Counterion relaxation

Dominant contributions are responsible for the a, fi, and y dispersions. They include for the a-effect, apparent membrane property changes as described in the text for the fi-effect, tissue structure (Maxwell-Wagner effect) and for the y-effect, polarity of the water molecule (Debye effect). Fine structural effects are responsible for deviations as indicated by the dashed lines. These include contributions from subcellular organelles, proteins, and counterion relaxation effects (see text). 

If they contain protein, an additional comparatively weak 6-dispersion due to the polarity of protein is added and a 6-dispersion. If the cells carry a net charge, an a-mechanism due to counterion relaxation is added and if their membranes relax on their own, as some excitable membranes do, an additional a-mechanism may appear. 

The dielectric properties of tissues and cell suspensions will be summarized for the total frequency range from a few Hz to 20 GHz. Three pronounced relaxation regions at ELF, RF and MW frequencies are due to counterion relaxation and membrane invaginations, to Maxwell-Wagner effects, and to the frequency dependent properties of normal water at microwave frequencies. Superimposed on these major dispersions are fine structure effects caused by cellular organelles, protein bound water, polar tissue proteins, and side chain rotation. 

Car-Parrinello techniques have been used to describe classical variables whose behavior, like quantum electrons in the Born-Oppenheimer approximation, is nearly adiabatic with respect to other variables. In simulations of a colloidal system consisting of macroions of charge Ze, each associated with Z counterions of charge —e, Lowen et al. [192] eliminated explicit treatment of the many counterions using classical density functional theory. Assuming that the counterions relax instantaneously on the time-scale of macroion motion, simulations of the macroion were performed by optimizing the counterion density at each time step by simulated annealing. 

The pores form a DC current path. The sum of their conductances is so large that the capacitive effect of the membrane as a dielectric is small at low frequencies. If there are not too many pores, most of the potential difference is over the membrane pores, and the E-field strength in the pores will be high. The counter-ions of the double layer on the pore walls will migrate synchronous with the E-field, and the solution inside the pore will be pumped back and forth by electroosmosis. At higher frequencies, the membrane susceptance will shunt the pores, and voltage across the pore will be reduced. Counterion relaxation will also occur, as shown in Figure 3.11. 

The sweat ducts of the skin introduce electrical shunt paths for DC current. Although lateral counterion relaxation effects have been demonstrated in pores, this effect is presumably negligible in sweat ducts hence, sweat ducts are predominantly conductive (Martinsen et al., 1998a). However, the DC conductance measured on human skin is not only due to the sweat ducts. Measurements on isolated SC as well as nail and hair reveal conductance values comparable to fliose found on. skin in vivo (Martinsen et al., 1997a,b). 

From experiments of this type it is possible to draw conclusions about the location of the solubilized molecules in the micelles since the counterion relaxation is sensitive to the charge density at the micellar surface. It could, in the case considered, be deduced that hexanol, benzene and N,N-dimethylaniline, which cause a marked lowering of the relaxation rate at high concentrations, are mainly solubilized at or near the interface between the micelle and the intermicel-lar solution. Cyclohexane, which does not affect counterion relaxation, appears to be located in the micellar interior. Furthermore, it was deduced that the first three compounds promote the sphere-to-rod transition, whereas no shape alteration is induced upon solubilization of cyclohexane [Z21],... 

As demonstrated in Ref. [327] both slow overall and fast local motions may, on the basis of an electrostatic model, produce relaxation rates of the observed order of magnitude. It is to be expected that in particular studies of the change in counterion relaxation rate with phase structure and length of the surfactant ion, as well as comparisons between quadrupole splittings and quadrupole relaxation rates, will come to be very helpful in attempts to elucidate the detailed relaxation mechanism in surfactant systems. It can finally be noted that electronic distortion effects on relaxation, as was discussed above for simple halides, have not been considered for halide ion quadrupole relaxation in surfactant systems. It appears that the electronic distortion model (see above) cannot provide a good rationalization of the observations quoted above. 

Aside from ion content, a wide range of properties is available in ionomers by control of various processing variables, such as degree of conversion (neutralization), type of counterion, plasticizer content and thermal treatment. Various examples illustrating possible effects of these variables on mechanical relaxation behavior and on such mechanical properties as stiffness, strength, and time- or energy-to-fracture have been given. 

Mechanisms of Sorption Processes. Kinetic studies are valuable for hypothesizing mechanisms of reactions in homogeneous solution, but the interpretation of kinetic data for sorption processes is more difficult. Recently it has been shown that the mechanisms of very fast adsorption reactions may be interpreted from the results of chemical relaxation studies (25-27). Yasunaga and Ikeda (Chapter 12) summarize recent studies that have utilized relaxation techniques to examine the adsorption of cations and anions on hydrous oxide and aluminosilicate surfaces. Hayes and Leckie (Chapter 7) present new interpretations for the mechanism of lead ion adsorption by goethite. In both papers it is concluded that the kinetic and equilibrium adsorption data are consistent with the rate relationships derived from an interfacial model in which metal ions are located nearer to the surface than adsorbed counterions. 

When counterion binding reaction II is extremely rapid, the concentration dependence of the relaxation time is given by (11)... 

Blatz and Mohler38 have performed 2D NOE NMR experiments on the protonated f-butylamine Schiff base of all-fraws-retinal using different counterions, each carrying at least one nonexchangeable proton. The study has indicated that a proton on the counterion molecule is spatially close, in aprotic solvents, to the protons of the chromophore near the positively charged nitrogen. It has also shown that the ion-pair formation is relaxed in either the presence of excess carboxylic acid (the counterion) or when using methanol as a solvent. 

By accounting for the coupling between the dynamics of polyelectrolyte chains and their counterions and salt ions and assuming that small ions relax faster than polyelectrolyte chains, we have derived Df to be... 

Although the coupling of counterion dynamics and polyelectrolyte dynamics has been accounted for at the mean field level, the relaxation of counterion cloud needs to be included in comparing with experimental data. 

Equilibrium studies have shown that the first formation constant of the chromium(iii)-ethylenediamine system is < 10, over 10 -fold smaller than the value (10 ) previously reported. [Cr(en)3 (tn) ] (x = 0—3 and tn = tri-methylenediamine) complexes have been prepared and resolved using nitro-(-f )D-camphor. These mixed complexes have the same absolute configuration, A, as the pure [Cr(en)3] and [Cr(tn)3] species. Selective intervention of an optically active counterion in the relaxation processes of excited enantiomeric complexes can lead to partial resolution. This has been achieved for [Cr(phen)3] using D-tartrate. ... 

However, much of the relaxation is spread over a broad range of long times-out to and beyond the 40 ns upper limit of the experimental time range. Over the three decades in time that rue observed, the dynamics are logarithmic in time, i.e. the Stokes shift S(t) is given by S(i) = Sn + A0 log,0(t// ). Previous results have shown that this very unusual logarithmic relaxation is common to unmodified DNA, independent of the sequence of bases [7]. In a recent paper, we discuss the important role of counterions [8]. However, they do not cause the logarithmic dynamics, nor does their role vary between the samples examined here. 

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