Micelles formation constant

The micelle formation constant Kmic is therefore written as Kmic = [Mn]/[S]"... 

The type of behavior shown by the ethanol-water system reaches an extreme in the case of higher-molecular-weight solutes of the polar-nonpolar type, such as, soaps and detergents [91]. As illustrated in Fig. Ul-9e, the decrease in surface tension now takes place at very low concentrations sometimes showing a point of abrupt change in slope in a y/C plot [92]. The surface tension becomes essentially constant beyond a certain concentration identified with micelle formation (see Section XIII-5). The lines in Fig. III-9e are fits to Eq. III-57. The authors combined this analysis with the Gibbs equation (Section III-SB) to obtain the surface excess of surfactant and an alcohol cosurfactant. 

Salt formation. The resin acids have a low acid strength. The pa s (ionization constants) values of resin acids are difficult to obtain, and values of 6.4 and 5.7 have been reported [23] for abietic and dehydroabietic acids, respectively. Resin acids form salts with sodium and aluminium. These salts can be used in detergents because of micelle formation at low concentrations. Other metal salts (resinates) of magnesium, barium, calcium, lead, zinc and cobalt are used in inks and adhesive formulations. These resinates are prepared by precipitation (addition of the heavy metal salt to a solution of sodium resinate) or fusion (rosin is fused with the heavy metal compound). 

Changes in the shape of the absorption spectrum correspond very well with micelle formation. The ratio of absorbance at 550 nm to that at 500 nm(both are absorptions of merocyanine) is constant below the CMC whereas the value increases continuously with concentration above CMC. This indicates that the merocyanine is a sensitive probe to detect micelle formation. During the photoirradiation experiment shown in Figure 2, the ratio of absorbance started to increase at the A /Aq value where the surface tension showed a sudden drop. 

When the initial concentration of the merocyanine form is lower than the CMC of the spiropyran form, the change in surface tension is gradual all through the progression of photoreaction. The value of Ajjq/Acqq remains constant during photoirradiation. Unfortunately, reversibility of this photochromism is poor and the micelle formation/dissociation cycle deteriorates rapidly. 

The behavior of metal ions in reversed micelles may be more interesting, since the reversed micelle provides less solvated metal ions in its core (Sunamoto and Hamada, 1978). Through kinetic studies on the hydrolysis of the p-nitrophenyl ester of norleucine in reversed micelles of Aerosol OT and CC14 which solubilize aqueous cupric nitrate, Sunamoto et al. (1978) observed the formation of naked copper(II) ion this easily formed a complex with the substrate ester (formation constant kc = 108—109). The complexed substrate was rapidly hydrolyzed by free water molecules acting as effective nucleophiles. 

Therefore, the physical meaning of the solubility curve of a surfactant is different from that of ordinary substances. Above the critical micelle concentration the thermodynamic functions, for example, the partial molar free energy, the activity, the enthalpy, remain more or less constant. For that reason, micelle formation can be considered as the formation of a new phase. Therefore, the Krafft Point depends on a complicated three phase equilibrium. 

In conclusion, micelle formation of an ionic surfactant is found to take place at a constant activity,i.e., critical micelle activity, cma, irrespective of counter ion concentration. 

Hetaeric chromatography, 230, 231 effect of charge on hetaeron, 233 retention model of, 231-238 Hetaeron. 191, 230, 231, 240, 243, 249, 280 see also Complexing agent adsorption on the stationary phase, 231, 249,230 amphiphilic, 243 cetrimide, 248 decylsulfonate, 230 dodecylbenzenesulfonate, 230 formation constant of complexes, 276 lauryl sulfate, 230 metal chelating, 262 micelle formation, 230 optically active, 262 surface concentration of, 232... 

O, the surface charge density of the micelle and At, a constant of the system. For simplification, it is assumed that the surface charge density of the micelle does not change appreciably when the alcohol molecules are solubilized into the micelle. Then the equation for the micelle formation may be written as... 

Fig. 21. The micelle formation equilibrium constant K = —- of PIOP-n as function of the num-...

Increasing the hydrophobic part of the surfactant molecules favours micelle formation (see Table 4.3). In aqueous medium, the c.m.c. of ionic surfactants is approximately halved by the addition of each CH2 group. For non-ionic surfactants this effect is usually even more pronounced. This trend usually continues up to about the C16 member. Above the C18 member the c.m.c. tends to be approximately constant. This is probably the result of coiling of the long hydrocarbon chains in the water phase50. 

In calorimetric studies of micelle formation it is often difficult to relate the measured enthalpy changes to specified steps in the aggregation process. Instead one perferably determines the partial molar enthalpy hA of the amphiphile as a function of concentration12). The ideal case of the phase separation model predicts that hA is constant up to the CMC where it discontinuously jumps to another constant value. 

The most straightforward approach to the micelle formation is through equilibrium constants. For an ionic amphiphile the association can be described through a number of equilibria... 

Similar investigations were performed by Elworthy and McIntosh60 using lecithin in suitable water-ethanol-benzene mixtures. In water large micelles of about 6400 monomers are formed, while with decreasing dielectric constant the tendency towards micelle formation decreases. In a 93.4% ethanol - 6.6% H20 mixture no aggregation occurred. At further decrease of the dielectric constant the conditions become suitable with respect to the formation of reversed micelles (see Fig. 21). In... 

The micelle formation process and structure can be described by thermodynamic functions (AG°mjc, AH°mjc, AS°mic), physical parameters (surface tension, conductivity, refractive index) or by using techniques such NMR spectroscopy, fluorescence spectroscopy, small-angle neutron scattering and positron annihilation. Experimental data show that the dependence of the aggregate nature, whether normal or reverse micelle is formed, depends on the dielectric constant of the medium (Das et al., 1992 Gon and Kumar, 1996 Kertes and Gutman, 1976 Ward and du Reau, 1993). The thermodynamic functions for micellization of some surfactants are presented in Table 1.1. 

Interactions Give the relative order of strength of interactions (weak, medium, strong) in the following series of pairs in low-polar solvent, dielectric constant e<10 (a) solvent + additive, (b) Calcium benzenesulfonates reverse micelles formation, (c) strong acid (HS) + N-base, (d) weak acid (HA) + N-base, (e) soot particle + reverse micelle, and (f) mechanically activated surface processes and molecular decomposition. 

The equilibrium aspect of micelle formation can be considered by application of the second law of thermodynamics. The equilibrium constant for the process represented by Eq. (3) is given by... 

Table 3.1 [15] lists the first-order rate constants, which are corrected for hydrolysis of ester in buffer alone. Propylamine served as a reference amine in its presence 102k (min-1) for aminolysis decreased progressively from 0.98 to 0.51 to 0.05 as the acryl group increased from 2 to 12 carbons (Table 3.1). The sharp drop for nitrophenyl lau-rate may be the result of micelle formation (even at 6 x 10-6 M).

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