Surface Polanyi relation

In the present chapter, we have attempted to illustrate how surface bonding and catalytic activity are closely related. One of the main conclusions is that adsorption energies of the main intermediates in a surface catalyzed reaction is often a very good descriptor of the catalytic activity. The underlying reason is that we find correlations, Brpnsted-Evans-Polanyi relations, between activation barriers and reaction energies for a number of surface reactions. When combined with simple kinetic models such correlations lead to volcano-shaped relationships between catalytic activity and adsorption energies. 

While identifying the rate determining parameters of the catalytic trans formation schemes under consideration, we understand better the reason for possible energy correlations in catalysis, the Broensted Polanyi relations for the transition state energies of surface transformations being typically apphed. Such an approach was intensively used in 1960s—1970s to... 

One may suppose that changes in the particle size should result in changes of of the surface transition state, the changes being described correctly enough by the Broensted Polanyi relation with the increment Ak of substance K at its dispersing ... 

This subsection begins with a short summary of particle-size-dependence observations of chemical bond activation. Next, the Bronsted-Evans-Polanyi relation that relates activation energies of elementary surface reaction steps with the corresponding reaction energies is introduced. In the subsections that follow, the... 

As long as the structures of ttansition state and dissociated state are close, changes in metal-atom interactions will lead to the Bronsted-Evans-Polanyi relation between activation energy and reaction energy of a surface elementary reaction. Interestingly, microscopic reversibility imphes that the Bronsted-Evans-Polanyi proportionality constant for recombination is typically 0.1. This implies that the ratio of the energy of the surface fragments in the transition state compared to the dissociated state is a constant and on the order of 90%. 

Reactant or product states of surface reactions are often (de-)stabilized by the presence of other adsorbates. This implies a change in the reaction energy as a function of overlayer composition. The Brpnsted-Evans-Polanyi relation again provides an elegant procedure to estimate the effect of lateral interactions on changes in the activation energies. 

Cushing GW, Navin JK, Donald SB, et al C-H bond activation oflight alkanes on Pt(lll) dissociative sticking coefficients, Evans-Polanyi relation, and gas-surface energy transfer, JPhys Chem C 114(40) 17222-17232, 2010. 

This relation is credited to Svante Arrhenius and is called the Arrhenius temperature dependence. Arrhenius was mainly concerned with thermodynamics and chemical equilibrium. Some time later Michael Polanyi and Eugene Wigner showed that simple molecular arguments lead to this temperature dependence, and this form of the rate is frequently called the Polanyi-Wigner relation. They described chemical reactions as the process of crossing a potential energy surface between reactants and products (see Figure 2-3), where f and... 

The VB simplified model of ground-state potential energy surface H3 system considered as transition state and stabilization valleys of the H + H2 reaction is also an early problem, belonging to the history of physical chemistry under the name London-Eyring-Polanyi-Sato (LEPS) model that continues to serve as basis of further related developments [17,18], The actual analysis is a new a focus on the JT point of this potential energy surface able to absorb results of further renewed CASCCF type calculations on this important system. 

The easiest test concerns Eq. (22a) describing the LJ-type dissociation. The equation establishes the linear correlation between the dissociation barrier A for a homonuclear admolecule A2 and the atomic heat of chemisorption Qh with the slope of k = 3/2. As seen from Table V, for H2, 02, and N2 dissociated on surfaces of metals as varied as Fe, Ni, Cu, W, and Pt, the experimental values of k lie within the range k = 1.4-1.7, that is, within 10-15% of the theoretical LJ value of k = 1.5. It should be stressed that, unlike similar linear relations between the activation barriers and the heats of reactions (Brpnsted, Polanyi, Frumkin-Temkin-Semye-nov, etc.), Eq. (22a) is not a postulate but a corollary of the general principle (BOC-MP) applied to the one-dimensional dissociation ABS As + Bs. 

Applying the Broensted Polanyi correlations is sometimes useful for describing the dependence of the reaction rate on the size of the catalyti caUy active component. A huge amount of experimental data have been compiled to date regarding the effect of the particle size of the catalyst active components on the specific catalytic activity, SCA, as well as on the turnover frequency, TOP, of the active center. Both parameters do not relate to the total surface area of the catalyticaUy active phase or to the total number of active centers and, therefore, characterize directly the properties of the active center. There are also some experimental data on the size dependence of the adsorption properties of small metal parti cles, as well as on the selectivity of a few catalytic processes. 

LEPS (London-Eyring—Polanyi—Sato) Potential—approximate polyatomic potential surface obtained from diatomic Morse functions and related repulsive functions. 

Then, in the temperatiare range T>T- /2 the empirical Polanyi-Semenov relations (224.Ill) become identical with the theoretical equations (63.1) based on the properties of the potential energy surfaces. However, the condition T>T /2 is necessary for the validity of equations (231.Ill) but is not sufficient for the realization of inequalities (240.Ill) which lead to equations (241.III). The latter require the stronger limitation so that the reaction proceeds entirely in the classical temperature range T>2T in which the nuclear tunneling is quite negligible. This requirement may be sufficient if the motion along the classical reaction path is very fast compared to the nonreactive modes. Then, expression (216.Ill) yields, indeed, E, since for 8 =... 

---