Van Hove Correlation Function Research Articles

Chlorophyll-Induced Lamellar to Nonlamellar Phase Transitions and Dynamical Heterogeneity in Plant Thylakoid Membranes.

Chlorophyll a (CLA) pigments and thylakoid membranes are crucial components of plants for photosynthesis. To understand the effect of CLA on the structure and dynamics of thylakoid membranes, coarse-grained molecular dynamics (CG MD) simulations of thylakoid membranes are performed by varying the numbers of CLA at 293 K using MARTINI-2 force fields. The membrane undergoes a lamellar to nonlamellar phase transition above a critical concentration of CLA. The CLAs dynamically form aggregates of different orders and preferentially fetch the least unsaturated nonbilayer-forming lipids around them, resulting in a nonlamellar phase with fused regions. These fused regions cause a structural arrest of CLA and lipids, inducing dynamic heterogeneity manifested by non-Gaussian parameters and van Hove correlation functions. The lamellar to nonlamellar phase transition of the membrane is associated with a drastic reduction in correlation length of the immobile CLA and lipids governed by the fused topology. Such insights into CLA-induced structural transitions in thylakoid membranes are pertinent for understanding nonphotochemical quenching mechanisms and hold promise for designing future artificial photosynthetic materials and applications in photodynamic therapy.

Dynamic Ion Correlations and Ion-Pair Lifetimes in Aqueous Alkali Metal Chloride Electrolytes.

Electrolytes are central to many technological applications, as well as life itself. The behavior and properties of electrolytes are often described in terms of ion pairs, whereby ions associate as either contact ion pairs (in which ions are "touching") solvent-separated ion pairs (in which ions' solvent shells overlap) or solvent-solvent-separated ion pairs (in which ions' solvent shells are distinct). However, this paradigm is generally restricted to statistically averaged descriptions of solution structure and ignores temporal behavior. Here we elucidate the time-resolved dynamics of these ion-ion interactions in aqueous metal chloride electrolytes using the partial van Hove correlation function, based on polarizable molecular dynamics simulations. Our results show that the existence and persistence of ion pairs in aqueous metal chloride electrolytes should not be assumed a priori, but in fact are ion specific features of the solution with lifetimes on subpicosecond time scales.

Real-space local self-motion of protonated and deuterated water.

We report on the self-part of the Van Hove correlation function, the correlation function describing the dynamics of a single molecule, of water and deuterated water. The correlation function is determined by transforming inelastic scattering spectra of neutrons or x rays over a wide range of momentum transfer Q and energy transfer E to space R and time t. The short-range diffusivity is estimated from the Van Hove correlation function in the framework of the Gaussian approximation. The diffusivity has been found to be different from the long-range macroscopic diffusivity, providing information about local atomic dynamics.

Comparative assessment of the performance of density functionals and dispersion correction on different properties of dicationic ionic liquids - an ab initio molecular dynamics (AIMD) study.

In this study, we investigated the effect of DFT density functionals and dispersion correction on an imidazolium-based dicationic ionic liquid (DIL) using ab initio molecular dynamics simulations. To achieve this purpose, the electronic structures, as well as the structural and dynamical properties of [C3(mim)2][NTF2]2 DIL, were obtained using the BLYP and PBE functionals, both with and without D3-correction, and the results were compared with experimental values. Radial distribution functions and structure factors revealed that applying D3-correction increases the interaction between the anion and hydrogen atoms of the rings and side chains. The simulation of the studied DIL with the BLYP-D3 functional depicted lower structural heterogeneity compared to the other functionals. Analysis of Voronoi tessellation and linkage chain conformations showed a reduction in the aggregation of the linkage alkyl chains in the presence of D3-correction, which is more pronounced in the BLYP functional than in PBE. Additionally, it was observed that the probability of forming a hydrogen-bond network depends on both the type of used density functionals and applying dispersion correction. The results of dynamical properties, such as the self-diffusion coefficients, velocity autocorrelation function, and van Hove correlation function, as well as ion pair, ion cage, and hydrogen bond dynamics, indicated that applying D3-correction in both density functionals leads to an increase in the dynamics of the studied DIL. Additionally, the ratio of self-diffusion coefficients of the anion to the cation in the BLYP functional is closer to experimental values compared to the PBE functional. Furthermore, the electronic structure, including dipole moment distribution, and also infrared (IR) and power spectra were studied. Applying D3-correction and the type of density functionals have a significant effect on the dipole moment distribution of ions. Moreover, the results of IR and power spectra demonstrated that only in the BLYP functional, by applying D3-correction, the hydrogen bonding between the anion and the hydrogen atoms of the cation is strengthened at high wavenumbers. Thus, we conclude that applying D3 correction to both the BLYP and PBE density functionals improves the accuracy in describing the various properties of the studied system. Overall, the evaluation of different structural, dynamical, and vibrational properties of [C3(mim)2][NTF2]2 DIL suggests that the BLYP-D3 density functional may be the best choice among the studied density functionals.

Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories.

Confinement breaks translational and rotational symmetry in materials and makes all physical properties functions of position. Such spatial variations are key to modulating material properties at the nanoscale, and characterizing them accurately is therefore an intense area of research in the molecular simulations community. This is relatively easy to accomplish for basic mechanical observables. Determining spatial profiles of transport properties, such as diffusivity, is, however, much more challenging, as it requires calculating position-dependent autocorrelations of mechanical observables. In our previous paper (Domingues, T.S.; Coifman, R.; Haji-Akbari, A. J. Phys. Chem. B 2023, 127, 5273 10.1021/acs.jpcb.3c00670), we analytically derive and numerically validate a set of filtered covariance estimators (FCEs) for quantifying spatial variations of the diffusivity tensor from stochastic trajectories. In this work, we adapt these estimators to extract diffusivity profiles from MD trajectories and validate them by applying them to a Lennard-Jones fluid within a slit pore. We find our MD-adapted estimator to exhibit the same qualitative features as its stochastic counterpart, as it accurately estimates the lateral diffusivity across the pore while systematically underestimating the normal diffusivity close to hard boundaries. We introduce a conceptually simple and numerically efficient correction scheme based on simulated annealing and diffusion maps to resolve the latter artifact and obtain normal diffusivity profiles that are consistent with the self-part of the van Hove correlation functions. Our findings demonstrate the potential of this MD-adapted estimator in accurately characterizing spatial variations of diffusivity in confined materials.

Molecular dynamics study of shear-induced lamellar alignment of ABA triblock copolymer thin films.

In this study, the shear-induced lamellar alignment of a thin-film ABA triblock copolymer melt was achieved via a non-equilibrium coarse-grained molecular dynamics simulation. The ABA triblock copolymer system displayed a slightly different phase behavior under different shear conditions compared to the AB diblock copolymer system. Unlike previous studies that only considered the wall velocity, the Flory-Huggins parameter was considered in our study as a factor that determines lamellar alignment. Pre-aligned lamellae and randomly mixed polymers were used as the initial states for the shear simulation to compare the shear-induced lamellar alignment on each. The two initial conditions displayed different alignment behaviors; specifically, in the pre-aligned lamellae, a tilted structure was observed when the system was not aligned in the shear direction. To explain the difference between the tilted and realigned structures, the potential energy over the simulation time, polymer dynamics from the Van Hove correlation function, and the directional order parameter were investigated. It was inferred that a tilted structure is induced by the energy barrier of realignment originating from the restricted movement of the local polymer chains. Once they cross the energy barrier, block copolymers tend to align in the shear direction to attain energy stabilization through the polymer flow.

MembraneDyn: simulating the dynamics of supported membrane stacks on the nanosecond timescale

The static structure factor and the undulation dynamics of a solid-supported membrane stack have previously been calculated by Romanov and Ul'yanov [Romanov & Ul'yanov (2002). Phys. Rev. E, 66, 061701]. Based on this prior work, the calculation has been extended to cover the membrane dynamics, i.e. the intermediate scattering function as a Fourier transform of the van Hove correlation function of the membrane stack. Fortran code which calculates the intermediate scattering function for a membrane stack on a solid support is presented. It allows the static and dynamic scattering functions to be calculated according to the derivation of Romanov and Ul'yanov. The physical properties of supported phospholipid bilayers can be examined in this way and the results can be directly compared with results obtained from grazing-incidence neutron spin-echo spectroscopy experiments.

Normal and anomalous diffusion in the disordered wind-tree model.

Ehrenfests' wind-tree model (EWTM) refers to a two-dimensional system where noninteracting point tracer particles move through a random arrangement of overlapping or nonoverlapping square-shaped scatterers. Here, extensive event-driven molecular dynamics simulations of the EWTM at different reduced scatterer densities ρ are presented. For nonoverlapping scatterers, the asymptotic motion of the tracer particles is diffusive. We compare their diffusion coefficient D, as obtained from the simulation, with that predicted by kinetic theory where D^{-1} is expanded up to the second order in the scatterer density. While at low density quantitative agreement between theory and simulation is found, we show that beyond the low-density regime deviations to the theory are associated with the emergence of a maximum in the non-Gaussian parameter at intermediate times. For the case of overlapping scatterers, in agreement with a theoretical prediction, the asymptotic motion of the tracer particles is subdiffusive, i.e., the mean-squared displacement at long times t grows like t^{1-2ρ/3}. We propose a model of the van Hove correlation function that describes the density dependence of the tracer particles' asymptotic subdiffusive transport on a quantitative level.

Activation induced fluidization of a confined viscous liquid

Confinement of supercooled liquids into nano-pores induces a strong modification of the dynamics. In this work we raise the issue as how this confinement effect is modified when the liquid is out of equilibrium. To answer that question, we use molecular dynamics simulations to investigate the effect of confinement on a supercooled liquid activated by the periodic folding of a molecular motor. The excitation (i.e. elementary diffusion processes) density calculation shows that the motor’s opening angle controls the activation of the medium. We then use that result to study the effect of different activations on the confined supercooled liquid. When our liquid is not activated, the confinement generates a strong slowing down of the dynamics, and the excitation density decreases sharply around the pore wall. In contrast when the liquid is activated the motor generates excitations inside the medium localized mostly in the pore center. The combination of these two effects leads to a localization of the excitation density when the motor is on. Results show that the activation is able to wash out the confinement-induced slowing down while the main characteristics of supercooled liquids are maintained or increased. We observe actually an increase of the tail of the Van Hove correlation function upon activation inside the pores leading to the increase of the Non Gaussian parameter, two signatures of dynamic heterogeneity in supercooled liquids.

Real-Space Local Dynamics of Molten Inorganic Salts Using Van Hove Correlation Function.

Molten inorganic salts are attracting resurgent attention because of their unique physicochemical properties, making them promising media for next-generation concentrating solar power systems and molten salt reactors. The dynamics of these highly disordered ionic media is largely studied by theoretical simulations, while the robust experimental techniques capable of observing local dynamics are not well-developed. To provide fundamental insights into the atomic-scale transport properties of molten salts, we report the real-space dynamics of molten magnesium chloride at high temperatures employing the Van Hove correlation function obtained by inelastic neutron scattering. Our results directly depict the distance-dependent dynamics of a molten salt on the picosecond time scale. This study demonstrates the capability of the developed approach to describe the locally correlated- and self-dynamics in molten salts, significantly improving our understanding of the interplay between microscopic structural parameters and their dynamics that ultimately control physical properties of condensed matter in extreme environments.

Solidlike to liquidlike behavior of Cu diffusion in superionic Cu2X (X=S, Se) : An inelastic neutron scattering and ab initio molecular dynamics investigation

${\mathrm{Cu}}_{2}\mathrm{Se}$ and ${\mathrm{Cu}}_{2}\mathrm{S}$ are excellent model systems of superionic conductors with large diffusion coefficients that have been reported to exhibit different solidlike and liquidlike Cu-ion diffusion. In this paper, we clarify the atomic dynamics of these compounds with temperature-dependent ab initio molecular dynamics (AIMD) simulations and inelastic neutron scattering experiments. Using the dynamical structure factor and Van Hove correlation function, we interrogate the jump time, hopping length distribution, and associated diffusion coefficients. In cubic ${\mathrm{Cu}}_{2}\mathrm{Se}$ at 500 K, we find solidlike diffusion with Cu jump lengths matching well the first-neighbor Cu-Cu distance of \ensuremath{\sim}3 \AA{} in the crystal, and clearly defined optic phonons involving Cu vibrations. Above 700 K, the jump-length distribution becomes a broad maximum centered around 4 \AA{}, spanning the first and second neighbor lattice distances, and a concurrent broadening of the Cu-phonon density of states. Further, above 900 K, the Cu diffusion becomes close to liquidlike, with distributions of Cu atoms continuously connecting crystal sites, while the vibrational modes involving Cu motions are highly damped, though still not fully overdamped as in a liquid. At low temperatures, the solidlike diffusion is consistent with previous x-ray diffraction and quasielastic neutron scattering experiments, while the higher-temperature observation of the liquidlike diffusion is in agreement with previous AIMD simulations. We also report AIMD simulations in ${\mathrm{Cu}}_{2}\mathrm{S}$ in the hexagonal and cubic superionic phases, and observe nearly liquidlike diffusion above \ensuremath{\sim}500 K. The calculated ionic conductivity is in fair agreement with reported experimental values.

Long-time relaxation dynamics in nematic and smectic liquid crystals of soft repulsive colloidal rods.

Understanding the relaxation dynamics of colloidal suspensions is crucial to identifying the elements that influence the mobility of their constituents, assessing their macroscopic response across the relevant time and length scales, and thus disclosing the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft repulsive rodlike particles, which are able to self-organize into nematic and smectic liquid-crystalline phases. Rods are modeled as soft repulsive spherocylinders with a length-to-diameter ratio L^{★}=5, interacting via the truncated and shifted Kihara potential. By performing dynamic Monte Carlo simulations, we analyze the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess its dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.

Leaching and Reactivity at the Sodium Aluminosilicate Glass–Water Interface: Insights from a ReaxFF Molecular Dynamics Study

In this study, we used ReaxFF reactive force field molecular dynamics (MD) simulations to investigate the dynamics associated with reactivity at the sodium aluminosilicate (NAS) glass–water interface. By combining van Hove correlation functions and visual analysis of individual trajectories, we found that when a Na+ ion leaves its initial position at the glass surface under the effect of water, it can be replaced either by a H+ ion or by another diffused Na+, resulting in a (Na+ ⇌ H+) ion exchange or (Na+ ⇌ Na+) ion exchange, respectively. These rearrangements at the NAS glass–water interface take place through many events such as the formation of oxygen-bearing functional groups (silanol Si(OH), germinal silanol Si(OH)2, and Al(OH)) and the agglomeration of Na+ ions on the glass surface. The high affinity between water and Na+ ions leads to two events, namely, the penetration of the water molecule into the first glass layer and the release of Na+ ions into the bulk water. The release of sodium ions into bulk water takes place via several successive steps: (1) leaving their original position to an area more exposed to bulk water, (2) diffusion to the surface of the glass, (3) leaving the surface toward the solution, and (4) coming back to the glass surface. Statistical analysis shows that oxygen-bearing functional group formation occurs both by protonation of the nonbridging oxygen (NBO) site and by filling defects such as SiIII, AlIII, and AlIV by OH– resulting from the dissociation of water molecules, while in the bulk, they could be produced by the proton jumps between two adjacent NBO sites and dissociation of the water diffused in deep layers of glass. Germinal silanol groups (Si(OH)2) are present in small amounts in the first layer of the glass after the protonation of two NBOs from a single SiIV. This process is accompanied by the conversion of AlIII and AlIV units into AlV units and SiIII units into SiIV units. By comparing the networks of Si and Al, we found that Al is more impacted by the occurrence of water molecules than Si, which is explained by an increase in the diffusion coefficient of Al compared with Si when these units become protonated (Si(OH) and Al(OH)).

Investigating the Accuracy of Water Models through the Van Hove Correlation Function.

We present molecular-simulation-based calculations of the Van Hove correlation function (VHF) of water using multiple modeling approaches: classical molecular dynamics with simple three-site nonpolarizable models, with a polarizable model, and with a reactive force field; density functional tight-binding molecular dynamics; and ab initio molecular dynamics. Due to the many orders of magnitude difference in the computational cost of these approaches, we investigate how small and short the simulations can be while still yielding sufficiently accurate and interpretable results for the VHF. We investigate the accuracy of the different models by comparing them to recently published inelastic X-ray scattering measurements of the VHF. We find that all of the models exhibit qualitative agreement with the experiments, and in some models and for some properties, the agreement is quantitative. This work lays the foundation for future simulation approaches to calculating the VHF for aqueous solutions in bulk and under nanoconfinement.

Probability distribution for heat exchange in plastic deformation.

Fluctuation theorems allow one to obtain equilibrium information from nonequilibrium experiments. The probability distribution function of the relevant magnitude measured along the irreversible nonequilibrium trajectories is an essential ingredient of fluctuation theorems. In small systems, where fluctuations can be larger than average values, probability distribution functions often deviate from being Gaussian, showing long tails, mostly exponential, and usually strongly asymmetric. Recently, the probability distribution function of the van Hove correlation function of the relevant magnitude was calculated, instead of that of the magnitude itself. The resulting probability distribution function is highly symmetric, obscuring the application of fluctuation theorems. Here, the discussion is illustrated with the help of results for the heat exchanged during plastic deformation of aluminum nanowires, obtained from molecular dynamics calculations. We find that the probability distribution function for the heat exchanged is centrally Gaussian, with asymmetric exponential tails further out. By calculating the symmetry function we show that this distribution is consistent with fluctuation theorems relating the differences between two equilibrium states to an infinite number of nonequilibrium paths connecting those two states.

Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series.

Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.

Dehydration induced dynamical heterogeneity and ordering mechanism of lipid bilayers.

Understanding the influence of dehydration on the membrane structure is crucial to control membrane functionality related to domain formation and cell fusion under anhydrobiosis conditions. To this end, we perform all-atom molecular dynamic simulations of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dimyristoylphosphatidylcholine lipid membranes at different hydration levels at 308 K. As dehydration increases, the lipid area per head group decreases with an increase in bilayer thickness and lipid order parameters indicating bilayer ordering. Concurrently, translational and rotational dynamics of interfacial water (IW) molecules near membranes slow down. On the onset of bilayer ordering, the IW molecules exhibit prominent features of dynamical heterogeneity evident from non-Gaussian parameters and one-dimensional van Hove correlation functions. At a fully hydrated state, diffusion constants (D) of the IW follow a scaling relation, D∼τα -1, where the α relaxation time (τα) is obtained from self-intermediate scattering functions. However, upon dehydration, the relation breaks and the D of the IW follows a power law behavior as D∼τα -0.57, showing the signature of glass dynamics. τα and hydrogen bond lifetime calculated from intermittent hydrogen bond auto-correlation functions undergo a similar crossover in association with bilayer ordering on dehydration. The bilayer ordering is accompanied with an increase in fraction of caged lipids spanned over the bilayer surface and a decrease in fraction of mobile lipids due to the non-diffusive dynamics. Our analyses reveal that the microscopic mechanism of lipid ordering by dehydration is governed by dynamical heterogeneity. The fundamental understanding from this study can be applied to complex bio-membranes to trap functionally relevant gel-like domains at room temperature.

Heterogeneous Rotational Dynamics of Imidazolium-Based Organic Ionic Plastic Crystals.

Organic ionic plastic crystals (OIPCs) are a unique class of materials that undergo orientational and conformational motions while maintaining a long-range ordered lattice structure. OIPCs have attracted attention because the rotational motions were known to accelerate the diffusion of mobile ions such as lithium ions. However, only a small number of combinations of cations and anions lead to OIPCs because the rotational motion may be restricted by both the molecular structure and the crystal class. In this work, we perform molecular dynamics simulations to study the effects of the molecular structure and the crystal class on the rotational motion and the phase transitions. We investigate four imidazolium-based ionic crystals: (1) 1-methyl-3-methylimidazolium hexafluorophosphate ([MMIM][PF6]), (2) 1-methyl-3-methylimidazolium chloride ([MMIM][Cl]), (3) monoclinic 1-butyl-3-methylimidazolium chloride ([BMIM][Cl]), and (4) orthorhombic [BMIM][Cl] ionic crystals. We construct initial configurations of OIPCs by employing experimental crystalline structures. Then, we increase the temperature gradually and monitor the density and the radial distribution functions. We estimate the rotational van Hove correlation functions and find that molecules in plastic crystal phases undergo rotational hopping motions and OIPCs exhibit rotational dynamic heterogeneity significantly. The structure of anions and cations affect the phase transition of OIPCs. And the crystal class is also critical to the phase transition of OIPCs because the rotational motion of ions depends on the crystal class.

Experimental study of diffusion behaviors of an ellipsoidal colloid in spherical colloid systems

The diffusive transport in complex confined media is ubiquitous such as diffusions of micro- or nano-particles in glassy liquids and polymer solutions, protein diffusions under crowded conditions, and deliveries of drugs in the biological media. Therefore, the understanding of the diffusive transport arouses the great interest of researchers in the physics, materials science, and biology circles. Despite the fact that the shape of the colloidal particles acts as one of the important physical factors influencing their dynamic behaviors, the study of the anisotropic particles diffusing in confined media is still lacking. In this work, we propose a simple experimental model to investigate the confined diffusion of shape-anisotropic particles. The diffusion of an ellipsoid at different area fractions (<i>ϕ</i>) of colloidal spheres is investigated through video microscopy. At low <i>ϕ</i>, ellipsoid exhibits a random trajectory and free diffusion in translational and rotational degree of freedom; while at high <i>ϕ</i>, the trajectory is in a small spatial range with a nearly constant orientation of the particle, indicating that the arrested diffusion takes place in translational and rotational degree of freedom. The translational and rotational mean square displacement decrease with the increase of <i>ϕ</i>. By power-law fitting (~<i>t<sup>β</sup></i>), it is found that <i>β</i> decreases from 1 to a small value at high <i>ϕ</i>, demonstrating that the ellipsoid experiences a transition from normal diffusion to sub-diffusion. Moreover, <i>β</i> for rotational motion decreases faster than that for translational motion at high <i>ϕ</i>, which signifies that the the rotational motion decouples from the translational motion with increasing <i>ϕ</i>. The results from the van Hove correlation function show that the translational displacement along the major axis of the ellipsoid is always larger than that along the minor axis, manifesting the ellipsoid prefers to diffuse along its major axis independent of <i>ϕ</i>. Significant non-Gaussian tail is observed in the distribution of the translational displacement along the major axis with increasing <i>ϕ</i>. However, the distribution of the translational displacement along the minor axis presents a nearly Gaussian behavior independent of <i>ϕ</i>. This indicates that the translational motion along the major axis decouples from the translational motion along the minor with increasing <i>ϕ</i>. For the rotational displacement, the non-Gaussian tail is only observed at the intermediate <i>ϕ</i>. These non-Gaussian behaviors are confirmed by calculating the non-Gaussian parameter (<i>α</i><sub>2</sub>). Our experiments demonstrate that the confinements give rise to the anomalous diffusion behaviors of the anisotropic colloids, which is conducive to the understanding of transportations of anisotropic objects in complex environments.

Shear stress relaxation and diffusion in simple liquids by molecular dynamics simulations: Analytic expressions and paths to viscosity.

The results are reported of an equilibrium molecular dynamics simulation study of the shear viscosity, η, and self-diffusion coefficient, D, of the Lennard-Jones liquid using the Green-Kubo (GK) method. Semiempirical analytic expressions for both GK time correlation functions were fitted to the simulation data and used to derive analytic expressions for the time dependent diffusion coefficient and shear viscosity, and also the correlation function frequency transforms. In the case of the shear viscosity for a state point near the triple point, a sech function was found to fit the correlation function significantly better than a gaussian in the ballistic short time regime. A reformulation of the shear GK formula in terms of a time series of time integrals ("viscuits") and contributions to the viscosity from components based on the initial stress ("visclets") enable the GK expressions to be recast in terms of probability distributions which could be used in coarse grained stochastic models of nanoscale flow. The visclet treatment shows that stress relaxation is statistically independent of the initial stress for equilibrium and metastable liquids, suggesting that shear stress relaxation in liquids is diffusion controlled. By contrast, the velocity autocorrelation function is sensitive to the initial velocity. Weak oscillations and a plateau at intermediate times originate to a greater extent from the high velocity tail of the Maxwell-Boltzmann velocity distribution. Simple approximate analytic expressions for the mean square displacement and the self Van Hove correlation function are also derived.