Interactions between polyions

Repulsive coulombic forces exist between charged polyions. These are attenuated by the bound counterions conversely they are stronger for polyions having a higher concentration of free counterions. When the charge along the polyion, Q, is small the forces involved are purely coulombic repulsion forces. However, when Q exceeds a certain value, counterions condense on the polyions and reduce the repulsive forces. 

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. 

The repulsive force between polyions, calculated for the mean equilibrium distribution of the counterions, is 

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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. 

Imai, N. (1961). Interaction between polyions and low molecular weight ions. Journal of the Physical Society of Japan, 16, 746-60. 

Under the conditions of screening of electrostatic interactions between polyions, as occurs at high ionic strength (say, / > 0.1 mol dm- ), or in solutions containing neutral (non-ionic) polymers, the excluded volume term is the leading term in the theoretical equation for the second virial coefficient. In this latter type of situation, the sizes and conformation/ architecture of the biopolymer molecules/particles become of substantial importance. 

Without doing detailed quantitative analysis of the data, it can be stated that the polyion diffusion can be qualitatively described by two theoretical concepts. The first concept capable of qualitative explanation of the polyion diffusion is the concept based on considering polyions as interacting Brownian particles with direct interactions between polyions and hydrodynamic interactions. The short-time collective diffusion coefficient for a system of interacting Brownian particles treated by statistical mechanics is calculated from the first cumulant F of the dynamic structure factor S(q, t) as [15-17]... 

Consider the interaction between polyions and small ions. For a polyelectrolyte chain, the charges on the polymer chains repel each other so that the polymer chain tends to assume a more extended configuration. Because the diameter of a polymer chain is very small compared with it length, in many applications, a polyelectrolyte chain can be treated as a charged cylinder. Tlie interaction between small ions and a charged cylinder (rf infinite length can be described by the Poisson-Boltzmann equation 16-18)... 

Under these conditions the interaction between polyions can be appreciable. It seems then that the range of salt concentrations 10 M to 10 M is particularly interesting because it is compatible both with the notion of the electrolyte as a plasma and with the non-agregation of the polyions. 

The permeability of polyelectrolyte shells can be changed by addition of organic solvent to water suspension of microcapsules. 37,73 decrease in dielectric permittivity of microenvironment leads to the increase of electrostatic interaction between polyionic parts. The permeability of polyelectrolyte shells increases because of compression and curtailing polymeric chains. 

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]. 

As is clear from the above discussion, the definition of ion-binding is not unique. It depends on our assumption on the state of free ions. Sometimes, it is assumed that the free ions are the same as the ions in simple salt solutions at the same concentration. Sometimes, the electrostatic interaction between polyion and free counterions is taken into account. In the case, the so-called Debye-Huckel approximation may be assumed as the charge density is lowered with ion-binding. 

SHORT-RANGE INTERACTIONS BETWEEN POLYIONS AND SMALL IONS... 

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-... 

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