Bimetallic nanoparticles (BNPs) often possess peculiar segregation behavior as the particle size, composition, shape, and temperature are varied. However, a thermodynamic model for this phenomenon has been lacking thus far. We show for the first time that the distribution of metal species within a nanoparticle can be adequately captured in terms of distribution coefficients calculated for the facets, facet edges, and bulk regions. Thermodynamic relations for the distribution coefficients are derived. Only m distribution coefficients from the m(m − 1) distribution coefficients are independent, where m denotes the number of regions. The theory is applied to AuPt, NiPt, and AuAg BNPs. Distribution coefficients are calculated at 400 and 600 K using Monte Carlo (MC) simulations of varying BNP sizes and compositions. A wide range of mixing behavior from alloying to partial or full segregation and core−shell to onion-like structures can be observed. A key finding is that the distribution coefficients are independent of the BNP size. The observed size-dependent segregation can be attributed to the relative availability of surface and bulk sites, i.e., the area-to-volume (A/V) ratio. This implies that two bimetallic nanostructures of different sizes and shapes but the same A/V ratio may exhibit nearly identical segregation behavior. Thus, nanothermodynamic segregation in bimetallic alloys may be described concisely using a handful of distribution coefficients.

Nano-thermodynamic model captures thermodynamic preference of metal species for different regions of a nanoparticle while accounting for size effects.

We present a hierarchical coarse-grained simulation technique called the temperature programmed molecular dynamics (TPMD) method for accelerating molecular dynamics (MD) simulations of rare events. The method is targeted towards materials where a system visits many times a collection of energy basins in the potential energy surface, called a superbasin, via low-barrier moves before escaping to a new superbasin via a high-barrier move. The superbasin escape events are rare at the MD time scales. The low-barrier moves become accessible to MD by employing a temperature program, i.e., the MD temperature changes during the simulation. Once a superbasin is detected, transitions within the superbasin are ignored, in effect causing coarse-graining of basins. The temperature program enables the system to escape from the superbasin with reduced computational cost thereby overcoming the "low-barrier" problem. The main advantage of our approach is that the superbasin-to-superbasin transitions are accurately obtained at the original temperature with a reasonable computational cost. We study surface diffusion in Ag/Ag(001) system and demonstrate the ability of the TPMD method to span a wide-range of timescales.

Capturing segregation behavior in metal alloy nanoparticles accurately using computer simulations is contingent upon the availability of high-fidelity interatomic potentials. The embedded atom method (EAM) potential is a widely trusted interatomic potential form used with pure metals and their alloys. When limited experimental data is available, the A-B EAM cross-interaction potential for metal alloys AxB1−x are often constructed from pure metal A and B potentials by employing a pre-defined ‘mixing rule’ without any adjustable parameters. While this approach is convenient, we show that for AuPt, NiPt, AgAu, AgPd, AuNi, NiPd, PtPd and AuPd such mixing rules may not even yield the correct alloy properties, e.g., heats of mixing, that are closely related to the segregation behavior. A general theoretical formulation based on scaling invariance arguments is introduced that addresses this issue by tuning the mixing rule to better describe alloy properties. Starting with an existing pure metal EAM potential that is used extensively in literature, we find that the mixing rule fitted to heats of mixing for metal solutions usually provides good estimates of segregation energies, lattice parameters and cohesive energy, as well as equilibrium distribution of metals within a nanoparticle using Monte Carlo simulations. While the tunable mixing rule generally performs better than non-adjustable mixing rules, the use of the tunable mixing rule may still require some caution. For e.g., in Pt–Ni system we find that the segregation behavior can deviate from the experimentally observed one at Ni-rich compositions. Despite this the overall results suggest that the same approach may be useful for developing improved cross-potentials with other existing pure metal EAM potentials as well. As a further test of our approach, mixing rule estimated from binary data is used to calculate heat of mixing in AuPdPt, AuNiPd, AuPtNi, AgAuPd and NiPtPd. Excellent agreement with experiments is observed for AuPdPt.

A commonly used strategy to enhance the mass activity of Pt-based catalysts involves the synthesis of Au nanoparticles (NPs) with a monolayer-thick Pt-skin layer. The synergistic effect of Au and Pt results in a higher catalytic activity and better Pt utilization. However, the stability of the Pt-skin layer is questionable as our recent equilibrium Monte Carlo simulations predict that eventually the surface Pt is replaced by Au. The role of Au during destabilization of Pt-skin in vacuum and solution is investigated with the help of molecular dynamics. Different starting Au–Pt arrangements are studied mimicking various NP synthesis approaches. Beyond a critical number of atoms in a Pt cluster, the ideal Pt monolayer rapidly transforms to a three-dimensional (3D) Pt cluster. This is supported by our model predicting transition from the Pt monolayer to Volmer–Weber growth in the Au–Pt system. At room temperature, Pt atoms move into the subsurface layer at second timescales mainly via the exchange mechanism involving Au atoms or Au climbing on top of Pt. For all practical purposes, the experimental “Pt-skin” Au NPs may actually correspond to a single layer of surface Au over subsurface Pt layers. Presence of large 3D Pt clusters may slowdown the climbing of Au atoms on Pt, thereby delaying the formation of Au-skin.