Modeling solvent-diffusion’ model

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

KA Mazich, G Rossi, CA Smith. Kinetics of solvent diffusion and swelling in a model elastomeric system. Macromolecules 25 6929-6933, 1992. 

In polyisobutylene in the melt and in solution (CC14, CS2), McCall, Douglass, and Anderson 17) found that the activation energies for polymer diffusion increased with polymer concentration from the value at infinite dilution (approaching the pure solvent value) to the value in the melt. Solvent diffusion, and solvent effect on polymer diffusion, were also measured. The Stokes-Einstein model applied to this data yielded molecular dimensions too small by a factor of two or three. 

Some of the evidence for a Tg dependence relies on successful application of the WLF model to reaction rate data, using Tg as the reference temperature. There are several reasons for discrepancies among the theoretical WLF dependency of reactions that have been outlined by Le Meste et al. (1995) for frozen food systems. Of particular relevance, is the assertion that WLF kinetics predicts an overly strong temperature-dependence for the diffusion of reactants. This is because diffusion is not only affected by temperature, but also by solvent, diffusant size, and the fact that one or more reactants may not be diffusion-limited while others are. 

The Halpern procedure becomes less accurate when the fractional cage efficiency is not so close to one. A system with the activation parameters of Figure 6, except for a reduction of AH (i, models a more fluid solvent. Diffusive escape becomes faster, relative to cage combination, and this leads to reduced values of F (T). A reduction of the value of AH to 2.6 kcal/mole gives Fq(T) as 0.2 at the mean of the temperature range that would apply to a AH app value of 30.6 kcal/mole. The Halpern procedure leads to an estimated 28 kcal/mole for the BDE in this case, somewhat less than the actual 30 kcal/mole value. The value of Fq(T), the... 

Wrinkling from solvent diffusion was also used for other systems [29]. For instance, combining UV exposure and solvent diffusion, a zoo of morphology flowers, concentrated rings, and labyrinthine patterns can be obtained (Fig. 8.13). It should be noted however that there is no theoretical model to explain the transition between all these rather exotic patterns. 

Vrentas and Vrentas papers provide relevant modelling studies. These studies were initiated to explain the earlier observations by Crank which indicated that maintaining a slightly increased concentration of solvent in the air flowing over a drying material may actually increase the evaporation rate. Modelling of the process shows that although the diffusion of solvent cannot be inereased by an increased concentration of solvent on the material s surface, an increased coneentration of solvent in the air may be beneficial for the evaporation process because it prevents the formation of skin which slows down solvent diffusion. 

Whereas the value of n equals 0.5, the mechanism of diffusion described by Case I of Fickian model, when n values range between 0.5 and 1 that exhibits anomalous transport model and when n value equals 1, Case II of non-Fickian model is used to determine. Fickian model describing the rate of diffusion of penetrant molecule is much less than the relaxation rate of polymer chains while Case II of non-Fickian diffusion representing rate of diffusion is rapid than relaxation process. For the anomalous transport model, both solvent diffusion rate and polymer relaxation rate are comparable. Figure 27.2 shows various types of non-Fickian model anomalous transport and Case II of non-Fickian are included in this group. ... 

In dense polymers, the self-diffusion of small plasticising solvent molecules has been measured PGSE methods [105]. For polymers above the glass-transition temperature, it is common to model the solvent diffusion using the free volume theory as modified for polymer systems by Fujita [122] and by Vrentas and Duda [123]. For solvent diffusion in dense polymers below Tg, an alternative model has been given by Frisch and Stern [124]. 

For a given electrolyte composition and solvent reduction product, c, Cp, and A are all determined and thus are not adjustable parameters. Only the solvent diffusivity in the SEI may serve as an adjustable empirical parameter in this model. Finally, the model s analytical solution yields... 

Ploehn et al. in Chapter 6 use both macroscopic continuum and statistical mechanics-based models to simulate the SEI growth and to predict capacity loss in LIBs. Specifically the former model deals with the effects of electronic conductivity and solvent diffusion on SEI growth, while the latter is a lattice-gas model, which describes the thermodynamics of lithium-ion intercalation in carbons under the presence of a SEI. 

Ploehn, H.J., Ramadass, P., and White, R.E. (2004) Solvent diffusion model for aging of lithium-ion battery cells. /. Electrochem. Soc., 151 (3), A456-A462. 

Penetrant (solvent) diffusion In swellable polymers has been extensively studied and many models have been proposed (see for instance references 31 and 34). Experimental data concerning water penetration in hydrophilic polymers have been mainly concerned with crosslinked polymers with limited swelling. Investigations on linear macromolecules are complicated by concomitant dissolution of individual solvated chains that leads to some erosion of the hydrated polymer mass. 

H. J. Ploehn, P. Ramadass, and R. E. White,/. Electrochem. Soc., 151, A456 (2004). Solvent Diffusion Model for Aging of Lithium-Ion Battery Cells. 

In this paper, a 1-D diffusion model is used to calculate diffusivity. Extruded films containing 5 and 10 wt% CHA were used to obtain the film weight data as a function of time. Methanol was used to remove additive from the surface through two means short time surface washing and immersion with continuous stirring. The effect of solvent diffusion into the films was investigated by TGA. 

The simulation of molecules in solution can be broken down into two categories. The first is a list of elfects that are not defined for a single molecule, such as diffusion rates. These types of effects require modeling the bulk liquid as discussed in Chapters 7 and 39. The other type of effect is a solvation effect, which is a change in the molecular behavior due to the presence of a solvent. This chapter addresses this second type of effect. 

Equation 7 shows that as AP — oo, P — 1. The principal advantage of the solution—diffusion (SD) model is that only two parameters are needed to characterize the membrane system. As a result, this model has been widely appHed to both inorganic salt and organic solute systems. However, it has been indicated (26) that the SD model is limited to membranes having low water content. Also, for many RO membranes and solutes, particularly organics, the SD model does not adequately describe water or solute flux (27). Possible causes for these deviations include imperfections in the membrane barrier layer, pore flow (convection effects), and solute—solvent—membrane interactions. 

Reviews of concentration polarization have been reported (14,38,39). Because solute wall concentration may not be experimentally measurable, models relating solute and solvent fluxes to hydrodynamic parameters are needed for system design. The Navier-Stokes diffusion—convection equation has been numerically solved to calculate wall concentration, and thus the water flux and permeate quaUty (40). 

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