Langevin Dynamics of a Polymer with Internal Distance Constraints

Details Langevin Dynamics of a Polymer with Internal Distance Constraints Langevin Dynamics of a Polymer with Internal Distance Constraints

1996-11-06

arxiv.org/abs/cond-mat/9611041v1

Physics

Condensed Matter

Soft Condensed Matter

To appear in PRE, Figures on request

Scientific paper

10.1103/PhysRevE.55.3037

We present a novel and rigorous approach to the Langevin dynamics of ideal polymer chains subject to internal distance constraints. The permanent constraints are modelled by harmonic potentials in the limit when the strength of the potential approaches infinity (hard crosslinks). The crosslinks are assumed to exist between arbitrary pairs of monomers. Formally exact expressions for the resolvent and spectral density matrix of the system are derived. To illustrate the method we study the diffusional behavior of monomers in the vicinity of a single crosslink within the framework of the Rouse model. The same problem has been studied previously by Warner (J. Phys. C: Solid State Phys. {\bf 14}, 4985, (1981)) on the basis of Lagrangian multipliers. Here we derive the full, hence exact, solution to the problem.

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