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Freely Suspended Semiflexible Chains in a Strong Aligning Field: Simple Closed‐Form Solutions for the Small‐Angle Approximation
Author(s) -
Kloza Philipp A.,
Elliott James A.
Publication year - 2020
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.202000049
Subject(s) - chain (unit) , monte carlo method , trigonometric functions , statistical physics , corollary , field (mathematics) , physics , simple (philosophy) , function (biology) , coupling (piping) , mathematics , materials science , geometry , quantum mechanics , philosophy , statistics , epistemology , evolutionary biology , pure mathematics , metallurgy , biology
A worm‐like chain model for a single, freely suspended semiflexible macromolecule with an aligning field of arbitrary coupling order is presented. Using a small‐angle approximation and Ginzburg–Landau theory, exact closed‐form solutions of the model are derived in the regime of a strong aligning field in arbitrary dimensions. Expressions for the mean cosine of the chain alignment angle, orientational order parameters, and the two‐point correlation function are found. As a corollary, the persistence length is confirmed as a valid threshold for rigid behavior of the chain. The theoretical results are validated with Monte Carlo simulations in two and three dimensions. It is shown that the solutions for the small‐angle approximation are within 0.1 % of the simulated values for the exact model for chain‐field alignment angles θ ≲ 20°. As a practical application, the findings are applied to carbon nanotubes in an aligning electric field.