Showing papers by "Moungi G. Bawendi published in 1987"

A lattice field theory for polymer systems with nearest‐neighbor interaction energies

Abstract: We generalize a lattice field theory that formally provides an exact description of the statistical mechanical entropy of nonoverlapping flexible polymers to enable treatment of nearest‐neighbor interaction energies. The theory is explicitly solved within an extended mean field approximation for a system of polymer chains and voids, and we also provide mean field results for polymer–solvent–void and binary blend–void mixtures. In addition to recovering the Flory–Huggins mean field approximation for these systems, our extended definition of the mean field approximation contains a set of corrections to Flory–Huggins theory in the form of an expansion in powers of the nearest‐neighbor interaction energies.

Lattice models of polymer solutions: Monomers occupying several lattice sites

Abstract: An exact field theory is presented to describe a system of self‐avoiding lattice polymer chains with arbitrary regularly branched architecture. Equivalently, the chains can be viewed as linear and as composed of structural units (monomers) having a chosen shape and size and therefore each occupying more than one lattice site. The mean field approximation coincides with Flory’s theory, and it does not distinguish among chain geometries. However, we develop a systematic expansion for corrections to mean field approximation in powers of z−1 where z is the lattice coordination number. The entropy per site, the pressure and the chain insertion probability are computed for various chain architectures to O(z−2). At equal lattice site coverages per chain and total polymer volume fraction, the more compact the polymer chain geometry the higher is the insertion probability.

A lattice model for self‐ and mutually avoiding semiflexible polymer chains

Abstract: We introduce a spin field theory for many self‐ and mutually avoiding polymers with arbitrary stiffness on a regular lattice. The model allows for the complete crossover between flexible polymers and rods. The model also includes arbitrary polymer length distributions and arbitrary volume fractions from the highly dilute regime to the melt. The mean field approximation to the full theory reproduces Flory theory, but our model permits a rigorous and systematic evaluation of corrections to the mean field approximation. The corrections are in the form of a double expansion in powers of the volume fraction ψ and, formally, in powers of the inverse lattice coordination number z−1. We present the correction to first order in z−1 and discuss its relevance to the entropic contribution to the Flory χ parameter for semiflexible polymers.