Radii of gyration and screening lengths of polystyrene in toluene as a function of concentration

Review: Kirkwood-Riseman Model in Non-Dilute Polymeric Fluids

In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of polymeric fluid dynamics, such as reptation/scaling models. One therefore rationally asks whether there is a replacement. There is, namely by extending the Kirkwood-Riseman model. Here, I present a comprehensive review of one such set of extensions, namely the hydrodynamic scaling model. This model assumes that polymer dynamics in dilute and concentrated solution is dominated by solvent-mediated hydrodynamic interactions; chain crossing constraints are taken to create only secondary corrections. Many other models assume, contrariwise, that in concentrated solutions, the chain crossing constraints dominate the dynamics. An extended Kirkwood-Riseman model incorporating interchain hydrodynamic interactions is developed. It yields pseudovirial series for the concentration and molecular weight dependencies of the self-diffusion coefficient Ds and the low-shear viscosity η. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler positive-function renormalization group are presented. The rationales correctly predict how Ds and η depend on polymer concentration and molecular weight. The renormalization group approach leads to a two-parameter ansatz that correctly predicts the functional forms of the frequency dependencies of the storage and loss moduli. A short description is given of each of the papers that led to the hydrodynamic scaling model. Experiments supporting the aspects of the model are noted.

Conformation of Network Strands in Polymer Gels

Small angle neutron scattering was used to measure single chain radii of gyration of end-linked polymer gels before and after cross-linking to calculate the prestrain, which is the ratio of the average chain size in a cross-linked network to that of a free chain in solution. The prestrain increased from 1.06 ± 0.01 to 1.16 ± 0.02 as gel synthesis concentration decreased near the overlap concentration, indicating that the chains are slightly more stretched in the network than in solution. Dilute gels with higher loop fractions were found to be spatially homogeneous. Form factor and volumetric scaling analyses independently confirmed that elastic strands stretch by 2-23% from Gaussian conformations to create a space-spanning network, with increased stretching as network synthesis concentration decreases. Prestrain measurements reported here serve as a point of reference for network theories that rely on this parameter for the calculation of mechanical properties.

Quantitative determination of the spring entropy effect and its indication of the conformational change of polymer coils with varying concentration in aqueous poly(N-isopropylamide) solutions

The lower critical solution temperature (LCST) phase separation behaviors of thermosensitive poly(N-isopropylacrylamide) (PNIPAM) aqueous solutions were investigated by power-compensation differential scanning calorimetry (DSC). The entropic effect and hence the change of swelling state of PNIPAM polymer coils in homogeneous concentrated aqueous solutions with varied solution composition was elucidated by the isothermal enthalpy demixing recovery behaviors in distinct concentration regions.

Location of Imbibed Solvent in Polymer-Grafted Nanoparticle Membranes

Membranes made purely from nanoparticles (NPs) grafted with polymer chains show increased gas permeability relative to the analogous neat polymer films, with this effect apparently being tunable with systematic variations in polymer graft density and molecular weight. To explore the structural origins of these unusual transport results, we use small angle scattering (neutron, X-ray) on the dry nanocomposite film and to critically examine in situ the structural effects of absorbed solvent. The relatively low diffusion coefficients of typical solvents (∼10^-12 m²/s) restricts us to thin films (≈1 μm in thickness) if solute concentration profiles are to equilibrate on the 1 s time scale. The use of such thin films, however, renders them as weak scatterers. Inspired by our nearly two decades old previous work, we address these conflicting requirements through the use of a custom designed flow cell, where stacks of 10 individual ≈1 μm thick supported films are used, while ensuring that each film is individually exposed to solvent vapor. By using isotopically labeled solvents, we study the solvent distribution within the film and show surprisingly that the solvent homogeneously swells the polymer under all conditions that we examined. These results are not anticipated by current theories, but they suggest that, at least under some conditions, the free volume increases due to the grafting of chains to nanoparticles is apparently distributed isotropically in these materials.

Structural effect of glyme–Li+ salt solvate ionic liquids on the conformation of poly(ethylene oxide)

Conformation of poly(ethylene oxide) in solvate ionic liquids is affected by the solvent structure.

Conformation of poly(ethylene oxide) dissolved in the solvate ionic liquid [Li(G4)]TFSI

PEO dissolves in [Li(G4)]TFSI via coordination with Li⁺.

Shielding effects in polymer-polymer reactions. V. Concentration dependence of contact formation between star-branched and linear chains

By use of the Dissipative Particle Dynamics (DPD) simulation technique mixtures of star-branched (arm number F = 4) and linear chains in athermal (good) solvent are analyzed regarding probabilities for intermolecular contacts of various reactive sites within different polymer coils. The accompanying sterical hindrances are described in the framework of shielding factors in order to investigate reactions and side reactions in radical polymerization and other techniques that involve polymer–polymer coupling. The shielding factors are studied as a function of total concentration from high dilution up to the bulk for different chain lengths of star-shaped and linear chains. Results indicate that their concentration dependence can be described by a power law for systems above the overlap concentration, whereas the chain length dependence vanishes when extrapolating to infinite chain lengths in that concentration range. Also the influence of the ratio of star chains and linear chains is studied for various concentrations.

Compression of random coils due to macromolecular crowding: scaling effects

The addition of a macromolecular crowding agent to a dilute solution of polymer exerts a compressive force that tends to reduce the size of the chain. We study here the effect of changing the size ratio between the random coil and the crowding agent. The compression occurs at lower crowding agent concentration, Φ when polymer molecular weight increases. The Flory exponent ν(Φ) decreases from ν(0)≃0.48 in water down to 0.3 with macromolecular crowding. The effective polymer-polymer interactions change from repulsive to strongly attractive inducing aggregation of the chains. This effect changes drastically for larger polymer sizes, being much more pronounced at high molecular weights.

Polymer dimensions in good solvents: crossover from semidilute to concentrated solutions

Using small-angle neutron scattering, we studied the variation of the polymer radius of gyration (R_{g}) as a function of polymer concentration (varphi) for solutions of a flexible-chain poly(methyl methacrylate) in chloroform. We observed for the first time a distinct crossover between swollen coils in the semidilute regime, where R_{g};{2} proportional, variantvarphi;{-0.26+/-0.03}, and unperturbed coils in the concentrated regime, where R_{g} is independent on concentration. The crossover occurs at varphi;{double dagger} approximately 0.15, a value that agrees reasonably well with varphi;{double dagger} approximately 0.21 +/- 0.035, estimated with a scaling relationship between varphi;{double dagger} and the coil overlap concentration varphi;{*}.

Universal aspects of macromolecules in polymer blends, solutions, and supercritical mixtures

We demonstrate that macromolecules in miscible polymer blends may behave as good, Theta, and poor polymeric solvents for each other. We construct a conceptual phase diagram, delineating the range of validity of the random-phase approximation, outside of which polymers contract or expand beyond their unperturbed dimensions, contrary to common assumptions. Remarkably, the correlation length for polymer blends, solutions, and supercritical mixtures collapses onto a master curve, reflecting universal behavior for macromolecules in polymeric and small-molecule Theta solvents.

Effects of bead-bead interactions on the static and dynamical properties of model polymer solutions

The effects of segment-segment interactions on the static and dynamical properties of model polymer solutions are examined by Brownian dynamics simulations in the free-draining limit over a wide concentration range. A bead-and-spring model is used to describe the polymer chains at a coarse-grained level, in which segment-segment interactions are represented by a bead-bead pair potential with a Gaussian analytic form, beta u(ev)(r)=A exp(-r(2)/2 sigma(2)), where beta=1/k(B)T and A and sigma are characteristic energy and distance scales, respectively. The chain dimensions, self-diffusion coefficient, and viscosity of the systems are studied as functions of number density of beads of the system, rho, at given excluded-volume potential parameters, A and sigma. Our results show that in the limit of infinite dilution even for short chains (N approximately 10) there is statistically significant scaling behavior in the static and dynamical properties. For a system with given values of A and sigma the change in polymer coil size shows a realistic trend as the concentration of the system increases. In the dilute and concentrated regions the coil size decreases as a result of increasing interchain repulsions, while in the highly concentrated region the coil size increases again, showing a return to Rouse-like behavior because the intrapolymer and interpolymer segment-segment interactions become effectively indistinguishable for an arbitrary bead and to a large extent are "balanced out." In the limit of infinite dilution, the self-diffusion coefficient of the center of mass, D(cm), depends on N only and not on the potential parameter A, while in contrast the specific viscosity eta(sp) depends on both N and A. As the concentration increases D(cm) decreases and eta(sp) increases consistent with the behavior of real polymers. When the system becomes highly concentrated, however, both D(cm) and eta(sp) unrealistically return to the Rouse limit. This suggests that from the concentrated region upward in concentration, the entanglement or the topological constraints caused by the physical connectivity of the chains significantly influence their dynamical behavior. The mean-field segment-segment interactions or excluded-volume effects incorporated in the current coarse-grained bead-spring approach cannot capture this entanglement effect, and therefore give rise to unrealistic dynamical behavior in the concentrated regime.