Chemical Potential of Metal Atoms in Supported Nanoparticles

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The Chemical Potential of Metal Atoms in Supported Nanoparticles: Dependence upon Particle Size and Support Charles T. Campbell, and Zhongtian Mao ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b03090 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 7, 2017

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The Chemical Potential of Metal Atoms in Supported Nanoparticles: Dependence upon Particle Size and Support Charles T. Campbell* and Zhongtian Mao Department of Chemistry, Campus Box 351700 University of Washington Seattle, WA 98195-1700 USA * Corresponding author: [email protected] Abstract Metal nanoparticles supported on oxide surfaces form the basis for many industrial catalysts and promise to play an ever increasing role in future energy and environmental technologies. The chemical potential (µ) of the metal atoms in these particles depends strongly on particle size and support, and is an important factor that determines their catalytic properties, including their binding strengths to adsorbed reaction intermediates and their long-term stability against sintering. We present here a method for estimating this chemical potential as a function of particle size for different metals / oxide combinations. We show that this chemical potential for later transition metals is well approximated for a particle of diameter D by µ(D) = [(3γm – Eadh)(1 + Do/D)](2Vm / D), where γm is the surface energy of the bulk metal, Eadh is the adhesion energy at the bulk metal / oxide interface, and Do is ~1.5 nm, and Vm is the molar volume of the bulk metal. We further show that Eadh increases with: (1) increasing heat of formation of the most stable oxide of the metal from metal gas atoms plus O2(gas) per mole of metal atoms, (2) decreasing enthalpy of reduction of the oxide to its next lower oxidation state plus O2(gas), per mole of oxygen atoms, and (3) increasing density of surface oxygen atoms on the oxide surface. The linear scaling of Eadh with these properties allows estimations if Eadh for a variety of metal / oxide combinations. Using this Eadh estimate in the above equation with known values for γm allows estimates of metal chemical potential versus particle size for late transition metals on various oxide supports. This will improve our ability to understand structure-property relations in catalysis and design better catalysts.

Keywords: nanoparticles, catalyst support, adhesion energy, particle size effects, support effects, catalyst design, sintering, coarsening.

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I. Introduction Nanoparticles of late transition metals dispersed across support materials form the basis for a wide variety of catalysts, electrocatalysts and photocatalysts which are either currently used industrially for energy, chemical and environmental technologies, or hold promise for such applications in the future. It is well known that the rates (per surface metal atom) and selectivities of catalytic, electrocatalytic and photocatalytic reactions often depend strongly upon both the particle size and the nature of the material upon which they are supported, especially when the particles are smaller than ~7 nm in diameter.1-17 A holy grail of catalysis research is to understand at a predictive level how particle size and support affect activity and selectivity for a given catalytic metal. A common problem with such catalysts is that they deactivate over time during use by sintering (also called coarsening), whereby the particles increase in average size and get fewer in number. It has recently become obvious that both catalytic reactivity and the rate of catalyst sintering correlate strongly with the chemical potential of the metal atoms in these supported metal particles.18-23 The definition of “chemical potential” underlies the reason for using these particular words to describe this highly important thermodynamic property: It describes the potential of a given species (in this case, metal atoms) to do chemistry. The higher its chemical potential, the less stable and thus the more reactive it is. In terms of “higher reactivity” for metal atoms, we refer here both to their strength of adsorption of small molecules and their rate of deactivation by sintering. Thus, metal chemical potential is one very important descriptor for understanding and even predicting catalytic performance. We present here new relationships that allow one to predict how metal chemical potential depends upon particle size and support. Let us consider first sintering rates, where the relationship to metal chemical potential is already quantitatively established. The loss of activity over long time during use due to sintering is a huge problem in catalysis 23-26, so there has been much work in developing models that predict the rate of sintering. The goal is to use short-term measurements of particle size distibutions to predict particle sizes at the long times needed for industrial applications (~1 year) 22,27

. In general, the sintering rates of individual particles has been shown to increase with µ(R),

the chemical potential of metal atoms in that particle, which itself is a function of the particle radius R (or “effective radius” for particles that are not partial spheres, defined such that the particle’s volume equals that for a hemisphere of that radius). Here we define µ(R) such that it is

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the chemical potential relative to that for an infinitely large particle of the same metal (i.e., for bulk metal(solid)), which we define as the reference state of zero chemical potential. As an example of a sintering rate equation, we developed a model for sintering rates 22,23 that is based on an atomistic mechanism originally developed by Wynblatt and Gjostein 28. When Ostwald ripening is the dominant mechanism, the radius of any given particle at any time is changing with a rate 22,23:

 µ ( R*)  µ (R )   dR K   -E    =  exp  tot    exp  exp     dt R  kT kT  kT       

(1)

where K and Etot are system-dependent constants, and R* is the equilibrium radius for the concentration of diffusing monomers at that time. This concentration is determined by the entire size distribution of particles (i.e., the probability of R versus R). Particles with R < R* (radius smaller than this critical radius) get smaller with time, and those with R > R* get larger. The rates at which this happens for a given radius is a very strong function of µ(R) in a way very similar to it making a negative contribution to the activation energy 22,23. The higher µ(R) is for a small particle, the faster it gets smaller. This expression was derived assuming that monomer detachment from the particle is rate determining. The values Etot and K are combinations of prefactors and energies for elementary atom-migration steps. They depend on fundamental properties of the metal and the support, such as the energy difference between a metal atom when it is an isolated monomer on the support surface versus when present in a metal particle of infinite size. The sintering kinetic model in 22,23 was further improved by Datye’s group29 by improving the way µ(R*) is calculated. This factor eµ(R)/kT in Eq. (1) also appears in a variety of other rate expressions for sintering kinetics derived assuming different elementary steps control the rate instead. 22 Other kinetic models for sintering mechanisms assume that the rate is dominated by particle diffusion / agglomeration instead of Ostwald ripening, since that mechanism sometimes dominates under certain conditions. This factor eµ(R)/kT also appears directly in the rate expression for sintering by that alternate mechanism, at least in some derivations based on an atomistic mechanism.22 A consequence of metal chemical potential that is even more important than its effect on sintering rates is its effect on the reactivity of supported nanoparticles in their interactions with gases, e.g., when binding adsorbed catalytic reaction intermediates. We have pointed out with

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numerous examples that the same metal atoms will bind small adsorbates more strongly when they are in a structure with high chemical potential, and more weakly when in a structure with lower chemical potential.18-20 Thus, when present in the form of tiny (1-2 nm effective diameter) nanoparticles, where the metal chemical potential is very high18-20, they bind small adsorbates more strongly than large particles or bulk metal 18-20,30. For example, oxygen adatoms bind to ~1 nm Au nanoparticles on TiO2(110) so strongly that the activation energy for their desorption as O2 is ~50 kJ/mol O2 (~40%) higher than from bulk Au single crystal surfaces 21. The dominant effect here is associated with the fact that the surface metal atoms are more coordinativelyunsaturated on smaller particles, as investigated in detail by DFT on unsupported Au and Pt clusters from 13 to 1415 atoms, or ~0.7−3.6 nm in diameter,31,32 which is the same reason step edges usually bind small adsorbates more strongly than close-packed terraces. Conversely, when metal atoms are present in certain bimetallic surfaces where they are more stable (i.e., have lower chemical potential) than in the pure bulk metal (e.g., when combined with other metals with which they make highly exothermic alloys), they bind adsorbates more weakly than the surface of the pure bulk metal.18 For example, for a Pd monolayer on Ta(110), the isosteric heat of adsorption of CO is smaller than on pure Pd(111) by ~63 kJ/mol (~40%), and the TPD peak for adsorbed CO is shifted by more than 200 K to lower temperature 33. Rodriguez and Goodman34 showed that for seven such metal-on-metal systems involving Pd and Ni monolayers, the more stable the Ni or Pd monolayer (as estimated by its peak temperature in temperature programmed desorption (TPD) from the underlying metals), the more weakly it adsorbs CO (as estimated by the CO TPD peak temperature). It is clear that the thermodynamic stability of metal atoms correlates in many systems with their chemical reactivity: The higher the metal’s chemical potential, the more strongly it bonds small adsorbates. (This is true in chemisorption, but likely to break down when van der Waals interactions dominate the adsorption energy rather than usual chemisorption bonds, since larger metal particles should have higher polarizability.) We also note that there may be exceptions to this trend. For example, palladium metal may present exceptions. 35,36 Since no one has reported that step edges on Pd(111) bind CO more strongly than terraces, and DFT calculations indicate weaker binding at Pd(111) steps than terraces,37 whereas steps are commonly reported to bind CO more strongly on similar metals like Pt, the correlation between chemical reactivity and degree of coordinative unsaturation may break down on Pd surfaces for as-yet unknown reasons.

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It is nevertheless clear that metal chemical potential is a powerful descriptor for catalytic performance, whether with regards to the catalyst’s chemical reactivity or its long-term resistance to deactivation by sintering. Thus, there is strong motivation to develop predictive ability in estimating metal chemical potential in catalyst nanostructures. We present here new methods for predicting metal chemical potential in oxide-supported metal nanoparticles. In spite of the emphasis in this paper on metal chemical potential as an important descriptor of various aspects of catalyst performance, we emphasize that it is not the only important aspect. For example, there is increasing evidence that catalytic reactions often happen at sites on the periphery of the metal nanoparticles where adsorbed intermediates are able to interact with both the metal sites and sites of the support surface, or at special sites at the boundary where the metal – support interaction alters the electronic character of these sites.38,39

II. Chemical potential versus particle size We have recently derived the relationship between metal chemical potential and the particle radius (R) for hemispherical metal particles attached to a support surface for which the adhesion energy at the metal / support interface is Eadh,19 giving: µ(R) = (3 γm – Eadh)(Vm / R) = (3 γm – Eadh)(2Vm / D) = µ(D) ,

(3)

where γm and Vm are the surface energy and molar volume of the bulk metal and D is the diameter. This is very similar to the Gibbs-Thomson relation, which gives the chemical potential of unsupported particles versus size,23 but this new equation now includes the metal / support interfacial energetics. It assumes that the surface energy and adhesion energy are independent of size. As quantified in some detail below, this assumption breaks down for D less than about 4 nm, where both γm and Eadh are expected to increase above their bulk values. Figure 1 shows the metal chemical potential (relative to bulk metal solid) versus effective particle diameter for Ag on three different oxide surfaces, and for Ag, Cu and Au on a slightly reduced CeO2(111) surface, all measured in this group using metal adsorption calorimetry.40-45 The predictions of Eq. (3), using surface energies and adhesion energies taken from ref. 19, is shown for comparison. It correctly predicts a strongly increasing chemical potential with particle size below 6 nm diameter. However, the increase is not as rapid as seen experimentally. Calorimetric measurements have shown that γm increases with decreasing particle radius below 3 nm,22,23 and this was attributed to the increasing fraction of low-coordinate metal atoms at the

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surface, like at step edges, kinks and corners. (This is the same reason that more open crystal facets of metal have higher surface energies, e.g., the (110) face of FCC metals has higher γm than the closest-packed (111) face.) Since lattice strain (per unit area) should increase with increasing particle size at lattice-mismatched metal/support interfaces, and since surface facets with higher γm generally bind more strongly to adsorbates, we also predicted that Eadh will probably increase with decreasing R below 3 nm.19 To model these effects of γm and Eadh increasing with decreasing size, we modified Eq. (3) by scaling (3 γm – Eadh) with the factor (1 + Do/D), where Do is parameter used to tune the strength and size range of this increase. With this addition, Eq. (3) is replaced with: µ(D)

= [(3 γm – Eadh)(1 + Do/D)](2Vm / D).

(4)

As seen in Fig. 1, Eq. (4) gives markedly improved fits to the experimental dependences of the metal chemical potential on particle diameter for all five cases studied involving three different metals and three different oxides. Values of Do in the range from 1 to 2 nm provide an excellent approximation to the experimental data. This means that the value of (3 γm – Eadh) doubles from its value in the large-particle limit when D has decreased to 1 to 2 nm (Do). These data are for oxide surfaces which cover the range from some of the largest to smallest adhesion energies to noble metals.19 Equation (4) seems to overestimate the chemical potential when approaching the single-atom size limit for metal clusters. This small-size limit (one atom) was reached for Cu and Au on CeO2-x(111) at 100 K on Fig. 1, but not for the other systems there. For clusters of only few atoms, chemical potential may vary rather dramatically with each added atom, although these variations are probably masked to a large extent by the (relatively) broad particle size distributions in the measurements of Fig. 1 (when greater than one atom in size). Figure 1 also shows the predictions of Eq. (4) for Do = 1.5 nm for all five plots. This single Do value of 1.5 nm gives a good fit to all five metal/oxide combinations independent of system, except when the particles are clusters of only a few atoms. The average absolute error from 0.6 to 6 nm for the five curves in Fig. 1 ranges between 2.6 and 11.3 kJ/mol, averaging 6.6 kJ/mol. Most of this error appears to be due to noise-relative fluctuations in the experimental data. Thus, Eq.(4) with Do = 1.5 nm provides reasonably accurate predictions of chemical potential versus particle size down to ~0.6 nm. Since γm is fairly well known for all the late transition metals, the only parameter one needs to make these predictions is the adhesion energy for that particular metal/oxide combination. We next describe a method for predicting Eadh for 6


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such systems. We note first that Eq. (4) will be much more broadly applicable for predicting chemical potentials versus size of supported nanoparticles than the “modified bond additivity model” we proposed previously,22,23 which itself was a major improvement over the GibbsThomson relation since it corrected for the increase in γm with decreasing size below 6 nm. However, it did not include adhesion energy and so it works well on when Eadh is very small. Thus, Eq. (4) will be much more accurate for predicting sintering rates using kinetic models that require µ(D), like those developed by Wynblatt and Gjostein 28, improved by Campbell and Parker,22,23 and further improved by Datye’s group.29

III. Adhesion energy prediction We have shown previously that the adhesion energies of different metals for a given oxide surface correlate strongly with the metal element’s oxophilicity, or the strength of bonds which that metal makes to oxygen atoms.19 As an estimate of the metal’s oxophilicity, we took the quantity (∆Hsub,M-∆Hf,MOx), where ∆Hsub,M is the metal’s bulk sublimation enthalpy (per mole of metal), ∆Hf,MOx is the heat of formation of the most stable oxide of the metal (per mole of metal). This quantity equals the heat of formation of the metal’s most stable oxide from a metal gas atom plus O2(g), per mole of metal. Since adhesion energies have units of Joules per unit area, we divide (∆Hsub,M-∆Hf,MOx) by Vm2/3, which is approximately the surface area per mole of metal atoms, thus normalizing this energy to the interfacial area (instead of to the number of moles of metal atoms). In Fig. 2, we reproduce a plot of experimentally measured values of Eadh versus this quantity (∆Hsub,M-∆Hf,MOx)/Vm2/3, taken from ref. 19. These Eadh values came from measurements of particle shape or calorimetry under the clean conditions of ultrahigh vacuum (UHV) where the oxide surface was first verified to be clean using surface spectroscopies. This is important since adhesion energies are routinely much lower at surfaces that were not verified to be clean.18,19 We have omitted here one point for Cu on CeO1.80(111), since the Cu does not like oxygen vacancies and thus these Cu particles are attached to parts of the surface that more closely resemble stoichiometric CeO2(111), as described in the original paper.19 As seen, the correlation of Eadh with (∆Hsub,M-∆Hf,MOx)/Vm2/3 is very strong. For both MgO(100) and slightly reduced CeO2(111), the data are well fit by a straight line with the same slope (0.147 ± 0.001), albeit with a huge offset (~2 J/m2) in the y-axis. This correlation emphasizes that the dominant bonding at the metal / oxide interface involves bonds from the metal particle to surface O atoms 7


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(rather than to surface metal atoms of the oxide lattice). Janik and Mallouk’s groups46 have more recently shown that both theoretical (in vacuum) and experimental (in liquid phase) heats of adsorption of single metal atoms on oxide surfaces correlate with this same measure of the metal atom’s oxophilicity used in Fig. 2 (i.e., ∆Hsub,M-∆Hf,MOx). The fact that the slope of the lines in Fig. 2 is the same for these very different oxides suggests that a similar slope will be seen for most oxides. Thus, to predict adhesion energies, we only need to know how to predict the offset between these parallel lines in Fig. 2. Table 1 lists the values of this offset (at the near-average X-axis value in Fig. 2 of X = (∆Hsub,M ∆Hf,MOx)/Vm2/3 = 12) for the five different oxide surfaces represented in Fig. 2, estimated assuming that all oxides have this same slope as MgO(100) and CeO1.95(111). Since the bonding at the metal / oxide interface is mainly to the oxygen atoms of the oxide surface, we divided this offset in Eadh at X = 12 by the number of oxygen surface atoms per unit area for each oxide, to get the adhesion energy in units of energy per surface oxygen atom, listed in the 4th column. Finally, Table 1 also lists the standard enthalpy of reduction of the oxide (∆Hred,OxSup) either to the metal or, if that metal has a stable oxide of lower oxidation state, to that lower oxide plus O2(gas), per mole of oxygen atoms, calculated using standard heats of formation from the NIST Tables and Handbook of Chemistry and Physics. 47,48 We take this as a measure of the strength with which the oxide lattice holds its surface oxygen atoms, or its resistance to giving up an oxygen atom. Based on the principle of bond energy-bond order conservation, the stronger these surface oxygen atoms are bonded to the oxide lattice, the weaker should be their bonds across an oxide/metal interface.

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Table 1. The adhesion energy Y-axis offsets from Fig. 2 (per mole of surface O atoms) for each oxide support studied and the enthalpy cost to reduce them. , , , Oxide

2 2 Surface (O atoms/cm ) (J/m ) (kJ/mol O) Fe3O4(111) 3.19 1.42 x 1015 305 136 14 CeO2(111) 2.96 7.89 x 10 196 226 15 Al2O3(0001) 2.74 1.59 x 10 559 104 15 MgO(100) 1.06 1.12 x 10 602 57 14 TiO2(110) 1.13 5.20 x 10 367 134 These Y-axis offsets were estimated from Fig. 2 as the adhesion energy at an X-axis value of 12, Eadh,X=12. For oxides with Eadh for only one metal, we assumed its line in Fig. 1 has the same slope as the nearest oxide with enough points to establish a slope. The 3rd column lists the surface oxygen atom densities of each oxide, NO. The 4th column shows this Eadh,X=12 offset value divided by NO and multiplied by Avagadros number, to convert it to adhesion energy per mole of surface oxygen atoms. The last column lists the standard enthalpy of reduction of the oxide (∆Hred,OxSup) to its next lower oxidation state plus O2(gas). Figure 3 shows that indeed, the Eadh,X=12 offset value per mole of surface oxygen atoms correlates linearly with the enthalpy of reduction of the oxide (∆Hred,OxSup), with a negative slope. The best fit straight line is given by: Eadh,X=12 per mole surface oxygen atoms = -0.333 ∆Hred,OxSup + 266 kJ/mol O,

(5)

with a low standard deviation (σ = 23 kJ/mol O). This confirms the expectation that the adhesion energy per surface oxygen atom of different oxides increases with decreasing oxophilicity of the oxide. That is, the weaker an oxide holds its oxygen atoms, the larger is its Eadh to a given metal, per mole of its surface oxygen atoms. Equation (5) can be used to estimate the adhesion energy of any oxide to a hypothetical metal with an X value of 12 J/m2 in Fig. 2. The standard deviation (σ) suggests an average error of 23 kJ/mol O for this. For an oxide with a typical surface O atom density of 1.00 x 1015 O atoms per cm2, this corresponds to an error of ~0.38 J/m2. The slope of Fig. 2 (0.147) can then be used to extrapolate from X = 12 J/m2 to the X value for any real late transition metal to get Eadh for that metal / oxide combination. Thus, the combination of Fig. 3 (i.e., Eq. (5)) with the slope of the lines in Fig. 2 (0.147) provides powerful predictive ability for estimating adhesion energies for arbitrary late transition metal / oxide interfaces. Because this method uses the surface oxygen atom density, NO, it will predict different values of Eadh in J/m2 for different crystal faces of the same oxide, with Eadh proportional to NO. There are no experimental data yet

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for different faces of the same oxide (measured under UHV conditions) to test whether this is accurate. Nevertheless, that prediction is certainly consistent with the trends reported here and with the results from DFT calculations that the dominant bonding across the metal / oxide interface is to the surface oxygen atoms of the oxide lattice (see above). It is also consistent with recent DFT results that show that the adsorption energies of single metal atoms on different oxide surfaces increases with decreasing energy of formation of a surface oxygen vacancy on the oxide (Michael J. Janik, private communication).

IV. Using predicted adhesion energies to predict metal chemical potential versus particle size One can use the adhesion energies predicted with this method to further estimate metal atom chemical potential versus particle effective diameter, µ(D), for metal nanoparticles supported on that oxide. To do this, one would simply use Eq. (4) with Do = 1.5 nm and the surface energy of that metal from the literature.18,49 Let us consider the size of error these approximations produce in µ(D) for a system that has an error in Eadh from in Eq. (5) close to its standard deviation of 23 kJ/mol surface O. As seen in Fig. 3, for CeO2 this method predicts an adhesion energy that is too low by ~23.4 kJ/mol surface O, or too low by 0.31 J/m2 for the CeO2(111) face, compared to measurements on the slightly reduces surface. The factor (3 γm – Eadh) that appears in Eq. (4) for µ(D) is thus to large by this same amount. Using the experimental values of γm for Cu, Ag and Au from ref. 18 and Eadh on (slightly reduced) CeO2(111) from ref. 19, (3 γm – Eadh) is too large by only 18, 23 and 16%, respectively. Thus, the chemical potential for these three metals on CeO2(111) will be larger than the values shown on the curves of Eq. (4) with Do = 1.5 nm for these three systems in Fig. 1 by these same small percentages (16-23%). Looking at the experimental data points shows that this is similar in size to the error in Eq. (4). Noting that CeO2(111) is the oxide for which Eadh comes closest to 3 γm shows that the relative errors in chemical potential using this procedure will be considerably smaller for weakly interacting oxides like MgO(100) and TiO2(110) where Eadh is much smaller than 2 γm, with the error in chemical potential (relative to bulk metal) dropping below 10%. Thus, the predictive ability of this approach for estimating metal chemical potential versus particle size (i.e., combining Equations (5) and (4) with the slope

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of Fig. 3) seems to be very accurate, at least for the metal / oxide combinations where we have Eadh data on clean interfaces. The percentage error in chemical potential is smaller than the relative error in Eadh because the factor (3 γm – Eadh) is dominated by 3 γm . Note that Eadh is always less than 2 γm for metals that grown as 3D particles, since complete wetting occurs when Eadh equal 2 γm or larger.18 (That is, 3D particles of the metal would not form at equilibrium on a metal / oxide combination when Eadh ≥ 2 γm.)

Conclusions Recent calorimetric measurements have provided the chemical potential of metal atoms in late transition metal nanoparticles supported on clean oxide single crystal surfaces as a function of particle size in ultrahigh vacuum. For particles larger than a few atoms, these chemical potentials are well modeled for all systems studied, which involves three different late transition metals and three different oxide supports, by Eq. (4) using the parameter Do = 1.5 nm. Thus, Eq. (4) allows reasonably accurate predictions of the chemical potential when the adhesion energy at the metal/oxide interface is known, with an average absolute error down to 0.6 nm that is ~7 kJ/mol). Equation (5) combined with the slope of Fig. 2 (0.147) allows estimates of this adhesion energy for arbitrary combinations of late transition metals and oxide surfaces. Together, these results allow predictions of metal chemical potential versus particle size for different metals on different oxide supports for the first time, with accuracy better than ~20%. They also allow a great deal of qualitative insight into metal chemical potential of nanoparticle catalysts in different catalyst structures. For the same small sizes (below 6 nm in effective diameter), the chemical potential increases with increasing bulk metal surface energy and decreases with increasing adhesion energy. The adhesion energy in turn increases with: (1) increasing heat of formation of the most stable oxide of the metal from metal gas atoms plus O2(gas) per mole of metal atoms, (2) decreasing enthalpy of reduction of the oxide to its next lower oxidation state plus O2(gas), per mole of oxygen atoms, and (3) increasing density of surface oxygen atoms on the oxide surface.

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Acknowledgements The authors gratefully acknowledge financial support for this work by DOE-OBES Chemical Sciences Division under grant #DE-FG02-96ER14630. They thank Gabriel M. Feeley for help in plotting and fitting some of the data here, and Michael J. Janik for helpful discussions.

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Figure 1. Metal chemical potential versus average effective diameter of metal nanoparticles on different single crystal oxide surfaces, measured by metal adsorption calorimetry in ultrahigh vacuum. Values taken from 40-45. Red points are at 300 K and blue points at 100 K (for smaller sizes). Due to small errors in the absolute calibration of the calorimeter used to measure these, the measured heats in those references showed errors (0 to 5%, or 0 to 15 kJ/mol in the large-size limit where the measured heat is largest). We have corrected for this here by adding a constant value to the chemical potentials plotted here for each system, to force the large-size limit to agree with Eq. (3) and (4). These corrections are +15, +6, +14, +3 and +9 kJ/mol for the systems Cu, Ag and Au on CeO2-x(111), Ag on Fe3O4(111) and Ag on MgO(100), respectively. Also shown are the predictions of Eq. (3) (dashed curve) and Eq. (4) (solid black curve for the Do value listed, and solid grey curve for Do = 1.5 nm).

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Figure 2. Experimental adhesion energies of different metals (as continuous films or for the largest nanoparticles studied) to various oxide surfaces versus (∆Hsub,M-∆Hf,MOx)/Vm2/3, or X, which is a measure of the oxophilicity of the metal element, per unit surface area. (Different colors refer to different oxide surfaces.) These measurements were all done in ultrahigh vacuum on clean oxide surfaces, using either single-crystal adsorption calorimetry (SCAC) or particleshape measurements by electron microscopy or grazing-incidence Xray scattering. Adapted with permission from Reference #19. Copyright American Chemical Society 2017.

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ACS Catalysis

Figure 3. The adhesion energy (Y-axis) offset of the trend lines from Fig. 2 for different oxide surfaces (i.e., in their experimental adhesion energies to different metals versus (∆Hsub,M∆Hf,MOx)/Vm2/3) plotted versus the standard enthalpy of reduction of the oxide (∆Hred,OxSup) either to the metal or, if that metal has a stable oxide of lower oxidation state, to that lower oxide, plus O2(gas), per mole of oxygen atoms (i.e., per ½ mole of O2(g) product). As a measure of this Yaxis offset, we use the value of the trend line’s adhesion energy (in J/m2) at the X-axis value of 12 J/m2 [i.e., (∆Hsub,M-∆Hf,MOx)/Vm2/3 = X = 12 J/m2 in Fig. 2. To convert the units on this Eadh offset from J/m2 to energy per mole of surface oxygen atoms, we have divided each value by that oxide’s surface oxygen atom density. The value of ∆Hred,OxSup is a measure of how much that oxide holds it surface lattice oxygen atoms, or its oxophilicity. The best-fit line shown indicates that the more strongly that an oxide holds these oxygen atoms, the less strongly they bind to metal atoms across the metal / oxide interface.

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References (1) Valden, M.; Lai, X.; Goodman, D. W. Science 1998, 281, 1647-1650. (2) Haruta, M. Catalysis Today 1997, 36, 153. (3) Haruta, M. Cattech 2002, 6, 102-115. (4) Gunter, P. L. J.; Niemantsverdriet, J. W. Catal Rev-Sci Eng 1997, 39(1&2), 77. (5) Vaarkamp, M.; Miller, M. T.; Modica, F. S.; Koningsberger, D. C. J. Catal. 1996, 163, 294. (6) Hayden, B. E.; Pletcher, D.; Suchsland, J. P.; Williams, L. J. Physical Chemistry Chemical Physics 2009, 11, 9141-9148. (7) Judai, K.; Abbet, S.; Worz, A. S.; Heiz, U.; Henry, C. R. Journal of the American Chemical Society 2004, 126, 2732-2737. (8) Rodriguez, J. A.; Liu, P.; Hrbek, J.; Evans, J.; Perez, M. Angewante Chemie 2007, 46, 1329-14. (9) Goodman, D. W. Chemical Reviews 1995, 95, 523-536. (10) Rodriguez, J. A.; Liu, P.; Wang, X.; Wen, W.; Hanson, J.; Hrbek, J.; Perez, M.; Evans, J. Catalysis Today 2009, 143, 45-50. (11) Deluga, G. A.; Salge, J. R.; Schmidt, L. D.; Verykios, X. E. Science 2004, 303, 993-997. (12) Schubert, M. M. H., S.; VanVeen, A.C.; Muhler, M.; Plzak, V.; Behm, R.J. J. Catal. 2001, 197, 113-22. (13) Chen, M. S.; Goodman, D. W. Accounts of Chemical Research 2006, 39, 739746. (14) Lei, Y.; Mehmood, F.; Lee, S.; Greeley, J.; Lee, B.; Seifert, S.; Winans, R. E.; Elam, J. W.; Meyer, R. J.; Redfern, P. C.; Teschner, D.; Schlogl, R.; Pellin, M. J.; Curtiss, L. A.; Vajda, S. Science 2010, 328, 224-228. (15) Min, M. K.; Cho, J. H.; Cho, K. W.; Kim, H. Electrochimica Acta 2000, 45, 42114217. (16) Silva, C. G.; Juarez, R.; Marino, T.; Molinari, R.; Garcia, H. Journal of the American Chemical Society 2011, 133, 595-602. (17) Bezemer, G. L.; Bitter, J. H.; Kuipers, H.; Oosterbeek, H.; Holewijn, J. E.; Xu, X. D.; Kapteijn, F.; van Dillen, A. J.; de Jong, K. P. Journal of the American Chemical Society 2006, 128, 3956-3964. (18) Campbell, C. T.; Sellers, J. R. V. Faraday Discussions 2013, 162, 9-30. (19) Hemmingson, S. L.; Campbell, C. T. ACS Nano 2017, 11, 1196-1203. (20) Campbell, C. T. Accounts of Chemical Research 2013, 46, 1712-1719. (21) Campbell, C. T.; Sharp, J. C.; Yao, Y. X.; Karp, E. M.; Silbaugh, T. L. Faraday Discussions 2011, 152, 227-239. (22) Parker, S. C.; Campbell, C. T. Physical Review B 2007, 75, 035430. (23) Campbell, C. T.; Parker, S. C.; Starr, D. E. Science 2002, 298, 811-814. (24) Hansen, T. W.; Delariva, A. T.; Challa, S. R.; Datye, A. K. Accounts of Chemical Research 2013, 46, 1720-1730. (25) Jones, J.; Xiong, H. F.; Delariva, A. T.; Peterson, E. J.; Pham, H.; Challa, S. R.; Qi, G. S.; Oh, S.; Wiebenga, M. H.; Hernandez, X. I. P.; Wang, Y.; Datye, A. K. Science 2016, 353, 150-154.

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Page 16 of 19

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(26) Borup, R. L.; Davey, J. R.; Garzon, F. H.; Wood, D. L.; Inbody, M. A. Journal of Power Sources 2006, 163, 76-81. (27) Parker, S. C.; Campbell, C. T. Topics in Catalysis 2007, 44, 3-13. (28) Wynblatt, P.; Gjostein, N. A. In Progess in Solid State Chemistry; McCaldin, J. O., Somorjai, G. A., Eds.; Pergamon: Oxford, 1975; Vol. 9, p 21. (29) Houk, L. R.; Challa, S. R.; Grayson, B.; Fanson, P.; Datye, A. K. Langmuir 2009, 25, 11225-11227. (30) den Breejen, J. P.; Radstake, P. B.; Bezemer, G. L.; Bitter, J. H.; Froseth, V.; Holmen, A.; de Jong, K. P. Journal of the American Chemical Society 2009, 131, 7197-7203. (31) Li, L.; Larsen, A. H.; Romero, N. A.; Morozov, V. A.; Glinsvad, C.; AbildPedersen, F.; Greeley, J.; Jacobsen, K. W.; Norskov, J. K. Journal of Physical Chemistry Letters 2013, 4, 222-226. (32) Kleis, J.; Greeley, J.; Romero, N. A.; Morozov, V. A.; Falsig, H.; Larsen, A. H.; Lu, J.; Mortensen, J. J.; Dulak, M.; Thygesen, K. S.; Norskov, J. K.; Jacobsen, K. W. Catalysis Letters 2011, 141, 1067-1071. (33) Campbell, C. T. In The Handbook of Heterogeneous Catalysis,; Ertl, G., Knözinger, H. and Weitkamp, J., Ed.; VCH: Weinhein, Germany, 1997, p 814-826. (34) Rodriguez, J. A.; Goodman, D. W. Science 1992, 257, 897-903. (35) Peter, M.; Camacho, J. M. F.; Adamovski, S.; Ono, L. K.; Dostert, K. H.; O'Brien, C. P.; Cuenya, B. R.; Schauermann, S.; Freund, H. J. Angewandte Chemie-International Edition 2013, 52, 5175-5179. (36) Sitja, G.; Le Moal, S.; Marsault, M.; Hamm, G.; Leroy, F.; Henry, C. R. Nano Letters 2013, 13, 1977-1982. (37) Orita, H.; Itoh, N.; Inada, Y. Surface Science 2004, 571, 161-172. (38) Kattel, S.; Ramirez, P. J.; Chen, J. G.; Rodriguez, J. A.; Liu, P. Science 2017, 355, 1296-+. (39) Rodriguez, J. A.; Grinter, D. C.; Liu, Z. Y.; Palomino, R. M.; Senanayake, S. D. Chemical Society Reviews 2017, 46, 1824-1841. (40) Larsen, J. H.; Ranney, J. T.; Starr, D. E.; Musgrove, J. E.; Campbell, C. T. Phys. Rev. 2001, B 63, 195410 (8 pp). (41) Sharp, J. C.; Yao, Y. X.; Campbell, C. T. Journal of Physical Chemistry C 2013, 117, 24932-24936. (42) Farmer, J. A.; Baricuatro, J. H.; Campbell, C. T. Journal of Physical Chemistry C 2010, 114, 17166-17172. (43) James, T. E.; Hemmingson, S. L.; Ito, T.; Campbell, C. T. Journal of Physical Chemistry C 2015, 119, 17209-17217. (44) James, T. E.; Hemmingson, S. L.; Campbell, C. T. ACS Catalysis 2015, 5, 56735678. (45) Hemmingson, S. L.; James, T. E.; Feeley, G. M.; Tilson, A. M.; Campbell, C. T. Journal of Physical Chemistry C 2016, 120, 12113-12124. (46) Strayer, M. E.; Senftle, T. P.; Winterstein, J. P.; Vargas-Barbosa, N. M.; Sharma, R.; Rioux, R. M.; Janik, M. J.; Mallouk, T. E. Journal of the American Chemical Society 2015, 137, 16216-16224. (47) NIST Chemistry Webbook, NIST Standard Reference Database Number 69. http://webbook.nist.gov/chemistry/

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(48) CRC Handbook of Chemistry and Physics; 77th ed.; Lide, D. R., Ed.; CRC Press, Inc.: Boston, 1996. (49) Vitos, L.; Ruban, A. V.; Skriver, H. L.; Kollar, J. Surface Science 1998, 411, 186202.

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For Table of Contents Only:

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Chemical Potential of Metal Atoms in Supported Nanoparticles

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