Abstract: The water self-diffusion in aqueous EO 99 -PO 65 -EO 99 (EO and PO being ethylene oxide and propylene oxide, respectively) solutions and gels has been studied with NMR. It was found that the water self-diffusion decreases monotonically with increasing polymer concentration, giving D/D 0 ≃0.5 at 40 wt %. In the analysis of the data, using the cell diffusion model, it was found that the decrease in D/D 0 with increasing polymer concentration can be reproduced by taking into account both the obstruction due to excluded volume and the hydration of the polymer molecules

Abstract: Monte Carlo simulation has been used to study titration and configurational properties of an isolated hydrophobic polymer containing weakly‐ionizable groups. Using a cubic lattice, simulations were performed in the grand canonical ensemble to include the effect of the local charge environment on the ionization of weak electrolyte segments. Properties were studied as a function of polymer hydrophobicity, fraction of ionizable segments, solution ionic strength, and pH. The polymer segments experienced three types of competing interaction: excluded volume, attractive nearest‐neighbor forces which account for the net balance of segment–segment, segment–solvent, and solvent–solvent interactions, and long‐range electrostatic forces between ionized segments, calculated with a screened Debye–Huckel potential. Simulations show that the model chain expands with chain ionization, which depends on solution pH. As the chain becomes increasingly charged, the ionization process becomes more difficult because of rising l...

Abstract: A method is presented for the simulation by molecular dynamics of stress relaxation in polymer melts. It is applied to dense model systems of short freely-jointed chains with repulsive excluded volume interactions. Stress histories are fitted by a Prony series. The model parameters when subjected to Caswell-Paboojian scaling agree well with values observed for real systems. In contrast to the usual assumption, the shear stress is found to be due to the excluded volume interactions and not to the forces in the covalent bonds of the chains.

Abstract: A previously developed theory for the delocalized binding of ions to polyelectrolytes was restricted to point ions and a structurally rigid polyelectrolyte. For the binding of substances like oligolysines and polyamines to DNA, the restriction to point ions would appear not to be realistic. For the binding of ions to flexible chains like single-stranded polynucleotides, the restriction to a rigid polyelectrolyte may not be realistic. In this article, we assess the effect of relaxation of these two restrictions. Excluded volume among bound ions is modeled by a hard-rod potential in the context of the theory of a one-dimensional fluid. The possibility that a flexible chain folds in some manner in the immediate vicinity of a bound ion is modeled by allowing the mean spacing between charged groups on the polymer to become smaller as the number of bound ions increases. We compare our results with recent data on the binding of a series of oligolysines to single-stranded polynucleotides, which conflict with the predictions of the original theory of delocalized binding of point ions to rigid polyelectrolytes. Inclusion of excluded volume among bound ions does not significantly improve agreement with the data. Substantial improvement in the level of agreement is obtained when the polyion chain is assumed to be flexible. One of our conclusions is that the excluded-site description of anticooperativity, which was designed for the binding of ligands to discrete sites on a polymer chain, and which does not include the effect of ionic forces, should not be used in cases of delocalized binding of ions.

Abstract: The light scattering function P(Θ) of charged isolated threefold rotational isomeric state model polymers was simulated by Metropolis Monte Carlo in the Debye–Huckel approximation. Number of chain units N (up to 250), and ratio (from 0.5 to 64) of Debye screening length κ−1 to bond length D were varied at a bond angle θ of 90°; θs of 70° and 45° were also investigated. Charge was fixed by setting the ‘‘Manning parameter’’ to 1. Because the properties of linear polyelectrolytes have been interpreted in terms of electrostatic excluded volume and electrostatic persistence lengths, similar chains with hard sphere repulsion were simulated, up to N=400, as were nearly wormlike chains with no repulsion. Overall, a function suggested by Noda et al. described the P(Θ) of both hard sphere chains and electrostatic repulsion chains with κ−1/D of 0.5 moderately well. However, first order renormalization group (RG) calculations correctly predict an intersection between this P(Θ) and that for Gaussian random coils, while the Noda et al. function does not. Requirements for experimental observation of excluded volume effects in polyelectrolytes are discussed. The P(Θ) of chains with large κ−1/D was not fit well by that of nonexcluded volume wormlike chains with the persistence lengths predicted by theory, possibly because excluded volume effects were not small. Linear fits to a log–log plot of 1/P(Θ) vs the square of the scattering vector times the radius of gyration gave the expected slopes, but not intercepts, as predicted by first order RG, probably because u was not large enough.

Abstract: We have used a novel Monte Carlo method to compute the gyration radius Rg and the hydrodynamic radius RH of excluded-volume polymer chains. The hydrodynamic radius scales as Ng05s (N is the number of bonds) over at least a decade of chain lengths, whereas the gyration radius exponent is close to the theoretical value of 0.59. The anomalous behavior Of RH is well-known experimentally; it is commonly attributed to the belief that polymers in mediocre solvents are not swollen on short length scales. However, the polymer chains in our simulations are uniformly swollen on all length scales; we suggest that the discreteness of the polymer chain is sufficient to explain the behavior of RH.

Abstract: We consider the kinetics of the reversible aggregation of monomers to form roughly spherical clusters where the effect of excluded volume is taken into account by using Lebowitz’s exact solution of the Percus–Yevick equation for a mixture of hard spheres, assuming rapid spatial equilibration relative to the rate of aggregation. Using the radial distribution function evaluated at the contact distance between two spheres, we obtain a differential equation for the aggregation process that is a sum over cubic terms in the appropriate cluster densities. The differential equation is converted into a recursion relation for the coefficients in a series in powers of the time. The series can then be used to estimate the asymptotic relaxation time for the aggregation process.

Abstract: Several studies have focused on developing a theory of the excluded volume effect in polymer solutions in good accord with experimental data. There are very few expressions for the interpenetration factor, Ψ, which can be chosen for a given theory of the expansion factor α3s. The combination of Kurata–Yamakawa theory for Ψ with Yamakawa–Tanaka theory for α is in good accord with experimental data on binary polymer systems. However, no self-consistent combination of theories can be chosen to describe the behaviour in ternary polymer systems. A modified expression for the interpenetration factor has been developed for ternary polymer systems. It depends on intrinsic viscosities and on the Kurata–Yamakawa binary interpenetration factor. Good qualitative agreement has been attained by comparing the modified (Ψ, α) plot with experimental data on reported ternary systems. A useful application is the theoretical calculation of second virial coefficients.

Abstract: The surface tension increment is evaluated for dilute polymer solutions. The first virial coefficient is calculated to first order in excluded volume near two limiting boundary conditions: repulsive (Dirichlet) and reflecting (von Neumann). An interpolation function extends the calculations to intermediate values of the polymer–surface interaction strength and provides the surface pressure as a function of both polymer–polymer and polymer–surface interactions. Comparison with experiments for polystyrene in toluene suggest the importance of nonuniversal contributions to the surface tension increment.

Abstract: The distribution coefficients of single- and double-stranded oligodeoxynucleotides in a PEG 8000/phosphate two-phase system are a function of their chain length. Values of the distribution coefficients are in general agreement with a simple extension of a model for excluded volume effects (the "available volume model") which was applied previously to the distribution of proteins in this system. The current results therefore provide a second set of examples for molecules of very different geometry where the distribution added molecules is controlled by excluded volume interactions between those molecules and the PEG 8000 of the two-phase system.

Abstract: In the last few years the use of poly(ethylene glycol) (or PEG) as an agent with which to modify the properties of macromolecules and surfaces has greatly increased, as witnessed by the contributions in this volume. In most instances, PEG is used because it exhibits the interesting property of being highly compatible with water (i.e., highly water soluble) while exhibiting strong incompatibility with a wide variety of other water-soluble substances. Incompatibility means that an unfavorable free-energy change occurs when a second species interacts with a solvated PEG molecule, resulting in a statistical tendency for the second species to be excluded from the region within or near the PEG chain. Such excluded volume effects are manifested in a variety of ways, including phase separation in mixtures with a second water-soluble polymer of salt, enhanced exclusion of PEG from chromatographic gel beads relative to other polymers of similar molecular weight, protein precipitation and reduced binding of external proteins to surfaces or molecules derivatized with PEG.1,2 Many of these kinds of interactions are described in this book.

Abstract: The Pearson walk model of a linear polymer with excluded volume is studied by analogy with a neighbor‐avoiding walk on a lattice. The pivot algorithm is used to model the excluded volume directly, with the strength of interaction controlled by bead diameter. The excluded volume per bead is shown to be nonanalytic, with two distinct excluded volume regimes corresponding to geometrically different polymer models.

Abstract: Like real polymer chains and unlike self‐avoiding lattice walks, neighbor‐avoiding lattice walks exhibit a reduction or mediation of the effective excluded‐volume interaction, and thus merit study as a model of real polymers. For small excluded volume, we extend the perturbation series of Domb and Joyce to neighbor‐avoiding walks. For large excluded volume we compute exactly the excluded volume per lattice site for short chains and estimate it by Monte Carlo for longer chains. We discuss the significance of chain stiffness for lattice models and suggest how the correct two‐parameter function might be determined numerically.

Abstract: Premiminary values of the exponent 2ν = d[ln ]/d[ln(N-1)] for the power-law dependence of mean-square end-to-end length (or other mean-square chain dimensions) upon the number N-1 of steps in the chain are obtained by least-squares fits of ln to linear functions of ln(N-1) for chains of from 9 to 99 beads. The results show that the apparent exponent 2ν increases smoothly with bead diameteras d increases from 0 to 1

Abstract: A one-dimensional model is used to study the tilt/no-tilt transition in the liquid condensed phase of a lipid monolayer at the air/water interface. The head groups are modelled by hard rods of length b and the alkane chains by rigid tails of length a(a>>b). The interaction between these model lipid molecules is purely repulsive with a soft, short range, repulsion allowed between the tilting tails. The model is aimed at highlighting the excluded volume role in the tilt/no-tilt transition. The model is solved analytically and, in the limit of the temperature T to 0, the equation of state exhibits-at most-three distinct phases; isotropic, 'tilting' and 'nontilting'. At finite temperatures the transition from one phase to the other is continuous but, at low temperatures, still sharp.

Abstract: Fundamental parameters in the Flory-Huggins theory of binary mixture, including the heat of mixing associated with pairwise interactions ( Δw 12 ) and the coordination number, z, are calculated through molecular simulations. The pair energies (w 11 , w 22 , w 12 ) are obtained by averaging a large number of configurations generated by a Monte Carlo approach which includes the constraints associated with excluded volume. The temperature dependence of the interaction parameter X is obtained from this study.

Abstract: Self-avoiding polymer chains in a random environment are considered by means of the renormalization group (RG) and without using the replica trick. The coupled differential equations of the RG for the excluded volume strength and for the strength of the disorder are derived and solved up to the first order of in =4-d. The quenched average of the number of states of a polymer chain is studied. In the case of finite volume the result obtained is in agreement with that derived earlier by Machta (1989). The radius of the collapsed polymer derived by Edwards and Muthukumar (1988) is rederived within the RG method. The quenched average of the second viral coefficient of a solution of polymers in the random environment is considered.

Abstract: A recently discovered connection between Dirac’s fermions and semiflexible polymers [Ann. Phys. (NY) 202, 186 (1990)] is developed further. The scattering form factor, diffusion and viscosity coefficients, and relaxation times are obtained for the arbitrary stiffness of the chain in the limit of infinite dilution. It is demonstrated explicitly how the excluded volume effects can be incorporated in calculations of the above observables. New methods of experimental determination of the persistence length in the presence of excluded volume effects are proposed along with a new method of experimental evaluation of the excluded volume parameter. Obtained results can be used for both homo and random semiflexible copolymers.

Abstract: The effective interaction between colloids in solutions containing dissolved polymer is investigated using integral equations. The colloidal particles are modeled as hard spheres, the polymer molecules are modeled as freely jointed hard chains, and the solvent is treated as a continuum that doesn't interact with either the colloidal particles or the polymer molecules. The model therefore concentrates on excluded volume effects in these systems. It is found that at low polymer volume fractions, the effective intermolecular potential (or potential of mean force) between the colloidal particles is attractive, thus facilitating a phase separation or precipitation of the colloids. As the polymer volume fraction is increased, the strength of this attraction increases; but a repulsive interaction appears at larger separations, which resembles the double-layer repulsion between charged colloidal particles in an aqueous solution. The effects of varying polymer chain length, colloid particle size, and polymer volume fraction on the effective potential are also studied.