Polyelectrolytes, linear osmotic pressures

We present a review of theoretical and experimental results on the swelling behavior and collapse transition in polymer gels obtained by our group at Moscow State University. The main attention is paid to polyelectrolyte networks where the most important factor is additional osmotic pressure created by mobile counter ions. The influence of other factors such as condensation of counter ions, external mechanical force, the mixed nature of low-molecular solvents, interaction of network chains with linear macromolecules and surfactants etc. is also taken into account Experimental results demonstrate a good correlation with theoretical analysis. 

Abstract Aqueous solutions of star-like polyelectrolytes (PEs) exhibit distinctive features that originate from the topological complexity of branched macromolecules. In a salt-free solution of branched PEs, mobile counterions preferentially localize in the intramolecular volume of branched macroions. Counterion localization manifests itself in a dramatic reduction of the osmotic coefficient in solutions of branched polyions as compared with those of linear PEs. The intramolecular osmotic pressure, created by entrapped counterions, imposes stretched conformations of branches and this leads to dramatic intramolecular conformational transitions upon variations in environmental conditions. In this chapter, we overview the theory of conformations and stimuli-induced conformational transitions in star-like PEs in aqueous solutions and compare these to the data from experiments and Monte Carlo and molecular dynamics simulations. 

Many macromolecules in aqueous solution are polyelectrolytes. The remarkable changes in the conformation of linear polyelectrolytes as a function of concentration, ionic strength, and pH are discussed. The various theories of chain expansion are reviewed. The thermodynamic properties of polyelectrolyte solutions reveal dramatic behavior. The large increase in the reduced osmotic pressure, jr/c, as the solution is diluted is explained in terms of the entropy of the counterions. The strong dependence of the conformation of the chains with solution conditions also leads to large changes in the viscosity. The viscosity is also explained in terms of the coil size and the interactions of the chains. 

The osmotic pressure of polyelectrolytes in salt-free solutions exceeds that of neutral polymers at similar polymer concentrations by several orders of magnitude. It increases almost linearly with polymer concentration and is independent of the chain molecular weight in a wide range of polymer concentrations. This almost linear concentration dependence of the osmotic pressure together with its strong dependence on added salt demonstrates that osmotic pressure is mainly due to coimterion and salt ion contribution. 

Figure 16 shows the dependence of the osmotic pressure of salt-free polyelectrolyte solutions. Through almost the entire concentration range considered, the osmotic pressure is proportional to the polymer concentration, supporting that it is controlled by the osmotic pressure of counterions, both above and below the overlap concentration. There appears to be a weak chain length dependence of the osmotic pressure for short chains. However, this iV-dependence is consistent with jN correction to the osmotic pressure due to chain translational entropy. The deviation from linear dependence of the osmotic pressure n occurs around polymer concentration c 0.Qla, which is above the overlap concentration for all samples. At very high polymer concentrations, where electrostatic interactions are almost completely screened by counterions and by charges on the... 

Rubbers swell if a solvent penetrates. This isotropic dilatation becomes particularly large if cross-linked polyelectrolytes are swollen by water. The equilibrium state here is controlled by both the osmotic pressure of the mobile counter-ions and the non-linear network properties. 

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