Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials

We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behavior of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (BCC) and face-centered-cubic (FCC) crystalline structures and the fluid phase. We confirm the existence of a reentrant BCC phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the BCC-FCC coexistence line of the inverse-power-law model as a function of the power exponent $n$ and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.Comment: 22 pages, 8 figure

Lattice density-functional theory of surface melting: the effect of a square-gradient correction

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour, liquid, and triangular solid. While a straightforward mean-field treatment of the interparticle attraction is unable to give a stable liquid phase, the correct phase diagram is obtained when including a suitably chosen square-gradient term in the system grand potential. Taken this theory for granted, I further examine the structure of the solid-vapour interface as the triple point is approached from low temperature. Surprisingly, a novel phase (rather than the liquid) is found to grow at the interface, exhibiting an unusually long modulation along the interface normal. The conventional surface-melting behaviour is recovered only by artificially restricting the symmetries being available to the density field.Comment: 16 pages, 6 figure

The ideal gas as an urn model: derivation of the entropy formula

The approach of an ideal gas to equilibrium is simulated through a generalization of the Ehrenfest ball-and-box model. In the present model, the interior of each box is discretized, {\it i.e.}, balls/particles live in cells whose occupation can be either multiple or single. Moreover, particles occasionally undergo random, but elastic, collisions between each other and against the container walls. I show, both analitically and numerically, that the number and energy of particles in a given box eventually evolve to an equilibrium distribution $W$ which, depending on cell occupations, is binomial or hypergeometric in the particle number and beta-like in the energy. Furthermore, the long-run probability density of particle velocities is Maxwellian, whereas the Boltzmann entropy $\ln W$ exactly reproduces the ideal-gas entropy. Besides its own interest, this exercise is also relevant for pedagogical purposes since it provides, although in a simple case, an explicit probabilistic foundation for the ergodic hypothesis and for the maximum-entropy principle of thermodynamics. For this reason, its discussion can profitably be included in a graduate course on statistical mechanics.Comment: 17 pages, 3 figure

Selective Aerobic Oxidation of Cumene to Cumene Hydroperoxide over Mono- and Bimetallic Trimesate Metal Organic Frameworks Prepared by a Facile Green Aqueous Synthesis

"This document is the Accepted Manuscript version of a Published Work that appeared in final form in ACS Sustainable Chemistry & Engineering, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acssuschemeng.8b06472"[EN] Co-Ni and Mn-Ni bimetallic trimesate MOFs prepared by a fast aqueous synthesis method are excellent and reusable catalysts for the selective aerobic oxidation of cumene to cumene hydroperoxide (CHP). Isolation of Co2+ (or Mn2+) in an inert Ni-BTC framework is a good strategy to optimize CHP selectivity above 90%: since only Co2+ sites catalyze CHP decomposition, a drop of the CHP selectivity is observed as the cobalt content in the bimetallic MOF increases. The statistical probability of having isolated Co2+ sites is calculated as a function of the total cobalt content of the bimetallic compound, assuming homogeneous distribution of Co2+ ions in the Ni-BTC framework and preferential occupation of terminal sites. Thus, in our best sample, with a Co:Ni ratio of 5:95, 73% of the total Co2+ ions are isolated so that CHP decomposition/overoxidation processes at the surface of the catalyst are not likely to occur before CHP desorption. This can explain the excellent CHP selectivity (91%) attained over this material. This "site isolation" effect is further supported by similar findings on Mn-Ni bimetallic compounds.This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 641887 (project acronym: DEFNET) and the Spanish Government through projects MAT2017-82288-C2-1-P and Severo Ochoa (SEV-2016-0683).Nowacka, AE.; Briantais, P.; Prestipino, C.; Llabrés I Xamena, FX. (2019). Selective Aerobic Oxidation of Cumene to Cumene Hydroperoxide over Mono- and Bimetallic Trimesate Metal Organic Frameworks Prepared by a Facile Green Aqueous Synthesis. ACS Sustainable Chemistry & Engineering. 7(8):7708-7715. https://doi.org/10.1021/acssuschemeng.8b06472S770877157