Chemical potential force

Additional forces would be added to the chemical potential force if, for example, the particle possessed a magnetic moment and a magnetic field were present. As will be seen, many possibilities for total forces exist depending upon the types of components and fields present. 

The above representation of external forces combined with the chemical potential force for molecules or ions is quite useful for those external force fields representable by the negative of the gradient of their scalar potentials. We indicate in Table 3.1.1 the value of for 1 gmol of the ith species for a few cases. For magnetic and nonuniform... 

Here p is the chemical potential just as the pressure is a mechanical potential and the temperature Jis a thennal potential. A difference in chemical potential Ap is a driving force that results in the transfer of molecules tlnough a penneable wall, just as a pressure difference Ap results in a change in position of a movable wall and a temperaPire difference AT produces a transfer of energy in the fonn of heat across a diathennic wall. Similarly equilibrium between two systems separated by a penneable wall must require equality of tire chemical potential on the two sides. For a multicomponent system, the obvious extension of equation (A2.1.22) can be written... 

The McMillan-Mayer theory allows us to develop a fomialism similar to that of a dilute interacting fluid for solute dispersed in the solvent provided that a sensible description of W can be given. At the Ihnit of dilution, when intersolute interactions can be neglected, we know that the chemical potential of a can be written as = W (a s) + IcT In where W(a s) is the potential of mean force for the interaction of a solute... 

Figure 3.10 is a plot of potential against distance from the wall for a liquid in a capillary of sufficient width for its middle A to be outside the range of forces from the wall. Since the capillary condensate is in equilibrium with the vapour, its chemical potential (=p represented by the horizontal line GF, will be lower than that of the free liquid the difference in chemical potential of the condensate at A, represented by the vertical distance AF, is brought about entirely by the pressure drop, Ap = 2y/r , across the meniscus (cf. Equation (3.6)) but at some point B. say, nearer the wall, the chemical potential receives a contribution represented by the line BC, from the adsorption potential. Consequently, the reduction Ap in pressure across the meniscus must be less at B than at A, so that again... 

Fig. 3.10 Contributions to the lowering of chemical potential of the condensed liquid in a capillary, arising from adsorption forces (c) and meniscus curvature (Ap). The chemical potential of the free liquid is , and that of the capillary condensed liquid is (= ) z is the distance from the capillary wall. (After Everett. )...

Before pursuing the diffusion process any further, let us examine the diffusion coefficient itself in greater detail. Specifically, we seek a relationship between D and the friction factor of the solute. In general, an increment of energy is associated with a force and an increment of distance. In the present context the driving force behind diffusion (subscript diff) is associated with an increment in the chemical potential of the solute and an increment in distance dx ... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

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... 

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 ... 

The primary driviag force for material transport comes from the chemical potential difference that exists between surfaces of dissimilar curvature within the system. The greater the curvature, ie, the finer the particle size, the greater the driving force for material transport and sintering. 

Ion-Dipole Forces. Ion-dipole forces bring about solubihty resulting from the interaction of the dye ion with polar water molecules. The ions, in both dye and fiber, are therefore surrounded by bound water molecules that behave differently from the rest of the water molecules. If when the dye and fiber come together some of these bound water molecules are released, there is an increase in the entropy of the system. This lowers the free energy and chemical potential and thus acts as a driving force to dye absorption. 

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. 

Driving Force Gas moves across a membrane in response to a difference in chemical potential. Partial pressure is sufficiently proportional to be used as the variable for design calculations for most gases of interest, but fugacity must be used for CO9 and usually for Hg... 

Another problem in the construction of tlrese devices, is that materials which do not play a direct part in the operation of the microchip must be introduced to ensure electrical contact between the elecuonic components, and to reduce the possibility of chemical interactions between the device components. The introduction of such materials usually requires an annealing phase in the construction of die device at a temperature as high as 600 K. As a result it is also most probable, especially in the case of the aluminium-silicon interface, that thin films of oxide exist between the various deposited films. Such a layer will act as a banier to inter-diffusion between the layers, and the transport of atoms from one layer to the next will be less than would be indicated by the chemical potential driving force. At pinholes in the AI2O3 layer, aluminium metal can reduce SiOa at isolated spots, and form the pits into the silicon which were observed in early devices. The introduction of a tlrin layer of platinum silicide between the silicon and aluminium layers reduces the pit formation. However, aluminium has a strong affinity for platinum, and so a layer of clrromium is placed between the silicide and aluminium to reduce the invasive interaction of aluminium. 

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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