NC-based energetic materials - stability, decomposition, and ageing

Transcription

NC-based energetic materials - stability, decomposition,
and ageing
Dr. Manfred A. Bohn
Fraunhofer-Institut für Chemische Technologie (ICT)
Postfach 1240, D-76318 Pfinztal-Berghausen, Germany
Presentation on the Meeting
Nitrocellulose - Supply, Ageing and Characterization
April 24 to 25, 2007
AWE, Aldermaston, England
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2007
Bohn / 1
Content
Abstract
Stability ’versus‘ ageing
Stability tests for NC and NC-based materials
Bergmann-Junk, Abel, Vacuum Stability, Mass Loss, Dutch Mass Loss Test
Aspects of NC decomposition
Thermolysis, hydrolysis, chain splitting, bond dissociation enthalpies
Accelerated ageing - objectives
Measurements on NC alone – Comparison of results of four stability tests
Modelling - benefits
Modelling of primary (added at production) stabilizer consumption
models ‘S: exponential + linear’, ‘S: nth order’, ‘S: extended’
Applications
Prediction of a real ageing over 16 years of a singlebase propellant used in automotive seat belt
restraint systems
Combined modelling of stabilizer consumption and the course of consecutive products
Forming reactivities of consecutive products of DPA
Modelling of molar mass decrease of NC
model 1: chain splitting by decomposition of chain element (= monomer unit)
model 2: chain splitting by bond breaking, number of chain elements is constant
Application, examples and meaning
molar mass decrease and shift of ductile-brittle transition temperature
molar mass decrease and decrease of mechanical strength
Ageing of New Type gun propellants
Literature
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2007
Bohn / 2
Abstract
Nitrocellulose (NC) has itself re-established as an essential ingredient in recent gun
propellant formulations containing RDX and newer type of plasticizers. All the efforts to
replace NC by other polymeric binders have been successful in a rather small part only.
Surely NC decomposition is present also in the modern formulations and the ageing of
such propellants has to be considered carefully. To master the ageing of NC based
energetic materials knowledge of the basic decomposition behaviour of NC is necessary.
Data of bond dissociation energies and activation energies of NC decomposition will be
compiled and discussed. Experimental results and quantum mechanically obtained data are
used for this. The way or the severity of NC decomposition will be discussed and
formulated in a scheme. Kinetic models to describe NC decomposition are presented for
mass loss and molar mass degradation.
Stabilization is a main issue with NC-based materials. Stabilizer reactions and their
modelling are presented. With examples of ageing of gun propellants and rocket
propellants including new type of gun propellants containing RDX, the way of prediction
of the use time (life time) is shown. Several experimental methods as mass loss, stabilizer
consumption, molar mass degradation, heat generation can be used and their suitability
and the special demands for prediction purposes are demonstrated.
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2007
Bohn / 3
Stability ‘versus’ Ageing
Stability tests use reduced time-temperature loads compared to ageing investigations,
typically only one temperature and one time period.
Stability tests determine the momentary state of the material.
In contrast the determination of ageing behaviour gives a prediction possibility based on
information obtained from an extended time-temperature behaviour of the material.
For both aspects molecular decomposition is the base, especially with chemical stability.
With ageing also physical phenomena are included as migration of surface treatment
agents (burning phlegmatizer for gun propellant grains)
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2007
Bohn / 4
Stability tests
The NC-decomposition causes
● formation of permanent gases
● formation of NOx
● generation of reaction heat
● polymer chain degradation
The older tests are based mainly on the generation of NOx caused by a time – temperature load
Using the effects of NO2 – namely oxidizing and forming of HNO3 , many tests have been developed
and most of these are connected with famous names:
Abel, Bergmann-Junk, Hanson-Metz, Vieille, Methyl-Violet-Test
time to visible NOx (the well-known 65.5°C (=150 °F) surveillance test, introduced by the
US Navy, about 1905)
Self ignition temperature, Silvered Vessel-Test (Dewar-Test)
Then somewhat later mass loss and gas generation (vacuum stability test) were used
Newer methods use the same basic effects but the detection is much improved
● NOx-Chemiluminescence
● GPC (SEC)
● microcalorimeter (heat generation rate), ARC (adiabatic self heating)
● gas analysis by FTIR-EGA, GC, GC-MS
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2007
Bohn / 5
Bergmann-Junk-Test (Bergmann-Junk-Siebert-Test)
Developed from E. Bergmann and A. Junk in Germany, improved by Siebert
Substance
amount
[g]
Test
temp.
[°C]
Test
time
[h]
Criterion:
consumption of 0.01n NaOH
to neutralize HNO3 formed by
absorbed and oxidized NO2
Nitrocellulose
2
132
2
≤ 12.5 ml/g
Sb gun propellant (propellant not
containing blasting oils)
5
132
5
≤ 10 to 12 ml/g *)
Db gun propellant with blasting oil
content up to 10 mass-%
5
115
16
≤ 10 to 12 ml/g *)
Db gun propellant with blasting oil
content greater than 10 mass-%
5
115
8
≤ 10 to 12 ml/g *)
Db rocket propellant
5
115
16
≤ 10 to 12 ml/g *)
substance
*) limit value is often fixed for the individual propellant in the range 10 to 12ml per g of propellant
This test is not used with triple base propellants
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2007
Bohn
6
Bergmann-Junk-Test (Bergmann-Junk-Siebert-Test)
Dimensions in mm
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2007
Bohn
7
Abel-Test - German conditions and typical results
Substance
test
temp.
[°C]
Sample
amount
[g]
test
limit
[min]
Nitroglycerine,
BTTN, TMETN,
DEGN
80
2
≥ 15
Nitrocellulose
80
1.3
≥ 10
TNT
80
1
≥ 30
KJ starch paper, wetted by water glycerine (1:1) to half length. At the
interface colour change occurs caused by
NO2 in oxidizing iodide to iodine and this
forms a coloured product with starch.
Time taken at this point
of colour change
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2007
Bohn
8
Vacuum stability test – German test conditions and criteria
Substance
amount [g]
Test temp.
[°C]
Test
time [h]
Criterion for ‘stable’
ml/g at STP
Sb gun propellant (propellant
not containing blasting oils)
2.5
100
40
≤ 1.2 to 2
High explosives as PETN, HMX,
RDX, explosive charges, HTPBcomposite propellants
2.5
100
40
≤ 1.2 to 2
Db gun propellant with blasting
oil
2.5
90
40
≤ 1.2 to 2
Db rocket propellant
2.5
90
40
≤ 1.2 to 2
substance
Recent tendency to unify conditions
for NC-based propellants
2.5
100
40
≤2
Non-NC high explosives
2.5
100
40
≤ 1.2
2 ml/g or 5ml/2.5g is the upper allowed limit. Between 1.2 and 2 ml/g the stability is considered as
borderline. Preferred are values ≤ 1.2ml/g or ≤ 3ml/2.5g
STP: standard temperature (=0°C) and standard pressure (=1 atm)
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2007
Bohn
9
Mass Loss Tests
Mass loss (ML) at 90°C for GP and RP
In most cases one ages 2g (up to 5g) of propellant in tubes with loosely inserted ground
stoppers over 18 days
Sample can be used as delivered (if not to wet !, water content not higher than 1.5 mass-%)
Criterion:
ML ≤ 3 % and no red-brown fumes (NOX) up to 18 days
initial mass loss can be subtracted, ML after one day as baseline
Applicable for all types of propellants (single, double, triple, semi-nitramine, new type,…)
Other test times - test temperatures (always
with 3 % limit)
For 50 years at
25°C
For 15 years at
25°C
100°C
6 days
1.8 days
90°C
18 days
5.4 days
80°C
54 days
16.2 days
75°C
93.5 days
28.0 days
70°C
162 days
48.6 days
Necessary equipment
• well temperature controlled oven
• glass tubes with ground stoppers
• analytical balance, well positioned
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2007
Bohn
10
Dutch Mass Loss Test
Mass loss after 72 h, reduced by the mass loss after the first 8 h in open tube
4g of sample in tubes closed with ground stoppers
at 105°C: double and triple base GP and RP
at 110°C: single base GP
Criterion: ML (72h-8h) ≤ 2%, all GP and RP
In principle also usable with high explosives as RDX, HMX, PETN
Also used for semi-nitramine and new-type propellants
Pure substances can be tested at 110°C
For other formulations the test temperature depends on ingredients;
with energetic plasticizers 105°C is suitable
Other conditions and test criterion remain the same
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2007
Bohn 11
Assessment of ageing and stability with mass loss
Three types of GP
doublebase GP L5460 shows after20d strong ML increase with visible NOx
triplebase GP Q 5560 shows smooth increase of ML without showing visible NOx
new type GP (see later) shows smooth increase of ML without showing NOx
9
ML [%]
8
mass loss at 90°C
GP, L5460, 120mm
7
6
GP Q 5560, 27mm MRCA
5
limit: ≤ 3%, 18 d
4
3
2
new type GP (contains RDX)
1
test time [d]
0
0
10
20
30
40
50
60
70
80
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2007
Bohn/
12
90
Comparison of mass loss: ball powder K6210 – 120mm GP L5460
Difference in stability can be revealed clearly with ML (18 days at 90°C corresponds to 50 years at 25°C isothermal)
db GP K6210 is stabilized with DPA (diphenylamine). In spite of not fulfilling the strong criterion it can be used
safely for certain time. Doblebase GP L5460 is stabilized with AK II (akardite II).
6
ML [%]
mass loss test at 90°C
5
at 18 days ML <= 3%
K6210
L5460
4
3
db ball powder K6210
2
db GP L5460 (120mm)
1
time [d]
0
0
2
4
6
8
10
12
14
16
18
20
22
24
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2007
Bohn/
13
Comparison of heat generation rate: ball powder K6210 – 120mm GP L5460
Difference in stability can be revealed also clearly with heat generation rate (dQ/dt) and heat generation (Q)
90
dQ/dt [µW/g]
db ball powder K 6210, Qex = 4059 J/g
db 120mm GP L5460, Qex = 4720 J/g
80
70
Q [J/g]
63
80°C
70
56
49
K6210
60
dQ-K6210
50
42
dQ-L5460
35
Q-K6210
40
28
Q-L5460
30
21
L5460
20
14
10
7
time [d]
0
0
0
1
2
3
4
5
6
7
8
9
10
11
12
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2007
Bohn/ 14
Aspects of NC decomposition
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2007
Bohn / 15
What determines the NC decomposition
NC and NC-based products decompose chemically.
This is because of the relatively small bond dissociation enthalpy in the nitrate ester group.
chemical bond
name
average bond dissociation
enthalpy at 25°C [kJ/mol]
CO − NO2
nitrate ester
C−C
carbon - carbon
342
C−H
carbon - hydrogen
416
C−O
carbon - oxygen
343
N − O (in NO2)
nitro group
305
C-NO2 (aromatic)
carbon – nitro group
295
165 to 170
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2007
Bohn 16
Decomposition of NC
Assumption: by splittingoff of one NO2 group
from any ester group the
corresponding glucose
ring will be destroyed.
This means the mean
molar masses of NC
decrease all the time
caused by the slow
intrinsic decomposition of
NC, which cannot be
stopped by stabilizers.
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2007
Bohn / 17
Weighing of reaction rates by the investigation temperature via activation energy
The weighing has an important effect: at higher temperatures the process with the higher activation
energy dominates the decomposition, at lower temperatures it is the one with smaller activation energy.
-14
ln(kA [1/s])
Arrhenius plot of the three
main decomposition types of NC
temperature range 10°C to 120°C
90°C
-18
60°C
40°C
-22
-CO-NO2
-26
-30
-34
ester thermolysis, 163 kJ/mol
ester hydrolysis,
100 kJ/mol
chain hydrolysis,
56 kJ/mol
ET+EH
ET+EH+CH
-38
0.0024
-COH + HNO2
0.0028
-CO-NO2
-CO• + •NO2
0.0032
1/T [1/K]
0.0036
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2007
Bohn
18
Stabilizer consumption: activation energy as function of temp.
decrease of stabilizer
DPA in single base GP
A5020 (20 mm machine
gun, older lot) /1/
change in Ea at about
65°C
higher temp. range has
more thermolytical
ester group
decomposition
lower temp. range has
more hydrolytical ester
group decomposition
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
Stabcon 2005
Bohn / 19
Molar mass decrease of NC: activation energy as function of temp.
decrease of molar mass of
NC in single base GP A5020
(20mm machine gun, older
lot) /1/
change in Ea at about 65°C
higher temp. range has
more thermolytical ester
group decomposition with
consecutive chain scission
lower temp. range has
more hydrolytical NC chain
splitting
Remark: the lot of A5020
investigated was already an
older one, means products
with effect on hydrolysis
present
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
Stabcon 2005
Bohn / 20
Temperature range dependence of Ea for PVN (polyvinylnitrate)
Also with other nitric acid ester compounds a temperature dependence of Ea is observable /2/
EatyQ [kJ/mol]
125
PVN-M (polyvinylnitrate)
EatyQ as function of conversion (reached Q)
70°C to 110°C and temp. range sections
90-110°C
120
115
70-110°C
110
70-110
70-90
90-110
70-90°C
105
Obtained from heat generation measurements
Q [J/g]
100
0
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 21
Nitrate esters NE decompose intrinsically, means by themselves,
because of the small bond energy in the nitrate ester group,
about 170 kJ/mol for thermolytical split-off of NO2; Further more
one has formation of water and acids, and additional products as
gases and organics.
k
⎯⎯NE
⎯→
NE
NE + P
S+P
k
⎯⎯auto
⎯
⎯→
k
⎯⎯SP
⎯→
P + R-NE + ∆HRID
intrinsic decomposition
2 P + R-NE + ∆HRAD autocatalytic decomp.
P-S + ∆HRS
stabilizer reaction
Decomposition scheme
of nitric acid esters NE
The decomposition
products NO2 and acids
act as catalysts P in
decomposing NE; a further
decomposition reaction
channel is opened – the
so named autocatalytic
decomposition.
The stabilizer S binds the NO2 and nitric acid and makes
the autocatalysts P in-effective. No autocatalytic
decomposition appears during active phase of stabilization.
– But the intrinsic decomposition goes on and causes mass
loss, energy loss, chain splitting of NC, gas and heat
generation.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
22
Experimental bond dissociation enthalpies
kcal/mol
kJ/mol
20
83.7
22
92.0
24
100.4
26
108.8
Nitrate RO - NO2
kJ/mol
Nitrite RO - NO
kJ/mol
iso-Propyl nitrate
172.0 ± 4.2
iso-Propyl nitrite
171.5 ± 7.5
n-Propyl nitrate
177.0 ± 4.2
n-Propyl nitrite
167.8 ± 7.5
Methyl nitrate
172.4 ± 4.2
Methyl nitrite
174.9 ± 3.8
28
117.2
Alkyl nitrate
170.3 ± 2.1
Alkyl nitrite
170.7 ± 4.2
29
121.3
30
125.5
32
133.9
34
142.3
36
150.6
Relation kcal to kJ
38
159.0
1 kcal = 4.184 kJ
40
167.4
Bond enthalpy
refers to the energy obtained when the
molecule is split into the elements
42
175.7
44
184.1
see for example with hydrazine in /3/
46
192.5
50
209.2
From CRC Handbooks
Please be aware of the difference in the terms
Bond dissociation enthalpy
refers to a specified bond which is split
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 23
NC-simulate and NCradicals to calculate
the bond dissociation
enthalpies of the
split-off of NO2
radical from the three
glucose ring positions
2, 3 and 6
Pos. 2
NC-simulate
Pos. 6
NO2 radical
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 24
Pos. 3
PVN-simulate and PVN-radical to calculate the bond dissociation enthalpy of the
split-off of NO2 radical
PVN (polyvinylnitrate) simulate
Split-off of NO2 from middle position
PVN was seen as a replacement for NC in former time.
Today it is a speciality energetic polymer, used as additive in TNT HE charges.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 25
Bond dissociation enthalpies at 298.15 K in different molecular environment
Calculation method:
DFT, BLYP, GGA all
electron treatment
Calculated values corrected by normalizing to
experimental average
value of alkyl nitrate of
170.3 kJ/mol; error in calc.
values ± 8 kJ/mol
Substance
[kJ/mol]
ME-NC-2NO2, (BDE in the nitrate group at position 2)
1.2
160.8
1.0
133.0
1.3
174.4
PVN simulate (polyvinylnitrate)
170.8
Nitroglycerine, split-off of NO2 from middle position
171.2
Nitroglycerine, split-off of NO2 from side position
174.5
PETN
170.0
Methyl nitrate
185.0
Iso-Propyl nitrate
170.3
n-Propyl nitrate
179.9
Iso-propyl peroxonitrate: i-PropOO-NO2; split-off of NO2 radical
118.6
Iso-propyl peroxonitrate: i-PropO-ONO2; split-off of NO3 radical
92.5
GGA: generalized gradient
approximation
Iso-propyl peroxonitrite: i-PropO-ONO; split-off of NO2 radical
64.5
Further conditions see /4/
Iso-propyl peroxonitrite: i-PropOO-NO; split-off of NO radical
87.2
DFT: (electron) density
functional theory
B: Becke gradient corrected exchange potential
LYP: Lee, Yang, Parr
gradient corrected electron correlation potential
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 26
Relation between nitrate, peroxo nitrite and peroxo nitrate
CH3
CH2 O NO2
170 kJ/mol
. NO 2
CH3
65 kJ/mol
.NO2
CH2 O.
CH3
CH3
+ .O
N
O
CH3
87 kJ/mol
.NO
CH3
CH2 O O NO
CH2 O O.
CH3
CH3
. NO2
.NO3
CH3
92 kJ/mol
119 kJ/mol
CH2 O O NO2
CH3
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 27
Accelerated ageing
ageing means generally: property change with time and temperature
Objectives
● To reach equivalent ageing in much shorter times than at target temperature,
for example at 25°C
● To find out the ageing process(es)
● To determine activation energies for the ageing process(es) or other parameters
to quantify the temperature dependence of the ageing
● To use the temperature dependence describing parameters to predict the ageing
at any time-temperature load
● To simulate real ageing using time-temperature profiles
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn 28
Arrhenius Plot according to STANAG 4582 (so-named heat flow (HFC) STANAG)
13
11
ln(kQ [µW/g])
Arrhenius plot of reaction rate constant kQ(T)
according to STANAG 4582
9
7
T S=60°C
120 kJ/mol
135°C
80 kJ/mol
5
3
1
-1
-3
-5
-7
0.0022
the composed Arrhenius line is used
kQ2 with EaQ2 = 80 kJ/mol
ZQ2 = 3.4099 E+13 µW/g
ln(kq1 [µW/g])
15°C
ln(kq2 [µW/g])
ln(kq [µW/g])
kQ1 with EQ1 = 120 kJ/mol
Ea divide
ZQ1 = 6.3719 E+19 µW/g
0.0024
1/T [1/K]
0.0026
0.0028
0.003
0.0032
0.0034
0.0036
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
29
HFC-STANAG 4582 (Heat generation rate (HGR)-STANAG)
Main points
Fixing of test times tT and upper limits for
HGR (heat flow) (dQ/dt)L at a series of test
temperatures TT
To fulfil the HGR limits during test time
at test temperature gives a safe time
interval against autoignition of 10 years
at isothermally 25°C
The test times and HGR limits are valid
only for a decomposition kinetics as it
is shown by NC-based propellants
Acceleration
with regard to
10 years at 25°C
TT [°C]
tT [d]
(dQ/dt)L
[µW/g]
60
123
9.8
30
65
64.9
18.5
56
70
34.8
34.5
105
71
30.8
39.0
119
75
19.0
63.1
192
80
10.6
114
345
89
3.83
314
954
90
3.43
350
1065
HGR limits have been determined with a finite element
programme for the solution of the heat balance
equation for the autoignition of a big caliber (230 mm in
diameter) cartridge
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
30
Arrhenius relation between ‘test (tt,Tt)‘ and ‘in-service (tE,TE)‘
With one activation energy valid in the considered temperature range TE to Tt
⎛ Ea ⎞
⎟⎟
ki = Z ⋅ exp⎜⎜ −
RT
⎝
i⎠
⎛ Ea ⎛ 1 1 ⎞ ⎞
k2
= exp⎜⎜ − ⋅ ⎜⎜ − ⎟⎟ ⎟⎟
k1
⎝ R ⎝ T2 T1 ⎠ ⎠
⎛ Ea ⎛ 1 1 ⎞ ⎞
t1
= exp⎜⎜ − ⋅ ⎜⎜ − ⎟⎟ ⎟⎟
t2
⎝ R ⎝ T2 T1 ⎠ ⎠
⎛ Ea ⎛ 1 1 ⎞ ⎞
tE = t t ⋅ exp⎜⎜ + ⋅ ⎜⎜ − ⎟⎟ ⎟⎟
⎝ R ⎝ TE Tt ⎠ ⎠
1
t∝
k
Reaction rate constant
reciprocal proportional
to time to reach a state
or conversion
By forming the ratio the timetemperature scaling is achieved
Caution
this procedure may be
simplifying to strong
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
tBohn
31
Extrapolation of test conditions to in-service conditions with factor F (works in
both directions: ac-celeration and de-celeration)
Factor 3 for 10°C temperature change corresponds to activation energy range of 80 to 120 kJ/mol
in the temperature range 20°C to 95°C
10
F [-]
Ea [kJ/mol]
factor F= k(T) / k(T-10K)
for dT = 10°C
9
160
140
120
100
80
8
7
6
5
4
3
2
T [°C]
1
0
10
20
30
40
50
60
70
80
90
100
110
120
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
32
Relation between test time - test temperature and in-service time - temperature
For chemically caused ageing processes the following formula has proven by experience as
suitable (Ea about 80 to 120 kJ/mol, temperature range 20°C to 95°C)
tE [a] = t T [d] ⋅ F( TT − TE ) / ∆TF / 365 .25d
tE
time in years at temperature TE
tT
test time in days at test temperature TT
F
reaction rate change factor per 10°C temperature change
De-celeration with temp. decrease / ac-celeration with temp. Increase
TT
test temperature in °C
TE
in-service temperature in °C
∆TF temperature interval for actual value of F, here ∆TF is always 10°C
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
33
Comparison of the STANAG extrapolation with the factor 3 extrapolation
100000
time-temperature relations
normalized to tE = 10 years at TE = 25°C
time tt [d]
TS=60°C
10000
80 kJ/mol
120 kJ/mol
curves with Ea1 and Ea2,
intersecting at 60°C
10 years at 25°C
1000
100
with Ea2 = 80 kJ/mol
factor 3
extrapolation
t [d] Ea1
10
t [d] Ea2
t [d] Ea1+Ea2
1
tt [d] F-3
with Ea1 = 120 kJ/mol
shifted up to intersection at 60°C
25°C reference
Ea divide
0.1
T t [°C]
0.01
0
10
20
30
40
50
60
70
80
90
100
110
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
34
120
Overview of some used test times – test temperatures extrapolated to 25°C
100000
80 a
time tt [d]
40 a
20 a
10000
TS = 60°C
80 kJ/mol
time-temperature relations
tE =10 years at TE = 25°C
extensions to other in-service times
Ea1 = 120 kJ/mol, Ea2 = 80 kJ/mol
120 kJ/mol
10 a
1000
STANAGs
5a
Example how to read: This point gives 5 years at 25°C
TE = 25°C
ML, 90°C, 18d
100
1 x te [d] = 10 a
2 x te [d]
8 x te [d]
DMLT-105°C, 72h
VST 100°C, 40h
ML 90°C, 18d
Abel, 80°C, 1 h
BJS, GP, 115°C, 8h
STANAG 4117, 65°C, 120d
Ea divide
10
1
0.1
0.5 x te [d]
4 x te [d]
DMLT-110°C, 72h
VST-100°C, 48h Dutch HGR-Test
VST 90°C, 40h
DHGT 85°C, 7d
VST, 100°C, 90°C
BJ, NC, 132°C, 2h
STANAG 4541, 60°C, 60d
Abel, 80°C
25°C reference
DMLT, 110°C, 105°C
Bergmann-Junk
Tt [°C]
0.01
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
35
150
Implicit limit in the HFC STANAG
Limit for the allowed energy loss of a gun (GP) or rocket (RP) propellant: ≤ 3%
For 10 years at 25°C
TT
[°C]
tT [d]
(dQ/dt)L
[µW/g]
QL [J/g]
60
123
9.8
104.1
65
64.9
18.5
103.7
70
34.8
34.5
103.7
71
30.8
39.0
103.8
75
19.0
63.1
103.6
80
10.6
114
104.4
89
3.83
314
103.9
QEX(gw) value with reaction water gaseous
90
3.43
350
103.7
QEX(lw) value with reaction water liquid
To extend the predicted time from
10 to 20 years implies to use the
double test times but also only half
the values for (dQ/dt)L
at 80°C, after 10.6 d
HGR
[µW/g]
Q
[J/g]
% of
QEX(gw)
L5460
db, 120mm
12.8
16.1
0.38
K6210
db ball, 9mm
68.2
57.1
1.53
QEX(gw)
[ QEX(lw) ]
[J/g]
Limit is
3% of
QEX(gw)
[J/g]
4238
[ 4610 ]
3730
[ 4040 ]
127
112
Energy loss limit is for the actual use of the propellant
more important than the danger of its autoignition
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
36
Measurements on NC alone – Comparison of stability tests
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 37
NC lot 1: HGR and HG at 90°C, measured under air and under argon
Measured at 90°C with TAMTM in closed steel ampoules with glass inserts, sample amounts about 0.2g
4000
100000
dQ/dt [µW/g]
90000
80000
NC-1
90°C
60000
50000
2800
in argon
2400
2000
in air
40000
30000
1600
1200
N=12.5 mass-%
QEX-wliqu = 3931 J/g
QEX-wgas = 3619 J/g
20000
3600
3200
dQ-NC53-Ar
dQ-NC53-Ar-2
dQ-NC53-Lu
zero
Q -NC53-Ar
Q -NC53-Ar-2
Q -NC53-Lu
70000
Q [J/g]
800
400
10000
0
0
time [d]
-400
-10000
-2
1
4
7
10
13
16
19
22
25
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 38
100
3000
dQ/dt [µW/g]
2700
Q [J/g]
NC-1
90°C
comparison between
air - argon
2400
90
80
70
2100
dQ-NC53-Ar
dQ-NC53-Lu
dQ-NC53-Ar-2
zero
Q -NC53-Ar
Q -NC53-Lu
Q -NC53-Ar-2
1800
1500
1200
900
60
50
40
30
600
20
300
10
0
0
time [d]
-300
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
-10
18
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 39
15
1500
dQ/dt [µW/g]
Q [J/g]
NC-2
90°C
1350
13.5
under argon
1200
1050
132°C, 2 h correspond to
90°C, 3.75 d with F = 2.5
90°C, 8.07 d with F = 3.0
12
10.5
under air
900
9
750
7.5
600
6
450
4.5
300
3
150
1.5
0
0
-150
-0.1
time [d]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
-1.5
1.3
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 40
Heat generation rates of dry and unstabilized NC samples – region 0 to 2 days
Measured at 90°C with TAMTM in closed steel ampoules with glass inserts in air, sample amounts about 0.2g
120000
110000
dQ/dt [µW/g]
NC, 90°C
comparison of NC-lots in air
100000
90000
dQ-NC-1
dQ-NC-2
80000
dQ-NC-3
70000
dQ-NC-4
dQ-NC-5
60000
dQ-NC-6
dQ-NC-7
50000
zero
40000
30000
20000
10000
0
-10000
-0.2
time [d]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 41
Heat generation rates of seven dry and unstabilized NC samples
Measured at 90°C with TAMTM in closed steel ampoules with glass inserts in air, sample amounts about 0.2g
120000
dQ/dt [µW/g]
110000
NC, 90°C
comparison of NC-lots in air
100000
90000
dQ-NC-1
80000
dQ-NC-2
dQ-NC-3
70000
dQ-NC-4
60000
dQ-NC-5
50000
dQ-NC-6
dQ-NC-7
40000
zero
30000
20000
10000
0
time [d]
-10000
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 42
Mass loss of dry and unstabilized NC lot 1 in the ‘linear range’ of preautocatalysis (means a reaction of zero order)
1.6
ML [%]
NC-1
mass loss in stoppered vials
90°C, air
region of 'pre-autocatalysis'
1.4
P1 [%]
P2 [%]
M [%]
1.2
1
visible NOx appeared;
this is named as start
of 'autocatalysis'
0.8
0.6
ML [%] = 0.165 [%/d] * t [d] + 0.5724 [%]
2
R = 0.904
0.4
0.2
The ‘linear range’ of pre-autocatalysis means a reaction of zero order in ML
time [d]
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 43
Mass loss of dry and unstabilized NC lot 1 at 90°C up to autocatalysis
50
ML [%]
NC-1
mass loss in stoppered vials
90°C, air
region up to 'autocatalysis'
45
40
P1 [%]
P2 [%]
M [%]
35
30
25
is , )
s
y
al ning
t
a
oc egin
t
u
f a at b
o
ge ially
n
Ra spec
(e
20
visible NOx
appeared
15
10
Pre-autocatalysis range
5
time [d]
0
0
1
2
3
4
5
6
7
8
9
10
11
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 44
Comparison of stability data of seven NC lots obtained with four methods
10.0
9.0
8.0
time to NOx [d]
time to max HGR [d]
BJ-value [ml/g 0.01 n
NaOH]
0.9
correlation of NC stability data
kml [%/d]
0.8
BJ value [ml/g 0.01n NaOH]
t(90°C) to NOx [d]
t(90°C) to max HGR [d]
kml [%/d]
7.0
0.7
0.6
6.0
Bergmann-Junk
0.5
5.0
ML reaction rate constant
0.4
4.0
0.3
3.0
time to visible NOx
2.0
0.2
time to max. HGR
0.1
1.0
NC NC
sample
lot
0
0.0
1
2
5
6
3
7
4
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 45
Photographs of NC residues after ageing at 90°C in mass loss vials
Brown to black
residues after the
‘cool‘ burning-out
of the NC samples.
Sample amount
about 0.6g to 0.8g
No ignition
occurred in any
case !
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 46
Photographs of NC residues in glass inserts after measurements in TAM at 90°C
Brown to black
residues after the
‘cool‘ burning-out
of the NC samples.
Sample amount
about 0.2g
No ignition
occurred in any
case !
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 47
Scheme of NC decomposition considering temperature-time exposure see /5/
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 48
Mitigation of ageing
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 49
Chemical formulas of the most used stabilizers in NC-based propellants
CH3
H
N
N
O=C
DPA
N
H
N
H
HN
C2H5
C2H5
N
O=C
N
NO2
NO2
EC, Centralite I
Ak II, Akardite II
2NDPA,
2-NO2-DPA
MNA, pNMA
C 2H 6
N
NO
N
CH3
O=C
N
HN
CH3
CH3
OH
O=C
N
OH
N-NO-DPA
N-nitroso-DPA
MC, Centralite II
Ak III, Akardite III
Resorcinol
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn 50
STANAGs for assessment of chemical stability / ageing using stabilizer consumption
STANAG 4117
STANAG 4541
STANAG 4542
STANAG 4527
SB with DPA
SB with DPA and EC
DB with EC
DB with DPA only
(≤ 15% NG)
DB with 2-NO2-DPA
(≥ 15% NG)
all NC-based propellants
multi-temperature test
60 days at 65.5°C
or 120 days at 65.5°C
60 days at 60°C
35 days at 60°C
40 – 90°C
120 d: DPAeff ≥ 0.3 mass-%
abs. decr. ≤ 0.5 mass%
120 d: EC ≥ 0.3 mass-%
rel. decrease ≤ 50%
DPAeff ≥ 0.5 mass-%;
rel. decrease ≤ 50%
2-NO2-DPA ≥ 0.2 mass-%
abs. decr. ≤ 0.5 mass-%
• Kinetic modelling with
0th or 1st order
• Arrhenius parameter
• definition of evaluation
is incomplete
• Existing standards use different test conditions, the reason is their historical development
it seems today not justified to define different test criteria as it was done in former times
each NC-based propellant should be assessed in the same way.
But: there exist different ranges of stability with different type of propellants !!
• Not all propellants are covered by these STANAGs named above
• Kinetic analysis and calculation of chemically determined safe time period is defined not precise enough
• Therefore: a unification was developed with AOP 48 Edition 2 which will replace all these STANAGs
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
51
Standards to assess chemically determined use time with stabilizer consumption
STANAG 4117
STANAG 4541
STANAG 4542
STANAG 4527
SB with DPA
SB with DPA and EC
DB with EC
DB with DPA
(≤ 15% NG)
DB with 2-NO2-DPA
(≥ 15% NG)
all NC-based propell.
multi-temperature test
STANAG 4620
Ö "Empty document"
Ö Refers to AOP 48
Ö In ratification
AOP 48 encourages the use
of kinetic description of
stabilizer consumption
with a model of nth order,
see later. dS( t )
dt
AOP 48 Edition 1
• Compilation of the 4 procedures from the 4 earlier STANAGs
• No changes of test procedures
• In ratification
AOP 48 Edition 2
• Same test procedure for all typical stabilizers and GP types
• Test conditions harmonized to other STANAGs (4582-HFC,
4147-Ed.3-Compatibility)
• In preparation, meanwhile near to ratification (May, 2007 )
= −k | ⋅ S( t )n
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
52
Modelling of stabilizer consumption
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 53
Benefits of modelling the ageing
See /6/
• minimize the risk of a mis-evaluation
• increase the reliability of the prediction of the ageing effects by a better description of
the measured data and by an inherently correct extrapolation along the time axis
• recognize a faulty measuring arrangement if the measured data are not conform to the
model
• identify a faulty production of a GP or RP
• support the find out of ageing reactions or ageing processes
• support the find out of measures against the effects of ageing processes
• support the planning and the realization of the acquisition of experimental data and of the
procurement of substance data to assess ageing and safety
• support the decision about the employability of energetic components and of formulations
• full use of the service time capacity of a GP or RP
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn 54
Kinetic description of stabilizer consumption - principles
Facts on stabilizer consumption, presented in way of reaction scheme /6,14/
Reaction scheme
NE
NE + P
S+P
k
⎯⎯NE
⎯→
k
⎯⎯auto
⎯
⎯→
k
⎯⎯SP
⎯→
P + R-NE
intrinsic decomposition
2 P + R-NE
autocatalytic decomposition
P-S
stabilizing reaction
a good stabilizer suppresses the autocatalytic decomposition of nitrate ester NE
by catching product P
A correct description of stabilizer depletion needs at least two reaction rate
constants:
kNE for NE decomposition
kSP for the stabilizer reaction: P reacts with S
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 55
Kinetic description of consumption of the primary stabilizer S – reaction scheme I
/7,11, 14/
Primary stabilizer is the
stabilizer added at production
reaction scheme RS I
NE
k
⎯⎯NE
⎯→
k
NE + P
⎯⎯auto
⎯
⎯→
S+P
⎯⎯SP
⎯→
k
P + R-NE
2 P + R-NE
P-S
intrinsic decomp.
autocat. decomp.
stabilizer reaction
dNE( t )
= −kNE ⋅ NE( t ) − kauto ⋅ NE( t ) ⋅ P( t )
dt
dP( t )
= +kNE ⋅ NE( t ) + kauto ⋅ NE( t ) ⋅ P( t ) − kSP ⋅ P( t ) ⋅ S( t )
dt
dS( t )
= −kSP ⋅ P( t ) ⋅ S( t )
dt
System of DEq for the above
reaction scheme
This DEq system is very probably not solvable analytically in closed form.
It is integrated and iterated numerically to determine the values of the three rate
constants.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn 56
Kinetic description of consumption of the primary stabilizer S – RS II
Approximation:
stabilizer S suppresses the autocatalytic decomposition and the corresponding reaction can
be deployed
reaction scheme RS II
k
NE
⎯⎯NE
⎯→
S+P
⎯⎯SP
⎯→
k
P + R-NE
P-S
Primary stabilizer is the
stabilizer added at production
intrinsic decomp.
stabilizer reaction
Corresponding differential equation system
dNE( t )
= −kNE ⋅ NE( t )
dt
dP( t )
(2)
= kNE ⋅ NE( t ) − kSP ⋅ S( t ) ⋅ P( t )
dt
dS( t )
(3)
= −kSP ⋅ S( t ) ⋅ P( t )
dt
(1)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 57
Simplified solution of DEq system of reaction scheme RS
dNE( t )
= −kNE ⋅ NE( t )
dt
dP( t )
(2)
= kNE ⋅ NE( t ) − kSP ⋅ S( t ) ⋅ P( t )
dt
dS( t )
(3)
= −kSP ⋅ S( t ) ⋅ P( t )
dt
(1)
Assumption: P(t) is constant, P(t) = Pc ; this holds at the beginning of stabilizer consumption
dS( t )
= −k′SP ⋅ S( t )
dt
S( t ) = S(0) ⋅ exp( −k′SP ⋅ t )
with k′SP = kSP ⋅ Pc
Stabilizer is consumed according to reaction of first order
means exponential decrease of stabilizer consumption
Further simplification:
for short times the first order reaction can be approximated by zero order reaction
S( t ) = S(0) ⋅ (1 − k′SP ⋅ t )
Linear decrease of stabilizer concentration, but only at the very beginning
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 58
Way of solution of not simplifying the DEq system, means with P(t) not assumed as
constant – it results in just one differential equation for the stabilizer decrease /7/
eq.(1) has the solution :
dNE( t )
= −kNE ⋅ NE( t )
dt
dP( t )
= kNE ⋅ NE( t ) − kSP ⋅ S( t ) ⋅ P( t )
(2)
dt
dS( t )
(3)
= −kSP ⋅ S( t ) ⋅ P( t )
dt
(1)
the expression for P(t) from the right is
inserted in eq.(3) of DEq-system. This
results in an expression containing
only S(t)
dS( t )
= −kSP ⋅ S( t ) ⋅ ⎛⎜ S( t ) + C − NE(0 ) ⋅ e− kNE ⋅ t ⎞⎟
⎝
⎠
dt
NE( t ) = NE(0) ⋅ exp( −kNE ⋅ t )
eq.(2) and eq.(3) give :
dP( t ) dS( t )
−k ⋅t
−
= kNE ⋅ NE( t ) = kNE ⋅ NE(0) ⋅ e NE
dt
dt
with the solution :
P( t ) − S( t ) = C − NE(0) ⋅ e
− kNE ⋅ t
and C is the integration constant :
C = NE(0) + P(0) − S(0)
NE(0): initial conc. of nitrate ester
P(0):
initial conc. of product P
S(0):
initial conc. of stabilizer S
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 59
Way of solution of the single differential equation for stabilizer decrease
• C ≅ NE(0 )
• NE(0) ⋅ exp( −kNE ⋅ t ) ≅ NE(0 ) ⋅ (1 − kNE ⋅ t )
Introducing reasonable approximations
C is dominated by NE(0)
the exponential can be well approximated by
Taylor series up to second term
dS( t )
≈ −kSP ⋅ S( t ) ⋅ (S( t ) + NE(0 ) ⋅ kNE ⋅ t )
dt
S( t ) =
(
1
+
S(0 )
Resulting rate equation for S
)
exp − NE(0 ) ⋅ kNE ⋅ kSP ⋅ t2
⎛ NE(0 ) ⋅ kNE ⋅ kSP ⎞
π
kSP
⋅
⋅ erf ⎜⎜
⋅ t ⎟⎟
2 NE(0 ) ⋅ kNE
2
⎝
⎠
Integrated rate equation
This is a kinetically correct description of stabilizer depletion, because two reaction
steps are involved - decomposition of NC and stabilizer reaction - so two reaction rate
constants must appear in the description.
⎞
2 ⎛⎜
z3
z5
z7
z9
erf(z ) =
⋅ ⎜z −
+
−
+
− .. + .. ⎟⎟
π ⎝
1!⋅3 2!⋅5 3!⋅7 4!⋅9
⎠
for z < ∞ ; erf(0) = 0
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn 60
Modelling with RS II, model ’S: extended‘
Good description of
the data of DPA
consumption in a
single base
propellant with
model ‘S: extended‘
————————————————————————————————————————————————
2007
Bohn / 61
Model ‘S: exponential + linear’ part 1 of 2
see /8/
Reactions of first order or zero order alone cannot give satisfying descriptions of stabilizer
decrease. To achieve at a better description the combination was tried.
Combination of the reactions of first and zero order
⎛ dS( t , T ) ⎞
⎜
⎟ = − k1 ( T ) ⋅ S( t , T ) − k0 ( T )
⎝ dt ⎠ T
)
(
k0 ( T ) = Z0 ⋅ exp(− Ea0 / RT )
k1 ( T ) = Z1 ⋅ exp − Ea1 / RT
Arrhenius behaviour
Integrated rate equation
⎛
S( t , T )=⎜ S(0) +
⎜
⎝
(
)
k0 ( T ) ⎞⎟
k (T)
⋅ exp − k1 ( T ) ⋅ t − 0
k1 ( T ) ⎟⎠
k1 ( T )
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn/
62
Model ‘S: exponential + linear’ part 2 of 2
Calculation of service times tyS(T)
Definition of degree of stabilizer consumption
yS =
S( t , T )
S(0)
therewith the times tyS(T) to reach yS can be calculated
⎞
⎛
k0 ( T )
⎟
⎜
⎟
⎜ 1+
1
1
S(0) ⋅ k1( T ) ⎟
⎜
ty S ( T ) =
⋅ ln
k1 ( T ) ⎜
k0 ( T ) ⎟
⎟
⎜ yS +
⎟
⎜
S
(
0
)
⋅
k
(
T
)
1
⎠
⎝
times to reach yS these are the looked for usetimes
⎛ S(0) ⋅ k ( T ) ⎞
1
t0 ( T ) =
⋅ ln⎜
+ 1⎟
⎜
⎟
k1 ( T ) ⎝ k0 ( T )
⎠
times to reach yS = 0
1
the model has a good extrapolation ability
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn/ 63
Stabilizer consumption: decrease of 2-nitro-DPA in a RP
description with
model 'S: expon. +
linear' in comparison
with description
according to first
order reaction
Data points marked
with arrows must have
been omitted with first
order reaction (model
‘S: exponential’) to
achieve acceptable
description at the
beginning, but not
with the model
'S: exponential + linear'
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 64
Model ‘S: exponential + linear’ for stabilizer consumption - extrapolation ability
Extrapolation ability of
model ’S: exponential +
linear‘
Black line: all points
have been used
Red line: points up to
red arrow have been
used
Blue line: points up to
blue arrow have been
used
Green line: points up to
green arrow have been
used
The resulting scattering
is within narrow range
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 65
Models to describe stabilizer consumption
Eq.
kinetic rate equation
kinetic type
name of model
suitability, how to handle
1
dS( t )
= −k 1 ⋅ S( t ) − k 0
dt
first + zero order,
two reactions
‘S: exponential + linear’ /8/
very suitable, easy to handle
2
dS( t )
= −k 1 ⋅ S( t )
dt
first order,
one reaction
‘S: exponential’
not suitable, easy to handle
3
dS( t )
= −k 0
dt
zero order,
one reaction
‘S: linear’
conditioned suitable, easy to handle
4
dS( t )
= −k | ⋅ S( t )n
dt
nth order,
one reaction
‘S: nth order’ (AOP 48 model)
well suitable, easy to handle
two reactions,
NE decomp. and
consump. of S
‘S: extended’ /7, 14/
suitable, to handle with advanced fit
codes (OriginTM, Origin Lab Corp.)
5
dS( t )
= −k SP ⋅ S( t ) ⋅ (S( t ) + NE(0) ⋅ kNE ⋅ t )
dt
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 66
Models to describe stabilizer consumption – integrated expressions
Eq.
1
2
time t0 to yS = S(t)/S(0) = 0
equation
⎛
k (T)
k (T) ⎞
⎟⎟ ⋅ exp(− k 1( T ) ⋅ t ) − 0
S( t , T ) = ⎜⎜ S(0) + 0
k 1( T )
k 1( T ) ⎠
⎝
S( t , T ) = S(0) ⋅ exp(− k1( T ) ⋅ t )
S( t , T ) = S(0 ) ⋅ [1 − (1 − n) ⋅ k( T ) ⋅ t ]
4
5
t 0 (T) =
⎛ 1 ⎞
⎜
⎟
⎝ 1−n ⎠
(
exp − NE(0) ⋅ k NE ⋅ k SP ⋅ t 2
S(0 )
k 0 (T)
1 ⎛ 1 ⎞
⎜
⎟
k( T ) ⎝ 1 − n ⎠
only for n < 1
t 0 (T) =
k| (T)
with k( T ) =
S(0 )1−n
S( t ) =
⎛ S(0) ⋅ k 1( T ) ⎞
1
⋅ ln⎜⎜
+ 1⎟⎟
k 1( T ) ⎝ k 0 ( T )
⎠
t0(T) → ∞
S( t , T ) = S(0) − k 0 ( T ) ⋅ t
3
t 0 (T) =
)
⎛ NE(0) ⋅ k NE ⋅ k SP ⎞
k SP
π
1
+
⋅
⋅ erf⎜
⋅ t⎟
⎜
⎟
S(0)
2 NE(0) ⋅ k NE
2
⎝
⎠
t0(T) → ∞
name of model
suitability, how to handle
‘S: exponential + linear’ /8/
suitable, easy to handle
‘S: exponential’
not suitable, easy to handle
‘S: linear’
conditioned suitable, easy
to handle
‘S: nth order’
suitable, easy to handle
‘S: extended’ /7, 14/
suitable, fairly to handle
with advanced fit codes
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
67
Description of stabilizer consumption with model ‘S: extended’
comparison of single temp. fit (sT) and all temp. fit (aT)
Model ‘S: extended‘
can describe
pronounced tailing
sometimes found
Data of stabilizer
consumption of
propellant P2
determined in
1987/1988 after
accelerated ageing
at 70°C, 80°C and
90°C.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
68
Description of stabilizer consumption with model ‘S: nth order’ (AOP 48 Ed. 2
model) - only all temperature (aT) fit is shown
0.9
Because the
reaction order n is
<1, the times t0(T)
to reach S(t,T) = 0
can be calculated
DPA [mass-%]
0.8
0.7
P2 NC-propellant
description with model 'S: nth order'
all temp. fit
90°C experiment
80°C experiment
70°C experiment
zero
90°C n th order
80°C n th order
70°C n th order
0.6
0.5
70°C
0.4
80°C
0.3
0.2
90°C
128.6 d
33.0 d
0.1
0
time [d]
9.1 d
-0.1
0
10
20
30
40
50
60
70
80
90
100
110
120
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
69
130
Description of stabilizer consumption with model ‘S: exponential + linear’
comparison of ‘single temperature fit’ (sT) and ‘all temperature fit’ (aT)
0.9
time t0(T) to
reach S(t,T) = 0
can be
calculated
always.
DPA [mass-%]
P2 NC-propellant
stabilizer consumption
determined at begin of natural ageing (1987)
description with model
'S: expon. + linear'
0.8
0.7
0.6
The t0(T) times
are shorter
0.5
than the ones
calculated with 0.4
model ‘S: nth
order’
0.3
90°C experiment
80°C experiment
70°C experiment
zero
90°C expon.+lin.-aT
90°C expon.+lin.-sT
70°C
80°C
to=7.05 d
to=25.86 d
to=102.36 d
to=6.63 d
to=25.83 d
to=107.02 d
90°C
0.2
0.1
7.05 d
107.02 d
25.86 d
0
6.63 d
25.83 d
time [d]
102.36 d
-0.1
0
10
20
30
40
50
60
70
80
90
100
110
120
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
70
130
Model ‘S: nth order’ (AOP 48 model) application with two stabilizers of different
reactivity
Model ‘S: nth
order‘ can cause
artificial shapes
of stabilizer
decrease curves
A bend upwards
with n<0 is not
reasonable for
stabilizer
consumption, as
shown with the
blue curve in
figure on the
right.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
71
Model ‘S: exponential + linear’ application with two stabilizers of different
reactivity
All models must
be applied in
two steps, each
stabilizer is
described
separately
DPA is much
more reactive
than Ak II.
As long as DPA
is active Ak II is
not changed in
concentration
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 72
Comparison of models: because of conservative character in extrapolation
model ‘S: exponential + linear’ is taken for evaluation
0.9
The times t0(T)
are shortest with 0.8
model
’S: exponential + 0.7
linear‘
The tailing of
model ‘S: nth
order’ is already
too strong to
include the
stabilizer
decrease up to
zero content in
the calculations
with profiles
Note: AOP 48, Ed 2
recommends not to
use model ‘S: nth
order‘ at S(t) below
20% of S(0)
DPA [mass-%]
P2 NC propellant
comparison of three models
all temperature fits
data for 70°C extracted
0.6
70°C
zero
70°C
70°C
70°C
0.5
0.4
experiment
expon.+lin.-aT to=102.36 d
nth order-aT
te=128.6 d
extended-aT
te=160 d
0.3
'S: extended'
0.2
'S: nth order'
'S: extended'
0.1
'S: exponential + linear'
0
time [d]
-0.1
0
20
40
60
80
100
120
140
160
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn
73
180
Prediction of a real ageing over 16 years of a singlebase
propellant used in automotive seat belt restraint systems
See also /9,10/
What is needed for this task:
• The representative time-temperature profile (usually compiled for one year) at ageing
site (best would be continuous measurements of the temperature course)
• Accelerated ageing of propellant sample to parameterize its stabilizer decrease
• A model description of the stabilizer consumption which follows it up to zero content
of primary (means added at the production) stabilizer
• The Arrhenius parameters for the stabilizer decrease obtained with the model
description
• Application of the model description with the time-temperature profile data
• Measurements on stabilizer consumption during the course of real ageing of the
propellant
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 74
Arrhenius parameters obtained with model for stabilizer consumption
‘all temperature fit’ – propellant P2, model ‘S: exponential + linear’
rate constant k1
rate constant k0
model
S(0)
[mass%]
Ea1
[kJ/mol]
lg(Z1 [1/d])
Ea0
[kJ/mol]
lg(Z0 [m.-%/d])
all temp. fit
0.78
138.1
19.001
138.9
18.796
R2
(from fit directly)
0.9935
Data of stabilizer consumption of propellant P2 determined in 1987/1988 after
accelerated ageing at 70°C, 80°C and 90°C.
Now after 19 years they are used to make the prediction for the real ageing
result of propellant P2, which was aged in Florida over 16 years in set belt
cartridges /10/
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 75
Experimental data on evolution of stabilizer concentrations
Concentrations of DPA and DPA consecutive products of single base P2
propellant in mass-% as function of ageing time at the test center in Miami
/9,10/.
ageing time at test center
Stabilizer
base
line
1a
4a
9a
16 a
DPA
0.780
0.690
0.585
0.030
0.000
0.135
0.370
0.110
0.100
0.160
0.230
0.020
0.170
0.300
N-NO-DPA
2-Nitro-DPA
4-Nitro-DPA
0.010
2,4’-Dinitro-DPA
0.000
2,2’-Dinitro-DPA
0.030
2,4,4’-Trinitro-DPA
0.017
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯−−−−−⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 76
Introduction
Company TRW Alfdorf, Germany has arranged a
long term natural ageing program with belt
restraint units equipped with ‘life’ gas generator
units of two types taken from the regular
production /9,10/
The ageing started in October 1987 in a test center near Miami, Florida, USA.
The restraint units have been mounted in such a way to simulate the situation in a car
In regular intervals samples were taken out and investigated
• Pressure-time curves made by TRW
• Chemical ageing and stability tests made by ICT
The ageing ended in October 2003. An ageing time of 16 years was realized at
ambient conditions.
But the propellants experienced elevated temperatures because of the housing of the
belt restraint units
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2006
Bohn /
77
Time-temperature profiles for Miami, Florida, USA
40
time-temperature profiles
time interval [d]
35
Miami BMP
Miami AMB
30
Miami AMB: Tm = 24.9°C
25
20
Miami BMP: Tm = 34.3°C
15
55°C
10
33°C
5
T [°C]
0
10
15
20
25
30
35
40
45
50
55
60
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯−−−−⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
78
Model ‘S: exponential+ linear’ for use with time-temperature profile data or
continuous time-temperature measurements
⎛
k (T ) ⎞
k (T )
S( ∆ti , Ti ) = ⎜⎜ S( ∆ti−1, Ti−1) + 0 i ⎟⎟ ⋅ exp(− k1( Ti ) ⋅ ∆ti ) − 0 i
k1( Ti ) ⎠
k1( Ti )
⎝
i = 1, 2, 3 ...n
S(∆ti-1,Ti-1)
∆ti
Ti
j
number of profile section i
for j=1 and i=1 S(∆ti-1,Ti-1) = S(0)
for j>1 and i=1 the value of S after profile passing j
is the start value for profile passing j+1
time interval of profile section i
temperature of profile section i
number of one full profile passing (profile cycle)
t (of one profile cycle ) =
n
∑ ∆t
i=1
ty S = j ⋅
i
(with profile BMP it is one year)
n
∑ ∆t
i=1
i
With continuous temperature data (these have also time ∆ti at Ti until next Ti+1) this same
procedure is taken
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
79
Prediction of stabilizer consumption in GG-P2 according to BMP profile load
and 4 loads with temperature-shifted BMP, model ‘S: exponential + linear’
0.9
propellant loaded by different profiles based on BMP profile
BMP shifted by -4°C
BMP shifted by -2°C
BMP
BMP shifted by +2°C
BMP shifted by +4°C
BMP
zero
BMP -2°C
0.2* S(0)
experim. data
BMP -4°C
DPA [mass-%]
0.8
0.7
0.6
0.5
0.4
0.3
BMP +2°C
0.2
8
0.1
29
15
BMP +4°C
11
0
S(0)*0.2
21
time [a]
-0.1
0
4
8
12
16
20
24
28
32
36
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2006
Bohn /
80
Modelling of stabilizer consumption
and the course of consecutive products
See also
/7,11,12,13, 14/
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 81
How to handle the total stabilizing capability of a typical stabilizer
Determination of
DPA consumption
and the evolution
of consecutive
products of DPA
by Dr. Fred Volk
(about begin of the
1980s)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 82
Modelling of stabilizer and its consecutive products – RS III
Reaction scheme for the course of DPA and its consecutive products up to the first nitration step /
nitrosation step /7/
reaction scheme III (RS III)
k
NC
⎯→ P + R
NC ⎯ ⎯
k
auto
⎯→ 2 P + R
NC + P ⎯ ⎯⎯
NNO →
DPA + P ⎯ ⎯⎯
N-NO-DPA
k
dxNC
= −kNC xNC − kautoxNC xP
dt
dxP
= kNC xNC + kautoxNC xP + kDPNNOxNNO
dt
− (kNNO + k4N + k2N )xPxDPA
k
− (kNNO− xNNO + k4N− x 4N + k2N− x2N )xP
k
dxDPA
= kDPNNOxNNO − (kNNO + k4N + k2N )xP xDPA
dt
dxNNO
= kNNOxP xDPA − kNNO− xP xNNO − kDPNNOxNNO
dt
dx 4N
= k4NxP xDPA − k4N− xP x 4N
dt
dx2N
= k2NxP xDPA − k2N− xP x2N
dt
4N
⎯→ 4-nitro-DPA
DPA + P ⎯ ⎯
2N
⎯→ 2-nitro-DPA
DPA + P ⎯ ⎯
k
DPNNO
→ DPA + P
N-NO-DPA ⎯ ⎯⎯⎯
k
NNO−
⎯→ DPANNON-NO-DPA + P ⎯ ⎯⎯
k
4N−
4-nitro-DPA + P ⎯ ⎯⎯
→ DPA4Nk
2N−
→ DPA2N2-nitro-DPA + P ⎯ ⎯⎯
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 83
Modelling of stabilizer and its consecutive products - P(t) is not constant.
RS III (continued) - with data newly measured from aged singlebase GP see /7/
Full lines:
model description with the above reaction scheme
Broken lines: connect the measured data for each of the four substances
0.009
reactant
singlebase GP, 90°C
0.008
[mol/mol ONO2]
RS III
xP(0)=0.00075
KK = 0.99
0.007
0.006
DPA calc.
DPA exp.
N-Nitroso-DPA calc.
N-Nitroso-DPA exp.
4-Nitro-DPA calc.
4-Nitro-DPA exp.
2-Nitro-DPA calc.
2-Nitro-DPA exp.
0.005
0.004
0.003
0.002
0.001
time [d]
0
0
5
10
15
20
25
30
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 84
Stabilizer and its consecutive products, RS III (continued) – values of the rate
constants obtained by the modelling
kauto = 10 kNC and kDPNNO ≠ 0 (N-NO-DPA to DPA)
temp. = 90°C,
all reaction rate constants in 1/d
different initial concentrations xP(0) for product P
constant
xP(0) [mol/(mol ONO2)]
xP(0) as fit paramet.
0.0
0.0005
0.00075
0.00128
kNC
0.00173
0.00159
0.00155
0.00157
kNNO
340.8
300.1
258.6
156.0
k4N
104.3
98.3
88.9
57.9
k2N
44.9
35.7
32.5
20.9
kDPNNO
0.089
0.0718
0.0513
0.0135
kNNO-
20.8
25.75
27.31
25.43
k4N-
22.1
26.1
25.0
18.2
k2N-
9.66
10.43
9.79
6.66
2.07 E-4
1.67 E-4
1.56 E-4
1.50 E-4
R2
st.dev.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 85
Modelling of high nitrated DPA products, P(t) is not constant – RS IV – part 1
Just for presentation, the result is shown in two figures. The first part looks like the result of RS III,
but it is not. The modelling has included all products up to tri-nitrated species at once! /7/
0.009
reactant
[mol/mol ONO2]
0.008
singlebase GP
RS IV
xP(0)=0.0005
part 1
0.007
DPA calc.
DPA exp.
N-nitroso-DPA calc.
N-nitroso-DPA exp.
4-nitro-DPA calc.
4-nitro-DPA exp.
2-nitro-DPA calc.
2-nitro-DPA exp.
0.006
0.005
0.004
0.003
0.002
0.001
time [d]
0
0
5
10
15
20
25
30
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 86
Modelling of high nitrated DPA products, P(t) is not constant – RS IV – part 2
0.003
reactant
[mol/mol ONO2]
0.0025
4,4'-dinitro-DPA calc.
4,4'-dinitro-DPA exp.
2,4,4'-trinitro-DPA calc.
2,4,4'-trinitro-DPA exp.
0.002
0.0015
0.001
singlebase GP
RS IV
xP(0)=0.0005
part 2
0.0005
time [d]
0
0
5
10
15
20
25
30
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 87
Relative reactivities of consecutive products with regard to DPA
From the modelling of the consecutive products of DPA their relative reactivity with
respect to DPA can be formulated /7/.
The advantages
• determined in a gun propellant matrix (single base GP) at 90°C
• based on reaction kinetics, reaction with the autocatalytic product
relative reactivity ERX obtained by RS IV
DPA
1.0
N-NO-DPA
0.041
4-N-DPA
0.074
2-N-DPA
0.055
4.4’-DN-DPA
0.008
2.2’-DN-DPA
0.004
2.4’-DN-DPA
0.016
2.4.4’-TN-DPA
8 E-5
N-NO-DPA has a lower
reactivity than the mononitro-DPAs
And it has a much lower
reactivity than DPA itself
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 88
Mechanistic modelling of
stabilizer reaction with RS I see /13/
Activation energy Ea of NC decompos.
is with 146 kJ/mol composed of two
reactions: thermolysis and hydrolysis
-5.5
-6.0
ln(k NC [1/d])
DPA decrease in a single base GP
k NC determ . according to RS I
90°C
-6.5
Ea = 145.8 ± 4.8 kJ/m ol
lg(Z[1/d]) = 18.097 ± 0.72
KK = 0.9978
85°C
-7.0
-7.5
80°C
-8.0
7.5
7.0
90°C
6.5
75°C
-8.5
D P A decrease in a sin gle base G P
to R S I
k D PA determ . according
-9.0
ln(k D PA [1/d])
6.0
80°C
70°C
E a = 132.4 ± 28 kJ/m ol
-9.5
lg(Z[1/d]) = 21.915 ± 4.1
K K = 0.9226
-10.0
5.5
65°C
-10.5
85°C
5.0
1/T [1/K]
75°C
-11.0
0.00270
0.00275
0.00280
0.00285
0.00290
0.00295
0.0030
4.5
70°C
4.0
3.5
65°C
3.0
1/T [1/K ]
2.5
0.00270
0.00275
0.00280
0.00285
0.00290
0.00295
0.00 3
Ea of stabilization reaction is with
132 kJ/mol in accordance with the
loss of aromaticity of benzene ring
(resonance energy)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 89
Modelling of molar mass decrease of NC
See also /14,15/
Generally there are two main models to describe the statistical chain splitting of NC or any polymer
Model 1
chain scission by decomposition of a chain element (= monomer unit)
with time the mass of the polymer sample decreases
the number of chain elements is decreasing
model 1 was developed at ICT
Model 2
chain scission by opening of the bond (bond splitting) between two monomer units
with time the mass of the polymer sample stays constant
the number of chain elements (monomer units) stays constant
model 2 is several times given in the literature, sometimes it is referred as Ekenstam model
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 90
Development of the kinetic model for polymer degradation – model 1 - part 1 /15/
Model 1: chain scission by chain element (=monomer unit)
decomposition
number of
chain
elements E,
from 1 to N
1
2
3
4
E-
E-
E-
E - ...
E-
E -....
number of polymer chain in
the sample, from 1 to nC
i
E-
E-
E-
E
E
1
i+1
E-
2
.
E-
E-
E-
N-1
N
.
E-
E
nC
total number of chain elements: N(0)
total number of chains: nC(0)
Pn=Mn/m: degree of polymerization
m: molar mass of chain element E
N( t , T ) = N(0 ) ⋅ exp (− kM ( T ) ⋅ t )
N(0) = nC (0) ⋅ Pn(0) = nC (0) ⋅
Mn(0)
m
N( t , T ) = nC ( t , T ) ⋅ Pn( t , T ) = nC ( t , T ) ⋅
Mn( t , T )
m
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 91
Development of the kinetic model for polymer degradation – model 1 - part 2
K( t , T ) = N(0 ) − N( t , T )
Formation of one new chain by each decomposition of one chain element
nC ( t , T ) = nC (0) + N(0) − N( t , T )
Mn(0)
1+
m
nC ( t , T ) = nC (0) ⋅
Mn( t , T )
1+
m
m
1
Mn(0)
1+
1+
N(0)
Mn( t , T )
Pn( t , T )
m
=
=
=
= exp(+ kM ( T ) ⋅ t )
Mn( t , T )
m
1
N
(
t
,
T
)
nC ( t , T ) ⋅
1+
1+
m
Mn(0)
Pn(0)
nC (0) ⋅
m
m ⎞
⎛
⎞ ⎛
⎟ ⋅ exp (+ kM ( T ) ⋅ t )
⎜1 +
⎟ = ⎜1 +
⎝ Mn( t , T ) ⎠ ⎝ Mn(0 ) ⎠
m ⎞
m ⎞
⎛
⎛
ln⎜1 +
⎟ = ln⎜1+
⎟ + kM( T ) ⋅ t
⎝ Mn( t , T ) ⎠
⎝ Mn(0) ⎠
Approximated formulas
m
m
=
+ kM( T ) ⋅ t
Mn( t , T ) Mn(0)
corresponding rate expression
⎛ ⎛ Mn( t , T ) ⎞ ⎞
⎜ d⎜
⎟⎟
2⎞
⎛
⎜ ⎝ m ⎠ ⎟ = −k ( T ) ⋅ ⎜ ⎛⎜ Mn( t , T ) ⎞⎟ + ⎛⎜ Mn( t , T ) ⎞⎟ ⎟
M
⎜⎝ m ⎠ ⎝ m ⎠ ⎟
⎟
⎜
dt
⎝
⎠
⎟
⎜
⎠T
⎝
⎛ ⎛ Mn( t , T ) ⎞ ⎞
⎜ d⎜
⎟⎟
2
Mn
(
t
,
T
)
m
⎛
⎞
⎝
⎠
⎜
⎟ = −k ( T ) ⋅ ⎜
⎟
M
⎜
⎟
dt
⎝ m ⎠
⎜
⎟
⎝
⎠T
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 92
Development of the kinetic model for polymer degradation – model 1 - part 3
time tyMn is the looked for life time;
this is the time to reach the degree of
degradation yMn=Mn(t)/Mn(0)
An ⋅ Mw (0 ) ⎞
⎛ 1
+
⎜
⎟
1
yMn
m ⋅ D(0 ) ⎟
⎜
tyMn ( T ) =
⋅ ln
kM ( T ) ⎜ 1 + An ⋅ Mw (0 ) ⎟
⎜
⎟
m ⋅ D(0 )
⎝
⎠
m ⋅ D( t , T ) ⎞
m ⋅ D(0) ⎞
⎛
⎛
ln⎜ 1 +
⎟ = ln⎜ 1+
⎟ + kM ( T ) ⋅ t
An ⋅ Mw (0 ) ⎠
An ⋅ Mw ( t , T ) ⎠
⎝
⎝
m ⋅ D( t , T ) m ⋅ D(0 )
=
+ An ⋅ kM ( T ) ⋅ t
Mw ( t , T ) Mw (0 )
D=
Mw
Mn
An: conversion factor from absolute to
relative Mn values: Mnabs = An Mnrel
Model conditions
• statistical chain splitting.
• the chain splitting occurs by decomposition of chain elements; with NC the triggering
is the thermolytic and /or hydrolytic degradation of the ≡CO-NO2 groups
• the total number of chain elements is much greater than the number of chains
• the total number of chain elements decreases with first order, rate constant kM(T)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 93
Kinetic model for polymer degradation based on model 2 – part 1
Model 2: chain scission by bond breaking between chain elements (monomer units)
total number of bonds at time zero: B(0)
total number of chain elements: N(0)
total number of chains: nC(0)
number of bonds in chain j: Bj(0)
number of chain elements in chain j: Nj(0)
B(0) = ∑ B j (0) = ∑ (N j (0) − 1) = N(0) − nC (0)
B( t , T ) = N(0) − nC ( t , T ) = N( t , T ) − nC ( t , T )
⎛ d(B( t , T ) ⎞
⎜
⎟ = −kB ( T ) ⋅ B( t , T )
dt
⎝
⎠T
n ( t, T )
1− C
B( t , T ) N(0) − nC ( t , T )
N(0)
=
=
n (0 )
B(0)
N(0) − nC (0)
1− C
N(0)
with N(0) = N(t, T)
B( t , T ) = B(0) ⋅ exp( − k B ( T ) ⋅ t )
nC ( t , T )
m
=
N(0)
Mn( t , T )
nC ( 0 )
m
=
N(0) Mn(0)
m
1
1−
Mn( t , T )
Pn( t , T )
=
= exp(− k B ( T ) ⋅ t )
m
1
1−
1−
Mn(0)
Pn(0)
1−
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn/
94
Kinetic model for polymer degradation based on model 2 – part 2
m
1
1−
Mn( t, T )
Pn( t , T )
=
= exp(− kB ( T ) ⋅ t )
m
1
1−
1−
Mn(0)
Pn(0)
1−
⎛ ⎛ Mn( t , T )⎞ ⎞
⎟⎟
⎜ d⎜
⎝
⎠⎟
m
⎜
⎜
⎟
dt
⎜
⎟
⎝
⎠
⎛ ⎛ Mn( t , T )⎞ ⎛ Mn( t , T )⎞ 2 ⎞
= −k B ( T ) ⋅ ⎜ − ⎜
⎟ +⎜
⎟ ⎟
⎝
⎠
⎝
⎠ ⎠
m
m
⎝
T
1 ⎞
⎛ An ⋅ Mw(0)
−
⎜
⎟
m
D
(0)
y
⋅
1
Mn
⎟
ty Mn ( T ) = −
⋅ ln⎜
An
⋅
Mw(0
)
⎜
⎟
kB (T)
−1 ⎟
⎜
m ⋅ D(0)
⎝
⎠
Signs in formula are different to the model
based on chain element decomposition
m ⎞
m ⎞
⎛
⎛
ln⎜1 −
⎟ = ln⎜1 −
⎟ − kB (T) ⋅ t
⎝ Mn( t , T )⎠
⎝ Mn(0)⎠
Signs in formula are different to the model
based on chain element decomposition
Approximated formulas
m
m
=
+ kB ( T ) ⋅ t
Mn( t , T ) Mn(0)
⎛ ⎛ Mn( t , T ) ⎞ ⎞
⎜ d⎜
2
⎟⎟
⎜ ⎝ m ⎠ ⎟ = −k ( T ) ⋅ ⎛⎜ Mn( t , T ) ⎞⎟
B
⎜
⎟
dt
⎝ m ⎠
⎜
⎟
⎝
⎠T
In approximated form model 2
and model 1 are equal
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn/
95
Definition of terms – mean molar masses
The polymer fraction i is characterized by some quantities; it is thought to be molecular uniform,
means it has only molecules of one molar mass Mi and the number of mols is ni
The polymer sample is characterized by a distribution function hxi, which can be of different kind
∑ hn (M) ⋅ M ∑ hm (M)
Mn =
=
hm (M)
hn
(
M
)
∑
∑ M
u ,i
i
u ,i
i
Mn: mean molar mass averaged according to the mol
number in the polymer fraction i (mol number weighing)
i
u ,i
u ,i
i
i
i
∑ hn (M) ⋅ M ⋅ M ∑ hm (M) ⋅ M
Mw =
=
hn
(
M
)
M
⋅
∑
∑ hm (M)
u ,i
i
i
u ,i
i
i
i
u ,i
i
Mw: mean molar mass averaged according to the mass
of the polymer fraction i (mass weighing)
u ,i
i
i
∑ hn (M) ⋅ M ⋅ M ⋅ M ∑ hm (M) ⋅ M ⋅ M ∑ hz (M) ⋅ M
=
=
Mz =
⋅
⋅
⋅
hn
(
M
)
M
M
hm
(
M
)
M
∑
∑
∑ hz (M)
u ,i
i
i
i
i
u ,i
i
i
i
u ,i
i
i
u ,i
i
i
i
u ,i
i
i
u ,i
i
Mz: mean molar mass averaged according to the z-mass of the polymer fraction i (z weighing)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn/
96
Definition of terms - distribution functions
hmu,i (M)
hni (M) =
hnu,i (M)
∑
hnu ,i (M)
=
i
∑
Mi
hmu,i (M)
hni(M)
Mi
i
polymer fraction mol number related
normalized molar mass distribution
ni is mol number in polymer fraction i
hzu,i (M)
hmi (M) =
hmu,i (M)
=
∑ hmu,i(M) ∑
i
i
hzi (M) =
hzu,i (M)
∑ hzu,i(M)
i
Mi
hzu,i (M)
hmi(M)
Mi
hzi(M)
polymer fraction mass related molar
mi = Mi*ni
mi is the mass of polymer fraction i
polymer fraction z-weight related
zi = Mi*mi = Mi*Mi*ni
zi is the z mass of polymer fraction i
hnu,i and hmu,i and hzu,i are un-normalized distribution functions
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn/
97
Examples of molar mass degradation
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 98
Modelling of the molar mass decrease of NC – model 1
Modelling of NC
degradation in a
double base rocket
propellant
on the ordinate the
model expression of
model 1 is shown
The full lines are the model
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 99
Modelling of the molar mass decrease of NC – model 1
Modelling of NC
degradation in a
double base rocket
propellant
on the ordinate
mean molar mass
Mw is shown, back
calculated from the
model expression of
model 1
the description of
the data is very good
The full lines are the model
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 100
Model for degradation of molar mass of NC - extrapolation ability – model 1
This graph shows the
good extrapolation
ability of the model 1.
The figure has two lines:
red and black.
The red one is
determined by using the
model 1 with data up to
30 days.
The black one is
determined with data
up to 60 days.
Both curves coincide.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 101
Molar mass distribution functions of aged PVN – determined by GPC /2/
PVN, polyvinylnitrate, an energetic speciality polymer
0.0045
hm(M)
0.004
0.0035
0.003
0.0025
0.002
0.0015
PVN-M
MMD based on polymer fraction mass
80°C
un-aged
80°C 1d
80°C 2d
80°C 3d
80°C 7d
80°C 10d
80°C 14d
80°C 18d
zero
The systematic in the
ageing is expressed in
a common crossing
‘point’ of the curves
at about M = 1.3E+05
g/mol
0.001
0.0005
0
-0.0005
1.E+03
M [g/mol]
1.E+04
1.E+05
1.E+06
1.E+07
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 102
Molar mass degradation of PVN - description with model 1
220000
Mn [g/mol]
PVN-M
description of Mn with kinetic model
based and statistical chain splitting
high molecular part
200000
80°C Mn-calc
75°C Mn-calc
70°C Mn-calc
180000
160000
70°C
140000
75°C
120000
80°C
100000
time [d]
80000
0
10
20
30
40
50
60
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 103
Molar mass degradation of PVN – description with model 1
For the chain
scission in PVN
an activation
energy of 146
kJ/mol is
determined /2/.
-11
ln(kMn [1/d])
PVN-M
MMD evaluation with model
high molecular part, Mn(0) = 189600 g/mol
80°C
-11.5
Such Ea values are
found also NC
based propellants
EaMn = 146.1 ± 13 kJ/mol
lg(ZMn [1/d]) = 16.748 ± 2
2
R =0.9918
-12
75°C
-12.5
70°C
1/T [1/K]
-13
0.00282
0.00284
0.00286
0.00288
0.0029
0.00292
0.00294
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 104
Application and meaning of molar mass decrease
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 105
Molar mass decrease - brittle ductile transition
shift of the brittle-ductile
transition temperature to
higher temperature values
with decreasing molar
mass = decreasing chain
length of NC
ageing causes increase in
brittle tendency
danger during firing
rounds with large grain GP
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 106
Example for molar mass decrease - brittle ductile transition
.
GP KN6540 (M30
type), triple base
GP, 110mm tank
gun
stress - strain
curves of nonaged and aged
samples as function of temperature determined
at high strain rate,
about 5000%/sec
the brittleness
increases with
ageing
non-aged
aged, 80°C, 29d
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 107
Molar mass decrease - brittle ductile transition
GP KN6540 (M30
type), triple base GP,
110mm tank gun
brittle stress
shift of the brittle
ductile transition
temperature with
ageing to higher
values
ductile, yield stress
.
non-aged
aged, 80°C, 29d
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 108
Correlation of molar mass decrease and decrease of mechanical strength
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 109
Ageing of db rocket propellant – correlation between molar mass decrease of NC
and decrease mechanical properties
Correlation between molar mass
decrease, stabilizer decrease and
decrease of strain at break and
tensile stress at break for the
doublebase RP DBE 44/36 /16/
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn 110
Ageing of new type gun propellants
See also /17/
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 111
Types of gun propellants - overview
Main types of GP (numbers give applied ranges in mass-%)
Single base
NC( N content 13 to 13.4 mass-%) 90-95, stabilizer 1-2, plasticizer 2-5,
graphite
Double base
NC (N content 12.3 to 12.6 mass-%), 30 to 60, blasting oils 25 to 50
(NG, DEGN, special types also with TMETN, BTTN), stabilizer 1-2,
graphite
Triple base
NC (N-content 12.3 to 12.6 mass-%) 30 to 40, blasting oils 20 to 30
nitroguanidine 25 to 40, stabilizer 1 to 2, plasticizer 5 to 10, graphite
NH2
HN
Semi nitramine
NC (N-content 12.3 to 12.6 mass-%) 30 to 40, blasting oils 20 to 30,
RDX 25 to 40, stabilizer 1 to 2, plasticizer 5 to 10, graphite
New-type of ICT
NC (N-content 12.3 to 12.6 mass-%) 30 to 40, DNDA (dinitro-diaza)-type
n
n+1
plasticizer 20 to 30, RDX 25 to 40, stabilizer 1 to 2, graphite
CH3
N
C
CH2
NO2
All show a standard decomposition behaviour with respect to NC and blasting oil decomposition.
But in triple base GP the NO2 is in part captured by nitroguanidine (NQ), because of reaction
between NO2 and the NH groups of NQ. This and the dilution effect for NC by NQ leads to the fact
that with triple base propellants no visible NO2 can be observed and no strong autocatalysis.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 112
NH
NO2
n+2
N
CH3
NO2
Type of gun propellants - shapes
Main types of GP according to shape and treatment
cylindrical grain with several holes, mostly 1, 7, 19
long tube
short tube
flake
stripe
ball (sphere, ellipsoids)
cube
ring
horseshoe
nudle (short rods)
Surface treatment:
phlegmatization to adapt burning behaviour
energetic enforcement by blasting oil treatment (Wimmis EI type)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Pecul
113
Energetic plasticizer DNDA
CH3
recent plasticizer based on the n,(n+2)-Di Nitro - n,(n+2)-Di Aza group
n
n+1
n+2
N
CH2
N
NO2
CH3
NO2
DNDA 57: liquid dinitro-diaza plasticizer
Mixture of three components: DNDA5 : DNDA6 : DNDA7, about 43 : 45 : 12 mass-%
CH3
N
CH2
N
CH2
CH2
2,4-dinitro-2,4-diaza-pentane, DNDA 5 (54°C)
N
CH2
CH3
2,4-dinitro-2,4-diaza-hexane, DNDA 6 (32°C)
NO2
NO2
CH3
CH3
NO2
NO2
CH3
N
N
NO2
CH2
N
CH2
CH3
NO2
3,5-dinitro-3,5-diaza-heptane, DNDA 7 (75°C)
DNDA 57 (Tm = -9°C) gels with NC
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 114
Defining the LTC effect for gun propellants
LTC:
low temperature coefficient (coefficient with small value)
means
A gun propellant which shows small to very small dependence of
maximum chamber pressure pmax on charge temperature TC
temperature range of interest is from -40°C (-54°C) to +63°C (+71°C)
These New Type GP of ICT show this interesting effect of low temperature coefficient
of maximum chamber gas pressure
This effect can be used the reduce weight of the gun system (small and light vehicles)
or to increase the charge mass to enhance the muzzle velocity of the projectile
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯−−−−−⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 115
maximum gas pressure
Comparison of typical gas pressure curves of conventional and LTC propellants
LTC Propellant
Pm
Conventional Propellant
4
0 0 0
-50
-40
-30
-20
-10
0
10
20
30
40
50
propellant temperature (°C)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
116
60
Some characteristic data of GP formulations
QEX
[J/g]
VEX at 25°C
[ml/g]
1170
3768
961
2906
1178
4198
939
193
2910
1180
4201
939
yes
198
2908
1185
4071
938
19
yes
189
2510
1060
4124
931
19
yes
199
2540
1080
4177
929
GP
web
LTC
effect
autoignition adiab. flame force
temp. [°C] temp. Tad [K] [J/g]
TLP 1N
7
yes
185
2905
TLP 2N
7
yes
220
TLP 3N
7
yes
TLP 4G
7
TLP 5W
TLP 6
For comparison the data of two typical conventional GP
JA2 ( L 5460, db)
7
no
168
3390
1139
4610
753
MRCA (Q 5560, tb)
19
no
172
3078
1040
3758
857
Adiabatic flame temperature Tad, force, heat of explosion QEX and gas volume VEX have been
calculated by ICT Thermodynamic Code using the data of the ICT Thermochemical Data Base
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
117
Adiabatic self heating determined by an ARCTM of typical conventional and of
new type GP, including the XM39 GP with a binder based on CAB
100
Comparison of adiabatic self heat rate
h [°C/min]
TLP 1N
TLP 4G
TLP 2N
10
M 30
JA2
TLP 6
TLP 5W
single base
CAB-LOVA
1
0.1
CAB-LOVA
T [°C]
0.01
125
135
145
155
165
175
185
195
205
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
118
9
ML [%]
mass loss at 90°C
1N
8
JA2
7
5W
2N
MRCA
6
4G
5
3N
limit: ≤ 3%, 18 d
4
3
2
6
1
test time [d]
0
0
10
20
30
40
50
60
70
80
90
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
119
100
Modelling of ML data with model ‘ML: minor 1st ord.; main 1st ord. + autocat.’
See also /6/
Reaction scheme
k1
A ⎯⎯→
k2
A + B ⎯⎯→
V
⎯⎯→
⎯
k
V
B+C+S
inherent decomp. of main comp. A:
C = gases, S= solids
2 B + C + S autocatalytic decomp. of main comp. A;
V_
decomp. of minor comp. V;
B acts autocatalytically
describes initial ML
Reaction kinetic formulation gives the following equation for total mass loss ML
⎫
⎧m ⎛
M (0) + MS(0) + MN ⎞
ML(t, T) = 100%⋅ ⎨ C ⋅ ⎜ (1− aV ) − B
⎟ ⋅ (1− MAr(t, T)) + aV ⋅ (1− exp(−k V (T) ⋅ t))⎬
M(0)
⎠
⎭
⎩mA ⎝
MN: mass of a
non-reacting
ingredient N in A
MAr(t, T) =
Decomposition of main component A
(
k1(T) + (F + 1) ⋅ k2(T)
)
((
Decomp. of minor comp. V
) )
k2(T) + k1(T) + F ⋅ k2(T) ⋅ exp k1(T) + (F + 1) ⋅ k2(T) ⋅ t
Parameters to be determined from the measurement curve:
k1, k2, kV, (aV)
Decomposition of main
component according to ‘1st
order + autocatalytic‘
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 120
NT-GP 6
Modelling of ML data with kinetic model
‘ML: minor: 1st order; main: 1st order+ autocat.‘
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
121
Times tyML to reach 3% mass loss in years calculated with Arrhenius parameters
obtained from mass loss measurements at 70°C, 80°C and 90°C
See /17/ for more explanations
1N
2N
3N
4G
5W
6
MRCA
JA2
JA2, HT
7
7
7
7
19
19
19
7
7
EaML [kJ/mol]
116.5
104.3
101.8
105.6
105.7
102.2
147.9
102.0
149.0
log(ZML [1/d])
15.23
5
13.28
6
12.86
5
13.45
7
13.56
12.888
19.837
13.282
20.102
web
time tyML to reach 3% mass loss ML in years at preset temperatures
65°C [a]
1.6
1.8
2.0
1.9
1.6
2.2
2.8
0.8
2.2
50°C [a]
10.6
10.3
10.6
11.1
9.2
11.9
31.9
4.5
26.3
35°C [a]
87.8
68.1
67.1
75.1
62.3
75.6
465.1
28.3
391.2
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯−−−−−⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 122
Assessment of ageing and stability by heat generation rate (dQ/dt) and heat
generation Q at 90°C - Part 1: NT-GP 1N, 2N, 3N and 4G
50
200
dQ/dt [µW/g]
Q [J/g]
heat generation rate (left ordinate) and
heat generation (right ordinate, bold lines)
at 90°C
180
45
40
160
1N
Q are the curves directed to the right upwards
140
35
30
2N
3N
120
25
100
4G
20
80
15
1N
60
2N
10
40
3N
5
20
time [d]
4G
0
0
0
1
2
3
4
5
6
7
8
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
123
Assessment of ageing and stability by heat generation rate (dQ/dt) and heat
generation (Q) at 90°C - Part 2: NT-GP 5W, 6 and JA2, MRCA,.
35
160
dQ/dt [µW/g]
Q [J/g]
heat generation rate (left ordinate) and
heat generation (right ordinate, bold lines)
at 90°C
140
MRCA
30
JA2
120
25
5W
100
20
80
6
15
60
MRCA
JA2
10
40
5W
5
20
6
time [d]
0
0
0
1
2
3
4
5
6
7
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
124
Times tyEL to reach 3% energy loss EL
Times tyEL in years calculated with Arrhenius parameters obtained from heat
generation rate measurements at 60°C, 70°C, 80°C and 90°C.
Reference quantity Qref is the individual heat of explosion QEX
See /17/ for more explanations
1N
2N
3N
4G
5W
6
MRCA
JA2
3768
4198
4201
4071
4124
4177
3758
4610
7
7
7
7
19
19
19
7
EaQ [kJ/mol]
112.3
115.6
121.6
118.2
111.5
113.9
130.0
128.2
log(ZQ
[µW/g])
17.971
18.217
19.059
18.436
17.633
17.847
20.426
20.056
QEX [J/g]
web
time tyEL to reach 3% energy loss EL in years at preset temperatures
65°C [a]
0.85
1.74
2.12
2.57
1.53
2.22
1.62
2.45
50°C [a]
5.4
11.7
15.8
18.1
9.6
14.6
13.8
20.3
35°C [a]
42
95
142
154
73
115
146
207
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
125
Literature – part 1 of 3
/1/
M.A. Bohn, F. Volk.
Aging Behavior of Propellants Investigated by Heat Generation, Stabilizer Consumption, and Molar Mass Degradation.
Propellants, Explosives, Pyrotechnics 17 (1992) 171-178.
/2/
M.A. Bohn, J. Aniol, M. Dörich, K. Hartlieb, H. Pontius
Stability, Ageing and Usetime Prediction of Polyvinylnitrate (PVN).
Paper 73 on the 37th International Annual Conference of ICT, June 27 to 30, 2006, Karlsruhe,Germany.
Proceedings 2006, pages 73-1 to 73-18. Fraunhofer-Institut für Chemische Technologie (ICT), D-76318 Pfinztal.
/3/
M.A. Bohn, T.M. Klapötke
DFT and G2MP2 Calculations of the N-N Bond Dissociation Enthalpies and Enthalpies of Formation of Hydrazine,
Monomethylhydrazine and Symmetrical and Unsymmetrical Dimethylhydrazine.
Z. Naturforschung 59b, 148-152 (2004)
/4/
M.A. Bohn and M.E. Grillo
Quantum mechanical calculations used to reveal decomposition ways of Ammonium Dinitramide (ADN).
Paper 74 on the 37th International Annual Conference of ICT, June 27 to 30, 2006, Karlsruhe, Germany.
/5/
M.A. Bohn, F. Volk, O. Brauer
Determining the Safe Lifetime of a Plasticized Nitrocellulose.
Proceed of the 8th International Syposium on ‘Loss Prevention and Safety Promotion in the Process Industries’ Vol. II
Ed. J.J. Mewis, H.J. Pasman, E.E. De Rademaeker
Elsevier Science B.V., Amsterdam, New York, Oxford Tokyo, 1995.
/6/
M.A. Bohn
Kinetic Description of Mass Loss Data for the Assessment of Stability. Compatibility and Aging of
Energetic Components and Formulations Exemplified with ε-CL20.
Propellants Explosives Pyrotechnics 27. 125-135 (2002).
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 126
/7/
M.A. Bohn, N. Eisenreich
Kinetic Modelling of the Stabilizer Consumption and of the Consecutive Products of the Stabilizer in a Gun Propellant.
Propellants, Explosives, Pyrotechnics 22, 125-136 (1997).
/8/
M.A. Bohn
Prediction of Life Times of Propellants - Improved Kinetic Description of the Stabilizer Consumption.
Propellants, Explosives, Pyrotechnics 19, 266-269 (1994).
/9/
M.A. Bohn
Ammunition monitoring in field situations by stabilizer consumption and molar mass decrease as predictive tools.
/10/
M.A. Bohn, F. Volk, S. Lütze, S. Strempel, K.-H. Köppel
Monitoring of the Natural Ageing over 16 years of two Single Base Propellants Used in Car Safety Systems.
/11/
M.A. Bohn
Kinetic modelling of the concentrations of the stabilizer DPA and some of its consecutive products
as function of time and temperature.
J. Thermal Analysis and Calorimetry 65, 103-120 (2001).
/12/
M.A. Bohn
Modelling of Stabilizer Reactions in Gun and Rocket Propellants.
in ‘Ageing Studies and Lifetime Extension of Materials’ pages 449 - 466. Editor: L.G. Mallinson.
Kluwer Academic / Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2001.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 127
/13/
M.A. Bohn, N. Eisenreich
Temperaturabhängigkeit der Zersetzung der Nitrocellulose bestimmt mit Modellierung des TGA-Massenverlusts und
Stabilisatorverbrauchs (Temperature dependence of the decomposition of nitrocellulose determined by TGA mass loss
and stabilizer consumption).
Paper 62 in Proceed. of the 31st Internat. Annual Conference of ICT 2000. pages 62-1 to 62-10. June 27-June 30, 2000,
Karlsruhe, Germany. Fraunhofer-Institut für Chemische Technologie (ICT). D-76318 Pfinztal-Berghausen. Germany.
/14/
M.A. Bohn
The Use of Kinetic Equations to Evaluate the Ageing Behaviour of Energetic Materials – Possible Problems.
Proceed. 11th Symp. on ‘Chemical Problems Connected with the Stability of Explosives’ (held in Båstad, May 24 to 28,
1998), pages 89-151. Editor: Jan Hansson, Ola Listh. 1999, Sundbyberg, Sweden.
/15/
A. Pfeil, H.H. Krause, N. Eisenreich.
The Consequences of Beginning Slow Thermal Decomposition on the Molecular Weight of Nitrated Cellulose.
Thermochimica Acta 85 (1985) 395-398.
/16/
F. Volk, M.A. Bohn, G. Wunsch.
Determination of Chemical and Mechanical Properties of Double Base Propellants during Aging.
Propellants, Explosives, Pyrotechnics 12 (1987) 81-87.
/17/
M.A. Bohn, D. Müller
Insensitivity aspects of NC bonded and DNDA plasticizer containing gun propellants.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn / 128
.
Thank you for your attention
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
2007
Bohn /
129

NC-based energetic materials - stability, decomposition, and ageing

Transcription

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