Temperature-jump

The temperature jump is undoubtedly the most versatile and useful of the relaxation methods. Since the vast majority of reactions have nonzero values for the assoeiated A//, a variation of equilibrium constant K with temperature is to be expected  

Most chemical reactions occur with a change in volume. The equilibrium position will be therefore changed by an applied pressure, which can therefore be used as a perturbation. Nearly always the progress of the reaction is observed at ambient pressures after the applied pressure has been terminated. 

There is finite temperature between the fluid temperature at the wall and wall temperature, which is known as temperature jump. 

We need to determine appropriate expressions for Cjuj p known as temperature jump coefficient. The thermal accommodation coefficient oj) was defined earlier as 

The second term of the above expression is approximately equal to zero as 

Noting that the net energy carried to the surface 2,- - 2r is equal to the heat flux at the wall. 

the temperature jump boundary condition, equation (9.14), can be written as 

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Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

With M = He, experimeuts were carried out between 255 K aud 273 K with a few millibar NO2 at total pressures between 300 mbar aud 200 bar. Temperature jumps on the order of 1 K were effected by pulsed irradiation (< 1 pS) with a CO2 laser at 9.2- 9.6pm aud with SiF or perfluorocyclobutaue as primary IR absorbers (< 1 mbar). Under these conditions, the dissociation of N2O4 occurs within the irradiated volume on a time scale of a few hundred microseconds. NO2 aud N2O4 were monitored simultaneously by recording the time-dependent UV absorption signal at 420 run aud 253 run, respectively. The recombination rate constant can be obtained from the effective first-order relaxation time, A derivation analogous to (equation (B2.5.9). equation (B2.5.10). equation (B2.5.11) and equation (B2.5.12)) yield... 

Markwalder B, Gozel P and van den Berg H 1992 Temperature-jump measurements on the kinetics of association and dissociation in weakly bound systems N2O4 + M = NO2 + NO2 + M J. Chem. Phys. 

Similarly, tlie most rapid relaxation metliod, temperature jumping by solvent absorjition of a brief pulse of optical... 

Fig. 2. Schematic of apparatus for temperature-jump (T-jump) measurements.

A large programme utilizing temperature-jump relaxation methods for the study of tautomerism in aqueous solution has led the Dubois group to determine the kinetic and thermodynamic parameters of the equilibrium (130a) (130b) (78T2259). The tautomeric... 

Surface Temperatures. At low temperatures, the oxidation reaetions on the eatalyst are kinetieally eontrolled, and the eatalyst aetivity is an important parameter. As the temperature inereases, the build-up of heat on the eatalyst surfaee due to the exothermie surfaee reaetions produees ignition and the eatalyst surfaee temperature jumps rapidly to the adiabatie flame temperature of the fuel/air mixture on ignition. Figure 10-26 shows a... 

The most widely used transient method is the temperature-jump (T-jump) method. This is based on the van t Hoff equation, which describes the temperature dependence of the equilibrium constant. 

Fig. 22. Relaxation time curves after temperature jump from 35 to 37 °C for trimer (A), dimer (B) and monomer (C) of crosslinked (Pro-Ala-Gly) (n = 12) (scale grand). Pants (O) denote the 0 values after 2 weeks at 5 °C. Solvent water concentration 2 mg/ml...

Temperature-jump experiments showed an evident increase of the rate of transition by using methanol as solvent instead of water. According to Fig. 31, this is mainly caused by the increase of the fast kinetic phase at the expense of the following slow phase. 

In this case, we point to the fact that a fast (r < 5 s) and a slow phase have been observed in temperature-jump experiments also with the peptide Col 1-3. The slow phase - as already mentioned - has been associated with the cis-trans isomerism of peptide bonds in the direct neighborhood of the helical part. Only peptide bonds to which proline or hydroxyproline contribute their secondary nitrogen are able to assume a cry-configuration at equilibrium (cis to trans ratios of 1 40 to 1 l)l45). Therefore, the fast... 

To answer the question whether the ds-transisomerization of the bridged polypeptides with a Ala-Gly-Pro sequence represents the rate-determining step, the following experiment was carried out The polypeptide with a chain length n = 8 was denaturated in a rapid reaction with a temperature jump from 9.2 to 30 °C and subjected to renatura-tion at 9.2 °C after an incubation time of 25 s. In a second and a third experiment, the incubation in the coiled state was prolonged respectively to 75 and 125 s. It could be observed that the amplitude of the rapid phase depends on the time that lapses between the denaturation and renaturation (Fig. 32). 

Fig. 32. Double-jump experiments of unfolding and refolding. The peptide [(Ala-Gly-Pro)s]3 in 50 ml phosphate buffer (pH 7.5) was incubated at 9.2 °C and quickly unfolded by a first temperature jump from 9.2 to 30 °C. This process took 25 s, the time needed to reach the final temperature. In a first experiment (curve A), the second jump back from 30 to 9.2 °C followed immediately after complete unfolding of the peptide, i.e. 25 s after the first jump. In a second and a third experiment (curve B, C), the time lapse between the first and the second jump was 75 and 125 s, respectively...

Schematic drawing of a temperature-jump apparatus (adapted from Ref. 13). Shown are the analyzing lamp, observation cell, monochromator, photomultiplier, oscilloscope, spark gap, and high-voltage supply.

A schematic representation of temperature and concentration profiles in a temperature-jump experiment. All scales are arbitrary, and the matter to be emphasized is that the temperature jump occurs rapidly compared with the re-equilibration reaction. 

Temperature-jump kinetics. The kinetics of complexation of lutetium(III) with anthrani-late ion was studied by the use of a temperature-jump method.25 The principal reaction is... 

Taft equation, 229-230 Temperature, effect on rate, 156-160 Temperature-jump method, 256 Termination reaction, 182 Thermodynamic products, 59 Three-halves-order kinetics, 29... 

In the study of reactions of the types ether than exchange mentioned previously, the usual technique involves the spectrophotometric examination of reaction mixtures. The absorbance changes that occur, at a suitable wavelength where only one species (either reactant or product) absorbs, as the reaction proceeds are measured (manually or recorded). Treatment of the data via the Beer-Lambert law enables rate coefficients and laws to be found in the usual manner. Stopped flow and temperature jump techniques have been used for very rapid reactions. 

Temperature jump method. " Stopped flow method. Direct spectrophotometry. 

The laser desorption experiments which we describe here utilize pulsed laser radiation, which is partially absorbed by the metal substrate, to generate a temperature jump in the surface region of the sample. The neutral species desorbed are ionized and detected by Fourier transform mass spectrometry (FTMS). This technique has... 

In this manuscript we will first describe the characteristics of the temperature jumps and the resulting molecular desorption which can be produced by a laser pulse. We then describe how we have implemented FTMS as a detection method in these experiments and present our results on several adsorbate systems. 

Laser-Induced Temperature Jumps and Molecular Desorption... 

For the solids of interest to us at present (metals) ic is typically O.lcm /sec. If we restrict t to be less than 10 microseconds then 4ict < lO- cm" and we will always have ilict d . In this limit the temperature jump for nonzero values of r is simply ... 

The peak surface temperature under the center of the laser beam is 990 C above the starting surface temperature. The detailed temporal shape of the surface temperature will depend on the detailed time profile of the laser pulse. However, two Important characteristics of the temperature jump which is generated will be retained ... 

Desorption Rates. Using the above model for the temperature jump associated with pulsed laser heating, the rate of desorption versus time and the total number of molecules desorbed from a finite surface area heated by the laser can be calculated. For the particular case of first-order desorption kinetics, the desorption rate is ... 

Figure 2. Plot of the desorption rate, molecules/sec, (solid circles) and the Integrated number of molecules desorbed (solid line) for an adsorbate with a desorption activation energy of 20Kcal/mole and a preexponentlal of 10 sec-. The temperature jump shown In Figure 1 was used for this calculation.

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