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, 12 99 (1998), preceding paper] introduce several mathematical criteria to asse ss the validity of the lattice cluster theory (LCT) and any theory for the thermodynamics of polymer systems, their main criticisms of the LCT apply e ither 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 ex pansion 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 wit h the LCT stem from the occurrence of a physically obvious extraneous root that is an inevitable consequence of truncating a high-temperature expansio n and that is readily rejected based on elementary physical grounds. Moreov er, the ''pathologies'' of the LCT alleged by Quinn and Gujrati for the inc ompressible polymer-solvent system are largely irrelevant to all applicatio ns of the lattice cluster theory to binary polymer blends. Finally, we disc uss how simple physical considerations and comparisons with Monte Carlo com putations provide far better insights into the practical limits of validity of the LCT than the purely mathematical criteria of Quinn and Gujrati as a pplied for unphysically low, dimensionless temperatures. (C) 1999 American Institute of Physics. [S0021-9606(99)50201-8].