Statistical mechanics of semiflexible polymers

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.

30 pages, 7 figures, changed content

References in corpus (6)

• Neutral and Charged Polymers at Interfaces
• Elasticity of semi-flexible polymers
• Triple minima in free energy of semiflexible polymers
• The distribution function of a semiflexible polymer and random walks with constraints
• A simple and exactly solvable model for a semiflexible polymer chain interacting with a surface
• Adsorption of a semiflexible polymer onto interfaces and surfaces

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• Scattering function of semiflexible polymer chains under good solvent conditions
• Elasticity of semiflexible polymers in two dimensions
• Semiflexible polymers: Dependence on ensemble and boundary orientations
• On the behaviour of short Kratky-Porod chain
• Bimodal distribution function of a 3d wormlike chain with a fixed orientation of one end
• Neural Network Model for Structure Factor of Polymer Systems
• Length distribution of stiff, self-assembled polymers at thermal equilibrium