The kinetics of micelle formation for a range of ionic surfactants in aqueous solution have been investigated using the ultrasonic relaxation technique. In order to understand the concentration dependance of both the relaxation time and the relaxation strength, and other aspects of the relaxation data, it was necessary to modify our previous two state kinetic model describing micellisation. In this new theoretical treatment the interchange of the monomers to and from the micelles is assumed to be an adsorption mechanism governed by the fundamental kinetic principles introduced by Langmuir in his adsorption theory. Finally we have reconsidered the origin of the chemical relaxation observed in detergent solutions resulting from temperature-and pressure-jump experiments.Chemical relaxation techniques including u l t r a ~o n i c s , ~-~ temperature-jump ''-I3 and pressure-jump 14* l 5 as well as stopped flow methods 1 6 -1 8 have been used to investigate the kinetics of micelle formation in surfactants. From these experiments relaxation times ranging from to lO-'s have been reported. The interpretation of experimental relaxation data in terms of rate constants connected with micelle formation has been discussed by several authors.6* 7 * l o Recently we proposed a successful two state kinetic model which was primarily used with ultrasonic data ; this model was also found to be consistent with temperature-jump measurements. The conclusion from a recent report l9 based on n.m.r. data indicates that whereas the rates of micellization found from ultrasonic experiments are consistent with n.m.r. considerations the rates found from temperature-jump data are too low. In an attempt to gain more information about the rates and also more details about the mechanism of micelle formation we have carried out ultrasonic relaxation measurements on a variety of detergents of the anionic and cationic variety. These results are discussed in terms of a modified version of the two state model and an attempt is also made to clarify the discrepancies concerning relaxation times and hence rate constants in monomer-micelle equilibria.
EXPERIMENTALThe ultrasonic absorption data for all the solutions studied were measured over the frequency range 1-100 MHz with a resonator 2 o (1-25 MHz) and pulse (15-100 MHz) apparatus 21 described previously. The relaxation data were displayed in terms of the frequency dependence of a'il where a' is the excess absorption of the solution over solvent at c
The temperature dependence of the rate of iiiicellization of sodium octyl sulphate have been investigated in the range 288-333 K where the experimentally determined critical micelle concentration (c.m.c.) passes through a minimum. The rate constant associated with the step where a monomer dissociates from a micelle shows normal Arrhenius behaviour in this range, giving an activation energy of 29 kJ mol-'. On the other hand the Arrhenius plot for the rate of association of a monomer to a micelle shows definite curvature. This result is discussed in terms of the minimum observed in the c.m.c. with temperature.
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