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    Surface-Bulk 2D Spin-Crossover Nanoparticles within Ising-Like Model Solved by Using Entropic Sampling Technique
    (MDPI, 2023-03-01)
    We model the thermal effects in different 2D spin-crossover (SCO) square lattices within the frame of the Ising-like model using Monte Carlo entropic sampling (MCES) method to enhance the scan of macrostates beyond the most probable thermal ones. In fact, MCES allows access to the metastable states, and it is then well adapted to study thermal hysteresis properties. In this contribution, we distinguish, for the first time, the interaction between molecules located in bulk at the surface and those connecting the bulk and surface regions of an SCO lattice. In addition, an extra ligand field contribution is assigned to surface molecules through an interaction parameter (Formula presented.). In the absence of environmental effects on surface nanoparticles, a single thermal hysteresis loop increasing with the lattice size is simulated with a unique bulk and surface equilibrium temperature (Formula presented.). When environmental effects are accounted for, a two-step behavior associated with two hysteresis loops of widths ΔTS (for the surface) and ΔTB (for the bulk) with an intermediate plateau 14 K wide is obtained in the thermal dependence of the high-spin (HS) fraction for the 6 × 6 lattice. The surface and bulk equilibrium temperatures are then different, both decreasing towards lower values, and the (Formula presented.) parameter controls the three states’ behavior as well as the hysteresis loop interval. Size effects show that the equilibrium temperature is governed by the surface atoms for a small lattice size (5 × 5) and by the bulk atoms for a large lattice size (7 × 7). Moreover, a change in the size of the lattice results in a variation of the order–disorder (or Curie) temperature, TO.D., and the surface equilibrium temperature, Teq, while only TO.D. changes in bulk.
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    A Comparative Study Between Monte Carlo Entropic Sampling Method and Local Mean Field Investigations of Thermal Properties of Spin-Crossover Nanoparticles Based on Ising-Like Model
    (OAE Publishing Inc., 2023-12-01)
    The thermally induced transitions between low-spin (LS) and high-spin (HS) configurations of spin-crossover (SCO) nanoparticles are simulated, focusing on the effects of localized surface and bulk interactions on the average magne-tization of 2D square lattices. The thermal behaviors and hysteresis cycles are investigated within the framework of the Ising model Hamiltonian and are conducted following two approaches: local mean field approximation (LMFA) and Monte Carlo entropic sampling (MCES) techniques. The results obtained by these two methods are compared for the two square lattice sizes, 6 × 6 and 7 × 7. Thus, when the bulk-surface interaction term is set to zero, the two approaches lead to identical values of the surface and bulk transition temperatures separated by a long intermediate plateau in both cases. Although hysteresis curves exhibit a similar shape, LMFA shows slightly larger widths ΔT than MCES. On increasing bulk-surface interaction term, the two methods lead to different shifts in equilibrium temperature values for both bulk and surface components, respectively, to lower and higher values by MCES. In general, it is found that LMFA shifts surface equilibrium temperature differently to lower values and enhances the hysteresis effect, particularly for surface molecules. On the other hand, for the 7 × 7 square lattice, the equilibrium temperatures are slightly higher by 1.5% and 3.2% for bulk and surface molecules, respectively, with a narrower hysteresis width in the surface. Moreover, with the MCES method, an abrupt transition instead of a hysteresis transition is calculated for surface molecules (Formula Presented).