Size-dependent strong metal-support interaction in TiO2 supported Au nanocatalysts

The strong metal-support interaction (SMSI) has long been studied in heterogonous catalysis on account of its importance in stabilizing active metals and tuning catalytic performance. As a dynamic process taking place at the metal-support interface, the SMSI is closely related to the metal surface properties which are usually affected by the size of metal nanoparticles (NPs). In this work we report the discovery of a size effect on classical SMSI in Au/TiO2 catalyst where larger Au particles are more prone to be encapsulated than smaller ones. A thermodynamic equilibrium model was established to describe this phenomenon. According to this finding, the catalytic performance of Au/TiO2 catalyst with uneven size distribution can be improved by selectively encapsulating the large Au NPs in a hydrogenation reaction. This work not only brings in-depth understanding of the SMSI phenomenon and its formation mechanism, but also provides an alternative approach to refine catalyst performance.


Supplementary Figures and Tables
It can be observed that even calcined at different temperature, the Au NPs had similar shape of truncated octahedron for Au-3nm and Au-7nm, with Au {111} and {100} facets mainly exposed, consisting with the equilibrium shape of fcc metals. 12,13 14

Supplementary information for the discussion of surface energy
Supplementary The intrinsic/bulk surface energy (also the solid-vapor interface energy, γ sv0 , a intrinsic physical quantity) of different metals are listed in Supplementary Table 2. The γ sv0 value of Au is obvious lower than that of Ir, Rh, Pt, Ni, and Pd. However, the reported surface energy value of TiO 2 , either calculated or experimental, are not uniform to be used as one parameter to compare with that of Au.
In nanoscale, size-dependence of surface tension is significant and has been well studied since Tolman 23 . Based on the long-term study of several research groups, 14,15,24-26 the size-dependent solid-vapor interface energy γ sv (d) could be approximately theoretical determined by Supplementary Equation (1), where d represents the diameter of Au NPs, and C represents a constant varied with different modeling method. It can be seen that the γ sν (d) value will increase with increasing of particle size if C is positive. In our system, this implies 15 a potential driving force for the size-dependent SMSI: the minimization of the surface free energy of Au NPs.
However, a few reports suggested an opposite trend mostly either simulation at 0K 27 or experimentally measured at low temperature 28 . A recent work by Molleman and Hiemstra performed a comprehensive study on the size-dependence of surface tension at nanoscale, 29 which is helpful to address the controversy. They showed that at high-temperatures positive relationship between particle size and surface tension is possible, as shown in   16 Therefore, it is speculated that the size-dependent SMSI is related to the size-dependency of the surface tension of Au NP. To manifest concrete variation illustration for this, an in-depth discussion and interpretation was done by establishing thermodynamic dynamic equilibrium for the encapsulation of Au by TiO 2 .
Supplementary Figure 12. Size-dependent surface tension calculated at 400 o C. Formulation, enthalpy, entropy and surface tension data used are from ref. 29 .

Formulation and numerical solution of the Au-TiO 2 encapsulation model
Based on our observation of TEM image (Figure 4a), as shown in Figure 4b, we try to establish a model to qualitatively reproduce our experimental results. Two variables, r and θ are used to represent the state of NP. r is the radius of NP (a globular model particle is used for simplicity, different crystal shape will only cause a slight scaling of radius, see ref. 29  (3) for the part of Au surface that has been covered by TiO 2-x , , Then, denoted that 32 (6) Also for part of Au surface that is still bare, for simplicity, (r, θ)-dependence of term γ TiO2-x is not considered, although for practical system, small γ TiO2-x is more favored for starting up mass transfer of overlayer species, 18 rearrangement after encapsulation is also reported 33 , but in our system, we did not observe significant structural difference. Collecting equations above, relationship between r and θ is obtained:  Reaction condotions: T