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A thermodynamical framework for chemically reacting systems

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Abstract

In this paper, we develop a thermodynamic framework that is capable of describing the response of viscoelastic materials that are undergoing chemical reactions that takes into account stoichiometry. Of course, as a special sub-case, we can also describe the response of elastic materials that undergo chemical reactions. The study generalizes the framework developed by Rajagopal and co-workers to study the response of a disparate class of bodies undergoing entropy producing processes. One of the quintessential feature of this framework is that the second law of thermodynamics is formulated by introducing Gibbs’ potential, which is the natural way to study problems involving chemical reactions. The Gibbs potential–based formulation also naturally leads to implicit constitutive equations for the stress tensor. Another feature of the framework is that the constraints due to stoichiometry can also be taken into account in a consistent manner. The assumption of maximization of the rate of entropy production due to dissipation, heat conduction, and chemical reactions is invoked to determine an equation for the evolution of the natural configuration κ p(t)(B), the heat flux vector and a novel set of equations for the evolution of the concentration of the chemical constituents. To determine the efficacy of the framework with regard to chemical reactions, those occurring during vulcanization, a challenging set of chemical reactions, are chosen. More than one type of reaction mechanism is considered and the theoretically predicted distribution of mono, di and polysulfidic cross-links agree reasonably well with available experimental data.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    K. Kannan

  2. Department of Mechanical Engineering, Texas A&M University, College Station, TX, 77840, USA

    K. R. Rajagopal

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  1. K. Kannan
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  2. K. R. Rajagopal
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Correspondence to K. R. Rajagopal.

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Submitted to Zeitschrift für Angewandte Mathematik und Physik (ZAMP).

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Kannan, K., Rajagopal, K.R. A thermodynamical framework for chemically reacting systems. Z. Angew. Math. Phys. 62, 331–363 (2011). https://doi.org/10.1007/s00033-010-0104-1

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  • DOI: https://doi.org/10.1007/s00033-010-0104-1

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