Elastic Effects in AdsorbateâAdsorbate Interactions of C and S on a

Article pubs.acs.org/JPCC

Elastic Effects in Adsorbate−Adsorbate Interactions of C and S on a Stepped Ru Surface M. F. Francis*,†,‡ and W. A. Curtin† École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Vaud, Switzerland Brown University, Providence, Rhode Island 02912, United States

† ‡

S Supporting Information *

ABSTRACT: We examine strain modification of adsorbate−adsorbate interaction in the (C*+S*)/fcc-Ru(211) system for relevance to biomass to hydrocarbon catalysis and the broader case of interaction changes under strain. Applied biaxial strains from −3% to +3% shift the C and S binding and interaction energies by ±0.3 eV for C and ±0.1 eV for S, binding and interaction being additive and leading to stronger binding with tension, creating larger total changes in binding for the covered surfaces. Changes in the near-neighbor interactions with strain are found to be primarily electronic in originthere is little change in mechanical interaction. While mixing and thermodynamic analysis reveals that the C+S system will mix over the complete range of strains studied, the application of strain, whether tensile or compressive, may lead to reduced sulfur coverage. For biomass catalysis, the implication is that strain may be used to optimize hydrocarbon chemistry with only improvements in poisoning due to site blocking. It is argued that the serendipitous addition of binding and interaction may not be specific but a general case and, therefore, contribute to the utility of strain engineering.

I. INTRODUCTION The current state of the art in catalyst design is based on the practice known as “descriptor theory”. Descriptor theory is a method of reducing parameters controlling catalytic performance down to a few binding energies.1,2 The reduction in complexity relies upon two relations, known as the Brønsted− Evans−Polanyi relation3,4 and binding energy scaling.5 The Brønsted−Evans−Polanyi3,4 relation is a linear relationship between the activation energy of a process and the reaction energy of that process. The binding energy scaling relation is a linear relationship between the binding energy of any species that bind through the same element.5 Combining the Brønsted−Evans−Polanyi and binding scaling relations allows the rate constants of any surface reaction to be written as a function of the binding elements. By assuming that adsorbate interactions are not significant, the chemical stationary state may be determined along with a plot of activity versus binding energies.6 These plots of activity versus binding energies are known as descriptor theory plots.7 The state of the art in catalyst design was first to construct a descriptor theory plot describing optimal binding and second to search for those materials demonstrating at or near optimal binding.1,6,8 This state of the art in catalyst design has been updated by new findings in the mediation of surface chemistry by mechanical strain. It had been thought that the changes in binding energies under strain were controlled by an electronic effect. When a strain is applied to a surface, a shift in the underlying band structure results. The shift in the band structure results in a shift in the orbital-band coupling and, consequently, the binding energy. As the underlying band is the same for all intermediates, all binding energies move together, resulting in a small change in reaction energy. The small change in reaction energy due to © XXXX American Chemical Society

the correlated electronic effects left the impression that mechanical strain would not be a useful tool in catalyst design.9 This impression was proven to be false when the electronic model was revealed to be incomplete. When adsorption occurs, the underlying surface undergoes structural relaxation. This structural relaxation is equivalently an adsorbate-induced strain field. The application of an external strain (or stress) to the surface couples with this adsorbate-induced strain and results in a mechanical work term. This mechanical work term is adsorbate-specific, directional, and may result in large changes in reaction energies.10 Combined, the electronic and mechanical effects enable large changes in activity under strain, the ability to continuously scan activity,11 and the ability to achieve peak activity with multiple alloys.11 The controlled application of strain is achieveable using core−shell nanoparticles.12 Controllable, designable strain is achievable due to the lattice misfit of the core relative to the shell, which leads to strains in the shell that depend on particle size, shape, and shell thickness.13 Core−shell nanoparticles have been synthesized with surface strains larger than 4% and have been shown to demonstrate novel activity in a number of cases.12,14−16 The third step in the state of the art in catalyst design is, therefore, to determine the activity−strain response for materials near peak activity and then to design core−shell nanoparticles to move materials with near peak activity to peak activity.10,11,17 The described state of the art in catalyst design breaks down when adsorbate−adorbate interactions become important. Adsorbate−adsorbate interactions may be controlling in Received: March 14, 2017 Revised: July 11, 2017 Published: July 12, 2017 A

DOI: 10.1021/acs.jpcc.7b02422 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C poisoning,18−21 promotion,22,23 the formation of chemically active surface phases,24−26 and the distortion of descriptor theory plots.27,28 Several catalytic processes cannot be described without interactions.18,19,22,23,28−34 Four types of adsorbate−adsorbate interactions have been articulated as important:35 (i) direct interactions due to the overlap of adsorbate wave functions, (ii) indirect interactions mediated by the electronic structure of the surface, (iii) nonlocal electrostatic interactions, and (iv) elastic interactions. Given the novel findings of mechanical work playing a large role in binding energy changes under strain and the ability to controllably engineer strain, revisiting changes in interactions under strain has become timely. A C+S mixture on a Ru step is used as a probe system to examine changes in interaction under strain. C+S adsorption on the Ru step is relevant to renewable fuel generation from biomass.36−39 Biomass may be converted into hydrocarbons through the aid of a supercritical water reactor and Ru catalysts. The conversion of biomass to natural gas is believed to occur through a scrambling mechanism at the step of the Ru surface.36,37 In this scrambling mechanism, the biomass feedstock is reduced down to bare atomic form, and carbon species are iteratively hydrogenated to form the product hydrocarbons.36,37 Under reaction conditions, the active interface is covered predominately by carbon, with the minority species being the partially hydrogenated intermediates.37 When the incoming feedstock contains sulfur, as natural biomass does, poisoning occurs;37 the amount of product is reduced and moves away from the desired hydrocarbons. It has been hypothesized that poisoning occurs through site blocking,36,37 but the precise mechanism, whether site blocking, direct chemical interference, or both, is unknown. Understanding C+S interactions and manipulating them through strain might benefit the understanding of biomass catalysis. If a mixing analysis were to reveal C+S to be phaseseparated, this would be strong evidence for the poisoning mechanism being principally site blocking. If C+S were mixed and strain could induce a phase separation, then direct interference by S could be avoided, leaving site blocking. If strain could reduce S coverage, this might reduce site blocking. If strain left S coverage relatively unaffected, strain could be used to optimize biomass to hydrocarbon chemistry without concern for poisoning. More broadly, explicitly decomposing the interaction energy changes into mechanical and electronic contributions allows inferences about strain engineering. Here, we demonstrate the following for (C+S)/fcc-Ru(211): (I) changes in adsorbate−adsorbate interactions are controlled by electronic effects; (II) an applied strain can lead to significant changes in adsorbate−adsorbate interaction energies and heats of mixing; (III) an applied strain may reduce S coverage, alleviating poisoning; (IV) reduction in S coverage with strain is possible and such that strain may be used to optimize biomass to hydrocarbon chemistry while S poisoning is reduced; and (V) we argue that band-mediated binding and interaction energy changes may always be additive, causing strain-mediated total binding changes to be large. The remainder of this paper is organized as follows. In section II, we formally describe binding energy, interaction energy, and the separation of mechanical and electronic contributions to both; we describe details of the density functional theory computational we apply. In section III, we present the results of the computation and separation into electronic and mechanical components, in which we determine

the binding and interaction response of C, S, and C+S mixtures to strain; the heat of mixing and coverage are discussed pertaining to poisoning; the ability of strain to impact the sulfur poisoning of ruthenium conversion of biomass to natural gas is discussed. In section IV, possible implications for biomass catalysis and strain engineering are discussed.

II. METHODS Binding Definitions. The binding energy, Ebe, of a molecule, A, to a surface, S, is defined as E be[A* /S] = E[A* /S] − (E[S] + E[A gas])

(1a)

Mechanical and electronic contributions to this binding may be readily decomposed. The mechanical energy is the elastic energy stored in the surface due to the relaxation process. If we represent the structure of the relaxed surface due to the presence of the molecule A, but in the absence of the molecule A, as Sdef(A), and the clean, unrelaxed surface as S, the mechanical energy associated with a bond may be identified as Emech[A*/S] = E[Sdef (A)] − E[S]

(1b)

The electronic contribution can be found by determining the energy changes upon adsorption to a mechanically prepared surface, or the reverse process, by computing the energy change upon removing the adsorbate from the fully relaxed surface without allowing the substrate to relax, which is given by Eelec[A*/S] = E[A*/S] − (E[Sdef (A)] + E[A gas])

(1c)

Interaction Definitions. Extending this concept to two adsorbates, A and B, we express the interaction energy as E int[(A*+B*)/S] = {E[(A*+B*)/S] + E[S]} − {E[A*/S] + E[B*/S]}

(2a)

The mechanical and electronic contributions to interactions can be defined as mech E int [(A*+B*)/S]

= {E[Sdef (A+B)] + E[S]} − {E[Sdef (A)] + E[Sdef (B)]}

(2b)

and elec E int [(A*+B*)/S]

= {E[(A*+B*)/S] − E[Sdef (A+B)]} − {E[A*/S] − E[Sdef (A)]} − {E[B*/S] − E[Sdef (B)]}

(2c)

d-Band Center Definition. For interpreting electronic contributions to the binding energy, we correlate the binding energy with shifts in the d-band center, Ed. Defining Ei as the energy level of a d-band state, Ef as the Fermi-level, and nd(Ei) as the density-of-states of a d-band state at energy Ei, the dband center Ed is computed as +∞

Ed =

∑ (Ei − Ef )nd(Ei) −∞

(3)

Strain Dependence. When the substrate is strained, all terms become strain-dependent. We analyze the contribution B


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The Journal of Physical Chemistry C

III. RESULTS The Monomer. Before we analyze the influence of an applied strain on binding and interaction energies, we determine the appropriate adsorption sites for the chosen system. We consider the various binding sites labeled in Figure 1. The computed binding energies for C and S are shown in

explicitly due to strain by subtracting the energy in the presence of strain from the value at zero strain. This gives the change in contribution of type j to the energy (Ej) as ΔEj(ε) = Ej(ε) − Ej(ε=0)

(4)

Model Geometry. The goal is to model the elastic response of an hexagonal close-packed (hcp) ruthenium step. The real step edge is an isolated A-type step surrounded by many rows of terrace and then a B-type step, where the alternating A−B structure is intrinsic to (0001)-terminated hcp. Resulting from the inability to isolate a particular step structure, there are two often used compromises when modeling the hcp step: one approach is to take an hcp(0001) surface and to remove rows of atoms, leaving a single cell with both A-type and B-type step terminations;40 the second approach is to model the hcp material as face-centered cubic (fcc) and model the step as an fcc(211) structure, leaving only one step similar to the hcp step.36 The goal here is to model the elastic response at the step. Using the first approach, the unconstrained surface layer suffers weak mechanical coupling to the underlying surface, resulting in a misrepresentation of both the stress field due to the applied strain and that due to the adsorbate-induced strain. Using the second approach, the coupling between the upper and lower layers is more physical; however, both the stiffness and electronic response of the hcp and fcc materials will be slightly different. It is therefore the case that neither approach ideally serves the goals of studying elastic coupling. We choose here the approach of using a fcc(211) surface, to ensure the best possible coupling, but note that neither is ideal. The fcc-Ru was found to have a lattice parameter of 3.823 Å, resulting in a cell structure oriented with X = 6.62 Å perpendicular to the step, Y = 5.41 Å along the line of the step, and Z = 27.57 Å normal to the plane of the surface. The fcc(211) structure has a depth of six layers, which is important to capture mechanical interaction energies, with thicker layers better capturing mechanical effects.10 Specific information on the structure of the supercell and surface slab is provided in the Supporting Information (SI). Application of Strain. We envision a biaxial stress applied to the surface, a biaxial stress being an equal stress along the line of the step and perpendicular to the step, which induces corresponding strains in the structure (SI). The strains are computed by application of Hooke’s law using the computed surface stiffness tensor (SI). The bottom two layers of atoms, and the overall cell geometry, are held fixed at the positions dictated by the computed strain tensor. The top four layers of atoms are free to relax, subject to the constraints on the simulation cell under the computed strain tensor.10 Computation with DFT. We use density functional theory (DFT) as implemented in VASP.41−43 A Monkhorst−Pack automatic k-mesh generation scheme was used with 40 subdivisions along each reciprocal lattice vector; the k-mesh was shifted with respect to the origin by 0.5 reciprocal lattice subdivisions. The automatic k-mesh generation resulted in a kmesh of 6 × 7 × 1 for the two-atom-wide fcc(211) cases and 6 × 5 × 1 for the three-atom-wide fcc(211) cases. Due to the inherent distortions associated with the application of strain, care was taken not to utilize symmetry-based algorithms. A kinetic energy cutoff of 700 eV was used in all calculations.30 Electronic structure calculations were converged to 1 × 10−5 eV; ionic relaxation calculations were converged to 1 × 10−4 eV. The Perdew−Wang 91 (PW91) functional was used.44

Figure 1. Schematic of available binding sites on an fcc(211) surface: “a”, atop; “b”, bridge; “f”, fcc; “h”, hcp; “h4”, hollow-four; the subscript numbers are a means of distinguishing between crystallographically similar sites.

Table 1. Binding Energies of C and S Atoms to the fccRu(211) Surfacea site

C

S

site

C

S

a1 a2 b1 b2 b3 b4

X X X X X X

X X −5.63 X X X

b5 f1 f2 h1 h2 h4

X −6.81 X −7.84 −7.49 −8.07

X −5.59 X −5.88 −5.73 −6.11

“X” indicates an unstable site; a number indicates the binding energy of a stable configuration in units of eV.

a

Table 1. In Table 1, “X” refers to an adsorbate−site combination which was found to be unstable. The most favorable binding site for both C and S is the hollow-4 (h4) site; stable C and S configurations were found for the hcp (h1, h2) and fcc (f1) sites, with S having an additional bridge site (b1). An fcc(211) slab, two-atoms-wide, was used in the simulation of the monomers. The changes in binding energies of C and S in the h4 site under strain, Ebe[Ch4*/fcc-Ru(211)] and Ebe[Sh4*/fcc-Ru(211)], are denoted for brevity as Ebe[C] and Ebe[S], and the strain (stress) effects are indicated by the value of the maximum principal strain associated with the applied biaxial stress. The configuration of and change in binding of Ch4 and Sh4 versus the (maximum principle) strain are shown in Figure 2a1,b1. For both Ch4 and Sh4, the binding energy increases (more negative) with increasing tensile strain. This is consistent with the trend predicted by the electronic d-band model. The electronic contribution versus strain, relative to the zero-strain case, is shown in Figure 2a2,b2. Comparison with the total binding energy changes versus strain shows that electronic effects dominate the binding energy changes over most of the strain range. The change in the average d-band center of the four surface atoms around the h4 site versus strain is also shown Figure 2a2,b2, and correlates with the change in electronic contribution to the binding, as predicted by the d-band model. C


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Figure 2. Changes in binding energy of (a) C and (b) S to the h4 site of fcc-Ru(211) as a function of applied strain. The total changes in binding energy, ΔEbe (black), in the upper panels, has been decomposed into changes in the electronic contribution, ΔEelec (red), in the middle panels, and mechanical contributions, ΔEmech (green), in the lower panels. The negative of the shift in the d-band center, −ΔEd (blue), is coplotted with the changes in electronic contribution to binding. The units of energy are eV.

with strain, while for Ch4−Ch4 the electronic contribution varies nonlinearly with strain. The mechanical contributions are shown in Figure 3a3,b3,c3. For Ch4−Ch4 and Ch4−Sh4 the mechanical contributions is nonlinear, while for Sh4−Sh4 it is linear with an applied strain. For the Ch4−Ch4 case, mechanical contributions to the interaction energy are quantitatively large, giving the impression of a significant interaction, but the interaction largely acts to cancel the initial mechanical energy stored by the monomer, as can be seen by looking at the total binding energy changes of Ch4−Ch4, as in Figure 4. Overall, we find that the interaction energies versus applied strain can be quantitatively significant and are controlled by electronic contributions. The interactions are not quantitatively predicted by a d-band picture and include factors from adsorbate−adsorbate wave function and charge effects, but the d-band picture does predict trends (Figure 3, SI). We can analyze the electronic contributions from the d-band using a linear regression fit. This can be done by fitting the monomer change in electronic binding, ΔEelec(ε), to the change in d-band center of the clean surface, ΔEd(ε). This fit of ΔEelec(ε) vs ΔEd(ε) is then used to predicted the d-band-mediated changes in interaction energy, ΔEd−band (ε), due to the presence of the coadsorbate (SI). The int notation to describe the interaction of a second species, B, bound to a surface, S, with a preadorbed species, A, is B/(A/S). These changes in the d-band contribution to interaction energy are shown in Figure 3 and are shown with the electronic changes in interaction energy. For the case of C−S coadsorption, the d-band-mediated changes in interaction energy are not uniquely defined; the electronic interaction energy may be considered due to an S atom binding to a surface that has an electronic structure perturbed by a C atom, Sh4*/(Ch4*/fcc-Ru(211)), or the electronic interaction energy

The mechanical contribution to the overall change in binding energy versus strain is shown in Figure 2a3,b3 and is nearly zero over most of the strain range. For Ch4, the mechanical contribution is nonzero and reaches −0.15 eV at a strain of −0.03, while for Sh4 the change in mechanical contribution to binding is negligible over the entire range. The mechanical interaction between the applied strain (εapp) and the adsorbateinduced strain (εads) scales as the product (εappεads) and is evidently small. This does not necessarily imply, however, that the mechanical interaction energy between two adsorbates A and B, which scales as εads(A) εads(B), is small, since it depends on the components of the adsorbate strains. Pair Interactions. Parts a, b, and c of Figure 3 show the changes in interaction energies under strain for Ch4−Ch4, Ch4− Sh4, and Sh4−Sh4, respectively. We note that, for the cell size used here, an isolated C or S adsorbate corresponds to adsorbates on every second site, while the adsorbate−adsorbate interaction energies correspond to full coverage of the h4 sites. The configuration studied for each of the cases is shown as an inset in Figure 3. The inset shows that both C and S are in the h4 sites with C binding closer to the surface than S. Over the range of −0.03 to +0.03 strains, the binding energy range for Ch4−Ch4 is from 0.1 to −0.14 eV, for Ch4−Sh4 is from 0.18 to −0.17 eV, and for Sh4−Sh4 is 0.3 to −0.26 eV. As shown by the inset, these interaction energy changes are for a fully covered step. These changes in interaction energy are quantitatively comparable to the changes in binding energy itself (∼0.45 for Ch4 and ∼0.15 eV for Sh4) and therefore play a comparable role in controlling total binding. We now decompose the C−C, C−S, and S−S interaction energies into their electronic and mechanical contributions. The electronic contributions are shown in Figure 3a2,b2,c2. For Ch4−Sh4 and Sh4−Sh4, the electronic contribution varies linearly D


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Figure 3. Changes in interaction energy of (a) C−C, (b) C−S, and (c) S−S bound to the h4 sites of fcc-Ru(211) as a function of applied strain. The changes in interaction energies, ΔEint (black), in the upper panels, have been decomposed into changes in the electronic contribution, ΔEelec int (red), (green), in the lower panels. The changes in the interaction energies have here been in the middle panels, and mechanical contributions, ΔEmech int divided by two so that the interaction energy changes may be intuitively compared to the binding energy changes. The units of energy are eV.

by the DFT-estimated changes in cohesive energy, ΔG ≈ ΔEDFT. The heat of mixing is not normally given as a change in energy, ΔE, but normalized to some unit size, here the step length, L, providing the energy per unit length as Δγmix = ΔEDFT/L. We consider here possible mixing of a surface completely covered by sulfur and a surface completely covered by carbon. The state of a completely covered surface is modeled by occupying all hollow-4 positions in the step, h4 in Figure 1, and all step hollow-3, h1 in Figure 1. This allows us to describe the surface through a single-coverage variable that we take to be that of sulfur, θS. θS = 0 is defined as all h4 and h1 being occupied by C, θS = 1 is defined as all h4 and h1 being occupied by S. All possible configurations of C and S for a given θS in cells of two and three atoms were examined by varying the occupation of h4 and h1. This is not an exhaustive compilation of site combinations, as other structures are not considered. The entire set of calculations was then used to determine the heat of mixing at the step according to

may be considered due to an C atom binding to a surface that has an electronic structure perturbed by a S atom, Ch4*/(Sh4*/ fcc-Ru(211)). Looking at ΔEd−band (ε) and ΔEelec int int (ε) together reveals that the two follow each other for C−S interaction and are qualitatively in the same direction for C−C and S−S but do not quantitatively match; this demonstrates d-band-mediated interactions under strain to be important but that there are other contributing factors not identified by this model. Mixing. Mixing results from a negative energy of mixing, energy gained due to mixing, and separation results from a positive energy of mixing, energy lost due to mixing. If entropic changes are ignored, the energy of mixing may be approximated

Δγ mix(θS ,ε) =

1 DFT {E (θS ,ε) − [(1 − θS)EDFT(θS=0,ε) L

+ θSEDFT(θS=1,ε)]}

(5)

Shown in Figure 5 are the lowest values of Δγmix for a given θS and ε forming the convex hull.26,45,46 For all applied strains, the heat of mixing is negative, indicating the C and S to be mixed under all examined strains. The maximum heat of mixing gained varies from −0.43 eV/Å at a strain of −0.03, to −0.29 eV/Å at a strain of 0.00, and to −0.25 eV/Å at a strain of 0.03. It is therefore the case that while the strain does not induce a phase change for (C+S)/fcc-Ru(211), the influence of the strain on the heat of mixing is on the order of the heat of mixing itself.

Figure 4. Change in the total binding energy (black) and electronic (red) and mechanical (green) contributions of two C atoms in the h4 positions of the fcc-Ru(211) surface. The units of energy are eV. E


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experimental chemical potential parameter is determined, μC − μS . We may now determine θS as a function of applied strain by minimizing Δγtot(θS,ε). Taking the determined value of μC − μS, and the calculated values of Δγbe(θS,ε), the values of θS, which minimize Δγtot(θS,ε), is determined and given in Figure 6. From ε = 0 to 0.03, the sulfur coverage drops from 0.4 to

Figure 5. Heat of mixing (convex Hull) of the (C+S)/fcc-Ru(211) as a function of applied strain. See the text for details.

S Coverage. The S coverage may be determined by minimizing the free energy of adsorption. With the heat of mixing in hand, and the awareness that mixture does occur, the binding energy per unit step length may be calculated. The binding energy per unit step length, Δγbe, is the total energy gained from binding and from mixing and is thus given by

Figure 6. Sulfur coverage versus applied strain determined by free energy minimization. See the text for details.

θ E (θ =1,ε) + (1 − θS)E be(θS=0,ε) Δγ (θS ,ε) = S be S L be

+ Δγ mix(θS ,ε)

(6a)

0.34, and from ε = 0 to −0.01 and −0.02 it goes up to 0.51 and then drops to 0.25 at a strain of −0.03. This means that the sites available for catalysis may increase by 10% at 0.03 strain, (1 − θS(εb=0.03))/(1 − θS(εb=0)) = 1.1, and may increase by 25% at −0.03 strain, (1 − θS(εb=−0.03))/(1 − θS(εb=0)) = 1.25. Whether tensile or compressive strain is applied, siteblocked-related poisoning may be mitigated and the selection of strain may otherwise be informed by additional factors, such as the influence of the applied strain on activity and selectivity.

This binding energy per unit step length can be equivalently directly determined from the DFT energies, without the heat of mixing analysis, using the number of binding sites, N, per unit length, L, according to Δγ be(θS ,ε) =

E be(θS ,ε) L

= {EDFT(ε)[θS] − EDFT(ε)[Ru(211)] − N (θSEDFT[Sgas] + (1 − θS)EDFT[Cgas])}/L

IV. DISCUSSION The recent finding of a new mechanical work term in surface chemistry has motived us to examine the possibility of strainmediated changes in interaction energies and any possible broader implications for catalyst design. We have chosen the probe system of C and S interaction on an Ru step because of its possible application to the synthesis of hydrocarbons from biomass and the poisoning of the desired hydrocarbon chemistry by S intrinsic to biomass. Implications for Biomass Catalysis. The existing hypothesis for the poisoning of S on biomass catalysis is a site-blocking mechanism.36,37 Here, it has been demonstrated that C+S will mix, meaning that reacting carbon species will have S in their local environment. The direct interaction of S with carbon species allows S to interfere with the desired hydrocarbon chemistrya spectator effect. Experimental measurements have revealed that when S is added to a biomass reactor, not only is the total product reduced but also the type of product changes.37 The change of the type of product implies that the nature of the chemistry has changed. Combining the knowledge of mixing and the measurement of reaction product changes upon addition of S is strong evidence

(6b)

The binding energy per unit length is shown in the SI for ε = −0.03, 0, 0.03. The total free energy per unit step length, Δγtot(θS,ε), is the binding energy per unit step length plus the chemical potential contributions from C and S, μC and μS, and is given by Δγ tot(θS ,ε) = Δγ be(θS ,ε) −

N[θSμS + (1 − θS)μC ]

(7) L Equation 7 is the quantity to minimize to determine coverage. Equation 6 is completely determinable from calculations, but the chemical potential terms in eq 7 require knowledge of environmental conditions. We use experimental measurements to parametrize the strain-free coverages and therefore the value μC − μS. Under operating conditions,18,19 the surface is completely covered, showing θC = 0.475, θCH = 0.102, θCH2 = 0.024, θCH3 ≈ 0.000, θS = 0.4 at T = 400 °C and P = 25 MPa; these measurements allow us to approximate the surface as covered either by C and S alone. Taking the DFT values of Δγbe(θS,ε), for θS = 0.4 and ε = 0, the value of μC − μS is determined, which minimizes Δγtot(θS,ε), and in this way the F


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induced strain field changes in response to the applied strain.50 Applying this principle to the bound C and S states, significant polarization effects are observed for C under compression and less for C and S otherwise. Mechanically mediated interaction energies between two adsorbates, A and B, may be defined by the surface stiffness tensor, Csurf(r), and the adsorbate-induced strain fields, εA(r) and εB(r), respectively, according to

for a combination of both the proposed site blocking mechanism and a spectator mechanism. The strain analysis has revealed that whether tensile or compressive strain is applied, reduced sulfur coverage is achievable (Figure 6). The possible improvement of site blocking, regardless of type of strain, leaves the strain as a tool to optimize the catalytic hydrocarbon chemistry. It has here been demonstrated that both the changes in binding energy and interaction energy of the C+S system over Ru move in the same direction, and due to their additive nature, they result in larger than anticipated changes in total binding. Strain may here be a valuable tool for engineering surface chemistry, not because of the role of a previously unconsidered mechanical work term but because of the serendipitous addition of binding and interaction energies. Implications for Strain Engineering. The serendipitous addition of changes in binding and interaction energies may be the rule rather than the exception, at least for band-mediated interactions. The d-band model, which successfully captures trends in electronic binding with strain, is a perturbation theory model.47 The model describes the coupling of molecular orbitals to solid-state bands as a perturbation and changes in binding due to strain as the result of strain-induced changes in the band structure.10,41 The shift in band structure due to strain has been shown to be the result of changes in metal−metal coupling, where compression leads to increased coupling and tension to reduced coupling. For late transition metals, where the band is more than half full, reduced perturbation from tensile strain results in a upward movement of the band and stronger binding; for early transition metals, where the bands are less than half full, reduced perturbation from tensile strain results in an downward movement in the band and weaker binding.48 If one views band-mediated adsorbate−adsorbate interaction as a perturbative process, the observations from band-mediated changes in binding due to strain may be used to make inferences. The presence of an adsorbate will act to perturb the underlying band structure. A tensile strain will reduce the adsorbate−metal coupling, as it does the metal−metal coupling, and therefore result in the same upward motion of the band for late transition metals and downward motion of the band for early transition metals. The adsorbate−metal coupling (s−d or p−d) is stronger than the metal coupling (d−d), resulting in a larger adsorbate−metal perturbation compared to metal− metal.49 This perturbative picture of band-mediated strain effects predicts changes in the d-band center and the interaction energy that are consistent with the observations here [Figures 3 and S1 (SI)]. This perturbative picture therefore predicts that band-mediated binding and interaction energy changes with strain will always be additive and therefore more significant. The dominance of electronically mediated changes in interaction energy over mechanically mediated changes may too be more generic. The mechanically mediated component of the changes in binding energy, ΔEmech be (ε), are controlled by the applied stress field, σapp(r), and the adsorbate induced strain field, εads(r), according to mech ΔE be (ε)

=

∫ σapp(r ) εads(r) dV

mech E int =

∫ Csurf (r ) εA (r ) εB(r ) dV

(9)

This analysis predicts that that mechanically mediated interaction energies will change with applied strain only when polarization is present, when either εA(r) or εB(r) have a dependency on εapp. Taking this polarization requirement for mechanically mediated changes in interaction and the observation of significant polarization in C under compression and less in C and S otherwise, one would anticipate significant changes in mechanically mediated interaction energies for any species interacting with C under compression and less otherwise. Changes in mechanically mediated C−C interactions are strongest in compression, C−S strongest in compression, and S−S slowly varying (Figure 3), in support of the nonlinearity in mech ΔEbe (ε) being the result of a polarization and that mech polarization being predictive of ΔEmech int (ε). ΔEint (ε) impiles polarization, but mechanically mediated changes in interaction do not necessarily lead to the larger role of mechanics in surface chemistry. It is entirely possible that those mechanically mediated changes in interaction ultimately counteract the mechanically mediated changes in binding, resulting in the reduced role of mechanics in surface chemistry, and ultimately, the dominance of electronic effects, as was observed here (Figures 2−4). The analysis presented in this discussion requires verification before broad statements may be made, but if the analysis bears out, the implications for strain engineering are significant. For the case of catalysis on low-coverage surfaces, strain engineering was found to be particularly valuable in those cases where the newly found mechanical work term was significant.11 In those cases where the newly found mechanical work term would not be significant, strain engineering would have had the reduced applicability previously thought, reducing the scope of strain engineering. Here, for the C+S on Ru system, electronically mediated interactions were found to dominate over mechanical effects. The total electronic effects are large due to the addition of the binding and interaction effects. It has been argued that band-mediated binding and interaction changes should always be additive. Should the superposition of binding and interaction effects be pervasive, the broad class of cases where surfaces are covered will find meritorious application of strain engineering.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b02422. Detailed information on the structure of the surface step, the method of application of strain, the observed correlations between electronic shifts in binding and the shifts in the d-band center, and total binding energy per unit step length (PDF)

(8)

If we assume σapp(r) to vary linearly with the applied strain, εapp, than any nonlinearity in ΔEmech be (ε) may be attributed to εads(r). The physical meaning of a nonlinearity in εads(r) with applied strain is polarization, wherein the structure of the adsorbateG


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AUTHOR INFORMATION

Corresponding Author

*E-mail: mff[email protected]. ORCID

M. F. Francis: 0000-0002-5430-0661 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support for this work was provided by the US Department of Defense, Army Research Office, through the Multi-University Research Initiative on “Stress-Controlled Catalysis via Engineered Nanostructures” at Brown University, grant number W911NF-11-1-0353.

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