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.

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Many catalysts consist of metal nanoparticles anchored to the surfaces of oxide supports. These are key elements in technologies for the clean production and use of fuels and chemicals. We show here that the chemical reactivity of the surface metal atoms on these nanoparticles is closely related to their chemical potential: the higher their chemical potential, the more strongly they bond to small adsorbates. Controlling their chemical potential by tuning the structural details of the material can thus be used to tune their reactivity. As their chemical potential increases, this also makes the metal surface less noble, effectively pushing its behavior upwards and to the left in the periodic table. Also, when the metal atoms are in a nanoparticle with higher chemical potential, they experience a larger thermodynamic driving force to sinter. Calorimetric measurements of metal vapor adsorption energies onto clean oxide surfaces in ultrahigh vacuum show that the chemical potential increases with decreasing particle size below 6 nm, and, for a given size, decreases with the adhesion energy between the metal and its support, Eadh. The structural factors that control the metal/oxide adhesion energy are thus also keys for tuning catalytic performance. For a given oxide, Eadh increases with (deltaHsub,M--deltaHf,MOx)/OmegaM2/3 for the metal, where deltaHsub,M is its heat of sublimation, deltaHf,MOx is the standard heat of formation of that metal's most stable oxide (per mole of metal), and OmegaM is the atomic volume of the bulk solid metal. The value deltaHsub,M--deltaHf,MOx equals the heat of formation of that metal's oxide from a gaseous metal atom plus O2(g), so it reflects the strength of the chemical bonds which that metal atom can make to oxygen, and OmegaM2/3 simply normalizes this energy to the area per metal atom, since Eadh is the adhesion energy per unit area. For a given metal, Eadh to different clean oxide surfaces increases as: MgO(100) approximately TiO2(110) < or = alpha-Al2O3(0001) < CeO2-x(111) < or = Fe3O4(111). Oxygen vacancies also increase Eadh, but surface hydroxyl groups appear to decrease Eadh, even though they increase the initial heat of metal adsorption.

Surface Reactions / Adsorbate / Kinetics / Kinetic Prefactors / Transition State TheoryAdsorbed molecules are involved in many reactions on solid surfaces that are of great technological importance. As such, there has been tremendous effort worldwide to learn how to theoretically predict rates for reactions involving adsorbed molecules. Theoretical calculations of rate constants require knowing both their activation energy and prefactor. Recent advances in ab initio computational methods (e.g., density functional theory with periodic boundary conditions and van der Waals corrections) promise to soon provide activation energies for surface reactions with sufficient accuracy to have real predictive ability. However, to predict reaction rates, we also need accurate predictions of prefactors. We recently discovered that the standard entropies of adsorbed molecules (S 0 ad ) linearly track the entropy of the gas-phase molecule at the same temperature (T ), such that S 0 ad (T ) = 0.70 S 0 gas (T ) − 3.3 R (R = the gas constant), with a standard deviation of only 2 R over a range of 50 R. This correlation, which applies only to conditions where their surface residence times are shorter than ∼ 1000 s, provides a powerful new method for estimating the partition functions for adsorbates and the kinetic prefactors for their reactions. For desorption, we show that the prefactors obtained with DFT using transition state theory (TST) and the harmonic oscillator approximation to get the partition function predicts prefactors for desorption that are of order 10 3 times larger than experimental values while our approach gives much better estimates. We also explore the applications of this approach to estimate prefactors within TST for the main classes of adsorbate reactions: desorption, diffusion, dissociation and association, and discuss its limitations. We discuss general issues associated with applying TST to rate laws and multi-step mechanisms in surface chemistry, and argue that rates of adsorbate reactions which are often taken to be proportional to coverage (θ) might better be taken as proportional to θ/(1 − θ) (unless the adsorbate forms islands), to account for the configurational entropy or excluded volume effects on the adsorbate's chemical potential.

Thin films of metals and other materials are often grown by physical vapor deposition. To understand such processes, it is desirable to measure the adsorption energy of the deposited species as the film grows, especially when grown on single crystal substrates where the structure of the adsorbed species, evolving interface, and thin film are more homogeneous and well-defined in structure. Our group previously described in this journal an adsorption calorimeter capable of such measurements on single-crystal surfaces under the clean conditions of ultrahigh vacuum [J. T. Stuckless, N. A. Frei, and C. T. Campbell, Rev. Sci. Instrum. 69, 2427 (1998)]. Here we describe several improvements to that original design that allow for heat measurements with ~18-fold smaller standard deviation, greater absolute accuracy in energy calibration, and, most importantly, measurements of the adsorption of lower vapor-pressure materials which would have previously been impossible. These improvements are accomplished by: (1) using an electron beam evaporator instead of a Knudsen cell to generate the metal vapor at the source of the pulsed atomic beam, (2) changing the atomic beam design to decrease the relative amount of optical radiation that accompanies evaporation, (3) adding an off-axis quartz crystal microbalance for real-time measurement of the flux of the atomic beam during calorimetry experiments, and (4) adding capabilities for in situ relative diffuse optical reflectivity determinations (necessary for heat signal calibration). These improvements are not limited to adsorption calorimetry during metal deposition, but also could be applied to better study film growth of other elements and even molecular adsorbates.