Electric field, separations based theory

John Newman/ Ph.D./ Profe.s.sor of Chemical Engineering, University of California, Berkeley Principal Inve.stigatoi Inorganic Materials Re.search Division, Lawrence Berkeley Laboratory. (Separation Proce.s.se.s Based Primarily on Action in an Electric Field Theory of Electrical Separation.s)... 

The present chapter is devoted mainly to one of these new theories, in particular to its possible applications to photon physics and optics. This theory is based on the hypothesis of a nonzero divergence of the electric field in vacuo, in combination with the condition of Lorentz invariance. The nonzero electric field divergence, with an associated space-charge current density, introduces an extra degree of freedom that leads to new possible states of the electromagnetic field. This concept originated from some ideas by the author in the late 1960s, the first of which was published in a series of separate papers [10,12], and later in more complete forms and in reviews [13-20]. 

The Mataga-Kakitani (M-K) theory is based on the rather general observation that e.t. processes which show the M.I.R. are mostly charge recombinations and charge shifts, whereas the photo-induced charge separations which start from neutral reactants follow Rehm-Weller behaviour. It is then suggested that the difference is due to the electric field which acts on the solvent in the field of ions or ion pairs, partial dielectric saturation of polar solvents would be reached, and this would restrict solvent motion. No such dielectric saturation effect would exist in the solvent shell of neutral reactants, so that solvent motion remains unhindered. 

The theory of PCM calculation of the effective polarizabilities is based on a time-dependent response theory that describes the interaction between the molecular solutes and the Maxwell electric field. We will review the method in three separate sections, the... 

In the absence of a field, previous theoretical predictions based on a long-range calculation predicted that the elastic quadrupolar repulsion force should follow the power law Prepukion° l [4> 7]. Under the present experimental conditions, i.e., in the presence of an electric field, we observe a steeper repulsion as shown by the log-log plot in the inset of Fig. 13. Two reasons might explain the discrepancy between the experimental measurements and the theory. First, since the electric field is likely to distort the ordering of the liquid crystal molecules in the vicinity of the drops, the measured quadrupolar repulsion may intrinsically depend on Eq. Second, short-range effects, not considered in the theoretical approach, may come into play in the experiments. Indeed, the maximum measured separation between two drops is of the order D. 

This chapter describes the theory, methodology, and application of a microfabrication process that uses phase-changing sacrificial layers (PCSLs) as intermediates to protect microchannel features during bonding or hydrogel polymerization. We focus on key process details associated with the fabrication of microchips, and the application of PCSL-formed microfluidic devices in CE separations and other electric field-based analysis methods. Finally, we provide a brief overview of potential future trends and applications of PCSL fabrication methods in microfluidics. 

While the separation of DNA based on hooking on micro- or nanoposts has presented an alternative method for gel electrophoresis, it still suffers from the fact that, when an electric field is applied to DNA molecules, different sizes of DNA molecules mobilize at the same speed. To circumvent this problem, an approach was developed by Duke, Austin and Ertas which take advantage of the fact that, while a molecules move, they diffuse at the same time—and at a diffusion rate that is size dependent. In theory, they have shown the possibility of using a two-dimensional obstacle course to sort the fast moving molecules from the slower ones. The elegance of this is that a regular lattice of asymmetric obstacle course, rectifies the lateral Brownian motion of the molecules, so molecules of different size follow different trajectories while they are passing into the device. 

From a physical point of view this relativistic model is also based on the perturbation approach, and at the second order, similarly as in the case of the standard J-O Theory, the crystal field potential plays the role of a mechanism that forces the electric dipole/ t—>f transitions. The only difference is that now the transition amplitude is in effectively relativistic form, as determined by the double tensor operator, but still of one particle nature. Furthermore, the same partitioning of space as in non-relativistic approach is valid here. The same requirements about the parity of the excited configurations are expected to be satisfied. As a final step of derivation of the effective operators, the coupling of double inter-shell tensor operators has to be performed. This procedure is based on the same rules of Racah algebra as presented in the case of the standard J-O theory. However, the coupling of the inter-shell double tensor operators consists of two steps, for spin and orbital parts separately. Thus, the rules presented in equations (10.15) and (10.16) have to be applied twice for orbital and spin momenta couplings, resulting in two 3j— and two 6j— coefficients. 

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