Contact diffusion controlled reactions

Contact diffusion controlled reactions (without change of chemical nature of fluorophore)... 

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

In the literature there are several, mostly just slightly different, equations that describe the rate coefficient of the diffusion controlled reactions these equations are usually based on the solutions of Pick II diffusion law assuming that the reaction probability at contact distance is 1. Andre et al. [131] used the following equation to describe the time dependence of excited molecule concentration [RH ] produced by an infinite excitation pulse ... 

In homogeneous solution, molecule B can diffuse from all directions to react with molecule A. In a diffusion-controlled reaction, when the contact of molecules A and B immediately yields the products, the molar flux of B, across the spherical surface of the radius of tab (= ta + tb) aroimd the centre of molecule A can be given by... 

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 ) ... 

R is the distance between the molecular centers of TIM and GAP at contact]. For such a rapidly gated, diffusion-controlled reaction, the gated rate constant k is simply given by the rate constant for the enzyme with the gate held open,i°2 and, to the substrate, the gates appear to be open all the time. Thus,... 

Meanwhile this study reveals that a much shorter dwell time was needed to form a-alumina from the gel powder than the boehmite powder at 1000 °C. This is possibly due to the difference in the crystallinity and the morphology of the gel powder and the boehmite powder. The gel powder is amorphous, while the boehmite is nanocrystalline with several broad peaks in the XRD pattern. Amorphous state is less stable than the crystalline phase, therefore the activation energy required for the transformation to a-alumina will be lower for the amorphous gel powder. Meanwhile, the flaky morphology of the boehmite makes less available contact points which might help to retard the possible diffusion controlled reaction leading to grain growth followed by phase transformation. ... 

The CVD technique is based on the diffusion of a carbonbearing gas into a porous substrate and the diffusion-controlled reaction of the gas on the hot substrate into carbon and gaseous by-products. A variety of parameters (such as temperature, pressure, flow rate, substrate density, and surface area) affect the quality and structure of the deposited carbon and the deposition presents a difficult and complex problem. The present deposition conditions are based on empirical observations. Various CVD techniques have been developed for the infiltration of porous substrates. The most extensively utilized are the isothermal and the temperature gradient processes. The isothermal process technique is illustrated schematically in Fig. 4a. The substrate is heated by an induction-heated susceptor (graphite). If the hydrocarbon gas comes in contact with the hot substrate, carbon is deposited and gaseous by-products (mainly H2) are released. The disadvantage of this technique is the overcrusting of the outer... 

Problem 6.28 The bimolecular chain termination in free-radical polymerization is a diffusion-controlled reaction that can be treated as a three-stage process (North and Reid, 1963 Odian, 1991), described below. Stage 1. Translational diffusion of the centers of gravity of two macroradicals to such close proximity that certain segments of each chain can be considered to be in contact ... 

Bismuth.— Tlie rate of formation of Bi in an aqueous solution of BiCls in HCl in contact with metallic bismuth is a first-order process, occurring by two stages. The first stage is faster than the second and is a diffusion-controlled reaction with an activation energy of 1.8 kcalmol". The kinetics of formation and dissociation of [Bie(OH)i8] + have been investigated. Under equilibrium conditions the pressure-jump method gives a rate law... 

For spherical particles, diffusion-controlled reaction rates are given by Equation (18.25). Diffusion control implies that reactions are fast. Other reactions involve additional rate-limiting steps that occur after the reacting molecules have come into contact with the sphere. Diffusion control defines an upper limit on the speed of reactions. Any other kind of process must be slower than the diffusion-controlled process because the reaction must take additional time to complete after contact. Association rates are often expressed in terms of a rate coefficient ka defined by 1(a) = -kaC, where... 

The foregoing brief discussion on diffusion-controlled reactions serves to call attention to the importance of random translational diffusion as a means whereby reactant molecules can come into contact, and to the influence of intermolecular forces. In the present chapter, we continue to explore, with the aid of simple models, the motions of solute and solvent molecules that govern the rate at which reactive collisions occur. 

The reactions with the highest values of k in Table 2.1 are those where orientational requirements would be expected to be unimportant. Reaction usually occurs at specific sites on molecules a collision will not result in reaction unless the reactive sites come into contact. Supposing the relative orientations of the reactant molecules A and B to be random as they approach each other, only a fraction of the colliding pairs will be in the correct orientation for reaction. The chance that reaction will occur immediately on collision is therefore less than unity it will depend on the fraction of the surface of each reactant molecule that is reactive. But once the reactant pair have met, they will undergo a series of recollisions (cf. above) between which there will be time for some reorientation, which may result in the next collision being correctly oriented for reaction. The restricted reaction sites will reduce the rate below that of a diffusion-controlled reaction occurring at every collision, but the reduction will be less than it would have been if there were no repeated collisions. Some attempts have been made to formulate theories for this situation, as follows. 

Beside theoretical indications for the existence of exciplexes in the fluorescence quenching of DBO by tertiary amines, further experimental evidence was obtained by observation of steric effects. DBO fluorescence quenching by sterically hindered amines is accompanied by a marked drop of the rate constant, which leads to the straightforward conclusion that chromophore and quencher react at contact distances, which is expected for the formation of compact structures such as exciplexes [59]. Noteworthy, benzophenone as stronger electron acceptor is quenched highly unselectively by sterically hindered amines in a diffusion-controlled reaction [193,194]. 

The initial morphology of the reactants exerts considerable influence on the reaction kinetics, even in purely diffusion-controlled reactions. The oxydation of metal spheres of radius rM [496], which are not in contact with each other, is a comparatively simple case. The solution is the Carter equation [497] ... 

This section will only cover reactions in aqueous solutions. Water molecules acting as either a proton acceptor or a proton donor will thus be in close contact with an acid or a base undergoing excited-state deprotonation or protonation, respectively. Therefore, these processes will not be diffusion-controlled (Case A in Section 4.2.1). 

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