Relaxation techniques pressure-jump method

Due to the fast kinetics of adsorption/desorption reactions of inorganic ions at the oxide/aqueous interface, few mechanistic studies have been completed that allow a description of the elementary processes occurring (half lives < 1 sec). Over the past five years, relaxation techniques have been utilized in studying fast reactions taking place at electrified interfaces (1-7). In this paper we illustrate the type of information that can be obtained by the pressure-jump method, using as an example a study of Pb2+ adsorption/desorption at the goethite/water interface. 

Table III suggests some of the proton transfer kinetic studies one is likely to hear most about in the near future. The very first entry, colloidal suspensions, is one that Professor Langford mentioned earlier in these proceedings. In the relaxation field, one of the comparatively new developments has been the measurement of kinetics of ion transfer to and from colloidal suspensions. Yasunaga at Hiroshima University is a pioneer in this type of study (20, 21, 22). His students take materials such as iron oxides that form colloidal suspensions that do not precipitate rapidly and measure the kinetics of proton transfer to the colloidal particles using relaxation techniques such as the pressure-jump method.

The p-jump method has several advantages over the t-jump technique. Pressure-jump measurements can be repeated at faster intervals than those with t-jump. With the latter, the solution temperature must return to its ini-lial value before another measurement can be conducted. This may take 5 min. With p-jump relaxation, one can repeat experiments every 0.5 min. One can also measure longer relaxation times with p-jump than with t-jump relax-mion. As noted earlier, one of the components of a t-jump experiment is It heat source such as Joule heating. Such high electric fields and currents can destroy solutions that contain biochemical compounds. Such problems lIo not exist with the p-jump relaxation method. 

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 steady-state and rapid equilibrium kinetics do not give detailed information on the existence of multiple intermediates or on their lifetimes. Such information is provided by fast (or transient) kinetics. The methods can be divided in two categories rapid-mixing techniques (stopped-flow, rapid-scanning stopped-flow, quenched flow) which operate in a millisecond time scale and relaxation techniques (temperature jump, pressure jump) which monitor a transient reaction in a microsecond time scale. Most of the transient kinetic methods rely on spectrophotomet-rically observable substrate changes during the course of enzyme catalysis. 

Polarographic data yield ki2 = 1.3 X lO W" sec, which agrees well with specific rates of similar reactions shown in Table II. The specific rate kn of the much slower dehydration reaction has been determined by both the temperature and pressure jump methods to be about 0.5 sec at pH 3 and 25 °C with some general acid-base catalysis. While the hydration-dehydration equilibrium itself involves no conductivity change, it is coupled to a protolytic reaction that does, and a pressure jump determination of 32 is therefore possible. In this particular case the measured relaxation time is about 1 sec. The pressure jump technique permits the measurement of chemical relaxation times in the range 50 sec to 50 tisec, and thus complements the temperature jump method on the long end of the relaxation time scale. 

Perturbation or relaxation techniques are applied to chemical reaction systems with a well-defined equilibrium. An instantaneous change of one or several state fiinctions causes the system to relax into its new equilibrium [29]. In gas-phase kmetics, the perturbations typically exploit the temperature (r-jump) and pressure (P-jump) dependence of chemical equilibria [6]. The relaxation kinetics are monitored by spectroscopic methods. 

The appearance or disappearance of the U.V. absorption of the carbonyl group can in principle be used for kinetic measurements. Bell and Jensen (1961) applied this method to 1,3-dichloroacetone the reaction is too fast in pure water, but proceeded at a convenient rate in 5% water-I-dioxan mixtures, in which there is about 50% hydration at equilibrium. Catalysis by many acids and bases was observed. Much faster reactions can be studied by relaxation methods, and the pressure-jump technique has been applied to the reaction Me0(OH)2.CO2H MeC0.C02H-hH20 by Strehlow (1962). 

The apparatus s step change from ambient to desired reaction conditions eliminates transport effects between catalyst surface and gas phase reactants. Using catalytic reactors that are already used in industry enables easy transfer from the shock tube to a ffow reactor for practical performance evaluation and scale up. Moreover, it has capability to conduct temperature- and pressure-jump relaxation experiments, making this technique useful in studying reactions that operate near equilibrium. Currently there is no known experimental, gas-solid chemical kinetic method that can achieve this. 

To study rapid reactions, traditional batch and flow techniques are inadequate. However, the development of stopped flow, electric field pulse, and particularly pressure-jump relaxation techniques have made the study of rapid reactions possible (Chapter 4). German and Japanese workers have very successfully studied exchange and sorption-desorption reactions on oxides and zeolites using these techniques. In addition to being able to study rapid reaction rates, one can obtain chemical kinetics parameters. The use of these methods by soil and environmental scientists would provide much needed mechanistic information about sorption processes. 

Methods such as nuclear magnetic resonance (NMR), electron spectroscopy for chemical analysis (ESCA), electron spin resonance (ESR), infrared (IR), and laser raman spectroscopy could be used in conjunction with rate studies to define mechanisms. Another alternative would be to use fast kinetic techniques such as pressure-jump relaxation, electric field pulse, or stopped flow (Chapter 4), where chemical kinetics are measured and mechanisms can be definitively established. 

Another consideration in choosing a kinetic method is the objective of one s experiments. For example, if chemical kinetics rate constants are to be measured, most batch and flow techniques would be unsatisfactory since they primarily measure transport- and diffusion-controlled processes, and apparent rate laws and rate coefficients are determined. Instead, one should employ a fast kinetic method such as pressure-jump relaxation, electric field pulse, or stopped flow (Chapter 4). 

However, p-jump techniques are not without fault (Takahashi and Alberty, 1969). Most chemical reactions are less sensitive to pressure than to temperature alterations. Thus, a highly sensitive detection method such as conductivity must be employed to measure relaxation times if p-jump is used. Conductometric methods are sensitive on an absolute basis, but it is also fundamental that the solutions under study have adequate buffering and proper ionic strengths. In relaxation techniques, small molar volume changes result, and consequently, even if a low level of an inert electrolyte is present, conductivity changes may be undetectable if pressure perturbations of 5-10 MPa are utilized (Takahashi and Alberty, 1969). 

Werner studied cobalt(III), chromium(III), platinum(II), and platinum(IV) compounds because they are inert and can be more readily characterized than labile compounds. This tendency has continued, and much of the discussion in this chapter is based on inert compounds because they can be more easily crystallized from solution and their structures determined. Labile compounds have also been studied extensively, but their study requires techniques capable of dealing with very short times (stopped flow or relaxation methods, for example, temperature or pressure jump, nuclear magnetic resonance). 

Measurements of the relaxation times by relaxation methods (involving a temperature jump [T-jump], pressure jump, electric field jump, or a periodic disturbance of an external parameter, as in ultrasonic techniques) are commonly used to follow the kinetics of very fast reactions. 

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). 

An important turning point in reaction kinetics was the development of experimental techniques for studying fast reactions in solution. The first of these was based on flow techniques and extended the time range over which chemical changes could be observed from a few seconds down to a few milliseconds. This was followed by the development of a variety of relaxation techniques, including the temperature jump, pressure jump, and electrical field jump methods. In this way, the time for experimental observation was extended below the nanosecond range. Thus, relaxation techniques can be used to study processes whose half lives fall between the range available to classical experiments and that characteristic of spectroscopic techniques. 

AiST Methods. After a rapid alteration of K by changing an external condition, the solution composition readjusts at a finite rate in an attempt to reattain equilibrium this process of adjustment is called relaxation. Several experimental techniques for achieving the necessarily rapid alterations of K have been developed. These include a pressure-jump (sound-absorption) method, an electric-field (dissociation) method, and a temperature-jump method. A temperature jump is brought about by passing an electrical current through the solution in a special cuvette, producing an abrupt, nearly instantaneous, rise in the temperature of the solution. A reaction then takes place as the concentrations adjust to the new temperature. Regardless of the type of perturbation used, the treatment of the data is essentially the same. 

Whenever a chemical equilibrium is subjected to a perturbation, most commonly a change in temperature, pressure, pH, or other concentrations, the system will start to relax back to a new equilibrium state. The kinetics of this relaxation can be followed. Methods for quickly inducing a perturbation followed by monitoring the relaxation are referred to as jump techniques. Changes in temperature, pH, and pressure can often be done fast enough that reactions with half-lives in the microsecond range can be followed. For example, the equilibrium positions of Bransted acid-base reactions are controlled by the pH, and therefore pH jump experiments are particularly useful with these reactions. 

Among the relaxation techniques (1) such as pressure-jump, electrical field-jump and ultrasonic absorption the temperature jump method is most widely used because almost every chemical equilibrium shows a variation with temperature. 

---