Maximum bimolecular rate constant

The first estimations of for photoinduced processes were reported by Dvorak et al. for the photoreaction in Eq. (40) [157,158]. In this work, the authors proposed that the impedance under illumination could be estimated from the ratio between the AC photopotential under chopped illumination and the AC photocurrent responses. Subsequently, the faradaic impedance was calculated following a treatment similar to that described in Eqs. (22) to (26), i.e., subtracting the impedance under illumination and in the dark. From this analysis, a pseudo-first-order photoinduced ET rate constant of the order of 10 to 10 ms was estimated, corresponding to a rather unrealistic ket > 10 M cms . Considering the nonactivated limit for adiabatic outer sphere heterogeneous ET at liquid-liquid interfaces given by Eq. (17) [5], the maximum bimolecular rate constant is approximately 1000 smaller than the values reported by these authors. 

The motion of molecules in a liquid has a significant effect on the kinetics of chemical reactions in solution. Molecules must diffuse together before they can react, so their diffusion constants affect the rate of reaction. If the intrinsic reaction rate of two molecules that come into contact is fast enough (that is, if almost every encounter leads to reaction), then diffusion is the rate-limiting step. Such diffusion-controlled reactions have a maximum bimolecular rate constant on the order of 10 ° L mol s in aqueous solution for the reaction of two neutral species. If the two species have opposite charges, the reaction rate can be even higher. One of the fastest known reactions in aqueous solution is the neutralization of hydronium ion (H30 ) by hydroxide ion (OH ) ... 

Exceptions are expected to arise when the driving force for a reaction is an irreversible proton transfer at the diffusion-controlled limit in water or a similar protic solvent. With a maximum bimolecular rate constant of 10 L/mol-s and a solvent concentration of 55.5 mol/L (pure water), a reactive intermediate could conceivably have a concentration as low as 10 mol/L and the reaction still proceed at a reasonable rate. 

A minor component, if truly minute, can be discounted as the reactive form. To continue with this example, were KCrQ very, very small, then the bimolecular rate constant would need to be impossibly large to compensate. The maximum rate constant of a bimolecular reaction is limited by the encounter frequency of the solutes. In water at 298 K, the limit is 1010 L mol-1 s"1, the diffusion-controlled limit. This value is derived in Section 9.2. For our immediate purposes, we note that one can discount any proposed bimolecular step with a rate constant that would exceed the diffusion-controlled limit. 

The ratio of maximum velocity, F ax, or kcat value to the true value for a particular substrate, with units of a bimolecular rate constant M sIn comparing substances that act as substrates for a single enzyme, a higher Fmax/ m or kgat/ m fafio rcflects a higher apparent rate of enzyme-substrate complexation. 

The kinetic course of the process is much simpler if the reaction takes place in excess of alcohol. In this case, the maximum reaction rate is observed in the very beginning of the reaction and the rate is described by the kinetics of a simple successive bimolecu-lar (actually, quasi-bimolecular) reaction 55). This procedure has been used by most researchers studying the kinetics of reactions of epoxy compounds with amines 50, 55-63) Unfortunately, the kinetic parameters obtained by different authors cannot be correlated since they depend on the nature of the alcohol used, exhibiting an increase with its acidity 55 56). On the other hand, the reaction rate constants obtained by using this approach are expected to depend on alcohol concentration and their values vary considerably. Nevertheless, a comparative study of the quasi-bimolecular rate constants under the same experimental conditions may serve for comparison. 

The maximum value for the bimolecular rate constant occurs when the activation energy act is zero and the steric factor is 1. The rate is then said to be diffusion-controlled, and it is equal to the encounter frequency of the molecules. Assuming that the reacting molecules are uncharged spheres of radius rA and rB, the encounter frequency may be calculated as... 

All bimolecular rate constants level off in a viscous media (the maximum value being that of the diffusion rate constant). 

Rate constants of bimolecular, micelle-assisted, reactions typically go through maxima with increasing concentration of inert surfactant (Section 3). But a second rate maximum is observed in very dilute cationic surfactant for aromatic nucleophilic substitution on hydrophobic substrates. This maximum seems to be related to interactions between planar aromatic molecules and monomeric surfactant or submicellar aggregates. These second maxima are not observed with nonplanar substrates, even such hydrophobic compounds as p-nitrophenyl diphenyl phosphate (Bacaloglu, R. 1986, unpublished results). 

The major part of the reports discussed above provides only a qualitative description of the catalytic response, but the LbL method provides a unique opportunity to quantify this response in terms of enzyme kinetics and electron-hopping diffusion models. For example, Hodak et al. [77[ demonstrated that only a fraction of the enzymes are wired by the polymer. A study comprising films with only one GOx and one PAH-Os layer assembled in different order on cysteamine, MPS and MPS/PAH substrates [184[ has shown a maximum fraction of wired enzymes of 30% for the maximum ratio of mediator-to-enzyme, [Os[/[GOx[ fs 100, while the bimolecular FADH2 oxidation rate constant remained almost the same, about 5-8 x 10 s ... 

The rate constants k and k+ in Table 5.1 are related through the CMC value and are thus not independent. In obtaining a molecular interpretation of the rate constants it seems most convenient to focus attention on the rate of the combination reaction, i.e., on k+. In the absence of long-range forces, the maximum diffusion-controlled rate of a bimolecular reaction is... 

As overlap of orbitals is necessary for energy transfer by an exchange mechanism, the maximum efficiency one would expect for this process corresponds to a diffusion controlled reaction. The rate constant for any bimolecular reaction, which depends only on the rate of diffusion of the reactants together, may be estimated from the following formula derived by Debye21... 

A.2.2. Diffusion-Controlled Rate Constant Recently, we have calculated the diffusion-controlled (i.e., attainable maximum) rate constant of ET at an OAV interface [49]. Figure 8.8 shows models for diffusion-controlled bimolecular reactions (a) in homogeneous solution and (b) at an O/W interface. 

There seems little doubt that in radiation induced polymerizations the reactive entity is a free cation (vinyl ethers are not susceptible to free radical or anionic polymerization). The dielectric constant of bulk isobutyl vinyl ether is low (<4) and very little solvation of cations is likely. Under these circumstances, therefore, the charge density of the active centre is likely to be a maximum and hence, also, the bimolecular rate coefficient for reaction with monomer. These data can, therefore, be regarded as a measure of the reactivity of a non-solvated or naked free ion and bear out the high reactivity predicted some years ago [110, 111]. The experimental results from initiation by stable carbonium ion salts are approximately one order of magnitude lower than those from 7-ray studies, but nevertheless still represent extremely high reactivity. In the latter work the dielectric constant of the solvent is much higher (CHjClj, e 10, 0°C) and considerable solvation of the active centre must be anticipated. As a result the charge density of the free cation will be reduced, and hence the lower value of fep represents the reactivity of a solvated free ion rather than a naked one. Confirmation of the apparent free ion nature of these polymerizations is afforded by the data on the ion pair dissociation constant,, of the salts used for initiation, and, more importantly, the invariance, within experimental error, of ftp with the counter-ion used (SbCl or BF4). Overall effects of solvent polarity will be considered shortly in more detail. 

---