Adsorption thermodynamics of a lattice-gas model with non-additive lateral interactions on triangular and honeycomb lattices

Adsorption thermodynamics of a lattice-gas model with non-additive interactions between adsorbed particles for triangular and honeycomb lattices is discussed in the present study. The model used here assumes that the energy which links a certain atom with any of its nearest-neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms and isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles) were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

Generalized statistical description of adsorption of polyatomics

Multisite-occupancy adsorption is described as a fractional statistic problem, based on Haldane’s statistics. Site exclusion is characterized by a statistical exclusion parameter, g, which relates to the molecular size and lattice geometry. A general adsorption isotherm is obtained and comparisons with experiments indicate that the spatial configuration of adsorbed molecules and lateral interactions may accurately be assessed from this theory. In addition, the theoretical framework developed in this paper allows to describe orientational transitions occurring in adlayers of polyatomics.     

Statistical thermodynamics of ligand binding to giant macromolecules

Summary A statistical thermodynamic model for ligand binding to giant respiratory macromolecules, such as molluscan hemocyanins, is proposed. The model complies with the fundamental structural organization of this class of proteins. It assumes that each morphological unit functions as the element of a one-dimensional Ising lattice, so that conformational transitions occurring upon ligand binding may be propagated to the whole macromolecule through nearest-neighbour interactions. An application of the model to the analysis of oxygen equilibria of the β-hemocyanin ofHelix pomatia is presented and its general properties are discussed in connection with other models.

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Riassunto Si propone un modello statistico per le interazioni proteina-substrato in sistemi macromolecolari giganti, quali le emocianine di mollusco. Il modello è basato su rilievi strutturali e fornisce un'interpretazione termodinamica dell'arrangiamento ciclico delle subunità morfologiche delle emocianine secondo il modello classico di Ising.

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Резюме Предлагается статистическая термодинамическая модель для связи лигандов в гигантских дыхательных макромолекулах, таких как гемоцианин молюсков. Эта модель согласуется со структурной организацией этого класса белков. Предполагается, что каждая морфологическая единица действует, как элемент одномерной решетки Пзинга, так что конформационные переходы, наблюдаемые на связях лигандов, могут распространяться вдоль всей макромолекулы через взаимодействия ближайших соседей. Предлагается применение этой модели к анализу кислородного равновесия для β-гемоцианина. Обсуждоются общие свойства в контексте с другими моделями.

     

Percolation of dimers on square lattices

A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for M=_Lx×_Ly$M=L_x\times L_y$ cells, with M$M$ varying from 16 to 36. The percolation process has been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied sites. The percolation threshold has been calculated by means of two complementary methods: one based on well-known renormalization techniques and the other based on determining the inflection point of the percolation function curves. A comparison of the results obtained by these two methods has been performed. The study includes the use of finite-size scaling theory to extrapolate numerical results towards the thermodynamic limit. The effect of jamming due to dimers is also established. Finally, the critical exponents ν$\nu$, β$\beta$ and γ$\gamma$ have been obtained and values compared with numerical results and expected theoretical estimations. The present results show agreement and even improvement (in the case of γ$\gamma$) with respect to some numeric values available in the literature.     

Statistics of adsorption on top and bridge sites of a square lattice: Transfer-matrix approach

Statistics of particles adsorbed on the lattice with a complex elementary cell are analyzed by employing the transfer-matrix technique. The results obtained are compared with those given by the cluster approximation and also with the experimental data for the CO/Ni(100) system. The transfer-matrix technique is shown to be very effective for studies of two-dimensional systems with complex lattices.     

Composite Anderson-Newns model and density of states due to chemisorption: Quasi-chemical approximation

In this paper a variation in density of states (DOS) of the substrate due to chemisorption of hydrogen on transition metals using composite Anderson-Newns model has been investigated for different coverages in quasi-chemical approximation of Fowler and Guggenhiem, which in the limitz→∞ gives the Bragg-Williams approximation as a special case. Variation in density of states has been studied for one-dimensional periodic substrate with change in adatom interaction energy and coverage. With increase in coverage, the bonding and antibonding (B-AB) peaks are found to shift towards higher energies and at the same time relative height of the peaks also increases. The interesting feature to observe is that both approximations for a particular coverage, give split-off states with different height for both (B-AB) peaks. It particularly indicates change in B-AB states, representing amount of chemisorption, with the change in interaction energy between adatoms. At the same time bond strength is also found to decrease with interaction between adatoms.     

Statistical thermodynamics of multicomponent systems (mixtures) in the quasilattice coordination approximation

Based on the well-known concepts of statistics of nearest neighbors in a lattice and on the BethePeierls-Guggenheim quasichemical approximation, combination rules are obtained allowing us to express the thermodynamic functions of multicomponent systems (mixtures) with given chemical and coordination composition in terms of thermodynamic functions of the pure subsystems.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 85–89, January, 1976.     

Statistical thermodynamics of soft surfaces

We review the continuum, statistical thermodynamics of surfaces and interfaces in soft matter where both the energy and entropy of the surface are comparable. These systems include complex fluids that are dominated by either surface tension or the interfacial curvature, such as: fluid and solid interfaces, colloidal dispersions, macromolecular solutions, membranes, and other self-assembling aggregates such as micelles, vesicles, and microemulsions. The primary focus is on the theoretical concepts, their universality, and the role of fluctuations and inhomogeneities with connections to relevant experimental systems.     

Statistical thermodynamics of block copolymers: Network statistics

The swelling behavior of a lamellar domain system of an ABA block copolymer is treated, with account taken of the relative population of the B chains as “loops” and “bridges.” The swelling behavior is not a sensitive function of these configurations, since both types in condensed systems are elastically effective, in contrast to the behavior of isolated chains.     

Statistical thermodynamics of an anharmonic oscillator

In the present study we investigate the statistical thermodynamics of the anharmonic oscillator, whose energies are characterized by the potential 1/2x ²+x ⁴. Employing the energies recently obtained by Hioe and Montroll, we compute the partition function and the thermodynamic quantities for the anharmonic and quartic oscillators. Low- and high-temperature formulas are presented for the thermodynamic quantities of the oscillators.     

Statistical thermodynamics of multicomponent systems of nonspherical molecules taking account of the short-range order in a quasichemical approximation

It is shown that short-range order can be taken into account effectively for a liquid multicomponent system (mixture) of molecules with internal (particularly orientation) degrees of freedom within the framework of a quasichemical approximation (in the Guggenheim formulation) by using a vector in the space of internal states of the molecule (correlation vector) which is introduced together with the ordinary set (vector) of occupation numbers describing the longrange order. A closed system of equations is obtained in the correlation vector representation for the thermodynamic functions and occupation numbers of chemically distinct components in the space of internal states of the molecule, and its variational formulation is given. The possibilities for using the results obtained in the theory of the liquid-crystal state are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 17–20, September, 1977.The author is grateful to Prof. V. K. Semenchenko for his interest in this work.     

一维谐振腔中的理想玻色气体的热力学性质

一维谐振腔中的理想玻色气体没有相变,但是在低温下存在玻色-爱因斯坦凝聚体.在高温情况下,该体系的内能等于力一位移的乘积;关于微观状态数计算,传统的方法有所不足,本文给出了正确方法.     

Physical cluster mechanics: Statistical thermodynamics and nucleation theory for monatomic systems

We extend previous computations of mechanical stability of atomic microclusters to the realm of statistical thermodynamics, obtaining thermodynamic functions for small, solid-like Van der Waals clusters of less than some 100 atoms possessing non-crystalline structures of ‘polytetrahedral’ type. These are shown to be almost invariably at a thermodynamic advantage over alternative lattice structures of the same number of atoms, at least for the Lennard-Jones potential in the harmonic-oscillator/rigid-rotor approximation. The dependence of thermodynamic functions upon cluster size appears to be essentially monotonic in the number of internal degrees of freedom; although there are certain exceptional structures, particularly with icosahedral symmetry, there proves to be little evidence for the occurrence of ‘magic numbers’ for stability at any temperature and within the size-range considered. Particular attention is given to the heat capacity of model systems in relation to their vibrational spectra. The Debye T ³ law appears reasonably well obeyed at low temperatures with no evidence for the existence of either ‘soft modes’ or distinct surface contributions.

The results for the free energy of formation of minimal clusters ΔG _f are then applied to the computation of nucleation rates in terms of the Becker-Döring-Volmer-Zeldovitch quasi-equilibrium theory. Gibbsian behaviour in the form of a maximum in the curve of ΔG _f versus size is observed with a critical nuclear size at realistic temperatures and pressures of the order of that predicted by macroscopic liquid-drop theories. These figures and those derived for nucleation rate and critical supersaturation appear remarkably insensitive to the details of the model used, in particular to the distinction between ‘microcrystalline’ and ‘amorphous’ atomistic models.

The general status of atomistic nucleation theory is critically examined in the light of these and similar results.     

Adsorption in one-dimensional channels arranged in a triangular structure: Theory and Monte Carlo simulations

Adsorption thermodynamics of interacting particles adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure is studied through Bragg-Williams approximation (BWA), Monte Carlo (MC) simulations and the recently reported Effective Substates approximation (ESA) [J.L. Riccardo, G. Zgrablich, W. A. Steele, Appl. Surf. Sci. 196 (2002) 138]. Two kinds of lateral interaction energies have been considered: (1) w_L, interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) w_T, interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transversal interactions (w_T>0), for which a rich variety of ordered phases are observed in the adlayer, depending on the value of the parameters k_BT/w_T (being k_B the Boltzmann constant) and w_L/w_T. Comparisons between analytical data and MC simulations are performed in order to test the validity of the theoretical models. Appreciable differences can be seen for the different approximations, ESA being the most accurate for all cases.     

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

The configurational entropy of straight rigid rods of length k (k-mers) adsorbed on square, honeycomb, and triangular lattices is studied by combining theory and Monte Carlo (MC) simulations in grand canonical and canonical ensembles. Three theoretical models to treat k-mer adsorption on two-dimensional lattices have been discussed: (i) the Flory-Huggins approximation and its modification to address linear adsorbates; (ii) the well-known Guggenheim-DiMarzio approximation; and (iii) a simple semi-empirical model obtained by combining exact one-dimensional calculations, its extension to higher dimensions and Guggenheim-DiMarzio approach. On the other hand, grand canonical and canonical MC calculations of the configurational entropy were obtained by using a thermodynamic integration technique. In the second case, the method relies upon the definition of an artificial Hamiltonian associated with the system of interest for which the entropy of a reference state can be exactly known. Thermodynamic integration is then applied to calculate the entropy in a given state of the system of interest. Comparisons between MC simulations and theoretical results were used to test the accuracy and reliability of the models studied.