Dilute gas viscosity of n-alkanes represented by rigid Lennard-Jones chains

ABSTRACT

The shear viscosity in the dilute gas limit has been calculated by means of the classical trajectory method for a gas consisting of chain-like molecules. The molecules were modelled as rigid chains made up of spherical segments that interact through a combination of site–site Lennard-Jones 12-6 potentials. Results are reported for chains consisting of 2, 3, 4, 6, 8, 12 and 16 segments in the reduced temperature range of 0.3–50 for site–site separations of 0.25σ, 0.333σ, 0.40σ, 0.60σ and 0.80σ, where σ is the Lennard-Jones length scaling parameter. The results were used to determine the shear viscosity of n-alkanes in the zero-density limit by representing an n-alkane molecule as a rigid linear chain consisting of n_c ? 1?spherical segments, where n_c?is the number of carbon atoms. We show that for a given n-alkane molecule, the scaling parameters ? and σ are not unique and not transferable from one molecule to another. The commonly used site–site Lennard-Jones 12-6 potential in combination with a rigid-chain molecular representation can only accurately mimic the viscosity if the scaling parameters are fitted. If the scaling parameters are estimated from the scaling parameters of other n-alkanes, the predicted viscosity values have an unacceptably high uncertainty.     

Simulation studies of shear viscosity time correlation functions in liquid CS2

The Green—Kubo time correlation function for the shear viscosity in liquid CS₂ has been simulated by molecular dynamics at several thermodynamic state points. The breakdown of this function into its kinetic and potential contributions as well as the cross-term between the two has been performed. Intermolecular interactions were obtained from a three-centre atom—atom (12/6) Lennard-Jones potential model. The time correlation functions for the potential part of the shear viscosity contain component two-, three- and four-body terms that were explicitly evaluated to show that they partially cancel each other at short times but at long times, they exhibit approximately exponential decays with magnitude ratios corresponding to nearly perfect cancellation. In this respect, the correlation functions for CS₂ resemble those of liquid argon. In addition, the microscopic stress tensor was separated into the portions arising from the repulsive and attractive branches of the Lennard-Jones model. This split gives rise to positive autocorrelation functions involving the repulsive and the attractive forces plus a negative cross-correlation function between the two that partially cancels the contributions of the autocorrelation functions. It is argued that the breakdown of the potential part of the shear viscosity into its component parts is helpful in elucidating the role of molecular re-orientation in determining the separate short and long time behaviours of this time correlation function for liquids such as CS₂.     

Prediction of transport properties of CO2-N2 binary mixtures via the inversion of reduced-viscosity collision integrals

In the present study, the main purpose is to extract information about the effective intermolecular potential energy function for binary mixture of nitrogen and carbon dioxide by the usage of a direct inversion of the experimentally reduced viscosity and second virial coefficient data and then to reproduce the dilute gas transport properties from the inverted potential energy. The Lennard-Jones (12, 6) potential energy function has been employed as the initial potential model required by the inversion method. The MSV potential obtained in this way is in reasonable agreement with the independently known Co₂-N₂ potential energy function. Using the inverted pair potential energies, the Chapman-Enskog scheme is employed to calculate transport properties of CO₂-N₂ in a wide composition and temperature range. The close agreement between the predicted values and the literature results of transport properties demonstrate the predictive power of the inversion scheme.     

Structures and autocorrelation functions of liquid Al and Mg modelled via Lennard-Jones potential from molecular dynamics simulation

The structures and autocorrelation functions of Al and Mg in the liquid state are investigated through the pair distribution functiong(r), the diffusion coefficients as well as the shear viscosity via the Green-Kubo and Einstein relations. From the structure and the Enskog relation we determined the frequency of collisions of atoms in the first shell ofg(r) in the systems. We also discovered that the packing fraction of Lennard-Jones liquids should be approximately half the reduced density value. This approximation is accurate to within 99%. The temperature dependence of the pair distribution function and the atomic mean square displacement are investigated by performing simulations at various experimental temperatures and corresponding densities. The structures of the systems are affected by temperature via movements of atoms in the first minimum ofg(r). The Lennard-Jones model shows that density dependence of the shear viscosity is in agreement with what is expected of simple liquids in the range of investigated temperatures and densities. In the gas limit, the Stoke-Einstein relationDη =K _BT /2πσ is grossly overestimated by Lennard-Jones model. This could not be attributed to deficiencies in the model, as other investigators using first principle method could not obtain the gas limit of the Stoke-Einstein relation.     

Thermodynamic and structural properties of liquids modelled by ‘2-Lennard-Jones centres’ pair potentials

Molecular dynamics calculations have been carried out for model liquid systems of N (=108 or 256) molecules interacting through two Lennard-Jones (12–6) centres coinciding with the positions of the atomic masses (the ‘atom-atom’ pair potential). The objectives were (a) to study the dependence of the properties on the molecular anisotropy defined by the reduced distance l*=l/σ between the centres in the range 0·5–0·8; and (b) to compare the computed quantities with those of real liquids (F₂, Cl₂, Br₂, CO₂). This paper deals with thermodynamic and structural features. Time-dependent correlations will be treated in a future communication.

In the liquid region not too far from the triple point the energy and pressure isochores are well represented by straight lines, the slopes of which increase with density and anisotropy. Thermodynamically consistent expressions for the energy and pressure as functions of density and temperature have been obtained for each system.

With Lennard-Jones parameters adjusted so as to secure the best overall fit, the agreement between experimental and computed thermodynamic properties is very satisfactory for F₂ (l*=0·505), quite good for Cl₂ and Br₂ (l*=0·608–0·63), but rather poor for CO₂ (l*=0·793). The ‘interatomic distances’ are close to the experimental values.

The static structural correlations are discussed in terms of the pair-correlation functions (pcf) g _A(r*) for the separation between ‘atoms’, the first few functions g_ll'm (R*) which arise from the expansion of the g(R*, θ₁, θ₂, φ₁₂) in spherical harmonics, and the pcf's for certain special near-neighbour configurations. The computed atom-atom structure factor is compared with the experimental data for liquid Br₂.

Mean square forces and torques have been evaluated and are related to some experimental results.     

Phase equilibria of confined liquid crystals

The differences between the phase diagram of the Gay-Berne potential confined by two identical walls versus the corresponding bulk phase diagram have been investigated. A wall-fluid interaction 9-3 Lennard-Jones potential was used. The study was performed in most cases by using the hybrid Monte Carlo method for the μVT ensemble. Several isotherms were analysed where vapour, liquid and smectic phases were observed. The smectic-isotropic coexistence region becomes wider, i.e. the isotropic coexistence line is shifted to lower densities but the smectic coexistence line remains nearly the same. The triple point temperature of the confined system is estimated to be in the vicinity of 0.45 versus 0.40 of the bulk system. For the isotherm at T? = 0.65 an orientational dependence was added to the 9-3 Lennard-Jones potential to model the wall-fluid interaction. For both kinds of walls, 9-3 LJ with and without orientational dependence, confinement was not found to stabilize a nematic phase as found by previous authors.     

Rydberg excitations in rare gas clusters: structure and electronic spectra of Ar* n (3 ≤ n ≤ 25)

Likely candidates are located for the global potential energy minima of Ar* _n (3 ≤ n ≤ 25) clusters using the diatomics-in-molecules (DIM) approach. The favoured geometries are found to be different from the structures of Ar⁺ _n and correspond to the trimer Ar*₃ bound to the surface of an Ar _n?2 core via a common atom. The Ar _n?2 core is usually only slightly distorted from its own global potential minimum, although in a few cases it corresponds to a nearby local minimum. Therefore, the ‘magic’ sizes of the excimer systems are predicted to differ from those of the ions and correlate instead with the stability of Ar _n?2. The predicted electronic photoabsorption and emission spectra of Ar* _n , and photoexcitation spectra of Ar _n are discussed in terms of experimental data. Global potential energy minima for neutral Ar _n up to n = 55 with the Aziz potential are summarized also; the structure is the same as for the Lennard-Jones potential except at n = 21 where the stabilities of the two lowest Lennard-Jones minima are reversed.     

Atom-atom potential in rotational line broadening for molecular gases: Application to CO lines broadened by CO,N2, O2 and NO

Linewidths in CO-CO, CO-N₂, CO-C₂ and CO-NO collisions have been calculated using an improved potential for atom-atom interactions in addition to the first-order terms of the electrostatic interaction. The energy parameters characterizing the Lennard-Jones potential have been estimated previously from second virial coefficients. Overall agreement between calculated and experimental linewidths (particularly for CO-O₂ mixtures for which the electrostatic contributions are weak) is thus obtained without any adjustable parameters. It is concluded that the atom-atom potential describes the angular dependence of the short-range forces in molecular collisions fairly adequately.     

Evaluation of Mori theory with a molecular dynamics simulation

A Mori three variable approximation (on the basis of Nee-Zwanzig formalism) is used in an attempt to describe analytically the results of a molecular dynamics simulation of 108 triatomic molecules ofC _2v symmetry interacting via a three centre Lennard-Jones atomatom potential. The simulation results expose the limitations of the analytical theory in that the latter is able to describe only the general features of the simulation.     

Calculated line broadening coefficients in the ν2 band of CH3D perturbed by helium

Line broadening coefficients have been calculated, at room temperature, for lines in the P and R branches of the ν₂ band of monodeuterated methane. A properly symmetrized semiclassical model with parabolic relative trajectories has been used. Two interaction potential models have been considered. The first is a Lennard-Jones type atom-atom potential, while the second one was derived from ab initio calculations. The calculated line widths were compared to the available experimental data and a satisfactory agreement was found, although the model contains no other adjustable parameters than the four atomic Lennard-Jones ones. Nonetheless, failures of calculations have also been evidenced for the highest rotational quantum numbers.     

Correlation of fragility with mechanical moduli in double-well potential for glass-forming liquid

The shoving model and the Vogel-Fulcher relation are employed to derive correlation of the fragility with the mechanical moduli for glass-forming simple liquids. The result shows that a liquid with smaller fragility will have larger ratio of K_∞/G_∞ in dilute liquid system. Based on radial distribution function with the Lennard-Jones potential modified by the Gaussian potential with a second minimum, fragility of the supercooled simple liquid is derived from the correlation between viscosity and shear modulus via configurational entropy. The results demonstrate that the fragility is determined by two parts: thermodynamic components and mechanical moduli. For a weak Gaussian potential liquid, the fragility is proportional to the T_g, while for a strong one, the fragility is inversely proportional to the T_g, and the Gaussian potential will increase fragility.     

On the limitations of the equation of state based on the Lennard-Jones potential

It is emphasized that any equation of state (EOS) based on the generalized Lennard-Jones potential or the Mie potential, suffers from two main shortcomings as pointed out by Stacey and Davis [2]. One of the shortcomings viz. the problem related to imaginary numbers for the exponents in the potential function, has been removed recently by Jiuxun [11] by using a relationship between the exponents. However, the modified EOS obtained by Jiuxun suffers from the second shortcoming viz. it gives lower values for −B ₀ B″₀, an important equation of state parameter related to the second pressure derivative of the bulk modulus. Values of B ₀ B″₀ obtained by Jiuxun are not consistent with those reported by Stacey and Davis.      

The Kirkwood-Salsburg integral equation and the virial coefficients of Lennard-Jones molecules

The fifth virial coefficients E_c and E_p are derived for a classical fluid composed of molecules interacting according to the Lennard-Jones potential. The calculations are based on the Kirkwood-Salsburg integral equation and the superposition approximation. It is found that, unlike the systems considered in a previous communication, satisfactory agreement between the present results and the known values is possible only at high temperatures.     

Enhancedt −3/2 long-time tail for the stress-stress time correlation function

Nonequilibrium molecular dynamics is used to calculate the spectrum of shear viscosity for a Lennard-Jones fluid. The calculated zero-frequency shear viscosity agrees well with experimental argon results for the two state points considered. The low-frequency behavior of shear viscosity is dominated by an ^1/2 cusp. Analysis of the form of this cusp reveals that the stress-stress time correlation function exhibits at ^–3/2 long-time tail. It is shown that for the state points studied, the amplitude of this long-time tail is between 12 and 150 times larger than what has been predicted theoretically. If the low-frequency results are truly asymptotic, they imply that the cross and potential contributions to the Kubo-Green integrand for shear viscosity exhibit at ^–3/2 long-time tail. This result contradicts the established theory of such processes.     

Thermodynamic description of the viscosity of liquid solder alloys with minor Co impurities

Because of the increasing complexity and cost of experiments carried out, the data for the multi-component alloy systems have frequently been obtained by numerical modelling. It is clear that the related calculations require reliable data dealing with the pure components and binary alloy systems. Selecting the reliable data concerning the pure components from the literature, the viscosities for the SAC and (SAC)_1?x Co_x solder alloys have been calculated using different viscosity models (geometric and physical). The viscosity decreases as the amount of tin content increases in the SAC387 alloy while the addition of the cobalt to SAC387 solder results in the increasing of the viscosity. Moreover, by computing the root mean square values between theoretical and experimental viscosities, it can be concluded that the lowest value among all models is that of obtained by Kaptay equation.     

Deriving analytical expressions for the state dependencies of the effective pair potential parameters using VIM theory

In this work, based on the variational inequality minimizing (VIM) theory of statistical thermodynamics and using the (6,12) Lennard-Jones potential function as an effective pair potential (EPP), analytical expressions for the temperature and density dependencies of the EPP parameters have been obtained. The resulting equation of state can predict thermodynamic properties such as internal energy and Helmholtz free energy for simple dense fluids such as Ar, CO, N₂, and CH₄ with differences less than 5%.     

The thermodynamics of symmetric two centre Lennard-Jones liquids

We have carried out molecular dynamic simulations for the thermodynamic properties of two centre Lennard-Jones fluids at lower densities and higher temperatures than have been studied previously, and have also made simulations for one additional shape. The results, together with results already given in the literature, are presented in a parameterized form which is very convenient to use in testing the simulation results against data for real liquids. Tables of second virial coefficients are also provided. We illustrate the use of our results by an analysis of pure liquid ethane, which is found to be well represented by such a model with L* = 0·67, ε/k = 137·5 K and σ = 3·506 Å. We also suggest that the experimental thermodynamic properties of suitable liquid mixtures can, with the aid of a theory for the equivalent pure liquid parameters (L _x *, ε _x , σ _x ), be satisfactorily interpreted using the general results given in this paper.     

Kinetic theory of dense fluids. IV. Entropy balance equation and irreversible thermodynamics

The viscosity coefficient obtained in a previous paper of this series is calculated as a function of density by developing the N-particle collision operator into a dynamic cluster expansion. The excess transport coefficient Δη is given in an exponential form, where η₀ is the two-body Chapman-Enskog result for the transport coefficient, n is the density, and β_l is a density-independent quantity consisting of connected cluster contributions of (l + 2) particles. Therefore, the leading term β₁ consists of connected three-body cluster contributions. The excess shear viscosity coefficient is calculated for a monatomic hard-sphere fluid by computing β_l up to the three-body contributions and the result is compared with the molecular dynamics result by Ashurst and Hoover and also with the experimental data on Ar at 75°C. In spite of the crudity of the potential model used and the approximations made the agreement is good. The result can be improved if l-body clusters (l 4) are included in the calculation. The thermal conductivity coefficient can be obtained in a similar form by using exactly the same procedure used for the viscosity coefficient.     

Coefficients of viscosity of a gaseous plasma

We present here an order of magnitude calculation for the coefficients of viscosity with the assumption that the drift velocity introduces asymmetry both in the single-particle distribution functionf ₁ and the correlation functionP(1, 2). These asymmetric parts have been estimated considering the self-relaxation of the system when the cause of drift velocity is suddenly removed. Using these, the kinetic part of the coefficient of electron viscosity has been calculated and the result fairly agrees with similar studies by others. The potential part of shear viscosity coefficient is found to be zero while both parts of the coefficient of bulk viscosity are non-zero.     

The pair polarizability anisotropy of SF6 in the point-atom-polarizability approximation

The depolarized light scattering intensity and second Kerr virial coefficient for SF₆ are two to three times the values calculated with the dipole-induced-dipole model for the pair polarizability anisotropy and a Lennard-Jones pair potential. Contrary to earlier suggestions, this discrepancy is not attributable to the distribution of polarizable matter within an SF₆ molecule, at least within the point-atom-polarizability approximation. However, the calculated thermal average of the square of the polarizability anisotropy for SF₆ can be doubled by replacing the Lennard-Jones potential with a modified Lennard-Jones potential.