Three-body Interaction Model Research Articles

A method to remove lower order contributions in multi-particle femtoscopic correlation functions

In recent years the femtoscopy technique has been used by the ALICE Collaboration in small colliding systems at the LHC to investigate the strong-interaction of hadron pairs in the low-energy regime. The extension of this technique to the study of many-body correlations aims to deliver in the next years the first experimental measurements of the genuine many-hadron interactions, provided that the contributions due to the lower order terms are properly accounted for. In this paper we present a method that allows to determine the residual lower order contributions to the three-body correlation functions, based on the cumulant decomposition approach and on kinematic transformations. A procedure to simulate genuine three-body correlations in three-baryon correlation functions is also developed. A qualitative study of the produced correlation signal is performed by varying the strength of the adopted three-body interaction model and comparisons with the expectations for the lower order contributions to the correlation function are shown. The method can be also applied to evaluate the combinatorial background in the two-body correlation functions, providing an improved statistical accuracy with respect to the standard techniques. The example of the contribution by the pK^+K^- channel to the recently measured pupphi correlation is discussed.

Viscosity and Density of 1-Alkanol (C3–C11) Quaternary and Quinary Systems at Different Temperature Levels.

The measured kinematic viscosity and density and the calculated absolute viscosity for selected quaternary and quinary n-alkanol mixtures are presented in this study. The mixtures are composed of 1-propanol, 1-pentanol, 1- heptanol, 1-nonanol, and 1-undecanol. Both the kinematic viscosity and density were measured for the pure components and several intermediate compositions for the selected mixtures at two temperature levels of 293.15 and 298.15 K. The measured data were used to test the predictive capability of different models. The McAllister three body interaction model and the GC-UNIMOD model showed the best overall predictive capability of all models.

Densities, viscosities, and refractive indices of binary and ternary mixtures of methanol, acetone, and chloroform at temperatures from (298.15–318.15) K and ambient pressure

Densities, viscosities, and refractive indices of binary and ternary liquid systems of methanol, acetone, and chloroform at temperatures from)298.15–318.15(K and ambient pressure were measured. In this regard, it should be stressed that the measurements covered the whole composition range of the components in the binary and the ternary systems. In addition, the experimental data have been utilized in order to extract some derived properties like excess molar volume (VE), viscosity deviation (Δη), and refractive index deviation (ΔnD). To correlate the aforementioned derived properties, the well-known Redlich-Kister and Cibulka equations were applied on the binary and ternary mixtures, respectively. Consequently, the control parameters, as well as the corresponding standard deviations, were completely reported. Moreover, for further validation, the McAllister three-body interaction model for kinematic viscosity and Grunberg-Nissan model for dynamic viscosity were examined and the results were thoroughly compatible with the Redlich-Kister polynomial equation. By using the derived properties, the nature of the intermolecular interactions and the hydrogen bond between solvents in the binary and ternary mixtures were discussed and the results are satisfying in terms of matching to the theoretical models.

Thermodynamics of Viscous Flow of tert-Butanol with Butylamines: UNIFAC–VISCO, Grunberg–Nissan and McAllister Three Body Interaction Models for Viscosity Prediction and Quantum Chemical (DFT) Calculations

Thermodynamic activation parameters, enthalpies (ΔH‡), entropies (ΔS‡) and Gibbs energies (ΔG‡) for viscous flow of the systems tert-butanol (TB)+n-butylamine (NBA), TB+di-n-butylamine (DBA) and TB+tri-n-butylamine (TBA) have been calculated from measured density and viscosity data at temperatures ranging from 303.l5 to 323.15 K over the composition range 0 ≤ x2 ≤ 1, where x2 is the mole fraction of TB. For all systems, the corresponding excess properties ΔH‡E, ΔS‡E and ΔG‡E have been determined, which are negative in the whole range of composition. The observed negative excess activation properties have been accounted for in terms of dispersive forces and H-bonding. The derived properties are well represented by fourth degree polynomial equations whereas the excess properties could be fitted to third degree Redlich–Kister polynomial equations. Furthermore, the viscosities have been predicted by using the UNIFAC–VISCO model, Grunberg–Nissan model and McAllister three-body interaction model. The UNIFAC–VISCO model and Grunberg–Nissan model do not show good agreement with the experimental data, whereas the McAllister three-body interaction model shows excellent agreement for all three systems, with small average absolute percent deviations (AAD% = 0.6–2.3). The DFT-B3LYP method with the 6-311 G (d, p) basis set has been employed for the optimization of the geometry and calculation of the total energies of the pure compounds and their binary complexes.

RETRACTED ARTICLE: Density, viscosity and speed of sound of benzaldehyde with benzene at 303.15, 308.15, and 313.15 K

The values of density, viscosity and speed of sound for the binary liquid mixture of Benzaldehyde with Benzene were measured over the entire range of composition at 303.15, 308.15, and 313.15 K. These values are used to calculate the excess molar volume (VE), deviation in viscosity (Δη), deviation in speed of sound (ΔU), deviation in isentropic compressibility (Δβs), excess internal pressure (Δπ), excess intermolecular free length (ΔLf), excess free volume (VEf) and excess acoustic impedance (ΔZ). McAllister’s three-body interaction model is used for correlating Kinematic Viscosity of binary mixtures. The excess values were correlated using the Redlich–Kister polynomial equation to obtain their coefficients and standard deviations. The thermophysical properties (density, viscosity, and speed of sound) under the study were fit to the Jouyban–Acree model.

First-principles modeling of three-body interactions in highly compressed solid helium

We present a set of three-body interaction models based on the Slater-Kirkwood (SK) potential that are suitable for the study of the energy, structural, and elastic properties of solid $^{4}\mathrm{He}$ at high pressure. Our effective three-body potentials are obtained from the fit to total energies and atomic forces computed with the van der Waals density functional theory method due to Grimme, and represent an improvement with respect to previously reported three-body interaction models. In particular, we show that some of the introduced SK three-body potentials reproduce closely the experimental equation of state and bulk modulus of solid helium up to a pressure of $\ensuremath{\sim}60$ GPa, when used in combination with standard pairwise interaction models in diffusion Monte Carlo simulations. Importantly, we find that recent predictions reporting a surprisingly small variation of the kinetic energy and Lindeman ratio on quantum crystals under increasing pressure are likely to be artifacts deriving from the use of incomplete interaction models. Also, we show that the experimental variation of the shear modulus, ${C}_{44}$, at pressures $0\ensuremath{\le}P\ensuremath{\le}25$ GPa can be quantitatively described by our set of SK three-body potentials. At higher compression, however, the agreement between our ${C}_{44}$ calculations and experiments deteriorates and thus we argue that higher order many-body terms in the expansion of the atomic interactions probably are necessary in order to better describe elasticity in very dense solid $^{4}\mathrm{He}$.

An investigation on the structural transition and stability of some actinide nitrides under pressure

A theoretical study of the structural and related properties of some actinide nitrides under high pressure has been carried out using three-body interaction (TBI) potential model. The present TBI model constitutes the long range Coulombic, three body interaction forces with inclusion of covalency effect, van der Waals’ interaction and short range overlap repulsive forces operative up-to next nearest neighbor ions. The covalency effect is introduced to explain the partial covalent nature of the present compounds. Using this static simulation technique we have investigated the phase transition pressures, volume collapses and elastic behaviour of ThN, NpN and CmN at high-pressures. A detailed discussion of stability criteria using various theories has also been done. The results found are well agreed with available experimental and other data.

Can an Ab Initio Three-Body Virial Equation Describe the Mercury Gas Phase?

We report a sixth-order ab initio virial equation of state (EOS) for mercury. The virial coefficients were determined in the temperature range from 500 to 7750 K using a three-body approximation to the N-body interaction potential. The underlying two-body and three-body potentials were fitted to highly accurate Coupled-Cluster interaction energies of Hg2 (Pahl, E.; Figgen, D.; Thierfelder, C.; Peterson, K. A.; Calvo, F.; Schwerdtfeger, P. J. Chem. Phys. 2010, 132, 114301-1) and equilateral-triangular configurations of Hg3. We find the virial coefficients of order four and higher to be negative and to have large absolute values over the entire temperature range considered. The validity of our three-body, sixth-order EOS seems to be limited to small densities of about 1.5 g cm(-3) and somewhat higher densities at higher temperatures. Termwise analysis and comparison to experimental gas-phase data suggest a small convergence radius of the virial EOS itself as well as a failure of the three-body interaction model (i.e., poor convergence of the many-body expansion for mercury). We conjecture that the nth-order term of the virial EOS is to be evaluated from the full n-body interaction potential for a quantitative picture. Consequently, an ab initio three-body virial equation cannot describe the mercury gas phase.

Densities, Viscosities, Speeds of Sound, and Refractive Indices of Binary Mixtures of 2-Ethyl-1-hexanol with Benzene and Halobenzenes

Densities, \(\rho \), viscosities, \(\eta \), speeds of sound, \(u\), and refractive indices, \(n_\mathrm{D} \), of binary liquid mixtures of 2-ethyl-1-hexanol with benzene, chlorobenzene, and bromobenzene have been measured over the entire range of composition at 298.15 K, 303.15 K, and 308.15 K and at atmospheric pressure. From the experimental data of the density, speed of sound, viscosity, and refractive index, the values of the excess molar volume, \(V^\mathrm{E}\), isentropic compressibility, \({\kappa _{S}}\), and deviations in molar refraction, \(\Delta R\), have been calculated. The viscosity data have been correlated using McAllister’s three-body interaction model at different temperatures. The calculated excess and deviation functions have been analyzed in terms of molecular interactions and structural effects.

Density, Viscosity, Sound Speed, and Thermoacoustical Parameters of Benzaldehyde with Chlorobenzene or Nitrobenzene at 303.15 K, 308.15 K, and 313.15 K

The values of the density, viscosity, and speed of sound for binary liquid mixtures of benzaldehyde with chlorobenzene or nitrobenzene have been measured over the entire range of composition at (303.15, 308.15, and 313.15) K. These values have been used to calculate the excess molar volume (\(V^\mathrm{E}\)), and excess free volume (\(V_\mathrm{f}^\mathrm{E}\)). McAllister’s three-body interaction model is used for correlating the kinematic viscosity of binary mixtures. The thermophysical properties (density, viscosity, and ultrasonic velocity) under study were fit to the Jouyban–Acree model.

Densities and Viscosities of the Quinary System: Cyclohexane (1) $$+$$ + $$\varvec{m}$$ m -Xylene (2) $$+$$ + Cyclooctane (3) $$+$$ + Chlorobenzene (4) $$+$$ + Decane (5) and Its Quaternary Subsystems at 308.15 K and 313.15 K

The volumetric and viscometric properties of the quinary system: cyclohexane + $$m$$ -xylene + cyclooctane + chlorobenzene + decane, were measured over the entire composition range at 308.15 K and 313.15 K. The experimental data obtained in the course of the present study were employed to analyze the predictive capability of six semi-theoretical and empirical well-known viscosity models reported in the literature, namely, the generalized McAllister three-body interaction model, the pseudo- binary McAllister model, the group contribution model, the generalized corresponding states principle model, the Allan and Teja correlation, and the Grunberg and Nissan law of viscosity. The predictive capabilities of the models were compared using the percentage average absolute deviation (%AAD). The final results showed that the generalized McAllister model gives the lowest AADs of 3.3 % and 3.7 % at 308.15 K and 313.15 K, respectively.

Densities and viscosities of ten binary and ten ternary regular solution systems at 308.15 and 313.15 K

The densities and kinematic viscosities of binary and ternary regular mixtures containing cyclohexane, m-xylene, chlorobenzene, cyclooctane and decane were measured over the entire composition range at 308.15K and 313.15K, respectively. The experimental results were used to test the predictive capability of the six viscosity models available in the literature; namely, the generalized McAllister three-body interaction model, the pseudo-binary McAllister model, the group contribution (GC-UNIMOD) model, the generalized corresponding states principle (GCSP) model, the Allan and Teja correlation and the Grunberg and Nissan law of viscosity. The percentage average absolute deviation (%AAD) was employed as the criterion for comparing the predictive capabilities of the aforementioned models. The experimental pure component data obtained in the present study agreed well with the corresponding literature values at both designated temperatures. The model testing results showed that the generalized McAllister showed the best predictive capability resulting in the lowest %AADs; viz., 3.3 and 3.7 at 308.15K and 313.15K, respectively.

Thermodynamic and transport properties for binary and ternary mixtures of 2-methyltetrahydrofuran + chlorobenzene + cyclopentanone at T = 298.15 K

Experimental densities ρ, viscosities η, and refractive indices n D of the ternary mixtures consisting of 2-methyltetrahydrofuran + chlorobenzene + cyclopentanone and constituted binary mixtures were measured at T = 298.15 K for the liquid region and at ambient pressure for the whole composition range. Excess molar volumes $$V_{\text{m}}^{\text{E}}$$ , deviations in the viscosity Δη, and deviations in the refractive index Δn D from the mole fraction average for the mixtures were derived from the experimental data. The excess partial molar volumes $$V_{{\text{m}},i}^{\text{E}}$$ were also calculated. The binary and ternary data of $$V_{\text{m}}^{\text{E}}$$ , Δη, and Δn D were correlated as a function of the mole fraction by using the Redlich–Kister and the Cibulka equations, respectively. McAllister’s three-body interaction model is used for correlating the kinematic viscosity of binary mixtures with the mole fraction.

Densities, speeds of sound and viscosities of binary liquid mixtures of octan-2-ol with benzene and halobenzenes at 298.15 and 303.15 K

Densities ρ, speeds of sound u, viscosities η and refractive indices n D of binary mixtures of octan-2-ol with benzene, chlorobenzene and bromobenzene have been measured over the entire range of composition at 298.15 and 303.15 K and atmospheric pressure. From the experimental data, excess molar volumes V E , isentropic compressibilities κ S , excess isentropic compressibilities κ S E , and deviations of speeds of sound u D , have been calculated at 298.15 and 303.15 K. These excess functions have been fitted to the Redlich–Kister polynomial equation. The viscosity data have been correlated using Kendall–Monroe, Grunberg–Nissan, Tamura–Kurata, Hind–Mclaughlin Ubbelohde and Katti–Chaudhary viscosity models, and McAllister's three-body interaction model at different temperatures.

Density, Viscosity, and Speed of Sound of (1-Octanol + 2-Methoxyethanol), (1-Octanol + N,N-Dimethylacetamide), and (1-Octanol + Acetophenone) at Temperatures of (298.15, 308.15, and 318.15) K

Densities and viscosities of the binary mixtures of 1-octanol + 2-methoxyethanol (2ME), + N,N-dimethylacetamide (DMAc), and + acetophenone (APH) were measured over the entire range of composition at T = (298.15, 308.15, and 318.15) K. Ultrasonic speeds of these binary mixtures have also been measured at 298.15 K. From the experimental data, values of excess molar volumes (VE), viscosity deviations (Δη), and excess isentropic compressibility (κSE) have been calculated. These results were fitted to the Redlich−Kister polynomial equation. Partial molar volumes of 2ME/DMAc/APH in 1-octanol at infinite dilution and at different temperatures have also been evaluated. The results were discussed in terms of molecular interactions prevailing in the mixtures. The measured viscosities were correlated with McAllister’s three-body interaction model.

Quantum discord in matrix product systems

We consider a class of quantum systems with spin-flip symmetry and derive the quantum correlation measured by the quantum discord (QD). As an illustration, we investigate the QD in a three-body interaction model and an XYZ interaction model, whose ground states can be expressed as matrix product states, and the QD is exactly soluble. We show that the QD behaves differently than the quantum entanglement (QE) in many ways; for example, they may show opposite monotonicity and completely different finite-size effects. Furthermore, we compare the capability of the QD and the QE to detect quantum phase transitions (QPTs) and find that the QD is more reliable than the QE for signaling QPTs in these models: In the three-body interaction model, the QE is singular at the quantum critical point, however, it exhibits an additional singularity in the noncritical region, while the analyticity of the QD can be used to identify the quantum critical point perfectly; and in the XYZ interaction model, the QE vanishes in the thermodynamic limit, thus losing its ability to detect QPTs, while the QD still functions very well.

Studies on Transport and Thermodynamic Properties of Binary Mixtures of Hexan-1-ol with Halogenated Compounds at 293.15 K

Viscosities (η) of binary mixtures of hexan-1-ol with 1,2-dichloroethane, 1,2-dibromoethane, and 1,1,2,2-tetrachloroethene have been determined at 293.15 K and at the atmospheric pressure for the whole composition range. Deviations in viscosity (Δη) from the mole fraction average have been derived from the experimental data. The viscosity data have been correlated using Kendall−Monroe, Lobe, Grunberg−Nissan, Tamura−Kurata, Hind−Mclaughlin−Ubbelohde, and Katti−Chaudhary viscosity models and McAllister’s three-body interaction model.

Densities and Kinematic Viscosities of Ten Binary 1-Alkanol Liquid Systems at Temperatures of (293.15 and 298.15) K

The densities and viscosities of ten binary mixtures of 1-propanol, 1-pentanol, 1-heptanol, 1-nonanol, and 1-undecanol have been measured over the entire composition range at temperatures of (293.15 and 298.15) K. The experimental data were employed to test the predictive capabilities of viscosity models including the generalized McAllister three-body interaction model, the GC-UNIMOD model, the generalized corresponding states principle (GCSP) model, and the Allan and Teja correlation. The analysis of the models shows that the generalized McAllister three-body interaction model provided the best predictions for the 1-alcohol mixtures investigated.

Densities and Viscosities of Binary Mixtures of Methyl 4-Chlorobutyrate with Aromatic Hydrocarbons at T = (298.15 to 318.15) K

Densities and viscosities of the binary mixtures of methyl 4-chlorobutyrate with benzene, toluene, o-xylene, m-xylene, and p-xylene have been measured at different temperatures (298.15, 308.15 and 318.15) K and atmospheric pressure over the whole range of compositions. The excess molar volumes were calculated from the experimental data and correlated by the Redlich−Kister polynomial equation. McAllister’s three-body and four-body interaction models are also used to correlate the kinematic viscosities of these binary mixtures.

Densities and Viscosities of Binary Mixtures of Cyclopropanecarboxylic Acid with Methanol, Ethanol, Propan-1-ol, and Butan-1-ol at Different Temperatures

Densities and viscosities of the binary mixtures of cyclopropanecarboxylic acid with methanol, ethanol, propan-1-ol, and butan-1-ol have been measured at different temperatures (298.15, 308.15, 318.15, 328.15, and 338.15) K and atmospheric pressure over the whole range of compositions. The excess molar volumes were calculated from the experimental data and correlated by the Redlich−Kister polynomial equation. McAllister’s three-body and four-body interaction models are also used to correlate the kinematic viscosities of these binary mixtures.