Estimation of Long-Range Interaction in Coarse-Grained Rotational Isomeric State Polyethylene Chains on a High Coordination Lattice

Abstract

A new Monte Carlo simulation on a coarse-grained tetrahedral lattice was recently developed for rotational isomeric state polyethylene chains. The short-range interaction was included by extending the classical statistical weight matrix. To describe the cohesive nature of realistic polyethylene systems, nonbonded long-range interaction was considered. The second virial coefficient B 2 of two chains under an interparticle potential was suitably written in a discretized form to be analyzed for this new lattice. Utilizing the vanishing B 2 of a ϑ chain was previously suggested for the estimation of interaction parameters representing several nearest neighbors. This approach was shown to be sufficient for treatment of dilute solutions, where long-range interactions are relatively infrequent. This study presents an alternative method of parameter estimation which is more appropriate for the bulk state, where long-range interactions are abundant. Interaction parameters were defined from an averaging procedure of the Mayer function in the expression of B 2. In the latter method, the widely used Lennard-Jones potential and associated parameters for the monomeric unit were used to calculated the average Mayer function. The estimated interaction parameters were used to simulate the average neighbor occupancy and the nonbonded energy per monomer. The nonbonded energy showed a minimum when it was plotted as a function of density. The latter method is considered better for the estimation of long-range interaction and yielded the density of minimum energy in a physically reasonable range. The calculated cohesive energy was shown to be close to the range defined by experiment.

A second generation of mapping/reverse mapping of coarse-grained and fully atomistic models of polymer melts

“…It forces the beads in the coarse-grained chain, part c, to retain the local conformational characteristics of the real chain from which they were derived 17) . Simulation of a multichain system on the high coordination lattice, at the density of a polyethylene melt, requires occupancy of only about 1/6 of the sites 18) . Equilibration of the model for the melt on the sparsely occupied high coordination lattice can be achieved more quickly than the equilibration of an alternative representation of the melt which employs the fully atomistic description of the system 19) .…”

Simulation of an amorphous polyethylene nanofiber on a high coordination lattice

“…One type of implementation of these methods involves the mapping of rotational isomeric state models onto a high coordination lattice [21][22][23] , with subsequent reverse mapping of the equilibrated model to an atomistic description in continuum space 24) . Doruker and Mattice 25) used this approach to simulate static properties of coarse-grained free-standing thin films of amorphous polyethylene.…”

“…The LJ potential for polyethylene is changed to accommodate the 2nnd lattice where every bead represents an ethylene unit rather than a methylene unit. The calculation of the average interaction energies between lattice sites is performed through the second virial coefficient expression 23) . The LJ parameters and interaction energies between first, second and third neighboring shells are given in Tab.…”

“…This initial step employs only selfavoiding walks with the excluded volume condition. Next, intramolecular and intermolecular interactions are introduced 22,23) . The initial structure is then relaxed in order to minimize its potential energy by the Dynamic Monte Carlo technique.…”

“…The initial structure is then relaxed in order to minimize its potential energy by the Dynamic Monte Carlo technique. Details for these previous PE bulk simulations are presented elsewhere 23,24,32) .…”