Detailed balance, significance

One of the most significant recent insights in surface chemical dynamics is the idea that the principle of detailed balance may be used to infer the properties of a dissociative adsorption reaction from measurements on an associative desorption reaction.51,52 This means, for example, that the observation of vibrationally-excited desorption products is an indicator that the dissociative adsorption reaction must be vibrationally activated, or vice versa the observation of vibrationally-cold desorption products indicates little vibrational promotion of dissociative adsorption. In this spirit, it is... 

They also first proposed the use of detailed balance to relate dissociative adsorption to associative desorption. In hindsight, both the experiments and the PES derived by them to fit the experiments were in significant quantitative error, but this in no way minimizes the major contribution of this early work to the development of reactive gas-surface dynamics. 

Quantum calculations of spectral profiles based on Eqn. (3) are known isotropic interaction is commonly assumed. Such quantum calculations account for detailed balance in exact ways and consider not only the free-state to free-state transitions of binary complexes but also the bound-free and bound-bound transitions involving bound van der Waals pairs that are an inseparable part of the CILS spectra. These bound-free and bound-bound components can be quite significant, especially at the lower temperatures and for massive systems [266, 302, 328] see also related work on dimer spectra [262, 263], and the review papers on CILS lineshapes [227, 231, 271]. Lineshape calculations are useful for the detailed comparison of the fundamental theory with spectroscopic measurements. For helium pairs, a close agreement between the fundamental theory and the recent measurements is now observed similarly for the neon pair [45]. 

At sufficiently low temperature only the two funnels will be significantly occupied at equilibrium. Therefore, provided that the initial probability is itself eonfined to the funnels, Pa(0 + Pb(0 = 1- Using this equation and the detailed balance condition k-P — k P ), integration of Eq. (1.51) gives the basic result of first-order kinetics for a two-state model ... 

In one experiment (224), Zare and co-workers measured the j distributions of H2 and D2 desorbed from the Cu(110) and Cu(lll) surfaces. They found that although these distributions had a mean rotational energy somewhat less than kHTs (where kH is the Boltzmann constant and Ts is the surface temperature), they did not deviate significantly from a Boltzmann distribution. Since the measured rotational state distributions seemed to have enhance populations at low j, application of the principle of detailed balancing led Zare and co-workers to propose that rotation might slightly hinder dissociative chemisorption. 

The most significant consequence of this principle for kineticists is that if in a system at equilibrium there is a flow of reacting molecules along a particular reaction path, there must be an equal flow in the opposite direction. This principle implies that the reaction path established as most probable for the forward direction must also be the most probable path for the reverse reaction. This consequence is also known as the principle of detailed balancing of chemical reactions. Its relationship to the principle of microscopic reversibility has been discussed by Denbigh (19). If we consider a substance that can exist in three intraconvertible isomeric forms, A, B, and C (e.g., frani-butene-2, cw-butene-2, and butene-1), there is more than one independent reaction that occurs at equilibrium. The conditions for thermodynamic equilibrium would be satisfied if there were a steady unidirectional flow at the molecular level around the cycle... 

Ratner and Levine assumed that in the precursor and successor complexes, one can define thermodynamic properties for the individual partners, (A" ), (B ), (A ) and (B ). This amounts to assuming that there is no significant bonding between the partners in the precursor and successor complexes. For such a condition, it was shown earlier by Levine that detailed balance requires that the free energies of the precursor and successor complexes must be equal, so that... 

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