Equilibrium Shape of Metal Nanoparticles under Reactive Gas

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Equilibrium Shape of Metal Nanoparticles Under Reactive Gas Conditions Beien Zhu, Jun Meng, and Yi Gao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b13021 • Publication Date (Web): 27 Feb 2017 Downloaded from http://pubs.acs.org on March 2, 2017

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The Journal of Physical Chemistry

Equilibrium Shape of Metal Nanoparticles under Reactive Gas Conditions

Beien Zhu1,2, Jun Meng1,3, Yi Gao1,2* 1

Division of Interfacial Water and Key Laboratory of Interfacial Physics and Technology,

Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China 2

Shanghai Science Research Center, Chinese Academy of Sciences, Shanghai 201204, China 3

University of Chinese Academy of Sciences, Beijing 100049, China

*E-mail: [email protected].

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ABSTRACT To characterize and control the shape of nanoparticles has a primary importance in nanoscience and nanotechnology since most of the physical and chemical properties are shape-dependent. In recent years, many in-situ experimental observations have shown that metal nanoparticles could change their shapes and structures dramatically and reversibly under reactive gas conditions. However, despite the experimental achievements, the precise theoretical prediction of this kind of shape evolution is still a challenging and demanding task. In this work, using CO@Pt as a benchmark, we develop a multiscale model to quantitatively illuminate the equilibrium geometries of metal nanoparticles at given temperature and gas pressure. This model perfectly reproduces the experimental results and well explains some intriguing phenomena, including the CO induced break-up of Pt surfaces. The shape evolution results of Pt, Pd, Cu and Au nanoparticles under CO and NO gas environment are presented. Our study provides useful guides for improving and developing real catalysts.


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INTRODUCTION Metal nanoparticles (NPs) have attracted intensive attention in nanoscience and nanotechnology due to their unique physical and chemical properties, which are mainly determined by their sizes and shapes. Thus, how to predict and control the shape of metal NPs has been a hot topic for their optical and catalytic applications.1-4 The recent in-situ observations shown that metal NPs may undergo surface reconstruction,5-10 resegregation,11-14 phase transition15-16 and reshaping17-21 dynamically under reaction conditions. These observations suggest that the effects of environments on the shape of metal NPs must be taken into consideration in today’s study of nanoscience. So far, many reactive gas conditions have been studied in in-situ experiments, among which the CO@Pt system is one of the most interesting and studied systems. The CO@Pt system has been worked as a benchmark with remarkable interests in catalysis study since 1920s.22 In 2001, Thostrup et al. noticed CO could induce the steps formation on the Pt(110) surface.5 After that Tao et al. observed that Pt (557) and (332) surfaces broke up into nanometer-sized clusters under CO conditions using high-pressure scanning tunneling microscopy.7 Recently, Vendelbo et al. visualized oscillatory reshaping of Pt NPs during CO oxidation by environmental transmission electron microscopy.17 However, the in-situ observations could not cover all experimental conditions. Thus, to predict whether and how a NP may vary its shape at given temperature and reactive gas pressure theoretically is a highly demanding task. In the past few years, some preliminary works have been carried out theoretically to study the deformation, sintering and dispersion phenomenon of heterogeneous nanocatalysts under CO conditions.23-29 In our previous work, we successfully predicted the shape evolution of metal nanoparticles in water vapor environments by developing a multiscale structure reconstruction


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(MSR) model.30 However, the quantitative description of the morphology change induced by CO adsorption is still missing due to the lack of effective theoretical methods. In order to fill this gap, we developed a quantitative model combining the first-principle calculations, Wulff construction model and the Fowler-Guggenheim (F-G) adsorption isotherm to study the structure evolutions of metal NPs under gas conditions. In this work, Pt, Pd, Cu and Au NPs under CO and NO conditions have been studied respectively, and the CO@Pt system is discussed in detail as a benchmark. Our theoretical model is able to reproduce the reported experimental results perfectly. In addition, the model indicates the high coverage of CO will induce the negative surface energy, which could well explain and even predict the break-up of metal surface and the dispersion of metal NPs under reaction conditions. This work gives new insights for both experimental and theoretical researchers in nanocatalysis and other nanoscience-related fields. RESULTS AND DISCUSSION Wulff stated in 1901 that a crystal with the lowest surface energy is such that the distance from its center to each face is proportional to the surface tension of the respective facet.31 Following this principle, the shape of an equilibrium crystal can be constructed. The Wulff construction has been widely used in crystalline science in the last century,32 and has been extended to nanoscience for characterizing the equilibrium shape of NPs in recent decades.29, 33-38When a NP is interacting with the environment, the surface tension should be corrected to be the interface tension,

30

= + ( ⁄ )

(1)


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where is the adsorption energy of reactant, is the surface coverage of adsorbates, is the surface area per surface atom. Thermodynamically, could be determined by the adsorption energy ( ), gas pressure (P) and temperature (T). A proper description of the relationship between and (T, P, ) is a key point for the environmental Wulff construction.30 In the present work, this relationship is described by the Fowler-Guggenheim (F-G) adsorption isotherm, so that the lateral interactions can be taken into account by

= c=

(2)

(3)

where R is the gas constant, z is the number of the nearest neighbors of a adsorption site on the surface, is the interaction energy between two adsorbed molecules.39 K in Equation (2) is the adsorption equilibrium constant which can be written as

∆%

= ! "− & = exp (−

+,-. /0,-. 01,. 2

)

(4)

where 3 (34 ) is the entropy of adsorbed (gas-phase) molecule, respectively. The F-G model can be understood that when a molecule adsorbs on the surface the chance to find other adsorbed molecules in its nearest neighbors is 5 . Within this model, the interface tension is thus modified as

= + (( − 5 )⁄ )

(5)


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Using this model and the parameters discussed in the computational method section, the structures of Pt NP under CO condition have been constructed. The size of the NP is around 10 nm, 60000 atoms. The temperature changes from 200 K to 1000 K, while the CO pressure changes from 1 Pa to 800 Pa. The structure of Pt NP is constructed using our theoretical model for every each 5 K and 5 Pa. To identify the different nanoparticle structures, one morphology 8888) parameter is calculated as the average coordination number of surface atom sites (67

:;
67 7:;
700K), Pt NP’s shape is faceted under lower CO pressure ( 100 Pa). With high-resolution TEM images, they found more open (110) planes and step sites in the more spherical state. This is exactly what we can find in our constructions. It can be seen in Figure 1b and Figure 1c that at 800 K when 8888 decreases. This the CO pressure crosses over 100 Pa, fraction of (110) facets increases and 67 corresponds to the shape change of the NP from a truncated octahedron to a more spherical one (see the structures in Figure 1d and Figure S1). In the left of the blue region in Figure 1a, there is a region where the adsorption of CO is so strong that the surface energies of (110) facets and (100) facets are negative at low temperature and/or high pressure (Figure S2b). In a single-component metal system, the surface energy shall always be positive since cleaving a surface from a bulk material creates dangling metal bonds. While in a multicomponent system, the interaction between the metal surface and the environments could cover the energy loss of the dangling bonds. When the interaction is strong enough the surface energy could be negative as suggested by Lodziana et al. and Mathur et al.4041

It has been discussed both experimentally and theoretically that on the nanoscale the negative

surface energy could induce the thermodynamic stability of nanostructures.42-43 Here, we show


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the CO adsorptions on Pt (110) and (100) facets are capable of resulting in negative surface energies. We predict that the negative surface energy would cause the increase of the interface and induce the redispersion of nanoparticles to nanoclusters. This negative surface energy could also explain the experimental observations that Pt (100) and Pt (110) surfaces reconstructed to form nanoscale islands under CO conditions while there is no such reconstruction on Pt (111) surface.5-6 In addition, the experiments found at room temperature Pt (110) surfaces are not stable even at low CO pressure which is consistent with our results that negative surface energy on that surface appears in the low temperature and low pressure region. In this work, the simulations give a clear picture of the break-up of metal surfaces and the dispersion of metal NPs under reaction conditions. The white lines in Figure 1a are the contours between two color zones numerically fitted by the same function

8888) ∗ D − E(67 8888)) = ! (B(67

(7)

8888) and E(67 8888) are two fitted parameters which are 8888 67 dependent. For any given (T, where B(67 8888 of a Pt NP under such condition can be predicted on the condition that P), the 67

8888) ∗ D − E(67 8888)2 ≥ > ! (B(67 8888 + 0.1) ∗ D − E(67 8888 + 0.1)) !/B(67

(8)

With the full sets of constructed structures shown in Figure S1, we can precisely predict whether and how the structure of the NP shall vary at (T, P). Moreover, the (T, P) region where the negative energy appears can also be numerically predicted.


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Besides 10 nm Pt NPs, 8 nm and 12 nm Pt NPs are also constructed under the same CO conditions. As shown in Figure S3, the contour plots of the three size NPs are very similar. No considerable size effect is found. This can be understood because is size independent.

8888 contour plots of 10 nm Pd, Cu and Au NPs under CO conditions are shown in Figure The 67 2. It can be seen that the shape evolution of Pd and Pt under CO conditions is qualitatively similar but quantitatively different. It should be mentioned that a black region representing negative surface energy of (110) surface appears again, which agrees with the recent observations of the formation of second-generation nanoclusters on Pd NPs under CO conditions.44 Compared to the cases of Pt and Pd, CO adsorptions on Cu and Au are rather weaker. Thus, the rhombic dodecahedron structures and the negative surface energy regions are not observed. Full sets of the constructed structures are listed in Figure S4.


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Figure 2. Contour plots of 10 nm (a) Pd, (b) Cu and (c) Au under CO conditions, color mapped with 8888 ?@. The typical constructed structures are shown beside.

The contour plots of 8888 67 of Pt, Pd, Cu, Au NPs under NO conditions are shown in Figure 3 as well as the typical constructed structures. Basically, these metal NPs undergo similar reconstructions as in CO. However, the shift of the isotherms, the appearance of blue and light blue region in the contour plots of Au and Cu NPs are different. In addition, the black region is found in both cases of Pt and Pd. It indicates NO holds the ability to disperse these NPs, consistent with the in-situ observations of Newton et al..19 The full sets of constructed structures are listed in Figure S4.


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Figure 3. Contour plots of 8888 ?@ of 10 nm (a) Pt, (b) Pd, (c) Cu and (d) Au under NO conditions. The typical constructed structures are shown below.

All the contours in Figure 2 and Figure 3 are fitted using Equation (7). The fitted parameters are listed in Table S1. As we discussed above, these data can be useful information for further theoretical and experimental NPs shape reconstruction studies. In this work we focus on the studies of CO and NO at low pressure range for the comparisons with existed experimental results. Other gases such like O2, H2 and N2 at atmospheric pressures shall be studied in our future work.


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CONCLUSIONS In this work, we provide an environment Wulff construction model to study the reshaping of NPs induced by reactive gas adsorptions theoretically. Based on this model, we perfectly reproduce the experimental visualization of the refacetting of Pt NPs during CO oxidation and give precise predictions of its structure evolution. It is shown that the shape evolution of metal NPs (Pt, Pd, Cu, Au) under reactive gas conditions (CO, NO) can be totally understood by the changes in the surface energies of different facets. In particular, the CO and NO adsorption energies on (110) and (100) surfaces of Pt, Pd can be large enough to cause the surface energies negative, which could explain the break-up of metal surfaces and the dispersion of metal NPs under reaction conditions. The behavior of metals under different (T, P) condition has been well predicted. This work cannot only be useful guides for in-situ observations, but also give insights into the reconstruction behavior of metal-gas system for real catalysis applications.

COMPUTATIONAL DETAILS Surface tensions and adsorption energies (KLMN , PQRS ). Spin-unrestricted density functional theory (DFT) calculations are performed to calculate the surface energies and adsorption energies. The energy cutoff for the plane-wave expansion is 400 eV. The convergences of the electronic self-consistent energy and forces in a conjugate-gradient algorithm are set to be 10-4 eV and 0.05 eV/Å, respectively. The projector augmented-wave method (PAW) is employed.45-46 All calculations are carried out using the Vienna Ab initio Simulation Package (VASP).47 The Perdew, Burke and Erzernhof functional (PBE) is used to calculate the surface energies.48 The periodic 2-D (1x1) slabs with increasing atomic layers are used to get accurate surface energies


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as suggested by Fiorentini and Methfessel.49 More details can be found in our previous work.30 The calculated surface tensions ( ) as well as the atomic surface areas ( ) have been shown in Supplementary Table S2. It should be noted the revised-PBE (RPBE) developed by Hammer et al. gives more accurate adsorption energies for small molecules (CO, NO, etc.) on metal surfaces except for Au and Ag, suggested by Gajdos et al.50-52 Thus, we chose the RPBE for Pt, Pd, Cu and the PBE for Au to calculate the adsorption energies in this paper. For the calculation UV of adsorption energy of isolated adsorbate ( ), periodic 2-D (4x4) slabs are used. The T points is set to be (2x2x1). The surface coverage is small enough that there is none lateral interaction between the adsorbates. In each case, the different adsorption sites (top site, bridge site, hollow site) have been checked carefully to find the lowest adsorption energy. The results of CO and NO on (111) metal surfaces from our calculations agree with the reported experimental results quite well (Supplementary Figure S5). The full data of is shown in Table S3. Noted that here we focus on the adsorption energy not the adsorption site. Lateral interactions (zw). According to Equation (5), the effective adsorption energy with coverage can be written as W

Equilibrium Shape of Metal Nanoparticles under Reactive Gas

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