Fast Lattice Monte Carlo Simulations of Polymer Brushes

Fast lattice Monte Carlo (FLMC) simulations^[1] with multiple occupancy of lattice sites and Kronecker δ-function interactions give orders of magnitude faster/better sampling of the configuration space of multi-chain systems than conventional lattice MC simulations with self- and mutual- avoiding walks and nearest-neighbor interactions. Using FLMC simulations with canonical-ensemble, Wang-Landau – Transition-Matrix and Wang-Landau – Optimized-Ensemble sampling, we have studied polymer brushes both in an implicit and in an explicit solvent.^[2] For the latter system, we have also studied the brush compression by an impenetrable plane.  Comparing various quantities (including the internal energy, Helmholtz free energy, constant-volume heat capacity, pressure, segment distributions, and chain dimensions) obtained from FLMC simulations with predictions from the corresponding lattice self-consistent field (LSCF) calculations based on exactly the same model system (Hamiltonian) as used in FLMC simulations (thus without any parameter-fitting), we unambiguously and quantitatively reveal the effects of system fluctuations and correlations neglected in the LSCF theory.

[1] Q. Wang, Soft Matter 5, 4564 (2009); 6, 6206 (2010).

[2] P. Zhang, B. Li, and Q. Wang, Macromolecules 44, 7837 (2011); 45, 2537 (2012).