Journal of Chemical Physics, Vol.110, No.2, 1307-1312, 1999
Pragmatic analysis for the range of validity of the lattice cluster theory
While Quinn and Gujrati [B. Quinn and P. D. Gujrati, J. Chem. Phys. 110, 1299 (1998), preceding paper] introduce several mathematical criteria to assess the validity of the lattice cluster theory (LCT) and any theory for the thermodynamics of polymer systems, their main criticisms of the LCT apply either to temperatures far below those sensible in view of the derivation of the LCT, which retains only the first few terms from a high-temperature expansion of the free energy, or to regions of the phase diagram for which a mean-field theory is well known to be inadequate. Additional complaints with the LCT stem from the occurrence of a physically obvious extraneous root that is an inevitable consequence of truncating a high-temperature expansion and that is readily rejected based on elementary physical grounds. Moreover, the ''pathologies'' of the LCT alleged by Quinn and Gujrati for the incompressible polymer-solvent system are largely irrelevant to all applications of the lattice cluster theory to binary polymer blends. Finally, we discuss how simple physical considerations and comparisons with Monte Carlo computations provide far better insights into the practical limits of validity of the LCT than the purely mathematical criteria of Quinn and Gujrati as applied for unphysically low, dimensionless temperatures.
Keywords:MULTICOMPONENT POLYMER BLENDS;MONOMER STRUCTURE;COMPRESSIBLESYSTEMS;THEORY COMPUTATIONS;PHASE-EQUILIBRIA;PVME BLENDS;SIMULATION;MODEL;MISCIBILITY;MIXTURES