Potential energy surfaces, Arrhenius equation

Free energy diagrams for enzymes REACTION COORDINATE DIAGRAM ENZYME ENERGETICS POTENTIAL-ENERGY SURFACES TRANSITION-STATE THEORY ARRHENIUS EQUATION VAN T HOFF RELATIONSHIP... 

The Arrhenius Equation 187 Collision Theory 188 Potential Energy Surfaces 191... 

Both the Arrhenius rate law and the Eyring equation tell us that rate constants are temperature dependent. However, the potential energy surface is generally treated as being temperature independent. The barrier heights and the heat of reaction are determined solely by the structures of the molecules undergoing reaction. Sometimes, a heat capacity difference between individual species on the surface can lead to a temperature dependence of the surface (see Chapter 3 for a discussion of heat capacity). However, this is rare, and we will not consider this possibility further here. 

If then we can calculate the potential surface for the reaction and so identify the transition state, we can estimate the parameter E (i.e., the activation energy) in the Arrhenius equation (5.13) what about the other parameter, A1... 

An Arrhenius type equation is obtained for the apparent reaction rate constant. Equations for the apparent activation energy and for the frequency factor are established as functions of Hamaker s Constant, ionic strength, surface potentials and particle radius. 

In this paper it is shown that the rate of deposition of Brownian particles on the collector can be calculated by solving the convective diffusion equation subject to a virtual first order chemical reaction as a boundary condition at the surface. The boundary condition concentrates the surface-particle interaction forces. When the interaction potential between the particle and the collector experiences a sufficiently high maximum (see f ig. 2) the apparent rate constant of the boundary condition has the Arrhenius form. Equations for the apparent activation energy and the apparent frequency factor are established for this case as functions of Hamaker s constant, dielectric constant, ionic strength, surface potentials and particle radius. The rate... 

Often, the exponential dependence of the dark current at semiconductor-electrolyte contacts is interpreted as Tafel behavior [49], since the Tafel approximation of the Butler-Volmer equation [50] also shows an exponential increase of the current with applied potential. One should, however, be aware of the fundamental differences of the situation at the metal-electrolyte versus the semiconductor-electrolyte contact. In the former, applied potentials result in an energetic change of the activated complex [51] that resides between the metal surface and the outer Helmholtz plane. The supply of electrons from the Fermi level of the metal is not the limiting factor rather, the exponential behavior results from the Arrhenius-type voltage dependence of the reaction rate that contains the Gibbs free energy in the expraient It is therefore somewhat misleading to refer to Tafel behavior at semiconductor-electrolyte contacts. 

The solution of these equations gives the potential distribution in the electrodes and in the electrolyte. The reaction terms couple the electrolyte and electrode potentials through the reaction kinetics, which are described by Arrhenius expressions for both forward and backward reactions at one electrode surface for a one-electron charge transfer reaction. These terms become a Butler-Volmer expression by introducing the contribution of the electric potential difference at the electrode surface to the activation energy. This results in the following expression for the local charge transfer current density in the electrode [142] ... 

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