Temperature For Liquid-gas Phase Transition Research Articles

The liquid–gas phase transition in a variational approach and the role of three-body force

The thermal properties of hot baryonic matter and its isospin dependence for a wide range of densities and temperatures have been investigated within the lowest order constrained variational (LOCV) approach by employing the bare two-body interaction AV18 with the inclusion of a phenomenological three-body force (3BF) UIX as well as relativistic corrections (RC). The critical temperature and the liquid–gas (LG) phase transition have been calculated with and without the inclusion of 3BF both in the LOCV and its relativistic expansion, namely (RLOCV) approach. Our results have been compared with other predictions. It turns out that the 3BF gives a repulsive contribution to the equation of state (EOS) which is stronger at higher density and as a consequence reduces the critical temperature of LG phase transition while RC has no special effect on the critical point. The temperature dependence and the isospin dependence of other physical quantities, such as the specific heat capacity, latent heat, entropy, critical exponents, symmetry free energy, incompressibility and the role of UIX 3BF on these quantities have also been studied. At a given temperature, we find a reduction in critical temperature, latent heat, critical asymmetry parameter, and incompressibility when 3BF is added to the bare interaction, while 3BF has no effect on entropy and specific heat capacity, as expected. We observed that the stiffness of density-dependence of symmetry free energy affects on the critical point of LG phase transition. Stiffer symmetry free energy has a smaller critical temperature. Also, by including 3BF, the critical point is obtained in KBT=17.1MeV at 0.06 fm−3 , and the maximum value of latent heat is found in the range ∼31.8MeV.

Thermal behavior of Bi-Ni core-shell nanoparticles with different Ni shell thicknesses: A molecular dynamics study

In present work, molecular dynamics study method has been used to explore thermal behavior of Bi-Ni core-shell nanoparticles with different coating layer thicknesses during consecutive heating. Computational total energy curves between 300 K and 2000 K are utilized to confirm the phase transitions of nanoparticles with various Ni shell thicknesses. The thermal physical properties of Bi-Ni core-shell nanoparticles with various Ni shell thicknesses are different. The results show that the Ni shell has an inhibitory effect on the volatilization of Bi core for Bi-Ni core-shell nanoparticles with a particle radius of 40 Å during the heating from 300 to 2000 K, which effect increases with the Ni shell thickness. Structural changes of nanoparticles during heating have been discovered by the common neighbor analysis, the mean square displacement and the radial distribution function. The research demonstrates that when the thickness of Ni shell layer is greater than 20 Å, the Bi atoms are perfectly bound in the Ni shell and the volatilization of Bi elements is null. The Ni shell can effectively increase the yield of Bi elements. For Bi-Ni core-shell nanoparticles with Ni shell thickness less than 20 Å, the Ni shells rupture and the rupture temperature increases with the increase of Ni shell thickness when the temperature has not yet reached 2000 K. In addition, for Bi-Ni core-shell nanoparticles with Ni shell thickness over 20 Å, the Ni shell does not rupture when the temperature is within 2000 K with the total energy jumping twice. Furthermore, the first energy jump temperature is the melting temperature of the Ni shell, which is almost the same for all nanoparticles. The second energy jump temperature is the liquid-gas phase transition temperature of the Bi core, which increases with the increase of Ni shell thickness.

Experimental study of the critical and supercritical phenomena in ternary mixture of water + 1-propanol + n-hexane

The liquid-gas phase transition (PS, TS, ρS) and PρT properties of the ternary water + 1-propanol + n-hexane mixture with fixed concentration of 0.3333 mole fraction of each component (equimolar mixture) were measured. Measurements were focused in the immediate vicinity of the critical and supercritical regions in order to closely observe the features of the mixture critical behavior. Measurements were made along 29 liquid and vapor isochores between (25.03 and 646.59) kg·m−3 and over the temperature range from (373.15 to 673.15) K at pressures up to 60 MPa. For each isochore most measurements were made in the immediate vicinity of the liquid-gas phase transition temperature (in the single- and two-phase regions) where the break of the P-T isochore's slopes is observing. Temperatures and pressures (TS, PS) at the liquid-gas phase transition point for each fixed density (isochore, ρ) were measured using the isochoric P–T break point technique in the immediate vicinity of the critical point of the mixture. The critical property data TC = 510.85 K, PC = 6.09 MPa, and ρC = 255.22 kg·m−3 for the ternary mixture were extracted from the detailed PρT and (PS, TS, ρS) measurements near the critical point. The combined expanded uncertainty of the density, ρ, pressure, P, temperature, T, and concentration, x, measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 0.2% (density in the liquid phase), 0.3% (density in the gas phase); 0.5% (density in the critical and supercritical regions); 0.05% (pressure), 15 mK (temperature), and 0.01 mol% (concentration). The excess molar volumes (VmE) of the ternary mixture were calculated using the measured molar volumes Vm of the mixture and the reference molar volumes of the pure components for various experimental temperatures and pressures in the supercritical region. Also, the measured PρT data at low densities (vapor phase) were used to calculated the second and third virial coefficients of the mixture at high temperatures.

Simultaneously measurements of the PVT and thermal – pressure coefficient of benzene in the critical and supercritical regions

The values of pressure (P), the temperature derivative, γV = (∂P/∂T)V, and the density (ρ) of benzene have been simultaneously measured in the near- and supercritical regions using high-temperature and high-pressure piezo-calorimeter. Measurements were made along 10 liquid and vapor isochores between (265.5 and 653.9) kg·m−3 and at temperatures from (346.03 to 615.92) K and at pressures up to 9.171 MPa. For each isochore most measurements were made in the immediate vicinity of the liquid-gas phase transition temperature (single- and two-phase regions) where the break of the P-T isochores and the jumps of the thermal –pressure coefficient γV are observing. Temperatures and pressures (TS, PS) at the liquid-gas phase transition curve for each constant density (isochore, ρ) and the critical parameters (TC,PC,ρC) for benzene were measured using the isochoric P − T break point and thermal –pressure coefficient jump techniques. The expanded uncertainty of the pressure (P), density (ρ), and thermal –pressure coefficient (γV) measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be, 0.16%, 0.05% and (0.12 to 1.5) % (depending on temperature and pressure), respectively. The measured pressures (PVT) and thermal –pressure coefficients (γVVT) have been used to calculate of the internal pressure (or energy-volume coefficient) as (∂U∂V)T=T(∂P∂T)V−P. We have also measured the temperature derivatives of the internal energy (∂U∂T)V=CV (isochoric heat capacity) using the same piezo-calorimetric cell. The effect of pressure and temperature on the internal pressure was studied. Isochoric P-T curve break point and isochoric thermal-pressure coefficient jump techniques were used to accurately determine of the phase transition and critical points parameters. The measured values of the thermal-pressure coefficient were interpreted in term of scaling theory of critical phenomena. The measured values of pressure (P), temperature derivative, (∂P/∂T)V, temperature and density at the saturation curve together with our previous isochoric heat capacity measurements were used to calculate other thermodynamic properties of benzene at saturation curve.

Shear viscosity to entropy density ratio in nuclear multifragmentation

Nuclear multifragmentation in intermediate-energy heavy-ion collisions has long been associated with liquid-gas phase transition. We calculate the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ for an equilibrated system of nucleons and fragments produced in multifragmentation within an extended statistical multifragmentation model. The temperature dependence of $\ensuremath{\eta}/s$ exhibits behavior surprisingly similar to that of ${\mathrm{H}}_{2}$O. In the coexistence phase of fragments and light particles, the ratio $\ensuremath{\eta}/s$ reaches a minimum of depth comparable to that for water in the vicinity of the critical temperature for liquid-gas phase transition. The effects of freeze-out volume and surface symmetry energy on $\ensuremath{\eta}/s$ in multifragmentation are studied.

Hot nuclear matter equation of state with a three-body force

The finite temperature Brueckner-Hartree-Fock approach is extended by introducing a microscopic three-body force. In the framework of the extended model, the equation of state of hot asymmetric nuclear matter and its isospin dependence have been investigated. The critical temperature of liquid-gas phase transition for symmetric nuclear matter has been calculated and compared with other predictions. It turns out that the three-body force gives a repulsive contribution to the equation of state which is stronger at higher density and as a consequence reduces the critical temperature of liquid-gas phase transition. The calculated energy per nucleon of hot asymmetric nuclear matter is shown to satisfy a simple quadratic dependence on asymmetric parameter $\ensuremath{\beta}$ as in the zero-temperature case. The symmetry energy and its density dependence have been obtained and discussed. Our results show that the three-body force affects strongly the high-density behavior of the symmetry energy and makes the symmetry energy more sensitive to the variation of temperature. The temperature dependence and the isospin dependence of other physical quantities, such as the proton and neutron single particle potentials and effective masses, are also studied. Due to the additional repulsion produced by the three-body force contribution, the proton and neutron single particle potentials are correspondingly enhanced as similar to the zero-temperature case.

Cluster emission and phase transition behaviours in nuclear disassembly

The features of the emissions of light particles (LP), charged particles (CP), intermediate mass fragments (IMF) and the largest fragment (MAX) are investigated for 129Xe as functions of temperature and ‘freeze-out’ density in the frameworks of the isospin-dependent lattice gas model and the classical molecular dynamics model. Definite turning points for the slopes of average multiplicity of LP, CP and IMF, and of the mean mass of the largest fragment Amax are shown around a liquid–gas phase transition temperature and while the largest variances of the distributions of LP, CP, IMF and MAX appear there. It indicates that the cluster emission rate can be taken as a probe of nuclear liquid–gas phase transition. Furthermore, the largest fluctuation is simultaneously accompanied at the point of the phase transition as can be noted by investigating both the variances of their cluster multiplicity or mass distributions and the Campi scatter plots within the lattice gas model and the molecular dynamics model, which is consistent with the result of the traditional thermodynamical theory when a phase transition occurs.

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)L × SU(3)R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(2) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.

ON THE SATURATION PROPERTIES AND THE LIQUID-GAS PHASE TRANSITION OF FINITE NUCLEAR MATTER WITH GOGNY INTERACTION

The Hill-Wheeler formula is applied to deriving the equation of state for finite nuclei with the Gogny effective interaction in the framework of the Hartree-Fock theory. The reasonable zero-temperature saturation properties is obtained, and the critical temperature for liquid-gas phase transition of finite nuclei is found to be around 12MeV. It is found that the phenomenological formula for surface energy which is used widely is not available when the density is far away from the normal nuclear density, and a new formula is proposed.

ON THE SATURATION PROPERTIES AND THE LIQUID-GAS PHASE TRANSITION OF FINITE NUCLEAR MATTER WITH GOGNY INTERACTION

The Hill-Wheeler formula is applied to deriving the equation of state for finite nuclei with the Gogny effective interaction in the framework of Hartree-Fock theory. The reasonable zero-temperature saturation properties is obtainde, and the critical temperature for liquid-gas phase transition of finite nuclei is found to be around 12 MeV. In addition it is found that the phenomenological formula for surface energy used widely is not available when the density is far away from the normal nuclear density, and a new formula is suggested.

Critical phenomena in nuclear matter with Gogny interaction

The finite temperature real time Green function method with normal pair cut off (NPC) approximation is applied to deriving the equation of state for finite and asymmetric nuclear matter with the Gogny effective interaction. The dependences of the critical temperature for liquid-gas phase transition on nucleon number, asymmetry and Coulomb potential are discussed.

Liquid-gas phase transition and compressibility of nuclear matter

A new equation of state is proposed based on the condition that the mean field potential has a minimum at normal density. Some consequences for giant resonances and low-energy heavy-ion reactions are deduced. A value for the compressibility of 225 MeV and a critical temperature for liquid-gas phase transition of 9 MeV is calculated.