# Diffusion-controlled reaction

Diffusion-controlled reaction

Diffusion-controlled (or diffusion-limited) reactions are reactions that occur so quickly that the reaction rate is the rate of transport of the reactants through the reaction medium (usually a solution).[1] As quickly as the reactants encounter each other, they react. The process of chemical reaction can be considered as involving the diffusion of reactants until they encounter each other in the right stoichiometry and form an activated complex which can form the product species. The observed rate of chemical reactions is, generally speaking, the rate of the slowest or "rate determining" step. In diffusion controlled reactions the formation of products from the activated complex is much faster than the diffusion of reactants and thus the rate is governed by diffusion.

Diffusion control is rare in the gas phase, where rates of diffusion of molecules are generally very high. Diffusion control is more likely in solution where diffusion of reactants is slower due to the greater number of collisions with solvent molecules. Reactions where the activated complex forms easily and the products form rapidly are most likely to be limited by diffusion control. Examples are those involving catalysis and enzymatic reactions. Heterogeneous reactions where reactants are in different phases are also candidates for diffusion control.

One classical test for diffusion control is to observe whether the rate of reaction is affected by stirring or agitation; if so then the reaction is almost certainly diffusion controlled under those conditions.

## Applications in biology

The theory of diffusion-controlled reaction was originally utilized by R.A. Alberty, G.G. Hammes, and Manfred Eigen to estimate the upper limit of enzyme-substrate reaction [2] [3] According to their estimation [2][3], the upper limit of enzyme-substrate reaction was 109 / Msec.

In 1972, it was observed that in the dehydration of H2CO3 catalyzed by carbonic anhydrase, the second-order rate constant obtained experimentally was about $1.5 \times 10^{10}/\text{Msec}$, [4] which was one order of magnitude higher than the upper limit estimated by Alberty, Hammes, and Eigen based on a simplified model[2][3]. However, after taking into account the spatial factor and force field factor between the enzyme and its substrate, Kuo-Chen Chou and co-workers found that the upper limit could reach 1010 / Msec, [5] [6] [7] and can be used to explain some surprisingly high reaction rates in molecular biology. [4] [8] [9]

The new upper limit found by Chou et al. for enzyme-substrate reaction was further confirmed by a series of follow-up studies (see, e.g., [10] [11]). A detailed comparison between the simplified Alberty-Hammes-Eigen’s model and the Chou’s model was elaborated in the paper. [12]

## References

1. ^ Atkins, Peter (1998), Physical Chemistry (6th ed.), New York: Freeman, pp. 825–828
2. ^ a b c Alberty R. A., Hammes G. G. (1958) Application of the theory of diffusion-controlled reactions to enzyme kinetics. J. Phys. Chem. 62, 154-159.
3. ^ a b c Eigen M., Hammes G. G. (1963) Elementary steps in enzyme reactions (as studies by relaxation spectrometry). Advances In Enzymology and Related Subjects of Biochemistry 25, 1-38.
4. ^ a b Koening S. H., Brown R. D. (1972) H2CO3 as substrate for carbonic anhydrase in the dehydration of H2CO3-. Proc Natl Acad Sci USA 69, 2422-2425.
5. ^ Chou K. C., Jiang S. P. (1974) Studies on the rate of diffusion-controlled reactions of enzymes. Scientia Sinica 17, 664-680.
6. ^ Kuo-Chen Chou (1976) The kinetics of the combination reaction between enzyme and substrate. Scientia Sinica 19, 505-528.
7. ^ Li T. T., Chou K. C. (1976) The quantitative relations between diffusion-controlled reaction rate and characteristic parameters in enzyme-substrate reaction system: 1. Neutral substrate. Scientia Sinica 19, 117-136.
8. ^ Riggs A. D., Bourgeois S., Cohn M. (1970) The lac repressor-operator interaction. 3. Kinetic studies. Journal of Molecular Biology 53, 401-17.
9. ^ Kirschner K., Gallego E., Schuster I., Goodall D. (1971) Co-operative binding of nicotinamide-adenine dinucleotide to yeast glyceraldehyde-3-phosphate dehydrogenase. I. Equilibrium and temperature-jump studies at pH 8-5 and 40 degrees C. Journal of Molecular Biology 58, 29-50.
10. ^ Chou K. C., Zhou G. P. (1982) Role of the protein outside active site on the diffusion-controlled reaction of enzyme. Journal of American Chemical Society 104, 1409-1413.
11. ^ Zhou G. Z., Wong M. T., Zhou G. Q. (1983) Diffusion-controlled reactions of enzymes. An approximate analytic solution of Chou's model. Biophys Chem 18, 125-32.
12. ^ Zhou G. Q., Zhong W. Z. (1982) Diffusion-controlled reactions of enzymes. A comparison between Chou's model and Alberty-Hammes-Eigen's model. Eur J Biochem 128, 383-7.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Reaction–diffusion system — Reaction–diffusion systems are mathematical models which explain how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are transformed… …   Wikipedia

• Reaction rate — Iron rusting a chemical reaction with a slow reaction rate. Wood …   Wikipedia

• Diffusion control — refers to reactions whose rate is governed by transport of the reactants through the reaction medium (usually a solution). The process of chemical reaction can be considered as involving the diffusion of reactants till they encounter each other… …   Wikipedia

• reaction mechanism — Introduction       in chemical reactions (chemical reaction), the detailed processes by which chemical substances are transformed into other substances. The reactions themselves may involve the interactions of atoms (atom), molecules (molecule),… …   Universalium

• electrochemical reaction — ▪ chemistry Introduction       any process either caused or accompanied by the passage of an electric current and involving in most cases the transfer of electrons between two substances one a solid and the other a liquid.       Under ordinary… …   Universalium

• Chemical reaction — Chemical reactions redirects here. For the 2007 television episode, see Chemical Reactions (Men in Trees). A thermite reaction using iron(III) oxide. The sparks …   Wikipedia

• cell — cell1 cell like, adj. /sel/, n. 1. a small room, as in a convent or prison. 2. any of various small compartments or bounded areas forming part of a whole. 3. a small group acting as a unit within a larger organization: a local cell of the… …   Universalium

• Corrosion — v · d · e Materials failure modes Buckling · …   Wikipedia

• Marcus theory — is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called …   Wikipedia

• Cyclic voltammetry — Typical cyclic voltammogram where ipc and ipa show the peak cathodic and anodic current respectively for a reversible reaction. Cyclic voltammetry or CV is a type of potentiodynamic electrochemical measurement. In a cyclic voltammetry experiment… …   Wikipedia