Heat Capacities Of Clusters Research Articles

Finite Systems under Pressure: Assessing Volume Definition Models from Parallel-Tempering Monte Carlo Simulations.

We have investigated different approaches to handling parallel-tempering Monte Carlo (PTMC) simulations in the isothermal-isobaric ensemble of molecular cluster/nanoparticle systems for predicting structural phase diagram transitions. We have implemented various methodologies that consist of treating pressure implicitly through its effect on the volume. Thus, the main problem in the simulations under nonzero pressure becomes the volume definition of the finite nonperiodic system, and we considered approaches based on the particles' coordinates. Various volume models, namely container-volume, particle-volume, average-volume, ellipsoids-volume, and convex hull-volume, were employed, and the required corrections for each of them in the Monte Carlo computations were introduced. Finally, we explored the effects of volume/pressure changes for all models on structural phase transitions of a test system, such as the small "icelike" (H2O)12 water cluster. The temperature and pressure dependence of the cluster's heat capacity and energy-volume Pearson correlation coefficient were studied, phase diagrams were constructed using a multiple-histogram method, and attempts were made to identify phase transitions to particular cluster structures. Our results show significant differences between the employed volume models, and we discuss all pressure-induced, such as solid-solid-, solid-liquid-, and liquid-gas-like, phase transformations in the present study.

Experimental nanocalorimetry of protonated and deprotonated water clusters.

An experimental nanocalorimetric study of mass selected protonated (H2O)nH(+) and deprotonated (H2O)n-1OH(-) water clusters is reported in the size range n = 20-118. Water cluster's heat capacities exhibit a change of slope at size dependent temperatures varying from 90 to 140 K, which is ascribed to phase or structural transition. For both anionic and cationic species, these transition temperatures strongly vary at small sizes, with higher amplitude for protonated than for deprotonated clusters, and change more smoothly above roughly n ≈ 35. There is a correlation between bonding energies and transition temperatures, which is split in two components for protonated clusters while only one component is observed for deprotonated clusters. These features are tentatively interpreted in terms of structural properties of water clusters.

Heat capacities from Born–Oppenheimer molecular dynamics simulations: [formula omitted] and [formula omitted

State-of-the-art first-principle all-electron density functional theory Born–Oppenheimer molecular dynamics simulations on cationic aluminum clusters with 27 and 28 atoms are presented. The cluster heat capacities were calculated from these simulations with the multiple histogram method. The obtained latent heats and heat capacities are compared with available experimental results. In agreement with experiment our study shows a well defined peak in the heat capacity curve for the Al28+ cluster, whereas for the Al27+ a very small broad peak is observed. To the best of our knowledge this is the first all-electron ab initio calculation of thermodynamics properties of small finite systems. The good qualitative and quantitative agreement with experiments underlines the high accuracy of all-electron ab initio Born–Oppenheimer molecular dynamics simulations.

On the Conundrum of the Heat Capacityof Metallic Nanoclasters

<p>The heat capacity of nanoclusters was investigated using thermodynamics of surfaces, taking into account the surface enthalpy introduced by E. Guggenhein. It is shown that the cluster heat capacity <em>C<sub>p</sub></em> should be greater than the heat capacity of the corresponding bulk phase. However, the ratio should not exceed 50% up to very small clusters containing 100 atoms. Theoretical estimations agree with molecular dynamics results. So, experimental data on metallic nanoclusters and nanostructures demonstrating that <em>C<sub>p</sub></em> exceeds in 2-5 times should be incorrect.</p>

Structural transitions and dipole moment of water clusters (H2O)n=4–100

The properties of water clusters (H(2)O)(n) over a broad range of sizes (n=4-100) were studied by microcanonical parallel tempering Monte Carlo and replica exchange molecular dynamics simulations at temperatures between 20 and 300 K, with special emphasis in the understanding of relation between the structural transitions and dipole behavior. The effect of the water interaction potential was analyzed using six nonpolarizable models, but more extensive calculations were performed using the TIP4P-ice water model. We find that, in general, the dipole moment of the cluster increases significantly as the cluster melts, suggesting that it could be used to discriminate between the solidlike and liquidlike phases. The effect of a moderate electric field on the cluster heat capacity and total dipole moment was found to be negligible.

Structural-thermodynamic analysis of the relationship between the half-width and the position of the absorption band maxima in the low-frequency IR spectra of liquid systems

The cluster-continuum approximation of the method of thermodynamic functionals of the internal structural coordinates is used to carry out a theoretical structural-thermodynamic analysis of the relationship between the half-width and the position of the absorption-band maxima in the low-frequency IR spectra of liquid systems. By considering the thermodynamic theory of fluctuations, it is shown that this relationship is strictly functional and is determined by the ratio of the effective cluster heat capacities or of the generalized thermodynamic susceptibilities in the ground and excited states. For molecular liquids, it follows from this theory that the half-width is directly proportional to the position of the low-frequency IR absorption-band maxima, with a slope close to unity.

Remarks on Negative Heat Capacities of Clusters

AbstractThe concept of negative heat capacities of clusters has been examined and argued. This discussion examines the arguments and concepts with the goal of clarifying the inherent ambiguities in the concept itself. We also show how one must use caution with this and related concepts that extend to nonequilibrium systems properties that are well defined just for equilibrium systems.

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.

A Monte Carlo study of methanol clusters (CH3OH)N, N=5–256

The thermodynamic and structural properties of methanol clusters (CH3OH)N, N=5–15, 20, 30, 60, 128, 256 and the bulk liquid have been investigated using Monte Carlo simulation. Calculated properties as a function of size include electrostatic and dispersive contributions to the configurational energy, configurational heat capacities, fractal dimension, density profiles, order parameters characterizing dipole and bond vector orientation, and the Lindemann index. The cluster heat capacities as a function of N possess an interior maximum near N=128 and converge to the bulk value from above. Monocyclic, semiplanar structures are found to persist at liquidlike temperatures up to about N=12, followed by bi- and polycyclic structures for N=13–20, with the larger clusters gradually becoming more spherical. The average density of the larger clusters is fairly well represented by the bulk value. For clusters with 30 or more molecules, there is a net tendency for the molecular dipoles to lie flat on the cluster surface. The observed trends in heat capacities, density profiles, and dipole alignments parallel to the cluster surface are likely to be general features of clusters of polar molecules.

A computational study of 13-atom Ar–Kr cluster heat capacities

Heat capacity curves as functions of temperature were calculated using Monte Carlo methods for the series of Ar13−nKrn clusters (0≤n≤13). The clusters were modeled classically using pairwise additive Lennard-Jones potentials. J-walking (or jump-walking) was used to overcome convergence difficulties due to quasiergodicity present in the solid–liquid transition regions, as well as in the very low temperature regions where heat capacity anomalies arising from permutational isomers were observed. Substantial discrepancies between the J-walking results and the results obtained using standard Metropolis Monte Carlo methods were found. Results obtained using the atom-exchange method, another Monte Carlo variant designed for multicomponent systems, were mostly similar to the J-walker results. Quench studies were also done to investigate the clusters’ potential energy surfaces; in each case, the lowest energy isomer had an icosahedral-like symmetry typical of homogeneous 13-atom rare gas clusters, with an Ar atom being the central atom.

Fluctuations, temperature, and detailed balance in classical nucleation theory

The role of temperature in classical nucleation theory is examined. It is shown that while even small clusters are assigned a temperature in the classical theory, this must be a fluctuating quantity. Stochastic simulations of cluster evaporation and growth are presented to track the temperature fluctuations in time. The relation 〈‖δT‖2〉=kT20/Cν for the mean square temperature fluctuation is confirmed, where k is the Boltzmann constant, Cν is the cluster heat capacity, and T0 is the bath temperature. For small capillary drops (50–100 molecules), the resulting rms temperature fluctuations of 10°–20° might be expected to have a significant effect on the nucleation rate. However, the simulations reveal a cluster temperature distribution that is centered several degrees below T0. A theory is presented to explain this effect. To first order, which includes Gaussian fluctuations of the cluster temperature T, we find that the effective temperature for cluster evaporation is T−h/2Cν, where h is the latent heat. This temperature correction is precisely that required by detailed balance and results both in a centering of the cluster temperature distribution on T0 and a cancellation of any significant effect of temperature fluctuations on the nucleation rate.