Constant Volume Heat Capacity Research Articles

Thermodynamic properties of double square-well fluids: Computer simulations and theory

Computer simulations have been performed to obtain the thermodynamic properties of fluids with double square-well potentials, that is, potentials consisting of two adjacent square wells with different depths. The compressibility factor, excess energy, chemical potential, constant-volume excess heat capacity, and other derived properties have been obtained. These data have been used to test the performance of several perturbation theories for predicting the thermodynamic properties of this kind of fluids. Good agreement is found on the whole between theory and simulation at supercritical temperatures. The possible presence of anomalous behavior at high densities in the fluids considered has been also analyzed in light of the same theories, with the result that in general, they do not predict such anomalous behavior, with the possible exception of a Monte Carlo-based perturbation theory for relatively large potential widths at high densities and very low temperatures.

Third-order thermodynamic perturbation theory for effective potentials that model complex fluids

We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.

Thermodynamic entropy and the accessible states of some simple systems

Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in a simple thermodynamic system with temperature-independent constant-volume heat capacity, C, is TC/k. A physical interpretation of this function is given for three such systems: an ideal monatomic gas, an ideal gas of diatomic molecules with rotational motion and a solid in the Dulong–Petit limit of high temperature. T1/2 emerges as a natural measure of the number of accessible states for a single particle in one dimension. Extension to N particles in three dimensions leads to TC/k as the total number of possible arrangements or microstates. The different microstates of the system are thus shown a posteriori to be equally probable, with probability T−C/k, which implies that for the purposes of counting states the particles are distinguishable. The most probable energy state of the system is determined by the degeneracy of the microstates.

Heat Capacity and Gruneisen Parameter for GaN with Zinc-Blende Structure

A shell model molecular dynamics method is used to investigate the behavior of the pressure-volume relationship, heat capacities at constant pressure and constant volume, Gruneisen parameter for GaN with zinc-blende cubic structure at high pressures and high temperatures. The interactions between Ga-Ga, Ga-N, and N-N are described with polarizable potential models which have assigned two different partially ionic charges to Ga and N by taking into account of the ionic character of GaN. It is shown that the calculated thermodynamic parameters at ambient condition are in good agreement with the available theoretical results. Compared with the results from first-principles calculations, the discrepancy of constant-volume heat capacity at lower temperature may be explained well with different approximation mechanisms. The properties of GaN with zinc-blende structure are summarized in the temperature range of 300-2000 K and pressure up to 40 GPa.

Thermodynamic properties at constant volume around the solid–liquid phase transition in single metals by using molecular dynamics

Molecular dynamics simulations were performed for eight different metals to calculate their constant volume heat capacity and latent heat in both liquid and solid phases. The atomic interaction for the simulations is taken as modeled by the n-body semi-empirical Gupta potential. The per atom energies of the simulation as a function of the temperature are recognized as the caloric curves of the systems and therefore the slopes of these curves represent the constant volume heat capacities. The values obtained in the simulation for the constant volume heat capacity are in good agreement with the Dulong and Petit law for solids at high temperature, which indicates that the equipartition of energy is well recovered in the simulations. The maximum deviation from this law occurs for metals with the slightest atomic masses. The obtained values for the constant volume heat capacities in the liquid phase are systematically smaller than those in the solid phase, this being physically correct.

A new coordination number model and heat capacity of square-well fluids of variable width

A new coordination number model for square-well fluid is proposed in this work. The model modifies the theory previously developed for the coordination number of square-well fluids derived on the basis of the generalized van der Waals theory by Largo and Solana. In the present work, we have calculated the co-ordination number of a square-well fluid on the basis of high temperature expansion (HTE) approach along with the modified formula of the maximum reduced density and a novel approach to derive the coordination number of hard sphere fluids. We have also performed the theoretical predictions of constant-volume excess heat capacity of the square-well fluids. It is shown that the theoretical predictions of the constant-volume excess heat capacity determined by second-order perturbation term are in much better agreement with simulation data than to the values of C V E / N K obtained by other workers due to the better description of the second-order term.

Calculation of heat capacities of light and heavy water by path-integral molecular dynamics

As an application of atomistic simulation methods to heat capacities, path-integral molecular dynamics has been used to calculate the constant-volume heat capacities of light and heavy water in the gas, liquid, and solid phases. While the classical simulation based on conventional molecular dynamics has estimated the heat capacities too high, the quantum simulation based on path-integral molecular dynamics has given reasonable results based on the simple point-charge/flexible potential model. The calculated heat capacities (divided by the Boltzmann constant) in the quantum simulation are 3.1 in the vapor H2O at 300 K, 6.9 in the liquid H2O at 300 K, and 4.1 in the ice Ih H2O at 250 K, respectively, which are comparable to the experimental data of 3.04, 8.9, and 4.1, respectively. The quantum simulation also reproduces the isotope effect. The heat capacity in the liquid D2O has been calculated to be 10% higher than that of H2O, while it is 13% higher in the experiment. The results demonstrate that the path-integral simulation is a promising approach to quantitatively evaluate the heat capacities for molecular systems, taking account of quantum-mechanical vibrations as well as strongly anharmonic motions.

Two-Gaussian excitations model for the glass transition

We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple two-state models ("logarithmic" model in configuration space) and the random energy model ("Gaussian" model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constant-volume heat capacity found by recent simulations for binary mixed Lennard-Jones and soft-sphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excited-state Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the possibility of first-order phase transitions for fragile liquids. The analysis of laboratory data for toluene and o-terphenyl indicates that fragile liquids resolve the Kauzmann paradox by a first-order transition from supercooled liquid to ideal-glass state at a temperature between T(g) and Kauzmann temperature extrapolated from experimental data. We stress the importance of the temperature dependence of the energy landscape, predicted by the fluctuation-dissipation theorem, in analyzing the liquid thermodynamics.

The gas–liquid phase-transition singularities in the framework of the liquid-state integral equation formalism

The singularities of various liquid-state integral equations derived from the Ornstein-Zernike relation and its temperature derivatives, have been investigated in the liquid-vapor transition region. As a general feature, it has been found that the existence of a nonsolution curve on the vapor side of the phase diagram, on which both the direct and the total correlation functions become complex-with a finite isothermal compressibility-also corresponds to the locus of points where the constant-volume heat capacity diverges, in consonance with a divergence of the temperature derivative of the correlation functions. In contrast, on the liquid side of the phase diagram one finds that a true spinodal (a curve of diverging isothermal compressibilities) is reproduced by the Percus-Yevick and Martynov-Sarkisov integral equations, but now this curve corresponds to states with finite heat capacity. On the other hand, the hypernetted chain approximation exhibits a nonsolution curve with finite compressibilities and heat capacities in which, as temperature is lowered, the former tends to diverge.

Molecular dynamics simulation of zirconia-based inert matrix fuel

The structure and thermal properties of the zirconia-based inert matrix fuel were evaluated by the molecular dynamics (MD) simulations. For the yttria-stabilized zirconia doped with erbia and ceria (or plutonia), Er x Y y M z Zr 1− x− y− z O 2−( x+ y)/2 (where M = Ce or Pu), the MD simulation have been performed using the Born–Mayer–Huggins interatomic potential. The lattice constant, pair-correlation function and oxygen coordination number were discussed in terms of content of tetravalent ion, Ce 4+ or Pu 4+. The vibration properties of constituent ions could be deduced from the phonon-level densities for Er 0.05Y 0.10Ce 0.10Zr 0.75O 1.925 and Er 0.05Y 0.10Pu 0.10Zr 0.75O 1.925. The constant-volume heat capacity was calculated based on the harmonic oscillation model, and the dilatation contribution was evaluated from thermal expansion and bulk modulus. The constant-pressure heat capacity thus obtained from MD simulation was comparable with that estimated by Neumann–Kopp rule.

Thermal conductivity of gas by pulse injection techniques using specific thermal conductivity detector (TCD)

This paper presents a procedure to determine the thermal conductivity of gases by pulse injection, using a thermal conductivity detector (TCD). The measurements are taken at 323K and atmospheric pressure with a 160 omega tungsten filament sensor. Under well defined approximations the original nonlinear second order equation, which describes the sensors output, as a function of thermal conductivity and constant volume specific heat was transformed into a linear first order equation. According to this equation the time integrated, second order sensors electrical output signal, multiplied by the constant volume heat capacity is proportional to the constant volume heat capacity, divided by the thermal conductivity. The experimental results obtained with Ar, N2, O2, CH4, CO2, C2H4, C3H6 and i-C4H8 gases are in good agreement with the proposed theoretical model and the linearity correlation confirms the validity of the proposed method.

Constant-volume heat capacity in a near-critical fluid from Monte Carlo simulations

We consider a near-critical fluid of hard spheres with short-range interactions (approximately r(-6)) and obtain its constant-volume heat capacity C(V) by means of Monte Carlo calculations in the canonical ensemble. The question addressed is whether or not the heat capacities of the finite-size systems studied in simulations can provide a reliable indication of nonclassical criticality. For the model fluid considered here this is found to be the case. The heat capacity along the critical isochore shows a peak near the critical temperature, with a system size dependence that is consistent with the known Ising universality class of the model. The relevance of our results to recent attempts to determine the universality class of ionic fluids through calculations of C(V) is briefly discussed.

Melting and Gr neisen 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 Gruneisen 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.

Effect of phase behavior, density, and isothermal compressibility on the constant-volume heat capacity of ethane + n-pentane mixed fluids in different phase regions

The phase behavior, density, and constant-volume molar heat capacity ( C v,m ) of ethane + n-pentane binary mixtures have been measured in the supercritical region and subcritical region at T=309.45 K. In addition, the isothermal compressibility ( κ T ) has been calculated using the density data determined. For a mixed fluid with a composition close to the critical composition, C v,m and κ T increase sharply as the pressure approaches the critical point (CP), the dew point (DP), or the bubble point (BP). However, C v,m is not sensitive to pressure in the entire pressure range if the composition of the mixed fluid is far from the critical composition. To tune the properties of the binary mixtures effectively by pressure, both the composition and the pressure should be close to the critical point of the mixture. The intermolecular interactions in the mixture are also discussed on the basis of the experimental results.

Exploring repulsive interactions in a model helical peptide: A parallel tempering Monte Carlo study

By implementing the parallel-tempering algorithm to the canonical ensemble, the conformational changes of an isolated Ac–W(RAAAR)5A–NH2 model peptide were determined. The interparticle interactions were modeled using a minimalist potential, i.e., a beadlike model that uses harmonic oscillators to describe covalent interactions and modified Lennard-Jones potentials to model nonbonding interactions. In particular, the interactions between arginines are modeled by repulsive interactions, causing a stabilization of the alpha-helix structure at low temperatures. The conformational changes were identified by anomalies in the constant volume heat capacity as a function of temperature. Namely, the temperature at which the constant volume heat capacity reached a maximum in the transition region was associated with the temperature at which a conformational change occurred. The transitions were also characterized by computing the radius of gyration of the peptide and the most probable isomeric structure obtained at a given temperature. Three changes were observed at low temperatures and one at high temperature. The low temperature transitions were analogous to the peptide folding, whereas the high temperature transition was related to the peptide unfolding. The results obtained were compared with experimental data generated from isotope edited Fourier transform infrared spectroscopy and two-dimensional correlation analysis for a similar peptide containing salt bridge interactions.

Liquid–vapor criticality in a fluid of charged hard dumbbells

The vapor–liquid criticality of a fluid of charged hard dumbbells is investigated employing grand canonical Monte Carlo simulations and mixed-field finite-size scaling methods. The reduced critical temperature and density obtained are Tc*=0.04911±0.00003 and ρc*=0.101±0.003, respectively. The critical temperature is very close to that of the restricted primitive model (RPM) for ionic fluids, while the critical density is ∼25% larger than that of the RPM. The “fits” to the Ising ordering operator distribution are good, and are of similar quality to those found for the RPM with systems of comparable size. However, for the finite-size systems simulated, the constant volume heat capacity, CV, gives no indication of an Ising-type “divergence” at Tc. This is analogous to the RPM, and serves to demonstrate that this still puzzling behavior is not restricted to that model.

Effect of phase behavior on the constant volume heat capacity of ethane + ethanol and ethane + acetone mixed fluids near the critical region and the intermolecular interaction

The phase behaviors, constant volume heat capacity ( C v), and isothermal compressibility ( K T) of ethane+ethanol and ethane+acetone binary mixtures have been measured in supercritical (SC) region and subcritical region near the critical point (CP) of the mixtures at 309.45 K. The experiments have also been carried at the conditions far from the critical point of the mixtures. It is demonstrated that in supercritical region there exists a maximum in C v versus pressure curve ( C v max) at fixed composition, which occurs at the pressure where K T is the largest. In subcritical region, C v and K T increase sharply as pressure approaches the critical point or bubble point (BP), and the C v at CP or BP can be several times larger than that of the fluids far from the phase separation pressures. On the basis of the experimental results, the intermolecular interaction is discussed.

Heat capacity of square-well fluids of variable width

We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibility factor. This is illustrated by comparing the reported simulation data for the heat capacity with the theoretical predictions given by the Barker-Henderson perturbation theory as well as with those given by a non-perturbative theoretical model based on Baxter's solution of the Percus-Yevick integral equation for sticky hard spheres. Both theories give accurate predictions for the equation of state. By contrast, it is found that the Barker-Henderson theory strongly underestimates the excess heat capacity for low to moderate temperatures, whereas a much better agreement between theory and simulation is achieved with the non-perturbative theoretical model, particularly for small well widths, although the accuracy of the latter worsens for high densities and low temperatures, as the well width increases.

The constant-volume heat capacity of near-critical fluids with long-range interactions: A discussion of different Monte Carlo estimates

The constant-volume heat capacities, CV, of various near-critical fluids with long-range potentials have been obtained using both canonical and grand-canonical Monte Carlo (GCMC) calculations. In the case of the restricted primitive model it is shown that the large discrepancies between previously reported results arise from the use of different simulation ensembles. In order to investigate how well the different ensemble estimates of CV obtained with small systems can indicate the universality class of the bulk fluid, calculations have been performed for fluids with attractive pair interactions which vary like −1/ra, with a=6, 4, and 3.1. For a=6, Ising-type criticality is expected, while for a=4 and 3.1 the criticality is mean-field. For each of these models the canonical-ensemble estimates of CV do not provide unambiguous confirmation of the expected critical behavior, and hence this is not a reliable method for determining the universality class. This is also true of the GCMC estimates of CV, which appear consistent with Ising-type behavior for all of the systems studied, even for those which are known to exhibit mean-field criticality in the thermodynamic limit. We suggest that these are artifacts associated with finite system size, and we speculate as to why they appear in canonical and GCMC calculations.

The tau-oscillator

The tau-oscillator is a one-dimensional quantum-mechanical oscillator which can exist only below a critical temperature Tmax. Its quantized energy levels have the usual form but, unusually, these degeneracies involve the energy levels. A generalized equipartition law is also found and the constant volume heat capacity can exhibit a Schottky anomaly.