Concentration chemical potential

It is interesting to frame these very tentative considerations in terms of rod diffusion, since this is the process by which the polymer-rich phase must be formed. However, care must be taken to isolate the effects of mutual diffusion of the collection of rods as a (phenomenological) response to a concentration (chemical potential) gradient and simple self diffusion of a single rod, which is the case treated by Doi and Edwards.(24)... 

Examples of the ambient can be the living atmosphere, a drop of blood, a cooled cryostatic chamber in which interacting or noninteracting gases are present, etc. Thus the ambient can be characterized by physical parameters such as temperature, pressure, density, and/or chemical parameters such as concentration, chemical potential, and activity. 

A similar technique is used to study the concentration - chemical potential relationships in nonstoichio-metric solids. In this case, -> solid materials are to be equilibrated with a gas phase, resulting in adsorption or desorption of a component the determination of compositional changes in the solid is based on the gas coulo-metric titration. The relaxation curves may be used to calculate the -> exchange currents and -> diffusion coefficients (see also -> Diffusion determination in solids). 

The three types of phase behaviour are illustrated in Fig. 6.7 in a representation showing colloid volume fraction adsorbing polymer) concentration in the system rather than the polymer concentration (chemical potential) in the reservoir. Using the relation ... 

At constant concentration (chemical potential), and hence pressure for each of the reservoirs we have the relation... 

Osmotic pressure measurements offer a very convenient method for estimating the molecular weight of macromolecules (in the range 10 000-1 000 000 g mol ) as described by Shaw (1992). Osmosis takes place when a solution and a solvent (or two solutions of different concentrations) are separated from each other by a semipermeable membrane, i.e. a membrane that is permeable to the solvent and not the solute. The tendency to equalize the concentrations (chemical potentials) on either side of the membrane results in a net diffusion of solvent across the membrane. The counter-pressure necessary to balance this osmotic flow is termed osmotic pressure (Figure 8.7). 

The concentration profile of the actively transported species has two limiting shapes a full wave for the maximum intensity of the net active transport (when concentrations are identical on both sides) or with an inflexion point for zero net flow but maximum difference between the substrate concentrations (chemical potentials) on both sides of the membrane (Figure 13). 

Analytic teclmiques often use a time-dependent generalization of Landau-Ginzburg ffee-energy fiinctionals. The different universal dynamic behaviours have been classified by Hohenberg and Halperin [94]. In the simple example of a binary fluid (model B) the concentration difference can be used as an order parameter m.. A gradient in the local chemical potential p(r) = 8F/ m(r) gives rise to a current j... 

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

The rate of storage of chemical potential (in other words, the power P carried by the chemical reaction) isypg, where j = d/j/dt = the net flux per unit volume (here, as elsewhere, lower case letters denote concentrations,... 

As noted above, all of the partial molar quantities are concentration dependent. It is convenient to define a thermodynamic concentration called the activity aj in terms of which the chemical potential is correctly given by the relationship... 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

Ice formation is both beneficial and detrimental. Benefits, which include the strengthening of food stmctures and the removal of free moisture, are often outweighed by deleterious effects that ice crystal formation may have on plant cell walls in fmits and vegetable products preserved by freezing. Ice crystal formation can result in partial dehydration of the tissue surrounding the ice crystal and the freeze concentration of potential reactants. Ice crystals mechanically dismpt cell stmctures and increase the concentration of cell electrolytes which can result in the chemical denaturation of proteins. Other quaHty losses can also occur (12). 

A reverse osmosis membrane acts as the semipermeable barrier to flow ia the RO process, aHowiag selective passage of a particular species, usually water, while partially or completely retaining other species, ie, solutes such as salts. Chemical potential gradients across the membrane provide the driving forces for solute and solvent transport across the membrane. The solute chemical potential gradient, —is usually expressed ia terms of concentration the water (solvent) chemical potential gradient, —Afi, is usually expressed ia terms of pressure difference across the membrane. 

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 ... 

For the solute flux, it is assumed that chemical potential difference owing to pressure is negligible. Thus the driving force is almost entirely a result of concentration differences. The solute flux, J), is defined as in equation 6 ... 

Expressions of supersaturation can then be formulated as follows (/) the difference between the chemical potential of the system and the chemical potential of at saturation, ji — ji where the chemical potential is a function of both temperature and concentration (2) the difference between the solute concentration and the concentration at equiUbrium, c — c (J) the difference between the system temperature at equiUbrium and the actual temperature,... 

Rate of Diffusion. Diffusion is the process by which molecules are transported from one part of a system to another as a result of random molecular motion. This eventually leads to an equalization of chemical potential and concentration throughout the system, and in the case of dyeing an equihbrium between dye in the fiber and dye in the dyebath. In dyeing there are three stages to diffusion diffusion of dye through the bulk solution of the dyebath to the fiber surface, diffusion through this surface, and diffusion of dye from the surface into the body of the fiber to allow for more dye to diffuse through the surface layer. These processes have been summarized elsewhere (9). 

Since the infinite dilution values D°g and Dba. re generally unequal, even a thermodynamically ideal solution hke Ya = Ys = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require a thermodynamic correction factor to retain the true driving force for molecular diffusion, or the gradient of the chemical potential rather than the composition gradient. That correction factor is ... 

This expression can be used to describe both pore and solid diffusion so long as the driving force is expressed in terms of the appropriate concentrations. Although the driving force should be more correctly expressed in terms of chemical potentials, Eq. (16-63) provides a qualitatively and quantitatively correct representation of adsorption systems so long as the diffusivity is allowed to be a function of the adsorbate concentration. The diffusivity will be constant only for a thermodynamically ideal system, which is only an adequate approximation for a limited number of adsorption systems. 

Mass transfer Irreversible and spontaneous transport of mass of a chemical component in a space with a non-homogeneous field of the chemical potential of the component. The driving force causing the transport can be the difference in concentration (in liquids) or partial pressures ( in gases) of the component. In biological systems. 

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