Trends in Adhesion Energies of Metal Nanoparticles on Oxide Surfaces: Understanding Support Effects in Catalysis and Nanotechnology Stephanie L. Hemmingson and Charles T. Campbell* Department of Chemistry University of Washington Seattle, Washington 98195-1700, United States ABSTRACT: Nanoparticles on surfaces are ubiquitous in nanotechnologies, especially in catalysis, where metal nanoparticles anchored to oxide supports are widely used to produce and use fuels and chemicals, and in pollution abatement. We show that for hemispherical metal particles of the same diameter, D, the chemical potentials of the metal atoms in the particles (μM) differ between two supports by approximately −2(Eadh,A − Eadh,B)Vm/D, where Ead,i is the adhesion energy between the metal and support i, and Vm is the molar volume of the bulk metal. This is consistent with calorimetric measurements of metal vapor adsorption energies onto clean oxide surfaces where the metal grows as 3D particles, which proved that μM increases with decreasing particle size below 6 nm and, for a given size, decreases with Eadh. Since catalytic activity and sintering rates correlate with metal chemical potential, it is thus crucial to understand what properties of catalyst materials control metal/oxide adhesion energies. Trends in how Eadh varies with the metal and the support oxide are presented. For a given oxide, Eadh increases linearly from metal to metal with increasing heat of formation of the most stable oxide of the metal (per mole metal), or metal oxophilicity, suggesting that metal− oxygen bonds dominate interfacial bonding. For the two different stoichiometric oxide surfaces that have been studied on multiple metals (MgO(100) and CeO2(111), the slopes of these lines are the same, but their offset is large (∼2 J/m2). Adhesion energies increase as MgO(100) ≈ TiO2(110) < α-Al2O3(0001) < CeO2(111) ≈ Fe3O4(111). KEYWORDS: nanoparticles, adhesion energy, catalyst support, metal catalyst, sintering, oxide surface, gold on MgO(100)
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further showed 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.48−50 Thus, knowing how metal/oxide adhesion energies correlate with the properties of the materials used in making the catalysts is crucial for understanding and tailoring catalytic performance. We present below a summary of experimental measurements of Eadh performed in the clean conditions of ultrahigh vacuum and derive important trends that should allow predictive ability in how Eadh depends on the nature of the metal and of the support surface. These results and trends presented below will also provide important experimental benchmarks for validating the accuracy of quantum mechanical calculations that are used to estimate adhesion energies. We first derive a few relationships to show how chemical potential depends upon particle size and adhesion energy.
etal nanoparticles dispersed across the surfaces of oxide and carbon supports form the basis for many catalysts and electrocatalysts of importance to future energy technologies, pollution prevention, and environmental protection, which are all necessary for any sustainable technological infrastructure that maintains a high quality of life. The activity and lifetime of such catalysts depend upon the details of their structure. The catalytic rate per surface metal atom and selectivity can vary with particle size when the metal particles are below about 7 nm in diameter1−28 and on the choice of support and its extent of oxidation/reduction, even for particles of the same size.1,2,7−9,11,13,24,27,29−47 We have shown previously that the chemical reactivity of the surface metal atoms on supported nanoparticles correlates with the chemical potential of the metal atoms in these particles:48 the higher their chemical potential, the more strongly they bond small adsorbates. As their chemical potential increases, the metal becomes less noble, effectively pushing its behavior to the left and up 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 and deactivate during use more rapidly via sintering.48−50 We © 2016 American Chemical Society
Received: November 7, 2016 Accepted: December 6, 2016 Published: December 6, 2016 1196
DOI: 10.1021/acsnano.6b07502 ACS Nano 2017, 11, 1196−1203
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Table 1. Adhesion Energies of Solid Metals Measured on Clean Oxide Surfaces under Ultrahigh Vacuum Conditionsa metal
oxide
Eadh (J/m2)
ΔHsub,M (kJ/mol M)
ΔHf,MOx (kJ/mol M)
particle size (nm)
Eadh /2γM
method
citation
Pb Ag
MgO(100) MgO(100) CeO1.9(111) CeO1.8(111) Fe3O4(111) MgO(100) MgO(100) TiO2(110) TiO2(110) CeO1.95(111) CeO1.80(111) MgO(100)
0.57* 0.30 2.3 2.5 2.5 0.67* 0.31 0.54* 0.71* 2.53 2.83 1.11* 1.34* 1.92 3.52 3.45 3.43 3.3 1.51*
195 285
−219 −15.1
>10 6.6 3.6 3.6 3.6 1−5 7 2−8 >4 3.6 2.5 10−15 2−8 >10 2.2 2.2 2.2 3.2 1−5
0.65 0.12 0.94 1.0 1.0 0.22 0.10 0.18 0.24 0.84 0.94 0.28 0.34 0.55 0.98 0.96 0.96 0.92 0.30
SCAC SCAC SCAC SCAC SCAC HRTEM SCAC GISAXS HRSEM SCAC SCAC HRTEM GISAXS SCAC SCAC SCAC SCAC SPR GISAXS
57 53 50 50 58 59 this work 60 61 62 62 63 64 65 66 66 66 67 68
Au
Pd Cu
Pt
MgO(100) CeO1.95(111) CeO1.90(111) CeO1.80(111) Al2O3(0001) MgO(100)
368
9.65
−85.4
377
−168
337
−54.3
566
a
Methods used are based either on the particle shape from microscopy (HRTEM, HRSEM, or SPM) or Xray scattering (GISAXS) or on the integral heat of adsorption of metal vapor at multilayer coverage (SCAC). All data are from the citations listed, but the values marked with an asterisk have been recalculated based on newer values for the surface energies of the pure metals (γM) reported in ref 56. Also listed is the heat of formation of the most stable bulk oxide of that metal (per mole of metal atoms), ΔHf,MOx. Metals are ordered by their bulk heat of sublimation, ΔHsub,M, divided by the area per metal atom, using the values given in ref 48, where the γM values used here can also be found.
RESULTS/DISCUSSION Relationship between Chemical Potential of Metal Atoms in Nanoparticles, Particle Size and the Adhesion Energy to Its Support. To quantify the relationship between adhesion energy and metal atom chemical potential in supported metal nanoparticles, let us remember the relationship between the total internal energy U of a system consisting of a metal nanoparticle containing n moles of metal atoms attached to a support material in vacuum. We have shown that48 U = nUM,bulk + USup + γMAM − EadhA ̅
μM (r ) = (δG /δn)T,P,etc. = (δU /δn)T,P,etc. − T(δS /δn)T,P,etc = UM,bulk + (2/3)(3γM − Eadh){π[3Vm/(2π )]2/3 }n−1/3 − TSM,bulk ̅ ̅ = G̅ M,bulk + (2/3)(3γM − Eadh){π[3Vm/(2π )]2/3 }n−1/3
Using the relationship above between n and r to simplify this gives μM (r ) = G̅ M,bulk + (3γM − Eadh)(Vm/r )
(4)
This result is similar to the Gibbs−Thomson relation, which gives the chemical potential of unsupported particles versus size52 and is thus missing the adhesion energy term. The first term here drops to zero (G̅ M,bulk = 0) if we define the bulk metal (for infinite size particles) as the reference state of zero energy or zero chemical potential. Thus, μM increases with γM and decreases with Eadh and with particle size. As the adhesion energy increases, the metal’s chemical potential decreases. Consider a hemispherical particle of this same element and same radius sitting on two different support surfaces, A and B. The difference in chemical potential for the atoms in the particles on these two different supports, μM,A(r) − μM,B(r), is obtained by subtracting two equations identical to eq 4 above, but replacing Eadh with Eadh,A for the adhesion energy to support A and Eadh,B for the adhesion energy to support B. This gives
(1)
where U̅ M,bulk is the molar internal energy of the pure, bulk metal (which we set to zero as the reference energy below), USup is the total internal energy of the particle-free support before adhesion of the metal particle to it, γM is the surface energy of the metal/vacuum, AM is the particle’s total surface area, and A is the total area of metal/support contact. Both AM and A depend on n. For a hemispherical nanoparticle of radius r, AM = 3πr2 = 3π[3Vm/(2π)]2/3n2/3, and A = πr2 = 1π[3Vm/ (2π)]2/3n2/3, where Vm is the molar volume of the bulk metal. In this case, U = nUM,bulk + (3γM − Eadh){π[3Vm/(2π )]2/3 }n2/3 ̅ + USup
(3)
(2)
μM,A (r ) − μM,B (r ) = −(Eadh,A − Eadh,B)(Vm /r )
To semiquantitatively show the effect of Eadh on metal chemical potential (μM), we will assume that both γM and Eadh do not vary with particle size (which is true for large particles, but not true below 6 nm, where they get larger)50,51 and that the molar entropy of the metal atoms (S̅M) does not depend strongly on particle size or support, always remaining at its bulk value (SM ̅ ,bulk). In this case, the chemical potential of metal atoms, which is the partial derivative of the total free energy of the system (G = U − TS) with respect to n, is given at radius r by
(5)
Therefore, for the same diameter (D) hemispherical particle, μM differs between two supports by −2VmΔEadh/D. Thus, the difference in chemical potential is proportional to the difference in adhesion energies and opposite in sign, and it increases with decreasing particle size. This is qualitatively consistent with our measurements of the chemical potential of Ag atoms in Ag nanoparticles as a function of size on different supports, where μM for particles smaller than 6 nm was found to be lower on 1197
DOI: 10.1021/acsnano.6b07502 ACS Nano 2017, 11, 1196−1203
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important results from those TPD measurements in comparison to Table 1 here are that Eadh is
