Electric Field Strength Gradients

Endo, Y. Yoshida, C. Baba, Y. DNA sequencing by capillary array electrophoresis with an electric field strength gradient. J. Biochem. Biophys. Meth. 1999, 41 (2-3), 133-141. 

There are different variants of the conjugate gradient method each of which corresponds to a different choice of the update parameter C - Some of these different methods and their convergence properties are discussed in Appendix D. The time has been discretized into N time steps (f, = / x 8f where i = 0,1, , N — 1) and the parameter space that is being searched in order to maximize the value of the objective functional is composed of the values of the electric field strength in each of the time intervals. 

Here (j is the CG update parameter. In the above equations, e = e (tj) o vector notation for the discretized electric field strength, = g (fj) o objective functional J with respect to the field strength (evaluated at a field strength of e t) and dk = d (t ) o search direction at the feth iteration. The time has been discretized into N time steps, such as that tj=jx )t, where j = 0,1,2, , N. Different CG methods correspond to different choices for the scalar (j. ... 

The ionic concentration gradients in the transition layer constitute the reason for development of the diffusion component E of electric field strength (the component arising from the difference in diffusion or mobihties between the individual ions). The diffusion potential between the solutions, 9 = - / can be calculated... 

When charges are separated, a potential difference develops across the interface. The electrical forces that operate between the metal and the solution constitute the electrical field across the electrode/electrolyte phase boundary. It will be seen that although the potential differences across the interface are not large ( 1 V), the dimensions of the interphase region are very small (—0.1) and thus the field strength (gradient of potential) is enormous—it is on the order of 10 V cm. The effect of this enormous field at the electrode/electrolyte interface is, in a sense, the essence of electrochemistry. 

Clearly the pH gradient, the electrical field strength, and a number of other parameters can be controlled in a calculable way to achieve desired resolution levels. The excellence of resolution between components having almost identical isoelectric points was illustrated in Figure 8.8. 

The electric field strength at any point is the spatial derivative or gradient of the electrostatic potential at that point. The electrostatic potential for various geometries and boundary conditions for regions with no charge is given by Laplace s equation... 

Table 1. Relationship between X and the physical solute properties using different FFF techniques [27,109] with R=gas constant, p=solvent density, ps=solute density, co2r=centrifugal acceleration, V0=volume of the fractionation channel, Vc=cross-flow rate, E=electrical field strength, dT/dx=temperature gradient, M=molecular mass, dH=hydrodynamic diameter, DT=thermal diffusion coefficient, pe=electrophoretic mobility, %M=molar magnetic susceptibility, Hm=intensity of magnetic field, AHm=gradient of the intensity of the magnetic field, Ap = total increment of the chemical potential across the channel...

Ordinary diffusion depends on the partial Gibbs free energy and the concentration gradient. The pressure diffusion is considerable only for a high-pressure gradient, such as centrifuge separation. The forced diffusion is mainly important in electrolytes and the local electric field strength. Each ionic substance may be under the influence of... 

The study of the electric field strength effect on the shape of the density gradient formed in the TLF cell indicated an important difference compared with the first approximation theoretical model. A series of experimental data and the theoretically calculated curves are shown in Figure 6. The difference can be caused by the interactions between the colloidal particles of the binary density forming carrier liquid. Moreover, the electric field strength across the cell or channel thickness was estimated from the electric potential measured between the electrodes, but the electrochemical processes at both electrodes can contribute to this difference. 

Figure 6. Theoretical (Y) and experimental (E) shapes of the steady-state density gradients formed due to the different electric field strengths in Percoll diluted with water in TLF cell. Initial average density of Percoll was 1.024 gJmL. Experimental points correspond to the positions of the focused zones of density marker beads.

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