Relaxation time chemical

Figure B2.5.4. Periodic displacement from equilibrium through a sound wave. The frill curve represents the temporal behaviour of pressure, temperature, and concentrations in die case of a very fast relaxation. The other lines illustrate various situations, with 03Xj according to table B2.5.1. 03 is the angular frequency of the sound wave and x is the chemical relaxation time. Adapted from [110].

Figures 3 and 4 illustrate how G( r) changes with Keq in the fast reaction regime (tc -C to). For both figures, k and the equilibrium constant A e( = l

T( herri td = (o2/4D. the chemical relaxation time is much smaller than the... 

Tj-hem TD = to2/4Dt the chemical relaxation time is much larger than the characteristic diffusion time so that there is no chemical exchange during diffusion through the excitation volume. The autocorrelation function is then given by... 

Calculate the mole fraction of nitric oxide that ultimately will form, assuming that the elevated temperature and pressure created by the shock are sustained indefinitely. Calculate the time in milliseconds after the passage of the shock for the attainment of 50% of the ultimate amount this time may be termed the chemical relaxation time for the shock process. Calculate the corresponding relaxation distance, that is, the distance from the shock wave where 50% of the ultimate chemical change has occurred. 

Conductance data clearly show that low polarity solutions of tetraalkylammonium salts behave rather simply at low salt concentration and the main properties can be completely described by the simple equilibrium [1] between an lon-parl and the free Ions. For such an equilibrium the chemical relaxation time can be wrltted as ... 

It must be emphasized, however, that a AM which is directly proportional to E as specified by (67) rests on the implicit assumption that the rate of polarization is much faster than the rate of chemical relaxation. Such an assumption is very well justified for small molecular dipoles which can freely rotate in a liquid. Then we have a rotational relaxation time Tr 10 —10 s which is small compared with pertinent chemical relaxation times r, in almost all cases of practical interest. Under these drcumstances, chemically induced dielectric behaviour cannot be possible for small E. It can occur, on the other hand, in the reverse case of > tci,. This condition may actually be encountered in macromolecular reaction... 

In this chapter, the focus will be on how information can be extracted, utilizing the second category described earlier (Fig. 8.1b). In its general form, the normalized autocorrelation function of the detected fluorescence fluctuations will show a complex dependence on the reaction rates and the coeflicients of the translational diffusion, and cannot be expressed in an analytical form. Fortunately, for a rather broad range of molecular reactions the reaction-induced fluorescence fluctuations can be treated separately from those due to translational diffusion [19]. If diffusion is much slower than the chemical relaxation time(s) and/or the diffusion coeflicients of all fluorescent species are equal, then the time-dependent fluorescence correlation function can be separated into two factors. The first factor, Gd( ), depends on transport properties (diffusion or flow) and the second, R t), depends only on the reaction rate constants ... 

It is, when possible, very convenient to be able to treat the kinetics of the chemical reaction separately from the translational diffusion in the fluctuation analysis. As mentioned, a rather broad range of chemical reactions fulfills the criteria for (8.3)-(8.5). In addition, for a reaction which under standard conditions does not fulfill these criteria, it is sometimes possible to modify the conditions. For instance, the dwell times can be retarded with respect to the chemical relaxation times by expanding the observation volume or by speeding up the reactions under study, for instance by using higher concentrations of unlabelled reactants. 

Fig. 11. Variation of (xla> ) with to for a system possessing two chemical relaxation times.

Turner, M.S. Cates, M.E. Linear viscoelasticity of living polymers a quantitative probe of chemical relaxation times. Langmuir 1991, 7 (8), 1590-1594. 

A basic assumption, which is made when writing such equations, is that the chemical relaxation time is much longer than other characteristic times in the system, such as internal (vibrational, rotational) or translational relaxation times. One might inquire about the generalization of the rate law when such a time-scale separation is not satisfied. From a theoretical point of view, a convenient generalization of (2.8) is ... 

Chemical Relaxation TIme Tch at 176°F (80°C) for Polysulfide Rubber Cured with Different Chemicai Agents... 

Closed models (chemical relaxation) time of mass transport At = 0, scales t and events Models of total equilibrium scales are absent Models of mass transfer scales of t and physicochemical events... 

SI. equal to 0 and concentration, temperature and pressure gradients are absent. They are similar to periodical action reactors, in which chemicals are loaded, mixed under assigned stable conditions and instantaneously brought to total chemical equilibrium. This type of models are intended for a forecast not of processes but the state of hydrogeochemical medium when the flow time At. and chemical relaxation time At are equal to 0. For this reason they are often called zero-dimension models (Ozyabkin, 1995 Chen Zhu, Anderson, 2002). In the Western literature they are called... 

From the concentration dependence of the chemical relaxation time the dissociation and recombination rate constant k for the simple ion-pairing equilibrium were obtained as indicated this was only possible in the concentration domain for which the reciprocal relaxation time is a linear function of the square root of electrolyte concentration. 

The plateau value of the time-dependent rate coefficient k t) = kAB t) + kBA t), which is the sum of the forward and reverse rate constants, determines the overall chemical relaxation time, tchem = for the proton transfer. The nonadiabatic time-dependent rate coefficient k t) is shown in Figure 10.2. The rate constant extracted from the plateau value of this plot is k = 0.163 ps Up to six nonadiabatic transitions were required to obtain converged results. An examination of the trajectories in the ensemble revealed that the major nonadiabatic correction to the rate comes from two quantum transitions ground state -> coherent state ground state. This picture of how nonadiabatic transitions influence the reaction rate is quite different from that in standard surface-hopping methods. 

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. 

The theory formulated by Aniansson and Wall and its modifications by Kahlweit and co-workers [34,64-66] have been the basis for most interpretations of chemical relaxation times and provided valuable information on kinetics of mi-cellization. 

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