Phase factors theoretical background

In any of the reciprocal space methods, which are based exclusively on the use of the observed structure factors, the powder diffraction pattern must be deconvoluted and the integrated intensities of all, or as many as possible, individual Bragg reflections determined with a maximum precision. Only then, Patterson or direct phase angle determination techniques may be employed to create a partial or compete structural model. Theoretical background supporting these two methods was reviewed in section 2.14. 

Abstract The mass transferred from one phase to the adjacent phase must diffuse through the interface and subsequently may produce interfacial effect. In this chapter, two kinds of important interfacial effects are discussed Marangoni effect and Rayleigh effect. The theoretical background and method of computation are described including origin of interfacial convection, mathematical expression, observation, theoretical analysis (interface instability, on-set condition), experimental and theoretical study on enhancement factor of mass transfer. The details of interfacial effects are simulated by using CMT differential equations. 

Shibukawa et al. [109] published a new liquid chromatographic method for the determination of acid dissociation constants. On the basis of theoretical equations regarding the effect of background mobile phase ions on the retention of ionic analytes on a non-ionic polymer packing, they could determine simultaneously the dissociation constants (p/fa) and the charges of analyte molecules. They used chloride and perchlorate ions in the mobile phase as they exhibit large differences in the retention on the hydrophilic polymer packings used, so that the effect of the mobile phase electrolyte on the retention factor of an ionic analyte could be clearly evaluated. 

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