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Crush hour in the test-tube

Overcrowding spoils the law of mass action

Munich, 03/07/2012

The rate at which two chemical species react with one another is partly determined by the probability that they will collide. The so-called law of mass action explicitly takes account of this fact, stating that the reaction rate is dependent on the product of the concentrations of participating reactants. With the aid of mathematical modeling, LMU Professor Erwin Frey and his PhD student Anton Winkler at the Arnold Sommerfeld Center for Theoretical Physics have taken a new look at the validity of the law. They show that it is violated when particle densities become sufficiently high. As Professor Frey explains, “The deviation can be attributed to so-called many-body effects, and its magnitude can be derived from the number of elementary reactions per unit time.” (Physical Review Letters, 5.3.2012)

At the most basic level, physical laws describe the effects of forces that act between two particles only, but interactions in large collections of particles can lead to unforeseen phenomena. The LMU researchers have developed a theory to investigate the role of many-body effects on chemical reaction rates. An example of a simple reaction is the formation of stable molecular hydrogen (H2) from two hydrogen atoms (H). At low particle densities, the reaction rate given by the model agrees precisely with that predicted by the law of mass action. “However, as the concentration of the reactants is increased, the law is violated,” says Anton Winkler. “We can explain the deviations by invoking many-body effects that lead to unexpectedly strong correlations.”

The deviations that appear are of a universal nature, i.e. are independent of parameters such as the size or shape of reacting particles. Furthermore, they are directly related to the underlying reaction rate, defined as the number of elementary reactions per unit time. However, the violations are so small that it constitutes a significant challenge to measure them. Nevertheless, Frey and Winkler are confident that the new theory can be tested experimentally. The work was carried out under the auspices of the Nanosystems Initiative Munich (a Cluster of Excellence) and supported by DFG Collaborative Research Center TR12 (Symmetries and Universality in Mesoscopic Systems). (rüth/göd)

On the Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes
Anton Winkler, Erwin Frey
DOI: 10.1103/PhysRevLett.108.108301

Prof. Dr. Erwin Frey
Institute of Statistical and Biological Physics, LMU
Phone: +49 89 / 2180 – 4538


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