Flux-potential relationship

Keep in mind that Eqs. (8-14) are only valid for small Kr, when the electrophoresis retardation (electric-field-induced movement of ions in the electric double layer, which is opposite to the direction of particle movement) is unimportant [41J. This limitation is inherent to the Hiickel equation. Practically, a colloidal suspension always contains charged particles dispersed in a medium with surfactants (or electrolytes) of both polarities. In this case the Poisson s equation must be used for deriving the surface charge density and Zeta potential relationship. Under the Dcbyc-Hiickel approximation, i.c., the small value of potential, zey/ kgT, where v is the potential and z is the valency of ion, a simple relationship between the surface charge density and Zeta potential can be easily obtained [7], The Poisson s equation simply says that the potential flux per unit volume of a potential field is equal to the charge density in that area divided by the dielectric constant of the medium. It can be mathematically expressed as ... 

It is assumed that the chloride ion is transported passively across the membrane. Using an approach similar to the formulation of Eqs (2.1.2), (2.3.26) and (2.5.23), relationships can be written for the material fluxes of sodium and chloride ions, /Na+ and Jcr (the driving force is considered to be the electrochemical potential difference), and for the flux of the chemical reaction, Jch ... 

Given this relationship between POC and PIC, any change in their relative abundance would be expected to affect their export efficiency, i.e., the percentage of the production flux that reaches the seafloor. For example, an increase in the coc-colithophorid population relative to other phytoplankton would be expected to lead to an increased export efficiency of POC and PIC. Such changes have the potential to affect the CO2 content of the ocean and hence the atmosphere and thereby alter climate. 

The vast majority of small-amplitude methods are based on small-amplitude potential excitations with potential control of the surface concentrations. In earlier chapters, the relationship between surface concentration and electrode potential was explored and the concept of concentration profiles was presented. Whenever there is a flux of electrons at the electrode surface, the concentration profiles of at least two species will exhibit nonzero slopes at the electrode surface, as the electrochemical conversion of one member of a couple into another takes place and mass transport processes act to reestablish a uniform concentration distribution. These processes occur irrespective of whether the current flux arises from a potential or current excitation of the cell. In either case, they result in a perturbation from the previously existing concentration profile. The initial surface concentrations (which existed prior to the application of the new perturbation) are often termed the dc surface concentrations. It is useful to note that at any time, the distance integral of the concentration excess or defect is directly proportional to the charge passed due to that per-... 

To solve the electrical problem at the electrodes, two variables need to be found (i.e., the electrical potential (scalar) and the current density (vector)). By analogy, two variables are also needed to find the ionic flux and the potential distribution. The vector relationship is given by Ohm s law (3.10), while the scalar relation is provided by expression (3.5), which can be re-written as ... 

Fluorescent-based flux or membrane potential assays provide superior throughput compared to traditional electrophysiology-based screening technologies. For fluorescent-based membrane potential assays, however, the response to increasing channel activity can be non-linear due to the inherent non-linear relationship between channel activity and membrane potential (Fig. 4A). This prevents an accurate readout of efficacy and reduces the reso-... 

These last two expressions are forms of the Tafel law. They are an example of a linear free energy relationship (linear relation between a kinetic and a thermodynamic parameter) the parameters in this case being the flux (or the current) and the potential. 

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