Concentration jump relaxation method

The barred quantities indicate equilibrium concentrations. We draw attention to this simple case as it is of such widespread importance (e.g. O2 binding to respiratory proteins binding of substrate or inhibitor to an enzyme) and to illustrate the equivalence for this mechanism between perturbation and flow methods (see above) when one component is in excess. Indeed, flow methods may be considered as a concentration-jump relaxation method. 

The principles and the experimental aspects of the solvent-jump (or concentration-jump) relaxation method are discussed. 

Kao and Tsien studied the Ca +-binding kinetics of fura-2 and azo-1 by temperature-jump relaxation methods. In 140 mM KCl at 20°C, the respective association and dissociation rate constants for fura-2 were 6x10 M s and 97 s these kinetic properties were insensitive to hydrogen ion concentration over the pH range from 7.4 to 8.4. Azo-1 was studied in 140 mM KCl At 10°C, azo-... 

The recent application of a concentration-jump relaxation technique to the kinetics of the chromate-dichromate equilibrium (Swinehart and Castellan, 1964) could lead to the analysis of many comparatively slow, interdependent reactions with the mathematics of the relaxation method. The interpretation of complex reactions may be greatly simplified by such an approach. 

Concentration-jump methods, such as the pH-jump technique cited earlier, can be used in relaxation kinetics, but this approach is described later (Section 4.4). 

Consideration of the thermodynamics of a representative reaction coordinate reveals a number of interesting aspects of the equilibrium (Fig. 5). Because the complex is in spin equilibrium, AG° x 0. Only complexes which fulfill this condition can be studied by the Raman laser temperature-jump or ultrasonic relaxation methods, because these methods require perturbation of an equilibrium with appreciable concentrations of both species present. The photoperturbation technique does not suffer from this limitation and can be used to examine complexes with a larger driving force, i.e., AG° 0. In such cases, however, AG° is difficult to measure and will generally be unknown. 

The stopped-flow method is more often used than any other technique for observing fast reactions with half-lives of a few milliseconds. Another attribute of this method is that small amounts of reactants are used. One must realize, however, that flow techniques are relaxation procedures that involve concentration jumps after mixing. Thus, the mixing or perturbation time determines the fastest possible rate that can be measured. Stopped-flow methods have been widely used to study organic and inorganic chemical reactions and to elucidate enzymatic processes in biochemistry (Robinson, 1975 1986). The application of stopped-flow methods to study reactions on soil constituents is very limited to date (Ikeda et ai, 1984a). 

The perturbation of the equilibrium normally is a change in temperature, pressure or concentration of one of the reagents and the methods are known as temperature jump, pressure jump and concentration jump, respectively. The advantage of these methods is that the perturbation, especially of temperature and pressure, can be applied very quickly and reactions with half-times in the microsecond range can be observed. The major limitation is that the equilibrium position of the reaction must involve significant concentrations of both reactants and products. Thus relaxation methods are not applicable to essentially irreversible reactions. 

In this method the solution is pressurized to several thousand atmospheres. At a desired time a diaphragm is mechanically ruptured. The system then relaxes to the equilibrium position at atmospheric pressure. The magnitude of the concentration jump depends on the value of A V. For an equilibrium reaction with A V = 5 cm3 mol-1, the constant K will change by about 2 percent per 100 bars of pressure. 

Temperature-jump relaxation and the stopped-flow methods are suitable to follow the concentration changes over extremely short time intervals. Such studies have indicated that immune reaction kinetics resemble other biological systems in which ligands are bound to proteins (Weber, 1975) in that the binding strength of small molecules is largely dictated by the constant. The association rate constants ka, are very similar for various antibody-antigen systems, i.e., for... 

A number of soil chemical phenomena are characterized by rapid reaction rates that occur on millisecond and microsecond time scales. Batch and flow techniques cannot be used to measure such reaction rates. Moreover, kinetic studies that are conducted using these methods yield apparent rate coefficients and apparent rate laws since mass transfer and transport processes usually predominate. Relaxation methods enable one to measure reaction rates on millisecond and microsecond time scales and 10 determine mechanistic rate laws. In this chapter, theoretical aspects of chemical relaxation are presented. Transient relaxation methods such as temperature-jump, pressure-jump, concentration-jump, and electric field pulse techniques will be discussed and their application to the study of cation and anion adsorption/desorption phenomena, ion-exchange processes, and hydrolysis and complexation reactions will he covered. 

For reactions that occur on time scales < 15 s, none of the techniques given above is satisfactory. To measure these reactions, one can employ relaxation methods (Table 3-1), such as pressure-jump, temperature-jump, concentration-jump, and electric-field pulse (Bernasconi, 1976 Gettins and Wyn-Jones, 1979 Bernasconi, 1986 Sparks, 1989, 1990). 

One can divide relaxation methods into those that are either transient or stationary. Transient methods include temperature-, pressure-, and concentration-jump and electric-field pulse techniques. With these, tht... 

Temperature jump is another relaxation methods used for rapid reactions. The procedure for T-jump includes the following steps let the system equilibrate at T, increase the temperature instantaneously to T2 and then follow the change in the concentrations of the reactants and products (Figure 8.2). 

Thus far we have considered only perturbations of equilibrium states. This generally requires that the equilibrium constants be such that appreciable concentrations of both reactants and products are present. However, perturbations of steady states also can be realized. The mathematical analysis is quite similar to that already discussed for equilibrium systems except that steady-state concentrations are utilized rather than equilibrium concentrations and the principle of detailed balance cannot be used. For example, a rapid mixing apparatus might be used to establish a steady state which is then perturbed by a temperature jump. While steady-state perturbations have not yet been extensively used, they represent a potentially important application of relaxation methods. 

Some reactions, however, are so rapid that mixing cannot be achieved sufficiently rapidly. For such reactions the relaxation methods, such as the temperature-jump (T-jump) method may be used. They were developed in 1954 by M. Eigen (b. 1927). In this technique a reaction system at equilibrium is subjected to a very rapid rise in temperature which causes the equilibrium to shift (relax) to a new position of equilibrium. Physical methods are available for following the concentration changes during this relaxation, and the results can be analyzed to give the rate constants and the order of reaction. 

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... 

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