Electric long-range attractive

Though the theory of Derjaguin-Landau-Verwey-Overbeek (DLVO) [17, 18] was essentially designed for hydrophobic colloids, it is often applied to the analysis of the stability of polyelectrolyte solutions. According to this approach an overlap of the electrical double-layers of two charge-like colloidal spheres in an electrolyte solution always yields a repulsive screened Coulomb interaction, and the van der Waals forces are responsible for the attraction. A number of experiments in the recent decades, however, provide evidence that the effective interparticle potential shows a long-range attraction which cannot be ascribed to the van der Waals forces [15, 88-93], In spite of numerous theoretical attempts to explain this phenomena (for a review see [7, 8, 10, 94,... 

Rather high electrolyte concentrations characteristic of natural and waste waters, substantially weaken non-equilibrium surface forces of the diffusion - electric nature but scarcely affect nonequilibrium surface forces caused by the dynamic adsorption layer of nonionic surfactant (Dukhin 1981). Therefore, we consider such forces are important and their mechanism deserves special attention. The flotation of tiny particles is, nevertheless, possible if the distance between the bubble and particle surfaces becomes smaller than a critical value h j-. The film of thickness h r is thiimed, becomes unstable, and collapses if long-range attractive forces exist between the particle and the bubble, drawing them together. 

When a conductive probe is biased with respect to the conducting sample, its resonant frequency is shifted to lower frequency due to long-range attractive forces. This shift in frequency and the related shift of the phase are caused by the gradient of the electric field near the surface of the sample using a sharp conductive probe. The electrostatic force F(z] between the tip and the surface at the relative separation z is related to the local capacitance C between the tip and the sample by... 

Note that the long-range classical electrostatic limit furnishes an excellent approximation for the electrical attraction of the end groups, since these are separated far outside the range of significant exchange interactions. 

The allowance for polarization in the DH model obviates the need for separation of long-range and short-range attractive forces and for inclusion of additional repulsive interactions. Belief in the necessity to include some kind of covolume term stems from the confused analysis of Onsager (13), and is compounded by a misunderstanding of the standard state concept. Reference to a solvated standard state in which there are no interionic effects can in principle be made at any arbitrary concentration, and the only repulsive or exclusion term required is that described by the DH theory which puts limits on the ionic atmosphere size and hence on the lowering of electrical free energy. The present work therefore supports the view of Stokes (34) that the covolume term should not be included in the comparison of statistical-mechanical results with experimental ones. 

PB equation is based on the mean-field approximation, where ions are treated as continuous fluid-like particles moving independendy in a mean electric potential. The theory ignores the discrete ion properties such as ion size, ion-ion correlation and ion fluctuations. Fail to consider these properties can cause inaccurate predictions for RNA folding, especially in the presence of multivalent ions which are prone to ion correlation due to the strong, long-range Coulomb interactions. For example, PB cannot predict the experimentally observed attractive force between DNA helices in multivalent ion solutions. 

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