Configurational entropy of adsorbed rigid rods: Theory and Monte Carlo simulations

Centres, P. M.; Ramírez-Pastor, A. J.

doi:10.1016/j.physa.2009.01.038

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…However, a convenient formulation of the problem of hard rectangles on the RLTL is lacking. Therefore, we resort to an ad-hoc Bethe approximation introduced by DiMarzio to estimate the entropy of hard rods on a cubic lattice [44], and later used for studying the statistics of hard rods on different lattices [38,45,46]. However, a straightforward extension of this method to a system of rectangles suffers from the enumeration result depending on the order in which the rectangles are placed.…”

Section: A Bethe Approximationmentioning

confidence: 99%

Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries for the system of hard rectangles on a square lattice

Kundu

Rajesh

2015

Phys. Rev. E

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A system of hard rectangles of size m×mk on a square lattice undergoes three entropy-driven phase transitions with increasing density for large-enough aspect ratio k: first from a low-density isotropic to an intermediate-density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high-density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with m=1,2, and 3, that the transition density for the isotropic-nematic transition is ≈A(1)/k when k≫1, where A(1) is independent of m. We estimate A(1)=4.80±0.05. Within a Bethe approximation and virial expansion truncated at the second virial coefficient, we obtain A(1)=2. The critical density for the nematic-columnar transition when m=2 is numerically shown to tend to a value less than the full packing density as k(-1) when k→∞. We find that the critical Binder cumulant for this transition is nonuniversal and decreases as k(-1) for k≫1. However, the transition is shown to be in the Ising universality class.

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Section: A Bethe Approximationmentioning

confidence: 99%

Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries for the system of hard rectangles on a square lattice

Kundu

Rajesh

2015

Phys. Rev. E

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“…However, it is not straightforward to determine the thermodynamic properties such as free energy and configurational entropy from the original Metropolis schemes. Much effort has been devoted to addressing this problem, and the thermodynamic integration (TI) method is a convenient and widely used solution. , …”

Section: Introductionmentioning

confidence: 99%

“…Much effort has been devoted to addressing this problem, and the thermodynamic integration (TI) method is a convenient and widely used solution. 28,29 In this work, we first evaluate the thermodynamic stability of SACs on TMDs under electrochemical conditions, with a constant-potential calculation scheme to compute the potential-dependent binding energies. We will show that both MSI and metal−metal interaction (MMI) are essential descriptors for predicting the feasibility of electrochemical deposition in fabricating SACs.…”

Section: ■ Introductionmentioning

confidence: 99%

Predicting the Stability and Loading for Electrochemical Preparation of Single-Atom Catalysts

et al. 2022

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Underpotential electrochemical deposition is a convenient approach for precisely controlling the fabrication process of single-atom catalysts (SACs). In achieving a balance between raising the loading of SACs and suppressing the aggregation of the adsorbates, the working electrode potential should be deliberately optimized, for which the adsorption isotherm of the loading of atomically dispersed adsorbates versus electric potential is of crucial importance in performance tuning. We report an integrated theoretical scheme for simulating the adsorption isotherm, which can enormously accelerate the evaluation of the adsorption energy for large model systems by combining our recently proposed constant-potential calculation scheme with the cluster expansion (CE) model, as well as accurately estimate the configurational effect through a thermodynamic integration (TI) computation based on Monte Carlo (MC) simulations. With the established simulation scheme, the surface map of the adsorption free energy as a function of deposition coverage and electric potential is computed for atomically dispersed copper on 1T′-MoS2, which is further employed to reasonably estimate the equilibrium coverage of the deposit at varying electric potentials and predict the feature of the adsorbate distribution pattern, as well as simulate the cyclic voltammogram (CV). Besides, based on the study of nine metal/transition-metal dichalcogenide (TMD) systems, we demonstrate that the well-characterized potential-related metal–substrate and metal–metal interactions provide rational criteria for evaluating the stability of SACs against aggregation under electrochemical conditions.

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“…The most well-known analytical approximation is: 1) the theory of Flory-Huggins [48,[55][56][57][58], which is a generalization of the theory of binary solutions of polymer molecules in a monomolecular solvent for the twodimensional case. The fact that in the framework of lattice gas model the problem of k-mer adsorption on homogeneous surfaces is isomorphic to the problem of binary solutions of polymer in a monomolecular solvent, 2) Guggenheim-DiMarzio approximation [59,60], which is based on calculating the number of possible ways of packaging rigid k-mers on lattices with different coordination numbers 3) the approximation based on the extension of the exact solution for a one-dimensional case [52,53] to higher dimensions [49,61], 4) well known quasichemical approximation [62] and mean-field approximation [63], 5) fractional statistical theory (FSTA) for the adsorption of polyatomic molecules, based on Holdan statistics [64], 6) semi-empirical model [61,65], etc. Unfortunately, none of these approximations is universal, and each shows quite good results, depending on the parameters of the model -a flexible or rigid k-mer, the length of k-mer, the presence or absence of lateral interactions between adsorbed molecules, etc.…”

Section: The Models Of Dimer and K-mer Adsorptionmentioning

confidence: 99%

Statistical Thermodynamics of Lattice Gas Models of Multisite Adsorption

Fefelov¹,

Горбунов²,

Myshlyavtsev³

et al. 2012

Thermodynamics - Fundamentals and Its Application in Science

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Configurational entropy of adsorbed rigid rods: Theory and Monte Carlo simulations

Cited by 6 publications

References 21 publications

Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries for the system of hard rectangles on a square lattice

Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries for the system of hard rectangles on a square lattice

Predicting the Stability and Loading for Electrochemical Preparation of Single-Atom Catalysts

Statistical Thermodynamics of Lattice Gas Models of Multisite Adsorption

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