Chemical potential profiles

The classification of separations should reflect the patterns of component transport and equilibrium that develop in the physical space of the system. The transport equations show that we have two broad manipulative controls that can be structured variously in space to affect separative transport. First is the chemical potential which controls both relative transport and the state of equilibrium. Chemical potential, of course, can be varied as desired in space by placing different phases, membrane barriers, and applied fields in appropriate locations. A second means of transport control is flow, which can be variously oriented with respect to the phase boundaries, membranes, and applied fields—that is, with respect to the structure of the chemical potential profile. 

Viewed in this way, chemical potential profiles (along with flow) govern separation different phases, membranes, and applied fields are simply convenient media for imposing the desired profiles. The media are selected on pragmatic grounds chemical compatibility with the components and the system, selectivity between components, noninterference with detectability, ease of solvent removal (another separation process), facilitation of rapid transport, and so on. 

It could be argued, of course, that the differences and similarities cited above stem from the fact that solvent extraction is essentially a steady-state (equilibrium) process while electrophoresis and sedimentation are transient (rate) processes. However, such an argument would overlook the fact (to be explained later) that the different forms of the chemical potential profile determine which systems can be run successfully in the steady-state mode and which in the transient mode. Thus the chemical potential profile and associated flow structure emerge as dominant influences that should be classified at the very beginning of any attempt to organize separation phenomena into a cohesive discipline. 

The basic combinations of chemical potential profiles and flow structures are limited in number. The following major categories can be distinguished. 

First, the overall chemical potential profile p (representing the sum of external field effects and internal molecular interactions)... 

Figure 7.1. Three basic classes of chemical potential profiles in separation systems.

The combination of the fundamental arrangements of chemical potential profiles and flow structure outlined above yields nine possible categories of separations. These are shown in Table 7.1. 

A glass jar is partially filled with carbon tetrachloride and water, which form two immiscible phases. Air in the system constitutes another phase. A small amount of iodine is introduced into the system the iodine distributes selectively into the carbon tetrachloride. The jar is capped. Sketch the chemical potential profile /ll = /Lt° of the iodine along the entire axis of the jar, extending from a point just outside the lid (x = 0) to a point 1 mm within the glass bottom (x = h). 

In comparing separation techniques, we generally find a striking difference in methods based on continuous (c) chemical potential profiles and those involving discontinuous (d or cd) profiles. There is, for example, a glaring contrast in instrumentation, applications, experimental techniques, and the capability for multicomponent separations between the two basic static systems, Sc (e.g., electrophoresis) and Sd (e.g., extraction). Similarly, there... 

Figure 1.3 Excess chemical potential profile for methane for the 90/10 water/methanol mobile phase. Energies are given in kcalmoP Distances along z perpendicular to the interfacial plane are given in A.

Figure 1.4 Excess chemical potential profiles (kcalmoF ) for a 2.0A hard-sphere solute along the z axis. The tethered chains are on the left. The three curves correspond to pure water (top), a 50/50 mixture (middle), and 90% methanol (bottom) by volume. Energies are in kcalmor Distances along z perpendicular to the interfacial plane are given in A.

Figure 1 depicts the time evolution of various quantities. The TD chemical potential profile helps [17] dividing the whole collision process into three distinct... 

The correlation (1.15) plays an important role in the analysis of processes stipulated by the small electron conductivity of solid electrolytes, such as the electrolytic permeability of the solid state or the establishment of the chemical potential profile of the elements of solid electrolytes. 

Fig. 2.17. Schematic illustration of the various quantities used to describe the growth of an amorphous interlayer. The composition profiles, chemical potential profile, etc., are shown. The quantity xA is the concentration of element A in the diffusion couple (in the text xA = 1 — x), while X, and X2 are the positions of the amorphous/crystal interfaces...

I only hope that more progress can be realized, especially in solving the central probl in e ll this vdiich was mentioned above, namely, that of evetluating the individual ionic conductances and chemical potential profile in an operating cell. And of course I hope I CM be a partial contributer to such future progress. Or better yet, that somebody in the audience will be led to conten late the issues I have discussed here and perhaps find a better way to analyze mixed conduction in multicomponent electrolytes. 

Choudhury NS, Patterson IW (1970) Steady-state chemical potential profiles in solid electrolytes. 1 Electrochem Soc 117 1384—1388... 

Chemical potential profile, p(z), of solute across a hpid bilayer and adjacent water phase is obtained by inserting the solute numerous times into randomly selected positions in the system obtained by MD simulation and calculating the interaction energy, E(z), between the inserted solute and all the molecules in the system. From t, where <...>t denotes the thermal average over insertions of solute with randomly chosen orientations into configurations of the system at depth z unperturbed by the solute, the excess chemical potential, p(z), and thereby the free energy of transfer, AG(z), from bulk water to the bilayer interior at the depth z are obtained AG(z) =p (z) - ]i (water)... 

Consider, in addition, the nature of the force beli used in separation. Since there is adsorption and/or desorption of solutes between the mobile fluid and the stationary solid phases, the potential profile under consideration for each solute is discontinuous, a simple step function (see Figure 3.2.2) there are no external forces. According to Section 3.2, such a system in a closed vessel without any flow does not have any multicomponent separation capability. Multicomponent separation capability is, however, achieved in elution chromatography by having bulk flow perpendicular to the direction of the discontinuous chemical potential profile. The velocity here functions exactly like the quantity (- ) in equation (3.2.37). 

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