Van Hove Distribution Function Research Articles

Molecular simulation study of the glass transition in a soft primitive model for ionic liquids

In this paper, we present a molecular dynamics study of the glass transition for a soft-core primitive model for ionic liquids, in which cations are fully flexible chains of tangent soft spherical monomers, being the positively charged monomer at one of the ends of the chain, and anions as charged soft spheres. We have monitored transport coefficients such as the self-diffusion coefficients and the shear viscosity, as well as correlation functions such as the mean-square displacement, the self-intermediate scattering function, and probes of heterogeneous dynamics such as the van Hove distribution function and the four-points susceptibility. The analysis of these properties indicates that, for a given pressure, the glass transition shows a weak temperature dependence on the cation length, occurring first for short-chain than for long-chain ionic liquids.

Dynamics from elastic neutron-scattering via direct measurement of the running time-integral of the van Hove distribution function

We present a new neutron-scattering approach to access the van Hove distribution function directly in the time domain, I(t), which reflects the system dynamics. Currently, I(t) is essentially determined from neutron energy-exchange. Our method consists of the straightforward measurement of the running time-integral of I(t), by computing the portion of scattered neutrons corresponding to species at rest within a time t, (conceptually elastic scattering). Previous attempts failed to recognise this connection. Starting from a theoretical standpoint, a practical realisation is assessed via numerical methods and an instrument simulation.

Structural relaxation and diffusion in a model colloid-polymer mixture: dynamical density functional theory and simulation

Within the Asakura–Oosawa model, we study structural relaxation in mixtures of colloids and polymers subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self and distinct parts of the van Hove distribution function G(r,t) by means of dynamical density functional theory (DDFT) using an accurate free-energy functional based on Rosenfeld’s fundamental measure theory. In order to remove unphysical interactions within the self part, we extend the recently proposed quenched functional framework (Stopper et al 2015 J. Chem. Phys. 143 181105) toward mixtures. In addition, we obtain results for the long-time self diffusion coefficients of colloids and polymers from dynamic Monte Carlo simulations, which we incorporate into the DDFT. From the resulting DDFT equations we calculate G(r, t), which we find to agree very well with our simulations. In particular, we examine the influence of polymers which are slow relative to the colloids—a scenario for which both DDFT and simulation show a significant peak forming at r = 0 in the colloid–colloid distribution function, akin to experimental findings involving gelation of colloidal suspensions. Moreover, we observe that, in the presence of slow polymers, the long-time self diffusivity of the colloids displays a maximum at an intermediate colloid packing fraction. This behavior is captured by a simple semi-empirical formula, which provides an excellent description of the data.

The geometric mean squared displacement and the Stokes-Einstein scaling in a supercooled liquid.

It is proposed that the rate of relaxation in a liquid is better described by the geometric mean of the van Hove distribution function, rather than the standard arithmetic mean used to obtain the mean squared displacement. The difference between the two means is shown to increase significantly with an increase in the non-Gaussian character of the displacement distribution. Preliminary results indicate that the geometric diffusion constant results in a substantial reduction of the deviation from Stokes-Einstein scaling.

Ab initio based understanding of diffusion mechanisms of hydrogen in liquid aluminum

Ab initio molecular dynamics simulations are used to describe the diffusion of hydrogen in liquid aluminum at different temperatures. We show that the hydrogen motion does not follow a Brownian motion caused by a broad distribution of spatial jumps that can exceed 15 times the interatomic AlH distance. This breakdown is also evidenced in the calculation of the self-part of the van Hove distribution function that is not the Gaussian expected for a Fickian process. We show that the hydrogen motion can be described well by a generalized continuous time random walk model leading to computed self-diffusion coefficients of H in liquid aluminum in good agreement with experimental ones. Finally, the impact of impurities and alloying elements is discussed.

The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.

Molecular dynamics simulations of the chain dynamics in monodisperse oligomer melts and of the oligomer tracer diffusion in an entangled polymer matrix

The apparent analogy between the self-diffusion of linear oligomers in monodisperse systems, 2 up to 32 monomers, and their tracer diffusion in an entangled polymer matrix of length 256 is investigated by molecular dynamics simulations at constant pressure. Oligomers and polymers are represented by the same coarse-grained (bead-spring) model. An analysis based on the Rouse model is presented. The scaling relationship of the self-diffusion coefficient D with the chain length N written as D proportional, variantN(-alpha) is analyzed for a wide range of temperatures down to the glass transition temperature T(g). Near T(g), the heterogeneous dynamics is explored by the self-part of the van Hove distribution function and various non-Gaussian parameters. For the self-diffusion in a monodisperse system a scaling exponent alpha(T)>1 depending on temperature is found, whereas for the tracer diffusion in an entangled matrix alpha=1 is obtained at all temperatures, regardless of the oligomer length. The different scaling behavior between both systems is explained by a different monomer mobility, which depends on chain length for monodisperse systems, but is constant for all tracers in the polymer matrix.

A random walk description of the heterogeneous glassy dynamics of attractingcolloids

We study the heterogeneous dynamics of attractive colloidal particles close to the geltransition using confocal microscopy experiments combined with a theoretical statisticalanalysis. We focus on single particle dynamics and show that the self-part ofthe van Hove distribution function is not the Gaussian expected for a Fickianprocess, but that it reflects instead the existence, at any given time, of colloidswith widely different mobilities. Our confocal microscopy measurements can bedescribed well by a simple analytical model based on a conventional continuoustime random walk picture, as already found for several other glassy materials. Inparticular, the theory successfully accounts for the presence of broad tails in the vanHove distributions that exhibit exponential, rather than Gaussian, decay at largedistance.

Configurational Statistics of Macromolecules in Solution from Correlations of Liquid Molecules

We address the relevant quest for a simple formalism describing the microstructure of liquid solutions of polymer chains. On the basis of a recent relativistic-type picture of self-diffusion in (simple) liquids named Brownian relativity (BWR), a covariant van Hove's distribution function in a Vineyard-like convolution approximation is proposed to relate the statistical features of liquid and chain molecules forming a dilute polymer solution. It provides an extension of the Gaussian statistics of ideal chains to correlated systems, allowing an analysis of macromolecular configurations in solution by the only statistical properties of the liquid units (and vice versa). However, the mathematical solution to this issue is not straightforward because, when the liquid and polymer van Hove's functions are equated, an inverse problem takes place. It presents some conceptual analogies with a scattering experiment in which the correlation of the liquid molecules acts as the radiation source and the macromolecule as the scatterer. After inverting the equation by a theorem coming from the Tikhonov's approach, it turns out that the probability distribution function of a real polymer can be expressed from a static Ornstein-Uhlenbeck process, modified by correlations. This result is used to show that the probability distribution of a true self-avoiding walk polymer (TSWP) can be modeled as a universal Percus-Yevick hard-sphere solution for the total correlation function of the liquid units. This method suits in particular the configurational analysis of single macromolecules. The analytical study of arbitrary many-polymer systems may require further mathematical investigation.

Covariant van Hove function in dilute polymer solutions

A statistically covariant relation, based on a recent Brownian relativity that was able to provide a new macromolecular scaling picture, has been obtained in order to connect the statistical features of liquid and chain molecules forming a polymer solution. A generalized van Hove distribution function turns out to extend the Gaussian statistics to correlated media and, for dilute polymer solutions with large chain unit numbers, infers the form of a Vineyard-like convolution integral for density correlations. Depending on the imposed covariance, and the link to fundamental issues in fluid statistical mechanics, this picture encourages us to investigate conformational statistics of macromolecules in terms of the surrounding liquid correlations alone, and seeking further, which general scaling principles a Brownian-like statistic may generally undergo.

Numerical Calculation of the Density Autocorrelation Function for Liquid Argon

Numerical calculations of the dynamic scattering function $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}, \ensuremath{\omega})$, the intermediate scattering function, and the van Hove distribution function $\mathrm{G}(\stackrel{\ensuremath{\rightarrow}}{\mathcal{r}}, t)$, based on an approximate expression for $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}, \ensuremath{\omega})$ proposed in an earlier paper, are presented. The liquid structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ and first two even moments of $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}, \ensuremath{\omega})$, which are needed as input, are obtained by means of the Percus-Yevick equation with a Lennard-Jones potential, making the calculation entirely self-contained. The calculation is applied to the liquid-argon case studied through molecular dynamics by Rahman; comparisons with these results and those of experiment show good qualitative agreement. A brief description of the numerical procedure is included.

New Approximation for the Calculation of Neutron Scattering from a Simple Liquid

A conceptually simple and easily applied approximation is made for the Van Hove distribution function $G(\mathbf{R},t)$ of a classical liquid. This approximation gives a less rapid temporal decay of $G(\mathbf{R},t)$ than is found in the Vinevard convolution approximation. In addition, by requiring that the sum rules be satisfied, we find that for $t$ smaller than about 0.5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}13}$ sec the "correlations" in a liquid may be said to be increasing. Comparisons are made with recent neutron scattering experiments. There is fair agreement between the theoretical and experimental results.