Time correlation functions for a model of liquid carbon disulphide

Translational and rotational diffusion of rod shaped molecules by molecular dynamics simulations

The results of molecular dynamics simulations of the dynamical evolution of assemblies of linear rigid rods of variable aspect ratio, a, and number density, ρ, in the isotropic phase are reported. The rods consist of m equally spaced sites interacting with the Weeks-Chandler-Andersen repulsive pair potential, where 2 < m < 16. With increasing m, features specific to long rods, such as anisotropic self-diffusion, become apparent. There is also an increasing separation between the characteristic relaxation times of the torque, angular velocity, and reorientational time correlation functions with increasing density. The latter is exponential at high densities even for dimers. The isotropic translational diffusion coefficient, D_i, and rotational diffusion coefficient, D_r, are reported as a function of m and ρ or volume fraction, ξ. The mD_i data scale with ξ throughout much of the simulated range, while the rotational diffusion coefficients scale approximately as m³D_r against ρ at low densities but as ∼m⁶D_r at high ρ, consistent with theories of colloidal and noncolloidal rod-containing liquids. The crossover density between the two regimes is parameterized in analytic form. The probability distribution functions for displacements and angular jumps in a given time show evidence of non-Gaussian behavior with increasing density. The shear viscosity and D_i scale approximately as m and m^-1, respectively, in the semidilute regime, which is consistent with a Stokes-Einstein-like relationship. At high concentrations, a frustrated or glassy structure formed in which the rods were randomly oriented.

Molecular polarizability anisotropy of liquid water revealed by terahertz-induced transient orientation

Reaction pathways of biochemical processes are influenced by the dissipative electrostatic interaction of the reagents with solvent water molecules. The simulation of these interactions requires a parametrization of the permanent and induced dipole moments. However, the underlying molecular polarizability of water and its dependence on ions are partially unknown. Here, we apply intense terahertz pulses to liquid water, whose oscillations match the timescale of orientational relaxation. Using a combination of terahertz pump / optical probe experiments, molecular dynamics simulations, and a Langevin dynamics model, we demonstrate a transient orientation of their dipole moments, not possible by optical excitation. The resulting birefringence reveals that the polarizability of water is lower along its dipole moment than the average value perpendicular to it. This anisotropy, also observed in heavy water and alcohols, increases with the concentration of sodium iodide dissolved in water. Our results enable a more accurate parametrization and a benchmarking of existing and future water models.

The intermolecular dynamics of liquid water impact most biological processes. Here, the authors use intense terahertz electromagnetic pulses to generate a transient, out-of-equilibrium state of the water network to show that the molecules become oriented and probe the polarizability of this anisotropic state.

Structure and dynamics of liquid CS2: Going from ambient to elevated pressure conditions

Molecular dynamics simulation studies were performed to investigate the structural and dynamic properties of liquid carbon disulfide (CS₂) from ambient to elevated pressure conditions. The results obtained have revealed structural changes at high pressures, which are related to the more dense packing of the molecules inside the first solvation shell. The calculated neutron and X-ray structure factors have been compared with available experimental diffraction data, also revealing the pressure effects on the short-range structure of the liquid. The pressure effects on the translational, reorientational, and residence dynamics are very strong, revealing a significant slowing down when going from ambient pressure to 1.2 GPa. The translational dynamics of the linear CS₂ molecules have been found to be more anisotropic at elevated pressures, where cage effects and librational motions are reflected on the shape of the calculated time correlation functions and their corresponding spectral densities.

The stress tensor in thermodynamics and statistical mechanics

We prove that the stress tensor, tau(ab), of a molecular system with arbitrary, short-range interactions can be point-wisely expressed as the functional derivative of the partition function with respect to the local deformation tensor. In this approach, the set of components of tau(ab) has a simple interpretation as the set of Lagrangian multipliers which one needs to introduce to enforce the conditions relating point particle displacements to the body local deformation tensor. The question of the possible nonuniqueness of the formula for tau(ab) is discussed.

Analysis of the transverse and the longitudinal pseudodiffusion of CO2 in sub- and supercritical states: a molecular-dynamics analysis

We have performed molecular-dynamics simulations of CO(2) system along the gas-liquid coexistence curve and on the isochore 94.22 cm(3) mol(-1) (which corresponds to the critical isochore). The calculation has been carried out in order to analyze the diffusion of CO(2) and particularly to figure out how the diffusion coefficient may be decomposed along the molecular axes. This makes it possible to analyze the anisotropy of the diffusion along these axes and to shed light on the microscopic changes which accompany such behavior. This anisotropy is traced back to the effect of the translation-rotation coupling (TRC) along the molecular axes. Along the liquid-gas coexistence curve, the pseudolongitudinal diffusion is found to be more rapid than the transverse one. The opposite trend is found along the isochore 94.22 cm(3) mol(-1). The role of the local structure was explored by calculating intermediate scattering function and the autocorrelation functions for the forces acting along the molecular axes. It is shown that the strength of the TRC effect is correlated to the difference between the relaxation times of the local structure, that of the reorientation along the molecular axes, and that of the translational motion. The analysis of the correlation time and the average mean square force along the longitudinal and transverse directions confirms the anisotropy of the local environment that determines the translational dynamics of a molecule.

Multiple short time power laws in the orientational relaxation of nematic liquid crystals

Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.

Theoretical and computational investigations on thermodynamic properties, effective site diameters, and molecular free volume of carbon disulfide fluid

A newly proposed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was extended to polyatomics and applied to compute the density and temperature dependence of the effective site diameters of carbon disulfide fluids. The generic van der Waals (GvdW) theory was also extended to polyatomics in order to calculate the GvdW parameters and the molecular free volume using the effective site diameters as the repulsion-attraction separation distance. A three-site Lennard-Jones potential available in the literature was slightly modified and used in Monte Carlo simulations to obtain the functions appearing in the effective site diameter and GvdW expressions. The interaction potential was examined to reproduce the fluid phase thermodynamic properties using Gibbs ensemble Monte Carlo simulations and also the equation of state in the liquid phase using NVT Monte Carlo (NVT-MC) simulations. Comparison between the simulation results and experimental data shows excellent agreement for the densities of the coexisting phases, the vapor pressure, properties of the predicted critical point, and the equation of state. NVT-MC simulations were performed over a wide range of densities and temperatures in sub- and supercritical regions to compute the effective site diameters, the GvdW parameters, and the molecular free volume. The molecular structure in terms of the site-site pair correlation functions, the density dependence of the effective site diameters, and the density and temperature dependence of the GvdW parameters and molecular free volume were studied and discussed. The GvdW parameters were fitted to empirical expressions as a function of density and temperature. The computed molecular free volume will be used in future investigations to study the transport properties of carbon disulfide.

Analysis of the Effect of Translation−Rotation Coupling on Diffusion along the Molecular Axes

The analysis of the microscopic diffusion processes of CO(2) and H(2)O in the coordinate system defined by the molecular orientation allows a new criterion to be introduced which provides information on the short and long time behavior of the rotation-translation coupling as well as to quantify the strength of this coupling. We discuss the general conditions under which this affects the translation diffusion "seen" by the molecule along its molecular axes. The results show that the translation-rotation coupling is correlated to the local environment in shaping the longitudinal and transversal translation dynamics of a molecule at a microscopic level.

Molecular structure and dynamics of liquids: aqueous urea solutions

In this review a multi-technical approach to the analysis of the structure and dynamics of the urea/water system is described. The reorientational movement of the solute molecule is investigated by the analysis of spectral band-shapes, as well as with the use of the optical Kerr effect (OKE) and molecular dynamics simulation (MDS). The effect of solute concentration on the structure and dynamics of the aqueous solutions (aggregation, orientational distribution, solvation...) is studied by molecular dynamics simulation and neutron scattering. The results obtained by other techniques are included to provide a critical analysis. Finally, the low-frequency Raman spectra of the system are interpreted on the basis of the semi-quantitative information obtained by molecular dynamics simulation.

Calculation of flexoelectric coefficients for a nematic liquid crystal by atomistic simulation

Equilibrium molecular dynamics calculations have been performed for the liquid crystal molecule n-4-(trans-4-n-pentylcyclohexyl)benzonitrile (PCH5) using a fully atomistic model. Simulation data have been obtained for a series of temperatures in the nematic phase. The simulation data have been used to calculate the flexoelectric coefficients e(s) and e(b) using the linear response formalism of Osipov and Nemtsov [M. A. Osipov and V. B. Nemtsov, Sov. Phys. Crstallogr. 31, 125 (1986)]. The temperature and order parameter dependence of e(s) and e(b) are examined, as are separate contributions from different intermolecular interactions. Values of e(s) and e(b) calculated from simulation are consistent with those found from experiment.

In search of temporal power laws in the orientational relaxation near isotropic–nematic phase transition in model nematogens

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

Probes of heterogeneity in rotational dynamics: application to supercooled liquid CS2

The distribution of individual molecular contributions to the second-rank rotational correlation function is introduced and used to construct probes of heterogeneity in rotational dynamics. The ideas are tested in a molecular dynamics simulation of supercooled liquid CS2. Both the quantity of heterogeneity and its lifetime or exchange time tau(ex) increase as the temperature is lowered through the supercooled state, and increase strongly as the mode-coupling temperature T(c) is approached. Crossover from Arrhenius to super-Arrhenius behavior of the rotational relaxation times tau(1) and tau(2) is observed, direct evidence of fragility in CS2. The T dependence of tau(ex) is stronger than that of the rotational times, and it may approach them from below at T(c), although the simulation is then very difficult. A detailed characterization of other aspects of the dynamical crossover is obtained, and the general implications of rotational heterogeneity for supercooled dynamics are discussed.