1. Kinetic Data for Polymers
Sergey Vyazovkin

2. Bulk kinetics Polymers are materials
Processes of interest: Thermal and oxidative degradation Molding (thermoplastics) Reactive injection molding (thermosets) Fire resistance
Methods: DSC (heat release kinetics) TGA (mass loss kinetics)

3. Importance of TGA and DSC
ISI Web of Science ®:
DSC and polymer - 3,900
TGA and polymer – 1,200
FTIR and polymer – 2,900

4. Application to particular processes
DSC and crystallization and kinetics – 820
Microscopy and crystallization and kinetics – 810
DSC and curing/cure and kinetics
FTIR and curing/cure and kinetics - 247
TGA and polymer and degradation/decomposition – 420
FTIR and polymer and degradation/decomposition – 540

5. Kinetics by TGA and DSC

6. Typical kinetic approach
Single-step treatment preferred over multiple-step
Nonisothermal conditions preferred over isothermal
Single heating rate data analysis preferred over multiple heating programs

7. Single step rate equation
k(T) – rate constant
f() – reaction model

8. Arrhenius equation (1889)
Svante Arrhenius

9. Single step rate equation
“Kinetic triplet”:
E – activation energy
A – preexponential factor
f() – reaction model, f()= (1-)n

10. Transition state theory
ORIGINAL
Henry Eyring
E  activation energy

11. Transition state theory
Henry Eyring
1. no medium (gas phase) 2. single-step reaction

12. Multiple reactions

13. Diffusion

14. Condensed phase Reactions occur in the solid or liquid medium
Medium affects the temperature dependence of the rate
Experimental E involves physical properties of the medium

15. Single heating rate data analysis
Coats-Redfern method (1964): ~2000 citations!
TGA or DSC at 1 heating rate
 vs T data fit to different g() models

16. Compensation effect
Large uncertainty in E and lnA!

17. Compensation effect, lnA=aE+b
Decomposition of HMX T.B. Brill et al J. Phys. Chem. 1994, 98, 12242

18. Solid state reaction models

19. HMX: Kinetic triplets by Coats-Redfern method
 Best fits

20. Practical purpose: predictions

21. HMX: Predictions

22. Thermal degradation of PMMA
Atmosphere
Step 1
E / kJ mol-1
Step 2
Step 3
Experiment
Reference
vacuum
130 – 176
Isothermal manometry
1, 2
138
Isothermal TGA 3
242
117 5 N2
150 – 250
Nonisothermal TGA 8
210 9
154
133 11 12 31
224
233
104
Isothermal heating 13
113 15
130 – 180 16
[1] Single E values are listed under Step 1 regardless of the number of steps reported
[2] E increases with 
[3] Not reported

23. Thermal degradation of PP
Atmosphere
E / kJ mol-1
Method
Ref N2
244
Nonisothermal TGA 10
216
isothermal TGA 11
214 18
160 22
115 – 200 19
130 – 200 23
230
Factor-jump TGA
Vacuum
257 Ar
98, 328 25

24. ICTAC Kinetics Project

25. ICTAC Kinetics Project
Thermochim. Acta 355(2000)125
Single heating rate methods should be avoided
Use multiple heating rate methods instead
Importance of detecting complex processes

26. “Model-free” kinetics
Rate equation
Log derivative

27. “Model-free” kinetics
Isoconversional principle
Uses multiple heating rates
Yields a model-free estimate E

28. Isoconversional method
E varies with   multi-step process

29. Thermal degradation of PP
Atmosphere
E / kJ mol-1 N2
244
216
214
160
115 – 200
130 – 200
230
Vacuum
257 Ar
98, 328

30. Epoxy-amine cure: Variation of Eα with α
Decrease in Eα suggests a shift from kinetic to diffusion control that usually associated with vitrification.

31. TTT cure diagram
In the glassy state molecular motion is largely reduced

32. Detecting vitrification by temperature modulated DSC

33. Epoxy-amine cure: Variation of Eα with α70
2.68 -1 60 -1 K
/ kJ mol
2.64 -1
/ J g E a
Vitrification 50 *
2.60 C p 40
2.56
0.2
0.4
0.6
0.8
1.0 a
Epoxy-amine cure: Variation of Eα with α
Decrease in Eα is actually caused by vitrification

34. Melt crystallization kinetics
Poly(ethylene terephthalate)
Aldrich, MW ~18,000, Tm=280oC
Cooled from 290 to 25C
β = -3, -4, -6, -8, -12C/min

35. Temperature dependence of growth rate
Hoffman-Lauritzen theory:

36. Evaluating Kg and U* E vs   E vs T:
I: Kg= K2 , U*=4300 J/mol
II: Kg= K2 , U*=2300 J/mol
Macromol. Rapid Commun. 2004, 25, 733

37. Model-free predictions
Assuming that kinetic triplet (E, A, reaction model) at a given  does not change when changing T

38. Model-free predictions

39. Model-free predictions, HMX

40. Model-free predictions, shelf-life

41. Model-free predictions, shelf-life

42. Model-based methods
Model-based methods that use multiple heating programs are being developed
By far less common than model-free methods

43. Model-based Model-free
Model-based and model-free methods are interrelated via E dependence

44. Conclusions
E dependence can generally be interpreted as a function of the activation energies of individual steps
E is useful in exploring reaction mechanisms
The model-free approach requires only E for kinetic predictions
E dependence provides a link to model-based methods
Model-free approach can serve as a uniform framework for creating a database of bulk polymer (and solid-state) kinetics of thermal reactions

45. “The 16 questions” (polymers and solid-state)
3) nonisothermal data important
4) include overall or both (overall and elementary) reactions
7) complex reactions unavoidable
8) cannot be limited to single dif. Eq.
9) the database should include:
D) solid-state reactions
H) macromolecular reactions
I) polymerization reactions

46. “The 16 questions” (polymers and solid-state)
11) long term success via agreements w/journals
13) critical assessment is important

47. ThermoML

48. ThermoML @ J. Chem. Eng. Data
ThermoML is an XML-based format for the exchange and storage of thermophysical property data
Authors download and use the GDC software to capture the experimental property data that has been accepted for publication.
The output of the GDC Software converted into ThermoML format at TRC
Upon release of the manuscript the ThermoML files are posted on the public-domain TRC Web site

49. “KineticML” @ Thermochim. Acta?