Brownian dynamics simulations of needle chain and nugget chain polymer models--rigid constraint conditions versus infinitely stiff springs.

It is well known that orientational correlations appear in polymer chain models when the subunits are linked by ball-socket joints implemented as rigid constraint conditions. These correlations do not appear when the subunits are connected by springlike potential forces, even in the limit of infinitely stiff springs. In a widely used class of algorithms for Brownian dynamics simulations, inertia effects are ignored. However, in the recently introduced needle chain and nugget chain algorithms, the rigid constraint correlations depend on the mass and moment of inertia. This inconsistency does not appear in the bead-rod (Kramers) polymer chain model, which also has orientational correlations introduced by rigid constraint conditions. Explicit expressions for the correlation functions are given for thermodynamic equilibrium states. Analytical expressions for the associated forces ("metric forces") and simulation results showing how the rigid constraint correlations influence dynamical properties, are also presented. Further we discuss the physical relevance of these correlations and show via simulations that their influence on stationary and dynamical properties depend significantly on chain length. We further show that if the metric forces are removed, algorithms designed with rigid constraint conditions describe a chain of segments connected by infinitely stiff springs. Finally we show that the results presented here for needle chains are relevant also for the bead-rod (Kramers) chain model, making it possible to simulate a bead-spring chain with infinitely stiff springs.