Multivalent counterion effects

A. O. Sharif, Z. Tabatabaian, and W. R. Bowen, /. Colloid Interface Sci., 255,138 (2002). The Wall and Multivalent Counterion Effects on the Electrostatic Force Between Like-Charged Spherical Particles Confined in a Charged Pore. 

The procedure used for testing the ideal Donnan theory is applicable to any model that decouples ionic effects from network elasticity and polymer/solvent interactions. Thus we require that nnet depend only on EWF and not C. While this assumption may seem natural, several models which include ionic effects do not make this assumption. For example, the state of ionization of a polymer chain in the gel and the ionic environment may affect the chain s persistence length, which in turn alters the network elasticity [26]. Similarly, a multivalent counterion can alter network elasticity by creating transient crosslinks. 

Qualitatively, the phase diagram fits very well to the phase diagram known for single-chain polyelectrolytes, the phase boundaries are only slightly shifted. In principle, the parameter space for polyelectrol ffes has far more dimensions, such as the solvent quality parameter, the valency of monomers or counterions, and additional salt concentration in the system. Especially for multivalent counterions, one can expect an even more complex picture, since correlation effects are known to play an important role even for single chains. 

The nature of the charged groups (sulfate or sulfonate) and the nature of the backbone of the polyelectrolyte have little effect on the phase diagram of polyelectrolyte/counterion mixtures. Therefore the electrostatic attractions can be considered as the principal driving force for phase separation of highly charged strong polyelectrolytes in the presence of multivalent counterions. A universal behavior is observed whatever the nature of polyelectrolyte or counterions. 

Hayakawa K, Kwak JCT. Study of surfactant—polyelectrolyte interactions. 2. Effect of multivalent counterions on the binding of dodecyltrimethylammonium ions by sodium dextran sulfate and sodium poly(styrenesulfonate) in aqueous solution. J Phys Chem 1983 87 506-509. 

A polymer may modify this entropy contribution in a number of different ways. If it is ionic and has a similar charge, then we have a simple and relatively moderate electrolyte effect. If its charge is opposite, and it acts as a multivalent counterion, then the interaction becomes very strong since an association between polymer and micelle leads to a release of the counterions of both the micelles and the polymer molecules a very similar effect will be obtained in mixtures of two oppositely charged polymers. Indeed there is for such a case a lowering of the CMC by orders of magnitude. 

Recently, we have demonstrated that SPEBs undergo a collapse in the presence of a mixture of monovalent and multivalent counterions. The collapse crossover was well described by a mean-field approach. The application of a mean-field approach is well founded by simulation results done with MD. MD simulations show that the effects of ion correlation and fluctuations can be neglected over a wide range of multivalent coimteiion concentration. Higher valent counterions are shown to interact strongly with the polyelearolyte chains of the SPEB and thus exhibit a much reduced osmotic activity in the system. This reduaion is the driving force for the collapse. 

What are the limits of the approximated expression Eq. 4 Mainly those due to the mean-field nature of PB. For, say, 99 % of the studied systems, the ions are monovalent, ion-ion correlations in water can be safely ignored, and the standard expression is valid. This is no more the case in presence of multivalent counterions (or monovalent ions in solvent of low e). That opens to the fascinating concept of electrostatic attraction between hke-charged colloids, subject of numerous false analyses, debates, and controversies in the literature for 30 years. Figure 1 presents Monte Carlo (MC) simulations data for the force vs. separation law within the primitive model (two latex colloids and ions in continuous solvent) in presence of counterions of increasing valence. While the PB/DLVO prediction remains everywhere repulsive, the exact MC behavior deviates at intermediate separation and develops an attractive well deeper and deeper as the valence increases above 3. This non mean-field effect is due to the repulsions and correlations among the counterions localized in the intersticial region (discreteness of the condensed layer). The same type of colloidal attraction is responsible for a liquid-gas (concentrated solution-dilute solution) phase separation, observed... 

More recent experimental data [4] show that considerable deviations from the conventional DLVO theory appear for short surface-to-surface distance hydration repulsion) and in the presence of bivalent and multivalent counterions ionic correlation force). Both effects can be interpreted as contributions to the double-layer interaction not accounted for in the DLVO theory see Sec. VLB. 

---