An off-lattice Metropolis Monte Carlo algorithm with reptation is used to find the average fractional ionization a as a function of pH for a generic ionizable linear polyelectrolyte in a salt solution. The polyelectrolyte is treated as a threefold rotational isomeric state model polymer; each unit can bear a negative charge or not with intrinsic ionization constant pK a. Debye-Huckel screening is assumed between the charges. For computational convenience, the dielectric constant of the polymer is taken to be that of the solvent. The number of units Nwas either 50 or 100. Monte Carlo results were collected for various Debye screening lengths at six combinations of number of chain units N, bond angle (J, and Manning parameter when fully charged, So. For four of the combinations, So was 1 to take partial account of counterion condensation. These runs had Nand (J of 50 and 1°, 50 and 70°, 100 and 1°, and 100 and 70°. The fifth combination had N = 50, (J = 70°, and So = 2.85. The sixth had N = 50, (J = 27.34°, and So = 0.72, for comparison with data for hyaluronate. The Monte Carlo results are compared to third nearest-neighbor linear Ising type calculations and to simple mean field theories in a. Mean field theory in a worked very well in the (nearly rodlike) (J = 1° cases using the known distance between units. Mean field theory in a using an estimate for the distance between units based on the ideas of electrostatic persistence length and excluded volume worked equally well for the (J = 1° cases and moderately well for the (J = 70° cases. The free energy and entropy per simulated chain were calculated by thermodynamic integration of the Monte Carlo results for a as a function of pH.

SYNOPSISHigh purity, high molecular weight hyaluronate from bacteria and rooster comb exhibited clear polyelectrolyte properties, as observed by static and dynamic light scattering. The scattered intensity of hyaluronate solutions increased markedly with ionic strength, while the radii of gyration decreased. Apparent persistence lengths within the wormlike chain model in the coil limit were estimated as a function of ionic strength. The total apparent persistence length varied from about 87 8, in the high ionic strength limit to nearly 400 8, at 1 m M added NaC1. The apparent electrostatic persistence length varied approximately as the inverse square root of the ionic strength. Deviations from the theoretically predicted inverse ionic strength dependence were investigated in terms of excluded volume effects. Dynamic light scattering yielded "ordinary phase" diffusion coefficients whose dependence on polymer and salt concentration agreed reasonably well with hydrodynamic coupled mode theory in the linear limit. Extrapolations to infinite polymer dilution at fixed salts yielded, surprisingly, a constant diffusion coefficient. Thus, there was no evidence of either polyion expansion or electrolyte friction effects in the infinite dilution diffusion coefficients. Since clear evidence for polyion expansion was seen in the static scattering, it is thought that the relative stiffness and consequent openness of the hyaluronate coils lead to partial free draining behavior. There was no evidence for an "extraordinary phase" under no added salt and low added salt conditions. The overall results are contrasted with the very different behavior previously reported for medium purity hyaluronate from animal sources.

An off-lattice rotational isomeric state model Monte Carlo algorithm for a polyelectrolyte with Debye-Hueckel screening and no hard core repulsion is used to generate short (up to 150 unit) chains at (1) different ionic strengths, (2) varying uniform charge densities, and (3) pH-pK 0 governed ionization. The mean square radii of gyration are related to the apparent total persistence lengths of the polyelectrolytes via the wormlike chain model. Near the random coil limit the apparent electrostatic persistence length varies approximately as the inverse square root of the ionic strength and linearly with charge density. The persistence length behavior is very similar in cases (2) and (3). These approximate power laws agree well with those found experimentally for hyaluronate and variably ionized poly acrylic acid. The original electrostatic persistence length theory, which does not contain excluded volume effects, predicts power law exponents which are twice these. Corrections due to polyelectrolyte excluded volume theories do not consistently yield good fits to the data, but do give "pseudo-," or weakly changing power laws similar to those obtained from the Monte Carlo and experimental data. The similarity between the Monte Carlo and experimental results may indicate that the Debye-Hueckel approximation is reasonable, and that the neglect of hard core repulsion (e.g., zero chain diameter) is insignificant compared to electrostatic effects. This lends strength to the interpretations that electrostatic excluded volume effects explain much of the apparent deviation from the electrostatic persistence length theory and that the approximation of a smeared out line charge works fairly well, even when the actual charges are irregularly spaced.

Hyaluronate was investigated over a wide pH range, and at near zero and intermediate ionic strength, using dynamic and total intensity light scattering. Commercially obtained rooster comb hyaluronate was purified, and solutions were prepared in pure water by low-power bath ultrasonication and subsequent filtering. These solutions were of low polydispersity and appeared to contain single molecules of hyaluronate. Despite the absence of added electrolyte, these solutions yielded well-behaved Zimm plots. Increasing ionic strength and changing pH decreased radii of gyration and increased diffusion constants. Except for what appeared to be slow hydrolysis at either extreme of pH, molecular weights remained constant under all pH and ionic strength conditions. Under all solvent conditions investigated, diffusion coefficients increased with decreasing hyaluronate concentration. Unsonicated, lightly centrifuged solutions without added electrolyte were polydisperse, and their light scattering intensity was dominated by what appeared to be stable hyaluronate aggregates. The results are interpreted in terms of the polyelectrolyte properties of hyaluronate and its tendency to form stable entanglements, especially at low ionic strength. Previous light scattering studies in the literature on hyaluronate have shown widely varying results. The present article briefly reviews this literature and attempts to explain the variation among the previous results, emphasizing the Kuhn statistical segment length as an indicator of whether results are influenced by polydispersity or contaminants causing hyaluronate aggregation.

The scattering of light by a dilute monodisperse population of random-coil molecules is approximately described by the well-known function P(0) = (2/ u 2) (e-U + U-I), where u = R ii, Rg is the radius of gyration of the random coils, and q = (41Tn/ A) sin (0/2) is the magnitude of the scattering vector. We show that if the molecules in this population undergo random scission, then P(O) is still given by the above formula where, however, u is now equal to R ioi + r, where r is the average number of scissions per molecule in the originally monodisperse population and Rgo is the original radius of gyration. It is suggested that this could be useful for determining depolymerization rate constants, and for investigating whether various forms of scission are actually random. Results from initial experiments which apply the theory to the acid hydrolysis of hyaluronic acid are presented. The rate constants found are in reasonable agreement with values in the literature.