Simple Liquid Model Research Articles

A general heat capacity model of simple liquids using phonon theory

To develop a general theoretical model of heat capacity is a long-term goal for liquid thermophysical property studies. However, previously reported models cannot meet this requirement due to their dependence on free fitting parameters, leading to an ambiguous interpretation of liquid heat capacity. In view of this problem, a general heat capacity model for simple liquids was proposed, without free fitting parameters. The present model was established based on the solid phonon theory (quasi-harmonic Debye model), with some modifications made for considering the distinction between liquids and solids, to calculate the liquid heat capacity. The proposed model was applied to seven simple liquids (Ar, Na, Ne, N2, CH4, CHF3, CH2F2). The calculation was performed in the temperature range between 50 and 810 K and pressures from 0.1 to 800 MPa. The results show that the calculated data are in good agreement with the corresponding literature values, yielding an average absolute deviation (AAD) of 2.07%. Moreover, compared with previous liquid phonon theory model, the present model can be employed without thermal expansion coefficients. In addition, the effect of temperature and pressure on heat capacity was explained using the liquid relaxation time τ on the basis of the present model. This work provides guidance for the measurement and modeling of liquid heat capacity.

Self-consistent construction of bridge functional based on the weighted density approximation.

A parameter-free bridge functional is presented using a weighted density approximation (WDA). The key point of this scheme is the utilization of Baxter's relation connecting the second-order direct correlation function (DCF) to the higher-order DCF with the density derivative. The free energy density required for the WDA is determined in a self-consistent manner using Baxter's relation and Percus's test particle method. This self-consistent scheme enables us to employ any type of potential model for simple liquids. The new functional is applied to calculate density distribution functions for the inhomogeneous fluids interacting via the hard-sphere, Lennard-Jones, and hard-core Yukawa potentials under an external field from a planar wall and a slit pore.

Three-gradient regular solution model for simple liquids wetting complex surface topologies.

We use regular solution theory and implement a three-gradient model for a liquid/vapour system in contact with a complex surface topology to study the shape of a liquid drop in advancing and receding wetting scenarios. More specifically, we study droplets on an inverse opal: spherical cavities in a hexagonal pattern. In line with experimental data, we find that the surface may switch from hydrophilic (contact angle on a smooth surface θY < 90°) to hydrophobic (effective advancing contact angle θ > 90°). Both the Wenzel wetting state, that is cavities under the liquid are filled, as well as the Cassie–Baxter wetting state, that is air entrapment in the cavities under the liquid, were observed using our approach, without a discontinuity in the water front shape or in the water advancing contact angle θ. Therefore, air entrapment cannot be the main reason why the contact angle θ for an advancing water front varies. Rather, the contact line is pinned and curved due to the surface structures, inducing curvature perpendicular to the plane in which the contact angle θ is observed, and the contact line does not move in a continuous way, but via depinning transitions. The pinning is not limited to kinks in the surface with angles θkink smaller than the angle θY. Even for θkink > θY, contact line pinning is found. Therefore, the full 3D-structure of the inverse opal, rather than a simple parameter such as the wetting state or θkink, determines the final observed contact angle.

Communication: relative diffusion in two dimensions: breakdown of the standard diffusive model for simple liquids.

Using molecular dynamics simulations for a liquid of identical soft spheres we analyze the relative diffusion constant DΣn(r) and the self diffusion constant Dn where r is the interparticle distance and n = 2, 3 denotes the dimensionality. We demonstrate that for the periodic boundary conditions, Dn is a function of the system size and the relation: DΣn(r = L/2) ≅ 2Dn(L), where L is the length of the cubic box edge, holds both for n = 2 and 3. For n = 2 both DΣ2(r) and D2(L) increase logarithmically with its argument. However, it was found that the diffusive process for large two dimensional systems is very sensitive to perturbations. The sensitivity increases with L and even a very low perturbation limits the increase of D2(L → ∞). Nevertheless, due to the functional form of DΣ2(r) the standard assumption for the Smoluchowski type models of reaction kinetics at three dimensions:DΣn(r) ≈ 2Dn leads to giant errors if applied for n = 2.

Liquid phase dynamics of molten M2S2O7 (M = K, Cs): A temperature dependent Raman spectroscopic study

The dynamics of M2S2O7 (M=K, Cs) pyrosulfate salts in the liquid state is investigated by steady-state Raman spectroscopic experiments performed at temperatures up to 600°C. The symmetric stretching modes of the S2O72− ions have been used as probes of the dynamics of these melts. Contrary to the most previous picosecond dynamics studies performed by means of Raman line profile analysis, we have employed in this work an approach that enables the extraction of valuable information concerning short-time dynamics by calculating time correlation functions of vibrational relaxation by fits in the frequency domain. The fitting method used enables the modeling of the real line profiles in a manner that is intermediate between Lorentzian and Gaussian by means of a function, which has an analytical counterpart in the time domain. The vibrational time correlation functions for both molten salts studied are rather adequately interpreted within the assumption of exponential modulation function concerning the environmental modulation in the context of Kubo–Rothschild approach and indicate that the system experiences an intermediate dynamical regime that gets only slower with increasing temperature. Continuous temperature dependence of the dephasing parameters is observed, while the temperature dependence of the dispersion parameter α indicates deviation from the simple liquid model and offers a complete picture of the way a complex liquid attains the condition of a simple one. The evolution of the dispersion parameter is indicative of the reduction of the coherence decay in the perturbation potential as a consequence of local short-lived aggregates. The experimental results are discussed in terms of theoretical models providing insight in the intermolecular coupling mechanisms.

Local structural motifs and extended-range order in liquid and solid ammonia under pressure

Neutron-diffraction measurements of the local structure in deuterated ammonia have been conducted up to pressures of 2.1 GPa at ambient temperature. Total pair-distribution functions, determined by Fourier analysis of the static structure factor, are used to examine the structural changes from the first neighbors to extended ranges of $\ensuremath{\sim}$30 $\AA{}$ in both the liquid and solid state. In the proton-disordered crystalline phase III, the first coordination shell is almost identical to that of the higher-pressure, ordered phase IV. The H-bond correlation is observed as a distinct shoulder at 2.5 $\AA{}$. A similar local structure is seen in the liquid at a pressure just below freezing, and, in particular, a pronounced H-bond correlation is observed in the liquid across the pressure range studied. A substantial increase in the ordering length scale of the liquid is observed at high pressure with correlations extending to at least 25 $\AA{}$ compared to $\ensuremath{\sim}$12 $\AA{}$ at ambient. The decay of the primary oscillations in the extended range is exponential and well described by a simple-liquid model, implying that, despite persistent H bonding, packing considerations become the dominant structural driver as density increases.

Simple Liquid Models with Corrected Dielectric Constants

Molecular simulations often use explicit-solvent models. Sometimes explicit-solvent models can give inaccurate values for basic liquid properties, such as the density, heat capacity, and permittivity, as well as inaccurate values for molecular transfer free energies. Such errors have motivated the development of more complex solvents, such as polarizable models. We describe an alternative here. We give new fixed-charge models of solvents for molecular simulations--water, carbon tetrachloride, chloroform, and dichloromethane. Normally, such solvent models are parametrized to agree with experimental values of the neat liquid density and enthalpy of vaporization. Here, in addition to those properties, our parameters are chosen to give the correct dielectric constant. We find that these new parametrizations also happen to give better values for other properties, such as the self-diffusion coefficient. We believe that parametrizing fixed-charge solvent models to fit experimental dielectric constants may provide better and more efficient ways to treat solvents in computer simulations.

Local anisotropy of fluids using Minkowski tensors

Statistics of the free volume available to individual particles have previously beenstudied for simple and complex fluids, granular matter, amorphous solids, andstructural glasses. Minkowski tensors provide a set of shape measures that arebased on strong mathematical theorems and easily computed for polygonal andpolyhedral bodies such as free volume cells (Voronoi cells). They characterize the localstructure beyond the two-point correlation function and are suitable to define indices0 ≤ βνa, b ≤ 1 of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurationsof simple liquid models, including the ideal gas (Poisson point process), the hard disks andhard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowskitensors provide a robust characterization of local anisotropy, which ranges fromβνa, b≈0.3 for vapor phases to for ordered solids. We find that for fluids, local anisotropy decreases monotonically with increasingfree volume and randomness of particle positions. Furthermore, the local anisotropy indicesβνa, b are sensitive to structural transitions in these simple fluids, as has been previously shown ingranular systems for the transition from loose to jammed bead packs.

Cooling rate dependence of the glass transition at free surfaces

In situ x-ray reflectivity measurements are used to determine the cooling rate dependent freezing of capillary waves on the oligomer poly(propylene glycol). Only above the glass transition temperature ${T}_{\mathrm{G}}$ can the surface roughness $\ensuremath{\sigma}$ be described by the capillary wave model for simple liquids, whereas the surface fluctuations are frozen-in at temperatures below ${T}_{\mathrm{G}}$. As the state of a glass forming liquid strongly depends on its thermal history, this effect occurs for fast cooling rates already at a higher temperature than for slow cooling. For the fastest cooling rates a very large shift of ${T}_{\mathrm{G}}$ up to $240\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ compared to the bulk value of $196\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ was observed.

Effect of Temperature and Pressure on Surface Tension of Polystyrene in Supercritical Carbon Dioxide

The surface tension of polymers in a supercritical fluid is one of the most important physicochemical parameters in many engineering processes, such as microcellular foaming where the surface tension between a polymer melt and a fluid is a principal factor in determining cell nucleation and growth. This paper presents experimental results of the surface tension of polystyrene in supercritical carbon dioxide, together with theoretical calculations for a corresponding system. The surface tension is determined by Axisymmetric Drop Shape Analysis-Profile (ADSA-P), where a high pressure and temperature cell is designed and constructed to facilitate the formation of a pendent drop of polystyrene melt. Self-consistent field theory (SCFT) calculations are applied to simulate the surface tension of a corresponding system, and good qualitative agreement with experiment is obtained. The physical mechanisms for three main experimental trends are explained by using SCFT, and none of the explanations quantitatively depend on the configurational entropy of the polymer constituents. These calculations therefore rationalize the use of simple liquid models for the quantitative prediction of surface tensions of polymers. As pressure and temperature increase, the surface tension of polystyrene decreases. A linear relationship is found between surface tension and temperature, and between surface tension and pressure; the slope of surface tension change with temperature is dependent on pressure.

Monte Carlo intrinsic surfaces and density profiles for liquid surfaces

Operational definitions for the intrinsic surface to be used in computer simulations of liquid surfaces are discussed and tested along with Monte Carlo simulations of simple liquid models. The results are contrasted with the theoretical framework of the capillary wave theory (CWT), and with the strongly structured intrinsic profiles used in the interpretation of x-ray reflectivity experiments for cold liquid metals. The definition of a minimal area intrinsic surface pinned to a set of pivot atoms at the surface leads to intrinsic density profiles with the sharpest atomic resolution, but which are beyond the assumption of the CWT, with strong correlations between the intrinsic profiles and the fluctuations of the intrinsic surface and with an effective wave-vector-dependent surface tension.

Correlated Surfaces of Free-Standing Polystyrene Thin Films

We have performed X-ray specular and off-specular measurements of free-standing polystyrene thin films as a function of molecular weight and thickness. The results show films thicker than a few radii of gyration (Rg) are well fit by a simple liquid model. This confirms the assumption that the anomalies previously reported in the scattering intensity from polymer films of comparable thickness were mostly due to confinement by long-ranged interactions with the substrate rather than a fundamental property of viscoelastic fluids. The simple liquid model was found to be insufficient to fit the transverse diffuse data for films thinner than a few Rg. Longitudinal diffuse scattering data demonstrated that the roughness at the two interfaces is highly correlated when the film thicknesses are approximately 2Rg. Hence, very thin films do not exhibit liquidlike behavior, and higher-order elastic terms may have to be included into models to describe their rheological behavior.

Application of the XPS method to the study of relaxation processes in transition metal melts

The structure of metallic melts cannot be explained in terms of a simple liquid model. The liquid state of metallic melts has a complex structure which is formed as a result of the interaction of the constituent elements. The evolution of the surface layer composition in the melt has the oscillatory character. The amplitude of the oscillations decreassa with time. In comparing the data of the XPS studies of the solid amorphous and the liquid state, one may conclude that the two types of clusters are involved in the competitive process: the clusters which enrich the surface of the amorphous alloy or the melt when the thermodynamical equilibrium is achieved, and the clusters which are located in the subsurface layer.

Monte Carlo study of solid electrolytes

A simple version for superionic conductors, of the soft-core model for simple liquids is proposed. That is, the model potential is composed of only the soft-core and Coulomb potentials. Monte Carlo simulations for two solid electrolytes, α-AgI and CaF 2, are made with a fine-grained lattice for a 108-ion system and a 324- or 96-ion system, respectively, at several temperatures. For both systems we have observed sublattice disordering for an appropriate temperature range. We have obtained the partial pair distribution functions, one-body distribution of ions and mean-square displacement of ions as a function of the Monte Carlo time-step. Our results are satisfactorily compared with experimental findings and with molecular dynamics calculations. It is found for CaF 2 that as the temperature increases the fractional number of anions in the tetrahedral locations shows a drop in magnitude for a narrow temperature range, and that results obtained on the fluctuations of potential energies in the superionic phase present a rather large system-size-dependency.

Monte Carlo Study of the Soft-Core Model for α-AgI

A simple version for superionic conductors, of the soft-core model for simple liquids is proposed. That is, the model potential is composed of only the soft-core and the Coulomb potentials. Monte Carlo simulations for α-AgI are made with a fine-grained lattice for a 108-ion system at several temperatures. Sublattice disordering of cations is observed for an appropriate temperature range. At lower temperature the bcc lattice of anions becomes unstable and changes to an fcc-like structure, and at the same time cations show almost localized motions. These results are consistent with the experiments for AgI. The characteristics of the resulting structural properties for cations are also found to be consistent with the recent experimental results.

Vibrational relaxation of small molecules in the liquid phase: Liquid nitrogen doped with H2 or D2

Experimental results, using a pulsed laser technique to study the vibrational relaxation of nitrogen in solutions with H2 or D2 show that the system N2–H2 relaxes 100 times faster than N2–D2. The rate constants are kN2–H2= (1.5±0.2) ×105 and kN2–D2 = (1.8±0.4) ×103 s−1 (mol fraction)−1. From the experimental rate constants, transition probabilities 〈P〉N2–H2=9.0×10−9 and 〈P〉N2–D2=1.5×10−10 were calculated using a simple liquid model. This model treats the liquid as a dense gas and assumes that isolated binary collisions are causing the vibrational relaxation. Theoretical calculations of transition probabilities based on the first order distorted wave approximation were used to estimate the importance of V–T, V–T,R, or V–V channels to the relaxation of vibrationally excited nitrogen in the presence of H2 or D2. These calculations favor the V–T channel over the V–T,R channel for both N2–H2 and N2–D2 systems at 77 K. Relaxation of N2 by H2 is more effective than by D2 because collisions of the lighter isotopes occur with higher velocities. Relaxation by the V–V channel is unimportant in these systems. Our conclusions are consistent with those of others who have shown that the V–T channel is primarily responsible for vibrational relaxation for similar systems, CO–H2 and CO–H2 in the gas phase at low temperatures.

Theory of hydrophobic bonding. III. Method for the calculation of the hydrophobic interaction based on liquid state perturbation theory and a simple liquid model

In a previous paper, the solubility of liquid hydrocarbons at a pressure of 1 atm in water was correlated with the surface area of the solvent cavity that accommodates the hydrocarbon molecule. In this study, the authors calculate the solubility of gaseous hydrocarbons in water and develop a method to calculate the hydrophobic interactions between hydrocarbon molecules and between hydrocarbon side chains of molecules. The method is based on the first-order perturbation theory of liquid mixtures, and uses a computer-calculated solvent cavity surface area to define solute size. (28 refs.)

Transport properties of a dense fluid of molecules interacting with a square‐well potential: Part II

AbstractThe equations developed by Davis, Rice, and Sengers for the transport properties of a model fluid whose molecules interact according to a square‐well potential are utilized herein to calculate the transport coefficients of krypton, xenon, and argon. With the use of theoretically determined pair correlation functions and experimental P‐V‐T data, results are obtained that indicate that the square‐well theory provides a useful model for simple liquids. Master graphs of the transport coefficients as functions of reduced parameters are presented. An investigation of the relative importance of the contributions by kinetic transfer and by intermolecular collisional transfer leads to the conclusion that kinetic transfer can provide a sizable contribution to transport properties.

An Atomic Distribution Function for Liquid Sodium

An atomic distribution function for liquid sodium is developed. A simple liquid model of the quasi-solid type is assumed in which each atom is trapped by its immediate neighbors in a small spherical cell within which it is free to move about. The resulting distribution function contains three parameters which are evaluated by fitting the function to the experimental distribution curves for liquid sodium given by Trimble and Gingrich. An approximate value of the free volume of the liquid as a function of the absolute temperature is obtained. By means of the free energy equation the entropies and latent heats of fusion and vaporization for liquid sodium are calculated and compared with the observed values.