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Item type:Publication, Hexagonal-shaped spin crossover nanoparticles studied by Ising-like model solved by local mean field approximation(MDPI AG, 2021-05-01)The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short-and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D. ) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq ) of external origin. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, A first-order phase transition studied by an Ising-like model solved by entropic sampling Monte Carlo method(MDPI AG, 2021-04-01)Two-dimensional (2D) square, rectangular and hexagonal lattices and 3D parallelepipedic lattices of spin crossover (SCO) compounds which represent typical examples of first order phase transitions compounds are studied in terms of their size, shape and model through an Ising-like Hamiltonian in which the fictitious spin states are coupled via the respective short and long-range interaction parameters J, and G. Furthermore, an environmental L parameter accounting for surface effects is also introduced. The wealth of SCO transition properties between its bi-stable low spin (LS) and high spin (HS) states are simulated using Monte Carlo Entropic Sampling (MCES) method which favors the scanning of macro states of weak probability occurrences. For given J and G, the focus is on surface effects through parameter L. It is shown that the combined first-order phase transition effects of the parameters of the Hamiltonian can be highlighted through two typical temperatures, TO.D., the critical order-disorder temperature and Teq the equilibrium temperature that is fixed at zero effective ligand field. The relative positions of TO.D. and Teq control the nature of the transition and mediate the width and position of the thermal hysteresis curves with size and shape. When surface effects are negligible (L = 0), the equilibrium transition temperature, Teq. becomes constant, while the thermal hysteresis’ width increases with size. When surface effects are considered, L ≠ 0, Teq. increases with size and the first order transition vanishes in favor of a gradual transition until reaching a threshold size, below which a reentrance phenomenon occurs and the thermal hysteresis reappears again, as shown for hexagonal configuration. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, 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.