Extraction self-diffusion coefficients

For similar solvent polymeric membranes (78 wt.% dicresyl butyl phosphate in polyvinyl chloride) self-diffusion coefficients of the order of 10-7 cm2s 1 have been reported.12 These diffusion coefficients, as well as measurements of rotational mobilities,14 indicate that the solvent polymeric membranes studied here are indeed liquid membranes. This liquid phase is so viscous, however, that convective flow is virtually absent. This contrasts with pure solvent membranes where an organic solvent is interposed between two aqueous solutions either by sandwiching it between two cellophane sheets or by fixing it in a hole of a Teflon sheet separating the aqueous solutions.15 The extremely high convective flow is one of the reasons why the term membrane for extraction systems... 

To dearly distinguish between these two modes of solvent penetration of the gel, we immersed poly(acrylamide-co-sodium methacrylate) gels swollen with water and equilibrated with either pH 4.0 HQ or pH 9.2 NaOH solution into limited volumes of solutions of 10 wt % deuterium oxide (DzO) in water at the same pHs. By measuring the decline in density of the solution with time using a densitometer, we extracted the diffusion coefficient of D20 into the gel using a least squares curve fit of the exact solution for this diffusion problem to the data [121,149]. The curve fit in each case was excellent, and the diffusion coefficients obtained were 2.3 x 10 5cm2/s into the ionized pH 9.2 gel and 2.4 x 10 5 cm2/s into the nonionized pH 4.0 gel. These compare favorably with the self diffusion coefficient of D20, which is 2.6 x 10 5 cm2/s, since the presence of the polymer can be expected to reduce the diffusion coefficient about 10% in these cases [150], In short, these experiments show that individual solvent molecules can rapidly redistribute between the solution and the gel by a Fickian diffusion process with diffusion coefficients slightly less than in the free solution. 

The models, which have been developed in the literature, concern essentially incoherent scattering, i.e., self-diffusion. Much less work has been performed on jump diffusion of coherent scatterers [5,11]. If one considers only isotropic systems, the scattering fimction will always be a Lorentzian function, but the width (HWHM) of the energy spectra will differ from the simple DQ behavior. For each spectrum measured at a given Q value, one can extract a diffusion coefficient D. One has to extrapolate D(Q) to small Q values to obtain the Fickian diffusivity. 

E. J. M. Hensen, A. M. de Jong, and R. A. van Santen have written Chapter 7, which introduces the tracer exchange positron emission profiling (TEX-PEP) as an attractive technique for in-situ investigations, for example, in a stainless steel reactor, of the adsorption and diffusive properties of hydrocarbons in zeolites under chemical steady-state conditions. Self-diffusion coefficients of hydrocarbons, labeled by proton-emitting C at finite loadings and even in the presence of another imlabeled alkane, may be extracted. The method is illustrated by adsorption and diffusion measurements of linear (n-hexane) and branched (2-methylpentane) alkanes in Fl-ZSM-5 and silicalite-1. 

As it can be seen from Fig. 3, CO2 as well as other supercritical solvents exhibit rather small viscosities [26] and high self-diffusion coefficients [27], which resemble more those of gases than those of liquids. Similar properties are also found in dilute solutions of low-volatile samples in supercritical solvents of this kind. In addition, the supercritical solvent is also considerably soluble in the coexisting liquid phase making viscosities lower, and diffusion coefficients higher. In this way, mass transfer and equilibration rate are much improved for SEE in comparison with liquid solvent extraction (see Sect. 4). 

The chain self-diffusion coefficient can be extracted only when gcM(n) becomes... 

One point to emphasize at this stage concerns the measurement of the self-diffusion coefficients, particularly in the mixed conducting perovskite materials. An extended review and description of diffusion measurement and techniques have been published by Philibert [1]. There are many electrochemical methods whereby various diffusion coefficients can be extracted from ceramic samples. In the main, data obtained using these methods must be treated with some circumspection because there are many sources of possible error, particularly with porous samples when gas diffusion down pores can... 

From the applications point of view, mutual diffusion is far more important than self-diffusion, because the transport of matter plays a major role in many physical and chemical processes, such as crystallization, distillation or extraction. Knowledge of mutual diffusion coefficients is hence valuable for modeling and scaling-up of these processes. 

---