Davies group number

Table 2.2 shows the Davies group numbers for a range of common substituents. 

The HLB system has heen put on a more quantitative basis by Davies, who calculated group contributions (group numbers) to the HLB number such that the HLB was obtained from... 

The above simple equations cannot be used for surfactants containing propylene oxide or butylene oxide neither can they be apphed for ionic surfactants. Davies [19, 20] devised a method for calculating the HLB number for surfactants from their chemical formulae, using empirically determined group numbers that are assigned to various component groups. A summary of the group numbers for some surfactants is provided in Table 10.3. 

Davies also found that erythro- Xl could be preferentially obtained if tetrahy-dropyridine 148 was used as the substrate [109], The Davies group then synthesized a number of analogs of methylphenidate, both threo and erythro, by varying the aryl component of the diazo compound. Their binding affinities for both serotonin and dopamine transporters were evaluated, and some were found to be up to 15 times more potent than Ritalin itself [110],... 

The HLB concept was originally introduced in 1949 by Griffin specifically for nonionic surfactants. It was later extended by Davies who introduced a scheme to assign HLB group numbers to chemical groups composing a surfactant. For details see [46]... 

An important contribution to the HLB concept was made by Davies (266, 267), where the so-called group numbers were introduced, that is, HLB numbers which correspond not to the molecule as a whole entity, but to the constituting groups (molecular structural units). Once the group numbers gf are known, one can calculate the HLB number from the chemical formula of a surfactant using the equation ... 

For hydrophilic groups g > 0, while for lipophilic groups gj < 0. The group numbers for some groups calculated by Davies (266, 267) are listed in Table 3. 

From analysis of the destruction rates for oil-in-water and water-in-oil emulsions, Davies was able to relate the group numbers with the ratio of coalescence rates for these two types of emulsion. Another correlation was shown to exist to this ratio and the two equilibrium concentrations of the surfactant in the aqueous and oil phases, (c /c"— distribution coefficient). Finally, the Davies theory leads to die relation ... 

In the framework of Davies concept, the relation [Eq. (119)] is empirical. This relation implies the additivity of group numbers. There is evidence for the fact that the hy-drophilicity and lyophilicity of various groups depend on their position in the molecule this is true, e.g., for isomers. The location of the benzene ring within the alkyl benzene... 

Some typical group numbers as Usted by Davies and Rideal, as well as other investigators, are listed in Table 11.4. 

TABLE 11.4. Group Numbers for the Calculation of HLBs According to Davies and Rideal... 

Another method was set up by Davies (1957). Davies noticed that the hydrophilic and hydrophobic characters depend on the steric hindrance and on the interactions between the specific groups of the surfactive molecule. Thus, hydrophilic groups are characterized by positive numbers, whereas lipophilic groups are by negative ones. The net HLB value of a specific molecule is given by adding to 7 the sum of the group numbers specific to this molecule. Refer to Table 2 hereafter. 

Several approaches to the evaluation of the hydrophilic-lipophilic properties of chemical compounds are known from the literature. For example, in order to evaluate the HLB of surfactants, Davies developed a system based on the analysis of group numbers. The "group number" characterizes the contribution of each specific functional group to the energy that would be required if a solvent molecule were changed from water to an organic solvent. 

The problem of axial conduction in the wall was considered by Petukhov (1967). The parameter used to characterize the effect of axial conduction is P = (l - dyd k2/k ). The numerical calculations performed for q = const, and neglecting the wall thermal resistance in radial direction, showed that axial thermal conduction in the wall does not affect the Nusselt number Nuco. Davis and Gill (1970) considered the problem of axial conduction in the wall with reference to laminar flow between parallel plates with finite conductivity. It was found that the Peclet number, the ratio of thickness of the plates to their length are important dimensionless groups that determine the process of heat transfer. 

The main, currently used, surface complexation models (SCMs) are the constant capacitance, the diffuse double layer (DDL) or two layer, the triple layer, the four layer and the CD-MUSIC models. These models differ mainly in their descriptions of the electrical double layer at the oxide/solution interface and, in particular, in the locations of the various adsorbing species. As a result, the electrostatic equations which are used to relate surface potential to surface charge, i. e. the way the free energy of adsorption is divided into its chemical and electrostatic components, are different for each model. A further difference is the method by which the weakly bound (non specifically adsorbing see below) ions are treated. The CD-MUSIC model differs from all the others in that it attempts to take into account the nature and arrangement of the surface functional groups of the adsorbent. These models, which are fully described in a number of reviews (Westall and Hohl, 1980 Westall, 1986, 1987 James and Parks, 1982 Sparks, 1986 Schindler and Stumm, 1987 Davis and Kent, 1990 Hiemstra and Van Riemsdijk, 1996 Venema et al., 1996) are summarised here. 

Although this route was successful in producing gram quantities of enantiomerically pure (+)-16, because of the linear nature of this route, the number of low-temperature reactions involved and the relatively low yields in some of the final steps (especially the final purification), its potential for scale-up to provide the kilogram quantities needed for further development was low. Thus, for the synthesis to be economically viable, an entirely different approach was taken by the Parke-Davis chemical development group of Butler, et. 

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