Attraction between polyions

The binding of multivalent counterions decreases the repulsion and causes attraction between polyions. This attraction is the result of the fluctuation of the counterion distribution and is equivalent to a multivalent counterion bridge between polyions. 

Cations can be seen as acting as ionic crosslinks between polyanion chains. Although this may appear a naive concept, crosslinking can be seen as equivalent to attractions between polyions resulting from the fluctuation of the counterion distribution (Section 4.2.13). Moreover, it relates to the classical theory of gelation associated with Flory (1953). Divalent cations (Zn and Ca +) have the potential to link two polyanion chains. Of course, unlike covalent crosslinks, ionic links are easily broken and re-formed under stress there could therefore be chain slipping and this may explain the plastic nature of zinc polycarboxylate cement. 

Ion binding by reduction of repulsive forces also causes the attractive forces between polyions to increase, and the cement paste thickens. This interaction between polyions may be regarded as a kind of bridge formed by multivalent ions located between the polyions. At this stage the cement paste has the characteristic of a lyophilic sol - high viscosity. 

J. J. Arenzon, J. F. Stilck, and Y. Levin. Simple model for attraction between like-charged polyions. European Physical Journal B 12 79-82 (1999). 

The driving force for the formation of the ordered phase is still unclear and has been a matter of much controversy. It has been claimed by Ise and Sogami [lOS, 106] that the densely ordered phase originates from attractive interactions between polyions, a point of view that has been heavily criticized by others [107]. For a detailed discussion of this controversy see [8]. 

In the above derivation, it is again assumed that the counter-ions as well as the polymeric ions and by-ions distribute uniformly in the solution, and moreover, the hydrodynamic interaction between polyion coils is negligible. As the hydrodynamic interaction is included in both and however, the effect should be cancelled in Equation (34). Because the counter-ions are strongly attracted around the polymeric ions, the poly electrolyte solutions are highly non-ideal so that both and A 2 may deviate from the calculated values of Equations (31) and (32). However, it is ] easonable to assume that the equality in Equation (34) should hold if we use the experimental values for all k and A2-... 

Oppositely charged ions are attracted to each other by electrostatic forces and so will not be distributed uniformly in solution. Around each ion or polyion there is a predominance of ions of the opposite charge, the counterions. This cloud of counterions is the ionic atmosphere of the polyion. In a dynamic situation, the distribution of counterions depends on competition between the electrostatic binding forces and the opposing, disruptive effects of thermal agitation. 

Schmitz et al (31) have proposed that the discrepancy between QLS and tracer diffusion measurements can be reconciled by considering the effects of small ions on the dynamics and scattering power of the polyelectrolyte. In this model, the slow mode arises from the formation of "temporal aggregates . These arise as the result of a balance between attractive fluctuating dipole forces coming from the sharing of small ions by several polyions, and repulsive electrostatic and Brownian diffusion forces. This concept is attractive, but needs to be formulated quantitatively before it can be adequately tested. 

It is known that interactions between ionic surfactants and polyions with the opposite charge lead to the formation of soluble colloidal complexes. The polyelectrolyte chain binds to surfactant molecules through Coulombic attractions, and the hydrophobic moieties of the surfactant molecules stabilize the complexes due to hydrophobic interactions in the aqueous solution (Morris and Jennings, 1976 Satake and Yang, 1976 Osica etal., 1977 Fendler, 1982 Hayakawa et al., 1983 Jonsson et al, 1998). 

Ray, J. and Manning, G.S. (1994) An attractive force between two rodlike polyions mediated by the sharing of condensed counterions. Langmuir, 10,2450-2461. 

There are several characteristics of the near region. First, if a counterion of valence Z is brought from a distance far away from the polyion to the near region, then Z univalent counterions are released into the bulk aqueous solution [43]. Thus, the near region is associated with the condensed layer. Second, the interaction potential between counterion-polyion is unscreened, attractive, and is proportional to 2Zo ln(r/2h) [43]. 

Diffusion coefficients and molecular/ionic interactions between polymers and other species appear to have attracted some interest, particularly with regard to polyions. Quantitative information on coil size and associated changes therein together with the degree of aggregation in blends of polymers and copolymers has been shown to be possible using fluorescence depolarisation measurements. Using copolymer... 

Turbidimetric Titrations. The abrupt turbidity increases in Figure 1 correspond to phase separation of the polymer-protein complex. pHcritical increases with I because the attractive Coulombic interactions between the protein and polyion are screened by added salt, so that a larger net negative protein charge is required for phase separation (10). 

Figure 4 presents a graph of Q(r) for a pair of identical rodlike polyion segments in parallel with separation distance r. Note the large increase as the two polyions approach through the intermediate range of distances. In a free volume interpretation, the condensed layers expand, providing an increased entropy that would tend to drive an attractive interaction between the poly ions. 

The inverted attractive force between two identical parallel polyion segments creates a single polyion-polyion peak at intermediate distances in the... 

The cause of the inverted attraction in the polyion-polyion case is the strong distance dependence of the condensed layer partition function Q(r) revealed in Figure 4. The entropic tendency toward attraction mentioned above in connection with Figure 4 turns out to dominate the balance of forces. Staying with a free volume interpretation of Q(r), we can observe that when two polyions approach, their electric fields merge, and the common field is relatively flat in the space between the polyions. The barrier to entropic expansion of the condensed layers having been removed, the condensed counterions flood into the large volume of space between the poly-... 

A similar physical picture of counterion binding can be adopted for systems containing surfactant counterions, although in this case some additional effect may be expected. The main factors that influence the binding of ionic surfactants to polyelectrolytes with opposite charge are (1) the charge density of the polyion, A, (2) the hydrophobic character of the surfactant (the length of its hydrocarbon chain), (3) the additional attractive forces between the... 

---