Diatomic Liquids Research Articles

Bridgman formula for the thermal conductivity of atomic and molecular liquids

A simple and popular Bridgman’s model predicts a linear correlation between the thermal conductivity coefficient and the sound velocity of dense liquids. A proportionality coefficient proposed originally is fixed and independent of the liquid molecular structure. This work reports a systematic analysis of correlations between thermal conductivity and sound velocity in simple model systems (hard sphere and Lennard-Jones fluids), monoatomic liquids (argon and krypton), diatomic liquids (nitrogen and oxygen), and several polyatomic liquids (water, carbon dioxide, methane, and ethane). It is demonstrated that linear correlations are well reproduced for model fluids as well as real monoatomic and diatomic liquids, but seem less convincing in polyatomic molecular liquids. The coefficient of proportionality is not fixed; it is about unity for monoatomic liquids and generally increases with molecular complexity. Some implications for the possibility to predict the thermal conductivity coefficients are discussed.

Renormalized site density functional theory

Site density functional theory (SDFT) provides a rigorous framework for statistical mechanics analysis of inhomogeneous molecular liquids. The key defining feature of these systems is the presence of two very distinct interactions scales (intra- and inter-molecular), and as such proper description of both effects is critical to the accuracy of the calculations. Current SDFT applications utilize the same approximation scheme for both interaction motifs, which negatively impacts the results. Dual space methodology, used in this work, alleviates this issue by providing the flexibility of evaluating part of the interactions in traditional field representation. For molecular liquid this translates into retaining density representation for inter-molecular interactions but describing stiff intra-molecular remainder by more appropriate conventional field based methods. This opens the way to decouple analysis of the two interactions scales—the idea which is developed further in this work for the case of homogeneous reference approximation of inter-molecular interactions. We demonstrate that by defining new collective variables, the behaviour of the original molecular liquid system at the inter-molecular level can be transformed to resemble that of an effective simple fluid mixture. The latter is linked to intra-molecular scale through renormalized interaction parameters. We illustrate this renormalization procedure for several types of diatomic liquids, showing that this approach cures many of the shortcomings of existing SDFT methods.

Introducing thermal effects in the rotational energy of diatomic molecules

At relatively high temperatures, the state-of-the-art of the diatomic liquid phononic theory applied to supercritical fluids shows that there exists discrepancies between the theoretical predictions and the experimental data. To overcome this difference, a new formulation of the rotational energy of single molecules that considers the thermal effect upon their moment of inertia, is presented. For a wide range of reduced temperatures and pressures, the predicted values are in very good agreement with CO, O2 and N2 molecular data. It is possible to reduce these discrepancies by a factor of 2 up to around 70 times for some cases. This is essentially because the proposed model improves the rotational energy of the molecule. It implicitly satisfies both the Dulong-Petit law for ideal gases as well as the Frenkel’s line thermodynamic limit.

Molecular size and shape effects: Rotational diffusion and the Stokes-Einstein-Debye relation

Formulation of rotational diffusion coefficient and the Stokes-Einstein-Debye (SED) relation is presented for diatomic molecular liquids by molecular dynamics simulation with two-center Lennard-Jones (2CLJ) potentials. Shear viscosity ηsv and rotational diffusion coefficient Dr are expressed as a function of molecular mass and number density N/V, or moment of inertia, packing fraction, temperature T, interaction energy, and molecular elongation l∗ ≡ l/σ, where N is the number of molecules included in the system volume V, l the bond length in the diatomic molecules, and σ the size parameter used in the LJ potentials. The packing fraction and elongation are the variables expressing molecular size and shape, respectively. These results produce directly a molecular-basis SED relation as Drηsv/T ∝ vm∗1/3l∗−3(N/V), where vm∗ is the dimensionless molecular volume expressed as an analytical function only of elongation l∗. That is, this SED equation depends not on the size but on the shape. This is highly contrasted with the original SED relation based on the size, which suggests overall reconsideration of the relation on a molecular scale. The shape term accounts for a paradox that more spherical molecules such as N2 deviate more strongly from the original SED equation based on a spherical particle. In addition, the SED relation without the size is consistent with the Stokes-Einstein relation for both the Lennard-Jones and 2CLJ liquids expressed as Dηsv/T ∝ (N/V)1/3, where D is the translational self-diffusion coefficient.

Chemical bond effects in classical site density functional theory of inhomogeneous molecular liquids.

Intra-molecular interactions or chemical bonds represent one of the main distinguishing characteristics of molecular fluids. Development of accurate and practical methods to treat these effects is one of the long standing problems in classical site density functional theory (SDFT). One particular instance when these issues become particularly severe is the case of classical interaction potentials with auxiliary sites or dummy atoms. In this situation, current SDFT implementations, such as the three-dimensional reference interaction site model, lead to nonphysical results. We re-examine this issue in this work using our recent reformulation of SDFT (Valiev and Chuev, J. Stat. Mech.: Theory Exp. 2018, 093201). We put forward a simple practical solution to this problem and illustrate its utility for the case of spherical solutes in diatomic liquids.

A theory of diffusion controlled reactions in polyatomic molecule system.

The conventional Smoluchowski equation has been extensively utilized to investigate diffusion controlled reactions. However, application of the equation is limited to spherical-particle system. In the present study, a new Smoluchowski equation for polyatomic molecular system is derived based on Zwanzig-Mori projection operator method and reference interaction site model (RISM) theory. The theory is applied to monoatomic molecular liquid, and the obtained time-dependent rate constant is virtually identical with that from conventional Smoluchowski equation. For diatomic molecular liquid, time-dependent distribution function and rate constant are obtained, showing a good agreement with those from molecular dynamics simulation.

Enhanced diffusion in finite-size simulations of a fragile diatomic glass former.

Using molecular dynamics simulations we investigate the finite-size dependence of the dynamical properties of a diatomic supercooled liquid. The simplicity of the molecule permits us to access the microsecond time scale. We find that the relaxation time decreases simultaneously with the strength of cooperative motions when the size of the system decreases. While the decrease of the cooperative motions is in agreement with previous studies, the decrease of the relaxation time opposes what has been reported to date in monatomic glass formers and in silica. This result suggests the presence of different competing physical mechanisms in the relaxation process. For very small box sizes the relaxation times behavior reverses itself and increases strongly when the box size decreases, thus leading to a nonmonotonic behavior. This result is in qualitative agreement with defect and facilitation theories.

Observable-dependence of the effective temperature in off-equilibrium diatomic molecular liquids.

We discuss the observable-dependence of the effective temperature Teff, defined via the fluctuation-dissipation relation, of an out-of-equilibrium system composed by homonuclear dumbbell molecules. Teff is calculated by evaluating the fluctuation and the response for two observables associated, respectively, to translational and to rotational degrees of freedom, following a sudden temperature quench. We repeat our calculations for different dumbbell elongations ζ. At high elongations (ζ > 0.4), we find the same Teff for the two observables. At low elongations (ζ ⩽ 0.4), only for very deep quenches Teff coincides. The observable-dependence of Teff for low elongations and shallow quenches stresses the importance of a strong coupling between orientational and translational variables for a consistent definition of the effective temperature in glassy systems.

Vibrational Energy Relaxation Rates via the Linearized Semiclassical Method without Force Derivatives

A new computational scheme for calculating vibrational energy relaxation rate constants is presented that is based on applying the linearized semiclassical approximation to the symmetrized force-force correlation function. Unlike the previous scheme of Geva and Shi [Shi, Q.; Geva, E. J. Phys. Chem A 2003, 107, 9059], which was based on applying the linearized semiclassical approximation to the standard force-force correlation function, the new scheme does not involve a power expansion of the initial force in terms of the Wigner transform integration variable Delta and as a result is more accurate and does not require force derivatives as input. The main disadvantages of the new scheme are its slower convergence rate in comparison to the Shi-Geva scheme and its ambiguity with respect to the choice of configuration around which the local harmonic approximation is performed. The computational feasibility and accuracy of the new approach is demonstrated on a number of benchmark models, including the highly challenging case of nonpolar diatomic liquids. It is observed that performing the local harmonic approximation around the configuration used for computing the initial force yields the best agreement with experiment.

Thermal conductivity of diatomic liquid in a narrow channel including a nanobubble

The thermal conductivity of a diatomic liquid in a narrow channel including a nanobubble is analyzed using a nonequilibrium molecular dynamics method. Oxygen is assumed as the liquid and the two-center Lennard-Jones model is used to express the intermolecular potential acting on liquid molecules. Heat conduction of the liquid at various states (single phase, two-phase including a nanobubble and separated two-phase) at T = 0.7 T cr is simulated and the thermal conductivity is estimated, where T is temperature and T cr is the critical temperature. These values are shown to be consistent with experimental data within 10% accuracy. The thermal conductivity decreases with the decrease in the pressure in a single phase, whereas they are almost independent of the bubble size in two-phase including a nanobubble. Detailed analysis of the molecular contribution to the thermal conductivity reveals that the contribution of the heat flux caused by translational energy transfer to the thermal conductivity is dominant and the heat flux passing through the liquid phase increases with the decrease in the effective cross-section of liquid.

Vibrational Energy Relaxation Rates via the Linearized Semiclassical Approximation: Applications to Neat Diatomic Liquids and Atomic−Diatomic Liquid Mixtures

We report the results obtained from the application of our previously proposed linearized semiclassical method for computing vibrational energy relaxation (VER) rates (J. Phys. Chem. A 2003, 107, 9059, 9070) to neat liquid oxygen, neat liquid nitrogen, and liquid mixtures of oxygen and argon. Our calculations are based on a semiclassical approximation for the quantum-mechanical force-force correlation function, which puts it in terms of the Wigner transforms of the force and the product of the Boltzmann operator and the force. The calculation of the multidimensional Wigner integrals is made feasible by the introduction of a local harmonic approximation. A systematic analysis has been performed of the temperature and mole-fraction dependences of the VER rate constant, as well as the relative contributions of centrifugal and potential forces, and of different types of quantum effects. The results were found to be in very good quantitative agreement with experiment, and they suggest that this semiclassical approximation can capture the quantum enhancement, by many orders of magnitude, of the experimentally observed VER rate constants over the corresponding classical predictions.

Molecular dynamics study for the thermal conductivity of diatomic liquid

The thermal conductivity of diatomic liquids was analyzed using a nonequilibrium molecular dynamics (NEMD) method. Five liquids, namely, O 2 , CO, CS 2 , Cl 2 and Br 2 , were assumed. The two-center Lennard-Jones (2CLJ) model was used to express the intermolecular potential acting on liquid molecules. First, the equation of state of each liquid was obtained using MD simulation, and the critical temperature, density and pressure of each liquid were determined. Heat conduction of each liquid at various liquid states [metastable ( ρ =1.9 ρ cr ), saturated ( ρ =2.1 ρ cr ), and stable ( ρ =2.3 ρ cr )] at T =0.7 T cr was simulated and the thermal conductivity was estimated. These values were compared with experimental results and it was confirmed that the simulated results were consistent with the experimental data within 10%. Obtained thermal conductivities at saturated state were reduced by the critical temperature, density and mass of molecules and these values were compared with each other. It was found that the reduced thermal conductivity increased with the increase in the molecular elongation. Detailed analysis of the molecular contribution to the thermal conductivity revealed that the contribution of the heat flux caused by energy transport and by translational energy transfer to the thermal conductivity is independent of the molecular elongation while the contribution of the heat flux caused by rotational energy transfer to the thermal conductivity increases with the increase in the molecular elongation. Moreover, by comparing the reduced thermal conductivity at various states, it was found that the increase of thermal conductivity with the increase in the density, or pressure, was caused by the increase of the contribution of energy transfer due to molecular interaction .

Simulation of a Diatomic Liquid Using Hard Spheres Model

In this work we demonstrate the possibility of including constraints in hard systems, using the simple case of a dimer of hard spheres, where the analytical solution exists. We make a detailed description of the model and show that the system's dynamics can be solved in a rigorous way. We also illustrate our theoretical results with some numerical calculations on a simple diatomic liquid.

Molecular dynamics study for the thermal conductivity of diatomic liquid

The thermal conductivity of diatomic liquids was analyzed using a nonequilibrium molecular dynamics (NEMD) method. Five liquids, namely, O 2, CO, CS 2, Cl 2 and Br 2, were assumed. The two-center Lennard-Jones (2CLJ) model was used to express the intermolecular potential acting on liquid molecules. First, the equation of state of each liquid was obtained using MD simulation, and the critical temperature, density and pressure of each liquid were determined. Heat conduction of each liquid at various liquid states [metastable ( ρ=1.9 ρ cr), saturated ( ρ=2.1 ρ cr), and stable ( ρ=2.3 ρ cr)] at T=0.7 T cr was simulated and the thermal conductivity was estimated. These values were compared with experimental results and it was confirmed that the simulated results were consistent with the experimental data within 10%. Obtained thermal conductivities at saturated state were reduced by the critical temperature, density and mass of molecules and these values were compared with each other. It was found that the reduced thermal conductivity increased with the increase in the molecular elongation. Detailed analysis of the molecular contribution to the thermal conductivity revealed that the contribution of the heat flux caused by energy transport and by translational energy transfer to the thermal conductivity is independent of the molecular elongation while the contribution of the heat flux caused by rotational energy transfer to the thermal conductivity increases with the increase in the molecular elongation. Moreover, by comparing the reduced thermal conductivity at various states, it was found that the increase of thermal conductivity with the increase in the density, or pressure, was caused by the increase of the contribution of energy transfer due to molecular interaction.

METALLIZATION AND DISSOCIATION OF FLUID HYDROGEN AND OTHER DIATOMICS AT 100 GPa PRESSURES

Dynamic compression of diatomic liquids using both single-shock (Hugoniot) and multiple-shock (reverberating-shock) compression achieves pressures which range up to a few 100 GPa (Mbar), densities as high as tenfold of initial liquid density in hydrogen, and temperatures up to several 1000 K. Single-shock compression produces substantial heating, which causes a limiting compression. Multiple-shock compression is quasi-isentropic, which achieves lower temperatures and higher densities than single shocks, and has no limiting compression. Diatomic fluids have universal behaviors under dynamic compression. Under multiple-shock compression, these fluids undergo density-driven nonmetal-metal Mott transitions, probably in the monatomic state, with common density scaling at ∼100 GPa. Under single-shock compression, these fluids have essentially the same Hugoniot in velocity space. D2 undergoes temperature-driven dissociation to a poor metal at ∼50 GPa. These results provide insight into which of the two published D2 Hugoniots is probably correct.

Theoretical study of the molecular motion of liquid water under high pressure

The pressure effects on the molecular dynamics of liquid water are investigated using the site–site generalized Langevin modified mode-coupling theory. The calculations are performed for temperatures from 273 to 373 K and densities from 0.9 to 1.2 g/cm3. The static structure factor required as input is obtained from the reference interaction-site model hypernetted chain integral equation. The shear viscosity, the dielectric relaxation time, the translational diffusion coefficient, and the first-rank reorientational relaxation times are evaluated. All these quantities show unusual pressure dependence in the low-density, low-temperature region in that the molecular mobility is enhanced by applying the pressure. The magnitude of the enhancement is larger on the reorientational motions than on the translational ones. These tendencies are consistent with experimental observations, although the quantitative agreement is not so good. An analysis of the theory indicates that the decrease in the dielectric friction on the collective polarization at small wave numbers upon increasing pressure is the principal reason for the pressure-induced enhancement of the dielectric relaxation and the decrease in the dielectric relaxation time affects other motions. The decrease in the dielectric friction is caused by the decrease in the number-density fluctuation around the low-wave-number edge of the first peak of the structure factor by compression. The comparison between the results for water and acetonitrile extracts two characteristic features of water that are important for the anomalous pressure effect on its molecular motion. The first one is the small collisional friction on the reorientation due to the spherical repulsive core, and the second one is the strong short-range Coulombic interaction caused by the formation of the hydrogen bonding. A theoretical calculation on a model diatomic liquid consisting of oxygen and hydrogen atoms proposes that the above two characteristic properties of water are sufficient for the emergence of the anomalous pressure dependence. This conclusion is also supported by the molecular dynamics simulation performed on the same model diatomic liquid.

Effect of molecular elongation on the thermal conductivity of diatomic liquids

The effect of molecular elongation on the thermal conductivity of diatomic liquids has been analyzed using a nonequilibrium molecular dynamics (NEMD) method. The two-center Lennard-Jones model was used to express the intermolecular potential acting on liquid molecules. The simulations were performed using the nondimensional form of the potential so that the molecular elongation, d/σ, was the only parameter varied in the simulation. The simulations were performed for five values of this parameter. First, the equation of state of each liquid was obtained using equilibrium molecular dynamics simulation, and the critical temperature, density, and pressure of each liquid were determined. Then, NEMD simulations of heat conduction in the five liquids were performed using values for temperature and density which were identical among the five liquids when they were reduced by their respective critical temperature and density (T=0.7 Tcr and ρ=2.24 ρcr). Obtained thermal conductivities were reduced by the critical temperature, density, and molecular mass of each compound, and these values were compared with each other. It was found that the reduced thermal conductivity increased as molecular elongation increased. Detailed analysis of the molecular contribution to the thermal conductivity revealed that (a) the contribution of the heat flux caused by energy transport and by translational energy transfer to the thermal conductivity is independent of the molecular elongation, and (b) the contribution of the heat flux caused by rotational energy transfer to the thermal conductivity increases with the increase in the molecular elongation.

Slow Relaxations in the Supercooled State of a Model Diatomic Molecular Liquid

We report results of molecular dynamics simulation for the supercooled state of a model diatomic molecular liquid possessing a rotational degree of freedom. We develop a new technique to extract th...

Investigation of Thermal Conductivity of Diatomic Liquid by Molecular Dynamics Method

In this paper the effect of molecular structure on thermal conductivity of diatomic liquid is analyzed by the Molecular Dynamics (MD) Method. Five liquids such as O2, CO, CS2, Cl2 and Br2 are assumed and 2 center Lennard-Jones (2 CLJ) potential is used for these molecules. First, simulations are performed at various combinations of density and temperature and Equation of State (EOS) of each liquid is obtained by using these results. Using the equations critical temperature and density of each liquid is obtained. Thermal conductivities of these liquids at the corresponding state based on each critical temperature and density (T=0.7Tcr and ρ=2.24ρcr) are simulated and the results are compared with experimental results. Moreover, these results are reduced based on m, ρcr and Tcr and compared with each other. The reduced thermal conductivity increases as the elongation of molecule increases.

The hydrogen liquids

When average one-particle densities are spatially uniform at a microscopic level the state is considered to be a homogeneous liquid. A prescription is required for the basic dynamical elements involved in the averaging itself, and for hydrogen, at low densities and temperatures, these are the familiar hydrogen molecules. But, at compressions now achievable both by static and dynamic means, a more basic description in terms of protons and electrons incorporating residual pairing correlations is necessary. The latter are dependent in large part on the nature of effective state-dependent pair interactions between protons, and in a narrow band of densities near rs = 1.33, these may be especially weak. The hydrogen liquids refers to the (quantum) diatomic liquid, the high density monatomic liquid, and the variably correlated transition phases between the two.