Kramers’ rate theory

The theory proposed by Halperin and Alexander (H-A theory) [60] is based on the structural scaling description of polymeric micelles outlined in Sect. 2.1.2. Using a combination of scaling theory and Kramers rate theory for diffusirai in an external potential [61], the expulsion rate for both crew-cut and star-like spherical micelles was derived. Moreover, Halperin and Alexander discussed different scenarios of chain exchange between micelles. 

For one-dimensional stationary flow in a potential well, Kramers rate theory gives the following expression for the outgoing flux, / ... 

The elements of the transition rate matrix A in the DRIS model are estimated from the multidimensional energy surface associated with the interdependent rotation of neighboring bonds u g Kramers rate theory, as described above. Accordingly, the probability of occurrence of a given isomeric state for a bond depends on the state of its first neighbors aloi the chain. Likewise, in the kinetic Ising model the transition rate Wi(Oi) of the i-th spin is assumed to be coupled to the state of its first iKighbors by the relation... 

The transition from k to on the low-pressure side ean be eonstnieted using iiiidtidimensional unimoleeular rate theory [1, 44], if one knows the barrier height for the reaetion and the vibrational frequeneies of the reaetant and transition state. The transition from to k y ean be deseribed in temis of Kramers theory [45]... 

This ensures the correct connection between the one-dimensional Kramers model in the regime of large friction and multidimensional imimolecular rate theory in that of low friction, where Kramers model is known to be incorrect as it is restricted to the energy diflfiision limit. For low damping, equation (A3.6.29) reduces to the Lindemann-Flinshelwood expression, while in the case of very large damping, it attains the Smoluchowski limit... 

Hanggi P, Talkner P and Borkovec M 1990 Reaction-rate theory fifty years after Kramers Rev. Mod. Phys. 62 251-341... 

Berezhkovskii A M, Berezhkovskii L M and Zitserman V Yu 1989 The rate constant in the Kramers multidimensional theory and th Chem. Phys. 130 55-63... 

Talkner P and Hanggi P (eds) 1995 New Trends in Kramers Reaction Rate Theory (Dordrecht Kluwer)... 

Hanggi, R, Talkner, P., Borkovec, M. Reaction-rate theory fifty years after Kramers. Revs Modern Phys. 62 (1990) 251-341. 

S. C. Tucker, Variational transition state theory in condensed phases, vaNew Trends in Kramers Reaction Rate Theory, P. Hanggi and P. Talkner (eds.), Kluwer Academic, The Netherlands, 1995, pp. 5—4-6. 

New Trends in Kramer s Reaction Rate Theory edited by P. Talkner and P. Hanggi, (Kluwer, Dordrecht, 1994). 

P. Hanggi, P. Talkner, M. Borkovec, Reaction-Rate Theory Fifty Years After Kramers, Rev. Mod. Phys. 62 (1990) 251. 

Other reactions have been studied that appear to also require consideration of non-Markovian effects. For example, in a recent study of the photoisomerization of tra/u-stilbene and trdeviations from the Kramers rate in the case of /ranj-stilbene. These discrepancies were tentatively related to the larger flexibility of this molecule but appeared to be well simulated by the non-Markovian theory of Grote and Hynes. ... 

A Kramers reaction rate theory for electrochemical ion transfer reactions. M. T. M. Koper and W. Schmickler, Chemical Physics 211, 123 (1996). 

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