Correction Cite This: ACS Catal. 2018, 8, 8763−8764
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Correction to “Chemical Potential of Metal Atoms in Supported Nanoparticles: Dependence upon Particle Size and Support” Charles T. Campbell* and Zhongtian Mao
ACS Catal. Downloaded from pubs.acs.org by 91.216.3.20 on 08/25/18. For personal use only.
ACS Catal. 2017, 7, 8460−8466 (DOI:10.1021/acscatal.7b03090) Page 8464: The authors regret that three mistakes were made in the entries in Table 1, as follows: • For Fe3O4(111), the entry below NO (column 3) should have been 1.31 × 1015, rather than the published value of 1.42 × 1015; • Also for Fe3O4(111), the entry below Eadh,X=12 (column 4) should have been 147, rather than the published value of 136; and • For CeO2(111), the entry for ΔHred,OxSup should have been 382, rather than the published value of 196. The first two errors are minor, but the last error is a major error and requires several other important changes in the paper, as listed below. While these errors do not affect any of the qualitative conclusions of the paper, nor the paper’s abstract, they do change Figure 3 and all the quantitative aspects that pertain to the fit of Figure 3 with eq 5. They increase the error that results from the use of eq 5 for estimating adhesion energies and chemical potentials. Thus, we
present below a revised version of Figure 3 and the text that follows its first mention in the text. Given this revision of Figure 3, the text, starting with the paragraph near the end of section 3 that begins “Figure 3 shows that indeed,...” and continuing to the start of the Conclusions section no longer accurately describes the results. This text is now described more accurately as follows: 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 (ΔHred,OxSup), with a negative slope. The best-fit straight line is given by Eadh, X = 12 per mole surface oxygen atoms = −0.344ΔHred,OxSup + 286 kJ/mol O
with a standard deviation (σ) of 39 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 Figure 2. The standard deviation (σ) suggests an average error of 39 kJ/mol O for this. For an oxide with a typical surface O atom density of 1.00 × 1015 O atoms per cm2, this corresponds to an error of ∼0.64 J/m2. The slope of Figure 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 Figure 3 (i.e., eq 5) with the slope of the lines in Figure 2 (0.147) provides the ability for roughly 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 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). [This latter citation has since been
Figure 3. Adhesion energy (Y-axis) offset of the trend lines from Figure 2 for different oxide surfaces (i.e., in their experimental adhesion energies to different metals versus (ΔHsub,M − ΔHf,MOx)/ Vm2/3) plotted versus the standard enthalpy of reduction of the oxide (ΔHred,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 1/2 mol of O2(g) product). As a measure of this Y-axis 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., (ΔHsub,M − ΔHf,MOx)/ Vm2/3 = X = 12 J/m2 in Figure 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 ΔHred,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. © XXXX American Chemical Society
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DOI: 10.1021/acscatal.8b02990 ACS Catal. 2018, 8, 8763−8764
Correction
ACS Catalysis published: O’Connor, N. J.; Jonayat, A. S. M.; Janik, M. J.; Senftle, T. P. Nat. Catal. 2018, 1, 531−539.]
4. USING PREDICTED ADHESION ENERGIES TO ESTIMATE 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 39 kJ/mol surface O, or ∼0.64 J/m2 for an oxide with a typical surface O atom density. The factor (3γm − Eadh) that appears in eq 4 for μ(D) is thus in error by this same amount. Using the experimental values of γm for Cu, Au, and Ag from ref 18 and a typical Eadh of 2 J/m2 from Figure 2, (3γm − Eadh) is off by 19%, 25%, and 39%, respectively. Thus, the chemical potential for these three metals will be off by these same percentages (19%−39%). While this is less accurate than desired, these qualitative trends offer new understanding. The percentage error in chemical potential is often smaller than the relative error in Eadh because the factor (3γm − Eadh) is often dominated by 3γm. Note that Eadh is always
