Remarkable NanoConfinement Effects on Equilibrated Reactions: Statistical-Mechanics Modeling Focused on Ir Dimerization Beneath Surface Sites in Pd–Ir Nanoparticles

The Thermal Stability of Asymmetric Separated Configurations inside Alloy Nanoparticles: Atomic-Scale Modeling of Pd-Ir Nanophase Diagrams

Compared to alloy bulk phase diagrams, the experimental determination of phase diagrams for alloy nanoparticles (NPs), which are useful in various nanotechnological applications, involves significant technical difficulties, making theoretical modeling a feasible alternative. Yet, being quite challenging, modeling of separation nanophase diagrams is scarce in the literature. The task of predicting comprehensive nanophase diagrams for Pd-Ir face-centered cubic-based three cuboctahedra is facilitated in this study by combining the computationally efficient statistical-mechanical Free-energy Concentration Expansion Method, which includes short-range order (SRO) with coordination-dependent bond-energy variations as part of the input and with rotationally symmetric site grouping for extra efficiency. This nanosystem has been chosen mainly because of the very small atomic mismatch that simplifies the modeling, e.g., in the assessment of vibrational entropy contributions based in this work on fitting to the Pd-Ir experimental bulk critical temperature. This entropic effect, together with SRO, leads to significant destabilization of low-T Quasi-Janus (QJ) asymmetric configurations of the NP core, which transform to symmetric partially mixed nanophases. First-order and second-order intracore transitions are predicted for dilute and intermediate-range compositions, respectively. Caloric curves computed for the former case yield the NP-size dependent transition latent heat, and in the latter case critical temperatures exhibit a specific scaling behavior. The computed separation diagrams and intracore solubility diagrams reflect enhanced elemental mixing in smaller QJ nanophases. In addition to these diagrams, the revealed near-surface compositional variations are likely to be pertinent to the utilization of Pd-Ir NPs, e.g., in catalysis.

Adsorption under nanoconfinement: a theoretical-computational study revealing significant enhancement beyond the Langmuirian levels

The principal goal of this work is to predict characteristics unique to equilibrated adsorption of a small number of molecules on atomic sites located inside a closed nanoscale space. Compared to the thermodynamic limit of macroscopic systems, significantly enlarged adsorbate coverage under nanoconfinement constitutes a major finding of the modeling. Concomitantly, nanoconfined adsorbates are expected to exhibit extra thermal stability against desorption. These effects on adsorption are explored using canonical partition-functions as well as an original relationship between coverage variations and the Langmuir constant, both in the frameworks of the ideal gas and lattice-gas models. With reported DFT adsorption-energies as input, adsorption isotherms are derived numerically for H2 on Ti-doped graphene-like nanostructures. Remarkable deviations from the classical Langmuir isotherm are predicted for the first time, namely, system-size dependent enhanced H2 adsorbate coverage. The effects are computed also for CO2 inside MOF single-molecule traps, including their relationships to adsorption-energy, specific-heat and to coverage fluctuations. According to preliminary modeling, nanoconfinement effects are anticipated also for adsorption in nanopores undergoing molecular exchange with the external environment, and for impurity segregation in nanoparticle and nanocrystalline solids. The entropic origin of the nanoconfinement effect on equilibrium adsorption (NCEEA) is demonstrated analogously to the nanoconfinement effect on equilibrated chemical reactions studied by us previously. Besides unraveling some basic theoretical issues in physical nanochemistry, this study is expected to be pertinent to nanotechnological applications, such as gas storage and separation in nanoporous materials and other solid adsorbents.

Stochastic or Not? Method To Predict and Quantify the Stochastic Effects on the Association Reaction Equilibria in Nanoscopic Systems

The stochastic nature of chemical reaction and impact of the stochasticity on their evolution is soundly documented. Both theoretical predictions and emerging experimental evidence indicate the influence of stochastic effects on the equilibrium state of association reaction. In this work simple mathematical formulas are introduced to estimate these effects. First, the dependence of the ratio of observed reactants (apparent association constant, equivalent of macroscopic association constant in stochastic analysis) on the volume and the number of molecules of reagents is discussed and the limiting factors of this effect are shown. Next, the apparent association constant is approximated for nanoscale systems by closed-form formulas derived for this purpose. Finally, an estimation for the macroscopic constant value from the apparent one is provided and validated on the published experimental data. This work was inspired by chemical reactions occurring in biological compartments, but the results can be used for all systems belonging to the stochastic regime of chemical reactions.