Statistical mechanics of semiflexible polymers

TL;DR

This paper develops a statistical-mechanical framework for semiflexible polymers by linking the Kratky-Porod model with quantum rigid rotator theory, enabling analysis of their structure, fluctuations, and surface interactions.

Contribution

It introduces a novel approach connecting polymer physics with quantum mechanics, generalizing flexible polymer relations to semiflexible ones, and provides tools for studying polymers in external fields and interfaces.

Findings

Derived expressions for the structure factor of semiflexible polymers.

Analyzed transversal fluctuations and localization near interfaces.

Established a framework for studying polymer adsorption and boundary effects.

Abstract

We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, $1/(k^{2}/3+p)$, through the matrix $\tilde{P}(k,p)=(I+ikDM)^{-1}D$, where $D$ and $M$ are related to the spectrum of the quantum rigid rotator, and considers an appropriate matrix element of the expression under consideration. The present work provides also the framework to study polymers in external fields, and problems including the tangents of semiflexible polymers. We study the structure factor of the polymer, the transversal fluctuations of a free end of the polymer with fixed tangent of another end, and the localization of a semiflexible polymer onto an interface. We obtain the partition function of a semiflexible polymer in half space with Dirichlet boundary condition in terms of the end-to-end distribution function of the free semiflexible polymer, study the behaviour of a semiflexible polymer in the vicinity of a surface, and adsorption onto a surface.