A thermodynamical framework for chemically reacting systems

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 62, Issue 2, 2011, Pages 331-363

  Kannan, K ^a   Rajagopal, K R ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

^b Texas AandM University   (United States)

Author keywords

Chemical reactions; Entropy production; Gibbs potential; Rubber chemistry; Thermodynamics

Indexed keywords

CHEMICAL CONSTITUENTS; CHEMICALLY REACTING SYSTEMS; ELASTIC MATERIALS; ENTROPY PRODUCTION; EXPERIMENTAL DATA; GIBBS POTENTIAL; HEAT FLUX VECTORS; NATURAL CONFIGURATIONS; REACTION MECHANISM; SECOND LAW OF THERMODYNAMICS; STRESS TENSORS; THERMODYNAMIC FRAMEWORK; VISCO-ELASTIC MATERIAL;

CONSTITUTIVE EQUATIONS; ENTROPY; HEAT FLUX; RUBBER; STOICHIOMETRY; TEACHING;

CHEMICAL REACTIONS;

EID: 79953725703     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-010-0104-1     Document Type: Article

References (42)

1. Abhilash P. M., Kannan K., Varkey B.: Simulation of curing of a slab of rubber. Mater. Sci. Eng. B 168, 237-241 (2010).
2. Bjornbom P. H.: The independent reactions in calculations of complex chemical equilibria. Ind. Eng. Chem. Fundam. 14, 102-106 (1975).
3. Brinkley S. R.: Note on conditions of equilibrium for systems of many constituents. J. Chem. Phys. 14, 563-564 (1946).
4. Chong E. K. P., Zak S. H.: An Introduction to Optimization. Wiley (Asia) Pte. Ltd., Singapore (2004).
5. Coran A. Y.: Vulcanization. part vi. a model and treatment for scorch delay kinetics. Rubber Chem. Technol. 37, 689-697 (1964).
6. Coran, A. Y.: Vulcanization. In: Mark, J. E., Erman, B., Eirich, F. R. (eds.) The Science and Technology of Rubber, pp. 321-367. (2005).
7. Denbigh K.: The Principles of Chemical Equilibrium. Cambridge University Press, London (1971).
8. Ding R., Leonov A.: A kinetic model for the sulfur accelerated vulcanization of rubber compound. J. Appl. Polym. Sci. 69, 455-463 (1996).
9. Ding R., Leonov A., Coran A. Y.: A study of the vulcanization kinetics of an accelerated-sulfur sbr compound. Rubber Chem. Technol. 69, 81-91 (1996).
10. Eckart C.: The thermodynamics of irreversible processes. IV. The theory of elasticity and anelasticity. Phys. Rev. 73, 373-382 (1948).
11. Fan R., Zhang Y., Huang C., Gong P., Zhang Y.: Simulation and verification for sulfur accelerated vulcanization of gum natural rubber compound. Rubber Chem. Technol. 75, 287-297 (2002).
12. Geyser M., McGill W. J.: A study of the rate of formation of polysulfides of tetramethylthiuram disulfide. J. Appl. Polym. Sci. 55, 215-224 (1995).
13. Geyser M., McGill W. J.: Thiuram-accelerated sulfur vulcanization. I. The formation of the active sulfurating agent. J. Appl. Polym. Sci. 60, 425-430 (1996).
14. Geyser M., McGill W. J.: Thiuram-accelerated sulfur vulcanization. II. The formation of crosslink precursors. J. Appl. Polym. Sci. 60, 431-437 (1996).
15. Ghosh P., Katare S., Patkar P., Caruthers J. M., Venkatasubramanian V., Walker K. A.: Sulphur vulcanization of natural rubber for benzothiazole accelerated formulations: From reaction mechanisms to a rational kinetic model. Rubber Chem. Technol. 76, 592-693 (2003).
16. Green A. E., Nagdhi P. M.: On the thermodynamics and the nature of the second law. Proc. R. Soc. A 357, 253-270 (1977).
17. Jog C. S.: Continuum Mechanics. Narosa Publishing House Pvt. Ltd., New Delhi (2007).
18. Kannan K., Rajagopal K. R.: A thermomechanical framework for the transition of a viscoelastic liquid to a viscoelastic solid. Math. Mech. Solids 9, 37-59 (2004).
19. Loo C. T.: High temperature vulcanization of elastomers: 2. Network structures in conventional sulphenamide-sulphur natural rubber vulcanizates. Polymer 15, 357-365 (1974).
20. Loo C. T.: High temperature vulcanization of elastomers: 3. Network structures of efficiently vulcanized natural rubber mixes. Polymer 15, 729-737 (1974).
21. Malek J., Rajagopal K. R.: A thermodynamic framework for a mixture of two liquids. Nonlinear Anal. Real World Appl. 9, 1649-1660 (2008).
22. Malik, W. A., Rajagopal, S., Darbha, S., Rajagopal, K. R. Maximizing the algebraic connectivity with at most a prescribed number of edges. In: Sivasundaram, S., Vasundhara, J., Udwadia F. E., Lasiecka, I. (eds.) Advances in Dynamics and Controls: Theory, Methods and Applications. (2009).
23. Moakher M.: Fourth-order cartesian tensors: Old and new facts, notions and applications. Q. J. Mech. Appl. Math. 61, 181-203 (2008).
24. Morgan B., McGill W. J.: Benzothiazole accelerated sulfur vulcanization. iv. effect of zno and bis(2 mercaptobenzothiazole)zinc(ii) on 2 bisbenzothiazole 2, 2 polysulfide formation in 2 bisbenzothiazole 2, 2 disulfide and 2 bisbenzothiazole 2, 2 disulfide/sulfur. J. Appl. Polym. Sci. 76, 1405-1412 (2000).
25. Morgan B., McGill W. J.: Benzothiazole accelerated sulfur vulcanization. v. 2 bisbenzothiazole 2, 2 disulfide/zno and 2 bisbenzothiazole 2, 2 disulfide/(2 mercaptobenzothiazole)zinc(ii) as accelerators for 2, 3 dimethyl 2 butene. J. Appl. Polym. Sci. 76, 1413-1421 (2000).
26. Onsager L.: Reciprocal relations in irreversible thermodynamics. Phys. Rev. 37, 405-426 (1931).
27. Prasad S. C., Rajagopal K. R.: A continuum model for the creep of single crystal nickel-base superalloys. Acta Mater. 53, 669-679 (2005).
28. Rajagopal K. R., Srinivasa A. R.: A thermodynamic frame work for rate type fluid models. J. Nonnewton. Fluid Mech. 88, 207-227 (2000).
29. Rajagopal K. R., Srinivasa A. R.: On the thermomechanics of materials that have multiple natural configurations - part i: Viscoelasticity and classical plasticity. Zeitschrift für Angew. Mathematik Phys. 55, 861-893 (2004).
30. Rajagopal K. R., Srinivasa A. R.: On the thermomechanics of materials that have multiple natural configurations-part ii: Twinning and solid to solid phase transformation. Zeitschrift für Angew. Mathematik Phys. 55, 1074-1093 (2004).
31. Rajagopal K. R., Srinivasa, A. R.: A gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials. Proceedings of the Royal Society A, pp. 1-20. (2010).
32. Rajagopal K. R., Tao L.: Mechanics of Mixtures. World Scientific Publishing Co. Pte Ltd., Singapore (1995).
33. Rajagopal K. R., Tao L.: Modeling of the microwave drying process of aqueous dielectrics. Zeitschrift für Angew. Mathematik Phys. 53, 923-948 (2002).
34. Rao I. J., Rajagopal K. R.: A thermodynamic framework for the study of crystallization in polymers. Zeitschrift für Angew. Mathematik Phys. 53, 365-406 (2002).
35. Schrodinger E.: What is Life?. Cambridge University Press, Cambridge (1992).
36. Smith G. F.: On isotropic integrity basis. Arch. Ration. Mech. Anal. 18, 282-292 (1965).
37. Spencer A. J. M., Rivlin R. S.: The theory of matrix polynomials and its application to the mechanics of isotropic continua. Arch. Ration. Mech. Anal. 2, 309-336 (1958).
38. Tao, L., Rajagopal, K. R.: On the construction of constitutive relations in hyperelasticity. In preparation.
39. Truesdell C., Noll W.: The Non-linear Field Theories of Mechanics. Springer, Berlin (1992).
40. Zeleznik F. J., Gordon S.: Calculations of complex chemical equilibria. Ind. Eng. Chem. 60, 27-57 (1968).
41. Ziegler, H.: Some extremum principles in irreversible thermodynamics with application to continuum mechanics. In: Sneddon I. N., Hill R. (eds.) Progress in Solid Mechanics, vol. 4, pp. 3-113. (1963).
42. Ziegler H., Wehrli C.: The derivation of constitutive relations from the free-energy and the dissipation function. Adv. Appl. Mech. 25, 183-238 (1987).