2008/05/03 by Jaydeep A. Kulkarni, Joydeep Mukherjee, Kulkarni, Jaydeep A. +7 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Block Copolymer Self-Assembly #FOS: Physical sciences #Phase Equilibria and Thermodynamics #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0805.0381
24 pages
arxiv created 2008/05/03 · openalex publication_date 2008/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.