Michael HessDepartment of Physical Chemistry

University Duisburg-EssenCampus Duisburg

47048 Duisburg, Germanye-mail: hi259he@uni-duisburg.de

Balance

oven

Thermocouple

ConrollerAnalyzerData output

Zero control

Mass compensation

Optionaltoanalyzer:IRGC-MSetc.

Carrier gas: N2, air, O2, …

Principle scheme of a thermogravimetric system

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

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

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

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.

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

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

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)

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

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:

1-C

T [K] 1T [K-1]

slope m = -0.457 Ea/Rlg

1

2

3

2

1

3

Ozawa method

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:

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

(random) bond scission

volatile products

volatile products

radical transfer (chain transfer)

disproportionation

Some examples of pyrolytic reactions