Peculiar thermodynamic properties of LJ<Subscript> N</Subscript> (N = 39–55) clusters

The solid-liquid phase transitions of Lennard-Jones clusters LJ_N (N=39–55) were simulated by a microcanonical molecular dynamics method using Lennard-Jones potential, and their thermodynamic quantities were calculated. The caloric curves of clusters (except N=42) have S-bend. To understand this behaviour, configurational and total entropies were evaluated, and dents on the entropy curves were taken as a sign of negative heat capacity. The heat capacities were evaluated for N=39–55 clusters using configurational entropy data. The potential energy distributions have bimodal behaviour for all clusters in the given range at the melting temperature. The distinct melting behaviour of LJ₄₂ was explained by the topology of the potential energy surface by examining the isomer distributions at phase transitions for LJ₃₉-LJ₅₅. The isomer distributions were found to be a useful way to interpret this behaviour and melting dynamics in general. Melting temperature, latent heat and entropy change upon melting values were reported and are consistent with literature values and values calculated from bulk thermodynamic properties. The dependence of these quantities on the size of the clusters was examined and it is found that latent heat is the key quantity to determine the magic numbers.     

Heat capacity of isolated clusters

The character of interaction between thermal (vibrational) and configurational cluster excitations is considered under adiabatic conditions when a cluster is a member of a microcanonical ensemble. The hierarchy of equilibration times determines the character of atomic equilibrium in the cluster. The behavior of atoms in the cluster can be characterized by two effective (mean) temperatures, corresponding to the solid and liquid aggregate states, because the typical time for equilibration of atomic motion is less than the transition time between aggregate states. If the cluster is considered for a time much longer than the typical dwell time in either phase, then it is convenient to characterize the system by only one temperature, which is determined from the statistical-thermodynamic long-time average. These three temperatures are not far apart, nor are the cluster heat capacities evaluated on the basis of these definitions of temperature. The heat capacity of a microcanonical ensemble may be negative for two coexisting phases if the mean temperature is defined in terms of the mean kinetic energy, rather than as the derivative of energy with respect to microcanonical entropy. However, if the configurational excitation energy is smaller than the total excitation energy separating the phases, then the two-state model predicts a positive heat capacity under either definition of temperature. Moreover, if the cluster is sufficiently large, then the maximum values of the microcanonical and canonical heat capacities are equal.     

Partial equivalence of statistical ensembles and kinetic energy

The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore, the configurational microcanonical entropy is a smooth function, whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble. In the presence of a standard kinetic energy contribution, partial equivalence is removed and a nonanalyticity arises also microcanonically. Hence in contrast to the common belief, kinetic energy, even though a quadratic form in the momenta, has a nontrivial effect on the thermodynamic behaviour. As a by-product we present the microcanonical solution of the mean-field spherical model with kinetic energy for finite and infinite system sizes.     

Effect of an ionic impurity on the caloric curves of water clusters

The equilibrium heat capacities of model pure and heterogeneous water clusters have been calculated using exchange Monte Carlo simulations. For the pure water cluster (H₂O)₂₀, microcanonical and canonical caloric curves obtained from various rigid intermolecular potentials indicate the onset of melting to lie in the range 140–180 K, in reasonable agreement with previous estimates. Clusters doped with a single hydronium or ammonium impurity show a significant shift of the melting point in the 20-molecule system, but a reduced effect when 50 molecules are reached.     

Microcanonical equilibrium properties of chiral liquid crystals—a Monte Carlo study

Chiral liquid crystals have been investigated by means of a multicanonical Monte Carlo approach in order to characterize their phase behaviour by microcanonical equilibrium properties. The liquid crystals were described by three-dimensional lattice systems with intermolecular interactions given by the chiral Lebwohl-Lasher potential. Self-determined boundary conditions have been applied in order to enable the formation of chiral phases with equilibrium pitch. Selected thermodynamic properties, e.g. microcanonical entropy, temperature, heat capacity and a set of order parameters have been determined with dependence on microcanonical total energy. A cholesteric phase with temperature-induced helix inversion could be proven where the helical superstructure of the single component system studied changed its handedness through an infinite-pitch system. The thermodynamical behaviour in the microcanonical ensemble was found to be very similar to the behaviour in the canonical ensemble. The study of microcanonical equilibrium properties by means of multicanonical Monte Carlo simulations was shown to be a powerful tool for the study of the phase behaviour of model liquid crystals.     

Structural phase transition in a large cluster

The effect of a phase transition between structures in a large cluster with a pair interatomic interaction on the thermodynamic parameters of the cluster is analyzed. The statistical parameters of a cluster consisting of 923 atoms are determined for an icosahedron and a face-centered cubic (fcc) structure. The specific heat and entropy of this cluster are calculated in the case when the transition between the icosahedron and fcc structures has the greatest effect on these parameters, so that at zero temperature this cluster has the structure of an icosahedron, and as the temperature increases to the melting point it assumes an fcc structure. Even with this, the contribution of the excitations of the atomic configurations to the thermodynamic parameters of a cluster is small compared with the excitation of vibrations in the cluster. The contribution of a configurational excitation in the thermodynamic parameters of a cluster becomes substantial for the liquid state of clusters.     

The Generalized Canonical Ensemble and Its Universal Equivalence with the Microcanonical Ensemble

This paper shows for a general class of statistical mechanical models that when the microcanonical and canonical ensembles are nonequivalent on a subset of values of the energy, there often exists a generalized canonical ensemble that satisfies a strong form of equivalence with the microcanonical ensemble that we call universal equivalence. The generalized canonical ensemble that we consider is obtained from the standard canonical ensemble by adding an exponential factor involving a continuous function g of the Hamiltonian. For example, if the microcanonical entropy is C², then universal equivalence of ensembles holds with g taken from a class of quadratic functions, giving rise to a generalized canonical ensemble known in the literature as the Gaussian ensemble. This use of functions g to obtain ensemble equivalence is a counterpart to the use of penalty functions and augmented Lagrangians in global optimization. linebreak Generalizing the paper by Ellis et al. [J. Stat. Phys. 101:999–1064 (2000)], we analyze the equivalence of the microcanonical and generalized canonical ensembles both at the level of equilibrium macrostates and at the thermodynamic level. A neat but not quite precise statement of one of our main results is that the microcanonical and generalized canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the generalized microcanonical entropy s–g is concave. This generalizes the work of Ellis et al., who basically proved that the microcanonical and canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the microcanonical entropy s is concave.     

Microcanonical ensemble study of a gas column under gravity

The study of a classical ideal gas column of finite height H in a uniform gravitational field g is made by the microcanonical ensemble at energy E. The primary functions of this ensemble, the phase volume and the density of states, are derived. Related statistical quantities, such as the entropy, the temperature and the heat capacity, are also reported. The equivalence in the thermodynamic limit between the calculated microcanonical expressions and those obtained from the canonical ensemble is shown numerically. The expression for the temperature is used to analyze the temperature change when the gas is permitted to expand into an evacuated region increasing the height of the column from H ₁ to H ₂. The microcanonical single-particle momentum and height distributions are also reported.     

Level density and thermal properties in rare earth nuclei

A convergent method to extract the nuclear level density and the γ-ray strength function from primary γ-ray spectra has been established. Thermodynamical quantities have been obtained within the microcanonical and canonical ensemble theory. Structures in the caloric curve and in the heat capacity curve are interpreted as fingerprints of breaking of Cooper pairs and quenching of pairing correlations. The strength function can be described using models and common parametrizations for the E1, M1, and pygmy resonance strength. However, a significant decrease of the pygmy resonance strength at finite temperatures has been observed.     

Phase transitions in small systems: Microcanonical vs. canonical ensembles

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g., temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.     

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.     

Transition from icosahedral to decahedral structure in a coexisting solid-liquid nickel cluster

We have used molecular dynamics simulations to construct a microcanonical caloric curve for a 1415 atom Ni icosahedron. Prior to melting, the Ni cluster exhibits static solid-liquid phase coexistence. Initially, a partial icosahedral structure coexists with a partially wetting melt. However, at energies very close to the melting point the icosahedral structure is replaced by a truncated decahedral structure that is almost fully wet by the melt. This structure remains until the cluster fully melts. The transition appears to be driven by a preference for the melt to wet the decahedral structure.     

Direct experimental evidence for a negative heat capacity in the liquid-to-gas phase transition in hydrogen cluster ions: backbending of the caloric curve

By selecting specific decay reactions in high-energy collisions (60 keV/amu) of hydrogen cluster ions with a helium target (utilizing event-by-event data of a recently developed multicoincidence experiment) and by deriving corresponding temperatures for these microcanonical cluster ensembles (analyzing respective fragment distributions), we are able to construct caloric curves for H+3(H2)(m) cluster ions (6相似文献   

Molecular dynamics simulation of a graphite-supported copper nanocluster: thermodynamic properties and gas adsorption

Molecular dynamics simulations were conducted for a cubic Cu cluster supported on a graphite bilayer. The Sutten–Chen and Lennard–Jones potentials were used for metal–metal and metal–graphite interactions, respectively. Heating and cooling processes were performed by NVT simulations at different temperatures in the range 200 to 1800?K. The melting point was identified on the basis of caloric and heat capacity curves. The calculated melting point was 770?K, far below the bulk melting point of crystalline copper. Several phenomena such as the appearance of a hysteresis (irreversibility) in caloric curves, surface melting, and cluster-induced surface wetting were justified from the results. The simulation of cluster in the presence of gas atmosphere showed that the CO gas is adsorbed more than H₂ and it has a greater impact on the cluster's structure.     

Ensemble inequivalence in random graphs

We present a complete analytical solution of a system of Potts spins on a random k-regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different branches, resulting in a non-concave entropy function. The analytical solution is confirmed with numerical Metropolis and Creutz simulations and our results clearly demonstrate the presence of a region with negative specific heat and, consequently, ensemble inequivalence between the canonical and microcanonical ensembles.     

Extended gaussian ensemble solution and tricritical points of a system with long-range interactions

The gaussian ensemble and its extended version theoretically play the important role of interpolating ensembles between the microcanonical and the canonical ensembles. Here, the thermodynamic properties yielded by the extended gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range interactions are analyzed. This model presents different predictions for the first-order phase transition line according to the microcanonical and canonical ensembles. From the EGE approach, we explicitly work out the analytical microcanonical solution. Moreover, the general EGE solution allows one to illustrate in details how the stable microcanonical states are continuously recovered as the gaussian parameter γ is increased. We found out that it is not necessary to take the theoretically expected limit γ → ∞ to recover the microcanonical states in the region between the canonical and microcanonical tricritical points of the phase diagram. By analyzing the entropy as a function of the magnetization we realize the existence of unaccessible magnetic states as the energy is lowered, leading to a breaking of ergodicity.     

Configurational entropy of systems with non-additive lateral interactions

The configurational entropy per site of a lattice gas model with non-additive interactions between adsorbed particles for square, 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 canonical ensemble by following the algorithm of parallel tempering and the thermodynamic integration method the configurational entropy per site has been calculated. By analyzing the behavior of the configurational entropy per site, the different low-temperature-ordered phases are described. The dependency of the critical temperature of the system as a function of characteristic parameters of the model is established.     

Microcanonical versus canonical analysis of protein folding

The microcanonical analysis is shown to be a powerful tool to characterize the protein folding transition and to neatly distinguish between good and bad folders. An off-lattice model with parameter chosen to represent polymers of these two types is used to illustrate this approach. Both canonical and microcanonical ensembles are employed. The required calculations were performed using parallel tempering Monte Carlo simulations. The most revealing features of the folding transition are related to its first-order-like character, namely, the S-bend pattern in the caloric curve, which gives rise to negative microcanonical specific heats, and the bimodality of the energy distribution function at the transition temperatures. Models for a good folder are shown to be quite robust against perturbations in the interaction potential parameters.     

Melting and Grüneisen parameters of NaCl at high pressure

The Buckingham potential has been employed to simulate the melting and thermodynamic parameters of sodium chloride (NaCl) using the molecular dynamics (MD) method. The constant-volume heat capacity and Grüneisen parameters have been obtained in a wide range of temperatures. The calculated thermodynamic parameters are found to be in good agreement with the available experimental data. The NaCl melting simulations appear to validate the interpretation of superheating of the solid in the one-phase MD simulations. The melting curve of NaCl is compared with the experiments and other calculations at pressure 0－30GPa range.