Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.     

Mesomorphic polymer solutions

Summary A mean-field theory for the nematic-isotropic phase transition in semi-rigid polymer solutions is proposed. Phase diagrams are calculated. New effects due to chain flexibility are found for the transition temperature and the nematic order parameter of the polymer. An abrupt increase of chain extension in the nematic phase is demonstrated. Paper presented at the ?Meeting on Lyotropics and Related Fields?, held in Rende, Cosenza, September 13–18, 1982.     

Triplet interactions in star polymer solutions

We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short-distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is attractive but only 11% of the pairwise part even for a close approach of three star polymers. We have also performed extensive computer simulations for different arm numbers f to extract the effective triplet force. The simulation data show good correspondence with the theoretical predictions. Our results justify the effective pair potential picture even beyond the star polymer overlap concentration. Received 1 September 1999 and Received in final form 18 January 2000     

Unusual thermal diffusion in polymer solutions

Thermal diffusion forced Rayleigh scattering results on thermal diffusion of poly(ethylene oxide) (PEO) in ethanol/water mixtures are presented. In water-rich solvent mixtures, PEO is found to migrate towards regions of lower temperature. This is typical for polymer solutions and corresponds to a positive Soret coefficient of PEO. In solvent mixtures with low water content, however, the polymer is found to migrate towards higher temperatures, corresponding to a negative Soret coefficient of PEO in ethanol-rich solutions. To our knowledge, this is the first observed sign change of the Soret coefficient of a polymer in solution. We also present a simple lattice model for the polymer solvent system and calculate Soret coefficients with statistical mechanics methods. The calculated values agree qualitatively with the experimental results.     

Cooperative diffusion in concentrated polymer solutions

Summary Concentrated solutions of polystyrene in dioctylphthalate have been examined as a function of temperature over the concentration range 0.2 to 0.9 g/ml. The static screening length and the hydrodynamic screening length evaluated from the cooperative-diffusion coefficient are compared with the predictions of current models. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Equilibrium ring formation in polymer solutions

This paper delivers a flexible formalism for handling equilibrium ring formation. Based on graphical models of polymerization, it includes as special cases the Flory-StockmayerRA _f model, the FloryA _f RB _g model, and Gordon's branching process formalism. When simple ring formation occurs in equireactive systems, it also includes the Jacobson-StockmayerRA ₂ and HoeveRA _f models. The formalism is built from first principles in statistical mechanics and all assumptions are clearly stated. All parameters are given in terms of thermodynamic variables. With ring weights generalizing the Jacobson-Stockmayer Gaussian random walk, the formalism yields results for branchingRA _f ,A _f RB _g , andRA _f -RB _g polymer models. Equireactivity then gives explicit solutions. The equireactiveRA _f -RB _g model compares favorably with data from gel-point vs. dilution experiments. With the exception of the Spanning Tree Approximation, graphical models of polymerization suffer from combinations of the following defects: equireactivity assumptions, restrictions to one type of monomer or bond, absence of rings, or absence of fused rings. This paper provides a promising exact approach to handling all of these problems simultaneously.     

Viscosity of concentrated polymer solutions

In investigations of the Newtonian viscosity of polymer fluids, two concentration regions have received the major attention. One is the dilute solution where the contributions of the individual solute entities are essentially additive with only small interaction perturbations. The other is the bulk polymer or plasticized melt. We are concerned here with the broad intermediate region.     

Turbulent dynamics of polymer solutions

We study properties of dilute polymer solutions. The probability density function (PDF) of polymer end-to-end extensions R in turbulent flows is examined. We show that if the value of the Lyapunov exponent lambda is smaller than the inverse molecular relaxation time 1/tau then the PDF has a strong peak at the equilibrium size R0 and a power tail at R>R0. This confirms and extends the results of J. L. Lumley [Symp. Math. 9, 315 (1972)]. There is no essential influence of polymers on the flow in this regime. At lambdatau>1 the majority of molecules is stretched to the linear size R(op)>R0, which can be much smaller than the maximal length of the molecules due to their back reaction.     

The size and equation of state of an athermal polymer in a strong solution: A screened convolution approximation

The configurational and thermodynamic properties of an athermal polymer system are determined at intermediate to high concentrations.     

Microphase separation in polymer solutions containing surfactants

A microphase separation in solutions containing a polymer and a mixture of two solvents, one of which consists of amphiphilic molecules (surfactant), is considered theoretically in the weak-segregation regime. A surfactant molecule is described as a dimer consisting of hydrophobic and polar parts. The energy gain due to the orientation of surfactant molecules can lead to the appearance of non-homogeneities in the solution, where density fluctuations cause the orientational ordering of surfactant molecules. The difference in the interaction energies of hydrophobic and polar groups of a surfactant with solvent is considered as a main reason for orienting surfactant molecules. The free energy is calculated for various morphologies (lamellar, cylindrical hexagonal, spherical particles arranged at different cubic lattices). The phase diagrams are presented. With worsening the solvent quality, the transitions from disordered to a macro-separated state at low polymer and surfactant concentrations or to a body-centered-cubic, then hexagonal, and then lamellar structure at high polymer and surfactant concentrations are predicted. The amphiphilicity degree of surfactant molecules should exceed a certain critical value to make a microstructure formation possible. The period of the lamellar microstructure decreases with increasing the surfactant and polymer concentrations.     

Drying and advancing droplets of polymer solutions

In this paper, we report on the competition between evaporation and hydrodynamics for advancing drops of polymer solutions. We thus study advancing drops which are allowed to evaporate. Drying drives the accumulation of polymer at the contact line, whereas the advancing motion tends to homogenize the drop. At high velocity, we experimentally verify classical hydrodynamics predictions. At intermediate velocities, drying dominates and the contact line becomes more viscous than the bulk droplet. In the limiting case of very low velocities, the contact line can be partially pinned on the substrate because of the formation of a glassy defect at the contact line.     

Shear-induced effects on miscibility in polymer solutions

Methods of macromolecular integral equation theory are employed to calcuate the correlation functions of flexible linear homopolymers deformed by shear flow. The extent of coil deformation is calculated from bead-spring models that include corrections for finite chain extensibility and pre-averaged hydrodynamic interactions. The spinodal boundaries for sheared polymer solutions are obtained from the compressibility route under conditions of constant strain rate. It is shown that accounting for changes in the cohesive energy arising from flow-induced coil deformation may lead to non-monotonic shifts in the cloud point as a function of applied shear, even in the absence of nonlinear viscoelastic response. These model calculations are compared with experimental measurements of the cloud point for sheared solutions of polystyrene in dioctyl phthalate.