Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

Separation of acidic and basic compounds in capillary electrochromatography with polymethacrylate-based monolithic columns

Methacrylate-based monolithic columns with electroosmotic flow (EOF) or very weak EOF are prepared by in situ copolymerization in the presence of a porogen in fused-silica capillaries pretreated with a bifunctional reagent. Satisfactory separations of acidic and basic compounds on the column with EOF at either low or high pH are achieved, respectively. With sulfonic groups as dissociation functionalities, sufficient EOF mobility still remains as high as 1.74 x 10(-4) cm(2) s(-1) V-1 at low pH. Under this condition, seven acidic compounds are readily separated within 5.7 min. Moreover, at high pH, the peak shape of basic compounds is satisfactory without addition of any masking amines into running mobile phase since the secondary interaction between the basic compounds and the monolithic stationary phase are minimized at high pH. Reversed-phase mechanism for both acidic and basic compounds is observed under investigated separation conditions. In addition, possibilities of acidic and basic compound separations on a monolithic column with extremely low EOF are discussed. (C) 2004 Elsevier B.V. All rights reserved.

Protocol of capillary isoelectric focusing to separate extremely acidic and basic proteins

A new set-up was constructed for capillary isoelectric focusing (CIEF) involving a sampling capillary as a bypass fixed to the separation capillary. Sample solutions were subjected to a previously established pH gradient from the sample capillary. Besides performing conventional CIEF, the separation of ampholytic compounds with isoelectric points (p/s) beyond the pH gradient was carried out on this system. This method was termed as pH gradient driven electrophoresis (PGDE) and the basic mathematical expressions were derived to express the dynamic fundamentals. Proteins such as lysozyme, cytochrome C, and pepsin with p/s higher than 10 or below 3 were separated in a pH gradient provided by Pharmalyte (pH 3-10). Finally, this protocol convincingly exhibited its potential in the separation of a solution of chicken egg white.