Elasticity of Highly Entangled Polymer Networks and Gels: Review of Models and Theory of Nonaffine Deformations

S. V. Panyukov; Панюков С. В.

doi:10.31857/S2308114723700310

Elasticity of Highly Entangled Polymer Networks and Gels: Review of Models and Theory of Nonaffine Deformations

Authors: Panyukov S.V.¹^,2
Affiliations:
1. Lebedev Physics Institute, Russian Academy of Sciences
2. Moscow Institute of Physics and Technology
Issue: Vol 65, No 1 (2023)
Pages: 31-50
Section: Articles
URL: https://cardiosomatics.ru/2308-1147/article/view/674805
DOI: https://doi.org/10.31857/S2308114723700310
EDN: https://elibrary.ru/HXDKTD
ID: 674805

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Abstract
About the authors
References
Supplementary files
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Abstract

The main models of phantom and topologically entangled polymer networks are surveyed. A theory of anisotropic and nonaffine deformation of both swollen and deswollen (with partial solvent removal) strongly entangled polymer networks in athermal and θ-solvents has been developed. It is shown that under weak anisotropic deformations of the deswollen network, the entanglement tube consists of fractal loopy globules. In a θ-solvent, slight deformations of the network lead to a decrease in the overlap of loopy globules without changing their sizes. Deformations of swollen networks, as well as strong deformations of deswollen networks, are described in terms of the slip-tube model. An effective Hamiltonian has been derived that determines the entropy of fractal loopy globules. Based on the Hamiltonian, it is shown that topological constraints can be described using the polymer–quantum diffusion analogy. The connection between topological and quantum entanglements is demonstrated.

About the authors

S. V. Panyukov

Lebedev Physics Institute, Russian Academy of Sciences; Moscow Institute of Physics and Technology

Author for correspondence.
Email: s.panyukov@gmail.com
Moscow, Russia; Dolgoprudnyi, Moscow oblast, Russia

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