Excluded Volume Effects in Polymer Solutions: II. Comparison of Experimental Results with Numerical Simulation Data

The effect of excluded volume on the coil size of dilute linear polymers was investigated by off-lattice Monte Carlo simulations. The radius of gyration R{sub g} was evaluated for a wide range of chain lengths at several temperatures and at the athermal condition. The theta temperature and the corresponding theta chain dimensions were established for the system, and the dependence of the size expansion factor, a{sub s} = R{sub g} /(R{sub g}){sub {theta}}, on chain length N and temperature T was examined. For long chains and at high temperatures, a{sub s} is a function of N/N{sub s}{sup 2} alone, where the length scale N{sub s}{sup 2} depends only on T. The form of this simulations-based master function compares favorably with {alpha}{sub s}(M/M{sub s}{sup 2}), an experimental master curve for linear polymers in good solvents, where M{sub s}{sup 2} depends only on polymer-solvent system. Comparisons when N{sub s}{sup 2}(T) and M{sub s}{sup 2}(system) are reduced to common units, numbers of Kuhn steps, strongly indicate that coil expansion in even the best of good solvents is small relative to that expected for truly athermal solutions. An explanation for this behavior is proposed, based on what would appear to be an inherent difference in the equation of state properties for polymeric and monomeric liquids

Individual Entanglements in a Simulated Polymer Melt

We examine entanglements using monomer contacts between pairs of chains in a Brownian-dynamics simulation of a polymer melt. A map of contact positions with respect to the contacting monomer numbers (i,j) shows clustering in small regions of (i,j) which persists in time, as expected for entanglements. Using the ``space''-time correlation function of the aforementioned contacts, we show that a pair of entangled chains exhibits a qualitatively different behavior than a pair of distant chains when brought together. Quantitatively, about 50% of the contacts between entangled chains are persistent contacts not present in independently moving chains. In addition, we account for several observed scaling properties of the contact correlation function.Comment: latex, 12 pages, 7 figures, postscript file available at http://arnold.uchicago.edu/~ebn

Self-diffusion in binary blends of cyclic and linear polymers

A lattice model is used to estimate the self-diffusivity of entangled cyclic and linear polymers in blends of varying compositions. To interpret simulation results, we suggest a minimal model based on the physical idea that constraints imposed on a cyclic polymer by infiltrating linear chains have to be released, before it can diffuse beyond a radius of gyration. Both, the simulation, and recently reported experimental data on entangled DNA solutions support the simple model over a wide range of blend compositions, concentrations, and molecular weights.Comment: 10 pages, 2 figure

Tube Models for Rubber-Elastic Systems

In the first part of the paper we show that the constraining potentials introduced to mimic entanglement effects in Edwards' tube model and Flory's constrained junction model are diagonal in the generalized Rouse modes of the corresponding phantom network. As a consequence, both models can formally be solved exactly for arbitrary connectivity using the recently introduced constrained mode model. In the second part, we solve a double tube model for the confinement of long paths in polymer networks which is partially due to crosslinking and partially due to entanglements. Our model describes a non-trivial crossover between the Warner-Edwards and the Heinrich-Straube tube models. We present results for the macroscopic elastic properties as well as for the microscopic deformations including structure factors.Comment: 15 pages, 8 figures, Macromolecules in pres

Equilibrium swelling and universal ratios in dilute polymer solutions: Exact Brownian dynamics simulations for a delta function excluded volume potential

A narrow Gaussian excluded volume potential, which tends to a delta-function repulsive potential in the limit of a width parameter d* going to zero, has been used to examine the universal consequences of excluded volume interactions on the equilibrium and linear viscoelastic properties of dilute polymer solutions. Brownian dynamics simulations data, acquired for chains of finite length, has been extrapolated to the limit of infinite chain length to obtain model independent predictions. The success of the method in predicting well known aspects of static solution properties suggests that it can be used as a systematic means by which the influence of solvent quality on both equilibrium and non-equilibrium properties can be studied.Comment: Revised version submitted to Physical Review Letters. 4 pages, 2 figures (revised with additional data