Diffusion control rates

Collins F C and Kimball G E 1949 Diffusion-controlled rate processes J. Colloid Sol. 4 425... 

Pulse radiolysis results (74) have led other workers to conclude that adsorbed OH radicals (surface trapped holes) are the principal oxidants, whereas free hydroxyl radicals probably play a minor role, if any. Because the OH radical reacts with HO2 at a diffusion controlled rate, the reverse reaction, that is desorption of OH to the solution, seems highly unlikely. The surface trapped hole, as defined by equation 18, accounts for most of the observations which had previously led to the suggestion of OH radical oxidation. The formation of H2O2 and the observations of hydroxylated intermediate products could all occur via... 

Kinetic studies have shown that the enolate and phosphorus nucleophiles all react at about the same rate. This suggests that the only step directly involving the nucleophile (step 2 of the propagation sequence) occurs at essentially the diffusion-controlled rate so that there is little selectivity among the individual nucleophiles. The synthetic potential of the reaction lies in the fact that other substituents which activate the halide to substitution are not required in this reaction, in contrast to aromatic nucleophilic substitution which proceeds by an addition-elimination mechanism (see Seetion 10.5). 

Consider a dilute solution of two reactant molecules, A and B. Inevitably an A molecule and a B molecule will undergo an encounter, the frequency of such encounters depending upon the concentrations of A and B. If, upon each encounter of A and B, they undergo bimolecular reaction, then the rate of this reaction is determined solely by the rate of encounter of A and B that is, the rate is not controlled by the chemical requirement that an energy barrier be overcome. One way to find this rate is to treat the problem as one of classical diffusion, and so this maximum possible rate of reaction is often called the diffusion-controlled rate. This problem was solved by Smoluchowski. In the following development no provision is made for attractive forces between the molecules. ... 

Enzymes Whose Acat/Approaches the Diffusion-Controlled Rate of Association with Substrate ... 

The result of the fast reactions in the ion source is the production of two abundant reagent ions (CH5+ and C2H5+) that are stable in the methane plasma (do not react further with neutral methane). These so-called reagent ions are strong Brpnsted acids and will ionize most compounds by transferring a proton (eq. 7). For exothermic reactions, the proton is transferred from the reagent ion to the neutral sample molecule at the diffusion controlled rate (at every collision, or ca. 10 9 s 1). 

Most radicals are transient species. They (e.%. 1-10) decay by self-reaction with rates at or close to the diffusion-controlled limit (Section 1.4). This situation also pertains in conventional radical polymerization. Certain radicals, however, have thermodynamic stability, kinetic stability (persistence) or both that is conferred by appropriate substitution. Some well-known examples of stable radicals are diphenylpicrylhydrazyl (DPPH), nitroxides such as 2,2,6,6-tetramethylpiperidin-A -oxyl (TEMPO), triphenylniethyl radical (13) and galvinoxyl (14). Some examples of carbon-centered radicals which are persistent but which do not have intrinsic thermodynamic stability are shown in Section 1.4.3.2. These radicals (DPPH, TEMPO, 13, 14) are comparatively stable in isolation as solids or in solution and either do not react or react very slowly with compounds usually thought of as substrates for radical reactions. They may, nonetheless, react with less stable radicals at close to diffusion controlled rates. In polymer synthesis these species find use as inhibitors (to stabilize monomers against polymerization or to quench radical reactions - Section 5,3.1) and as reversible termination agents (in living radical polymerization - Section 9.3). 

The reaction between nitroxides and carbon-centered radicals occurs at near (but not at) diffusion controlled rates. Rate constants and Arrhenius parameters for coupling of nitroxides and various carbon-centered radicals have been determined.508 311 The rate constants (20 °C) for the reaction of TEMPO with primary, secondary and tertiary alkyl and benzyl radicals are 1.2, 1.0, 0.8 and 0.5x109 M 1 s 1 respectively. The corresponding rate constants for reaction of 115 are slightly higher. If due allowance is made for the afore-mentioned sensitivity to radical structure510 and some dependence on reaction conditions,511 the reaction can be applied as a clock reaction to estimate rate constants for reactions between carbon-centered radicals and monomers504 506"07312 or other substrates.20... 

Stable radicals can show selectivity for particular radicals. For example, nitroxides do not trap oxygcn-ecntcrcd radicals yet react with carbon-ccntcrcd radicals by coupling at or near diffusion controlled rates.179,184 This capability was utilized by Rizzardo and Solomon181 to develop a technique for characterizing radical reactions and has been extensively used in the examination of initiation of radical polymerization (Section 3.5.2.4). In contrast DPPH, w hile an efficient... 

Prior to the development of NMP, nitroxides were well known as inhibitors of polymerization (Section 5.3.1). They and various derivatives were (and still are) widely used in polymer stabilization. Both applications are based on the property of nitroxides to efficiently scavenge carbon-centered radicals by combining with them at near diffusion-controlled rates to form alkoxyamines. This property also saw nitroxides exploited as trapping agents to define initiation mechanisms (Section 3.5.2.4). 

All these results are consistent with the hypothesis that aryl cations react in aqueous media at diffusion-controlled rates with all nucleophiles that are available in the immediate neighbourhood of the diazonium ion. On this basis Romsted and coworkers (Chaudhuri et al., 1993a, 1993b) used dediazoniation reactions as probes of the interfacial composition of association colloids. These authors determined product yields from dediazoniation of two arenediazonium tetrafluoroborates containing ft-hexadecyl residues (8.15 and 8.16) and the corresponding diazonium salts with methyl groups instead of Ci6H33 chains. ... 

When die potential of the OTE is stepped to a value such that reaction (2-16) proceeds at a diffusion-controlled rate, die tune-dependent absorbance of R is given by... 

With this expression, kjkn can be obtained by the measurement of one set of [RI ], [R2 ] values, at full light intensity only. As to kii itself, which is needed to evaluate kc, one must either do a separate experiment by time-resolved EPR spectroscopy (see Chapter 11) or, with less accuracy and reliability, one can assign it the value for the diffusion-controlled rate constant in that solvent. 

Most of the chemical reactions presented in this book have been studied in homogeneous solutions. This chapter presents a conceptual and theoretical framework for these processes. Some of the matters involve principles, such as diffusion-controlled rates and applications of TST to questions of solvent effects on reactivity. Others have practical components as well, especially those dealing with salt effects and kinetic isotope effects. 

This value, often approximated as 1010 L mol"1 s 1, is referred to as the diffusion-controlled rate constant. It is rather insensitive to the chemical species that participate in the reaction. A larger molecule diffuses more slowly than a smaller one, but that effect is roughly compensated by a higher probability of encounter given its larger radius. 

For entities of molecular size the numerical coefficient in the denominator of Eq. (9-12) should be reduced from 6 to 4 or less,6 which would also alter the expression for the diffusion-controlled rate constant from the traditional form given in Eq. (9-13) ... 

Values of diffusion-controlled rate constants at 298 K calculated for different solvents according to Eq. (9-13)... 

The temperature dependence of a diffusion-controlled rate constant is very small. Actually, it is just the temperature coefficient of the diffusion coefficient, as we see from the von Smoluchowski equation. Typically, Ea for diffusion is about 8-14 kJ mol"1 (2-4 kcal mol-1) in solvents of ordinary viscosity. 

Influence" of ionic charges on second-order diffusion-controlled rate constants in aqueous solution at 25 °C... 

In an aqueous solution, solute molecules or ions require a certain amount of time to migrate through the solution. The rate of this migration sets an upper limit on how fast reactions can take place, because no reaction can take place faster than the ions can he supplied. This limit is known as the diffusion-controlled rate. It has been found that the diffusion rate for hydrogen ions is about three times as fast as that for other ions in aqueous solution. Explain why this is so. 

Alkoxy (R0 ) radicals react at near diffusion controlled rates with trialkyl phosphites to give phosphoranyl radicals [ROP(OR )3] that typically undergo very fast -scission to generate alkyl radicals (R ) and phosphates [OP(OR )3]. In a mechanistic study, trimethyl phosphite, P(OMe)3, has been used as an efficient and selective trap in oxiranylcarbinyl radical systems formed from haloepoxides under thermal AIBN/n-Bu3SnH conditions at about 80 °C (Scheme 27) [64]. The formation of alkenes resulting from the capture of allyloxy radicals by P(OMe)3 fulfils a prior prediction that, under conditions close to kinetic control, products of C-0 cleavage (path a. Scheme 27), not just those of C-C cleavage (path b. Scheme 27) may result. 

Nielsen, A.E. (1959b) The kinetics of crystal growth in barium sulphate precipitation. 111. Mixed surface reaction and diffusion-controlled rate of growth. Acta Chem. Scand., 13, 1680-1686. 

The feedback mode [Fig. 2(a)] is one of the most widely used SECM techniques, applicable to the study of interfacial ET processes. The basic idea is to generate a species at the tip in its oxidized or reduced state [generation of Ox] in Fig. 2(a)], typically at a diffusion-controlled rate, by electrolysis of the other half of a redox couple (Redj). The tip-generated species diffuses from the UME to the target interface. If it undergoes a redox... 

At time t > 0, the potential of the UME tip is stepped from a value where no electrode reaction occurs, to one sufficient to drive the oxidation of Red] at a diffusion-controlled rate. Species Red] is assumed to be inert with respect to the insulating glass sheath surrounding the electrode and to remain at bulk concentration values beyond the radial edge of the tip (throughout phase 1). In phase 2, species Red2 attains its bulk... 

A potential step is subsequently applied to the UME in phase 1, sufficient to electrolyze Red] at the tip, at a diffusion-controlled rate. This perturbs the interfacial equilibrium, inducing the transfer of the target species across the interface, from phase 2 to phase 1, as shown in Fig. 10. 

For these investigations, the UME was positioned in the aqueous subphase containing 0.1 M KNO3 and held at a potential to reduce oxygen at a diffusion-controlled rate, in order to promote the transfer of O2 from air (phase 2) to the aqueous solution (phase 1), with subsequent collection at the tip (Fig. 27). Under SECMIT conditions, the flux of oxygen from air to water is given by ... 

---