  In this work we illustrate our novel quantitative simulation approach for
dense amorphous polymer systems, as discussed in our previous work[Kulkarni et
al., A Novel Approach for Lattice Simulations of Polymer Chains in Dense
Amorphous Polymer Systems: Method Development and Validation with 2-D Lattices,
arXiV, 2008] in applications involving large lattice sizes and high energetic
bias. We first demonstrate how the topology of the microstate ensemble in 2-D
lattices presents a serious challenge for the collection of accurate and
reliable quantitative results (i.e., with simultaneous determination of error
bars) for large lattices. This necessitates a further enhancement of our Monte
Carlo simulation scheme to sample effectively a meaningful 2-D lattice
configurational subspace. Two techniques were investigated: simulated annealing
and parallel tempering, to avoid trapping near a local free energy minimum in
simulations at high energetic bias. Extensive results of the prediction of
various chain conformation statistics and thermodynamic quantities, in the
thermodynamic limit (i.e. infinite lateral sizes) are presented.
