Stepwise association

Atkinson, G. Kor, S. K. (1967). The kinetics of ion association in manganese sulphate solutions. II. Thermodynamics of stepwise association in water. Journal of Physical Chemistry, 71, 673-7. 

Polar, water-soluble analogs of these molecules (23 and 24) have also been studied and have been shown to form helical columns in a variety of polar solvents such as methanol, butanol, acetonitrile, and water, by virtue of solvophobic interactions between the large aromatic cores.82,83 A stepwise association process is observed when alcohol solutions of 24 are cooled. The... 

Pyronine Y (PY) with beta cyclodextrin by using the temperature-jump technique. It was found that the kinetic data could be adequately explained by a mechanism involving the stepwise association of two beta cyclodextrin molecules (C) to the dye. Thus,... 

The distinction between micellar and nonmicellar association may not always be immediately clear from experimental variable concentration data, but Muker-jee6,23,24 has in instructive papers presented methods to distinguish between proper micelle fromation and other types of stepwise association. As he demonstrates, erroneous conclusions may easily be drawn and are abundant in the literature. 

The total solubilizate concentration is a function of the stepwise association constant, K, between a solubilizate and a monomer concentration solubilizate. It is very useful to consider the factors influencing solubilization. These values determine the general behavior of solubilization as follows ... 

The micellization process can be described by the stepwise association equilibrium... 

A uniform stepwise association constant kj cannot produce abrupt changes in the physical properties such as those accompanying micellization. This requires a cooperative self-association, Le., kj should increase with j in the initial stages.7... 

Figure 4. In (kj/k) vs. aggregation number j for various values of

Let us now emphasize that the value c = 5 is more plausible from a physical point of view than the lower value (7 = 3 taken in ref 6. Figure 4 shows the size dependence of fhe stepwise association constant. For the values of the parameters used in ref 6, namely, A = 50, n = 40,... 

The stability constant given in Eq. 4 is an association constant. A dissociation constant is numerically equal to the reciprocal of the corresponding association constant. It is common practice to quote dissociation constants for acids (particularly organic acids), while association constants are used for complexes. For a monobasic acid, HL. there are no further complications. But for polybasic acids, the numerical order of the two sets is reversed. For example, for a dibasic acid, the first stepwise dissociation constant is equal to the reciprocal of the second stepwise association constant and vice versa. 

The Noncooperative Model, (a = 7 = 1, c= 0). This model applies to assembhes that involve only intemiolecular interactions without any allosteric effect. The occupation of the various binding sites of the receptor is dictated only by statistics. This model is the reference for spotting the presence of allosteric effects in real systems. It also applies to the formation of a given ohgomer in isodesmic polymerizations. This process is exemplified by a monomer A—B that undergoes a reversible polymerization in which all of the stepwise association constants are identical and equal to K. The formation constant of each oligomer (A—B), is given by Eq. [51] in which a = y = 1, c = 0, = 1 and f) = 1 -... 

The Allosteric Cooperative Model, a 1, y = l, c = 0). This model is typical of cooperative systems involving only intermolecular interactions such as haemoglobin. It also apphes to the reversible formation of linear oligomers under the condition of different stepwise association constants, as in the case of nucleation-growth polymerizations. " ... 

These results and those using other methods (Shah, 1971 Clausse, 1957 Ache, 1977) agree on the following interpretation. At low water concentration the surfactant molecules associate a few water and cosurfactant molecules around its polar part forming an aggregate such as the one in Fig. 5, A. With increasing water concentration a stepwise association to inverse micelles. Fig. 6, B, takes place (Eicke and Christen, 1974). ... 

Gill and Farquhar [22] have reported such an analysis. Equations relating l to AH° and K are obtained using the assumption of equal K s and AH°"s for a stepwise association. Included in their work are equations for the various stoichiometries from dimers to polymerization of unlimited species. We have applied their analysis to heat of dilution data for 1,1,3,3-tetramethyl urea. 

A theory for the stepwise association and dissociation of surfactant micelles was developed a few years ago. Its application to a large quantity of experimental data has provided a consistent interpretation of these data and enabled the extraction of basic kinetic and equilibrium parameters for these systems In the following extension to mixed micelles the concepts and assumptions used are closely analogous to those of the previous treatment to which the reader is referred for more details. For simplicity the treatment is limited to two-component micelles but the extension to larger number of components is quite straightforward. 

B3LYP/6-31 l-i-i-G(d,p) calculations, AIM calculations, and NBO analyses in the gas phase and using the CPCM method in water, THF, and diethyl ether have shown that the P-N hydrolysis of tepa and thiotepa in the gas phase and in water, THF, and diethyl ether occurs by a an acid-catalysed concerted backside attack rather than a stepwise associative, a stepwise dissociative, or a concerted frontside attack. B3LYP/6-31-i-i-G(d,p) level calculations of the 5 reactions between diethyl p-nitrophenylphosphate and methoxide ion and methyl thiolate ion in the gas phase and using the PCM model for the reaction in water have shown that with one exception, the 5[ 2 P reaction displacing thep-nitrophenoxide ion is faster than the 5N2-type reaction at the ethyl carbon in both the gas phase and in solution. The reaction at phosphorus... 

Ghosh and Mukerjee [230] have described the self-association of the cationic dye, methylene blue, using a stepwise association model in which all the equilibrium constants are assumed to be of equal value... 

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