Symmetry factor temperature dependent

Previous attempts at factoring the isotropic NMR shifts in uranocene and substituted uranocenes have assumed that these systems can be viewed as having effective axial symmetry. The temperature dependent 1h NMR spectra of uranocene and a variety of substituted uranocenes clearly verify this assumption and show that eq. 9 can be used to evaluate the pseudocontact contribution to the total isotropic shift in uranocenes. In this equation xx = Xy f°r substituted uranocenes and are replaced by Xj. ... 

Electrode Reactions with Symmetry Factors Linearly Dependent on Temperature... 

A detailed treatment of the temperature dependence and anisotropy of the magnetic moments of all the dx configurations in pseudo-axial (CooV) symmetry has though now been given by Warren (101), in which variation of the orbital reduction factor, k, and distortions from effective Cv symmetry were also considered. This has lately been followed by a similar treatment due to Cerny (102) of the d d2, d8, and d9 configurations but, although some sophistications were included the results are essentially equivalent to those of the author, and furthermore only the undistorted situation, with k = 1, was considered. Consequently the author s own treatment (101) is here briefly summarised, the theoretical approach being that most appropriate for the sandwich complexes of the 3 d series, to which the bulk of the available experimental material relates. 

It is interesting to note that the symmetry factor P did not appear in any of these equations. This is because the rate-determining step assumed here does not involve charge transfer. The current depends indirectly on potential, through the potential dependence of the fractional coverage 0. The transfer coefficient is = 2, as can be seen in Eq. 43F, corresponding to a Tafel slope of b = - 30 mV at room temperature. 

Theoretical treatments of the temperature dependence of the magnetic moments have been made by Warren ), and for some cases by Cerny ), in which details were given of the derivation of the quantities A and k, although the distortions from pseudo-axial symmetry represented by A were therein assumed to be static. However, Ammeter and his collaborators have shown ), that if the distortions are of dynamic Jahn-Teller origin, as seems to be the case for the metallocenes, then the apparent orbital reduction parameter, k , really represents a composite quantity which is actually the product of the true orbital reduction factor, kj, and a quantity, V, which is the vibrational overlap integral between the two orbital components of the ground state. 

Of special interest for the topic of the present chapter is the observation of Weaver that while the double-layer-corrected AS quantities are ligand sensitive, they are found to be independent of potential. This is not the case for the atom and electron transfer process involved in the hydrogen evolution reaction at Hg studied by Conway, et where an appreciable potential dependence of AS is observed, corresponding to conventionally anomalous variation of the Tafel slope with temperature. Unfortunately, in the work with the ionic redox reactions, as studied by Weaver, it is only possible to evaluate the variation of the transfer coefficient or symmetry factor with temperature with a limited variety of redox pairs since Tafel slopes, corresponding to any appreciable logarithmic range of current densities, are not always easily measurable. Alternatively, evaluation of a or /3 from reaction-order determination requires detailed double-layer studies over a range of temperatures. 

Chapter 2, by B. E. Conway, deals with a curious fundamental but hitherto little-examined problem in electrode kinetics the real form of the Tafel equation with regard to the temperature dependence of the Tafel-slope parameter 6, conventionally written as fe = RT/ aF where a is a transfer coefficient. He shows, extending his 1970 paper and earlier works of others, that this form of the relation for b rarely represents the experimental behavior for a variety of reactions over any appreciable temperature range. Rather, b is of the form RT/(aH + ctsT)F or RT/a F + X, where and as are enthalpy and entropy components of the transfer coefficient (or symmetry factor for a one-step electron transfer reaction), and X is a temperature-independent parameter, the apparent limiting... 

Temperature dependence of the kinetics to obtain reliable activation parameters and the temperature dependence of the Tafel slope and symmetry factor... 

The moment of inertia 7or (its value is given in Table IV) is estimated for a freely rotating symmetric top molecule (rotation about the principal axis normal to the symmetry axis). The moment 7or determines the frequency scale relevant to reorientation of dipoles in the hat well. Thus, 7or determines the temperature dependence of the fitted lifetime Tor and the strong-collision frequency yor estimated from Eqs. (2a) and (2b) with account of lifetime Tor. The dipole moment /ior of a librating dipole is expressed from Eq. (3) through that (/i0) of a free water molecule and through the fitted dipole-moment factor kiL, with n1 being the optical (measured near the frequency 1000 cm-1) permittivity (n 1.7). The factor kfl is rather close to unity. 

For water-type liquids (water. Si, Ge, Ga, etc.), the existence of short-range bond order with tetrahedral symmetry is evidenced by the shoulder in the high wave number (q) side of the first peak of the structure factor F (q), or the second peak of the radial distribution function g(r). For Si, for example, the first peak of g(r) is located around ri = 2.4 A, whereas the second one is around rz = 3.5 A[76]. The ratio of 3.5/2.4 = 1.46 is compatible with that of the two characteristic interatomic distances of the tetrahedral structures, 2 /6/3 = 1.63. For Si, the temperature dependence of the ratio of the height of the second peak to that of the first one of... 

Damjanovic A. Temperature dependence of symmetry factors and the significance of experimental activation energies. J Electroanal Chem 1993 355 57-7. 

Bockris JO M, Gochev A. Temperature dependence of the symmetry factor in electrode kinetics. J Electroanal Chem 1986 214 655-74. 

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