Polarization models, counterion

According to the fluctuation-dissipation theorem [1], the electrical polarizability of polyelectrolytes is related to the fluctuations of the dipole moment generated in the counterion atmosphere around the polyions in the absence of an applied electric field [2-4], Here we calculate the fluctuations by computer simulation to determine anisotropy of the electrical polarizability Aa of model DNA fragments in salt-free aqueous solutions [5-7]. The Metropolis Monte Carlo (MC) Brownian dynamics method [8-12] is applied to calculate counterion distributions, electric potentials, and fluctuations of counterion polarization. 

Experimentally, the molecular weight independence of the HF effect (in polyelectrolyte solutions) has been confirmed many times. Van der Touw and Mandel [64,65] attributed the HF dispersion to polarization of bound counterions along a part of the polyelectrolyte molecule. They introduced a model in which the polyelectrolyte is considered as a nonlinear sequence of rodlike subunits and the counterion polarization along the subunit is supposed to be responsible for the amplitude and the critical frequency of HF relaxation. Both quantities would essentially be independent of the molecular weight of the polyion. In solutions, where interactions between macromolecules are taken into account, the length of the above-mentioned subunit is related to the correlation distance between the macromolecular chains [25,26,92], Counterion polarization perpendicular to the polyion axis is pro-... 

To obtain Eqs. 11, 12, 13, and 14, it was assumed that the concentration of each ionic species within the electric double layer is related to the electric potential energy by a Boltzmann distribution. A comparison of Eq. 11 with the numerical results obtained by Prieve and Roman [2] shows that the thin-layer polarization model is quite good over a wide range of zeta potentials when Ka > 20. If 1(1 is small and Ka is large, the interaction between the diffuse counterions and the particle surface is weak and the polarization of the double layer is also weak. In the limit of... 

The classical model, as shown in Figure 1, assumes that the micelle adopts a spherical structure [2, 15-17], In aqueous solution the hydrocarbon chains or the hydrophobic part of the surfactants from the core of the micelle, while the ionic or polar groups face toward the exterior of the same, and together with a certain amount of counterions form what is known as the Stern layer. The remainder of the counterions, which are more or less associated with the micelle, make up the Gouy-Chapman layer. For the nonionic polyoxyethylene surfactants the structure is essentially the same except that the external region does not contain counterions but rather rings of hydrated polyoxyethylene chains. A micelle of... 

The Gouy-Chapman model describes the properties of the diffuse region of the double-layer. This intuitive model assumes that counterions are point charges that obey a Boltzmann distribution, with highest concentration nearest the oppositely charged fiat surface. The polar solvent is assumed to have the same dielectric constant within the diffuse region. The effective surface... 

In this section we shall consider the simplest model problem for the locally electro-neutral stationary concentration polarization at an ideally permselective uniform interface. The main features of CP will be traced through this example, including the breakdown of the local electro-neutrality approximation. Furthermore, we shall apply the scheme of 4.2 to investigate the effect of CP upon the counterion selectivity of an ion-exchange membrane in a way that is typical of many membrane studies. Finally, at the end of this section we shall consider briefly CP at an electrically inhomogeneous interface (the case relevant for many synthetic membranes). It will be shown that the concentration and the electric potential fields, developing in the course of CP at such an interface, are incompatible with mechanical equilibrium in the liquid electrolyte, that is, a convection (electroconvection) is bound to arise. 

Solutions of many proteins, synthetic polypeptides, and nucleic acids show large increases in permittivity c (u>) over that of solvent, normally aqueous, at sufficiently low frequencies f = w/2ir of steady state AC measurements, but with dispersion and absorption processes which may lie anywhere from subaudio to megahertz frequencies. Although our interest here is primarily in counterion fluctuation effects as the origin of polarization of aqueous DNA solutions, we first summarize some relevant results of other models for biopolymers. 

Actually a very crudal kinetic aspect has apparently always been overlooked so far. The original assumption of a proton mobility comparable to that in free solution which allows for dispersion frequencies in the MHz range must not be made in this special case. It is only applicable to the diffusion-controlled polarization of counterion atmospheres as discussed before. In contrast to those counterions the protons of the Kirkwood-Shumaker model are diemically bound at specific sites and must dissociate before they can jump to another site. Thus the lifetime of protons at a given site has to be taken into account with regard to the relaxation time of the overall fluctuation process. Its effect can be readily estimated on the basis of the rate constant of protolytic dissociation... 

Perhaps the most important chain configuration is the cis-, 4 structure favoured by reactions involving Li" counterion in non-polar solvents. In this instance a lithium compound modelling the active centre exists in both cis and trans forms in the ratio c/t, 35/65, and there seems no reason to suppose that... 

In order to elucidate this point, viscosity measurements of living and deactivated PDMA solutions were performed In toluene, with LI + [211] as counterion. As no significant change was observed. It can be deduced that the fraction of aggregates Is negligible (<1% for [C] 10 3 mole.l" ). Moreover, conductance measurements made on model sllanolates In THF Indicate that the fraction of free Ions Is very low. In benzene or toluene which are less polar than THF, the contribution to the reactivity from free Ions can be neglected. Thus It seems reasonable to assume that the main Ionic species are cryptated Ion pairs and... 

---