Brownian dynamics simulation of needle-spring chains

Abstract

Chains consisting of rigid segments connected by flexible joints constitute an important class of polymers. The joints may be modeled as rigid constraints (the needle chain polymer model) or as springs interconnecting the ends of nearest neighbor segments where both the equilibrium length and stiffness of each spring are selectable parameters (the needle–spring polymer model). Using kinetic theory as the starting point we have derived the theoretical foundation for a Brownian dynamics algorithm for needle-spring polymer chains. The employed polymer model is valid for some Reynolds numbers and includes needle translational–translational, translational–rotational and rotational–rotational hydrodynamic interactions, external forces, excluded volume effects, and bending and twisting stiffness between nearest neighbor needles. Studies reported in the literature on other polymer models show that polymer chain dynamics may depend significantly on whether the constraints are rigid or spring-like. It is therefore expected that the dynamics of some biopolymers may be more accurately modeled by the needle–spring rather than the needle-chain polymer model.