michael hess department of physical chemistry university duisburg-essen campus duisburg 47048...
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![Page 1: Michael Hess Department of Physical Chemistry University Duisburg-Essen Campus Duisburg 47048 Duisburg, Germany e-mail: hi259he@uni-duisburg.de](https://reader036.vdocuments.site/reader036/viewer/2022072011/56649e265503460f94b15e86/html5/thumbnails/1.jpg)
Michael HessDepartment of Physical Chemistry
University Duisburg-EssenCampus Duisburg
47048 Duisburg, Germanye-mail: [email protected]
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Balance
oven
Thermocouple
ConrollerAnalyzerData output
Zero control
Mass compensation
Optionaltoanalyzer:IRGC-MSetc.
Carrier gas: N2, air, O2, …
Principle scheme of a thermogravimetric system
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TGA-systems can be combined with:
IR-spectrometry GC-MSgas phase absorptionthinlayer chromatographyDSCDTA
Product identification
Enthalpy, phase transitions
Sample mass 1-20 mgSensitivity 10-3 mg
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Processes of interest in polymer science:
In general: m = f(T)dm/dt or m = f(t)T
thermal activated degradation (depolymerization)
thermo-oxidative degradation
Thermal stability i. e. upper limit of use under short-term heat-exposure
Determination of reaction-kinetical data such as:
reaction rate r,
rate constant k
apparent reaction energy Ea
apparent pre-exponential factor A (collision factor)
formal (apparent) reaction order n
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thermal activated degradation (depolymerization)
inert atmosphere, e. g. N2
e. g.: thermal depolymerization of poly(-methyl styrene):
ntmk
dt
dm
T
m
reactionofextend
d
d)(
with n = 1 in this case
This reaction is (during a large part of the reaction) a simple “un-zipping” of the polymer chain from its end, monomer after monomer.
In polystyrene the depolymerization occurs randomly along the chain
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thermo-oxidative degradation
More complex kinetics which is in particular influenced bythe diffusion process of O2 to the reaction site (char formation),the activities of flame retardants and inhibitors etc.
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In many cases
•there are complex kinetics
•there is influence of diffusion rates of reactants and products
•there are solid-state reactions
• there are incomplete polymerizations or crosslink reaktions (in thermosets)
•apparent reaction orders different from n = 1 can be observed
![Page 8: Michael Hess Department of Physical Chemistry University Duisburg-Essen Campus Duisburg 47048 Duisburg, Germany e-mail: hi259he@uni-duisburg.de](https://reader036.vdocuments.site/reader036/viewer/2022072011/56649e265503460f94b15e86/html5/thumbnails/8.jpg)
![Page 9: Michael Hess Department of Physical Chemistry University Duisburg-Essen Campus Duisburg 47048 Duisburg, Germany e-mail: hi259he@uni-duisburg.de](https://reader036.vdocuments.site/reader036/viewer/2022072011/56649e265503460f94b15e86/html5/thumbnails/9.jpg)
ni = ni0+ i
AA + BB+… mM + LL +…
reactants i 0 products i 0
r•= d/dt= - i-1dni/dt [mol s-1]
(rX•= dX/dt= - i-1dci/dt [mol L-1 s-1])
i= stoichiometric coefficientni = amount of substanceni0 = amount of substance at =0 (initial amount of substance) = extend of reactionci=(molar) concentrationX= conversionr=rate of reaction
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isothermal experiments: w = f(t)T
dynamic experiments: w = f (T)dT/dt = f (t)
w = sample massw0 = initial sample masst = timeT = temperature = heating rateC = conversion
tT
dd
The mass loss at any time is given by:
w = w0-w
so that the conversion C is given by:
C = w/w0 = (w0-w)/w0
(1-C) = w/w0
isothermal experiments are straight forwardbut they are experimentally difficult
(mass-loss fraction)
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rcA(A)
rcB(B
)
.
.
.
r= kn cA(A) cB
(B) …
kn= rate constant(A), (B) … = partial formal order of component A,
component B,…n = formal (total) order of reaction
kn = f(T, p, catalyst, solvent,…)
zi
ai
in
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In case of a pyrolytic reaction frequently the form:
wwnTR
EA
r
tw
tT
nwwTR
EA
tw
nwwnkt
w
0log1
302.2alog
dd
dd
log
1aexpdd
0dd
0
can be used:
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1-C
T [K] 1T [K-1]
slope m = -0.457 Ea/Rlg
1
2
3
2
1
3
Ozawa method
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TR
EAkeAk
a
nnTRaE 1
lnlnfactoryeffectivit
factorcollision factortialpreexponen
Ea = (apparent) activation energy [kJ/mol]
Arrhenius’ law:
rC •= dC/dt= - dm/dt [mg s-1]
C = conversion
In thermogravimetric experiments:
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example of a complex depolymerization
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
0,0 100,0 200,0 300,0 400,0 500,0 600,0 700,0 800,0 900,0
temperature [°C]
sa
mp
le m
as
s [
mg
]
nitrogen
Process I
Process II
Process III
Process IV
Residual material
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(random) bond scission
volatile products
volatile products
radical transfer (chain transfer)
disproportionation
Some examples of pyrolytic reactions
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