A Novel Approach for Lattice Simulations of Polymer Chains in Dense Amorphous Polymer Systems: Method Development and Validation with 2-D Lattices

We present here the systematic development of quantitative lattice simulations of dense polymers through a novel computational technique that allows for an efficient accounting of the chain conformations. Our approach is based on the decomposition of the original lattice into sublattices of optimal size. We develop and validate the method here for 2-D lattices using sublattices of 4x4 nodes. For each possible connectivity, i.e. arrangement of bonds connecting the 4x4 nodes of a sublattice with the rest of the nodes of the lattice, all possible sublattice microstates (submicrostates) are evaluated. We apply this technique to study the interlamellar amorphous phase in dense semicrystalline polymers where in polymer chains conform to a 2-D square lattice. For lattices of moderate size (up to 8x8 nodes), exact results can be obtained from an exhaustive enumeration of all the microstates corresponding to the fully dense (i.e. with no free chain ends) interlamellar amorphous phase of a semicrystalline system. For larger lattices, a stochastic enumeration technique (purely entropic) and an efficient Metropolis Monte Carlo scheme were developed. A large selection of Monte Carlo moves makes the correlation between the Monte Carlo moves especially short. Thus, statistical quantities of interest can be obtained with tight error bars (calculated concurrently with the averages) using small number of steps.