Chemical potential variation with distance

Fig. 9.1. Variation of potential energy with A-B and B-C distances for an ABC system in which the A-B-C angle is held fixed. [Adapted from K. J. Laidler, Chemical Kinetics (New York McGraw-Hill, 1965).]...

Hydrod5mamics is basically a classical theory and consequently the effects of the uncertainty principle can be neglected for the hydrodynamic variables. To see this in detail we suppose the variation in the thermodynamic variables, temperature, chemical potential, and velocity, to be characterized by a length / over distances of the order I these variables change by small amounts. One may then divide the system into volume elements with linear dimensions of the order a, and if < / the microscopic variables at a point may be replaced by their averages over the corresponding volume element. Now a particle can be localized to a region with dimensions of the order A = Uff, where for we may take the mean momentum per particle, or... 

Reactions between neutrals include atom/radical + radical and atom/radical + molecule reactions. As discussed above, the intermolecular forces are shorter range than is the case with ion-molecule reactions, so that it is necessary to consider chemical interactions explicitly when modelling a reaction. After a section on experimental methods, the ideas behind transition state (TS) theory and its variational modification are discussed, together with theories of reactions where the TS switches, as the temperature increases, from A-B distances mainly controlled by the potential arising from electrostatic interaction to shorter distances where chemical forces are important. While the pressure in the ISM is too low for pressure dependent reactions, this topic is important in the conditions used to measure rate coefficients and in the chemistry of planetary atmospheres, including those of the exoplanets (see Chap. 5). This topic is discussed in Sect. 3.4.4, which also introduces the ideas that lie behind master equation models, which are widely used for such reactions. These models can also be used for reactions in which the adduct AB from an A + B reaction dissociates into several products, and these ideas are discussed in Sect. 3.4.5. Section 3.4 concludes with discussion of two examples of neutral + neutral reactions. 

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