Entropy polyelectrolyte solutions

The addition of PVMI was expected to enhance the hydroxide-ion catalyzed hydrolysis of the anionic ester, since both the hydroxide ions and the negatively charged ester are attracted to the polycation so that the rate of their mutual collision is increased. For any given polyelectrolyte concentration the increase in the rate of hydrolysis should be independent of pH. And this is what has actually been found at pH values greater than 9. At lower pH values, however, a completely unexpected behavior resulted, i. e. the polycation was found to increase the rate of hydrolysis of NABS by the largest factor in that pH range (pH s 6) in which direct water attack on the ester makes the dominant contribution to the overall reaction rate (Fig. 8). The influence of hydrophobic forces appears to be ruled out in this case since PVMI has no effect on the solvolytic rate of the neutral ester p-nitrophenyl acetate and p-nitrophenyl hexanoate. Thus, the causes of the above-mentioned phenomenon are obscure this very fact adds, in the author s opinion, further interest to the study of reactions in polyelectrolyte solutions. The examination of such factors as the enthalpy and entropy of activation may be of particular relevance for a deeper insight into these complex reaction systems. 

The situation changes in a dramatic way if salt is added to the polyelectrolyte solution. For instance, let us assume that a small amount of CINa or of any similar salt is added in cell I (or in cell If). Each CINa gives a Cle ion and a Na ion that is able to cross the membrane. The entropy of the system is larger if all the Na counter-ions are distributed as uniformly as possible, over both cells, but electrical neutrality has to be preserved. Consequently, the co-ions Cle are attracted into cell II. This is the Dorman effect. Simultaneously, the osmotic pressure diminishes in a spectacular way, and the same is true for the contact potential between the two cells. If a lot of salt was added, one would find again... 

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. 

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... 

In a polyelectrolyte solution, the phase transition is driven by electrostatic solute-solvent interaction which results in a gain in the configurational entropy and the formation of amorphous randomly mixed polymer-rich phase remaining in equilibrium with dilute supernatant. Physical conditions for phase separation are deduced exphcitly when the complexation between oppositely charged polyelectrolytes leads to self-charge neutralizahon. 

This short summary of recent computer simulation results on the conformational properties of polyelectrolyte solutions showed that the classical pictures of screening and conformation changes for charged polymers need to be revised. At low concentrations the density fluctuations of the discrete counterions cause significant shape fluctuations, which go far beyond the short kink excitation driven by entropy. For increasing density with consequently increasing ionic strength, the chains dramatically shrink, before the classical overlapp concentration is reached. 

Abstract. The importance of experiments which may enable to describe accurately how free energy changes accompanying a variety of typical equilibrium processes in polyelectrolyte solutions are built up by enthalphy and entropy contributions is emphasized. 

In spite of the fact that the concentration of surfactants in the outer solution is assumed to be smaller than the critical micelle concentration, inside the network, micelles are supposed to be formed. The reason for this assumption is, first of all, intensive adsorption of surfactants on the network as a result of the ion exchange reaction. Moreover, in Refs. [38, 39], it was shown that critical concentration of micelles formation c c" within a polyelectrolyte network is much less than that in the solution of surfactant c° . Indeed, when a micelle is formed in solution immobilization of counter ions of surfactant molecules takes place, because these counter ions tend to neutralize the charge of micelles (see Fig. 13), whereas there is no immobilization of counter ions when the micelles are formed in the network the charge of micelles is neutralized by initially immobilized network charges which do not contribute to the translational entropy (Fig. 13). 

A variational theory which includes all these different contributions was recently proposed and applied for completely stretched polyelectrolyte stars (so-called porcupines ) [203, 204]. As a result, the effective interaction V(r) was very soft, mainly dominated by the entropy of the counterions inside the coronae of the stars supporting on old idea of Pincus [205]. If this pair potential is used as an input in a calculation of a solution of many stars, a freezing transition was found with a variety of different stable crystal lattices including exotic open lattices [206]. The method of effective interactions has the advantage to be generalizable to more complicated complexes which are discussed in this contribution-such as oppositely charged polyelectrolytes and polyelectrolyte-surfactant complexes-but this has still to be worked out in detail. 

Let us consider the conformation of polyelectrolyte macromolecules immersed in an infinite quantity of solvent. The counterions having high translational entropy are distributed over the whole volume of the solution their concentration in the vicinity of the macromolecules is extremely low, and their influence on the molecular conformation can be omitted completely. The conformation of the polyelectrolyte macromolecule is determined by rather strong unscreened repulsive interactions between charged groups attached to the chain. Due to this repulsion, the macromolecule assumes a strongly stretched conformation in the sense that its end-to-end distance R is a linear function of the degree of its polymerization m [14-18]. 

Insoluble polyelectrolyte complex may be formed when dissolved acidic and basic polyelectrolyte polymers are brought into intimate contact (131). Complex formation is generally agreed to be driven by the increase in entropy associated with the loss of small counterions into the bulk of the solution (132). Polyelectrolyte complex from concentrated solutions of strongly acidic and basic homopolymers has been shown to form sufficiently rapidly to produce a 20-30 nm thick membrane at the solution interface, as was found through reaction of dissolved poly(vinylbenzyl trimethylammonium chloride) with sodium poly (styrene sulfonate) (132). 

Dilute aqueous polymeric emulsions are commonly stabilized through the use of polymeric surfactants. If the stabilizer is uncharged, the emulsion is stabilized entropieally by segmental exclusion. In most instances, however, stabilization is a by product of coulombic repulsions generated by a polyelectrolyte surfactant. In a few instances the polymer itself is able to act as surfactant. For example, Eudragit RL, a commercially available partially quaternized cationic methacrylate based polymer, is able to form indefinitely stable emulsions in distilled water or buffered saline (141). These emulsions are prepared by adding polymer to boiling solution and are presumably stabilized by concentration of cationic functionality at the particle surface. 

We have already learnt that polyelectrolytes are much more soluble than the corresponding uncharged polymer, which we attribute to the entropy of the counterion distribution confining polymer molecules to part of the system costs little entropy due to the low number of entities. On the other hand, there is a large entropy loss on confining the (much more numerous) counterions. In mixed polymer systems, we see many consequences of the electrostatic interactions due to net charges. One is the low tendency to phase separation in a mixed solution of one nonionic and one ionic polymer in the presence of added electrolyte, this inhibition of phase separation is largely eliminated and typical polymer incompatibility is observed. 

Although their free solution behaviors are similar, flexible molecules (like DNA and denatured proteins) exhibit dramatically different behavior in a sieving matrix. Once the size of the pores in the gel becomes small relative to the radius of gyration of the polyelectrolyte chain, the polyelectrolyte chain must uncoil in order to move through the gel. Although the uncoiling process is entropically unfavorable (since it reduces the number of available conformations for the chain), the entropy loss is offset by the reduction in the electrical potential energy as the chain moves in the field. 

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