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Optical properties of semidilute solutions of a high-molecular-mass flexible-chain polyelectrolyte at various ionic strengths of the medium
Abstract
The flow birefringence and polarized light scattering techniques were applied to study semidilute water-salt solutions of a high-molecular-mass (Mw = 6 × 106) flexible-chain polyelectrolyte, the copolymer of 2-acrylamido-2-methylpropanesulfonic acid with acrylamide, at different ionic strengths of the medium (I = 1 and 0.1 mol/l). It was shown that "domain" structures with the morphology predetermined by the solution ionic strength were formed in the solutions of this copolymer. In the case of suppressed electrostatic interactions, a fluctuation network of entanglements was formed.
Aqueous-salt semidilute solutions of a high-molecular-weight polyelectrolyte, poly-2-acrylamido-2-methylpropanesulfonic acid, were studied by flow birefringence and light scattering methods at varied ionic strength of the medium.
Using a small-angle neutron scattering experiment, we measured the pair correlation function P(r) in polymer solutions in the interval 3 RG ≥ r ≥ l, where RG is the radius of gyration and I the step length. At the theta temperature, this function is known to follow the characteristic Debye law P(r) ∼ r-1. In good solvents (high temperature limit) and in the limit of zero polymer concentration this function is uniformly proportional to r-4/3, as predicted by S. F. Edwards. We observe however, that at higher concentrations or intermediate temperatures, P(r) exhibits both characteristic behaviours, depending on the range of r. The cross-over distances r* which separate the patterns are found to depend upon concentration and temperature. The scaling of r* is related to the scaling of the screening length ξ and the radius R G in the temperature-concentration diagram. La fonction de corrélation de paire P(r) pour les polymères en solution a été mesurée par diffusion de neutrons aux petits angles dans l'intervalle 3 RG ≥ r ≥ l où RG est le rayon de giration et l la longueur du monomère. A la température thêta cette fonction est décrite par la loi de Debye 1/r. En bon solvant (limite haute température) et à la limite de la concentration nulle, S. F. Edwards prédit que cette fonction est uniformément proportionnelle à r-4/3 . Cependant le résultat expérimental montre que pour des concentrations assez élevées ou pour des températures intermédiaires la fonction P(r) présente les deux comportements. On trouve qu'ils sont séparés par des longueurs de cross-over r* qui dépendent de la température et de la concentration. Le scaling de r* est relié au scaling de la longueur de corrélation ξ et du rayon RG dans le diagramme température-concen tration.
Rheological properties of concentrated polyelectrolyte solutions were studied using two samples of poly(N,N-dimethyldiallylammonium chloride) with different molecular masses. No anomalies in the viscosity behavior were observed in a broad range of concentrations, temperatures, and ionic strengths of solutions. The activation energies Ea of viscous flow were calculated for various solution concentrations and a concentration region featuring a change in the mechanism of mass transfer and the formation of a fluctuation network of entanglements was determined with the aid of a scaling approach. It was found that this region, independent of the molecular mass of polyelectrolyte, is situated significantly above the crossover concentration determined using the inverse intrinsic viscosities and is essentially the region of concentrations corresponding to the screening of electrostatic interactions, between macromolecular segments. In the presence of a low-molecular-mass electrolyte, the screening concentration somewhat decreases and the strength of the fluctuation entanglement network.
Structuring in aqueous and salt-containing aqueous solutions of poly(dimethyldiallyl ammonium chloride) in the concentration region close to the crossover concentration was studied by viscometry and quasi-elastic light scattering. In polyelectrolytes, crossover was shown to involve the development of oriented microdomain structure and is accompanied by no changes in the mass transfer mechanism upon viscous flow.
The aqueous-saline dilute solutions of high-molecular-mass flexible polyelectrolytes, salts of poly(2-methacryloyloxyethyltrimethyl ammonium) (M w = 9.6 × 10 6) and 2-acrylamido-2-methylpropanesulfonic acid copolymer with acrylamide (M w = 6 × 10 6) were studied by flow birefringence, viscometry, and light scattering. It was found that, in the region of moderate ionic strengths I, the shape asymmetry of polyions p varies from 2.0-2.5 at I = 1 mol/1 (a Gaussian coil) to ∼4-4.5 at I = 0.05 mol/1 (an extended asymmetric coil). The experimental evidence is compared with the results from the theoretical and experimental studies of p as a function of I.
It is proposed that the onset of entangled behavior with increasing N (degree of polymerization) in polymer solutions of concentration c > c* (overlap concentration) corresponds to the point where molecular diffusion becomes restricted to reptation alone. An internally self-consistent model for reptation in such solutions, based on a reptation and "tube"-reorganization concept, is developed. By treating the relaxation of molecules as a cooperative phenomenon the onset of reptation is identified as a second-order, ferromagnetic-like transition occurring at a critical N and entanglement density. It is possible to compare some predictions of our treatment with experiments on the variation of Nc (critical N for onset of entangled behavior) with c, by incorporating results of previous studies on static-correlation properties in semidilute polymer solutions. The agreement is surprisingly good.
An extensive discussion of the analytical solution for the Poisson-Boltzmann equation in cylindrical symmetry for strong polyelectrolytes in the cell model is presented. The reduced mean electrostatic potential μ at finite dilutions is discussed in terms of its dependence on the polyelectrolyte equivalent concentration C{sub e}, its charge density parameter ξ, and the distance of closest approach a of the counterions to the polyion. It is shown that in the limit a â 0 counterion condensation is expected. For more realistic nonzero values of a, the reduced potential μ at a given relative position r/R in the cell with radius R is practically independent of the linear charge density for ξ > 2, but its value depends on the product a²C{sub e}. The value μ(a) of the reduced potential near the surface of the polyion is ξ-dependent, however, under the same conditions. A large fraction of all the counterions in the cell accumulate, on the average, in the neighborhood of the polyion, this fraction being larger the higher ξ is and the lower the product a²C{sub e} is. The fraction of ions accumulated between the polyion surface at a and a distance from the polyion axis equal to the screening length 1/Ï is high, reaching values exceeding 80% and being higher the smaller a²C{sub e} is. This fraction of counterions (the {open_quotes}associated{close_quotes} counterions) occupies a smaller part of the total cell volume than the counterions situated between 1/Ï and R, which are characterized by a relatively low electrostatic interaction energy with the polyion, μ < 1 (the {open_quotes}free{close_quotes}counterions). 22 refs., 11 figs.