Equation Polanyi-Wigner

Representative kinetic data for dehydrations of crystalline hydrates and some comparisons with predictions of the Polanyi—Wigner equation [eqn. (19)]... 

Taylor [648] has shown that the deceleratory decomposition of HgO is satisfactorily described by the contracting volume equation [eqn. (7), n = 3], Calculated values of E (162—201 kJ mole rise with increasing crystallite size and are somewhat greater than the enthalpy of dissociation (160 kJ mole 1). Since estimated values of A are consistent with the predictions of the Polanyi—Wigner equation, eqn. (19), it is concluded that breakdown involves the detachment of individual molecules rather than the unzipping of the long zig-zag polymeric —Hg—O— chains which constitute the reactant lattice. 

Activation energy values for the recombination of the products of carbonate decompositions are generally low and so it is expected that values of E will be close to the dissociation enthalpy. Such correlations are not always readily discerned, however, since there is ambiguity in what is to be regarded as a mole of activated complex . If the reaction is shown experimentally to be readily reversible, the assumption may be made that Et = ntAH and the value of nt may be an indication of the number of reactant molecules participating in activated complex formation. Kinetic parameters for dissociation reactions of a number of carbonates have been shown to be consistent with the predictions of the Polanyi—Wigner equation [eqn. (19)]. 

Shannon27 analyzed in some detail the theory as it applies to the thermal decomposition of solids. He found that of the 31 reactions for which he compared experimental rate constants with those calculated from the Polanyi-Wigner equation, only a third showed order-of-magnitude agreement. In Shannon s view, the lack of agreement stems from neglecting rotational and other vibrational degrees of freedom. 

Young [17] discussed the Polanyi-Wigner equation in terms of the thermodynamics of the activation process (AS and A// ). Equation (4.2) may be written as ... 

Kinetic studies [37,40] of the dehydration of chrome alum (260 to 270 K) yielded Arrhenius parameters of greater magnitude than predicted by the Polanyi-Wigner equation ( , = 125 kJ mol, whereas the enthalpy of dehydration is 42 kJ (mol HjO) ). This was ascribed to systematic changes in the thickness of the transition layer and thus on impedance of flie escape of water vapour. At higher temperatures (288 to 308 K) a lower value of was found (96 kJ mol" ) and the Arrhenius... 

Arrhenius parameters for the dehydrations of ammonium and potassium aliuninium alums [38] were in agreement with the Polanyi-Wigner equation. Comparisons of the shapes of nuclei on different crystal surfaces indicated that reaction proceeds along (100) planes. The observed decrease of the rate in water vapour is attributed to the blocking of pores by adsorbed molecules. No intranuclear cracking was apparent and the product-reactant boimdaries became irregular because of the influence of water on reorganization of the product phase. The appearance of these nuclei contrasted markedly with those in mixed potassium chromium/aluminium alums, where there is an approximately concentric structure. 

Consistent [50] with this model is the observation [51] that incorporation of Cd " as an impurity in the AgjCOj lattice increases the reaction rate, because this introduction of divalent ions must be accompanied by formation of cation vacancies. Wydeven et al. [52-54] decomposed pure AgjCOj and compared behaviour with that of the salt doped with or Gd. They also studied the effect of water vapour. The kinetic observations fitted the Polanyi-Wigner equation and it was concluded that decomposition proceeds by an interface mechanism. 

P is the pressure increase, V is the volume of the chamber, S is Che pumping speed of the pumping system, and C is a constant depending on sample area, gas constant and gas phase temperature. If the desorption rate is small compared with the pumping speed, it will be proportional to the pressure P. The desorption rate is related Co desorption parameters through the following Polanyi-Wigner equation ... 

The method of determining these desorption energies differs between authors. The approach adopted by Redhead (22) is to use the Polanyi-Wigner equation for desorption, that is... 

In this section, the details of thermal desorption from surfaces will be considered. The rate of the process can be represented in an ideal form by the Polanyi—Wigner equation... 

The simple form of the Polanyi—Wigner equation is based on the assumption that any particle possessing the requisite activation energy desorbs during the period of a single vibration. If the recombination mechanism is written as... 

The basic problem, by whatever means the experiment is performed, is to establish the correct form of the rate equation which describes the desorption. The usual procedure is to postulate the simple, empiric form described as the Polanyi—Wigner equation... 

The prefactor Vd appearing in the Polanyi-Wigner equation is related to the entropy term in the relevant free enthalpy balance AG = fi = AH - TAS, i.e., Vd = exp(AS/ ). For the adsorbed noble gases the prefactor is usually of the order of lO to lO s and can be interpreted as an atterrrpt frequency for desorption associated with the (perpendicular) atom-smface vibration frequerrcy. 

Water desorption kinetics is referable to the Polanyi-Wigner equation, which is valid for an ideal (plane) energetically homogeneous surface, in which diffusion and readsorption phenomena are absent ... 

Thermal desorption (evaporation) can be handled by the so-called first-order Polanyi-Wigner equation, which for an individual grain takes the form ... 

The relation (4.7) is customarily used to describe the rate of desorption, and is known as Polanyi-Wigner equation. 

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