Diffusion in Solids

When extracting solutes from solid samples, one must not only overcome the solute-sample attraction, but the solute must diffuse with the solvent back out of the porous solid sample. This diffusion through the pores of a solid sample is influenced by the geometry or tortuosity of the pore structure (e.g. the diffusion path length). Diffusion in solids, assuming weak solute-sample sorption (i.e., a linear isotherm), is expressed by Deff = ($D)/y(KD + 1), where Deff is the effective (or apparent) diffusivity), $ is the fraction of space available to the extracting solvent, Kd is the distribution coefficient (expressed as the ratio of solute concentration in the solid volume to solute concentration in the solvent volume), D is the (true) diffusivity in the bulk solvent, and y is a tortuosity factor. With ionic solutes, if the pore wall carries an electric charge, diffusion is also affected by the electrical potential gradient.

This knowledge of diffusion through porous solids can provide an understanding of practical extractions. Figure 5 represents an overview of the processes occurring when extracting solutes from solids. This understanding is described in the 'hot-ball model' advocated by Professors Keith Bartle and Tony Clifford at Leeds University. For example, with small quantities of extractable compounds that diffuse out of the homogeneous spherical particle into the extraction solvent, the extracted compounds are infinitely dilute. The extraction rate is obtained through the expression for the ratio of the mass, m, of

Figure 5 Schematic diagram of major physical/chemical processes that may occur during the extraction of solutes from a solid sample particle.

extractable material remaining after time t to the initial mass of extractable material, m0, where m/m0 = (6/re2)£(1/«2)exp( — n2n2Dt/r2), where n is an integer, D is the diffusion coefficient of the material in the sample matrix, and r is the radius of the spherical sample. This equation reduces to a sum of exponential decays, and a plot of ln (m/m0) versus time eventually becomes linear. The physical explanation for the model is that, during the initial phases of an extraction, there is a concentration gradient at the surface of the sphere and diffusion from the sphere is rapid. This corresponds to the 'equilibrium' region (see Figure 1). When the concentration across the entire sphere becomes even and the rate of diffusion (and, hence, extraction) is a simple exponential decay, the 'diffusion' region of the extraction process (shown in Figure 1) is reached. Extrapolation of this linear portion of the plot of ln (m/m0) versus time can be used to determine the time (or amount of solvent) necessary to achieve quantitative extraction recoveries.

Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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