Van Hove Correlation Function Research Articles

Molecular dynamics simulations of the glass former ortho-terphenyl

An 18-site, three-ring model has been developed for the van der Waals system ortho-terphenyl (OTP) which has been studied extensively experimentally because of its glass forming ability. The method of constraints has been used to freeze out the fast internal modes of the molecule, but the model retains some internal motion in the form of side-ring torsions. When used in molecular dynamics simulations, the model provides a reasonable representation of the properties of OTP in the liquid and supercooled liquid states, including the volume–temperature behavior and diffusion coefficients. The glass transition temperature has been obtained from the break in the slope of the volume–temperature curve and found to agree with experimental values, given the high cooling rates of the simulations. The short time dynamics of the system have been probed using velocity autocorrelation functions, mean-square displacements, van Hove correlation functions, and intermediate scattering functions. The dynamics of the model can be interpreted consistently within a molecular cage framework. It is found that the lifetimes of the transient cages increase significantly with decreasing temperature until, in the glass, cage breakup can no longer occur on the time scale of the simulations. Two distinct regimes are seen in the single particle motion in the liquid; these correspond to localized motion within the cage and the diffusive motion that sets in after cage breakup. Around the supercooled liquid region, a subdiffusive behavior occurs between the two regimes—indicative of the increasing difficulty encountered by the cage breakup mechanisms.

Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture

Abstract We have performed a molecular dynamics computer simulation study to investigate the dynamical behavior of a supercooled simple liquid for comparison with the predictions of mode-coupling theory (MCT). By scaling the intermediate scattering function by the α-relaxation time r we find that the correlators fall onto a master curve extending over several decades in time. Thus we find that the time temperature superposition principle holds. In the late β-relaxation regime this master curve can be fitted very well by a master curve predicted by the idealized version MCT. However, there is no evidence for the presence of the critical decay predicted by the theory for the early part of the β-relaxation regime. We show that in the β-relaxation regime the van Hove correlation function obeys the factorization property. The scaling times r show at low temperatures a power-law behavior. The relation proposed by MCT between the critical exponent of this power-law and the von Schweidler exponent is fulfilled. A...

Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function.

We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time $tD(T)$, where $D(T)$ is the diffusion constant. The time range for which these curves follow the master curve is identified with the $\alpha$-relaxation regime of mode-coupling theory (MCT). This master curve is fitted well by a functional form suggested by MCT. In accordance with idealized MCT, $D(T)$ shows a power-law behavior at low temperatures. The critical temperature of this power-law is the same for both types of particle and also the critical exponents are very similar. However, contrary to a prediction of MCT, these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function [Phys. Rev. Lett. {\bf 73}, 1376 (1994)]. At low temperatures the van Hove correlation function (self as well as distinct part) shows hardly any sign of relaxation in a time interval that extends over about three decades in time. This time interval can be interpreted as the $\beta$-relaxation regime of MCT. From the investigation of these correlation functions we conclude that hopping processes are not important on the time scale of the $\beta$-relaxation for this system and for the temperature range investigated. We test whether the factorization property predicted by MCT holds and find that this is indeed the case for all correlation functions investigated. The distance dependence of the critical amplitudes are in qualitative accordance with the ones predicted by MCT for some other mixtures. The non-gaussian parameter for the self part of the van

A molecular dynamics study of the mixed alkali effect in silicate glasses

Mixed alkali silicate glasses have been studied in detail by the molecular dynamics method in order to understand the microscopic origin of the mixed alkali effect (MAE). Subtle structural variations in the local environment of alkali ions are observed as a function of the inter-alkali ratio. The MAE has been observed in the variation of self-diffusion coefficients and thus in the electrical conductivity. Cage vibration frequencies of the alkali ions remain unaffected in the mixed alkali regime. Van Hove correlation functions have been employed to study the nature of transport of the alkali ions. Results indicate that alkali ions preferentially jump only to like-ion sites which have been rationalized in terms of their site energies. The MAE has been attributed to blockage of preferred migration paths in interalkali compositions.

Rotational dynamics in ortho-terphenyl: a microscopic view

Molecular dynamics simulations of a simple model for ortho-terphenyl are used to investigate the microscopic nature of rotational dynamics in the supercooled regime. A detailed analysis of the van Hove correlation function, as well as direct examination of the orientational motion of selected molecules, show that, at sufficiently low temperatures and on the nanosecond timescale, orientational motion takes place in the near absence of translational motion. The nature of the orientational motion covers a large spectrum of situations, but we find a preponderance of rapid reorientations, i.e., jumps in two- (or multi-) level systems. It is noted, in addition, that the observed relaxation does not manifest itself as a peak in such quantities as the intermediate scattering function and the mean-square displacements. The feature sometimes observed (as in the simulations carried out by the present authors) in these functions is merely an artifact of the model coming from the use of a finite-size molecular dynamics supercell.

Inelastic neutron scattering from classical systems

The scattering law for inelastic neutron scattering from classical systems is derived by treating the wavefunctions of the scattering system in the stationary phase approximation and taking the classical limit of the Wigner phase space distribution function. In this way recoil effects are properly accounted for and the scattering law fulfils the relation of detailed balance. It is shown why classical van Hove correlation functions do not properly describe neutron scattering from classical systems.

Localization and glass transition in two-dimensional liquids

Molecular dynamic computer simulations of a two-dimensional Lennard-Jones liquid, along several isotherms, have been carried out to search for a distinct transition from a compressed liquid to an amorphous solid. The dynamics of the transition is examined in terms of tagged-particle van Hove correlation functions, for times up to 600 ps. The onset of localization and the transition to non-ergodicity occur simultaneously and abruptly within a very narrow range of density. Further analysis of the data on the intermediate scattering function indicate a good fit to a stretched exponential with an exponent beta equal to 0.62 and that this exponent is nearly independent of temperature. Thus, for the time scales investigated by this simulation, it is concluded that the transition observed is a glass transition.

Relaxation dynamics in a lattice gas: A test of the mode-coupling theory of the ideal glass transition.

By means of computer simulations we investigate the dynamical behavior of a binary lattice-gas mixture with short-range interactions in order to provide a stringent test of mode-coupling theory (MCT). The dynamics of the particles is given by Monte Carlo-like moves that change the positions of the particles and binary collisions that change the velocities. By monitoring the self part of the van Hove correlation function we find the low-temperature dynamics to be glasslike. In accordance with MCT, the imaginary part of the dynamic susceptibility χ'' shows a well-defined α peak whose high frequency wing follows a von Schweidler law with an exponent that is independent of temperature

Van Hove correlation functions in an interacting electron gas: Equation-of-motion approach

An extension of the classical van Hove correlation functions to a three-dimensional system of identical fermions is investigated, taking into account interaction effects. This is done within the framework of a Singwi-Tosi-Land-Sj\olander-like static local-field approximation, combined with second-order effects of plasmon damping. As a main result the relaxation of the Fermi hole around an instantaneously removed electron is presented.

A Molecular Dynamics Study for Lithium Metasilicate: Liquid and Quenched Supercooled States

Abstract A molecular dynamics (MD) simulation of the lithium metasilicate (Li2SiO3) system has been performed to study the dynamics and geometrical structure of a liquid state at 1673 K and a glassy state at 700 K. The long term dynamics of the glassy state is shown for the self-part of the van Hove correlation functions. In the glassy state, diffusion of lithium ion was found to occur mainly through jump motions among equilibrium sites surrounded by oxygen atoms. A geometric structural analysis with polyhedra made of oxygen atoms around lithium was applied to characterize the structure and dynamical behavior.

Correlations in the motion of atoms in liquid silicon.

A first-principles molecular-dynamics study of atomic dynamical correlations in liquid silicon is presented. The properties studied here include the van Hove correlation function, velocity autocorrelation function, spectral density, and non-Gaussian corrections to the incoherent van Hove function. It is shown that these correlation functions exhibit an oscillatory behavior at short and intermediate times due to stretching vibrations of covalent bonds that form in the metallic liquid. Quantitative estimates are given for the time scale of typical ionic relaxation times and for the self-diffusion coefficient.

Kinetics of low-frequency excitations in globular macromolecules

The kinetics of low-frequency rotational-vibrational excitations of globular macromolecules is studied. The macromolecule is modelled by a viscous liquid-like deformable body with the thermal motion being generated by the stochastic motion of its surface. The collective excitations are treated in terms of dynamic variables describing the deviations of the macromolecule shape from its equilibrium spherical form. Thermal fluctuations of the variables are described using the kinetic Einstein-Smoluchowski equation. The probability density of the change of the macromolecule dynamical state is found. The Van Hove correlation function determining the spectrum of the Rayleigh scattering of Mossbauer gamma-quanta is calculated. The spectrum is found for large values of the momentum transfer at the scattering, k. The effective width of the spectrum is shown to be proportional to k3T/η, where T is the temperature and η is the macromolecule viscosity.

Dynamics of the intercalated layer in C 36 Cs: dependence on the temperature and substrate potential

The influence of the interlayer coupling on the in-lane dynamics of stage-3 caesium-intercalated graphite is investigated. Comparison of the results from multi- and single-layer simulations shows that the in-plane dynamics are insensitive to the interlayer coupling. The single-particle dynamics, represented by the self-part of the Van Hove correlation function, and collective excitations, represented by a dynamical structure factor, point to coexistence of liquid- and solid-like components over a wide range of temperatures.

Van Hove correlation functions for identical fermions: Effects of interactions.

The self part of the dynamic structure factor for three-dimensional jellium is investigated within first-order perturbation theory. It is shown that using a screened Thomas-Fermi potential instead of the pure Coulomb interaction significantly reduces the breakdown range of the model to approximately q\ensuremath{\ll}\ensuremath{\surd}${r}_{s}$ ${k}_{f}$. .AE

Van Hove correlation functions from coherent neutron inelastic scattering

Experimentally determined coherent dynamic scattering functions for liquid bismuth and lead are used to derive the van Hove correlation functions G(r,t) and Gs(r,t). It is demonstrated that it is possible to obtain direct and physically adequate information on the atomic self-motion from a neutron inelastic scattering measurement on a completely coherent scatterer.

Depolarized light scattering and neutron scattering spectra for noble gas fluids

Using the technique of interaction-induced depolarized light scattering (DILS) the four-point dynamic correlation function is probed. Here, we discuss three different decoupling approximations which express the four-point dynamic correlation function in terms of two-point dynamic (Van Hove) correlation functions. We show that the experimental results of the integrated DILS intensity of Ar as a function of density can be reproduced satisfactorily by one of the decoupling approximations for densities up to the critical density. The line shape of the DILS spectrum of Xe in the liquid phase is compared with the decoupling approximation using the two-point dynamics correlation function obtained from neutron scattering experiments on Ar at the corresponding state. It is shown that the low-frequency part of the model calculation is consistent with the experimental DILS results. In this frequency range, in the liquid phase, the DILS spectrum appears to be mainly determined by density fluctuations with wavelengths of the order of the diameter of the particles. The influence of different expressions for the pair polarizability on the model calculations is discussed.

Molecular dynamics study of a lipid bilayer and a polymer liquid

We present molecular dynamics simulation of a lipid bilayer of 2 × 10 freely jointed chain molecules of 16 beads each. All beads interact with each other (via a Lennard-Jones potential) and with an aqueous medium. Terminal beads are bound near the bilayer surfaces by a harmonic potential. An algorithm for integrating the equations of motion of a molecular system in the presence of geometrical constraints, such as fixed bond lengths, is described. All results are compared with those obtained for an isotropic polymer liquid with the same Lennard-Jones interaction and density as for the bilayer. Equilibrium properties of the chains such as end-to-end distance, radius of gyration, molecular order parameters and pair correlation functions are computed. Dynamic properties considered include the time autocorrelation functions of various variables, the translational motion of chain beads and the space-time van Hove correlation functions. It is found that compared with the polymer liquid, the molecular motions in ...

Molecular dynamics simulation of hydrocarbon molecules in condensed phases. I. Liquid n-butane

A study is made of the feasibility of predicting the dynamical properties of liquid and solid hydrocarbons by means of molecular dynamics simulations using an empirical force field CFF developed for an entire family of alkanes. Results for mean square displacements and velocity autocorrelation functions are presented for liquid n-butane (C4H10). Vibrational frequencies are examined through a generalized density of states and compared with optical data. The van Hove correlation function for the protons is calculated and the result leads to a semiquantitative prediction of the energy distribution of neutron inelastic scattering. A certain deficiency of the force field is indicated by the present results.

ChemInform Abstract: Dynamics of Molecular Reorientations: Analogies Between Quasielastic Neutron Scattering and Deuteron NMR Spin Alignment.

AbstractIt is established that both methods supplement each other.

Dynamics of molecular reorientations: Analogies between quasielastic neutron scattering and deuteron NMR spin alignment

The analogies between incoherent quasielastic neutron scattering and deuteron spin alignment in studying single particle reorientations are pointed out. Quasielastic neutron scattering measures the full van Hove correlation function for correlation times shorter than 10−8 s. Spin alignment represents an orientational single particle function for correlation times longer than 10−4 s. The analogy is based on the fact that geometrical information is obtained in both methods by manipulation of an appropriate phase factor. In neutron scattering this phase factor is Q⋅a in momentum space, where Q is the momentum transfer and a is a jump length. In spin alignment the phase factor is δQ⋅τ1 in time space where δQ specifies the strength of the quadrupole coupling and τ1 is a pulse spacing defining the evolution period. It is shown that the measurements of the elastic incoherent structure factor as a function of Q⋅R and the spin alignment echo height as a function of δQ⋅τ1, respectively, yields largely equivalent information about the type of reorientational motion—although at different time scales. Therefore, both methods nicely supplement each other. Some examples (two-, four-, and six-fold jumps of dimethylsulfone, hexamethylenetetramine, and hexamethylbenzene as well as rotational diffusion of polystyrene in its viscous state) are discussed explicitly, where the geometry and time scale of slow molecular reorientations are identified directly.