Dense Polymer Melts Research Articles

Theory of melted flux liquids.

Novel intermediate flux states should be accessible in high-${T}_{c}$ superconductors, where it appears that the conventional Abrikosov flux lattice is melted over a significant portion of the (H,T) plane. We discuss the Lindemann criterion, and argue that fluctuations in a flux crystal are highly anisotropic, so that an asymptotically two-dimensional melting transition is possible as the shear modulus drops toward zero for many sample geometries and field orientations. We then describe the ``entangled flux liquid'' which arises at high-flux densities or thick samples. The statistical mechanics of this liquid is closely related to the physics of two-dimensional superfluids. The decay of vortex line correlations along the field direction is controlled by the superfluid excitation spectrum. A renormalization-group analysis shows how line wandering changes the nature of the B(H) constitutive relation near ${H}_{c1}$. We suggest that a heavily entangled flux liquid could exhibit a shear modulus on experimental time scales, in analogy with viscoelastic behavior in dense polymer melts.

Theory of polymer melts: an integral equation approach

A general theory is developed for the equilibrium structure of dense polymer melts. This theory is based on an integral equation approach developed by Chandler and co-workers for molecular liquids. We are able to construct a tractable formalism for the polymer problem by employing the fact that a polymer molecule in a melt is ideal. This leads to a set of integral equations for the intermolecular radial distribution functions. In the case of a polymer ring, this set reduces to a single integral equation, which we have solved numerically for the case of Gaussian intramolecular statistics with repeat units interacting via hard-core repulsions. From this solution we obtained the radial distribution function, structure factor, and compressibility as functions of liquid de,nsity and degree of polymerization. Unlike the random phase approximation (RPA) approach of de Gennes, the present theory allows for density fluctuations. These density fluctuations, which decay on a length scale comparable to a few monomer units, are crucial for the calculation of the structure factor and thermodynamic properties such as the equation of state of the polymer fluid. Generalizations of the present theory to include linear chains, chain stiffness effects, and attractive interactions are possible.

Integral-equation theory of the structure of polymer melts.

A general, analytically tractable, nonperturbative theory of the equilibrium structure of dense polymer melts is proposed on the basis of modern integral-equation theories of molecular liquids. Calculations are presented for polymer rings obeying Gaussian statistics and interacting via hard-core repulsions. The correlation hole, compressibility, and static structure factor are found to be sensitive functions of liquid density and degree of polymerization.

Dynamics of entangled polymer melts: A computer simulation

As a model for dense polymer solutions or melts we consider an ensemble of n freely jointed chains consisting of N rigid links in a box. A Lennard-Jones interaction is taken to model repulsive and attractive interactions between the units of the chains. Dynamics is introduced into the model by allowing for stochastic rotations of the beads of the chains, where the transition probability satisfies detailed balance and only such rotations are allowed which do not lead to any intersection of chains, in order to take entanglement restrictions into account. Although the chains treated by the simulation are very short (N = 16), with increasing density and/or decreasing temperature we do find a transition from a regime of essentially Rouse-like dynamics (with decreased mobilities) to a glass-like state, where the ’’monomer’’ displacements are very small and follow different power laws of time than in the Rouse model. We also treat the case where all chains apart from the mobile one are strictly frozen in, so that the mobile chain moves through fixed obstacles. We clearly confirm the de Gennes reptation mechanism for this case, while it does not become effective in the other cases above where either ’’tube rearrangement’’ is not negligible or all motions are more or less frozen. The experimental relevance of these results is briefly discussed.