Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties

Abstract

The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system's constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.

Lagrangian descriptors of driven chemical reaction manifolds

“…We are currently pursuing these methods to address reactions in solvent environments with cavitational heterogeneity [79], and specifically to coarse-grained mesoscale dynamics in which the underlying solvent has intrinsic softness [80][81][82][83][84][85]. Such systems are not presently amenable to analytic treatments because the mean-field representations of microscopic systems are not exactly renormalizable at the mesoscale.…”

Nonequilibrium structure in sequential assembly

“…The control of such processes allows for the development of molecular machinery with desired structural and dynamical properties [10,11]. In the self-assembly of soft materials [12][13][14], exotic phase behavior, such as quasicrystalline states [15][16][17] and cluster crystals [18][19][20][21][22][23][24][25], are observed. Thus, the geometries, and corresponding energetic connectivity networks, of the resulting assemblies can be harnessed for use in tailored materials with unique properties.…”