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Adsorption of 4 He on graphene substrates has been a topic of great interest due to the intriguing effects of graphene corrugation on the manifestation of commensurate solid and exotic phases in low-dimensional systems. In this study, we employ worm algorithm quantum Monte Carlo to study helium adsorbed on a graphene substrate to explore corrugation effects in the grand canonical ensemble. We utilized a Szalewicz potential for helium–helium interactions and a summation of isotropic interactions between helium and carbon atoms to construct a helium–graphene potential. We implement different levels of approximation to achieve a smooth potential, three partially corrugated potentials, and a fully ab initio potential to test the effects of corrugation on the first and second layers. We demonstrate that the omission of corrugation within the helium–graphene potential could lead to finite-size effects in both the first and second layers. Thus, a fully corrugated potential should be used when simulating helium in this low-dimensional regime. [ABSTRACT FROM AUTHOR]

In this paper, we will systematically present the method of collective variables with a reference system for a classical many-particle interacting system in the grand canonical ensemble. The emphasis will be placed on the details of calculations. In particular, the usage of total correlation functions defined for the grand canonical ensemble allows us to investigate very accurately the cumulants of the grand partition function for the reference system. It is shown that any cumulant Mn can be expressed as a product of three components: the average particle number within the reference system. Kronecker's symbol for n wave vectors, and the n-particle structure factor. The functional expression for the grand partition function is derived, with all coefficients explicitly defined. The coordinates of the critical point are computed in the mean field approximation. [ABSTRACT FROM AUTHOR]

A recently introduced recurrence-relation ansatz applied to the Fermi-Hubbard model gives rise to a soluble model and here is used to calculate several thermodynamic observables. The constraint of unit density per site, ρ= 1, is applied and some of the results are compared to cases where the constraint is not imposed. The modified model exhibits a continuous phase transition (second order) reminiscent of the integer quantum Hall resistance and a ground state, first-order phase transition. [ABSTRACT FROM AUTHOR]

A recently introduced recurrence-relation ansatz applied to the Bose-Hubbard model is here used in the Fermi-Hubbard model. The resulting modified Fermi-Hubbard model is soluble and exhibits a continuous phase transition (second order) reminiscent of the integer quantum Hall resistance and a ground-state, first-order phase transition. [ABSTRACT FROM AUTHOR]

Sodium chloride (NaCl) represents the principal component of atmospheric particulates of marine origin. To gain a molecular-level understanding of the adsorption process of water vapor on the NaCl surface, Monte Carlo simulations performed in the Grand Canonical ensemble were carried out, considering the water adsorption at different water pressures on a NaCl(001) surface. The calculated adsorption isotherm shows four different regions, whose coverages correspond to those of the low-, transition-, high-, and pre-solution-coverage regions experimentally observed. Detailed analysis reveals how the structure of the adsorbed water molecules (islands, layer, and multi-layer) changes depending on water pressure, and how their orientation with respect to the surface varies with the distance from the surface. This detailed information further supports the picture coming from previous experimental IR absorption spectroscopy studies. [ABSTRACT FROM AUTHOR]

This paper is aimed at studying the thermodynamic properties of quantum gases confined to a torus. To do that, we consider noninteracting gases within the grand canonical ensemble formalism. In this context, fermions and bosons are taken into account and the calculations are properly provided in both analytical and numerical manners. In particular, the system turns out to be sensitive to the topological parameter under consideration: the winding number. Furthermore, we also derive a model in order to take into account interacting quantum gases. To corroborate our results, we implement such a method for two different scenarios: a ring and a torus. [ABSTRACT FROM AUTHOR]

A theoretical model was selected among three potentially applicable models and then used to analyze the absorption isotherms of the hydrogen storage alloys LaNi5 and LaNi4.75Pb0.25 at three different temperatures (T = 303 K, 313 K, 323 K). The theoretical expressions of the model were based on the statistical physics formalism and simplifying hypotheses. The model selected was the one with the highest correlation with the experimental data. The model had six adjustable parameters: the number of hydrogen atoms per site nα, nβ, the receptor site densities Nα, Nβ and the energy parameters Pα, Pβ. The fitted parameters obtained for the Pb-doped and nondoped alloys were compared and discussed in relationship to the absorption isotherms. Finally, the fitted parameters or the model were further applied to calculate thermodynamic functions, such as entropy, Gibbs free energy and internal energy, which govern the absorption mechanism.

A generalized identity exchange algorithm is presented for Monte Carlo simulations in the grand canonical ensemble. The algorithm, referred to as molecular exchange Monte Carlo, may be applied to multicomponent systems of arbitrary molecular topology and provides significant enhancements in the sampling of phase space over a wide range of compositions and temperatures. Three different approaches are presented for the insertion of large molecules, and the pros and cons of each method are discussed. The performance of the algorithms is highlighted through grand canonical Monte Carlo histogram-reweighting simulations performed on a number of systems, which include methane+n-alkanes, butane+perfluorobutane, water+impurity, and 2,2,4-trimethylpentane+neopentane. Relative acceptance efficiencies for molecule transfers of up to 400 times that of standard configurational-bias Monte Carlo are obtained. [ABSTRACT FROM AUTHOR]

The investigation of the adsorption process putatively involved in the olfactory perception of apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol molecules on the mouse eugenol olfactory receptor mOR-EG was a very useful tool for comprising olfaction process at a molecular level. Indeed, the experimental data were correlated by using an advanced monolayer adsorption model with identical and independent binding sites. Thanks to the grand canonical ensemble in statistical physics formalism, the physico-chemical interpretations of modeling results indicated that the five odorants were adsorbed via a multi-molecular mechanism. Hence, the calculation of adsorption energies, that described the interaction between the odorant molecules and the olfactory receptor binding cavities, indicated that weak bonds were made between apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol molecules and mOR-EG binding pockets amino acid residues. In addition, theoretical stereographic and energetic characterizations of mOR-EG were made via the determination of the olfactory receptor site size distributions (RSDs) and the adsorption energy distributions (AEDs) relative to apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol, homoguaiacol molecules. The RSD provided the size of different binding cavities of mOR-EG. Indeed, the five RSDs spectrums situated between 0.5 and 10 nm were spread out around an average size each one. The mean values obtained from the peaks of the distributions were 2.14 nm, 2.20 nm, 2 nm, 2.10 nm and 1.83 nm for apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol molecules, respectively. The AED gave a whole spectrum of adsorption energies that was activated by the odorant molecule. Thus, the apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol AEDs were spread out from 5 to 27.5 kJ/mol, from 5 to 30 kJ/mol, from 5 to 35 kJ/mol, from 0 to 22.5 kJ/mol, 5 to 25 kJ/mol, respectively. The thermodynamic study, via the establishment of the adsorption entropy, indicated that the peak of the disorder was obtained when half of the binding sites were occupied. In addition, the Gibbs free enthalpy and the internal energy were determined and their negative values indicated that the adsorption phenomenon involved in the olfactory perception was spontaneous and exothermic physisorption phenomenon. • Modeling of concentration-olfactory response curves by an advanced monolayer adsorption model with identical sites. • Physico-chemical interpretations of the studied systems. • Quantitative characterizations of the five olfactory systems through the determination of the RSDs and the AEDs. • Determination of olfactory bands of the studied molecules. [ABSTRACT FROM AUTHOR]

For spectral actions consisting of the average number of particles and arising from open systems made of general free q -particles (including Bose, Fermi and classical ones corresponding to q = ±1 and 0, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cut-off. We treat both relevant situations relative to massless and non relativistic massive particles, where the natural cut-off is 1/ β = k B T and 1 / β , respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also treat in some detail the relativistic massive case for which the natural cut-off is again 1/ β. We then consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium, by also discussing the appearance of condensation phenomena occurring for Bose-like q -particles, q ∈ (0, 1]. We then compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum). [ABSTRACT FROM AUTHOR]

A theoretical model was selected among three potentially applicable models and then used to analyze the absorption isotherms of the hydrogen storage alloys LaNi5 and LaNi4.75Pb0.25 at three different temperatures (T = 303 K, 313 K, 323 K). The theoretical expressions of the model were based on the statistical physics formalism and simplifying hypotheses. The model selected was the one with the highest correlation with the experimental data. The model had six adjustable parameters: the number of hydrogen atoms per site n α , n β , the receptor site densities N α , N β and the energy parameters P α , P β . The fitted parameters obtained for the Pb-doped and nondoped alloys were compared and discussed in relationship to the absorption isotherms. Finally, the fitted parameters or the model were further applied to calculate thermodynamic functions, such as entropy, Gibbs free energy and internal energy, which govern the absorption mechanism. [ABSTRACT FROM AUTHOR]

Variations of the double layer capacitances (DLCs) at a platinum electrode with concentrations and kinds of salts in aqueous solutions were examined in the context of facilitating orientation of solvent dipoles. With an increase in ionic concentrations, the DLCs increased by ca. a half and then kept constant at concentrations over 1 mol dm−3. This increase was classically explained in terms of the Gouy–Chapman (GC) equation combined with the Stern model. Unfortunately, measured DLCs were neither satisfied with the Stern model nor the GC theory. Our model suggests that salts destroy hydrogen bonds at the electrode–solution interface to orient water dipoles toward the external electric field. A degree of the orientation depends on the interaction energy between the salt ion and a water dipole. The statistical mechanic calculation allowed us to derive an equation for the DLC as a function of salt concentration and the interaction energy. The equation took the Langmuir-type in the relation with the concentration. The interaction energy was obtained for eight kinds of salts. The energy showed a linear relation with the interaction energy of ion–solvent for viscosity, called the B-coefficient.

• Theoretical examination of adsorption systems. • Statistical physics modeling to experimental data of Remacryl Red TGL dye adsorption isotherms onto the untreated coffee residues. • Four different models are adopted: a monolayer with one or two or three horizontal energies and a double-layer with two vertical energies. • The adsorption process is found to be of chemisorptive nature. In this current paper, we perform a theoretical examination of adsorption systems undertaken through the application of statistical physics modeling to experimental data Remacryl Red TGL (BR) dye adsorption isotherms onto the untreated coffee residues (UCR) based adsorbents at 298–338 K range. The experimental values exhibited a strong agreement with the predicted values, and the developed model received high approval. Significant parameters are theoretically discussed such as thermodynamic, energetic, and stereographic factors which determine the (BR) adsorption onto UCR. In the pursuit of unraveling the adsorption mechanism, four different models are adopted: a monolayer with one energy (Model 1), a monolayer with two horizontal energies (Model 2), a monolayer with three energies (Model 3) and a double-layer with two vertical energies (Model 4). The analysis considered both steric and energetic parameters associated with the adsorption reaction, namely the number of adsorbed particles per site (n 1 and n 2), the receptor sites density (N 1m and N 2m), and the concentration at half-saturation. It appears that the experimental data aligns well with a monolayer model characterized by two energy states. The variations in these factors are examined in relation to the temperature of absorption isotherms. More importantly, the calculation of adsorption energies unequivocally pointed out that the adsorption process is of a chemisorptive nature. Our findings indicate that (UCR) could be utilized as a low-cost alternative adsorbent in wastewater treatment to eliminate the Remacryl Red TGL (BR) dye. [ABSTRACT FROM AUTHOR]

By means of the quantum field theory (QFT) in the one-loop approximation, we consider the finite-size effect of the quantum fluctuation energy of a weakly interacting Bose–Einstein condensate (BEC) gas confined between two parallel plates of a three-dimensional rectangular. We find the repulsive Casimir-type force acts on the plates when either Zaremba boundary condition (BC) or anti-periodic BC is imposed. Our results are obtained in both grand canonical ensemble (GCE) and canonical ensemble (CE). [ABSTRACT FROM AUTHOR]

Using a newly developed grand canonical Monte Carlo approach based on fractional exchanges of dissolved ions and water molecules, we studied equilibrium partitioning of both components between laterally extended apolar confinements and surrounding electrolyte solution. Accurate calculations of the Hamiltonian and tensorial pressure components at anisotropic conditions in the pore required the development of a novel algorithm for a self-consistent correction of nonelectrostatic cut-off effects. At pore widths above the kinetic threshold to capillary evaporation, the molality of the salt inside the confinement grows in parallel with that of the bulk phase, but presents a nonuniform width-dependence, being depleted at some and elevated at other separations. The presence of the salt enhances the layered structure in the slit and lengthens the range of inter-wall pressure exerted by the metastable liquid. Solvation pressure becomes increasingly repulsive with growing salt molality in the surrounding bath. Depending on the sign of the excess molality in the pore, the wetting free energy of pore walls is either increased or decreased by the presence of the salt. Because of simultaneous rise in the solution surface tension, which increases the free-energy cost of vapor nucleation, the rise in the apparent hydrophobicity of the walls has not been shown to enhance the volatility of the metastable liquid in the pores. [ABSTRACT FROM AUTHOR]

L -ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant L -ensembles are the subclass which are locally translationally invariant and furthermore subject to periodic boundary conditions. Existing theory can very simply be specialised to this setting, allowing for the derivation of formulas for the system pressure, and the correlation kernel, in the thermodynamic limit. For a one-dimensional domain, this is possible when the circulant matrix is both real symmetric, or complex Hermitian. The special case of the former having a Gaussian functional form for the entries is shown to correspond to free fermions at finite temperature, and be generalisable to higher dimensions. A special case of the latter is shown to be the statistical mechanical model introduced by Gaudin to interpolate between Poisson and unitary symmetry statistics in random matrix theory. It is shown in all cases that the compressibility sum rule for the two-point correlation is obeyed, and the small and large distance asymptotics of the latter are considered. Also, a conjecture relating the asymptotic form of the hole probability to the pressure is verified. [ABSTRACT FROM AUTHOR]

Copyright of China Plastics / Zhongguo Suliao is the property of Journal Office of CHINA PLASTICS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article introduces an efficient technique for the calculation of vapor-liquid equilibria of fluids. Umbrella Sampling Monte Carlo simulations in the grand canonical ensemble were conducted for various types of molecules. In Umbrella Sampling, a weight function is used for allowing the simulation to reach unlikely states in the phase space. In the present case this weight function, that allows the system to overcome the energetic barrier between a vapor and liquid phase, was determined by a trivialized Density Functional Theory (DFT) using the PC-SAFT equation of state. The implementation presented here makes use of a multicanonical ensemble approach to divide the space of fluctuating particle number N into various subsystems. The a priori estimate of the weight function from the analytic DFT allows the parallelization of the calculation, which significantly reduces the computation time. In addition, it is shown that the analytic equation of state can be used to substitute sampling the dense liquid phase, where the sampling of insertion and deletion moves become demanding. [ABSTRACT FROM AUTHOR]

In this work we explore the physical foundations of models that study the variation of the ground state energy with respect to the number of electrons (E vs. N models), in terms of general grand-canonical (GC) ensemble formulations. In particular, we focus on E vs. N models that interpolate the energy between states with integer number of electrons. We show that if the interpolation of the energy corresponds to a GC ensemble, it is not differentiable. Conversely, if the interpolation is smooth, then it cannot be formulated as any GC ensemble. This proves that interpolation of electronic properties between integer electron numbers is inconsistent with any form of ensemble averaging. This emphasizes the role of derivative discontinuities and the critical role of a subsystem's surroundings in determining its properties. [ABSTRACT FROM AUTHOR]

Since the grand partition function Zq for the so-called q-particles (i.e., quons), q∈(−1,1), cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for q=0, and its q-deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to q∈[−1,1]. We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., q=0) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor 1/n! in the n term of the power series expansion with respect to the fugacity z. As an application, we briefly discuss the equations of the state for a gas of free quons or the condensation phenomenon into the ground state, also occurring for the Bose-like quons q∈(0,1).

A lower bound on the grand partition function of a classical charge-symmetric system is adapted to the neutral grand canonical ensemble, in which the system is constrained to have zero total charge. This constraint permits us to consider two-body potentials that are only conditionally positive definite. [ABSTRACT FROM AUTHOR]

We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it equals the set of averages of all probability measures absolutely continuous with respect to the standard measure on the phase space (with the exception of the measure concentrated on the empty configuration). We also investigate how the set of constrains relates to the domain of the microcanonical thermodynamic limit entropy. We then show that, for fixed constraints, the parameters of the corresponding grand canonical distribution converge, as volume increases, to the corresponding parameters (derivatives, when they exist) of the thermodynamic limit entropy. The results hold when the energy is the sum of any stable, tempered interaction potential that satisfies the Gibbs variational principle (e.g. Lennard-Jones) and the kinetic energy. The same tools and the strict convexity of the thermodynamic limit pressure for continuous systems (valid whenever the Gibbs variational principle holds) give solid foundation to the folklore local homeomorphism between thermodynamic and macroscopic quantities. [ABSTRACT FROM AUTHOR]

Theoretical model expressions are used in order to adjust four absorption isotherms of hydrogen on LaNi4.6Al0.4 at four different temperatures (T = 288K, 293 K, 303 K and 313 K). The development of these expressions is based on statistical physics formalism and some working hypothesis. The physicochemical parameters intervening in the absorption process and involved in the model expressions could be directly deduced from the experimental absorption isotherms by numerical simulation. The best model that shows a good correlation with the experimental data has been determined. Six parameters of the model are adjusted, namely the numbers of hydrogen atoms per site n1 and n2, the receptor site densities N1m and N2m and the energetic parameters P1 and P2. The behaviors of these parameters are discussed in relationship with temperature of absorption isotherms. Then, a dynamic investigation of the simultaneous evolution with pressure of the two α and β phases is involved in the absorption process using the adjustment parameters. Thanks to the energetic parameters, we calculated the absorption energies, which are typically ranged between 109.871 and 133.634 kJ/mol comparable to usual chemical bond energies. The calculated thermodynamic parameters, such as entropy, Gibbs free energy and internal energy from fitted parameters values showed that the absorption of hydrogen in LaNi4.6Al0.4 alloy was spontaneous and exothermic in nature. [ABSTRACT FROM AUTHOR]

This study presents a molecular simulation method to insert and delete large objects, such as macromolecules or colloids, in a dense medium. This method is based on an extended Hamiltonian formulation that allows extra spatial dimensions for the atoms of the inserted object. By actively controlling the extra coordinates of the atoms, this method can prevent fatal instability in principle and is as efficient as FADE. Its implementation is a straightforward extension of a standard molecular simulation algorithm. This method is first applied successfully to three molecular systems: Ar liquid, linear polymer melts, and a carbon nanotube in an Ar solvent. Unlike FADE, this method does not require extensive pre-testing of each material system to obtain control parameters that depend less on the material properties. Insertion of a nanosized solid sphere, most disruptive to the potential field of the base medium among the objects, is also conducted. This method enables a robust mass exchange in molecular simulation, especially for macromolecules or colloids in complex molecular systems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shenzhen University Science & Engineering is the property of Editorial Department of Journal of Shenzhen University Science & Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)