On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends

The self-consistent field (SCF) theory of dense polymer liquids assumes that short-range correlations are almost independent of how monomers are connected into polymers. Some limits of this idea are explored in the context of a perturbation theory for mixtures of structurally identical polymer species, A and B, in which the AB pair interaction differs slightly from the AA and BB interaction, and the difference is controlled by a parameter alpha Expanding the free energy to O(\alpha) yields an excess free energy of the form alpha $z(N)\phi_{A}\phi_{B}$, in both lattice and continuum models, where z(N) is a measure of the number of inter-molecular near neighbors of each monomer in a one-component liquid. This quantity decreases slightly with increasing N because the self-concentration of monomers from the same chain is slightly higher for longer chains, creating a deeper correlation hole for longer chains. We analyze the resulting $N$-dependence, and predict that $z(N) = z^{\infty}[1 + \beta \bar{N}^{-1/2}]$, where $\bar{N}$ is an invariant degree of polymerization, and $\beta=(6/\pi)^{3/2}$. This and other predictions are confirmed by comparison to simulations. We also propose a way to estimate the effective interaction parameter appropriate for comparisons of simulation data to SCF theory and to coarse-grained theories of corrections to SCF theory, which is based on an extrapolation of coefficients in this perturbation theory to the limit $N \to \infty$. We show that a renormalized one-loop theory contains a quantitatively correct description of the $N$-dependence of local structure studied here.Comment: submitted to J. Chem. Phy

Exponential distributions of collective flow-event properties in viscous liquid dynamics

We study the statistics of flow events in the inherent dynamics in supercooled two- and three-dimensional binary Lennard-Jones liquids. Distributions of changes of the collective quantities energy, pressure and shear stress become exponential at low temperatures, as does that of the event "size" $S\equiv\sum {d_i}^2$. We show how the $S$-distribution controls the others, while itself following from exponential tails in the distributions of (1) single particle displacements $d$, involving a Lindemann-like length $d_L$ and (2) the number of active particles (with $d>d_L$).Comment: Accepter version (PRL

Food preservation I

June, 1954."University of Missouri College of Agriculture and the United States Department of Agriculture Cooperating"--Page [14].Title from caption

Bethe lattice solution of a model of SAW's with up to 3 monomers per site and no restriction

In the multiple monomers per site (MMS) model, polymeric chains are represented by walks on a lattice which may visit each site up to K times. We have solved the unrestricted version of this model, where immediate reversals of the walks are allowed (RA) for K = 3 on a Bethe lattice with arbitrary coordination number in the grand-canonical formalism. We found transitions between a non-polymerized and two polymerized phases, which may be continuous or discontinuous. In the canonical situation, the transitions between the extended and the collapsed polymeric phases are always continuous. The transition line is partly composed by tricritical points and partially by critical endpoints, both lines meeting at a multicritical point. In the subspace of the parameter space where the model is related to SASAW's (self-attracting self-avoiding walks), the collapse transition is tricritical. We discuss the relation of our results with simulations and previous Bethe and Husimi lattice calculations for the MMS model found in the literature.Comment: 25 pages, 9 figure

What thermodynamic features characterize good and bad folders? Results from a simplified off-lattice protein model

The thermodynamics of the small SH3 protein domain is studied by means of a simplified model where each bead-like amino acid interacts with the others through a contact potential controlled by a 20x20 random matrix. Good folding sequences, characterized by a low native energy, display three main thermodynamical phases, namely a coil-like phase, an unfolded globule and a folded phase (plus other two phases, namely frozen and random coil, populated only at extremes temperatures). Interestingly, the unfolded globule has some regions already structured. Poorly designed sequences, on the other hand, display a wide transition from the random coil to a frozen state. The comparison with the analytic theory of heteropolymers is discussed

Elasticity near the vulcanization transition

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change

Food preservation IV

September, 1954."University of Missouri College of Agriculture and the United States Department of Agriculture Cooperating"--Page 18.Title from caption