Diffusion coefficient solvent-fixed

When applied to a volume-fixed frame of reference (i.e., laboratory coordinates) with ordinary concentration units (e.g., g/cm3), these equations are applicable only to nonswelling systems. The diffusion coefficient obtained for the swelling system is the polymer-solvent mutual diffusion coefficient in a volume-fixed reference frame, Dv. Also, the single diffusion coefficient extracted from this analysis will be some average of concentration-dependent values if the diffusion coefficient is not constant. 

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... 

The third transport coefficient that we address is the diffusion coefficient. The simplest case is diffusion of a dilute species (solute) into another fluid (solvent) that is present in great excess. Consider the experiment shown schematically in Fig 12.3. In the bottom portion is a large well-mixed reservoir containing a mixture of solute held at fixed concentration c = C in a solvent. The top portion is a similar well-mixed reservoir of the mixture with solute concentration held fixed at c = C + AC. A permeable thin film separates each reservoir from the center fluid mixture. As such, in the center fluid region the concentrations of solute at the upper and lower edges equal the concentrations just across the permeable films that is, they equal the reservoir concentrations. 

The diffusion coefficient in Eq. 5.50 actually is a composite of diffusion tensor elements defined in a frame of reference fixed in the solvent phase (i.e., water). For a discussion of the ways in which the diffusion coefficient can be defined, see J. B. Brady, Reference frames and diffusion coefficients, Am. J. Sci. 275 954 (1975). 

In the aq/polymer/org situation, the organic solvent typically penetrates the polymer causing it to swell considerably, and the situation is very similar to that of MMLLE. With a fixed composition of the membrane, the possibilities for chemical tuning (such as application of carriers) of the separation process are greatly reduced compared to SLM extraction or MMLLE. Also, as diffusion coefficients in polymers are lower than in liquids, the mass transfer is slower, leading to slower extractions. On the other hand, as the membrane is virtually insoluble, any combination of aqueous and organic liquids can be used, and the entire system becomes very stable. 

SOLVENT MOBILITIES. One check on the physical significance and the reliability of the data representing the concentration dependence of the diffusion coefficient is to convert these results to solvent mobilities. The values should increase rapidly with increasing concentration and extrapolate to the self-diffusion coefficient for toluene. The procedure for carrying out the calculations was outlined in previous publication (11) and is repeated here in a brief form for convenient reference. The diffusion coefficient obtained directly in the vapor sorption experiment is a polymer, mass-fixed, mean diffusion coefficient, D, in the sorption interval. Duda et. al. (12) have shown that, if the concentration interval is small, the true diffusion coefficient, D, is simply related to the mean diffusion coefficient at a prescribed intermediate concentration in the interval ... 

The quantity directly associated with the translation of the polymer component relative to the solvent is not Dm, which is the volume-fixed diffusion coefficient, but the solvent-fixed diffusion coefficient D, which is defined by [19]... 

The 1/(1 - CO a) term is commonly referred to as the frame of reference term. For many cases of importance in polymeric systems such as in gas permeation, coa is relatively small, and the 1/(1 - >a) factor can safely be neglected so that the flux relative to fixed coordinates is equal to the flux relative to moving coordinates. Even for intermediate concentrations (0.1 < coa < 0.5), this factor may often be of second-order importance compared to difficulties in accurately determining the mutual diffusion coefficient due to strong concentration dependencies. However, not accounting for the factor 1/(1 — coa) can lead to very significant errors in flux calculations in highly swollen systems (eg, 90-95% solvent), even if the mutual diffusion coefficient is accurately determined (6). 

As an example of the different results which are obtainable by the two procedures, we shall consider data on urea-denatured horse serum albumin. These data were obtained from parallel diffusion and viscosity measurements in solvents containing various amounts of urea (Neurath and Saum, 1939). The intrinsic viscosity increased and the diffusion coefficient decreased with increasing urea concentration. The value of w (and, therefore, 7,) was arbitrarily fixed. This then permitted a calculation of p to be made from a single hydrodynamic measurement since the value of 7 was assumed known at each concentration of urea. Thus, p was computed from V, determined from an equation equivalent to Eq. (1-3), using the viscosity data. An independent value of p was computed from 1/f, determined from Eqs. (I-IO) and (I-ll), using the diffusion data. The values of the dimensions computed from the viscosity and from the diffusion data are shown in Table IV. 

Figure 8 shows the results on the diffusion coefficient of Fc in a water/acetone mixed solution obtained from the cyclic voltammogram using a microelectrode without the fixed gel and Eq. (3). This diffusion coefficient corresponds to the diffusion coefficient Dq of Fc in the external solution in Fig. 1. As the viscosity of acetone is less than that of water, Dq is larger in acetone. However, the Dq value does not change linearly with respect to the solvent composition and it shows a minimum at an acetone...

We consider the following infinitely dilute solution systems. For the solvent, we consider the same diatomic liquid as in Sec. 5.3 The number density is 0.012 molecules and the temperature is 250 K unless specified otherwise. To investigate the solute-charge effect on the friction coefficient, we consider a cationic solute (abbreviated as CU, which comes from Cationic solUte ) and a neutral solute (NU). We also deal with solutes of various sizes to see the solute-size dependence of the friction coefficients. These solutes are denoted as CUf (and NUf) where i varies from 1 to 10. a in LJ parameters for CUf (and NUf) is ai/2 = i A, while e is kept fixed to e = 0.44 kcal/mol for all the solutes. Note that, since here we are concerned only with the diffusive motion of a solute, it is not required to specify its mass. 

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