Relaxation equations pressure jump perturbations

The kinetics of formation and disintegration of micelles has been studied for about thirty years [106-130] mainly by means of special experimental methods, which have been proposed for investigation of fast chemical reaction in liquids [131]. Most of the experimental methods for micellar solutions study the relaxation of small perturbations of the aggregation equilibrium in the system. Small perturbations of the micellar concentration can be generated by either fast mixing of two solutions when one of them does not contain micelles (method of stopped flow [112]), or by a sudden shift of the equilibrium by instantaneous changes of the temperature (temperature jump method [108, 124, 129, 130]) or pressure (pressure jump method [1, 107, 116, 122, 126]). The shift of the equilibrium can be induced also by periodic compressions or expansions of a liquid element caused by ultrasound (methods of ultrasound spectrometry [109-111, 121, 125, 127]). All experimental techniques can be described by the term relaxation spectrometry [132] and are characterised by small deviations from equilibrium. Therefore, linearised equations can be used to describe various processes in the system. 

The forcing functions used to initiate chemical relaxations are temperature, pressure and electric held. Equilibrium perturbations can be achieved by the application of a step change or, in the case of the last two parameters, of a periodic change. Stopped-flow techniques (see section 5.1) and the photochemical release of caged compounds (see section 8.4) can also be used to introduce small concentration jumps, which can be interpreted with the linear equations discussed in this chapter. The amplitudes of perturbations and, consequently of the observed relaxations, are determined by thermodynamic relations. The following three equations dehne the dependence of equilibrium constants on temperature, pressure and electric held respectively, in terms of partial differential equations and the difference equations, which are convenient approximations for small perturbations ... 

The p-jump method can be used to monitor processes with relaxation times in the range between 100 xs and minutes. The method applies to aqueous solutions, where the perturbation occurs mainly through the p-jump ( 0 term in Equation 2.9, as the prefactor of the AH° term is close to zero). It also applies to solutions in organic solvents, where the perturbation occurs mainly through the temperature change associated with the essentially adiabatic pressure change (AH° term in Equation 2.9). In the case of micellar solutions, the p-jump method has been used for the study of... 

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