Science
Theory predicts thermal desorption rates Thermal desorption of atoms and molecules from a metal surface seems like it ought to be a relatively straightforward process. It isn't. Measuring desorption rates experi mentally is tricky and subject to a number of possible errors. The most common theoretical approach to ex plaining the process lacks, in many cases, predictive value. A new theoretical approach de veloped by chemists at California Institute of Technology, Pasadena, provides a rate expression for de sorption that includes only parame ters that can be measured experi mentally. Rates calculated using the expression agree well with experi mental values for a number of sys tems. The research was performed by Caltech chemistry professor William A. Goddard III and coworkers Anto nio Redondo and Yehuda Zeiri and supported in part by the Department of Energy. A report of the research will be published in a future issue of Surface Science. According to Goddard, a statistical thermodynamical approach based on transition state theory has been the most common method of treating desorption theoretically. Such a treatment provides a rationalization for the Arrhenius expression: R = Aexp(-E/kT) where R is the rate of desorption and Ε is, essentially, the enthalpy of the bond between the adsorbed atom or molecule and the surface. "The Arrhenius expression is a useful way to fit desorption data," Goddard says. The problem with it is that it does not lend itself to pre dicting rates from experimental data because the pre-exponential factor, A, is a function of the desorption transition state and that state is not well characterized. "It turns out that there are so many assumptions you can make about the transition state that you can't do much with the ex pression," says Goddard. Another problem is that, from transition state theory, one expects A to be on the order of 10 13 , and that is generally the case for atoms. How ever, experiments have shown that for molecules, A is about 1015. 24
February 21, 1983 C&EN
Goddard: parameters in rate equation can be measured experimentally "The way theorists normally look at processes on surfaces is to follow the trajectories of atoms or molecules as they bounce around," Goddard says. "The problem with that for de sorption is that an atom or molecule may bounce 10 13 times before it comes off. It is impractical to calculate things for that length of time." The expression developed by the Caltech chemists is based on a clas sical stochastic diffusion equation to circumvent that problem. That means, Goddard explains, that "the dynamics are being treated classi cally; we know the forces, which come from quantum mechanics, but we describe the motions of the atom on the surface classically." It is sto chastic because, in the way the for mulas are developed, all of the vi brational states of the surface are av eraged out by taking a stochastic, that is, statistical, limit. "The final ex pression boils down to just an equa tion for the molecule on the surface," he says. The expression that results is:
In it, Ω0/27Γ is the vibrational fre quency of the adsorbed atom or molecule on the surface and is char acteristic for a given system. D e is termed the well depth and is the
same as Ε in the Arrhenius expres sion. The key to the equation is the term f(T). For an atom, f(T) equals one. For a molecule, it is given by an expres sion that incorporates quantities that relate to what Goddard calls the frustrated rotational motion of the molecule at the surface. He uses car bon monoxide adsorbed onto a sur face to explain the concept. "If you think of the surface as being just one point and draw a line from the sur face to the carbon and then from the carbon to the oxygen, then in the equilibrium form that is linear. But the molecule vibrates so that the carbon and oxygen bend with respect to the surface. It bends back and forth in that mode." It is termed frustrated rotation because if the molecule were not on the surface, the mode would be a rotation. It is the frustrated rotation that causes the factor A to be higher than expected for molecules. "The energy that is in that mode at equilibrium gets used and converted to translational energy for the desorbing molecule," Goddard says. In other words, the energy in the frustrated rotational mode is assisting the mol ecule in leaving the surface. All of the terms in the expression can be determined separately by a variety of experimental techniques. However, Goddard believes the ex pression has importance beyond simply allowing calculation of rates. It allows the desorption process to be viewed in terms o.f microscopic properties and dynamics. He points out that it explains, in terms of mo lecular vibrations, the anomalously high A factors. "We still have a long way to go," Goddard says. The averaging process that allows the expression to be de rived in an explicit form is an across-the-board process. In studying many processes, certain trajectories need to be followed. "The problem we have left to solve is that there are reactions where we want to follow some of the surface atoms. For ex ample, we might want to pull out one surface atom to create a defect. Ulti mately, we have to figure out how to average out some degree of freedom while we are actually following the trajectories for other degrees of freedom," Goddard says. Π
