Chemical relaxation method

Chemical relaxation methods (CRM) observe a mixture of reactants and reaction products in thermodynamic equilibrium and perturb this equilibrium by generat- 

Chemical relaxation methods have been very useful in studies of micelliza-tion kinetics, based on the theory of Aniansson and Wall [167-169], modified by Kahlweit and coworkers [170-174]. Chemical relaxation techniques have been described in several articles and books [175-180] and reviewed by Lang and Zana [166]. 

The shock tube technique is somewhat similar. The bursting of the diaphragm generates a pressure drop which propagates through a tube half-filled with water or ethanol. Reflections of the pressure jump at the bottom and the top of the tube cause addition and subtraction of the incident and reflected pressure waves. As a result, the equilibrium is shifted by a rectangular change in pressure. 

The ultrasonic absolution method shifts the equilibrium periodically by harmonic changes of pressure and temperature caused by the propagation of ultrasonic waves in fluids. The stopped flow method involves rapid mixing of two solutions in less than a millisecond. Because the mixture observed is not in equilibrium, the stopped flow method is not truly a chemical relaxation method. The stopped flow method is useful, nevertheless, for observing perturbations by composition jumps. 

Dilute micellar solutions of surfactants are characterized by two well-separated relaxation times. The molecular origin of the fast relaxation time has been related to a monomer-micelle exchange [181-184]. It was realized later that the relaxation spectra of micellar solutions really exhibit two relaxation times. The theory of Aniansson and Wall [167,185] assumes a stepwise aggregation of surfactant monomers to form micelles [186]. The fast relaxation time is attributed to the exchange of monomeric surfactants between the micelles and the intermicel-lar solution. The slow relaxation time is attributed to micelle formation and breakdown. The theory and its modifications by Kahlweit and co-workers [170-174] 

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Consider this fast reaction as it would be studied by a small-perturbation chemical relaxation method. 

Chemical relaxation methods can be used to determine mechanisms of reactions of ions at the mineral/water interface. In this paper, a review of chemical relaxation studies of adsorption/desorption kinetics of inorganic ions at the metal oxide/aqueous interface is presented. Plausible mechanisms based on the triple layer surface complexation model are discussed. Relaxation kinetic studies of the intercalation/ deintercalation of organic and inorganic ions in layered, cage-structured, and channel-structured minerals are also reviewed. In the intercalation studies, plausible mechanisms based on ion-exchange and adsorption/desorption reactions are presented steric and chemical properties of the solute and interlayered compounds are shown to influence the reaction rates. We also discuss the elementary reaction steps which are important in the stereoselective and reactive properties of interlayered compounds. 

Chemical relaxation methods involve small perturbations of equilibrium (8). The dependences of the equilibrium constant K on tempera-... 

Another chemical relaxation method that can be used to determine the kinetics of fast reactions on soil constituents is the electric field pulse technique. This technique was developed by Hachiya et al. (1980) to study the kinetics of I03 adsorption and desorption on Ti02 and by Sasaki et al. (1983) to investigate ion-pair formation on the surface of a-FeOOH. Excellent review articles on electric field methods are found in DeMaeyer (1969), Hemmes (1979), and Eyring and Hemmes (1986). 

Ikeda, T., Sasaki, M., and Yasunaga, T. (1984b). Kinetic studies of ion exchange of NH7 in zeolite H-ZSM-5 by the chemical relaxation method. J. Colloid Interface Sci. 98, 192-195. 

A major advantage of the chemical relaxation method is that a successive change of the partial pressure allows the detection of Lf as well as of the properties measured in the homogeneous states... 

See especially Chaps. 2 and 3 in D. L. Sparks and D. L. Suarez, op. cit.10 A summary review of chemical relaxation methods is given by T. Yasunaga and T. Ikeda, Adsorption-desorption kinetics at the metal-oxide-solution interface studied by relaxation methods, Chap. 12 in J. A. Davis and K. F. Hays, op. cit.2... 

The electron transfer mechanism of azurin, a well known example for this type of proteins, has been systematically studied using the chemical relaxation method and a well defined inorganic outer sphere redox couple. In parallel, the investigations of the reaction with its presumed physiological partner, cytochrome c, were pursued (7). The specificity of the interaction between azurin and cytochrome c P-551 is expressed in higher specific rates and in the control of the electron transfer equilibrium by conformational transitions of both proteins. 

Chemical relaxation methods are widely used to study the kinetics of fast chemical reactions in solution. In particular, ultrasonic absorption techniques have been used to investigate fast exchange processes with relaxation times in the range 0.3 xs to 0.3 ns. The longer end of this time range has become accessible in recent years through the use of cylindrical resonator methods [1] which have lowered the frequency range covered by fictional pulse echo methods. 

In the chemical relaxation methods for following fast reactions, the rate coefficients are determined from a parameter called the relaxation time, x. The physical significance of x will be considered in terms of the step-function model, but the same quantity is measured by the other main group of relaxation methods, the stationary methods. 

I In some ways the nomenclature is a little confusing. In nmr it is traditional to use Ti and to describe the relaxation times of specific nuclear processes and t the mean lifetime of a nucleus in a particular state. In chemical relaxation methods, however, t refers to the relaxation time. Chemical relaxation methods and nmr are similar in that in each, one time function is measured and its variation with concentration is followed. The difference comes in the relationships of the respective time functions to the concentrations. 

The first order rate coeflScient (x is derived in all cases, and it refers to the system under conditions of chemical equilibrium cf. the rate coefficient derived from the chemical relaxation methods where this equilibrium is slightly displaced). In order to evaluate a, b,..., x is measured as a function of the concentrations of A, B,... 

Table 3-1. Chemical relaxation methods, reaction time scales that can be measured using...

With chemical relaxation methods, the equilibrium of a reaction mixture is rapidly perturbed by some external factor such as pressure, temperature, or electric-field strength. Rate information can then be obtained by following the approach to a new equilibrium by measuring the relaxation time. The perturbation is small and thus the final equilibrium state is close to the initial equilibrium state. Because of this, all rate expressions are reduced to first-order equations regardless of reaction order or molecularity. Therefore, the rate equations are linearized, simplifying determination of complex reaction mechanisms (Bernasconi, 1986 Sparks, 1989),... 

Chemical relaxation methods [52] show evidence of a distribution of relaxation frequencies rather than a single one as found with classic ion detergents [193]. Thus, in agreement with the above conclusions, NaC and NaDC apparently self-associate over a whole range of concentrations and not at some critical micellar concentration. Further, the relaxation frequencies are strongly concentration dependent, suggesting that the distribution of aggregate sizes is wide and shifts upwards as bile salt concentration is increased [52]. 

Lang, J. and Zana, R., Chemical relaxation methods, in Surfactant Solutions, R Zana (ed.), Marcel Dekker, New York, 1987, p. 405. 

This consideration about the analysis of overlapping relaxation effects holds for all chemical relaxation methods with pulse shaped perturbations, it is not restricted to the pressure jump. 

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