Generalized Statistical Mechanics and Scaling Behavior for Non-equilibrium Polymer Chains: II. Monomers Connected by Springs

Abstract

Using molecular dynamics simulation, we find that the velocity distributions of monomers in the system of non-equilibrium polymer chains and Lennard-Jones molecules in a wide range of simulation time can be well described by Tsallis q-statistics and a single scaling function; the value of q is related to the conformation constraining potential, the interactions with background fluid, or the destruction of chain homogeneity. This approach can be applied to other non-equilibrium systems.

Molecular Dynamics Approach to Relaxation and Aggregation of Polymer Chains

“…9) We have used molecular dynamics (MD) simulations to study relaxation processes in various systems of polymer chains and Lennard-Jones (L-J) molecules; two neighboring monomers along a polymer chain are connected by a rigid bond 10) or a spring of strength k spring . 11) We find that the velocity distributions of monomers in a wide range of simulation time can be well described by Tsallis q-statistics 14), 15) and a single scaling function, where q ≥ 1 and q-statistics becomes the Maxwell-Boltzmann distribution when q → 1. We also find that when neighboring monomers of a polymer chain have small or zero bending-angle and torsion-angle dependent potentials, then the polymer chains tend to aggregate.…”

“…11) We find that during the relaxation process the velocity distributions of monomers in a wide range of simulation time can be well described by Tsallis q-statistics 14), 15) with a generalized Maxwell-Boltzmann distribution (GMBD) 22)-24) and a single scaling function. The value of q is related to the conformation constraining potential, the interactions with background fluid, the destruction of chain homogeneity or the value of k spring .…”

Phase diagram and universality of the Lennard-Jones gas-liquid system

“…Very recently, Ma and Hu [39][40][41][42][43] used MD to study relaxation and aggregation of polymer chains, in which neighboring monomers of a polymer chain are connected by rigid bonds [39,41] or springs with various spring constants [40,42]. They found that when the bending-angle depending potential and the torsion-angle depending potential are zero or very small, polymer chains tend to aggregate [41][42][43].…”

Physical mechanism for biopolymers to aggregate and maintain in non-equilibrium states

“…Over the processes along the red dashed line on the right side of Fig. 1(e), the probability density function P GMB ( v ) for monomer speed v at each instant is well fitted by the generalized Maxwell-Boltzmann (GMB) speed distributionwhere the factor j G ( v ) = 4 πv 2 has been used in previous studies 51, 52 and A q is the normalization factor and all monomers are assumed to have equal masses, m  = 1. Note that, the choice of factor 4 πv 2 is compatible with the isotropic Maxwell’s distribution of speed (subscript ‘IMB’ for istropic Maxwell-Botzmann), which isas the special case of q  = 1.…”