Molecular thermodynamics of solid-fluid and solid-solid equilibria

Adatom surface diffusion of catalytic metals on the anatase TiO2(101) surface

Titanium oxide is often decorated with metal nano-particles and either serves as a catalyst support or enables photocatalytic activity. The activity of these systems degrades over time due to catalytic particle agglomeration and growth by Ostwald ripening where adatoms dissociate from metal particles, diffuse across the surface and add to other metal particles. In this work, we use density functional theory calculations to study the diffusion mechanisms of select group VIII and 1B late-transition metal adatoms commonly used in catalysis and photocatalysis (Au, Ag, Cu, Pt, Rh, Ni, Co and Fe) on the anatase TiO₂(101) surface. All metal adatoms preferentially occupy the bridge site between two 2-fold-coordinated oxygen anions (O_2c). Surface migration was investigated by calculating the minimum energy pathway from one bridge site to another along three pathways: two in the [010] direction along a row of surface O_2c anions and one in the [101[combining macron]] direction between two rows of surface O_2c anions. For all adatoms, migration along the [010] direction is favored over migration along the [101[combining macron]] direction due to closer packing of the atoms in the [010] direction and therefore stronger adatom-surface interactions. As the adatom hops along the [010] direction, it preferentially moves through a metastable OTiO structure in which the adatom partially embeds itself within the surface, with the exception of Au, which remains above the surface. The adatoms migrate with relative activation energies of: Au (0.24 eV) < Ag (0.48 eV) < Rh (0.60 eV) < Co (0.78 eV) < Pt (0.84 eV) < Ni (0.86 eV) < Cu (1.23 eV) < Fe (1.79 eV) along the favored pathway. This preference arises from the strength of adatom-surface bonding and the electronegativity difference between the metal adatom and the TiO₂ surface. We found a linear correlation between the binding energy/electronegativity and the activation energy for hopping where stronger binding energies and more oxidized adatoms have higher activation energies for adatom migration. The linear correlation developed in this work enables rapid estimations of the hopping rates of other transition metal adatoms across the TiO₂ surface.

Free energy calculations for molecular solids using GROMACS

In this work, we describe a procedure to evaluate the free energy of molecular solids with the GROMACS molecular dynamics package. The free energy is calculated using the Einstein molecule method that can be regarded as a small modification of the Einstein crystal method. Here, the position and orientation of the molecules is fixed by using an Einstein field that binds with harmonic springs at least three non-collinear atoms (or points of the molecule) to their reference positions. The validity of the Einstein field is tested by performing free-energy calculations of methanol, water (ice), and patchy colloids molecular solids. The free energies calculated with GROMACS show a very good agreement with those obtained using Monte Carlo and with previously published results.

Universal features of the free-energy functional at the freezing transition for repulsive potentials

The free-energy difference between coexisting solid and liquid phases is studied in the context of classical density functional theory (DFT). A bridge function is used to represent the higher-order (n>2) terms in the perturbative expansion of the excess Helmholtz free energy, and the values of this bridge function within the solid lattice are determined by inversion using literature Monte Carlo simulation results. Four potential models, specifically hard-sphere and inverse twelfth-, sixth-, and fourth-power repulsive, are studied. The face-centered cubic (fcc) solid is considered for the hard-sphere and inverse twelfth- and sixth-power potentials, while the body-centered cubic (bcc) solid is considered for the inverse sixth- and fourth-power potentials. For a given solid structure there is a remarkable similarity among the bridge functions for different potentials that is analogous to the universality in the sum of elementary diagrams, or bridge functions, of liquid-state theory as originally observed by Rosenfeld and Ashcroft [Phys. Rev. A 20, 1208 (1979)]. In further analogy with liquid-state theory, the bridge functions in the present problem are plotted as functionals of the second-order convolution term in the perturbative expansion. In each case, the plot indicates a unique functionality in the dense regions of the solid near the lattice sites but a scattered and nonunique behavior in the void regions. Interestingly, knowledge of the functional relationship in the unique region near the lattice sites seems to be sufficient to quantitatively model the solid-fluid phase transition. These qualitative observations are true for both fcc and bcc solid phases, although there are some quantitative differences between them. The findings suggest that pursuit of a closure-based DFT of solid-fluid transitions may be profitable.