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Construction of Approximate Entropic Forces for Finitely Extensible Nonlinear Elastic (FENE) Polymers
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| Macromolecular Theory Simul. |
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When the stress applied to a Rouse-like polymer chain is large enough, one must use anharmonic entropic spring forces in order to keep the chain contour length from increasing to unphysical values. Although one can derive 'exact' equations relating the spring extension to the entropic force produced by a finitely extensible non-linear elastic (FENE) random-walk polymer, such expressions are usually of little interest because their complexity would entail large evaluation times in numerical studies by computer. Moreover, these expressions can rarely be used directly in analytical studies. In this article, we describe a systematic method to construct analytically simple yet numerically accurate expressions to relate the entropic force to the extensions of an entropic spring for a random-walk polymer chain in arbitrary dimension d>=2. These expressions are modified Pade approximants which yield the correct asymptotic behaviours in both the small and large extension limits. It is shown that the well-known Warner empirical approximation is but a limiting case (for infinite dimensions).
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