Polyani

If the Evans-Polyani rule (Section 2.4.1)63 applies, the activation energy 6ijk will be proportional to the reaction enthalpy (-AT/yO and eq. 17 will hold. 

An early attempt to apply an Arrhenius-type equation to a decomposition reaction was by Polyani and Wigner [512] using the expression... 

Several empirical correlations are known for rate constants and activation energies of bimo-lecular radical reactions [1 4], Evans and Polyany [5] were the first to derive the linear correlation between the activation energy and the enthalpy of reaction of R,X with Na. Later Semenov [1] generalized this empirical equation for different free radical reactions in the following form ... 

Different scale features give different scale properties. At the smallest level, the lattice parameter is a key length scale parameter for atomistic simulations. Since atomic rearrangement is intimately related to various types of dislocations, Orowan [88], Taylor [89], Polyani [90], and Nabarro [91] developed a relationship for dislocations that related stress to the inverse of a length scale parameter, the... 

M.Z. Polyani Uber eine Art Gilterstorung die einen Kristall plastisch machen konnte. Z. Phys. 89, 660-664 (1934)... 

Figure 10.3 shows the I-V characteristics of transistors printed with a polyani-... 

The AutoShielding Potential (ASP) theory has shown an exponential relationship for the Polyani (Verb. Dtsch. Phys. Ges. (1914) 16 1012) sorption potential — defined as the reversible work required to achieve the equilibrium pressure, P, in a closed system. This is conveniently expressed for the single vapor component with respect to the liquid sorbate reference pressure, P(0), at a given temperature, T,... 

J. B. Condon, Equivalency of the Dubinin-Polyani Equations and the QM Based Isotherm Equation Part A. A Mathematical Derivation, Microporous and Mesoporous Materials, 38 (2000) 359 and Part B. Simulation of Heterogeneous Surfaces, ibid, p 377. 

J.B. Eiu, K.Y. Song, W.E. Hase and S.L. Anderson, Direct dynamics trajectory study of vibrational effects can polyani rules be generalized to a polyatomic system JACS, 126 (2004) 8602. 

Defining the activation energies according to Polyani-Semenov rule (20) we find... 

It is improbable that the value of the preexponential coefficient would exceed the frequency factor by one or two orders of magnitude. Possibly the reason for the abnormally high steric coefficient in Reaction 1 is its deviation from the Polyani-Semenov rule, although the activation energy calculated by Moin (15) gives the same result within the limits of the precision of this method. In any case, the low limit of the activation energy of the Voevodsky reaction is its thermal effect. Accepting the fact that Reactions 3 and 8 proceed without an activation barrier, P3 = 0.2 and P2 0.03. 

Bell-Evans-Polyani Relationship. The Bell-Evans-Polyani formula deals with the relationship between reaction rate and exothermicity for a series of related single-step reactions. Evans and Polyani pointed out that for a series of homolytic atom transfer reactions of the general type... 

Fig. 3.9. Energy profiles for series of related reactions illustrating the Bell-Evans-Polyani relationship.

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