Surface layer, chemical potential

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 ... 

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). 

Transfer matrix calculations of the adsorbate chemical potential have been done for up to four sites (ontop, bridge, hollow, etc.) or four states per unit cell, and for 2-, 3-, and 4-body interactions up to fifth neighbor on primitive lattices. Here the various states can correspond to quite different physical systems. Thus a 3-state, 1-site system may be a two-component adsorbate, e.g., atoms and their diatomic molecules on the surface, for which the occupations on a site are no particles, an atom, or a molecule. On the other hand, the three states could correspond to a molecular species with two bond orientations, perpendicular and tilted, with respect to the surface. An -state system could also be an ( - 1) layer system with ontop stacking. The construction of the transfer matrices and associated numerical procedures are essentially the same for these systems, and such calculations are done routinely [33]. If there are two or more non-reacting (but interacting) species on the surface then the partial coverages depend on the chemical potentials specified for each species. 

Figure 7.87 shows a AG -concentration diagram for Fe(j,-Zn( ). It was constructed from the experimental data shown in Table 7.37. The method of construction is described elsewhere. Figure 7.87 can now be used, by applying the constraints imposed by the tangency rule, to explain why in Fig. 7.88a and b, where the chemical potentials (shown in the diagram) of zinc vapour varied between 0 and - 1 - 81 kJ molthe total interaction surface layer consisted of T, T, 6, and flayers in Fig. 7.88c at a chemical potential only slightly lower ( — 2-11 kJmol ) only T and T, layers were present whilst at -2-55 kJ mol only a F outermost layer was formed. 

AB diblock copolymers in the presence of a selective surface can form an adsorbed layer, which is a planar form of aggregation or self-assembly. This is very useful in the manipulation of the surface properties of solid surfaces, especially those that are employed in liquid media. Several situations have been studied both theoretically and experimentally, among them the case of a selective surface but a nonselective solvent [75] which results in swelling of both the anchor and the buoy layers. However, we concentrate on the situation most closely related to the micelle conditions just discussed, namely, adsorption from a selective solvent. Our theoretical discussion is adapted and abbreviated from that of Marques et al. [76], who considered many features not discussed here. They began their analysis from the grand canonical free energy of a block copolymer layer in equilibrium with a reservoir containing soluble block copolymer at chemical potential peK. They also considered the possible effects of micellization in solution on the adsorption process [61]. We assume in this presentation that the anchor layer is in a solvent-free, melt state above Tg. The anchor layer is assumed to be thin and smooth, with a sharp interface between it and the solvent swollen buoy layer. 

For an ideally polarizable electrode, q has a unique value for a given set of conditions.1 For a nonpolarizable electrode, q does not have a unique value. It depends on the choice of the set of chemical potentials as independent variables1 and does not coincide with the physical charge residing at the interface. This can be easily understood if one considers that q measures the electric charge that must be supplied to the electrode as its surface area is increased by a unit at a constant potential." Clearly, with a nonpolarizable interface, only part of the charge exchanged between the phases remains localized at the interface to form the electrical double layer. 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

As previously noted the constancy of catalyst potential UWr during the formation of the Pt-(12xl2)-Na adlayer, followed by a rapid decrease in catalyst potential and work function when more Na is forced to adsorb on the surface, (Fig. 5.54) is thermodynamically consistent with the formation of an ordered layer whose chemical potential is independent of coverage. 

The work function of charged particles found for a particular conductor depends not only on its bulk properties (its chemical nature), which govern parameter but also on the state of its surface layer, which influences the parameter (a) xhis has the particular effect that for different single-crystal faces of any given metal, the electron work functions have different values. This experimental fact is one of the pieces of evidence for the existence of surface potentials. The work function also depends on the adsorption of foreign species, since this influences the value of... 

The surface potential of a solution can be calculated, according to Eq. (10.18), from the dilference between the experimental real energy of solvation of one of the ions and the chemical energy of solvation of the same ion calculated from the theory of ion-dipole interaction. Such calculations lead to a value of -1-0.13 V for the surface potential of water. The positive sign indicates that in the surface layer, the water molecules are oriented with their negative ends away from the bulk. 

Thermodynamic discussions of surface-layer properties rely on the assumption of adsorption equilibrium (i.e., on the assumption that for each component the chemical potential in the surface layer is equal to that in the bulk phase, = [ip). When... 

Monte Carlo simulations of this system have shown that by sweeping the chemical potential of Cu, a cluster is allowed to grow withiu the hole risiug four atomic layers above the surface. As iu the experimeuts, it is fouud that its lateral exteusiou remaius coufiued to the area defiued by the borders of the origiual defect. 

---