Solvent diffusion model

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. 

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

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. 

K Yoshimura, K Sekimoto. Coupling between diffusion and deformation of gels in binary solvents—A model study. J Chem Phys 101 4407-4417, 1994. 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

For a long time, the electric double layer was compared to a capacitor with two plates, one of which was the charged metal and the other, the ions in the solution. In the absence of specific adsorption, the two plates were viewed as separated only by a layer of solvent. This model was later modified by Stem, who took into account the existence of the diffuse layer. He combined both concepts, postulating that the double layer consists of a rigid part called the inner—or Helmholtz—layer, and a diffuse layer of ions extending from the outer Helmholtz plane into the bulk of the solution. Accordingly, the potential drop between the metal and the bulk consists of two parts ... 

Experimental data for the interligand electron transfer kinetics following photoexcitation of [Os(bpy)3] " " are in agreement with a reaction/diffusion model measurements were made in a range of solvents. The variable parameters in the model are interligand electronic coupling and solvent polarization barrier height. 

Peppas and Reinhart have also proposed a model to describe the transport of solutes through highly swollen nonporous polymer membranes [155], In highly swollen networks, one may assume that the diffusional jump length of a solute molecule in the membrane is approximately the same as that in pure solvent. Their model relates the diffusion coefficient in the membrane to solute size as well as to structural parameters such as the degree of swelling and the molecular weight between crosslinks. The final form of the equation by Peppas and Reinhart is... 

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. 

Figure 2.6 Chemical potential, pressure, and solvent activity profiles through an osmotic membrane following the solution-diffusion model. The pressure in the membrane is uniform and equal to the high-pressure value, so the chemical potential gradient within the membrane is expressed as a concentration gradient...

Dialysis is the simplest application of the solution-diffusion model because only concentration gradients are involved. In dialysis, a membrane separates two solutions of different compositions. The concentration gradient across the membrane causes a flow of solute and solvent from one side of the membrane to the other. 

Similar to the approach for solvents, both diffusive and convective transport of solutes can be modeled separately. For dense membranes, a solution-diffusion model can be used [14], where the flux / of a solute is calculated as ... 

Good quality RO membranes can reject >95-99% of the NaCl from aqueous feed streams (Baker, Cussler, Eykamp et al., 1991 Scott, 1981). The morphologies of these membranes are typically asymmetric with a thin highly selective polymer layer on top of an open support structure. Two rather different approaches have been used to describe the transport processes in such membranes the solution-diffusion (Merten, 1966) and surface force capillary flow model (Matsuura and Sourirajan, 1981). In the solution-diffusion model, the solute moves within the essentially homogeneously solvent swollen polymer matrix. The solute has a mobility that is dependent upon the free volume of the solvent, solute, and polymer. In the capillary pore diffusion model, it is assumed that separation occurs due to surface and fluid transport phenomena within an actual nanopore. The pore surface is seen as promoting preferential sorption of the solvent and repulsion of the solutes. The model envisions a more or less pure solvent layer on the pore walls that is forced through the membrane capillary pores under pressure. 

New models for the prediction of molecular diffusion coefficients are described, and compared to previously established ones. These are based on solute molecular size, solvent viscosity solvent molecular size, and temperature. The data set of diffusion coefficients used was primarily the one developed by Wilke and Chang and upon which their commonly used diffusion model is based (A.I.Ch.E. Journal, 1 (1955), 264). 

In the solution-diffusion model, the transport of solvent and solute are independent of each other, as seen in Equations 4.1 and 4.2. The flux of solvent through the membrane is linearly proportional to the effective pressure difference across the membrane (Equation 4.1) ... 

Figure 19 Parent bleach kinetics (open circles) of Re2(CO)io in (a) hexanes, (b) CC14, (c) CHCI3, and (d) CH2CI2. Fits to a diffusion model to account for geminate recombination are shown as solid lines. Except for the macroscopic viscosity, identical molecular parameters (see Fig. 20) are used for all the solvents studied.

Diffusion models of geminate pair combination connect the time-dependent pair survival probability, P t), with the macroscopic properties of the host solvent. Radicals are treated as spherical particles immersed in a uniformly viscous medium. The pair is assumed to undergo random Brownian movements that ultimately lead to either recombination or escape. The expression of P i) depends on the degree of sophistication of the theory chosen for analyzing the process. In the simplest theory,... 

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