Proton transfer rate limitations

Figure 3. Dependence of the observed first-order rate constant of Cun(H 2GGhis) on the trien concentration. Cu11 = 2 X 10 4M, pH 6.9, 1M NaClOJt, 25.0°. At high [trien]T the rate constant is proton transfer rate limited.

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

The rate of deprotonation of an acid by a base depends on their structures [41], on the solvent and temperature, and on the difference (ApKa) between the pKa of the acid and that of the base. When acid and base have the same pfCa (ApKa=0) the change of free energy for proton transfer becomes zero and the reaction becomes thermoneutral. Under these conditions the rate of proton transfer is limited only by the so-called intrinsic barrier [34], which is particularly sensitive to structural changes in the reaction partners [39]. When ApKa increases, the rate of proton transfer also increases and approaches a limiting value, which depends on the structures of the acid and base and on the experimental conditions. For normal acids (O-H, N-H) in water the rate of proton transfer becomes diffusion-controlled (ka=10loL mol-1 s"1) when ApKa>2, but in aprotic solvents the limiting proton transfer rate can be substantially lower [42]. 

The ionic resistance of a polymer electrolyte membrane is an important parameter in determining the mobility of protons through the membrane and the corresponding voltage loss across the membrane. Currently, the most commonly used membranes in PEM fuel cells are Nafion membranes produced by DuPont. However, these membranes are limited to low-temperature uses (usually below 80°C) because membrane dehydration at high temperatures can lead to reduced water content and then a lower proton transfer rate, resulting in a significant decrease in conductivity. The relationship between conductivity and the diffusion coefficient of protons can be expressed by the Nemst-Einstein equation ... 

The time scale of the classical temperatine-jnmp experiment ( 1 qs) as originally pioneered by Eigen has been shortened to nanoseconds and very recently to approximately 5 ps using lasers. The classical temperatnre-jump experiment has found only limited application to biological systems, in spite of its great success in determining, for example, proton transfer rates or keto-enol isomerizations. An important reason for its limited apphcation to enzyme research, apart from experimental difficulties such as optical artifacts as a result of the temperature-jump, is the relatively small deviation from equihbrium AG = AH —... 

Carbonic anhydrases accelerate CO2 hydration dramatically. The most active enzymes, typified by human carbonic anhydrase II, hydrate CO2 at rates as high as k =10 s, or a million times a second. Fundamental physical processes such as diffusion and proton transfer ordinarily limit the rate of hydration, and so special strategies are required to attain such prodigious rates. 

As a consequence of the limitations just mentioned, attempts to characterize the kinetic basicity of preparatively used EGBs by determination of proton-transfer rates have mainly been done on the first-mentioned group of radical anions, particularly radical anions derived from azobenzenes, and the group of dianions derived from activated alkenes. At the same time, these type of measurements have been used to compare kinetic and thermodynamic acidities of weak organic acids. 

The proton transfer rates in the reactions involving benzylidenemalononitrile could not be measured but lower limits can be given, for example k p >> 10 for the reaction T- +... 

The question remains, however, how an apparently normal ionic equilibrium in the gas phase with forward and reverse proton-transfer rates near the collision limit can be explained in light of the contradictory high-level ab initio calculations on energies of the presumed product ion structures. The... 

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

The chain polymerization of formaldehyde CH2O was the first example of a chemical conversion for which the low-temperature limit of the rate constant was discovered (see reviews by Goldanskii [1976, 1979]). As found by Mansueto et al. [1989] and Mansueto and Wight [1989], the chain growth is driven by proton transfer at each step of adding a new link... 

This variation from the ester hydrolysis mechanism also reflects the poorer leaving ability of amide ions as compared to alkoxide ions. The evidence for the involvement of the dianion comes from kinetic studies and from solvent isotope effects, which suggest that a rate-limiting proton transfer is involved. The reaction is also higher than first-order in hydroxide ion under these circumstances, which is consistent with the dianion mechanism. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

Diffusion-limited rate control at high basicity may set in. This is more eommonly seen in a true Br nsted plot. If the rate-determining step is a proton transfer, and if this is diffusion controlled, then variation in base strength will not affect the rate of reaction. Thus, 3 may be zero at high basicity, whereas at low basicity a dependence on pK may be seen. ° Yang and Jencks ° show an example in the nucleophilic attack of aniline on methyl formate catalyzed by oxygen bases. 

There are two cases in which the general base catalysis observed for an azo coupling reaction is due not to a rate-limiting proton transfer from the o-complex (Scheme 12-66) but to deprotonation of the coupling component when the species involved in the substitution is formed. These reactions are shown in Schemes 12-71 H I... 

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