Exact solution of the thermodynamics and size parameters of a polymer confined to a lattice of finite size: large chain limit.

We extend the exact solutions of the Di Marzio-Rubin matrix method for the thermodynamic properties, including chain density, of a linear polymer molecule confined to walk on a lattice of finite size. Our extensions enable (a) the use of higher dimensions (explicit 2D and 3D lattices), (b) lattice boundaries of arbitrary shape, and (c) the flexibility to allow each monomer to have its own energy of attraction for each lattice site. In the case of the large chain limit, we demonstrate how periodic boundary conditions can also be employed to reduce computation time.

Probing single nanometer-scale pores with polymeric molecular rulers.

We previously demonstrated that individual molecules of single-stranded DNA can be driven electrophoretically through a single Staphylococcus aureus alpha-hemolysin ion channel. Polynucleotides thread through the channel as extended chains and the polymer-induced ionic current blockades exhibit stable modes during the interactions. We show here that polynucleotides can be used to probe structural features of the alpha-hemolysin channel itself.

Configurational Entropy Approach to the Kinetics of Glasses.

A kinetic theory of glasses is developed using equilibrium theory as a foundation. After establishing basic criteria for glass formation and the capability of the equilibrium entropy theory to describe the equilibrium aspects of glass formation, a minimal model for the glass kinetics is proposed. Our kinetic model is based on a trapping description of particle motion in which escapes from deep wells provide the rate-determining steps for motion.

Mixing Plate-Like and Rod-Like Molecules With Solvent: A Test of Flory-Huggins Lattice Statistics.

Boehm and Martire have shown that the Flory-Huggins (FH) lattice model applied to mixtures of squares and rigid rods in solvent on a two dimensional lattice gives different results depending on whether rods or squares are placed first onto the lattice. This correct derivation places the validity of the FH model itself into question since the final result should be independent of the order of placement. An analysis of the FH model in terms of Poisson statistics suggests an alternative formula for the probability of successfully placing a rectangle into an area partially filled with other rectangles, which when incorporated into the FH counting procedure gives the exact thermodynamic result for the tiling of squares (i.

Dilute Solution Theory of Polymer Crystal Growth: Fractionation Effects.

A nonequilibrium (kinetic) theory of polymer molecular weight (MW) fractionation is formulated and applied to binary and multicomponent polyethylenes crystallized from unstirred xylene solutions. High MW components crystallize more readily than do low MW components. This fractionation effect is enhanced as the crystallization temperature is raised.