Micha Polak* and Leonid Rubinovich
Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
Received: 27 December, 2016; Accepted: 27 January, 2017; Published: 31 January, 2017
Micha Polak, Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel, E-mail:
Polak M, Rubinovich L (2017) Prediction of Enhanced Dimerization inside Dilute Alloy Nanoparticles. Int J Nanomater Nanotechnol Nanomed 3(1): 023-026. DOI: 10.17352/2455-3492.000017
Â© 2017 Polak M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Nanoconfinement; Alloy nanoparticles; Dimerization; Chemical-equilibrium; Mixing-entropy
According to a unique nano-confinement effect of entropic origin, predicted by us several years ago for the equilibrium state of chemical reactions, the equilibrium-constant and extent are greatly enhanced depending on the small number of molecules involved, and for many reactions also on the nano-space size. This work explored the validity of this effect in the case of elemental dimerization reactions within dilute alloy nanoparticles with separation tendency, Pd – Ir cuboctahedra in particular. Employing a simple model for the system energetics, computations based on the exact canonical partition-function reveal nano-confinement induced Ir2 dimer stabilization within Pd surface segregated nanoparticles, reflected e.g., by up to ~ 60% increased dimerization extent and by doubling of the 1n KD vs. 1/T slope, as compared to the macroscopic thermodynamic limit. The dual role of the configurational entropy, namely mixing of Ir/Ir2 vs. Pd/Ir is elucidated. Study based on more elaborate energetic models is desirable as the next step of this research.
As shown by us some years ago , the involvement of small numbers of molecules in a closed reaction space can considerably affect the chemical equilibrium. Thus, significant increase of the reaction extent was predicted for the case of exothermic reactions as compared to that of the corresponding macroscopic system (in the thermodynamic limit, TL). This nanoconfinement entropic effect on chemical equilibrium (NCECE) is universal in a sense that it stems only from the limited amount of molecules in a reaction mixture, resulting in a reduced number of mixed reactant-product microstates in the closed system [1,2]. The effect was predicted for the case of nucleotide dimerization within molecular cages  and verified for DNA hybridization  that was studied experimentally before . The NCECE is relevant to several advanced routes for the synthesis of encapsulated organic molecules, metallic or inorganic nanoclusters, and other nanoscale structures and applications.
While the NCECE is expected mostly in molecular nanosystems, this effect that arises from fundamental mixing-entropy variations can in principle be manifested also in other reaction classes, e.g., in alloy systems. The present study focuses on the distinct case of constituent atom equilibrated dimerization within phase-separating alloy nanoparticles (NPs). Namely, the main question of this study concerns whether confined dimerization can exhibit significant NCECE effects. Being a first stage in phase separation (or the main process in very dilute alloys) that can affect chemical and physical properties, dimerization inside NPs seems to be a sensible issue for theoretical-computational modeling. For this goal fcc-based Pd – Ir NPs have been chosen, because of the strong Pd tendency to segregate at the alloy surface, making the Pd rich core a natural confined space for Ir solute atoms entirely surrounded by 12 Pd nearest-neighbor (NN) Pd atoms. Moreover, Pd – Ir nanoparticles are efficient catalysts, e.g., promoting preferential oxidation of CO in the presence of excess H2 in proton exchange membrane fuel cells [5-7]. Recently, chemical-order in “magic-number” Pd – Ir NPs was studied by means of density functional theory (DFT) computations  and compared to those obtained by the Free-Energy Concentration Expansion Method (FCEM) , using derived coordination-dependent bond-energy variations (CBEV)  and by the Birmingham Cluster Genetic Algorithm with the Gupta potential .
In this work, Ir dimerization in cuboctahedron dilute cores of the magic-number size series  is studied (namely, 13, 55, 147, 309, 561 and 923 atom cores inside 55, 147, 309, 561, 923 and 1415 atom alloy NPs, respectively) in the framework of the NN interaction approximation. Energetic equivalence of all intra-core Ir atomic sites and of all Ir2 dimer locations is assumed, since, as noted above, they are all surrounded by Pd only (Figure 1). This includes also the subsurface sites, namely possible CBEV effects are ignored in this study. Correspondingly, the energy of the intra-core dimerization “reaction” equals the doubled bulk Effective Pair Interaction (EPI), ∆E = 2V = (wPdPd + wPdIr – 2 wIrIr) ≈ -74 meV, as derived from DFT-computed low-temperature formation enthalpy . Formulas for the equilibrium dimerization extent, equilibrium constant and the NP entropy are derived below based on canonical statistical mechanics and applied in MATLAB computations. Then, the results are evaluated for possible NCECE manifestations by comparison to the corresponding values of a hypothetical macroscopic alloy with the same composition and dimerization energy.
In the employed lattice-gas model  microstates correspond to different arrangements of two Ir solute atoms on n available atomic sites, and to the locations of a single Ir2 dimer at available n' bonds in the NP core (see examples in Figure 1b). Concentrations of Ir atoms and dimers are related to the nanoconfined (NC) reaction extent, ( ) for pure reactants, for pure products),
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