Polyion interactions attractive

Attractive forces arise from dipole interaction, a result of the fluctuations in the cloud of counterions. Although the mean distribution of counterions is uniform along the length of the polyion, there are fluctuations in the cloud of counterions which induce transient dipoles. When two polyions approach each other counterion fluctuations become coupled and enhance the attractive force. Since polyions have a high polarizability these attractive forces can be considerable. 

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. 

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). 

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. 

FIG. 7 The polyion-polyion radial distribution function at infinite polymer dilution. An attractive interaction in the intermediate region generates a peak position there. Debye screening length 30 A (0.01 M NaCl) polyion charge spacing 1.7 A. 

There is ample experimental evidence that identically charged polymers in the presence of ordinary univalent counterions have a tendency to form loose clusters in solution [65-70], and we have asked whether the attractive polyion-polyion potential discussed in Sec. Ill can stabilize a finite-sized cluster of parallel rodlike polyions without leading to precipitation [71,72]. The theoretical problem is complicated by a failure of pairwise additivity the work of assembling N polyions is not equal to the work of assembling the N(N — l)/2 polyion pairs, each in isolation from the other N 2 polyions. To be sure, the Debye-Htickel interaction term for a cluster (the generalization of Eq. 5 above) takes the form of a pairwise sum over polyions,... 

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]. 

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