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We present here the systematic development of quantitative latticesimulations of dense polymers through a novel computational technique thatallows for an efficient accounting of the chain conformations. Our approach isbased on the decomposition of the original lattice into sublattices of optimalsize. We develop and validate the method here for 2-D lattices usingsublattices of 4x4 nodes. For each possible connectivity, i.e. arrangement ofbonds connecting the 4x4 nodes of a sublattice with the rest of the nodes ofthe lattice, all possible sublattice microstates (submicrostates) areevaluated. We apply this technique to study the interlamellar amorphous phasein dense semicrystalline polymers where in polymer chains conform to a 2-Dsquare lattice. For lattices of moderate size (up to 8x8 nodes), exact resultscan be obtained from an exhaustive enumeration of all the microstatescorresponding to the fully dense (i.e. with no free chain ends) interlamellaramorphous phase of a semicrystalline system. For larger lattices, a stochasticenumeration technique (purely entropic) and an efficient Metropolis Monte Carloscheme were developed. A large selection of Monte Carlo moves makes thecorrelation between the Monte Carlo moves especially short. Thus, statisticalquantities of interest can be obtained with tight error bars (calculatedconcurrently with the averages) using small number of steps.

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