Kinetic depolarization

As the current correlation function in the time integral has sums over all charge velocities z, effects of cross terms between ionic and molecular motions appear which cannot be identified or separated by electromagnetic measurements. In addition to static solvation and saturation effects on permittivity often considered in biological contexts, Hubbard and Onsager have pointed out "kinetic depolarization" effects which need to be considered. In II, we discuss experimental evidence and implications of the theoretical predictions of such effects. 

The separation of the measured effect into ionic contributions requires assumptions on reference ions depending on the nature of the solvent. For acetonitrile solutions, a pattern of consistent solvation numbers is obtained at negligible kinetic depolarization for Li" (4),fVo (4),Br (2),Bu4fV+(0),/"(0),C /07(0) in agreement with those from FTIR measurements for Li., Na and CIO. Reasonable solvation numbers are found for Na ions in FA and DMF both for = 0(6) or 0(4). Independent of the choice... 

The decreases in permittivity when ions are added to a polar solvent were traditionally interpreted in terms of saturation or solvation of local ionic environments (76) until Hubbard and Onsager (77) (78) worked out a continuum theory of the kinetic depolarization effect. This arises from the fact that part of the electric field solvent dipoles near an ion is from the moving ion and similarly for the ion in the field of reorienting dipoles with the consequences that both responses are delayed in proportion to the relaxation time of the solvent polarization. The remarkably simple Hubbard-Onsager expression for the resulting decrement of static (or better limiting low frequency) permittivity can be written... 

Summary High frequency peimittivity measurements (1 to 40 GHz) are analyzed to yield information on kinetic processes in aqueous and non-aqueous electrolyte solutions. Information is obtained on the low and high frequency relaxation times of the solvent and their shifts by addition of electrolytes, rotational relaxation times of ion pairs, association constants, rate constants of ion-pair formation and decomposition, and kinetic depolarization. Examples are given for each process. 

The limiting slope, -S, the so-called dielectric decrement, is the quantity considered in theoretical concepts. The underlying models roughly can be classified into equilibrium approaches based on dielectic saturation, and dynamical theories based on kinetic depolarization. 

The theories of kinetic depolarization link the decrease of the static permittivity to ionic motions. Hubbard, Colonomos and Wolynes showed that the corrected original continuum theory 1 2 predicts proportionality of g(0 0)- g(0 c) and the specific conductance x... 

U. Kaatze, "Dielectric Effects in Aqueous Solutions of 1 1, 2 1, 5 1 valent Electrolytes Kinetic Depolarization, Saturation and Solvent Relaxation", Z. Phys. Chem.NF 155 51 (1985)... 

Kaatze U (1983) Dielectric effects in aqueous-solutions of 1-1, 2-1, and 3-1 valent electrolytes - kinetic depolarization, saturation, and solvent relaxation. Z Phys Chem Neue Fol 135 51-75... 

Activation is slower in less depolarized membranes and inactivation drains the open (and resting) state more effectively. In fact, real Na" " channels gate by more complex pathways, including several closed states intermediate between R and O, as well as multiple inactivated states. Inactivation from these intermediate states is probably faster than from / , and the entire activation process, in its fully branched entirety, is rich with kinetic possibilities. However, the effects of toxins may be understood in general by the simpler scheme presented in Figure 2. 

Figure 4. Effects of dihydro-brevetoxin B (H2BVTX-B) on Na currents in crayfish axon under voltage-clamp. (A) A family of Na currents in control solution each trace shows the current kinetics responding to a step depolarization (ranging from -90 to -I-100 mV in 10 mV increments). Incomplete inactivation at large depolarizations is normal in this preparation. (B) Na currents after internal perfusion with H2BVTX-B (1.2 a M). inactivation is slower and less complete than in the control, and the current amplitudes are reduced. (C) A plot of current amplitudes at their peak value (Ip o, o) and at steady-state (I A, A for long depolarizations) shows that toxin-mOdified channels (filled symbols) activate at more negative membrane potentials and correspond to a reduced peak Na conductance of the axon (Reproduced with permission from Ref. 31. Copyright 1984 American Society for Pharmacology and Experimental Therapeutics).

The Ca channels that have been the most extensively studied are the voltage-dependent Ca channels. These channels are usually found in plasma or transverse tubule membranes. Voltage-dependent Ca channels open in response to an appropriate membrane depolarization. Several different types of voltage-dependent Ca channels have been described and are characterized by differences in their activation and inactivation sensitivities to voltage, their kinetic properties, and their sensitivities to activation or inhibition by a variety of pharmacological agents. 

Depolarization of the synaptosomes with Ca-free media containing lOOmM K increased 86Rb efflux (figure 1, open squares) two kinetically and pharmacologically distinct K conductances could be discerned. Between 1 and 4 seconds, Rb efflux was linear and was 2.2 to 2.4%/sec (component "S"). Extrapolation of Rb efflux to the ordinate ("zero time") exposed an additional, rapid component of 86Rb efflux (component "T"). Component T reflects a distinct K channel that, unlike component S, appeared to inactivate in less than 1 second (Bartschat and Blaustein 1985a). 

Faradaic rectification polarographic studies have been carried out for a mixture containing several metal ions together and also for individual inorganic depolarizers so as to explore the applicability and limitations of the method and to determine kinetic parameters for some of them. For comparison, some of the dc and ac polarograms have also been recorded simultaneously. In the following, the details of the experimental technique used will be described and the potentiality of the technique in qualitative and quantitative analysis will be examined. The applicability of the method in the... 

Various mechanisms for electret effect formation in anodic oxides have been proposed. Lobushkin and co-workers241,242 assumed that it is caused by electrons captured at deep trap levels in oxides. This point of view was supported by Zudov and Zudova.244,250 Mikho and Koleboshin272 postulated that the surface charge of anodic oxides is caused by dissociation of water molecules at the oxide-electrolyte interface and absorption of OH groups. This mechanism was put forward to explain the restoration of the electret effect by UV irradiation of depolarized samples. Parkhutik and Shershulskii62 assumed that the electret effect is caused by the accumulation of incorporated anions into the growing oxide. They based their conclusions on measurements of the kinetics of Us accumulation in anodic oxides and comparative analyses of the kinetics of chemical composition variation of growing oxides. 

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