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In this paper, we continue investigations on the solution methods for the generalized Percus–Yevick equations for the pair correlation functions of polymers, which were formulated in the previous papers of this series [J. Chem. Phys. 99, 4084, 4103 (1993)]. Previously, they were reduced to recursive integral equations and solved numerically. In this paper, a translational invariance approximation is used to reduce the number of integral equations to solve. In this approximation, only N integral equations out of N2 integral equations are required for a polymer consisting of N beads (monomers). The behavior of an isolated polymer is studied with three different potential models, a soft sphere, a hard sphere, and a Lennard-Jones potential. The main motivation for considering these three potential models is in testing the idea of universality commonly believed to hold for some properties of polymers. We find that the universality holds for the power law exponent for the expansion factor of polymers at high temperatures. The end-to-end distance distribution functions, intermediate distribution functions, chemical potentials, the density distributions, and various expansion factors of the polymer chain are computed from the solutions of the integral equations in the case of coiled, ideal, and collapsed states of the polymer. The expansion factors in the collapsed regime are found to obey power laws with respect to the length of the polymer and [B(T)-B(θ)], where B(T) is the second virial coefficient and θ is a modified θ temperature. The values of these exponents approach those from the known theories of polymer collapse as the chain length becomes long and the ratio of bond length to bead radius becomes large. [ABSTRACT FROM AUTHOR]

The structural and dynamical properties of macromolecules in confining or crowded environments are different from those in simple bulk liquids. In this paper, both the conformational and diffusional dynamics of globular polymers are studied in solutions containing fixed spherical obstacles. These properties are studied as a function of obstacle volume fraction and size, as well as polymer chain length. The results are obtained using a hybrid scheme that combines multiparticle collision dynamics of the solvent with molecular dynamics that includes the interactions among the polymer monomers and between the polymer beads and obstacles and solvent molecules. The dynamics accounts for hydrodynamic interactions among the polymer beads and intermolecular forces with the solvent molecules. We consider polymers in poor solvents where the polymer chain adopts a compact globular structure in solution. Our results show that the collapse of the polymer chain to a compact globular state is strongly influenced by the obstacle array. A nonmonotonic variation in the radius of gyration with time is observed and the collapse time scale is much longer than that in simple solutions without obstacles. Hydrodynamic interactions are important at low obstacle volume fractions but are screened at high volume fractions. The diffusion of the globular polymer chain among the obstacles is subdiffusive in character on intermediate time scales where the dynamics explores the local structure of the heterogeneous environment. For large polymer chains in systems with high obstacle volume fractions, the chain adopts bloblike conformations that arise from trapping of portions of the chain in voids among the obstacles. [ABSTRACT FROM AUTHOR]

Polymers are naturally polydisperse. Polydispersity may have a large effect on the phase behavior of polymer solutions, in particular, on the liquid-liquid phase equilibria. In this paper, we determine the cloud and shadow curves bounded by lower critical solution temperatures for a number of polymer+solvent systems where the polymer is polydisperse in terms of molecular weight (chain length). The moment method [P. Sollich, P. B. Warren, and M. E. Cates, Adv. Chem. Phys. 116, 265 (2001)] is applied with the SAFT approach to determine cloud and shadow curves with continuous Schulz-Flory distributions. It is seen that chain length polydispersity always enhances the extent of liquid-liquid phase equilibria. The predicted cloud curves obtained for continuous distributions are very similar to those obtained for simple ternary mixtures with the same polydispersity index, while the corresponding shadow curves can be very different depending on the composition of the parent distribution. The ternary phase behavior can be used to provide an understanding of the shape of the cloud and shadow curves. Regions of phase equilibria between three liquid phases are found for ternary systems when the chain length distribution is very asymmetrical; such regions are not observed for Schulz-Flory distributions even in the case of a large degree of polydispersity. [ABSTRACT FROM AUTHOR]

This paper reports results of quantitative comparison between dynamic structure factors obtained experimentally and those calculated by using the Doi and Onuki (DO) theory for semidilute polymer solutions. The authors obtained the dynamic structure factors with dynamic light scattering (DLS) experiment while the dynamic structure factors were calculated by using DO theory with osmotic compressibility, viscoelastic relaxation function, and friction coefficient which are obtained independently of DLS experiment. Calculated dynamic structure factors agree with experimental ones well and can express the q-dependent fast modes and the q-insensitive slow mode which experimental ones show. The authors estimated the characteristic parameters, interdiffusion coefficient and cooperative diffusion coefficient, from experimental and calculated results by using the procedure proposed by Einaga and Fujita [Polymer 40, 565 (1999)]. The estimated parameters for the DLS experiment agree with those for the calculation. These agreements in dynamic structure factors and the parameters indicate that DO theory can describe well the relaxation processes of semidilute polymer solutions. [ABSTRACT FROM AUTHOR]

The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2×105 up to 11.4×106. The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented. [ABSTRACT FROM AUTHOR]

We propose a simulation method for infinitely dilute polymer solutions. In this method, an effective Hamiltonian of the solvated polymer chain is introduced to eliminate the degree of freedom of the solvent particle. The effective Hamiltonian is coupled with the density-functional theory (DFT) that we have developed for a polymer-solvent pair correlation function. All the equations proposed in this paper are derived from the first principle. This simulation method was applied to polymer chains in supercritical solvents. We observed anomalous behaviors of polymer chains near the liquid-vapor critical point: both solvophilic and solvophobic polymers expand significantly near the critical point; this is in contrast to the behavior of polymer chains in vacuum. This expansion can be interpreted as a cooperative phenomenon, which enhances the large long-wavelength density fluctuation of the solvent. [ABSTRACT FROM AUTHOR]

Microrheology of semidilute polymer solutions is investigated. In this paper we calculate a response function of a probe particle embedded in a semidilute polymer solution by analyzing the two-fluid model. We find that when the size of the probe particle is comparable to the viscoelastic length, the response from the longitudinal compression modes becomes more important than that of the transverse shear modes. As a result, depending on the circumstances, the obtained complex shear modulus cannot be well approximated by that measured in macroscopic rheology experiments. The present results are due to the dynamical asymmetry coupling and the existence of the cooperative dynamics, which are intrinsic to entangled polymer solutions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The theory of equilibrium solvation of polymers B by a relatively low molar mass solvent A, developed in the simplest form in Paper I, is used to explore some essential trends in basic thermodynamic properties of solvated polymer solutions, such as the equilibrium concentrations of solvated polymers AiB and free solvent molecules A, the mass distribution [lowercase_phi_synonym]AiB(i) of solvated clusters, the extent of solvation of the polymer [uppercase_phi_synonym]solv, the solvation transition lines Tsolv([lowercase_phi_synonym]B o), the specific heat CV, the osmotic second virial coefficient B2, phase stability boundaries, and the critical temperatures associated with closed loop phase diagrams. We discuss the differences between the basic thermodynamic properties of solvated polymers and those derived previously for hierarchical mutual association processes involving the association of two different species A and B into AB complexes and the subsequent polymerization of these AB complexes into linear polymeric structures. The properties of solvated polymer solutions are also compared to those for solutions of polymers in a self-associating solvent. Closed loop phase diagrams for solvated polymer solutions arise in the theory from the competition between the associative and van der Waals interactions, a behavior also typical for dispersed molecular and nanoparticle species that strongly associate with the host fluid. Our analysis of the temperature dependence of the second osmotic virial coefficient reveals that the theory must be generalized to describe the association of multiple solvent molecules with each chain monomer, and this complex extension of the present model will be developed in subsequent papers aimed at a quantitative rather than qualitative treatment of solvated polymer solutions. [ABSTRACT FROM AUTHOR]