. Neurosurg. 80, 515.
34
Davis, G. E., and Camarillo, C. W. (1995). Regulation of endothelial cell
morphogenesis by integrins, mechanical forces, and matrix guidance
pathways. Exp. Cell Res. 216, 113.
37
cells, which caused linear distortions of Matrigel; these distortions
correspond to the migration pathways of endothelial cell processes. These
authors call this phenomenon “matrix guidance pathways” and say it may
result from the generation of tension between endothelial cells. Tranquillo35
presented a similar concept for fibroblasts, proposing that “cells align, exert
traction and migrate preferentially in the direction in which surrounding
fibrils are aligned.” Deisboeck et al.18 presented a “least resistance, most
permission, highest attraction” concept for the emergence of invasive
branching patterns: brain tumor cells would follow each other because of
increased chemical attraction, enhanced haptotactic permission as well as
reduced mechanical resistance within a preformed path. The aforementioned
‘matrix guidance’ would thus be in accordance with this concept as it also
facilitates at least the haptotactic element. Our timelapse observations
indicate that the traction-induced tension associated with invasion is highly
localized at the tips of invasive branches and not alongside established
invasive branches closer to the MTS. The fairly constant average thermal
MSD of beads within the area near such invasive cell tips may argue for a
relatively minor role of proteolytic enzymes in the tip area, since substantial
matrix degradation would be expected to result in an increase in thermally35
Tranquillo, R. T. (1999). Self-organization of tissue equivalents: the
nature and role of contact guidance. Biochem. Soc. Symp. 65, 27.
38
driven bead fluctuations. However, since the parental cell line (U87MG) has
been shown to secrete MMP-2, which degrades collagen IV, a component of
GFR-Matrigel, and since the release of MMP-2 has been linked to collagen
contraction by endothelial cells13,14,15, the possibility that proteolytic
enzymes may contribute to tumor invasion also in the present study cannot
be eliminated. This is further supported by the findings of Vaithilingam et
al.36, who report an (primarily extracellular) increase of general proteolytic
activity in C6 astrocytoma spheroids with increasing spheroid diameter.
The 3D-assay system used in the current study does have potential
shortcomings. For example, the presence of some tissue culture medium
around the spheroid when the MTS is implanted cannot be avoided. The
early inward gel movement depicted in Figure 1.4 probably results from the
rapid metabolism of traces of incubation medium by highly proliferative
MTS surface cells. Generally, a higher incubation medium concentration
might produce an immediate environment that is more favorable for
volumetric tumor growth and hence result in the first marked increase of
MTS volume (I) in Figure 1.2. A loss of fluid from the gel towards the end
of the observation period is another concern and might indicate a rather
36
Vaithilingam, I. S., Stroude, E. C., McDonald, W., and Del Maestro, R. F.
(1991). General protease and collagenase (IV) activity in C6 astrocytoma
cells, C6 spheroids and implanted C6 spheroids. J. Neuro-Onc. 10, 203.
39
serious limitation of the assay, since the loss of fluid and the resulting
increased rigidity of the gel may render forward cell movement more
difficult. To address this issue, it is helpful to look carefully at the invasive
behavior, depicted in Figure 1.3. The invasion area clearly still continues to
increase towards the end of the observation period, which suggests a
relatively minor influence of drying on cell motility.
In summary, we have demonstrated that an expanding, microscopic
tumor system exerts significant mechanical forces upon its environment, in
this case a particular extracellular matrix gel-composition placed inside a
novel plexiglass cube. More specifically: (1) The multicellular brain tumor
spheroid system exerts both compressive pressure and tension on its
microenvironment. (2) These mechanical forces can be linked to the tumor’s
proliferative and invasive growth dynamics, which seem to induce each
other. (3) Spatially, the mechanical impact of the volumetrically growing
tumor propagates to at least twice its initial radius. (4) The growing MTS
exerts this outward pressure, but inward traction is generated by invasive
tips only. (5) Furthermore, this cell traction does not relax while volumetric
growth of the MTS ceases. Also, the invasive tip maintains this tension for
five consecutive days during which the overall invasive area increases
40
substantially. Cell-imposed traction and tumor invasion therefore seem
related.
ACKNOWLEDGEMENTS
This work was supported in part by grant CA69246 from the National
Institutes of Health and by grant DMR9971432 from the National Science
Foundation. The authors would like to thank Drs. Leonard M. Sander
(Department of Physics, University of Michigan), Daniel Fisher
(Department of Physics, Harvard University), Michael E. Berens (NeuroOncology Laboratory, Barrow Neurological Institute), Andrea Del Vecchio,
Xi Chen, and John Hutchinson (all, Division of Engineering and Applied
Sciences, Harvard University), Andreas Bausch (Technical University,
Muenchen, Germany), and Peter Friedl (University of Wuerzburg, Germany)
for inspiring discussions as well as Drs. Maria Kilfoil and You-Yeon Won
(both, Division of Engineering and Applied Sciences, Harvard University)
for assistance with the rheometer. D.A-A. gratefully acknowledges funding
by the Kennedy Memorial Trust.
41
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47
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48
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F. (1991). General protease and collagenase (IV) activity in C6 astrocytoma
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49
Chapter II
Colloidosomes: Self-assembled polymer capsules with colloidal
crosslinkers and environmentally sensitive release triggers
V. D. Gordon1, X. Chen2†, J. W. Hutchinson2, and D. A. Weitz1,2
1
Department of Physics and 2Division of Engineering and Applied Sciences,
Harvard University, Cambridge, MA 02138
†present address, Department of Civil Engineering and Engineering
Mechanics,
Columbia University, New York, NY 10027
ABSTRACT
We present a novel class of capsules with composite
membranes comprising a polymer network stabilized by crosslinking via adsorption to colloidal beads. These capsules are
fabricated via controlled self-assembly using only a few
processing steps.
To closely study system structure and
properties, we deform capsules using microcantilevers and
50
describe these deformations using finite element modeling.
Additional
properties.
experimental
tests
confirm
modeled
system
Understanding system properties allows the
development of non-mechanical release triggers exploiting
interactions with capsule environment.
Techniques for efficient and non-destructive encapsulation and
controlled delivery of active agents are being developed or used for an
increasing number of applications and may centrally underpin future
technologies of drug delivery, food function, biomedicine, and “smart”
materials37,38,39,40,41,42,43,44, 45 (references 1-9, present chapter). Encapsulating
37
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Science and Nutrition 50, 213 (1999).
38
E. L. Chaikof, Annual Reviews in Biomedical Engineering 1, 103 (1999).
39
I. Cohen, H. Li, J. L. Hougland, et al., Science 292, 265 (2001).
40
R. G. Willaert and G. V. Baron, Reviews in Chemical Engineering 12, 5
(1996).
41
R. P. Lanza, R. Langer, and J. Vacanti, Principles of Tissue Engineering
(Academic Press, San Diego, CA, 2000).
42
T. Joki, M. Machluf, A. Atala, et al., Nature Biotechnology 19, 35 (2001).
51
structures are also important to basic research as models for cell membranes
and as microscale reaction vessels. Many such structures are prepared via
self-assembly of lipids or small surfactants. Because polymers are often
stronger, more stable, and have more varied properties than small
amphiphiles, it is frequently desirable to construct capsules using polymeric
materials. This is done in many ways, including self-assembly of
amphiphilic block copolymers46 (reference 10, present chapter), layer-bylayer deposition of charged materials45; and emulsion polymerization47, 48, 49
(references 11-13, present chapter). Capsules have high potential for
enclosing sensitive or expensive materials until release into the extra-capsule
environment is appropriate. For this potential to be realized on large scales
43
T.-A. Read, D. R. Sorensen, R. Mahesparan, et al., Nature Biotechnology
19, 29 (2001).
44
I. G. Loscertales, A. Barrero, I. Guerrero, et al., Science 295, 1695 (2002).
45
F. Caruso, R. A. Caruso, and H. Mohwald, Science 282, 1111 (1998).
46
B. M. Discher, Y.-Y. Won, D. S. Ege, et al., Science 284, 1143 (1999).
47
O. Emmerich, N. Hugenberg, M. Schmidt, et al., Advanced Materials 11,
1299 (1999).
48
M. Sauer, D. Streich, and W. Meier, Advanced Materials 13, 1649 (2001).
49
D. M. Lynn, M. M. Amiji, and R. Langer, Angew. Chem. Int. Ed. 40,
1707 (2001).
52
and in a variety of applications, capsules should have very high
encapsulation efficiency and should be reproducibly fabricated using a
simple few-step process producing a single layer of polymer coating.
Furthermore, the resulting capsules should be mechanically tough and
resilient and have robust means of inducing release including both
mechanical perturbations and changes in the condition of the extra-capsule
environment.
We use controlled self-assembly to fabricate capsules
comprising a network of polymer crosslinked by adsorption to colloids. In
the general scheme of their fabrication, these structures are reminiscent of
capsules called “colloidosomes”50 (reference 14, present chapter) that are
stabilized by sintering colloidal beads on emulsion interfaces so that bead
characteristics and sintering time determine capsule modulus and porosity.
The present capsules are likewise made using directed self-assembly of
colloidal beads onto emulsion interfaces, but their fabrication specifics and
system properties are very different. These colloidosomes are not sintered
but are stabilized by adsorbing polymer onto beads; capsule properties are
determined primarily by the adsorbed polymer. While sintered
colloidosomes buckle and break like the porous elastic shells they are, these
50
A. D. Dinsmore, M. F. Hsu, M. G. Nikolaides, et al., Science 298, 1006
(2002).
53
adsorption-stabilized colloidosomes are very mechanically resilient and
behave as expected for composite membranes. Osmotic pressure from
internal polyelectrolyte inflates these capsules, allowing deflation and
release triggered by environmental conditions.
To make these colloidosomes, we first emulsify an aqueous solution
of poly-L-lysine (PLL) (0.1% w/v, MW 150-300 kD, Sigma-Aldrich) in a
toluene suspension of 1.3-µm-diameter polystyrene beads (Interfacial
Dynamics Corporation). Colloids self-assemble onto the emulsion
interfaces, where PLL molecules adsorb to and lock together neighboring
beads. Covered droplets are gently washed into octanol, which has a lower
interfacial tension with water than does toluene, and then centrifuged into an
aqueous solution of nonionic surfactant (TWEEN 20 or 80, 12.5 mg/mL).
Once in water, colloidosomes are highly permeable to aqueous dyes50,
demonstrating the removal of the templating interface. Radii of
colloidosomes in this study are in the range R~75-200 µm.
These capsules are almost always spherical, with size, shape, and
contents determined by the initial templating emulsion droplets, and they
remain intact and spherical for 2-4 days after centrifugation into water.
Bead density on colloidosome surfaces varies significantly and some intact,
spherical structures show large gaps between sparsely covering beads, as in
54
Figure 2.1. This indicates that beads are held by an adsorbed PLL network
that maintains capsule integrity and that these capsules are qualitatively
novel structures comprising a polymeric network established via directed
self-assembly in very few processing steps. To definitively evaluate
colloidosome structure, we deform capsules with calibrated
microcantilevers51, 52, 53, 54, 55, 56 (references 15-20, present chapter) and
describe the deformations with finite element modeling. Using additional
tests to evaluate a series of models, we arrive at a final model characterizing
mechanical and system properties of these novel capsules.
51
J. F. Leger, J. Robert, L. Bourdieu, et al., Proceedings of the National
Academy of Sciences of the United States of America 95, 12295
(1998).
52
S. Promkotra and K. T. Miller, in Colloidal Ceramic Processing: Nano-,
Micro-, and Macro-Particulate Systems, edited by W.-H. Shih, W. M.
Carty, Y. Hirata and N. Ninos (American Ceramic Society, 2003 (in
press)).
53
K. Moran, A. Yeung, and J. Masliyah, Langmuir 15, 8497 (1999).
54
D. Rossetti, X. Pepin, and S. J. R. Simons, Journal of Colloid and
Interface Science 261, 161 (2003).
55
A. K. C. Yeung and R. Pelton, Journal of Colloid and Interface Science
184, 579 (1996).
56
M. G. Poirier and J. F. Marko, Proceedings of the National Academy of
Sciences of the United States of America 99, 15393 (2002).
55
FIGURE 2.1 – Colloidosomes with different surface densities of beads
Colloidosomes are spherical capsules fabricated by the controlled selfassembly of colloidal beads onto emulsion droplets. For these
colloidosomes, polymer in aqueous solution adsorbs onto and bridges
between beads, locking them together and stabilizing the structure to allow
removal of the initial templating interface. Surface bead density varies
widely among colloidosomes and within individual colloidosomes.
56
1 µm
beads
100 to 300 µm colloidosome
diameter
Figure 2.1, continued
57
Mechanical properties of encapsulating structures constrain
application potential and may be exploited to trigger content release. We
characterize mechanical response by indenting capsules with calibrated
microcantilevers, maneuvered with a hydraulic micromanipulator, while
observing under a microscope. Microcantilevers are made by pulling glass
capillaries and rods in a micropipette puller. We calibrate the spring
constant of each reference microcantilever by positioning the pulled tip just
above a rigid straightedge mounted onto an analytical balance and then
moving the microcantilever base down; the deflection of the tip of the
microcantilever from its base is linear in applied force, allowing us to
determine its spring constant. The tips of secondary microcantilevers are
bent at right angles to their bases and shaped to define indenter geometries.
These secondary microcantilevers are calibrated against reference
microcantilevers and used to deform colloidosomes axisymmetrically. For
each trial, the microcantilever tip is initially positioned to lightly pin the
colloidosome against the rigid sample chamber wall and then the
microcantilever base is advanced incrementally; the deflection of the
microcantilever, and thus the force applied, is determined from the
difference between the observed displacement of the tip and the known
advancement of the base. Colloidosomes stabilized by PLL adsorption
58
recover resiliently from deformations of nearly a diameter. When indented
by a microcantilever with a small hemispherical tip, essentially a point
indenter, a deformed colloidosome conforms locally to the tip and elsewhere
is convex with smoothly varying local curvature, as typified in Figure 2.2
(B and C). A given indentation displacement perturbs a small structure more
than a large one, so we normalize indentation displacement and force by
colloidosome radius. Capsule displacement by a point indenter appears
linear in force, as shown by representative results in Figure 2.3 (A). We
estimate a capsule spring constant in response to point indentation, k~10-2
N/m, from which we define a modulus for the colloidosome, M=k/R~102 Pa.
This spring constant is comparable to oil-water interfacial tensions, but no
such interface remains. Therefore the elasticity must be caused by the
colloidosome structure itself.
59
FIGURE 2.2 – Colloidosome deforming under point indentation; [D]
indentation of an unpressurized thin elastic shell
(A) A microcantilever with a ~10 µm hemispherical tip indents a 330
µm colloidosome, (B) which deforms to a smoothly curved, convex
geometry and returns to its original unstressed geometry after release. (C)
The sketch traces the colloidosome’s deformed shape.
(D) The sketch shows the classically-characterized deformation of an
unpressurized thin elastic shell. Under a concentrated radial force, the shell
has spherical curvature, very nearly the mirror image of the unstrained
shape, over most of the deformed region. Indentation δ scales with the
square of the force applied.
60
A
50 mm
B
10 mm
C
D
Figure 2.2, continued
61
FIGURE 2.3 – Indentation with point (A) and large flat (B) indenters
Deformation data (symbols) are used to fit the model (lines) to determine
parameters for individual colloidosomes; distinct symbols are used for
different capsules. Capsule indentations were observed with an uncertainty
of less than 2 µm and force applied was determined with an uncertainty of
less than 0.3 µN for the small-tipped microcantilever and less than 2 µN for
the large flat microcantilever. Typical colloidosome radii were 100-200 µm.
Data and fits for two of nine studied colloidosomes are shown.
62
indentation / colloidosome radius
A
1.4
1.2
Et = 1.7 N/m
pR / 2Et = 0.002
1.0
0.8
0.6
0.4
0.2
Et = 0.3 N/m
pR / 2Et = 0.025
0.0
0.000
0.005
0.010
0.015
force / colloidosome radius (µN/µm)
indentation / colloidosome radius
B
1.0
Et = 0.3 N/m
pR / 2Et = 0.025
0.8
0.6
0.4
0.2
0.0
0.00
Et = 1.7 N/m
pR / 2Et = 0.002
0.01
0.02
0.03
0.04
0.05
0.06
force / colloidosome radius (µN/µm)
Figure 2.3, continued
63
0.07
To more closely explore these structures, we use finite element
modeling to investigate the indentation of a water-filled elastic sphere. For
such a shell axisymmetrically deformed by a point load, dimensional
analysis dictates that indentation displacement, δ , depends on the
indentation force or load, P , and the initial internal pressure, p , according
to:
δ
 P PR pR 
= f
, 3,

R
 EtR Et 2 Et 
(1)
where t is the thickness, E the Young’s modulus, and R the radius of the
shell. The first and second terms in (1) correspond, respectively, to
stretching and bending deformations caused by indentation. The third term
is the non-dimensionalized internal pressure. For an undeformed shell, the
membrane tension caused by internal pressure is S = pR / 2t , so the third term
in (1) is S / E , a measure of the stretching deformation caused by internal
pressure. A shell’s effective stretching stiffness is Et /(1 −ν 2 ) and its
effective bending stiffness is Et 3 /12(1 −ν 2 ) , where ν is Poisson’s ratio; the
bending stiffness depends more strongly on the shell thickness than does the
stretching stiffness.
As a first attempt at the structure of adsorption-stabilized
colloidosomes, we model a shell for which bending deformations are
64
important so that internal pressure causes negligible stretching and
permeability is unimportant to the deformation. For given shell parameter
values, f is computed using finite element analysis with the commercial
code ABAQUS57 (reference 21, present chapter). The mesh is axisymmetric
and consists of 400 3-node quadratic membrane elements. We assume rigid
indenters and frictionless contact. For a shell with thickness 1/1000 of the
radius, modeled curves describing point indentation are highly nonlinear,
increasing about 20 times less steeply with force for displacements about
δ=0.5R than for displacements about 0.2R. This does not agree with
experiment. However, as we increase the modeled shell thickness, the ratio
of bending to stretching stiffness increases and indentation becomes
increasingly linear in force. Appropriately linear curves can be fit to
experimental data to obtain a modeled shell thickness of about 1/8 of the
radius and a Young’s modulus of about 30kPa. This model successfully
reproduces the characteristic deformed shape of these colloidosomes.
However, ~1µm beads on the surface of a ~100µm colloidosome do not
form a thick shell, as Figure 2.2 shows; colloidosomes made with
fluorescent PLL show no sign of a thick adsorbed shell. The thick shell
model is not a physical depiction of capsule structure.
57
ABAQUS, (ABAQUS Inc., Pawtucket, RI, 1999).
65
From this, we infer that these colloidosomes can be described as thin
shells where t/R†1. For all further analysis we therefore remove the
dependence on the second term, PR/Et3, from Eq. (1). An unpressurized thin
shell deforms under an axisymmetric point load with a characteristic
spherical indented curvature, nearly mirroring the original undeformed
curvature and illustrated in Figure 2.2 (D)58 (reference 22, present chapter),
and such a shell’s indentation displacement scales with the square of the
force applied. The characteristic deformation of a colloidosome is strikingly
different from that of an unpressurized thin shell. Therefore, we must
include internal pressure to correctly model the structure of these capsules.
For a thin shell such that Et2/(12pR2)†1, the membrane limit, bending
stiffness is negligible compared to stretching stiffness. A membrane cannot
support a load unless constrained to stretch when deformed, as it is when
tensed by internal pressure. As a non-permeable membrane is deformed,
volume is conserved and internal pressure increases. Finite element
modeling of non-permeable membranes describes colloidosome indentations
reasonably well, better for small displacements than for large. However, this
58
L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd edition
(Pergamon Press, New York, NY, 1986).
66
model does not agree with observations that colloidosomes are permeable to
aqueous dyes, and inferably to water, and is therefore unphysical.
When deformed, a permeable membrane does not conserve volume
and has constant internal pressure. System parameters, Et and pR / 2 Et in
Eq. (1), are determined by fitting model indentations to experiment. Since
indentation displacement depends on two free system parameters, fitting to
point indentation data alone does not allow robust determination. To
provide an independent set of data, microcantilevers with flat tips much
larger than colloidosomes are also used to depress capsules in a planar
geometry. When the indenter tip is much larger than the shell, the loaddisplacement relationship has the same dimensional dependence as before,
δ
 P pR 
= g
,

R
 EtR 2 Et 
(2)
but the function g differs from f . The relationship between δ / R and
P / R is measured experimentally with both point and planar indenters nine
colloidosomes. We vary Et and pR / 2 Et over a wide range and determine
the parameter combination that best fits computed f and g to the
corresponding sets of experimental data. For these capsules, fitted values
range between 0.15 N/m < Et < 1.7 N/m and 0.002 < pR/2Et < 0.06.
Modeled deformations of such a membrane agree well with experiment for
67
all observed displacements, as shown for two typical colloidosomes in
Figure 2.3; inset sketches show finite element calculations of deformed
shapes, which agree excellently with observation. For these nine capsules,
average fitted parameters are pR/2Et=0.023 and Et=0.73N/m. We have
verified that internal pressure is sufficiently large that bending effects are
negligible compared to stretching: the membrane limit is valid.
To independently confirm this model, we deform colloidosomes using
a microcantilever with a thick hemispherical tip (~30 µm diameter), thereby
obtaining data independent of those used to fit model parameters. Using our
finite element analysis, load-displacement curves are modeled for average
colloidosome parameters and an indenter with this 30 µm geometry. These
curves follow experimental results closely, as Figure 2.4 shows; this further
supports this model’s validity.
68
140
Et = 0.73 N/m
pR / 2Et = 0.023
indentation (µm)
120
100
80
60
40
experiment
model
20
0
0
1
2
3
force (µN)
4
5
6
FIGURE 2.4 – Indentation with a large hemispherical indenter
Three colloidosomes, indicated by distinct symbols, are indented by a
microcantilever with a large hemispherical tip, ~30 µm in diameter. Data
from these colloidosomes were not used to fit model parameters, and these
deformations, which have a different functional form than those used to fit
model parameters, are predicted by our model using average fitted
parameters. Deflection is determined to within less than 2 µm and force is
determined to within less than 1 µN.
69
Our model implies that most colloidosomes are inflated to 100-500
Pa.
Indeed, if spherical colloidosomes are membranes, they must be
pressurized in order to keep this shape against gravity.
These water-
permeable capsules cannot sustain hydrostatic pressure.
However, the
solution of polyelectrolyte PLL used in fabrication should produce about 2
kPa of osmotic pressure in the absence of salt59, 60 (references 23, 24, present
chapter). Most of the PLL is incorporated into the membrane, where it does
not contribute to the osmotic pressure; the measured osmotic pressure is
consistent with roughly 75-95% of PLL being so incorporated. To test
whether it is PLL osmotic pressure inflating colloidosomes, we fabricate
capsules using a diluted PLL solution. Such colloidosomes are significantly
softer to point indentation and their deformed shape is not smoothly convex
but instead shows a near-conical indentation circumscribed by a sharp bend,
as in Figure 2.5 (a). This shape agrees with deformations modeled for low
internal pressure. These observations confirm that PLL osmotic pressure
inflates colloidosomes.
59
P. C. Hiemenz, Principles of colloid and surface chemistry, 2nd edition
(Marcel Dekker, Inc., New York, NY, 1986).
60
E. S. Pagac, R. D. Tilton, and D. C. Prieve, Langmuir 14, 5106 (1998).
70
FIGURE 2.5 – Partial and entire deflation of colloidosomes
Colloidosomes made with dilute poly-L-lysine (A) and those made with
undilute poly-L-lysine and immersed in 0.025M NaCl solution (B) deform
with near-conical indentations circumscribed by sharply bent regions,
strikingly unlike the smoothly convex indentations shown in Figure 1;
dashed lines are drawn as aids to the eye. This indentation shape and the
wrinkles observed in the colloidosome membrane indicate that osmotic
pressure inflating these colloidosomes has been lowered. Colloidosomes in
1 M salt solution (C) are almost entirely deflated.
71
A
B
C
72
The success of finite element analysis in this case is striking. Beads
are only two orders of magnitude smaller than capsules, yet our model treats
the colloidosome membrane as a continuum on the scale of the mesh
elements. Continuum treatment is appropriate and its success unsurprising if
membrane properties are dominated by a homogeneous layer of adsorbed
PLL. Shear rheology of interfacially adsorbed PLL films yields elastic
responses of about 10-2 to 10-1 N/m61 (reference 25, present chapter),
agreeing in magnitude with fitted Et values. We also recall that capsule
integrity is maintained despite large inter-bead gaps. All observations
demonstrate that these are PLL capsules with the polyelectrolyte membrane,
otherwise soluble in water, stabilized by adsorption to crosslinking beads.
Characterizing mechanical response allows mechanical deformation
and breaking to be exploited for controlled release.
Furthermore, we
develop environmental non-mechanical release triggers which deflate
capsules by exploiting polyelectrolyte behavior. In aqueous solutions, salt
reduces polyelectrolyte osmotic pressure. The colloidosome membrane is
permeable to small salt ions and aqueous counterions. Capsules in 0.025 M
NaCl solution become much softer to indentation and their deformed shape
61
B. Biswas and D. A. Haydon, Proceedings of the Royal Society of London
Series A - Mathematical and Physical Sciences 271, 296 (1963).
73
changes appropriately, as shown in Figure 2.5 (B). In 1 M NaCl solution,
colloidosomes are almost entirely deflated, as shown in Figure 2.5 (C).
Other possible release triggers include pH, temperature, and solvent, upon
which the charge and conformation of poly-L-lysine are known to depend62,
63, 64
(references 26-28, present chapter). We find that colloidosomes deflate
and break at low pH but remain intact and spherical at high pH. External
osmotic pressure from large molecules to which the colloidosome membrane
is impermeable could also trigger capsule collapse.
62
B. Davidson and G. D. Fasman, Biochemistry 6, 1616 (1967).
63
T. J. Yu, J. L. Lippert, and W. L. Peticolas, Biopolymers 12, 2161 (1973).
64
J. L. Koenig and P. L. Sutton, Biopolymers 9, 1229 (1970).
74
These novel polymer capsules are fabricated via an adaptable onestep process and are well-suited for controlled release triggered via their
striking mechanical resilience as well as environmental sensitivity.
Furthermore, this fabrication pathway is generally applicable to a number of
cross-linkers and surface-active polymers. To demonstrate this, we have
fabricated capsules stabilized by adsorption of
poly(diallyldimethylammonium chloride). Appropriate choice of polymer
will allow selective adaption of capsule compatability and functionality,
widening these structures’ range of potential applicability.
ACKNOWLEDGEMENTS
The authors thank M.G. Poirier (Laboritoire de Dynamicque des Fluides
Complexes) for instruction regarding microcantilevers, M. F. Hsu (Harvard
University) for instruction in colloidosome fabrication, and M. P. Brenner,
H. A. Stone (Harvard University), A. R. Bausch (Technische Universität
München) and A. D. Dinsmore (University of Massachusetts, Amherst) for
helpful discussions.
75
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
B. F. Gibbs, S. Kermasha, I. Alli, et al., International Journal of Food
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R. G. Willaert and G. V. Baron, Reviews in Chemical Engineering 12,
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R. P. Lanza, R. Langer, and J. Vacanti, Principles of Tissue
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I. G. Loscertales, A. Barrero, I. Guerrero, et al., Science 295, 1695
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O. Emmerich, N. Hugenberg, M. Schmidt, et al., Advanced Materials
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1006 (2002).
J. F. Leger, J. Robert, L. Bourdieu, et al., Proceedings of the National
Academy of Sciences of the United States of America 95, 12295
(1998).
76
16
17
18
19
20
21
22
23
24
25
26
27
28
S. Promkotra and K. T. Miller, in Colloidal Ceramic Processing:
Nano-, Micro-, and Macro-Particulate Systems, edited by W.-H. Shih,
W. M. Carty, Y. Hirata and N. Ninos (American Ceramic Society,
2003 (in press)).
K. Moran, A. Yeung, and J. Masliyah, Langmuir 15, 8497 (1999).
D. Rossetti, X. Pepin, and S. J. R. Simons, Journal of Colloid and
Interface Science 261, 161 (2003).
A. K. C. Yeung and R. Pelton, Journal of Colloid and Interface
Science 184, 579 (1996).
M. G. Poirier and J. F. Marko, Proceedings of the National Academy
of Sciences of the United States of America 99, 15393 (2002).
ABAQUS, (ABAQUS Inc., Pawtucket, RI, 1999).
L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd edition
(Pergamon Press, New York, NY, 1986).
P. C. Hiemenz, Principles of colloid and surface chemistry, 2nd
edition (Marcel Dekker, Inc., New York, NY, 1986).
E. S. Pagac, R. D. Tilton, and D. C. Prieve, Langmuir 14, 5106
(1998).
B. Biswas and D. A. Haydon, Proceedings of the Royal Society of
London Series A - Mathematical and Physical Sciences 271, 296
(1963).
B. Davidson and G. D. Fasman, Biochemistry 6, 1616 (1967).
T. J. Yu, J. L. Lippert, and W. L. Peticolas, Biopolymers 12, 2161
(1973).
J. L. Koenig and P. L. Sutton, Biopolymers 9, 1229 (1970).
77
Chapter III
Microcantilevered Deformation and Breaking of Sintered
Colloidosomes, with Finite Element Analysis
V. D. Gordon1, X. Chen2,*, J. Hutchinson2, D. A. Weitz1,2
1
Department of Physics and 2 Division of Engineering and Applied
Sciences, Harvard University, Cambridge, Massachusetts 02138
*present address, Department of Civil Engineering and Engineering
Mechanics,
Columbia University, New York, NY 10027
Techniques for efficient and non-destructive encapsulation and
controlled delivery of active agents are being developed or used for an
increasing number of applications and may centrally underpin future
technologies of drug delivery, food function, and
78
biomedicine65,66,67,68,69,70,71,72 (references 1-8, present chapter). Furthermore,
capsules have strong potential for use in catalysis and in “smart” coatings
and composite materials73 (reference 9, present chapter). Colloidosomes
stabilized by sintering are strong candidates for encapsulation applications.
Sintering not only stabilizes these shells to allow removal of the templating
oil interface, but also adjusts their permeability: colloidosomes sintered
longer times are less permeable than those sintered shorter times, as the
65
B. F. Gibbs, S. Kermasha, I. Alli, et al., International Journal of Food
Science and Nutrition 50, 213 (1999).
66
E. L. Chaikof, Annual Reviews in Biomedical Engineering 1, 103 (1999).
67
I. Cohen, H. Li, J. L. Hougland, et al., Science 292, 265 (2001).
68
R. G. Willaert and G. V. Baron, Reviews in Chemical Engineering 12, 5
(1996).
69
R. P. Lanza, R. Langer, and J. Vacanti, Principles of Tissue Engineering
(Academic Press, San Diego, CA, 2000).
70
T. Joki, M. Machluf, A. Atala, et al., Nature Biotechnology 19, 35 (2001).
71
T.-A. Read, D. R. Sorensen, R. Mahesparan, et al., Nature Biotechnology
19, 29 (2001).
72
I. G. Loscertales, A. Barrero, I. Guerrero, et al., Science 295, 1695 (2002).
73
F. Caruso, R. A. Caruso, and H. Mohwald, Science 282, 1111 (1998).
79
interstitial pores between beads become smaller74,75 (references 10,11,
present chapter). This should allow control of the rate at which encapsulated
contents diffuse out of these colloidosomes, allowing gradual and sustained
release over time, vital to some biomedical applications. However, ideal
encapsulating structures should have precisely controllable size, stability,
compatibility, and mechanical properties, as well as permeability. For any
such encapsulating structure, mechanical properties are especially important,
since they can allow content release as the structure deforms and breaks
appropriately in response to load and shear. Moreover, strength and
resilience constrain a structure’s potential application regardless of the
desired release mode. We expect that varying sintering time should not only
tune colloidosome shell porosity, but it should also modify colloidosome
modulus and other structural properties; as sintering time increases, the
interconnecting necks between beads should thicken and the colloidosome
should become stronger. Characterizing mechanical properties and
architecture are requisite to realizing these structures’, and any encapsulating
structure’s, full potential.
74
A. D. Dinsmore, M. F. Hsu, M. G. Nikolaides, et al., Science 298, 1006
(2002).
75
M. F. Hsu et al., manuscript in preparation
80
To evaluate the effect of sintering on colloidosome modulus as well as
deformation and breaking modes, colloidosomes were sintered at 105 °C for
5, 10, 15, 20, and 150 minutes and calibrated microcantilevers were used to
measure the force required to break or puncture a colloidosome. For
colloidosomes sintered five minutes and 150 minutes, indentation depth as a
function of increasing force was also examined. We find that increasing
sintering time does, on the whole, strengthen these capsules. Furthermore,
for very long sintering times these capsules’ modes of deformation and
breaking change as discrete covering beads anneal into a continuous shell.
When making sintered colloidosomes, 200 µL of an aqueous
suspension of biotin-coated 1.1µm-diameter beads with aldehyde sulfate
surface charge groups formed the continuous phase of the initial templating
emulsion. To form the dispersed emulsion phase, toluene and Wesson
vegetable oil, filtered with a 0.45µm-pore hydrophobic syringe filter, were
mixed in equal parts, and 2 µL of this mixture added to the aqueous phase.
Shearing by hand for a few minutes produced bead-covered droplets
typically tens of microns in diameter. Sintering was done by heating these
bead-covered droplets in solution in an oven at 105°C. To prevent boiling,
the solution was diluted with glycerol (to make a solution with 70:30
glycerol/water by weight).
81
Colloidosome mechanical response is characterized by indenting
capsules with calibrated microcantilevers, finely controlled with a hydraulic
micromanipulator, while observing under a microscope. Microcantilevers
are made by pulling glass capillaries and rods in a micropipette puller. We
calibrate the spring constant of each reference microcantilever by
positioning the pulled tip just above a rigid straightedge mounted onto an
analytical balance and then moving the microcantilever base down; balance
readings increase linearly as the base is deflected from the tip. The tips of
secondary microcantilevers are bent at right angles to their bases and shaped
to create well-defined hemispherical tip geometries, smaller than
colloidosomes.
These secondary microcantilevers are calibrated against
reference microcantilevers and used to deform colloidosomes. For each
trial, the microcantilever tip is initially positioned to lightly touch the
colloidosome and then the microcantilever base is advanced incrementally;
the deflection of the microcantilever, and thus the force applied, is
determined from the difference between the observed displacement of the tip
and the known advancement of the base. All measurements were performed
in water on colloidosomes that had been washed overnight in ethanol to
remove interior oil; the index of refraction contrast between water and oil
allowed ready identification of colloidosomes in which oil still remained.
82
Such oil-containing colloidosomes were not included in indentation and
breaking measurements. Colloidosomes adhered to glass cover slips during
sintering and remained fixed upon cooling and during microcantilever tests.
We observe that colloidosomes sintered 5 minutes usually indent
further before breaking than do colloidosomes sintered 150 minutes, with the
deformation localized in a small region around the microcantilever tip; this
area is typically larger for colloidosomes sintered 5 minutes than for
colloidosomes sintered 150 minutes. We expect that capsules should break
when the stress from indentation exceeds the bond strength among beads.
The maximum local tensile stress beneath the indenter tip scales with the
stiffness of the shell and is proportional to the indentation depth; since
colloidosomes sintered for a long time are stiffer than those sintered a short
time, larger deformation is seen before breaking less-sintered, more
compliant colloidosomes. Figure 3.1 shows colloidosomes sintered 5 and
150 minutes indented almost to the point of breaking.
83
Figure 3.1
Colloidosomes are indented by microcantilevers until just before breaking top: colloidosomes sintered 5 minutes; bottom: colloidosomes sintered 10
minutes. Capsules sintered 5 minutes typically indent more before breaking
than do those sintered 150 minutes. 10 µm scalebars.
84
For colloidosomes sintered 5 minutes, the deformed region often appears
similar to the ‘inverted cap’ form expected classically for the axisymmetric
indentation of a thin elastic shell with no internal pressure. When a thin,
hollow, elastic shell undergoes axisymmetric deformation by point
indentation like that applied by our microcantilevers, it will deform with a
geometry such that the indented curvature is spherical and very nearly the
mirror image of the original, undeformed shape76 (reference 12 in present
chapter), as shown in Figure 3.2. Such a shell’s indentation δ will scale
with the square of the force applied76. It is readily apparent from the
colloidosome indentation data shown in Figure 3.3 that such scaling does
not apply for these capsules. Furthermore, normalizing the indentation
depth to the colloidosome diameter does not collapse the data for the
different capsules, as would be expected if they were behaving as continuous
shells. This is so because surfaces of colloidosomes sintered for 5 minutes
are comprised of discrete beads only lightly joined. The continuum thin shell
theory does not apply to such porous capsules.
76
L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd edition
(Pergamon Press, New York, NY, 1986).
85
Figure 3.2
A thin elastic shell, under a concentrated radial force, has spherical
curvature, very nearly the mirror image of the unstrained shape, over most of
the deformed region. Indentation δ increases with the force squared.
86
Figure 3.3
Colloidosomes are indented until breaking. For colloidosomes sintered 5
minutes, indentation increases with force but does not show the quadratic
scaling with force expected for a classical thin, elastic shell. Distinct
symbols represent different colloidosomes within each graph. Normalizing
the indentation depth by the colloidosome diameter does not collapse the
data, a further indication that these capsules do not behave as thin elastic
shells. Representative subset of data shown.
87
Indenting colloidosomes sintered 5 minutes
8
7
indentation (µm)
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
force (µN)
indentation normalized to colloidosome size
indentation / capsule diameter
0.5
0.4
0.3
0.2
0.1
0.0
0
5
10
15
20
25
force (µN)
Figure 3.3 (continued)
88
30
35
40
Colloidosomes sintered for a very long time are better described by
the elastic thin shell theory than briefly-sintered colloidosomes because long
sintering times anneal the discrete beads comprising colloidosome surfaces
into a continuous shell, as seen in Figures 3.1 and 3.4. Such well-annealed
colloidosomes, sintered 150 minutes, do not indent as far before failure as do
those sintered 5 minutes. Normalizing indentation by colloidosome
diameter does noticeably collapse the data, as shown in Figure 3.5, which is
consistent with these structures behaving as continuous shells. However, for
none of these colloidosomes does indentation clearly depend on the square
of the force, and for a number indentation is quite far from quadratic in
force. This is expected because the deformation is not axisymmetric; the
indenting force is parallel to the adherent surface. This adhesion boundary
condition affects the indentation results significantly and classic thin shell
theory does not apply.
89
Figure 3.4
Colloidosomes have been sintered for 150 minutes and tested with a
microcantilever. TOP: A colloidosome with no visible defect sites is
broken to show a shell thickness of about 1 µm, in good agreement with the
polystyrene bead diameter. MIDDLE: A broken colloidosome with several
visible defects shows a wall thickness less than 1/3 µm at a defect site,
evidence that the stress-magnifying effects of defects should increase with
sintering time. BOTTOM: Two colloidosomes, one indented and one
broken, show deformation and failure as continuous shells.
90
Figure 3.4 (continued)
91
Figure 3.5
Colloidosomes are indented until breaking. For colloidosomes
sintered 150 minutes, indentation increases with force; distinct symbols
represent different colloidosomes within each graph. Normalizing the
indentation depth by the colloidosome diameter collapses the data
significantly, which indicates that these may be behaving more like
continuous shells than colloidosomes sintered 5 minutes. Nonetheless,
indentation does not show the scaling with the square of the force expected
classically for thin shells. Representative subset of data shown.
92
Indenting colloidosomes sintered 150 minutes
8
indentation (µm)
6
4
2
0
0
100
200
300
400
500
600
700
force (µN)
indentation / capsule diameter
indentation normalized to colloidosome size
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
100
200
300
400
force (µN)
Figure 3.5 (continued)
93
500
600
700
To analyze adhering colloidosomes, pinned to the glass cover slips,
three-dimensional finite element modeling is used based on the commercial
code ABAQUS. A modeled colloidosome with diameter 50 µ m is studied
with its bottom surface clamped to a rigid surface. A concentrated indenting
force parallel to the bottom surface is applied through the center of the
colloidosome shell. This modeled shell has a uniform thickness of 1µ m and
its elastic modulus is taken to be the same as that known for polystyrene,
3GPa . To take advantage of symmetry only half of the colloidosome is
taken into account. The finite element mesh consists of 6000 8-node
quadratic three-dimensional thin shell elements with reduced integration.
The deformed mesh agrees very well with experimental observation, as can
be seen by comparing Figure 3.6 with Figures 3.1 and 3.4. The indentation
load-displacement relationship obtained from the numerical simulation is
essentially linear and agrees with experimental measurements, as shown in
Figure 3.7; this confirms the observation that well-sintered colloidosomes
deform and break as continuous shells, not as assemblages of discrete beads.
94
Figure 3.6
Finite element simulation of an indented colloidosome, sintered for 150
minutes, which adheres to the rigid substrate. The colloidosome shell has a
diameter of 50 µ m , thickness 1µ m , and stiffness of 3GPa .
95
Figure 3.7
TOP: The normalized load-displacement relationship obtained from the
numerical simulation of the indentation of a well-sintered colloidosome
shows a linear dependence on force and agrees in magnitude with
experimental data for colloidosomes sintered 150 minutes (BOTTOM),
which show a near-linear dependence of indentation on force; distinct
symbols represent differerent colloidosomes. Discontinuities in the slope of
experimental data or significant deviations from linear scaling with force,
highlighted in data series shown with solid dots, are characteristic of
buckling. A representative subset of data is shown.
96
indentation / capsule diameter
Colloidosome indentation: finite element model
0.10
0.08
0.06
0.04
0.02
0.00
0
2
4
6
8
10
12
force / capsule diameter (µN/µm)
indentation / capsule diameter
Colloidosome indentation: experimental data
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
2
4
6
8
10
12
14
force / capsule diameter (µN/µm)
Figure 3.7 (continued)
97
16
For a few colloidosomes among those sintered 5 and 150 minutes, the
indenting microcantilever was withdrawn before the capsule broke. Upon
microcantilever withdrawal, colloidosomes did not return to their original,
undeformed shape, but remained dimpled; the bottom left image in Figure
3.4 shows an example. This permanent deformation is indicative of plastic
buckling, as are indentation data that show discontinuous jumps, as for the
three series shown by solid dots in Figure 3.7. Buckling is a geometric
nonlinear instability effect often triggered by small perturbations imposed on
the equilibrium state, when the compressive load applied on the structure
exceeds a certain limit. The buckling of shells requires and is very sensitive
to the distribution of defects, such as voids or non-uniform shell thickness,
which depend on the bead configurations and sintering conditions. Although
the critical buckling load can be obtained from the classic stability analysis
for a perfect thin elastic shell, it is generally difficult to model the postbuckling behavior of a thin shell with random defects.
The indentation measurements on colloidosomes sintered 5 and 150
minutes also include data on the force applied to break the colloidosomes.
To better evaluate how sintering time modifies colloidosome mechanical
strength, more colloidosomes were sintered for 10, 15, and 20 minutes and
the force to break them was measured using microcantilevers. The force
98
required to break the strongest colloidosomes increases with sintering time,
as Figure 3.8 data indicates. This is expected, since the critical force scales
with the stiffness of the shell, which should increase with sintering time. For
a given sintering time, grey symbols indicate another trial on a second batch
of colloidosomes with a different microcantilever, showing the
reproducibility of these measurements. Because colloidosomes sintered for
these times usually detach from the cover slip when indented from the side,
these colloidosomes were broken by microcantilevers pressing down from
above, along the direction of microscope objective focus, and indentation
was not observed; force applied was evaluated by assuming that the
microcantilever tip remained fixed and considering only the
micromanipulator-imposed deflection of the microcantilever base. Since the
largest indentation observed for colloidosomes sintered 5 minutes was less
than 10 microns and microcantilever bases were typically deflected by 50 to
100 microns, in increments of 10 microns, the breaking forces obtained by
this evaluation should be accurate to within 20 to 40 percent or less, since
colloidosomes sintered longer are expected to indent less before breaking.
99
Breaking sintered colloidosomes
900
force to break (µN)
800
Sintering time
5 minutes
10 minutes
15 minutes
20 minutes
150 minutes
700
600
500
400
300
200
100
0
0
20
40
60
80
100
120
140
160
sintering time (minutes)
Figure 3.8
The maximum force required to break or puncture colloidosomes increases
with sintering time. Some colloidosomes sintered for 150 minutes could not
be broken with any microcantilever attempted; data for these colloidosomes
is excluded from the graph.
100
The range of force required to break sintered colloidosomes also
increases for longer sintering times, as Figure 3.8 shows. This may result
from initial defects in bead distribution on the colloidosome surface
becoming more significant with respect to the defect-free rest of the
colloidosome. Colloidosomes can vary significantly in their amounts of
bead coverage and defects, as illustrated for the two colloidosomes in
Figure 3.9(top and middle), and as demonstrated by the buckling behavior
seen when shells are indented in Figure 3.7. Defects act to concentrate
stress, and should therefore dominate colloidosome breaking wherever they
are near the site of indentation. Indeed, it is known from elasticity that the
stress can be amplified by a factor of three on the edge of a hole in a thin
sheet under uniaxial tension. In addition, indentation produces localized high
tensile stresses in the vicinity of contact due to bending effects, since the
curvature of the shell at the indenter is much higher than that far away from
the contact area. Such high stress is further enlarged by the stress
concentration effect. When a critical stress level is exceeded, cracks will
initiate from the vicinity of defects and these cracks govern the failure of
colloidosomes. If such defects do not anneal away with sintering but are
instead magnified in some way, the resultant stress concentrations ought also
101
to be magnified and the spread in force required to break should therefore
increase, as observed. Figure 3.5(top and middle) shows colloidosomes
sintered 150 minutes and broken with a microcantilever. The top
colloidosome does not show any visible defect sites, and the colloidosome
wall thickness revealed by the break is slightly less than 1 µm, comparable
to the 1 µm beads used to make these colloidosomes. The middle
colloidosome shows several visible defects, and a magnified view of one
reveals a wall thickness of less than 1/3 µm at the defect site. This indicates
that at defect sites the wall thickness decreases as sintering time increases.
This magnifies the effect of the defect and therefore the spread in breaking
force.
102
Figure 3.9
TOP and MIDDLE: Colloidosomes vary widely in their surface bead
coverage and defects. BOTTOM: A colloidosome broken by a
microcantilever has failed by punching out discrete beads along the
perforated sintered connections. All three colloidosomes were sintered 20
minutes.
103
Figure 3.9 (continued)
104
Colloidosomes sintered short and long times have different failure
mechanisms. Colloidosomes sintered for short times and broken by a
microcantilever typically fail by punching out discrete beads along the
perforated sintered connections, as shown by the broken colloidosome in
Figure 3.9(bottom), which was sintered for 20 minutes. Outside of the
immediate area where the microcantilever tip punched through, the
colloidosome shell appears unaffected. Colloidosomes sintered 150
minutes, however, typically deform and break as continuous shells, as shown
in Figure 3.5. The contrast between these two failure mechanisms is also
shown in Figure 3.10, which normalizes the force required to break
colloidosomes by the square of the colloidosome diameter, typically 20-50
µm. While the range of breaking force is somewhat increased for
colloidosomes sintered for shorter times, it is noticeably collapsed for longer
times. This indicates that the force required to break well-sintered
colloidosomes is size-dependent, an indication that they are behaving as
continuous structures. On the other hand, the force needed to break more
lightly-sintered shells is only governed by the bonding between discrete
beads and is therefore size-independent, since this bonding is unaffected by
the structure or its deformation.
105
1.2
1.0
2
µN/(µm )
force to break / (capsule diameter)
2
Breaking sintered colloidosomes
normalizing breaking force to capsule diameter2
Sintering time:
5 minutes
10 minutes
15 minutes
20 minutes
150 minutes
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
120
140
160
sintering time (minutes)
Figure 3.10
When the force required to break colloidosomes is normalized by the square
of the colloidosome diameter, the range of breaking forces is slightly
magnified for short sintering times but collapses significantly for the longest
sintering time. This size-dependence indicates that colloidosomes sintered
150 minutes are breaking as continuous shells, whereas those sintered
shorter times are not.
106
The range of force required to break colloidosomes sintered a given
time is reproducible among different batches of colloidosomes, sintered
separately, measured with different microcantilevers. This demonstrates that
sintering, in addition to modifying colloidosome shell porosity, is a robust
method for tuning colloidosome mechanical strength. The trend toward
greater variance in the breaking force for colloidosomes sintered longer
times results from defects in the initial bead coverage of the templating
interface, which do not anneal away with sintering. For very long sintering
times, the capsules no longer behave as though they are composed of
discrete beads, but instead they deform and break as continuous structures,
which can be modeled using finite element analysis in agreement with
observation and with what is known from these structure’s fabrication ab
incepto.
REFERENCES
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M. F. Hsu et al., manuscript in preparation
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L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd edition
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108
Chapter IV
Engineering the formation of complex structures from diblock
copolymers
A. T. Nikova1, V. D. Gordon1, G. Cristobal-Azkarate1, M. R. Talingting2, D.
C. Bell3, C. Evans4, M. Joanicot2, J. Zasadzinski4, and D. A.Weitz1
1
Department of Physics and Division of Engineering and Applied Sciences,
and 3 Center for Imaging and Mesoscale Structures, Harvard University,
Cambridge, MA; 2 Complex Fluids Laboratory, Rhodia Inc., Cranbury
Research and Technology Center, Cranbury, NJ; 4 Department of Chemical
Engineering, Univ. of California Santa Barbara
We fabricate novel structures, stuffed vesicles and multiple emulsions,
from amphiphilic diblock copolymers in water by swelling the hydrophobic
parts of self-assembled aggregates with hydrophobic homopolymer.
Without homopolymer, the copolymer used forms micelles, but the system
incorporates homopolymer to form complex structures via a one-step
rehydration process. Stuffed vesicles incorporate varying amounts of
homopolymer to achieve different membrane thicknesses; this could allow
tuning membrane properties. Incorporating more homopolymer, multiple
emulsions are fabricated in one process step using a single surfactant. These
results indicate a novel strategy for preparation of self-assembled materials
with controllable properties from macromolecules.
109
In solution, amphiphilic molecules can self-assemble into a rich array
of intriguing and useful structures. The most widely studied and the most
important are in an aqueous continuous phase; these are the most
intrinsically bio-compatible, a quality essential for many encapsulation and
delivery applications. A vesicle encloses an internal aqueous space in one or
more bilayers of amphiphilic molecules; vesicles are important for
fundamental research as models for cell membranes and in technology as
encapsulants for drugs and other biomolecules. A multiple emulsion
contains internal aqueous droplets within the hydrophobic walls of a larger
sphere; multiple emulsions are of strong technological interest for
encapsulation and extended release of hydrophobic and hydrophilic
substances. A micelle encloses a hydrophobic region within an aqueous
environment via a spherical monolayer of amphiphiles with core-directed
hydrophobic groups; micelles are of interest for solubilizing hydrophobic
substances in water and encapsulating nonaqueous contents for delivery in
aqueous media.
Encapsulation and release require structures with well-characterized,
and preferably controllable, stability, permeability and mechanical strength.
Structures formed from small amphiphiles, such as lipids and surfactants, are
widely used. Additional structure versatility can be achieved by using
110
diblock copolymers, which have great varieties of possible molecular
architectures, block chemistry, and molecular weights. Diblock copolymer
vesicles are much tougher than their lipid counterparts77 (reference 1, present
chapter), and both membrane thickness and stability scale with the molecular
weight78 (reference 2, present chapter). Moreover, the properties of the
polymer membrane can be further modified by cross-polymerizing the
membrane79 (reference 3, present chapter). Diblock copolymer systems
offer an additional yet hitherto unexplored advantage: hydrophobic
homopolymer can be used as a building block to engineer new, more
versatile structures. As such homopolymer is incorporated into hydrophobic
regions of self-assembled structures it can modify membrane thickness and
generate new morphologies.
In this paper, we demonstrate the novel structures that can be achieved
with diblock copolymers in combination with additional hydrophobic
homopolymer. The homopolymer is incorporated, or “stuffed” within the
bilayer of vesicle membranes, thereby increasing the wall thickness. When
77
B. M. Discher, Y. Y. Won, D. S. Ege, et al., Science 284, 1143 (1999).
78
H. Bermudez, A. K. Brannan, D. A. Hammer, et al., Macromolecules 35,
8203 (2002).
79
B. M. Discher, H. Bermudez, D. A. Hammer, et al., Journal of Physical
Chemistry B 106, 2848 (2002).
111
more homopolymer is incorporated into structures, multiple emulsions form.
These structures contain several small drops of water within a larger sphere
of hydrophobic polymer, stabilized by the diblock. This is a new method for
fabricating multiple emulsions, requiring only a one-step process and a
single macromolecular surfactant. Stuffed vesicles and multiple emulsions
represent a new class of self-assembled aggregate. Such structures have
high potential for increased control of structural properties and for adaptable
and controlled encapsulation and release of both hydrophilic and
hydrophobic active agents.
We use polybutyl acrylate : polyacrylic acid (PBA:PAA) synthesized
by Madix radical polymerization. The two blocks determine the amphiphilic
character of the macromolecule: PAA is hydrophilic and PBA hydrophobic.
The homopolymer used for “stuffing” is polybutyl acrylate (hPBA), which is
chemically identical with the hydrophobic part of the diblock. The glass
transition temperature, Tg, for the PBA is -40°C, which makes selfassembled structures soft at room temperature. The molecular weight of the
diblocks is 15,000 g/mol. We prepare the self-assembled structures using
two different techniques, powder dispersion in water and film rehydration,
analogous to techniques commonly used for preparing phospholipid selfassemblies. To prepare samples by dispersion, water or a 1% aqueous
112
solution of tetrahydrofurane (THF) is added to a freeze-dried polymer
powder to achieve a final polymer concentration of 0.5-1%. The sample is
mixed by vortexing. To prepare a film for rehydration, stock solutions of
PBA:PAA and hPBA are prepared in tetrahydrofurane (THF) at
concentrations 5mg/ml and mixed at varying compositions of hPBA; we
form thin films by pipetting 25µL of each solution into a glass vial and
evaporating the solvent. These films are then rehydrated with 250 µL
deionized water under bubbling nitrogen for 1 hour. The structures of the
films to be rehydrated are evaluated by small-angle X-ray scattering (SAXS)
and observation of film birefringence80 (reference 4, present chapter). SAXS
was performed at the UPenn MAXS (generating up to 4.0 kW x-ray) in
LRSM facility, which can measure d-spacing as low as 50 Angstroms at a
sample-to-detector distance of 126 cm. Scattering intensity I is measured as
a function of varying scattering vector q. For a film of 70:30 PBA:PAA, the
plot of I(q) versus q is shown in Figure 4.1 with a fit to a spherical form
factor P(q).
P(q ) =
80
[sin(q * R) − (q * R) * cos(q * R)]
(q * R)
6
M. Freluche, (Rhodia, Inc., Cranbury, NJ, 2001).
113
2
where R is the radius of the sphere calculated to be 110 Å. The positions of
the first and second order peaks is close to inverted cylinders with peaks at
q* ratios of 1:√3 made of hydrophilic PAA cores in a hydrophobic PBA
continuous phase. It can be argued as inverted spheres, however, these films
exhibit birefringence, implying a presence of anisotropic structures of
cylinders. On the other hand, scattering intensities for films of symmetrical
diblocks 50:50 PBA:PAA and 60:40 PBA:PAA, seen in Figure 4.2, show
peaks at q ratios 1:2, indicative of lamellar morphologies.
114
10000
I (q )
1000
100
10
1
0.001
0.01
0.1
1
-1
q , Angstrom
Figure 4.1
For a film of 70:30 PBA:PAA, scattering intensity I is measured as a
function of scattering vector q using small-angle x-ray scattering. Measured
intensity is fit to a spherical form factor, but observed birefringence is
indicative of an inverted cylinder structure in the film.
115
100
1
10
2
1
60/40, x10
2
q x I(q)
1
2
50/50
0.1
0.01
0
0.02
0.04
0.06
0.08
-1
q, A
Figure 4.2
Small-angle x-ray scattering data for films of symmetrical diblocks 50:50
PBA:PAA and 60:40 PBA:PAA. The peaks at q ratios 1:2 indicate that
these films have a lamellar structure, unlike 70:30 PBA:PAA films.
116
The structure of the films is directly reflected in the structure of the
aggregates formed upon rehydration. Rehydration of a film of 50:50 diblock
with no homopolymer leads exclusively to micelles, imaged by transmission
electron microscopy in Figure 4.3; micelles also form when a powder of
symmetric 50:50 diblocks is dispersed in water [Cristobal-Azkarate et al,
manuscript in preparation].
117
100 nm
FIGURE 4.3
TEM imaging of a sample made by rehydrating 50:50 PBA:PAA from a film
into dilute aqueous solution shows micelles.
100 nm
118
In contrast, we observe vesicle formation upon rehydration of films of
70:30 PBA:PAA diblock with no homopolymer. We furthermore find that
much larger vesicles, up to tens of microns in diameter, are formed by
dispersing a powder of 70:30 PBA:PAA in aqueous solution with 1% THF.
To investigate the mechanical properties of these large vesicles, we employ
micropipette aspiration81 (reference 5, present paper); an example of such a
vesicle being aspirated is shown in Figure 4.4. Aspiration directly probes
the mechanical resilience of vesicles; the change in length of the vesicle
region aspirated into the micropipette, ∆L, is proportional, to first order, to
the change in area of the vesicle, ∆A. The diameters of the micropipette, Dp,
and vesicle, Dv, determine the tension τ at any given applied aspiration
pressure P:
∆A ≈ πD p (1 − D p / Dv )∆L
PD p
τ = 4(1− D / D )
p
v
The aspiration-induced membrane areal strain increases linearly as a
function of increasing membrane tension, as shown in Figure 4.5. The
inverse slope of this data provides a measure of the areal expansion
81
K. Olbrich, W. Rawicz, D. Needham, et al., Biophysical Journal 79, 321
(2000).
119
modulus, which is about 1000 mN/m. Vesicles are aspirated until failure
and the rupture tension ? is found to be about 40-60 mN/m; the areal strain at
rupture is about 5%. This areal expansion modulus is an order of magnitude
greater than for PEO:PEE and lipid vesicles and this rupture tension is about
twice that of PEO:PEE polymersomes and 5-10 times that of typical lipid
vesicles. However; PBA:PAA vesicles rupture at an areal strain of about 45%, much less than the critical areal strain of about 20% at which PEO:PEE
vesicles rupture but comparable to values found for lipid vesicles. Recent
studies of polymer vesicle elasticity and stability indicate the onset of chain
entanglement effects at molecular weights higher than 10000 g/mol. The
PBA:PAA diblock studied here has molecular weight 15,000 g/mol, so the
low critical strain for PBA:PAA vesicles may result from chain
entanglement of the hydrophobic regions of the diblock aggregates. To
investigate 70:30 PBA:PAA vesicles further we use electron microscopy to
examine vesicle cross-sections. Such vesicles made by powder dispersion
show a membrane thickness of ~50 nm to cryogenic transmission electron
microscopy (cryo-TEM), as Figure 4.6 (A) shows. Freeze-fracture electron
microscopy provides additional evidence that such structures are indeed
hollow vesicles, as shown in Figure 4.6 (B) for a vesicle made by film
rehydration.
120
10 mm
FIGURE 4.4
Vesicles made by dispersing a powder of 70:30 PBA:PAA in water are
aspirated into micropipettes to measure membrane mechanical response.
121
70:30 PBA:PAA vesicles aspirated until failure
membrane tension
(mN/m)
50
25
0
0.00
0.01
0.02
0.03
0.04
0.05
areal strain
α = ∆A/A0
Figure 4.5
Via micropipette aspiration, we measure the areal expansion of the 70:30
PBA:PAA vesicle membrane a = ? A/A0 as a function of the membrane
tension. Distinct symbols represent different vesicles. The expansion
modulus, Ka= ? t /? a, is approximately 1000 mN/m.
122
A
B
200 nm
200 nm
FIGURE 4.6
(A) Vesicles made by dispersing 70:30 PBA:PAA powder in water show a
membrane thickness of ~50 nm when examined by cryogenic transmission
electron microscopy. (B) Freeze-fracture electron microscopy of a 70:30
PBA:PAA vesicle made by film rehydration shows additional evidence that
these structures have a hollow interior.
123
Attempts, using film rehydration, to stuff the hydrophobic portion of
the 70:30 PBA:PAA bilayer with hPBA and form a thicker vesicle
membrane are unsuccessful, possibly because of macrophase separation of
the homopolymer from the diblock. However, when films formed with
50:50 PBA:PAA and hPBA are rehydrated we find larger structures, vesicles
and multiple emulsions, as well as smaller swollen micelles. These larger
structures are visible to optical microscopy but we require electron
microscopy to image swollen micelles, as done in Figure 4.7.
124
A
0.5 µm
B
0.5 µm
FIGURE 4.7 – TEM images of 5% (A) and 20% (B) hPBA samples
TEM images of samples made by rehydrating a polymer film composed of
50:50 PBA:PAA copolymer with 5% (A) and 20% (B) homopolymer PBA.
These samples are characterized by polymer globules, which appear to be
micelles swollen with hPBA.
125
The high number density of swollen micelles seen in samples
examined by cryo-TEM suggests that most of the homopolymer is
emulsified into such micelles. To confirm this, we prepare samples by
rehydrating a film made with fluorescently tagged hPBA and use fluorimetry
to measure sample fluorescence; the integrated fluorescence signal is
proportional to the amount of homopolymer present. We then pass samples
through a series of membrane filters, with smaller pores in each successive
filter. We perform fluorimetry after each filtering pass. The falloff in
fluorescence with filtering indicates that most of the homopolymer is
incorporated into structures between 100 nm and 800 nm in size. This
agrees with the size indicated for swollen micelles by TEM images.
Samples prepared with 5% and 20% hPBA show very similar decreases in
intensity with decreasing filter pore size, indicating that micelle size does
not vary significantly with the total homopolymer content of these samples.
We also performed dynamic light scattering on such samples at different
scattering angles; cumulant analysis indicates sizes and polydispersity in
agreement with fluorimetry and TEM. The preponderance of such swollen
micelles demonstrates that hPBA, a hydrophobic polymer, has been
solubilized in water by the 50:50 diblock; samples incorporating fluorescent
126
hPBA also allow observation of a very few microns-sized globes of
homopolymer without visible internal droplets.
Even more intriguing than swollen micelles, qualitatively distinct
structures are revealed by optical microscopy of samples prepared by
rehydrating a film containing hPBA. These structures, a few microns in
size, are vesicles, shown in Figure 4.8, and multiple emulsions, shown in
Figure 4.9. To probe these larger structures’ morphologies we use
fluorescence microscopy, rehydrating a film with aqueous solution of the
fluorescent dye Dextran-Texas Red (10K, Molecular Probes Inc.). This
allows us to visualize the encapsulated phase. After structures form,
encapsulating water and dye, the fluorescence signal from the bulk aqueous
phase is then eliminated by addition of a quencher (anti-Texas Red,
Molecular Probes Inc.). For many structures the entire interior fluoresces,
evidencing that these structures are vesicles, nonpermeable to the quencher.
127
Figure 4.8
Fluorescent images of vesicles formed by rehydrating films composed of
50:50 PBA:PAA with fluorescently tagged hPBA confirm that the
homopolymer is incorporated into the membrane and that the amount
incorporated can vary between vesicles.
128
A
B
C
FIGURE 4.9
(A) A multiple emulsion drop is formed by rehydrating a film composed of
50:50 PBA:PAA and additional hPBA. (B) A multiple emulsion formed in
water containing fluorescent dye shows internal droplets enclosing
fluorescent water after quencher is added to the continuous aqueous phase.
(C) A multiple emulsion formed from a film incorporating fluorescently
tagged hPBA shows that the homopolymer is incorporated into the structure.
129
As the amount of homopolymer incorporated into structures increases,
qualitatively new structures are observed - multiple emulsions, such as the
ones shown in Figure 4.9. When these structures are prepared by
rehydrating with fluorescently dyed water and quencher is then added to the
aqueous bulk phase, discrete droplets fluoresce within a larger nonfluorescent structure, as seen in Figure 4.9 (B). This indicates that these are
indeed aqueous droplets and that the structure is not permeable to the
quencher.
To investigate the membranes and walls of stuffed vesicles and
multiple emulsions, we rehydrate films made with fluorescently tagged
hPBA using nonfluorescent water. Vesicles made in this way have
fluorescent membranes, confirming that the hydrophobic homopolymer is
incorporated into the membrane bilayer. Moreover, different amounts of
hPBA are incorporated into different vesicles, varying the vesicle membrane
thickness as the vesicles imaged in Figure 4.8 illustrate.
Multiple emulsions prepared by rehydrating a film made with
fluorescently tagged hPBA show fluorescence only from the multiple
emulsion walls and no fluorescence from the entrapped internal droplets, as
in Figure 4.9 (C). This is additional evidence that the multiple emulsion
130
structure incorporates homopolymer into the hydrophobic regions of its
walls but not into the interior droplets.
Our results present a novel type of macromolecular self-assembled
structure with potentially tunable properties, including a novel one-step
method for forming multiple emulsions with a single surfactant. Varying
amounts of incorporated homopolymer observed in vesicles and multiple
emulsions indicates that it should be possible to develop techniques for
fabricating such structures that can control membrane thickness, tuning
mechanical response, permeability, thermal stability, and other properties as
may be required for particular technological applications.
References
1
B. M. Discher, Y. Y. Won, D. S. Ege, et al., Science 284, 1143
(1999).
2
H. Bermudez, A. K. Brannan, D. A. Hammer, et al., Macromolecules
35, 8203 (2002).
3
B. M. Discher, H. Bermudez, D. A. Hammer, et al., Journal of
Physical Chemistry B 106, 2848 (2002).
131
4
N. Garti and C. Bisperink, Current Opinion in Colloid & Interface
Science 3, 657 (1998).
5
J. N. Israelachvili, Intermolecular and surface forces (Academic
Press, London; San Diego, 1992).
6
D. F. Evans and H. Wennerstrom, The Colloidal Domain: where
physics, chemistry, and biology meet (Wiley-VCH, New York, 1999).
7
D. E. Discher and A. Eisenberg, Science 297, 967 (2002).
8
B. M. Discher, D. A. Hammer, F. S. Bates, et al., Current Opinion in
Colloid & Interface Science 5, 125 (2000).
9
L. F. Zhang, K. Yu, and A. Eisenberg, Science 272, 1777 (1996).
10
L. Desbaumes and A. Eisenberg, Langmuir 15, 36 (1999).
11
A. Choucair and A. Eisenberg, European Physical Journal E 10, 37
(2003).
12
K. Olbrich, W. Rawicz, D. Needham, et al., Biophysical Journal 79,
321 (2000).
132
Appendix A
Reprinted with permission from The Journal of Chemical Physics 113(13), 2000,
pp 5311-5320. Copyright 2000, American Institute of
Physics
133
134
135
136
137
138
139
140
141
142
143
Appendix B
Reprinted with permission from The Astrophysical Journal, 540, 2000 September
1, pp 286-291. Copyright 2000 The American Astronomical Society.
144
145
146
147
148
149
150
Appendix C
Reprinted with permission from The Astrophysical Journal Supplement, 134,
2001 June, pp 311-317. Copyright 2001 The American Astronomical
Society.
151
152
153
154
155
156
157
158
Appendix D
Reprinted with permission from The Astrophysical Journal Supplement, 138, 2002 February,
pp 297-303. Copyright 2002 The American Astronomical
Society.
159
160
161
162
163
164
165
166
Appendix E
Morphology and Mechanical Properties of Self-Assembled Shells
Composed of Polystyrene Particles
Ming F. Hsu, M. G. Nikolaides*, A. D. Dinsmore†, A. R. Bausch* and D.
A. Weitz
V. D. Gordon, X. Chen, and J. W. Hutchinson (precise author ordering
TBD)
Department of Physics and DEAS, Harvard University, Cambridge, MA
02138
(DRAFT 7/1/03)
† current address: Department of Physics, University of Massachusetts,
Amherst, MA 01003.
* current address: Lehrstuhl für Biophysik – E22, Technische Universität
München, 85747 Garching, Germany.
We create spherical shells of colloidal particles by selfassembly onto emulsion droplet templates. By choosing the
appropriate organic/aqueous solvent interface, we control the
particle-particle interactions at or near the interface to create
shells with a range of distinct morphologies and mechanical
properties: soft to rigid; single- to multi-layered; crystalline to
disordered.
To enhance mechanical stability, we reinforce
some shells through polymer adsorption and sintering before
removing the droplet interface. We remove droplet interfaces
by replacing the exterior fluid with a fresh solvent that is
miscible with the interior fluid, minimizing disturbance or
dilution of the encapsulant while allowing selective exchange
between the interior and exterior regions of the shells.
Quantitative characterization of mechanical properties is
167
attained from analysis of shell response to deformation by
calibrated microcantilevers.
1. Introduction
Assembly of particles onto emulsion droplet interfaces1-8 is a simple and
straightforward way to make structures with a wide range of interesting
properties. The mobility of the particles at the droplet interface can allow
formation of equilibrium structures, and the interface itself can modify the
interactions among particles, thus influencing the final structure.
Interactions9-11, ordering12, and emulsion-stabilizing properties13-15 of
particles adsorbed at interfaces have been studied. Recent experiments have
investigated long-ranged interparticle attraction16-18 and defects in the
packing of spheres on curved 2D surfaces19. The suitability of these
structures for encapsulation and delivery via selective permeability has
recently been demonstrated7. In some cases, charge on the surfaces of the
particles and droplets is used to direct assembly2-6. Here we discuss shells in
which particles are held at the emulsion droplet interface by minimization of
total interfacial energy9. We investigate a number of chemically distinct
solvent combinations and find that the interaction among adsorbed particles
varies due to differences in the relative strengths of electrostatic, steric, and
168
van der Waals forces. By controlling particle-particle interactions at or near
the interface through choice of solvent combination, we present a general
method of producing shells with a range of morphologies and mechanical
properties: soft to elastic; single- to multi-layered; crystalline to disordered.
We facilitate selective exchange between shell interior and exterior by
replacement of the exterior solvent with a fresh solvent that is miscible with
the interior, which removes the droplet interface while minimizing
disturbance or dilution of the encapsulant. Addition of co-solvent2-4,
centrifugation, and drying7 are interface removal techniques that each have
broad applicability. However, some shell types require additional
reinforcement in order to survive interface removal. We investigate the
stability of shells of different morphologies, as well as those reinforced by
sintering20-21 and polymer adsorption5-6, by observing response to interface
removal and deformation by calibrated microcantilevers.
2. Experimental Section
Materials.
Aqueous suspensions of polystyrene particles are
purchased from Interfacial Dynamics Corporation (IDC). Divinylbenzene
cross-linked particles 1.3 and 0.5µm in diameter with carboxyl surface
charge groups (DVB carboxyl particles) are used, along with biotin-coated
169
1.1µm-diameter particles with aldehyde sulfate surface charge groups
(aldehyde sulfate particles). Prior to being used, the contents of the bottle
are re-dispersed by vortexing for a few seconds and then cleaned as
described in the following Methods section.
The 1-octanol, toluene,
dodecane, glycerol (all 99% pure), dimethyldichlorosilane, TWEEN20, and
SPAN80 are purchased from Aldrich and not subject to further purification
before use. The silicone oil (Fluka, 10836), ethanol (200 proof, Pharmco),
acetone (Baker) and poly-L-lysine 0.1% w/v aqueous solution (Sigma,
P8920) are also used as obtained from the manufacturers. The de-ionized
water used for the experiments is purified by a Millipore Milli-Q system.
Wesson vegetable oil is filtered with a 0.45µm-pore hydrophobic syringe
filter prior to use.
Methods. Emulsion droplets are used as templates whose size and shape
control the overall size and shape of the shell. Figure E.1 outlines the
general principles of shell fabrication.
Fluid to be encapsulated is
introduced to particles suspended in an immiscible exterior fluid. Droplets
are formed by a gentle continuous shearing for several seconds (E.1a).
Particles adsorb at the interface to minimize total interfacial energy7-9,
forming a shell (E.1b). In some cases, particles are locked together at this
170
point via van der Waals forces, polycationic adsorption, or sintering in order
to strengthen the shell. The liquid interface is then removed via replacement
of exterior fluid: centrifugation7 or addition of co-solvent2-4 followed by
drying7. This step is important to facilitate selective exchange between
interior and exterior regions of the shell while minimizing disturbance or
dilution of the encapsulated droplet fluid (see Fig E.1c).
171
a
droplet
phase
b
droplet
phase
continuous
phase
c
droplet
phase
continuous
phase
continuous
phase
droplet phase
Figure E.1
Schematic illustration of shell fabrication process. (a) Emulsion droplets are
introduced to particles suspended in the continuous phase. (b) Particles
adsorb onto the interface to minimize total interfacial energy, forming a
shell. (c) Shell is transferred to droplet phase solvent (centrifugation
shown), effectively removing the interface and creating a free-standing,
porous shell. Not all particle shell types survive this step.
172
Particle suspensions are prepared in volumes of a few mL at volume
fractions of about 10-3 in 4mL glass vials with teflon-lined caps. To prepare
the aqueous particle suspensions, the original suspensions are cleaned by
repeating the following series of steps: dilution with de-ionized water,
sonication for 10 minutes (Aquasonic 50HT, VWR), centrifugation for 30
minutes at 800*g, and removal of the supernatant. De-ionized water is then
added to provide the desired volume fraction. To fabricate the non-aqueous
particle suspensions, water is first removed from the original suspension by
repeating the following series of steps: dilution with ethanol, sonication,
centrifugation, and removal of the supernatant. The above steps are then
repeated with octanol (in order to remove ethanol) to create a suspension of
about 1vol% of particles in octanol.
The suspension is completed by
diluting the octanol-particle solution 1:10 with the desired non-aqueous
solvent (octanol, dodecane, toluene, etc.).
Preparation of the particle shells begins by adding about 1µL of droplet
solvent to 200µL of particle suspension in a glass vial and vortexing for 5-10
seconds.
Particle shells typically form less than a few seconds after
agitation.
In the case of shells with polyelectrolyte adsorbed from the
interior fluid, we typically wait at least an hour following agitation before
proceeding. Sintering is done by heating shells of aldehyde sulfate particles
173
in solution in an oven at 105°C. To prevent boiling, the solution is diluted
with glycerol to make a solution with 70:30 glycerol/water by weight.
Polycation- and van der Waals-stabilized shells are transferred by
centrifugation to a fresh solvent that is miscible with and of smaller mass
density than the interior fluid. Since the particles have a greater mass
density than that of the solvents used, the shells are dragged downward into
the fresh exterior solvent. Polycation-stabilized shells formed in toluene are
first re-suspended in octanol, then transferred by centrifugation into water
containing 10 mg/mL Tween 20. Coated water droplets formed in silicone
oil are transferred by centrifugation into silicone oil of lower density
containing 1 mg/mL Span 80.
Transfer is accomplished by placing
approximately 1mL of surfactant solution in a 1.4mL centrifuge tube, then
adding about 100? L of solution containing particle shells on top. The tube
is then centrifuged at 9300gs for 10-15 min.
Solvent exchange by addition of co-solvent is done by transferring
approximately 100µL of solution containing particle shells into a few mL of
ethanol, which is miscible with all of the solvents used here. Drying is
accomplished by first immersing the shells in ethanol and then drying in air
for about one day.
174
To evaluate the effects of shell stabilization on mechanical response,
shells
are
incrementally
indented
and
broken
with
calibrated
microcantilevers controlled by a hydraulic micromanipulator and observed
via optical microscopy.
Microcantilevers are made by pulling glass
capillaries and rods in a micropipette puller (Flaming/Brown Micropipette
Puller P-97, Sutter Instruments) and calibrated with an analytical balance.
Microcantilever tips are hemispherical and small compared to particle shells.
For each trial, the microcantilever tip is initially positioned to lightly touch
the shell and then the microcantilever base is advanced incrementally; the
deflection of the microcantilever, and thus the force applied, is determined
from the difference between the observed displacement of the tip and the
known advancement of the base (cf Chapters 2 and 3). Shells sintered for
10-30 minutes usually detach from the cover slip when indented from the
side and are instead broken by pressing along the viewing direction,
obscuring microcantilever tip displacement measurement and resulting in a
force measurement uncertainty of about 40%.
Samples are examined by optical microscopy (Leica DMIRB,
transmitted illumination) and scanning electron microscopy (LEO 982).
Optical microscopy samples are imaged in glass sample chambers. When
observing soft shells encapsulating aqueous droplets, we use sample
175
chambers treated with dimethyldichlorosilane to minimize droplet wetting.
Images are obtained by using a digital CCD camera (Hammamatsu C474295) and saved onto a PC. Most images are obtained using 63x/0.70 air and
100x/1.40 oil objectives.
Sample preparation for scanning electron
microscopy consists of drying the shells on a coverslip, sputter-coating with
a 2-3 nm layer of gold, and imaging at 3keV.
3. Results and Discussion
Spontaneous adsorption of particles onto the droplets is driven by total
interfacial energy minimization7-9.
Particles assemble onto the droplet
interface provided that surface energy gained from the elimination of fluid
interface exceeds the energy required to replace particle-exterior fluid
interface with particle-interior fluid interface. That is, adsorption will be
energetically favorable if σi,e > |σp,i-σp,e|, where σi,e, σp,i, and σp,e are the
interior fluid-exterior fluid, particle-interior fluid, and particle-exterior fluid
surface energies, respectively22. If this condition is satisfied and there is no
aggregation in suspension, then particle monolayers form at the droplet
interface.
We have never observed a self-assembled particle thermally
176
desorb from the interface, indicating that the adsorption energy is much
larger than kBT, as expected9. Many of the emulsion droplets are completely
covered. Each batch results in approximately 103 particle shells ranging
from 10-200 µm in radius, the properties of which depend on solventdependent interparticle interactions.
3.1. Shell Morphology as a Function of Particle Stability
Stability of particle suspensions depends on the sum of electrostatic,
steric, and van der Waals forces between particles within a specific solvent2324
.
Polystyrene particles are stable in water because of electrostatic
repulsion25 and are stable in toluene, chlorobenzene and other good solvents
due to steric repulsion26, reduced van der Waals attraction, and possible
electrostatic repulsion23-24,27. Although particles always originate from the
exterior phase in this study, particle stability in the interior phase is also
significant. Shells assembled onto droplet interfaces composed of solvents
in which polystyrene particles are either stable or unstable exhibit different
morphologies and mechanical properties as shown in Figure E.2.
177
a
b
10µm
c
10µm
d
10µm
Figure E.2: The stability of particle suspensions in the solvent combinations
used influences particle shell type, shown in optical micrographs. Although
particles always originate from the continuous phase in this study, particle
stability in the droplet phase is also significant. (a) Particles are stable in
both droplet and continuous phases (water in toluene), yielding soft,
crystalline monolayers. (b/c) Particles are stable in toluene/water but selfassemble onto a droplet of polycation solution/vegetable oil, in which they
are unstable, resulting in rigid, polycrystalline monolayers. (d) Particles are
unstable in the continuous phase (water droplets in dodecane), resulting in
rigid, disordered multilayered shells. Shells are composed of either 1.0mm
DVB carboxyl (a), 0.5mm DVB carboxyl (b and d), or 1.1mm aldehyde
sulfate (c) polystyrene particles.
178
10µm
Interactions between particles adsorbed at a droplet interface also include
electrostatic and steric repulsion, along with van der Waals attraction.
However, the mismatch in dielectric constants of adjacent fluids can result in
asymmetric particle charging, creating an electrostatic repulsion between
effective dipoles9,12,28. There may also be an additional capillary attraction
induced by deformation of the fluid interface near the particles16-18.
Capillary attraction induced by gravity is not relevant here because of the
small size of the particles and the presence of solvents of similar mass
density10.
Soft Monolayers.
In a system of water droplets in toluene and/or
chlorobenzene, DVB carboxyl particles (stable in all three solvents) selfassemble to form soft, monolayered shells with nearly perfect crystalline
order19. The particles undergo thermal motion in the plane of the interface,
and the vast majority are dispersed as shown in Figure E.2a. Absence of
aggregation at the droplet interface enables particles to rearrange into singlecrystal monolayers.
Polycrystalline/Nearly Crystalline Monolayers. When DVB carboxyl
particles in toluene adsorb onto droplets of poly-L-lysine solution,
179
polycrystalline monolayered shells form. The particles are rigidly locked
together (Figure E.2b). Crystalline monolayers with regions of disorder are
obtained by assembly of aldehyde sulfate particles from water onto
vegetable oil (Figure E.2c) or silicone oil droplets. In all of these cases, the
particles are stable in the exterior solvent but aggregate in the interior
solvent.
Attractive interparticle forces are substantial and prevent
rearrangement into single-crystalline monolayers.
We have made shells corresponding to those in Figures E.2b-c with
greater agitation intensity and observed that the shells are non-spherical,
demonstrating that the shells are not only rigid, but also strong enough to
counterbalance oil-water surface tension stresses.
Disordered Multilayers.
Suspending DVB carboxyl particles in
dodecane and self-assembling onto water results in shells consisting of
disordered, multiple layers (Figure E.2d). Because particles are unstable in
the exterior phase, they either adsorb at the droplet interface as aggregates or
adhere to particles already at the interface, preventing rapid rearrangement
into locally crystalline order and accounting for the observed morphology.
We have also observed nonspherical shells when we apply greater agitation
intensity during fabrication.
180
3.2 Effects of Shell Reinforcement on Morphology
In addition to enhancing stability, polycation adsorption and sintering
greatly alter shell morphology. Adding poly-L-lysine to water-in-toluene
droplets stabilized by DVB carboxyl particles transforms soft, crystalline
shells (Figure E.2a) into relatively rigid, polycrystalline shells (E.2b) in
which particles are locked together by physisorbed polycations. Figure E.3
shows how aldehyde sulfate particle shells, initially stabilized only by van
der Waals attraction (E.2c), become smoother and less porous with
increasing sintering time. Interstitial pores are visible in most shells sintered
for five minutes (E.3b) and some shells sintered for 10 minutes, but pores
are closed in almost all shells sintered for 20 minutes (E.3c). After 2 hours
of sintering, individual particles are almost indistinguishable (E.3d),
indicating near-completion of the sintering process.
181
a
b
5µm
Figure E.3:
c
2µm
d
10µm
10µm
Effect of sintering time (105°C) on morphology of dried
particle shells. SEM images show that unsintered shells made of 1.1mm
aldehyde sulfate beads collapsed upon drying (a). After sintering for five
minutes, the shells survived drying (b). Interstitial pores gradually disappear
upon sintering for longer times, as shown in (c) and (d), which were sintered
for 20 minutes and two hours, respectively.
182
3.3. Shell Stability against Interface Removal
An important requirement for capsules is to allow diffusive exchange
across the shell surface while maintaining structural integrity. That is, the
shell must be structurally stable upon removal of the droplet interface.
Though addition of a co-solvent is the simplest method of exterior fluid
replacement, centrifugation can be essential if encapsulants include
biological cells, for which common co-solvents such as ethanol are toxic.
Drying can be of interest in applications where rehydration after extended
periods of storage time is desirable. We investigate the effectiveness of
various solvent replacement methods as well as sintering and polycation
adsorption. Results are presented in Table 1.
183
Method of interface
removal vs. shell type
Soft
Polycation
Stabilized
vdW
Stabilized
Sintered
Droplet dissolution
disintegrated
remained
intact
remained
intact
remained
intact
Centrifugation
disintegrated
remained
intact
remained
intact
not tested
not
applicable
flattened
flattened
remained
intact
Drying (after droplet
dissolution)
Table E.1: Typical result of different methods of interface removal on
different types of particle shells. Images of typical soft, polycationstabilized, van der Waals (vdW)-stabilized, and sintered shells appear in
Figures E.1a, E.1b, E.1c, and E.2b, respectively.
184
Addition of co-solvent. We remove the oil-water interface by diluting a
small amount of shell-stabilized emulsion with ethanol, which is miscible
with all of the solvents used here. Shells we classify as soft disintegrate, but
many rigid shells (poly-L-lysine-stabilized, van der Waals-stabilized, and
sintered) remain structurally intact. In typical batches of rigid shells, most
survive the addition of ethanol and appear qualitatively similar to the shells
prior to interface removal.
Thus, all methods of shell stabilization we
investigate maintain the structural integrity of most shells upon addition of
co-solvent.
Solvent Exchange by Centrifugation. We apply centrifugation to transfer
shells to a fresh exterior fluid that is miscible with the interior fluid.
Preparation begins by placing the shell-stabilized emulsion on top of a fresh
solvent in a vial (Figure E.1c). Subsequent centrifugation drags the shells
down, replacing the exterior solvent and removing the droplet interface.
Shells that we classify as soft disintegrate at the oil-water interface,
although there are occasionally particle clusters at the bottom of the
centrifuge tube. We have never found intact shells or shell fragments in
these cases. In contrast, polycation- and van der Waals-stabilized shells can
survive transfer. For example, approximately 1-10% of a typical batch of
185
polycation-stabilized shells of DVB carboxyl particles centrifuged from
toluene into water maintain their mechanical integrity.
The remainder
includes ripped shell fragments and slightly deformed and punctured shells.
Van der Waals-stabilized aldehyde sulfate shells encapsulating silicone oil in
water also survive centrifugation into silicone oil, but yields are often less
than 1%.
Drying following co-solvent addition. Before allowing shells to dry in air
at room temperature, droplet interfaces are first dissolved by immersion in
ethanol.
Aldehyde sulfate particle shells repeatably remain intact upon
drying only when sintered for longer than five minutes (Figure E.3b), in
contrast to unsintered shells (E.3a). Upon drying, all observed poly-Llysine- and van der Waals- stabilized shells collapse into flat structures, the
larger structures with wrinkles tens of microns in scale. In order to maintain
structural integrity upon drying, van der Waals and polycation stabilization
are inadequate and some degree of sintering is necessary.
3.4. Mechanical Properties of Sintered Shells
186
Shell stabilization can affect not only shell morphology, but also
mechanical properties of shells following interface removal.
After
centrifugation, poly-L-lysine-stabilized shells show remarkable elastic
resilience to deformation. Mechanical response is dominated by adsorbed
and free interior poly-L-lysine (cf Chapter 2), with typical structure spring
constant ~10-2 N/m. Sintered shells are more stiff and brittle than those
stabilized with poly-L-lysine, and shell modulus and breaking force can be
modified by varying sintering time; as this time increases the
interconnecting necks between particles thicken and interstitial pores anneal
away. Microcantilever measurement data plotted in Figure E.4 show that the
typical force needed to break shells increases with sintering time. Because
we expect that structural strength should increase with neck cross-sectional
area, it is not surprising that the formation and growth of necks with
progressively longer sintering times (Figure E.3) result in stronger shells.
However, for comparable shell size distributions, the range of breaking
forces also increases with sintering time. We have observed that instead of
annealing away upon sintering, ab incepto defects in particle coverage are
effectively magnified by the development of thin shell regions about the
initial defect; defects can concentrate stress and dominate shell breakage
when near the point of deformation. An increase in breaking force range
187
with sintering time is further evidence that sintering magnifies stressconcentrating defects.
188
Breaking sintered colloidosomes
900
force to break (µN)
800
Sintering time
5 minutes
10 minutes
15 minutes
20 minutes
150 minutes
700
600
500
400
300
200
100
0
0
20
40
60
80
100
120
140
160
sintering time (minutes)
Figure E.4
The maximum force required to break or puncture colloidosomes increases
with sintering time. Some colloidosomes sintered for 150 minutes could not
be broken with any microcantilever attempted; data for these colloidosomes
is excluded from the graph.
189
Representative
data
from
experiments
in
which
shells
are
incrementally indented until breakage show that shells sintered for longer
periods of time are stiffer and break at smaller strain values (Figures E.5 and
E.6). Results from many shells of different diameters are plotted. The data
collapse upon normalization by shell diameter for the well-sintered shells,
suggestive of continuum shell deformation.
Furthermore, when lightly-
sintered shells fail, microcantilevers typically punch out discrete particles
along perforated connections of lightly-sintered shells with minimal impact
on shell regions away from the puncture site (Figure E.7, bottom), in
contrast to continuum buckling and failure in well-sintered shells (Figure
E.8). Modeling a shell of uniform 1µm thickness and bulk elastic modulus
of polystyrene (3GPa) with the commercial finite element analysis code
ABAQUS yields a simulated indentation load-displacement relationship that
is essentially linear and consistent with measurements, additional
confirmation that well-sintered shells behave approximately as continuum
shells
190
Indenting colloidosomes sintered 5 minutes
8
7
indentation (µm)
6
5
4
3
2
1
0
0
5
10
15
20
25
30
35
40
force (µN)
indentation normalized to colloidosome size
indentation / capsule diameter
0.5
0.4
0.3
0.2
0.1
0.0
0
5
10
15
20
25
30
35
40
force (µN)
Figure – E.5 – Colloidosomes sintered 5 minutes, indentation until
breaking. Distinct symbols represent different colloidosomes within each
graph. Normalizing the indentation depth by the colloidosome diameter
does not collapse the data, indicating that these capsules do not behave as
continuum shells. Representative subset of data shown.
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Indenting colloidosomes sintered 150 minutes
8
indentation (µm)
6
4
2
0
0
100
200
300
400
500
600
700
force (µN)
indentation / capsule diameter
indentation normalized to colloidosome size
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
100
200
300
400
500
600
700
force (µN)
Figure E.6 – Colloidosomes sintered 150 minutes, indentation until
breaking. Distinct symbols represent different colloidosomes within each
graph. Normalizing the indentation depth by the colloidosome diameter
collapses the data significantly, which indicates that these may be behaving
more like continuous shells than colloidosomes sintered 5 minutes.
Representative subset of data shown.
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Figure – E.7 TOP and MIDDLE: Colloidosomes vary widely in their
surface bead coverage and defects. BOTTOM: A colloidosome broken by a
microcantilever has failed by punching out discrete beads along the
perforated sintered connections. All three colloidosomes were sintered 20
minutes.
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Figure E.8
Colloidosomes have been sintered for 150 minutes and tested with a
microcantilever. TOP: A colloidosome with no visible defect sites is
broken to show a shell thickness of about 1 µm, in good agreement with the
polystyrene bead diameter. MIDDLE: A broken colloidosome with several
visible defects shows a wall thickness less than 1/3 µm at a defect site,
evidence that the stress-magnifying effects of defects should increase with
sintering time. BOTTOM: Two colloidosomes, one buckled and one
broken, show deformation and failure as continuous shells.
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4. Summary
We have introduced a method of fabricating self-assembled shells of
polystyrene particles whose morphology and mechanical properties can be
tuned through selection of the appropriate solvents. When the particles are
stable in the exterior fluid, the particles self-assemble to form monolayer
shells. Of these systems, if the particles are stable in both exterior and
interior fluids, then the shell will be soft. Alternatively, if particles are
unstable in the interior fluid, then the shell will be relatively rigid. If the
particles are unstable in the exterior fluid, then shells will be multilayered
and disordered. With this latitude, shells have been made for applications
ranging from the study of particle interactions and ordering at spherical
interfaces to the fabrication of selectively permeable membranes for
encapsulation.
The fluid interface that is used to form the shells can be dissolved,
allowing diffusive exchange of small particles between the interior and
exterior regions of the shells7. We have demonstrated that van der Waalsand polycation-stabilized shells remain intact under solvent replacement via
195
centrifugation, and that some degree of sintering is needed to maintain
structural integrity when shells are dried. Microcantilever measurements
have shown that the mechanical properties of polycation-stabilized shells are
dominated by the polycation (cf Chapter 3), and that sintering strengthens
and stiffens by gradually transforming discrete particle shells into continuum
shells. These stabilization techniques are potential ways to gain tighter
control over mechanical properties under a range of experimental conditions.
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