T-jump relaxation

The strength of a solvent bond influences the rate of solvent substitution in a given compound. Kinetic measurements by means of the T-jump relaxation technique have illustrated that for the reactions of the solutions of SbCl5 with triphenylchloromethane in different solvents a relationship exists between the rate constant and the donicity of the solvent used. 

Bensaude et al. (78T2259) have used T-jump relaxation spectrophotometry to determine the rates of protonation and deprotonation of 3(5)-methyl-5(3)-phenylpyrazole anion (416") and cation (416H ), respectively. This study is a fundamental cornerstone in understanding annular tautomerism in azoles. The nondissociative intramolecular proton transfer in azoles is not observed (78T2259 86BSF429). 

Any device that heats a sample up uniformly quicker than the measured relaxation time can be used with t-jump relaxation. A number of devices can do this thermostated baths, electrical heating (Joule heating), micro-wave heating, and laser heating. Table 3-2 shows some characteristics of the four heat sources more detail can be found in Turner (1986). 

Table 3-2. Characteristics of heat sources that can be used with t-jump relaxation methods...

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. 

In general, the conversion of enzyme-substrate to enzyme-product occurs on the 1 ms time scale over a very wide range of enzymes [38]. Hence, if we are to understand how chemistry is catalyzed by enzymes, dynamical process on shorter time scales require investigation. For the NAD(P) systems, a very preliminary study was performed on LDH using laser induced T-jump relaxation spectroscopy [44]. 

More generally, the relaxation follows generalized first-order kinetics with several relaxation times x., as depicted schematically in figure B2.5.2 for the case of three well-separated time scales. The various relaxation times determine the turning points of the product concentration on a logarithmic time scale. These relaxation times are obtained from the eigenvalues of the appropriate rate coefficient matrix (chapter A3.41. The time resolution of T-jump relaxation techniques is often limited by the rate at which the system can be heated. With typical T-jumps of several Kelvin, the time resolution lies in the microsecond range. 

It has been demonstrated with a T-jump relaxation method, for instance, that in antimony pentachloride solutions, prepared with various donor solvents, there is a linear correlation between the rate of substitution by triphenylchloromethane of the donor solvent molecule bound at the sixth, free coordination site of the antimony and its donicity [Gu 71, Gu 72]. Both thermodynamic considerations and experimental data showed an analogous correlation between the rate of formation of CoClJ (by the interaction of C0CI3 and Cl ions dissolved in various donor solvents) and the Gutmann donicities of the donor solvents [Ma 75]. 

These rate constants were set to values in the calculations with the six-variahlc model that ensure they are not rate limiting steps. These values are smaller than anticipated from T-jump relaxation data. Choosing higher values will not modify any calculations. 

Fig. 3. Microwave T-jump relaxation of cytosine as a function of the number, n, of accumulations repetition rate 20 Hz. Experimental conditions X = 300 nm tf = 23°C pH 6.4 ...

A Joule heating temperature jump (T-jump) relaxation method study (8) of the kinetics of complexation of monovalent cations in methanol by dibenzo-30-crown-10 particularly intrigued us. Chock had found the rate of complexation of several monovalent cations (Na, K+,NHi +,etc.) to be almost diffusion controlled and essentially too fast for precise determination by T-jump equipment then available to him. He also noted an even faster relaxation process that was completely inaccessible. This latter relaxation process Chock ascribed to a conformational change of the dibenzo-30-crown-10 between two ligand conformers one of which is more suitable for complexing the cation. Such an inference is entirely consistent with known, rapid conformational equilibria in solutions of valinomycin (2), for example. 

FIG. 19 Scaling plot for the relaxation of the mean chain length L t) after a T-jump from Tq = 0.35 to a series of final temperatures, given as a parameter along with the respective L o s. The same Monte Carlo results [64] as in Fig. 5 are used. Full line denotes the scaling function f x = = (0.215 + 8x) . In the inset the... 

The several experimental methods allow a wide range of relaxation times to be studied. T-Jump is capable of measurements over the time range 1 to 10 s P-jump, 10 to 5 X 10" s electric field jump, 10 to 10 s and ultrasonic absorption, 10 to 10 " s. The detection method in the jump techniques depends upon the systems being studied, with spectrophotometry, fluorimetry, and conductimetry being widely used. 

Time-resolved IR spectra of similar peptides following a laser-excited temperature jump showed two relaxation times, unfolding 160 ns and faster components <10 ns (Williams et al., 1996). These times are very sensitive to the length, sequence, and environment of these peptides, but do show that the fundamental helix unfolding process is quite fast. These fast IR data have been contrasted with Raman and fluorescence-based T-jump experiments (Thompson et al., 1997). Raman experiments at various temperatures have suggested a folding in 1 /xs, based on an equilibrium analysis (Lednev et al., 2001). But all agree that the mechanism of helix formation is very fast. 

K. Murakami, T. Sano and T. Yasunaga, Bull. Chem. Soc. Japan 54, 862 (1981). This is unusual case where there are no temperature-jump relaxations. The interaction of bovine serum albumin with bromophenol blue is accompanied by four relaxations which are attributed to a fast second-order interaction followed by three first-order steps. 

Detailed information about the mechanism of carrier complex formation can be obtained by relaxation techniques (17) and NMR studies (80, 100—102). The rate constants of the formation reaction for monactin/Na+ (sound absorption) and valinomycin/Na+ (sound absorption, T-jump) in methanol are about 2 108 and 7 10 M-1 sec-1 respectively, and the corresponding rate constants of the dissociation reactions are 4 105 and 5 105 sec-1 (17). In contrast, the dissociation rate constant for some cryptates is much smaller (42, 103, 122). 

Consider a micellar solution at equilibrium that is subject to a sudden temperature change (T-jump). At the new temperature the equilibrium aggregate size distribution will be somewhat different and a redistribution of micellar sizes will occur. Aniansson and Wall now made the important observation that when scheme (5.1) represents the kinetic elementary step, and when there is a strong minimum in the micelle size distribution as in Fig. 2.23(a) the redistribution of micelle sizes is a two-step process. In the first and faster step relaxation occurs to a quasi-equilibrium state which is formed under the constraint that the total number of micelles remains constant. Thus the fast process involves reactions in scheme (5.1) for aggregates of sizes close to the maximum in the distribution. This process is characterized by an exponential relaxation with a time constant Tj equal to... 

Relaxation methods can be classified as either transient or stationary (Bernasconi, 1986). The former include pressure and temperature jump (p-jump and t-jump, respectively), and electric field pulse. With these methods, the equilibrium is perturbed and the relaxation time is monitored using some physical measurement such as conductivity. Examples of stationary relaxation methods are ultrasonic and certain electric field methods. Here, the reaction system is perturbed using a sound wave, which creates temperature and pressure changes or an oscillating electric field. Chemical relaxation can then be determined by analyzing absorbed energy (acous-... 

Ikeda, T., Sasaki, M., Astumian, R. D., and Yasunaga, T. (1981). Kinetics of the hydrolysis of zeolite 4A surface by the pressure-jump relaxation method. Bull. Chem. Soc. Jpn. 54, 1885-1886. 

Equilibrium acidities are usually determined by titration, either with indicators of known plCa [24] or by following the extent of dissociation spectroscopically (e.g. by UV-spectroscopy [35]). Kinetic acidities, i.e. the rates of deprotonation of acids, can be determined by measuring rates of racemization[36] or rates of H-D or H-T exchange [37, 38], by chemical relaxation experiments (e.g. T-jump method [35, 39]), or by H NMR (line broadening and saturation recovery [40]). 

The spin state lifetimes in solution of the complexes II and III have been measured directly with the laser Raman temperature-jump technique189). Changes in the absorbance at 560 nm (CT band maximum) following the T-jump perturbation indicate that the relaxation back to equilibrium occurs by a first-order process. The spin-state lifetimes are r(LS) = 2.5 10 6 s and r(HS) =1.3 10 7 s. The enthalpy change is AH < 5 kcal mol-1, in good agreement with that derived from x(T) data in Ref. 188. The dynamics of intersystem crossing processes in solution for these hexadentate complexes and other six-coordinate ds, d6, and d7 spin-equilibrium complexes of iron(III), iron(II), and cobalt(II) has been discussed by Sutin and Wilson et al.u°). 

Figure 55 sketches the situation. The realistic potential includes lattice potential and interaction potential. Two functions are crucial in the description of the jump relaxation model, developed and refined by Funke et al.217"219 (i) the probability W(t) that no correlated backward jump has occurred at time t (-W being the backward jump rate) and (ii) g(t) describing the positional mismatch (-g measuring the stabilization rate). The basic assumption of the jump relaxation model is... 

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