PROBLEMS WITH SEVERAL PUBLISHED SOLUTIONS

Problems with several published solutions This section gives you some real problems which have akesdy been solved by several different routes. You can check your answer against these published routes. 

U. Problems with several published solutions cis isomer alone has this smell and is used in... 

PROBLEMS WITH SEVERAL PUBLISHED SOLUTIONS, frames 420-424. 

In Example 10.1 the case where the aerosol concentration does not change with time was considered. In many practical situations, however, the aerosol concentration does change with time, possibly as a result of diffusion and subsequent loss of particles to a wall or other surface. In this event, Fick s second law, Eq. 9.2, must be used. Solution of this equation is possible in many cases, depending on the initial and boundary conditions chosen, although the solutions generally take on very complex forms and the actual mechanics involved to find these solutions can be quite tedious. Fortunately, there are several excellent books available which contain large numbers of solutions to the transient diffusion equation (Barrer, 1941 Jost, 1952). Thus, in most cases it is possible to fit initial and boundary conditions of an aerosol problem to one of the published solutions. Several commonly occurring examples follow. 

Furthermore, practical problems such as contact lens fouling, foaming of protein solutions, and fouling of equipment in the food processing industry, are direct consequences of the relatively high surface activity of proteins. In general, any process involving an interface in which contact with a protein solution occurs is likely to be influenced by protein adsorption to the interface. Thus, several reviews of protein adsorption have been published (1-5). 

Many cellulose derivatives form lyotropic liquid crystals in suitable solvents and several thermotropic cellulose derivatives have been reported (1-3) Cellulosic liquid crystalline systems reported prior to early 1982 have been tabulated (1). Since then, some new substituted cellulosic derivatives which form thermotropic cholesteric phases have been prepared (4), and much effort has been devoted to investigating the previously-reported systems. Anisotropic solutions of cellulose acetate and triacetate in tri-fluoroacetic acid have attracted the attention of several groups. Chiroptical properties (5,6), refractive index (7), phase boundaries (8), nuclear magnetic resonance spectra (9,10) and differential scanning calorimetry (11,12) have been reported for this system. However, trifluoroacetic acid causes degradation of cellulosic polymers this calls into question some of the physical measurements on these mesophases, because time is required for the mesophase solutions to achieve their equilibrium order. Mixtures of trifluoroacetic acid with chlorinated solvents have been employed to minimize this problem (13), and anisotropic solutions of cellulose acetate and triacetate in other solvents have been examined (14,15). The mesophase formed by (hydroxypropyl)cellulose (HPC) in water (16) is stable and easy to handle, and has thus attracted further attention (10,11,17-19), as has the thermotropic mesophase of HPC (20). Detailed studies of mesophase formation and chain rigidity for HPC in dimethyl acetamide (21) and for the benzoic acid ester of HPC in acetone and benzene (22) have been published. Anisotropic solutions of methylol cellulose in dimethyl sulfoxide (23) and of cellulose in dimethyl acetamide/ LiCl (24) were reported. Cellulose tricarbanilate in methyl ethyl ketone forms a liquid crystalline solution (25) with optical properties which are quite distinct from those of previously reported cholesteric cellulosic mesophases (26). 

Current interest is, however, mainly in the coupling of HPLC and TLC, to which considerable attention has been devoted for the solution of difficult separation problems. Since Boshoff et al. (39) first described the direct coupling of HPLC and TLC, several papers (40-43) have been published describing the on-line coupling of liquid chromatographic methods and PC, usually with different interfaces, depending on the first technique applied. If PC is used as the second method, all the MD methods discussed above can be applied to increase the separating power. 

The electrical double layer has been dealt with in countless papers and in a number of reviews, including those published in previous volumes of the Modem Aspects of Electrochemistry series/ The experimental double layer data have been reported and commented on in several important works in which various theories of the structure of the double layer have been postulated. Nevertheless, many double layer-related problems have not been solved yet, mainly because certain important parameters describing the interface cannot be measured. This applies to the electric permittivity, dipole moments, surface density, and other physical quantities that are influenced by the electric field at the interface. It is also often difficult to separate the electrostatic and specific interactions of the solvent and the adsorbate with the electrode. To acquire necessary knowledge about the metal/solution interface, different metals, solvents, and adsorbates have been studied. 

Solutions to problems (i) and (ii) were already available as a result of studies by Hoffmann and Wuts on the reactions of 7-alkoxyaIlyl-boronates with achiral aldehydes (Figure 6). 3 Relatively little information was available, however, regarding the stereochemistry of such reactions with chiral aldehydes. Hoffman had published several examples of reactions of (E)- and (Z)-crotylboronates (methyl replacing OMe in Figure 6) with chiral aldehydes such as 2-methylbutanal, but the best diastereofacial selectivity that had been reported was only 83 17.14 Thus, it was by no means certain that the chemistry summarized in Figure 7 would be successful.3a... 

In 1900 Max Planck proposed a solution to the problem of black-body radiation described above. He suggested that when electromagnetic radiation interacts with matter, energy can only be absorbed or emitted in certain discrete amounts, called quanta. Planck s theory will not be described here, as it is highly technical. In any case, Planck s proposal was timid compared with the theory that followed. He supposed that quanta were only important in absorption and emission of radiation, but that otherwise the wave theory did not need to be modified. It was Einstein who took a more radical step in 1905 (the year in which he published his first paper on the theory of relativity and on several other unrelated topics). Einstein s analysis of the photoelectric effect is crucial, and has led to a complete change in the way we think of light and other radiation. 

---