Temperature jump transfer

We therefore may also address the factor in Eq. (4.74), which corresponds to a as a stiffness coefficient , now related to the formation of a concentration wave. Interestingly enough, exactly this stiffness coefficient shows up again in Eq. (4.82) for apart from a trivial factor RT/vc. As S is determined by this factor only, it can replace the stiffness coefficient in equations. Clearly, the latter affects the relaxation rate and therefore has to be part of any equation for r. Since our system shows close similarities to an overdamped harmonic oscillator, both having the same equation of motion, we can also understand the linear dependence of F on S b Hence in conclusion, for temperature jumps within the one phase region, Eq. (4.106) looks perfectly reasonable. It may appear less obvious that its validity is maintained if temperature jumps transfer the system into the two-phase region so that spinodal decomposition sets in. One could argue that, in view of the continuous character of critical phase transitions, one could expect the same kinetic equations to hold on both sides of the phase boundary, but a direct proof is certainly necessary and is indeed provided by the theoretical treatments. 

The physical reason for the velocity slip is the fact that close to the wall the gas is not in thermal equilibrium. For the same reason, a temperature jump is induced, and a more detailed investigation based on the kinetic theory of gases shows that heat transfer and momentum transfer are coupled. Expressions for velocity slip and temperature jump valid in the case of non-isothermal conditions are given by... 

The first experimental data for a reaction involving proton transfer from a hydrogen-bonded acid to a series of bases which were chosen to give ApK-values each side of ApK=0 are given in Fig. 15 (Hibbert and Awwal, 1976, 1978 Hibbert, 1981). The results were obtained for proton transfer from 4-(3-nitrophenylazo)salicylate ion to a series of tertiary aliphatic amines in aqueous solution, as in (64) with R = 3-nitrophenylazo. Kinetic measurements were made using the temperature-jump technique with spectrophoto-metric detection to follow reactions with half-lives down to 5 x 10"6s. The reciprocal relaxation time (t ), which is the time constant of the exponential... 

The kinetics of proton transfer from protonated 1,8-bis(dimethyl-amino)-2,7-dimethoxynaphthalene to substituted phenolate ions (69) were studied in 70% (v/v) Me2SO—H20 using the temperature-jump technique with spectrophotometric detection to follow reactions with half-lives in the range 1-100 ms (Hibbert and Robbins, 1978). A limited... 

For cryptands in which the molecular cavity is larger than in the case of the [l.l.l]-species [78], proton transfer in and out of the cavity can be observed more conveniently. Proton transfer from the inside-monoprotonated cryptands [2.1.1] [79], [2.2.1] [80], and [2.2.2] [81 ] to hydroxide ion in aqueous solution has been studied by the pressure-jump technique, using the conductance change accompanying the shift in equilibrium position after a pressure jump to follow the reaction (Cox et al., 1978). The temperature-jump technique has also been used to study the reactions. If an equilibrium, such as that given in equation (80), can be coupled with the faster acid-base equilibrium of an indicator, then proton transfer from the proton cryptate to hydroxide ion... 

Ions and protons are much heavier than electrons. While electrons can easily tunnel through layers of solution 5 to 10 A thick, protons can tunnel only over short distances, up to about 0.5 A, and ions do not tunnel at all at room temperature. The transfer of an ion from the solution to a metal surface can be viewed as the breaking up of the solvation cage and subsequent deposition, the reverse process as the jumping of an ion from the surface into a preformed favorable solvent configuration (see Fig. 9.1). 

The His35, with coordinated His46 in close proximity, has frequently been suggested as a site for electron transfer reactivity of azurin. Two processes have been detected in a temperature-jump study on the equihbration of azurin with cytochrome C551, its physiological partner [57]. The fast process is assigned to electron transfer, and the slower process to a conversion between inactive and active forms of reduced azurin. It has been concluded that the active form is protonated. A second H-bonded form of His35 is believed to result from the protonation [2]. 

In recent years, evidence has been found that both mechanisms of proton transfer can occur for certain intramolecularly hydrogen-bonded acids. Also, new kinetic behaviour has been obtained which allows a much more detailed examination of the reaction steps in (22). Kinetic data for the second ionization of substituted phenylazoresorcinols in the presence of hydroxide ions (25) were some of the first to be obtained for an intramolecularly hydrogen-bonded acid. The reciprocal relaxation time (t ) for the approach to equilibrium in a temperature-jump experiment was measured at different hydroxide-ion concentrations. A linear dependence of x on [OH] was obtained of the form of (26) (Eigen and Kruse, 1963 Inskeep et al., 1968 Rose and Stuehr, 1971). However, careful measurements at lower hydroxide-ion concentrations (Perlmutter-Hayman and Shinar, 1975 Perl-mutter-Hayman et al., 1976 Yoshida and Fujimoto, 1977) revealed that the... 

An indication has been obtained that the opening of the salicylate hydrogen bond may become partially rate limiting in proton transfer (33) from substituted salicylate ions to hydroxide ions and buffer species in 50% (v/v) MejSO-HjO (Hibbert and Spiers, 1989a). Temperature-jump measurements of the equilibration between the salicylate ion and its dissociated species lead to curved plots of against buffer concentration and against hydroxide-ion concentration. Analysis of the results in terms of the mechanism in (33) gave the approximate values ki = 5x 10 s" and A, = 3 X 10 s ... 

Biochemical processes such as protein unfolding/refold-ing and supramolecular assembly/disassembly take place on a time scale of seconds to minutes after readjusting the temperature of a system. Most commercially available glass-jacketed cuvettes are not suitable for temperature jumps on this time scale, as a result of the slow kinetics of heat transfer across substances with characteristically high dielectric constants, and their use can convolute the time scale of the temperature change onto the time scale... 

Analogous to the slip velocity between gas and particle at Kn above the continuum flow range discussed in Section A above, a temperature discontinuity exists close to the surface at high Kn. Such a discontinuity represents an additional resistance to transfer. Hence, transfer rates are generally lowered by compressibility and noncontinuum effects. The temperature jump occurs over a distance 1.996kl 2 — a )/Fva k + 1) (K2, Sll) where is the thermal accommodation coefficient, interpreted as the extent to which the thermal energy of reflected molecules has adjusted to the surface temperature. 

In 1934 Nukiyama (N2) carried out a simple experiment which resulted in a great advance in the science of boiling. He submerged a thin platinum wire in water at 212° F. and heated the wire electrically to produce boiling. He discovered that the rate of heat transfer from the wire to the water increased steadily as the wire temperature was increased until the wire temperature reached about 300° F. At this temperature an unexpected thing happened the wire temperature jumped suddenly to about 1800° F. A further increase in the wire temperature resulted in a smooth increase in the heat transfer rate. 

Studies on the kinetic behaviour of nucleoside and nucleotide complexes are less common than those on structural aspects. This arises because of the rapid rates of the formation and dissociation reactions, requiring NMR or temperature-jump relaxation measurements. The number of species that can coexist in solution also hinders interpretation. The earlier kinetic studies have been reviewed by Frey and Stuehr.127 Two important biological reactions of the nucleotides are phosphoryl and nucleotidyl group transfers. Both reactions are catalytic nucleophilic reactions and they both require the presence of a divalent metal ion, in particular Mg2+. Consequently, one of the main interests has been in understanding the catalytic mechanism of the metal ion involvement. This has mainly involved studies on related non-enzymic reactions.128... 

Wray, W. O., Aida, T., and Dyer, R. B. (2002). Photoacoustic cavitation and heat transfer effects in the laser-induced temperature jump in water. Appl. Phys. B 74, 57—66. 

Similar expressions may be developed for low-density conduction between concentric cylinders. In order to predict the heat-transfer rate it is necessary to establish relations for the temperature jump for various gas-to-solid interfaces. 

Refs. [i] Bard AJ, FaulknerLR (2001) Electrochemical methods, 2nd edn. Wiley, New York, pp 487-516 [ii] Amatore C, Maisonhaute E (2005) Anal Chem 77-.303A [iii] FeldbergSW, Newton MD, Smalley JF (2003) The indirect laser-induced temperature jump method for characterizing fast interfacial electron transfer concept, application, and results. In Bard AJ, Rubinstein I (eds) Electroanalytical chemistry, vol. 22. Marcel Dekker, New York, pp 101-180... 

Bemasconi and co-workers have studied the kinetics of disproportion-ation-comproportionation in azaviolene systems by temperature jump, stopped-flow, and pH jump techniques, examining the electron transfer process in the light of Marcus theory.316-318... 

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