Bulk solution

Langmuir [ 146] gave an instructive interpretation to this rule. The work W to transfer one mole of solute from bulk solution to surface solution should be... 

Here (D is the diffusion coefficient and C is the concentration in the general bulk solution. For initial rates C can be neglected in comparison to C/ so that from Eqs. IV-59 and IV-60 we have... 

A number of electrokinetic phenomena have in common the feature that relative motion between a charged surface and the bulk solution is involved. Essen-... 

The adsorption of nonelectrolytes at the solid-solution interface may be viewed in terms of two somewhat different physical pictures. In the first, the adsorption is confined to a monolayer next to the surface, with the implication that succeeding layers are virtually normal bulk solution. The picture is similar to that for the chemisorption of gases (see Chapter XVIII) and arises under the assumption that solute-solid interactions decay very rapidly with distance. Unlike the chemisorption of gases, however, the heat of adsorption from solution is usually small it is more comparable with heats of solution than with chemical bond energies. 

Wang H, Yan E C Y, Borguet E and Eisenthal K B 1996 Second harmonic generation from the surface of centrosymmetric particles in bulk solution Chem. Phys. Lett. 259 15-20... 

Stripping voltammetry involves the pre-concentration of the analyte species at the electrode surface prior to the voltannnetric scan. The pre-concentration step is carried out under fixed potential control for a predetennined time, where the species of interest is accumulated at the surface of the working electrode at a rate dependent on the applied potential. The detemiination step leads to a current peak, the height and area of which is proportional to the concentration of the accumulated species and hence to the concentration in the bulk solution. The stripping step can involve a variety of potential wavefomis, from linear-potential scan to differential pulse or square-wave scan. Different types of stripping voltaimnetries exist, all of which coimnonly use mercury electrodes (dropping mercury electrodes (DMEs) or mercury film electrodes) [7, 17]. 

In voltammetry the working electrode s surface area is significantly smaller than that used in coulometry. Consequently, very little analyte undergoes electrolysis, and the analyte s concentration in bulk solution remains essentially unchanged. 

Earlier we described a voltammogram as the electrochemical equivalent of a spectrum in spectroscopy. In this section we consider how quantitative and qualitative information may be extracted from a voltammogram. Quantitative information is obtained by relating current to the concentration of analyte in the bulk solution. Qualitative information is obtained from the voltammogram by extracting the standard-state potential for the redox reaction. For simplicity we only consider voltammograms similar to that shown in Figure 11.33a. 

Thus, the limiting current, is a linear function of the concentration of O in bulk solution, and a quantitative analysis is possible using any of the standardization methods discussed in Chapter 5. Equations similar to equation 11.35 can be developed for other forms of voltammetry, in which peak currents are related to the analyte s concentration in bulk solution. 

Since the concentration of R in bulk solution is zero, this equation simplifies to... 

Several polymerization techniques are in widespread usage. Our discussion is biased in favor of methods that reveal additional aspects of addition polymerization and not on the relative importance of the methods in industrial practice. We shall discuss four polymerization techniques bulk, solution, suspension, and emulsion polymerization. 

Azobisnittiles are efficient sources of free radicals for vinyl polymerizations and chain reactions, eg, chlorinations (see Initiators). These compounds decompose in a variety of solvents at nearly first-order rates to give free radicals with no evidence of induced chain decomposition. They can be used in bulk, solution, and suspension polymerizations, and because no oxygenated residues are produced, they are suitable for use in pigmented or dyed systems that may be susceptible to oxidative degradation. 

Uses. The a2obisnitriles have been used for bulk, solution, emulsion, and suspension polymeri2ation of all of the common vinyl monomers, including ethylene, styrene vinyl chloride, vinyl acetate, acrylonitrile, and methyl methacrylate. The polymeri2ations of unsaturated polyesters and copolymeri2ations of vinyl compounds also have been initiated by these compounds. 

Any one of the five basic processes may be responsible for limiting the extraction rate. The rate of transfer of solvent from the bulk solution to the soHd surface and the rate into the soHd are usually rapid and are not rate-limiting steps, and the dissolution is usually so rapid that it has only a small effect on the overall rate. However, knowledge of dissolution rates is sparse and the mechanism may be different in each soHd (1). 

A key factor determining the performance of ultrafiltration membranes is concentration polarization due to macromolecules retained at the membrane surface. In ultrafiltration, both solvent and macromolecules are carried to the membrane surface by the solution permeating the membrane. Because only the solvent and small solutes permeate the membrane, macromolecular solutes accumulate at the membrane surface. The rate at which the rejected macromolecules can diffuse away from the membrane surface into the bulk solution is relatively low. This means that the concentration of macromolecules at the surface can increase to the point that a gel layer of rejected macromolecules forms on the membrane surface, becoming a secondary barrier to flow through the membrane. In most ultrafiltration appHcations this secondary barrier is the principal resistance to flow through the membrane and dominates the membrane performance. 

The phenomenon of concentration polarization, which is observed frequently in membrane separation processes, can be described in mathematical terms, as shown in Figure 30 (71). The usual model, which is weU founded in fluid hydrodynamics, assumes the bulk solution to be turbulent, but adjacent to the membrane surface there exists a stagnant laminar boundary layer of thickness (5) typically 50—200 p.m, in which there is no turbulent mixing. The concentration of the macromolecules in the bulk solution concentration is c,. and the concentration of macromolecules at the membrane surface is c. 

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