Diffusion-controlled collision

Approximation refers to the bringing together of the substrate molecules and reactive functionalities of the enzyme active site into the required proximity and orientation for rapid reaction. Consider the reaction of two molecules, A and B, to form a covalent product A-B. For this reaction to occur in solution, the two molecules would need to encounter each other through diffusion-controlled collisions. The rate of collision is dependent on the temperature of the solution and molar concentrations of reactants. The physiological conditions that support human life, however, do not allow for significant variations in temperature or molarity of substrates. For a collision to lead to bond formation, the two molecules would need to encounter one another in a precise orientation to effect the molecular orbitial distortions necessary for transition state attainment. The chemical reaction would also require... 

The kinetic problem for the intramolecular cross-linking reactions in general form was not yet solved. Only some particular cases, i.e. the cvclization of macromolecules, the intramolecular catalysis and diffusion-controlled collision of two reactive groups were studied theoretically bv Xorawetz, Sisido and Fixman... 

Marcus12 and others13 extended this model to include reactions in which electron transfer occurred during collisions between the donor and acceptor species, that is, between the short-lived Dn—Am complexes. In this context, electron transfer within transient precursor complexes ([Dn — A" in Scheme 1.1) resulted in the formation of short-lived successor complexes ([D(, + — A(m 1)] in Scheme 1.1). The Debye-Smoluchowski description of the diffusion-controlled collision frequency between D" and A " was retained. This has important implications for application of the Marcus model, particularly where—as is common in inorganic electron transfer reactions—charged donors or acceptors are involved. In these cases, use of the Marcus model to evaluate such reactions is only defensible if the collision rates between the reactants vary with ionic strength as required by the Debye-Smoluchowski model. The requirements of that model, and how electrolyte theory can be used to verify whether a reaction is a defensible candidate for evaluation using the Marcus model, are presented at the end of this section. 

Molecules in solution move haphazardly under the influence of thermal motion, and the rate at which they encounter one another will depend on their size and their diffusion coefficients (see Section 4.5 for details of diffusion). Large molecules will present larger targets for collision, but will also tend to have smaller diffusion coefficients, so will diffuse more slowly. This leads to an expression for the diffusion-controlled collision frequency ... 

Q Diffusion coefficients for small molecules in water at room temperature are about 1.5x 10 m s . What would be the diffusion controlled collision frequency assuming an encounter distance of 0.5 nm ... 

EXAMPLE 18.2 Diffusion-controlled rate. Compute the diffusion-controlled collision rate with a protein sphere having radius a = 10 A for benzene, which has a diffusion constant D = 1 x 10 cm sec. Equation (18.26) gives... 

We therefore find that under stagnant and neutral buoyancy conditions, the relative rate of diffusion controlled collision is dominated by the radius of the antifoam drops—the larger the drops, the slower the rate of collision because both the number concentration and the diffusion coefficients of drops are lower. Increasing viscosity of the detergent liquid and decreasing the volume fraction of the antifoam also both decrease the rate of flocculation. 

The above equation and other related classical treatments of the role of diffusion in solution kinetics (see references in Berg von Hippel, 1985) have been used to calculate the upper limits of the rates of second order reactions. This limit is usually defined as the diffusion controlled collision rate. This equation is only strictly applicable to spherical molecules with uniform reactivity over the two surfaces at a centre to centre distance equal to r/ +r and has been shown to have other theoretical limitations (Collins Kimball, 1949). 

Caldin E F, de Forest L and Queen A 1990 Steric and repeated collision effects in diffusion-controlled reactions in solution J. Chem. See. Faraday Trans. 86 1549-54... 

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). 

One facet of kinetic studies which must be considered is the fact that the observed reaction rate coefficients in first- and higher-order reactions are assumed to be related to the electronic structure of the molecule. However, recent work has shown that this assumption can be highly misleading if, in fact, the observed reaction rate is close to the encounter rate, i.e. reaction occurs at almost every collision and is limited only by the speed with which the reacting entities can diffuse through the medium the reaction is then said to be subject to diffusion control (see Volume 2, Chapter 4). It is apparent that substituent effects derived from reaction rates measured under these conditions may or will be meaningless since the rate of substitution is already at or near the maximum possible. 

All of the examples of singlet energy transfer we have considered take place via the long-range resonance mechanism. When the oscillator strength of the acceptor is very small (for example, n-> n transitions) so that the Fdrster critical distance R0 approaches or is less than the collision diameter of the donor-acceptor pair, then all evidence indicates that the transfer takes place at a diffusion-controlled rate. Consequently, the transfer mechanism should involve exchange as well as Coulomb interaction. Good examples of this type of transfer have been provided by Dubois and co-workers.(47-49)... 

Based upon their data and upon results in the literature, the authors concluded that hydrogenations using 24 or related species as catalyst precursor proceed in solution by mechanisms involving iridium(I)/(III) formal oxidation states. During the course of their discussions, the authors made the interesting observation that the rate of gas-phase collisions between the thermalized iridium organometallic ions and D2 under their experimental conditions in the oc-topole were similar to the rate of diffusion-controlled encounters between iridium species and D2 in solution. 

In fact, the only kinetic limitation to such a reaction is the speed at which they move through solution before the collision that forms product. This rate is itself dictated by the speed of diffusion (which is not generally an efficient form of transport). The rate of reactants colliding is, therefore, said to be diffusion controlled . Typically, diffusion-controlled processes in which Ea is tiny involve radical intermediates. 

The formation of excimers and exciplexes are diffusion-controlled processes. The photophysical effects are thus detected at relatively high concentrations of the species so that a sufficient number of collisions can occur during the excited-state lifetime. Temperature and viscosity are of course important parameters. 

The maximum value of ki is limited by the diffusion-controlled rate for collision between two molecules. For a small molecule binding to a macromolecular receptor, this rate is of the order of 10 to 10 M -s If the rates deviate from this markedly it suggests that the interaction of ligand with receptor is more complex. 

If ki and k.i are much larger than kj, the reaction Is controlled by kj. If however, ki and k.i are larger than or comparable to kz, the reaction rate becomes controlled by the translational diffusion determining the probability of collisions which Is typical for specific diffusion control. The latter case Is operative for fast reactions like fluorescence quenching or free-radical chain reactions. The acceleration of free-radical polymerization due to the diffusion-controlled termination by recombination of macroradicals (Trommsdorff effect) can serve as an example. 

Pick s laws describe the interactions or encounters between noninteracting particles experiencing random, Brownian motion. Collisions in solution are diffusion-controlled. As is discussed in most physical chemistry texts , by applying Pick s Pirst Law and the Einstein diffusion relation, the upper limit of the bimolecular rate constant k would be equal to... 

M -sec k The corresponding upper limit value for a bimolecular rate constant in the gas phase is about 10 M -sec k Thus in solutions, bimolecular rate constants cannot exceed 10 -10 M -sec since diffusion control takes over from collision control. 

A reaction velocity equal to the rate of encounter of reacting molecular entities (also known as diffusion-con-trolled rate). For a bimolecular reaction in aqueous solutions at 25°C, the corresponding second-order rate constant for the encounter-controlled rate is typically about 10 ° M s See Diffusion Control for Bimolecular Collisions in Solution... 

STEREOCHEMICAL TERMINOLOGY, lUPAC RECOMMENDATIONS ENANTIOSELECTIVE REACTION ASYMMETRIC INDUCTION ENCOUNTER COMPLEX ENCOUNTER-CONTROLLED RATE DIFFUSION CONTROL FOR BIMOLECULAR COLLISIONS ENDERGONIC PROCESS ENDO-a (or j8)-N-ACETYLGALACTOSAMI-NIDASE... 

If the electrostatic barrier is removed either by specific ion adsorption or by addition of electrolyte, the rate of coagulation (often followed by measuring changes in turbidity) can be described fairly well from simple diffusion-controlled kinetics and the assumption that all collisions lead to adhesion and particle growth. Overbeek (1952) has derived a simple equation to relate the rate of coagulation to the magnitude of the repulsive barrier. The equation is written in terms of the stability ratio ... 

Second, the room temperature rate constants increase with increasing size and complexity of the alkane and are of the order of 10-11 cm3 molecule-1 s-1 for the largest alkanes. To put this in perspective, a diffusion-controlled reaction, i.e., one that occurs on every collision of the reactants, is of the order of (3-5) X 10 10 cm3 molecule-1 s-1. Thus for the larger alkanes, reaction occurs in approximately one in 10 collisions, which is quite a fast process. 

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