Double layer relaxation

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

The effect of field variations on measured mobility are considerable and discussion of this in terms of double layer relaxations provides the major thrust of Stotz paper. When the field is applied to a particle and its double layer, the particle moves in one direction relative to the double layer and there is, therefore, an induced asymmetry. The relaxation time required to restore the original symmetry can be defined as... 

Forces due to the action of the electric field on ions of the opposite charge to that of the particle within the double layer relaxation effect)... 

Negative adsorption is a relatively import2mt phenomenon in concentrated disperse systems and in capillaries. It is responsible for the Donnan effect, for the exclusion of electrolytes from concentrated sols, dispersions and capillaries and the ensuing salt-sieving effect, already introduced in chapter I.l. It also plays a role in double layer relaxation as occurs in alternating fields or in particle-particle Interaction. As negative adsorption is a purely electrostatic feature and takes place far from the surface, in all these applications its computation from Polsson-Boltzmann statistics is reliable, especially at high ly l. 

First the phenomenology is discussed it applies for any double layer relaxation model. 

The equations discussed above are all first-order approximations. Actually, the movement of particles causes a deformation of the diffuse double layer (relaxation effect), which alters the above equations. ... 

The constant potential and constant charge density results given by Equations 3.41 and 3.44 are limiting cases of behavior that may occur as colloidal particles approach one another. In the constant potential case, the approach is slow enough that equilibrium of the potential determining ion is maintained between the surface and bulk solution. Adsorption or desorption occurs as necessary to maintain the equihbrium potential xpo. The opposite extreme is the constant charge density case where the particles approach so rapidly that no adsorption or desorption has time to occur. Qearly, intermediate situations are possible as well when the time constant for adsorption or desorption and double-layer relaxation are comparable to the approach time of the particles. 

When particle aggregates are formed, the movement of the aggregates is subject to the joint effect of shape and double-layer relaxation, which may increase the electrophoretic velocity of aggregates of 10-100 particles by a factor of approximately 3, in comparison with the velocity of individual particles. In suspensions of conductive or semiconductive materials, aggregation may reduce the electrophoretic velocity to zero because of the sharp decrease in mobility of conductive particles when Kd> I. 

In contrast, there will be many cases where continuum solvent models are less useful. These include situations where one of the goals of the simulation is to obtain a detailed picture of solvent structure, or where there is evidence that a particular structural feature of the solvent is playing a key role (for example, a specific water-macromolecule hydrogen bond). In these situations, however, explicit representation of some water combined with implicit solvation may suffice. Another example is when molecular dynamics simulations are used to study kinetic, or time-dependent phenomena. The absence of the frictional effects of solvent will lead to overestimation of rates. In addition, more subtle time-dependent effects arising from the solvent will be missing from continuum models. Continuum solvent models are in effect frilly adiabatic, in the sense that for any instantaneous macromolecular conformation, the solvent is taken to be completely relaxed. For electrostatic effects, this implies instantaneous dielectric and ionic double layer relaxation rates, and for the hydrophobic effect, instantaneous structural rearrangement. An exception would be dielectric models that involve a frequency-dependent dielectric. Nevertheless, continuum solvent models should be used with caution in studying the time dependence of macromolecular processes. 

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