Entropies of Adsorbed Molecules Exceed Expectations

Adsorbed molecules are involved in many reactions on solid surface that are of great technological importance. As such, there has been tremendous effort worldwide to learn how to predict reaction rates and equilibrium constants for reactions involving adsorbed molecules. Theoretical calculation of both the rate and equilibrium constants for such reactions requires knowing the entropy and enthalpy of the adsorbed molecule. While much effort has been devoted to measuring and calculating the enthalpies of well-defined adsorbates, few measurements of the entropies of adsorbates have been reported. We present here a new way to determine the standard entropies of adsorbed molecules (S(ad)(0)) on single crystal surfaces from temperature programmed desorption data, prove its accuracy by comparison to entropies measured by equilibrium methods, and apply it to published data to extract new entropies. Most importantly, when combined with reported entropies, we find that at high coverage, they linearly track the entropy of the gas-phase molecule at the same temperature (T), such that S(ad)(0)(T) = 0.70 S(gas)(0)(T) - 3.3R (R = the gas constant), with a standard deviation of only 2R over a range of 50R. These entropies, which are ~2/3 of the gas, are huge compared to most theoretical predictions. This result can be extended to reliably predict prefactors in the Arrhenius rate constant for surface reactions involving such species, as proven here for desorption.

We have measured the desorption of seven small n-alkanes (C(N)H(2N+2), N=1-4,6,8,10) from the Pt(111) and C(0001) surfaces by temperature programed desorption. We compare these results to our recent study of the desorption kinetics of these molecules on MgO(100) [J. Chem. Phys. 122, 164708 (2005)]. There we showed an increase in the desorption preexponential factor by several orders of magnitude with increasing n-alkane chain length and a linear desorption energy scaling with a small y-intercept value. We suggest that the significant increase in desorption prefactor with chain length is not particular to the MgO(100) surface, but is a general effect for desorption of the small n-alkanes. This argument is supported by statistical mechanical arguments for the increase in the entropy gain of the molecules upon desorption. In this work, we demonstrate that this hypothesis holds true on both a metal surface and a graphite surface. We observe an increase in prefactor by five orders of magnitude over the range of n-alkane chain lengths studied here. On each surface, the desorption energies of the n-alkanes are found to increase linearly with the molecule chain length and have a small y-intercept value. Prior results of other groups have yielded a linear desorption energy scaling with chain length that has unphysically large y-intercept values. We demonstrate that by allowing the prefactor to increase according to our model, a reanalysis of their data resolves this y-intercept problem to some degree.

We use molecular-dynamics simulations and importance sampling to obtain transition-state-theory rate constants for thermal desorption of an n-alkane series from Au(111). We find that the binding of a large molecule to a solid surface involves different types of local minima. The preexponential factors increase with increasing chain length and can be substantially larger than typical estimates for small molecules. Our results match recent experimental studies and indicate that a proper treatment of conformational isomerism and entropy, heretofore not found in coarse-grained models, is essential to quantitatively describe the thermal desorption of large molecules from solid surfaces.