A perturbed hard-sphere equation of state extended to imidazolium-based ionic liquids

A perturbed hard-sphere equation of state (EOS) has been previously employed to predict pressure–volume–temperature properties of some ionic liquids (ILs) with phosphonium-, pyridinium-, and pyrrolidinium cations. In this work, we have extended the considered EOS to another class of ILs in compressed states. This class consists of 14 imidazolium-based ILs. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 0.1 to 200 MPa. From 1,122 data points examined for the aforementioned ILs, the total average absolute deviation was found to be 1.05%.     

Modelling phase equilibria of pure ionic liquids from a new equation of state

A perturbed hard-trimer (PHT) equation of state (EOS) has been employed to model densities and some derived thermodynamic properties of 39 ionic liquids (ILs) considering a trimer expression obtained from the statistical associating fluid theory as the reference physical model. The van der Waals dispersion forces were applied as perturbation term. The proposed model was tested using ILs containing imidazolium, pyrrolidinium, pyridinium, phosphonium and piperidinium cations. Two parameters appeared in the PHT EOS which are temperature-dependent, reflecting the dispersive energy parameters among trimers, ε and the hard-core diameter, σ, were determined based on the molecular scaling parameters. The performance of the proposed PHT EOS has been evaluated by predicting the volumetric and first and second derivatives thermodynamic properties in the pressure and temperature ranges within 0.1–200 MPa and 273–472.6 K, respectively. From 6331 data points examined, the average absolute deviation (AAD) of the correlated (at 0.1 MPa) and predicted (at high pressures) densities from the experimental ones was found to be 0.18 %. Furthermore, the isothermal compressibilities and thermal expansion coefficients as well as the heat capacities were estimated through the PHT EOS with uncertainties of the order of ±11.09, ±11.76 and ±3.34 %, respectively. Further, the vapour pressures of ILs are also predicted by the proposed model. The trend of the predicted vapour pressure is in accord with those reported in literature.

     

Modification of Tao–Mason equation of state to ionic liquids

In our previous paper, we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids, using the speed of sound data. Here, we predict the equation of state for ionic liquids (ILs). The considered ILs are [Bmim][PF₆], [C₂mim][NtF₂], [C₃mim][NtF₂], [C₆mim][NtF₂], [C₇mim][NtF₂], [C₂mim][EtOSO₃], [Bmim][MeSO₄], [Bmim][OcSO₄], and [C₄mim][dca]. The equation of state consists of three temperature-dependent parameters: the second virial coefficient, a constant for scaling the softness of repulsive force, and an effective hard-sphere diameter equivalent to the van der Waals co-volume. The second virial coefficients of ILs are scare and there is no accurate potential energy function to allow their theoretical calculation. In this work, the second virial coefficient have been calculated using corresponding states correlation based on temperature and density at normal boiling point. The other two parameters of the equation of state can be calculated using a scaling rule. Analysis of our predicted results shows that the Tao?CMason equation of state is capable of accurately predicting the density of ILs at any temperature and pressure. The overall average absolute deviation densities for 1,633 data points are 2.05%. Also, the density of ILs obtained from the TM EOS has been compared with those calculated from vdW?CCS?C?? and Peng?CRobinson (PR) equation of state. Our results are in favor of the preference of the TM EOS over the two other equations of state. The overall average absolute deviation for 1,633 data points calculated by vdW?CCS?C?? and PR equation of state are 6.63% and 12.19%, respectively.     

Development of a perturbed hard-sphere equation of state for pure and mixture of ionic liquids

A perturbed hard-sphere equation of state (PHS EOS) was previously proposed to present the volumetric properties of ionic liquids by employing a variable parameter β being a function of acentric factor to justify the range of vdW dispersion forces (M. M. Papari, J. Moghadasi, S. M. Hosseini, F. Akbari, J. Mol. Liq. 158 (2011) 57–60). The main aim of the present study is to revise an attractive part of the preceding EOS by re-evaluating the above-mentioned variable parameter as well as the repulsive term. Two temperature-dependent parameters appearing in the revisited EOS have been determined from the corresponding states correlations using the interfacial properties of ILs, i.e., surface tension and liquid density, both at room temperature. The revisited EOS has been employed to model the volumetric properties of ionic liquids (ILs). The predictive power of the proposed model has been assessed by comparing the results obtained with 2189 experimental data points related to 24 ILs over a broad range of pressures and temperatures. The overall average absolute deviation (AAD) of the calculated densities from literature data was found to be 0.62 %. Furthermore, the revisited PHS EOS has been employed to model the volumetric properties of 23 mixtures including IL + IL and IL+ solvent over the vast range of temperatures. From 1580 data points of the binary mixtures of interest, the AAD of the correlated densities from the measurements was found to be 0.47 %.     

Modified equation of state extended to imidazolium-, phosphonium-, pyridinium-, pyrrolidinium- and ammonium-based ionic liquids

An analytical equation of state (EoS) has been previously employed by Hosseini and Sharafi (Ionics 17:511, 2011) for modelling of PVT data of some ionic liquids (ILs). In this work, we have extended the mentioned model to five classes of ILs by the use of alternative scaling constants for corresponding states correlation procedure. For this purpose, ILs involving imidazolium, phosphonium, pyridinium, pyrrolidinium and ammonium cations have been taken into account. From these, 1,294 experimental data points examined to show the reliability of the modified EoS. The comparison of predicted densities with the measured values over a broad range of temperature 293?C452 K and pressures up to 150 MPa led to the encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.73%. Moreover, to establish the predictive power of proposed model, the reproduced densities have been compared with those obtained by another literature work. Moreover, we have demonstrated the density behaviour of studied ILs in terms of alkyl chain length of imidazolium cation via proposed model.     

Thermophysical properties of ionic liquids and their mixtures from a new equation of state

In our previous work, a perturbed hard-trimer-sphere equation of state (PHTS EOS) was developed for modeling the phase equilibria of pure ionic liquids (ILs) (M.M. Alavianmehr et al., Ionics 22 (2016) 2447–2459). In this work, we have successfully extended the model to the mixtures of IL + IL and IL + solvent. Two temperature-dependent parameters appearing in the EOS are correlated with two microscopic scaling constants σ, the effective hard-sphere diameter, and ε, the non-bonded interaction energy. The overall average absolute deviation (AAD) of the estimated densities from the literature data using the proposed model with and without non-additivity parameter (λ _ij) was found to be 0.44 and 0.79%, respectively. A modified Enskog equation and rough hard-sphere (RHS) theory are combined with our proposed equation of state to calculate the viscosity coefficient of ionic liquids and their mixtures. Finally, from the results obtained, a linear relation between logarithm of surface tension and viscosity property of ionic liquid was developed.     

Perturbation approach for equation of state for hard-sphere and Lennard–Jones pure fluids

In this paper we have established the equation of state (EOS) for liquids. The EOS was established for hard-sphere (HS) fluid along with Lennard–Jones (LJ) fluid incorporating perturbation techniques. The calculations are based on suitable axiomatic functional forms for surface tension S _m (r), r ≥ d/2 with intermolecular separation r, as a variable, and m is an arbitrary real number (pole). The results for βP/ρ from the present EOS thus obtained are compared with Percus-Yevick (PY), scaled particle theory (SPT), and Carnahan–Starling (CS). In addition, we have found a simple EOS for the HS fluid in the region which represents the simulation data accurately.     

Volumetric and transport properties of <Emphasis Type="Italic">N</Emphasis>-Butyl-<Emphasis Type="Italic">N</Emphasis>-methylpyrrolidinium bis(Trifluoromethanesulfonyl)imide–methanol binary mixtures

Densities, viscosities, and ionic conductivities were measured for the binary mixtures containing the ionic liquid N-butyl-N-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide and methanol over the entire range of compositions at the temperature varying from 253.15 to 318.15 K. The densities and viscosities decrease monotonously with temperature and the content of ionic liquids (ILs). Furthermore, excess isobaric expansion coefficient has been calculated from the experimental densities. The dependence of temperature on the viscosity has been fitted to the Arrhenius law with high precision. The dependence of temperature on the ionic conductivity has also been gauged by both of the Arrhenius and Vogel–Tamman–Fulcher (VTF) equations. In fact, the shape of the curves shows that the temperature dependence of the conductivity does not follow a simple Arrhenius law, but a better fitting of experimental results is achieved using the VTF model. Additionally, the effects of ILs concentration on the viscosity and the conductivity have been examined using the Walden rule, which shows that the variation of conductivity is inversely proportional to viscosity. Excess molar volumes and viscosity deviations for all mixtures are evaluated and well fitted to the Redlich–Kister polynomial expansions. Physicochemical properties show two clearly distinguished behaviors corresponding to ILs-rich and methanol-rich regions, with distinct transport and volumetric properties. The obtained results are discussed in terms of dipolar interactions and hydrogen bonding establishment between ions of ILs and the methanol molecules.     

New isothermal equation of state of solids applied to high pressures

In the present paper, a new two-parameter inverted equation of state (EOS) is developed which is found to be working very well in the high-pressure region. To check its success and validity, this EOS has been applied in a number of solids. The computed volume compression is found to be in very good agreement with the experimental data in the whole range of pressure in all the solids. The minimum and the maximum pressure range used in the present study is 0–320 kbar and 0–3000 kbar, respectively.     

Thermodynamic properties of cubic boron nitride based on an analytic mean field approach

We present a detailed derivation of the analytic expressions for the equation of state (EOS) and internal energy of Morse model solids based on an analytic mean field potential (AMFP) method. The formalism is applied to cubic boron nitride (c-BN). One set of potential parameters are determined by fitting the experimental P-V-T data of c-BN up to 160 GPa at 295 K and 80 GPa in the range 500–900 K. Various physical quantities including the isothermals, thermal expansion, isochoric heat capacity, Helmholtz free energy and internal energy are calculated and analyzed. The theoretical results are consistent with the available experimental data and those calculated by others. These results presented in this paper verify that the AMFP method is a useful approach to consider the anharmonic effect at high temperature. Numerous reasonable predictions and the change trend of the properties for c-BN at extreme conditions have been given.     

A perturbed hard-sphere equation of state for phosphonium-, pyridinium-, and pyrrolidinium-based ionic liquids

In this work, a perturbed hard-sphere equation of state has been employed to predict the pressure–volume–temperature properties of some phosphonium-, pyridinium-, and pyrrolidinium-based ionic liquids in compressed states. Two temperature-dependent parameters that appeared in the equation of state have been determined using the critical properties of abovementioned ionic liquids as the scaling constant, i.e., knowing only two available scaling constants is sufficient to utilize the proposed equation of state to this class of fluids. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 1 to 65 MPa. From 550 data points examined for the aforementioned ionic liquids, the total average absolute deviation, AAD was found to be 1.12%.     

Quark–gluon plasma as a strongly coupled color-Coulombic plasma

We show that the extensively studied equation of state (EOS) of strongly coupled QED plasma fits the recent lattice EOS data of gluon plasma remarkably well, with appropriate modifications to take account of color degrees of freedom and the running coupling constant. Hence we conclude that the quark–gluon plasma near the critical temperature is a strongly coupled color-Coulombic plasma. Received: 13 January 1999 / Revised version: 22 March 1999 / Published online: 14 October 1999     

Ferromagnetic 0–<Emphasis Type="BoldItalic">π</Emphasis> Josephson junctions

We present a study on low-T_c superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson junctions. SIFS junctions have gained considerable interest in recent years because they show a number of interesting properties for future classical and quantum computing devices. We optimized the fabrication process of these junctions to achieve a homogeneous current transport, ending up with high-quality samples. Depending on the thickness of the ferromagnetic layer and on temperature, the SIFS junctions are in the ground state with a phase drop of either 0 or π. By using a ferromagnetic layer with variable step-like thickness along the junction, we obtained a so-called 0–π Josephson junction, in which 0 and π ground states compete with each other. At a certain temperature the 0 and π parts of the junction are perfectly symmetric, i.e. the absolute critical current densities are equal. In this case the degenerate ground state corresponds to a vortex of supercurrent circulating clock- or counterclockwise and creating a magnetic flux which carries a fraction of the magnetic flux quantum Φ₀. PACS  74.50.+r; 74.78.Fk; 74.81.-g; 85.25.Cp     

Correlation of volumetric properties of binary mixtures of some ionic liquids with alcohols using equation of state

In our previous paper, we extended the Tao and Mason equation of state (TM EOS) to pure ionic liquids. Here we apply TM EOS based on statistical?Cmechanical perturbation theory to binary mixtures of ionic liquids. Three temperature-dependent quantities are needed to use the equation of state: the second virial coefficient, B ₂, effective van der Waals co-volume, b, and a scaling factor, ??. The second virial coefficients are calculated from a correlation that uses the normal boiling temperature and normal boiling density. ?? and b can also be calculated from the second virial coefficient by scaling. In this procedure, the number of input parameters, for calculation of B ₂, ??, and b reduced from 5 (i.e., critical temperature, critical pressure, acetric factor, Boyle temperature T _B, and the Boyle volume ?? _B) to 2 (i.e., T _bp and ?? _bp). At close inspection of the deviations given in this work, the TM EOS predicts the densities with a mean AAD of 1.69%. The density of selected system obtained from the TM EOS has been compared with those calculated from perturbed-hard-sphere equation of state. Our results are in favor of the preference of the TM EOS over another equation of state. The overall average absolute deviation for 428 data points that calculated by perturbed-hard-sphere equation of state is 2.60%.     

Nuclear matter equation of state and σ-meson parameters

We try to determine phenomenologically the extent of in-medium modification of σ-meson parameters so that the saturation observables of the nuclear matter equation of state (EOS) are reproduced. To calculate the EOS we have used Brueckner-Bethe-Goldstone formalism with Bonn potential as two-body interaction. We find that it is possible to understand all the saturation observables, namely, saturation density, energy per nucleon and incompressibility, by incorporating in-medium modification of σ-meson-nucleon coupling constant and σ-meson mass by a few per cent.     

A modified equation of state for Xe at high pressures by molecular dynamics simulation

The exact equation of state （EOS） for the fission gas Xe is necessary for the accurate prediction of the fission gas behavior in uranium dioxide nuclear fuel, However, the comparison with the experimental data indicates that the applicable pressure ranges of existing EOS for Xe published in the literature cannot cover the overpressure of the rim fission gas bubble at the typical UO2 fuel pellet rim structure. Based on the interatomic potential of Xe, the pressure-volume-temperature data are calculated by the molecular dynamics （MD） simulation. The results indicate that the data of MD simulation with Ross and McMahan＇s potential [M. Ross and A. K. McMahan 1980 Phys. Rev. B 21 1658] are in good agreement with the experimental data. A preferable EOS for Xe is proposed based on the MD simulation. The comparison with the MD simulation data shows that the proposed EOS can be applied at pressures up to 550 MPa and 3 GPa and temperatures 900 K and 1373 K respectively. The applicable pressure range of this EOS is wider than those of the other existing EOS for Xe published in the literature.     

An equation of state for the detonation product of copper oxide/aluminum nanothermite composites

An equation of state (EOS) for the detonation product of the copper oxide/aluminum (CuO/Al) nanothermite composites is developed based on the Chapman–Jouguet (CJ) theory and the nanothermite detonation experiment. The EOS is implemented into a coupled computational fluid dynamics and computational solid dynamics code through the material point method for the model-based simulations of the detonation response of the CuO/Al nanothermite material placed in a small well. The simulations demonstrate the validity of the formulated EOS to catch the essential feature of the detonation response of the CuO/Al nanothermite. The EOS parameters are determined by comparing simulated and experimentally measured pressure–time histories.     

The rates of bimolecular thermal reactions taking into account local medium fluctuations

The contribution of local medium fluctuations to the rates of thermal chemical reactions was calculated for the first time. It was shown for the “ideal gas” model that the fluctuation contribution to a rate constant was proportional to the specific volume of particles and amounted to 1–10% already at densities of about 20 atmosphere densities. For this reason, chemical kinetics calculations of reaction rates should be performed taking into account local medium fluctuations before taking into account specific volume in the equation of state.     

A newly developed Fe-doped calcium sulfide nanoparticles with magnetic property for cancer hyperthermia

In this study, a magnetic iron-doped calcium sulfide (Fe–CaS) nanoparticle was newly developed and studied for the purpose of hyperthermia due to its promising magnetic property, adequate biodegradation rate, and relatively good biocompatibility. Fe–CaS nanoparticles were synthesized by a wet chemical co-precipitation process with heat treatment in a N₂ atmosphere, and were subsequently cooled in N₂ and exposed to air at a low temperature. The crystal structure of the Fe–CaS nanoparticles was similar to that of the CaS, which was identified by an X-ray diffractometer (XRD). The particle size was less than 40 nm based on a Debye–Scherrer equation and transmission electron microscope (TEM) examination. Magnetic properties obtained from the SQUID magnetometer demonstrated that the synthesized CaS was a diamagnetic property. Once the Fe ions were doped, the synthesized Fe–CaS converted into paramagnetism which showed no hysteresis loop. Having been heated above 600 °C in N₂, the Fe–CaS showed a promising magnetic property to produce enough energy to increase the temperature for hyperthermia. 10 mg/ml of the Fe–CaS was able to generate heat to elevate the media temperature over 42.5 °C within 6 min. The area of the hysteresis loop increased with the increasing of the treated temperature, especially at 800 °C for 1 h. This is because more Fe ions replaced Ca ions in the lattice at the higher heat treatment temperature. The heat production was also increasing with the increasing of heat treatment temperature, which resulted in an adequate specific absorption ratio (SAR) value, which was found to be 45.47 W/g at 37 °C under an alternative magnetic field of f = 750 KHz, H = 10 Oe. The in vitro biocompatibility test of the synthesized Fe–CaS nanoparticles examined by the LDH assay showed no cytotoxicity to 3T3 fibroblast. The result of in vitro cell hyperthermia shows that under magnetic field the Fe–CaS nanoparticles were able to generate heat and kill the CT-26 cancer cells significantly. We believe that the developed Fe–CaS nanoparticles have great potential as thermo-seeds for cancer hyperthermia in the near future.     

Holographic dark energy in Brans–Dicke theory with logarithmic correction

In the derivation of holographic dark energy density, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity, string theory and black hole physics. In this paper, we study cosmological implication of the interacting entropy-corrected holographic dark energy model in the framework of Brans–Dicke cosmology. We obtain the equation of state and the deceleration parameters of the entropy-corrected holographic dark energy in a non-flat Universe. As system’s IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as L = ar(t). We find out that when the entropy-corrected holographic dark energy is combined with the Brans–Dicke field, the transition from normal state where w _D > −1 to the phantom regime where w _D < −1 for the equation of state of interacting dark energy can be more easily achieved for than when resort to the Einstein field equations is made.