Relaxation amplitudes concentration-jump

The amplitudes of chemical relaxation processes are determined by the equilibrium concentrations (and strictly speaking, associated activity coefficients) and by thermodynamic variables appropriate for the particular perturbation method used. Thus, for example, an analysis of the amplitudes of relaxation processes associated with temperature jump measurements can lead to determination of the equilibrium constants and enthalpies associated with the mechanism under study. As might be anticipated from our previous discussion, the relaxation amplitudes are determined by normal mode thermodynamic variables which are linear combinations of the thermodynamic variables associated with the individual steps in the mechanism. The formal analysis of relaxation amplitudes has been developed in considerable detail [2, 5,7],... 

In pressure (-release ) jump techniques the perturbation of the chemical system is achieved by raising the pressure from the ambient to some higher value and a subsequent sudden drop back to the ambient value. To which extent the actual concentrations can assume their equilibrium values at high static pressure before the jump depends on the ratio of the relaxation time of the system and the pressure duration time 0, and also slightly on the time to needed for the pressure increase (see fig. 2). Here y and y refer to generalized concentration shifts where y is the equilibrium and y the actual shift, y is the equilibrium shift at high static pressure. Obviously the choice of the pressure duration time 6 is critical for the relaxation amplitude which is measured after the jump, because a jump before t 6i would lead to a reduction as compared to yQ. 

RELAXATION AMPLITUDES IN CONCENTRATION JUMP EXPERIMENTS. APPLICATION TO ANTHOCYANINS. 

The calculation of relaxation amplitudes by temperature jump is complex, except for very simple systems of the type A B or A + B C. This is unlike their calculation by concentration jump, since, in this case, the perturbation occurs at constant T and P, and the equilibrium constants remain unchanged. Moreover, we shov in this paper, that by proper use of the concentration jump method, one is able to measure the equilibrium constants of complicated as well as simple chemical systems. Whenever possible, the perturbation should be performed by rapidly modifying the concentration of a species that is characteristic of the type of reaction studied H or 0H for proton transfer, nucleophile for nucleophilic addition or substitution, etc... Thus, one can always write Z [X ] (t) = C, where represents the different... 

From an experimental standpoint, the observation of relaxation amplitudes by concentration jump requires only a classical spectrophotometer fitted with a stirred thermostatted cell. With... 

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 theoretical treatment of the model of Aniansson and Wall is not directly applicable to the time constants obtained in ultrasonic experiments, but this gap has been bridged.The amplitude is predicted to be zero at the c.m.c. then increases with concentration to a broad maximum and thence slowly decreases, as observed for sodium dodecyl sulphate. An analysis of amplitudes in P-jump kinetics implies the possibility of a third relaxation process due to a change in electrolyte properties. This counterion binding equilibrium may have been observed in ultrasonic studies of sodium decyl sulphate. Attempts by the former authors to modify the Aniansson and Wall theory... 

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