Showing papers by "Moungi G. Bawendi published in 1986"

A lattice model for self‐avoiding polymers with controlled length distributions. II. Corrections to Flory–Huggins mean field

Abstract: We continue the analysis of the lattice spin‐field theory which is introduced in paper I and which formally gives the exact entropy for a set of completely flexible self‐avoiding polymers on a lattice. The model allows for arbitrary chain length distributions and arbitrary polymer volume fractions. Use of random fields produces a field theory from which Flory–Huggins results are recovered in the mean field limit. Here we recast the mean field formulation to allow for the rigorous and systematic evaluation of corrections by means of a cluster expansion. We then calculate corrections to the mean field directly up to fourth order and provide a systematic diagrammatic method for evaluating general order corrections. Our results illustrate the polymer concentration dependence of the corrections to the Flory–Huggins mean field results as well as provide the origins for the entropic contribution to the Flory χ parameter and its concentration dependence. Generalizations to treat rods and semiflexible polymers will be given elsewhere.

Statistical mechanics of the packing of rods on a lattice: Cluster expansion for systematic corrections to mean field

Abstract: We introduce a lattice spin field theory which formally provides an exact description of the statistics of nonoverlapping, nonintersecting rods on regular lattices. The theory is applicable to arbitrary rod length distributions and arbitrary volume fractions. The mean field approximation reproduces Flory–Huggins theory for rods on a strict lattice, but our theory permits the rigorous and systematic evaluation of corrections to the mean field entropies. We present those corrections as a cluster expansion for the entropy density which involves a double expansion in powers of the volume fraction ψ and the inverse of the lattice coordination number z−1. Our results are compared for specific cases with those of DiMarzio’s theory which is more accurate than mean field. For dimers which are equally distributed among the possible lattice directions of a hypercubic lattice, we find very good agreement between our theory and DiMarzio’s with ours giving a slightly larger entropy density when corrections to mean fiel...

Renormalization group treatment of excluded volume effects in a polyelectrolyte chain in the weak electrostatic coupling limit. II. Decomposition of interactions and calculation of properties

Abstract: A theoretical description of excluded volume in polyelectrolytes is considered in the flexible chain limit. The approach generalizes the work of Kholodenko and Freed and removes some deficiencies, present in their work, which become apparent in further extensions of the theory. Renormalization group calculations are pursued to order e=4−d for the mean square end‐to‐end distance 〈R2〉, the radius of gyration 〈S2〉, and the second virial coefficient A2. The importance of including both a short range excluded volume interaction as well as a long range electrostatic one is stressed. The electrostatic interaction is effectively treated as a perturbation, so that the results are valid only in the weak electrostatic coupling region. The theory shows that polyelectrolyte excluded volume effects cannot generally be described in a scaling limit, and generalized scaling laws are derived which contain several parameters including the two interaction parameters. A qualitative comparison of the theory with available expe...