Theory of volume transitions in polyelectrolyte gels
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Theory of volume transitions in polyelectrolyte gels Mithun K. Mitra1 and M. Muthukumar1 Polymer Science and Engineering, University of Massachusetts Amherst, MA 01003, U.S.A. 1
ABSTRACT We present the key assumptions and results of a newly developed theory in order to account for the self-consistent cascade effects of counterion condensation and volume collapse of polyeletrolyte gels. In the present theory, the role of the specificity and valency of counterions on the volume transitions are also treated. These features and the fluctuations of monomer concentration and local electrolyte charge density are included on top of the familiar features of the Flory-Huggins theory and the classical rubber elasticity theory in the previously used FloryDusek-Patterson-Tanaka theory of polyelectrolyte gels. We have computed the swelling equilibria by satisfying the multicomponent nature of the system and the Donnan equilibria. A few major effects are illustrated in terms of the dependence of volume transition on the solvent quality, temperature, salt concentration, valency and specificity of the counterion, and polymer charge density. Criteria for the emergence of a reentrant volume transition are also derived. INTRODUCTION The prevalence of polyelectrolyte gels in the contexts of biology and biotechnology has attracted tremendous efforts to understand their behavior from a fundamental point of view [1-4]. Nevertheless, polyelectrolyte gels pose considerable challenges in terms of predicting their behavior. The general trends of the spectacular properties of polyelectrolyte gels are well known, partly due to the great efforts by Tanaka and collaborators [4-7]. As the solvent quality decreases or the charge density increases for a fixed solvent quality, the gel can undergo a spectacular volume change by even two orders of magnitude. The quantitative features of these volume transitions have been established by numerous researchers in terms of solvent quality, temperature, degree of ionization of the polymer backbone, presence of simple electrolytes, etc. [8-25]. The valency of the ions from the simple electrolyte is known to play a dramatic role. As an example, the concentration of divalent ions required to achieve the same volume change as that from monovalent ions is about three orders of magnitude smaller [5]. Furthermore, the specificity of the ions is established to be a very significant factor [26]. It is also well known that the gels possess considerable amount of structural heterogeneities as evident from various scattering techniques [27]. The dynamics of polyelectrolyte gels and kinetics of volume phase transitions have also been extensively studied [28-30]. There are also new puzzles emerging from new investigations on the dynamics of polyelectrolyte gels. The diffusion coefficient measured in polyelectrolyte gels exhibit substantial pretransitional slowing down before the macroscopic volume transition occurs [31]. All of the phenomenology on polyelectrolyte gels have been interpreted essentially by the Flory theory
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