Potential gradient of chemical

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... 

The gradient of chemical potential along the surface may also drive surface diffusion. The gradient of V2h is therefore a driving force for a flux Ns of material parallel to the surface. A differential material balance gives,... 

Even this more elaborated description of ion movements in response to gradients of chemical potential may turn out to be insufficient, in particular when uphill diffusion is active ... 

In reverse osmosis both solvent and solute diffuse because of gradients in their chemical potentials. For the solvent there is no gradient of chemical potential at an osmotic pressure of x at applied pressures p greater than 7r, there is such a gradient that is proportional to the difference p — ir. To a first approximation, the gradient of the solute chemical potential is independent of p and depends on the difference between concentrations on opposite sides of the membrane. This leads to the result that the fraction of solute retained varies as [1 + const./(p — 7r)] 1. Verify that the following data for a reverse osmosis experiment with 0.1 M NaCl and a cellulose acetate membrane follow this relationship ... 

The driving force for transport within the zeolite crystals appears to be the gradient of chemical potential rather than the concentration gradient, and, for systems with a nonlinear equilibrium isotherm, the diffusivity is therefore concentration dependent (6-8). 

In most sensing situations, the analyte molecules are transported to and from the sensor by diffusion. This is particularly true for sensors in which the analyte is chemically transformed, such as sensors that rely on catalysis or in amperometric sensors. Diffusion is another activated (see (B.5)) process in which time and temperature have to be considered. It is driven by the gradient of chemical potential (A. 19). Two kinds of diffusion are most relevant. These are the Fickian diffusion, which depends on molecular properties of both the diffusing medium and of the diffusing species, and the Knudsen diffusion which depends on the size of the vessel. 

In the realm of the previously stated principles, the real driving force behind mass transport is the gradient of chemical potential in this sense, in the absence of an external Newtonian force like that exerted in a charged species by an electric field, it is expressed as... 

The diffusion flux is proportional to the gradient of chemical potential [6], where the chemical potential of species i in a binary alloy is given by [7]... 

The concentration-dependent part of the gradient of chemical potential is... 

Qualitatively speaking, the macroscopic description of the transport process of diffusion is simple. The gradient of chemical potential resulting from a nonuniform concentration is equivalent to a driving force for diffusion and produces a diffusion... 

If no forces are pushing particles in the direction of the flow, then what about the driving force for diffusion, i.e., the gradient of chemical potential (Section 4.2.1) The latter is only formally equivalent to a force in a macroscopic treatment it is a sort of pseudoforce like a centrifugal force. The chemical-potential gradient is not a true force that acts on the individual diffusing particles and from this point of view is quite unlike, for example, the Coulombic force, which acts on individual charges. 

How can this be Surely the laws governing physical and chemical phenomena must be the same, and indeed they are. The answer is that in mechanics, as well as in chemistry, one can consider the gradient of chemical potential to be the real driving force. The chemical potential, being the free energy per mole for a pure substance, differs from the energy by an entropy term. 

Generalized Formalism A generalized membrane transport model, in the form of the black box models discussed earlier, can be considered in order to compare alternative mechanisms of water backflow in gradients of chemical potential, activity or concentration of water. Each of these gradients can be expressed by a gradient in w. The equation of net water flow is, thus,... 

Diffusion is the macroscopic result of the sum of all molecular motions involved in the sample studied. Molecular motions are described by the general equation of dynamics. However, because of the enormous difference in the orders of magnitude of the masses, sizes, and forces that characterize molecules and macroscopic solids, it can be shown [1] that, when a force field (e.g., an electric field to an ionic solution) is applied to a chemical system, the acceleration of the molecules or ions is nearly instantaneous, molecules drift at a constant velocity, and, in the absence of an external field and of internal forces acting on the feed components, which is the case in chromatography, the diffusional flux, /, of a chemical species i in a gradient of chemical potential is given by... 

When uphill diffusion can take place (because the directions of the gradients of chemical potential and of concentrations are opposed), the Pick approach fails, even at the qualitative level, to describe the mass transfer phenomena observed experimentally. Several known examples underly the shortcoming of the Pick s formulation [38]. 

There are obvious parallels between eqn. (10.5) and eqn. (10.2) in fact eqn. (10.5) suggests that continuum mechanics is just one more set of applications of the idea that materials tend to move down gradients of chemical potential. But there is also a conspicuous difference ideas in group A embody the idea that, at any point in space, a material component just has a chemical potential—a single value by contrast, group B embodies the idea that, under nonhydrostatic stress, it is a plane or a direction i that has a chemical potential associated with it, and that the potential associated with one plane can be different from the potential associated with another plane at the same point in space. The objective of this book is to treat situations where deformation and interdiffusion are occurring simultaneously that is to say, we want to combine eqns. (10.2) and (10.5), and hence the question, Is chemical potential single-valued or multi-valued must be faced. 

The phenomenological relations may be inverted to express the gradients of chemical potential as linear functions of the velocities, and therefore... 

Composition Dependence of Dab- The diffusion coefficient of a binary solution is a function of composition, ff the true driving Force for ordinary diffusion is the isothermal, isoharic gradient of chemical potential, then the binary diffusivity can be written in the form... 

Diffusion. Movement of a species under the influence of a gradient of chemical potential (i.e., a concentration gradient). 

The driving force for particle movement through the pore, the gradient of chemical potential, is balanced by the drag force acting on the particle ... 

Bi-directional flux of free cholesterol between cells and lipoproteins occurs, and rate constants characteristic of influx and efflux can be measured [17]. The direction of any net transfer of free cholesterol is determined by the relative free cholesterol/phospholipid molar ratios of the donor and acceptor particles. Cholesterol diffuses down its gradient of chemical potential generally partitioning to the phospholipid-rich particle. Such a surface transfer process can lead to delivery of cholesterol to cells. This mechanism operates independently of any lipoprotein internalization by the receptor-mediated endocytosis. The influence of enzymes such as lecithin-cholesterol acyltransferase and hepatic lipase on the direction of net transfer of free cholesterol between lipoproteins and cells can be understood in terms of their effects of the pool sizes and the rate constants for influx and efflux. 

---