Single-particle Dynamics Research Articles

Tracing Experimentally Compatible Dynamical and Structural Behavior of Atmospheric N2/O2 Binary Mixtures within Nanoporous Li–LSX Zeolite: New Insights to Influence of Extra-Framework Cations by MD Simulations

Along with available adsorption isotherms and uptake kinetic data, microscopic knowledge of the guest self-diffusion and intracrystalline movement of the simple air binary mixture of nitrogen (N2) and oxygen (O2) within Li–LSX zeolite is needed to optimize the design and to reach a breakthrough high-efficiency of air separation process based on the selective adsorption in this zeolite. In the current work for the first time, an all-atom molecular dynamics (MD) simulation is used to study the average single-particle dynamics, self-diffusion, and microscopic structure of the atmospheric binary gaseous mixtures of N2 and O2 in Li–LSX zeolite at temperatures between (260 and 700) K. The common order of magnitude of the computed guest self-diffusion coefficients at different temperatures is in the range of 10–9 - 10–8 m2·s–1 and corresponding activation energies obtained using the Arrhenius equation varied in the range of ∼0.6 for O2 to 1.6–3.3 kcal·mol–1 for N2 in simulations with mobile and with fixed extra-...

Single-particle dynamics near the glass transition of a metallic glass.

The single-particle dynamics of the glass-forming Cu_{50}Zr_{50} alloy, from the supercooled liquid well above the glass-transition temperature, T_{g} to the glassy state, is studied by using the molecular dynamics simulations. When the liquid is cooled below 1.2T_{g}, the dynamics heterogeneity characterized by the cage-jump motion becomes increasingly pronounced. The analyses based on the continuous time random walk method indicate that the liquid falls out of equilibrium in the present simulation time scale when it is cooled into the regime below 1.02T_{g}. However, we find that the jump length and the jump rate do not display the non-equilibrium behaviors even in the glassy state below T_{g}, which allows us to study the intrinsic dynamic characteristics through T_{g}. The mean waiting time between two successive jumps has a rapid growth following the Vogel-Fulcher-Tammann law as the non-equilibrium regime is approached, in analogy with the temperature behaviors of transport properties for fragile supercooled liquids. In contrast, the jump rate maintains the Arrhenius decay and the jump length has even a weaker temperature dependence when the liquid is cooled into glassy state. We find that a pronounced enhancement of the spatial correlation of jumps occurs accompanied by the glass transition: the string-like cooperative jumps dominate the fast motion instead of the uncorrelated and individual jumps. Our work offers an insight into the equilibrium effect of the single-particle dynamics in glass transition.

Lifting of the Vlasov–Maxwell bracket by Lie-transform method

The Vlasov–Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation (‘lift’) of the Vlasov–Maxwell bracket induced by the dynamical reduction of single-particle dynamics is investigated when the reduction is carried out by Lie-transform perturbation methods. The ultimate goal of this work is to provide an explicit pathway to the Hamiltonian formulations for the guiding-centre and gyrokinetic Vlasov–Maxwell equations, which have found important applications in our understanding of turbulent magnetized plasmas. Here, it is shown that the general form of the reduced Vlasov–Maxwell equations possesses a Hamiltonian structure defined in terms of a reduced Hamiltonian functional and a reduced bracket that automatically satisfies the standard bracket properties.

Molecular dynamics analysis of the effect of electronic polarization on the structure and single-particle dynamics of mixtures of ionic liquids and lithium salts.

We report a molecular dynamics study on the effect of electronic polarization on the structure and single-particle dynamics of mixtures of the aprotic ionic liquid 1-ethyl-3-methylimidazolium bis-(trifluoromethylsulfonyl)-imide ([EMIM][TFSI]) doped with a lithium salt with the same anion at 298 K and 1 bar. In particular, we analyze the effect of electron density fluctuations on radial distribution functions, velocity autocorrelation functions, cage correlation functions, mean-squared displacements, and vibrational densities of states, comparing the predictions of the quantum-chemistry-based Atomistic Polarizable Potential for Liquids, Electrolytes, & Polymers (APPLE&P) with those of its nonpolarizable version and those of the standard non-polarizable Optimized Potentials for Liquid Simulations-All Atom (OPLS-AA). We found that the structure of the mixture is scarcely modified by the fluctuations in electron charge of their constituents, but their transport properties are indeed quite drastically changed, with larger mobilities being predicted for the different species in the bulk mixtures with the polarizable force field. Specifically, the mean-squared displacements are larger for the polarizable potentials at identical time intervals and the intermediate subdiffusive plateaus are greatly reduced, so the transition to the diffusive regime takes place much earlier than in the non-polarizable media. Moreover, the correlations of the added cations inside their cages are weakened out earlier and their vibrational densities of states are slightly red-shifted, reflecting the weakening effect of the electronic polarization on the Coulomb coupling in these dense ionic media. The comparison of OPLS-AA with non-polarizable APPLE&P indicates that adding polarization to OPLS-AA is not sufficient to achieve results close to experiments.

Chirped resonance dynamics in phase space

The dynamics of passage and capture into resonance of a distribution of particles driven by a chirped frequency perturbation is discussed. The resonant capture in this case involves crossing of the separatrix by individual particles and, therefore, the adiabatic theorem cannot be used in studying this problem no matter how slow the variation of the driving frequency is. It is shown that, if instead of analysing complicated single particle dynamics in passage through resonance, one considers the slow evolution of a whole distribution of initial conditions in phase space, the adiabaticity and phase space incompressibility arguments yield a solution to the resonant passage problem. This approach is illustrated in the case of an ensemble of electrons driven by a chirped frequency wave passing through Cherenkov resonances with the velocity distribution of electrons.

Mott transitions in the periodic Anderson model

The periodic Anderson model (PAM) is studied within the framework of dynamical mean-field theory, with particular emphasis on the interaction-driven Mott transition it contains, and on resultant Mott insulators of both Mott–Hubbard and charge-transfer type. The form of the PAM phase diagram is first deduced on general grounds using two exact results, over the full range of model parameters and including metallic, Mott, Kondo and band insulator phases. The effective low-energy model which describes the PAM in the vicinity of a Mott transition is then shown to be a one-band Hubbard model, with effective hoppings that are not in general solely nearest neighbour, but decay exponentially with distance. This mapping is shown to have a range of implications for the physics of the problem, from phase boundaries to single-particle dynamics; all of which are confirmed and supplemented by NRG calculations. Finally we consider the locally degenerate, non-Fermi liquid Mott insulator, to describe which requires a two-self-energy description. This is shown to yield a number of exact results for the associated local moment, charge, and interaction-renormalised levels, together with a generalisation of Luttinger’s theorem to the Mott insulator.

Fluids by design using chaotic surface waves to create a metafluid that is Newtonian, thermal, and entirely tunable

In conventional fluids, viscosity depends on temperature according to a strict relationship. To change this relationship, one must change the molecular nature of the fluid. Here, we create a metafluid whose properties are derived not from the properties of molecules but rather from chaotic waves excited on the surface of vertically agitated water. By making direct rheological measurements of the flow properties of our metafluid, we show that it has independently tunable viscosity and temperature, a quality that no conventional fluid possesses. We go on to show that the metafluid obeys the Einstein relation, which relates many-body response (viscosity) to single-particle dynamics (diffusion) and is a fundamental result in equilibrium thermal systems. Thus, our metafluid is wholly consistent with equilibrium thermal physics, despite being markedly nonequilibrium. Taken together, our results demonstrate a type of material that retains equilibrium physics while simultaneously allowing for direct programmatic control over material properties.

First-principles investigation of cubicBaRuO3: A Hund's metal

A first-principles investigation of cubic-BaRuO$_3$, by combining density functional theory with dynamical mean-field theory and a hybridization expansion continuous time quantum Monte-Carlo solver, has been carried out. Non-magnetic calculations with appropriately chosen on-site Coulomb repulsion, $U$ and Hund's exchange, $J$, for single-particle dynamics and static susceptibility show that cubic-BaRuO$_3$ is in a spin-frozen state at temperatures above the ferromagnetic transition point. A strong red shift with increasing $J$ of the peak in the real frequency dynamical susceptibility indicates a dramatic suppression of the Fermi liquid coherence scale as compared to the bare parameters in cubic-BaRuO$_3$. The self-energy also shows clear deviation from Fermi liquid behaviour that manifests in the single-particle spectrum. Such a clean separation of energy scales in this system provides scope for an incoherent spin-frozen (SF) phase, that extends over a wide temperature range, to manifest in non-Fermi liquid behaviour and to be the precursor for the magnetically ordered ground state.

Two structural relaxations in protein hydration water and their dynamic crossovers.

We study the translational single particle dynamics of hydration water of lysozyme upon cooling by means of molecular dynamics simulations. We find that water close to the protein exhibits two distinct relaxations. By characterizing their behavior upon cooling, we are able to assign the first relaxation to the structural α-relaxation also present in bulk water and in other glass-forming liquids. The second, slower, relaxation can be ascribed to a dynamic coupling of hydration water motions to the fluctuations of the protein structure. Both relaxation times exhibit crossovers in the behavior upon cooling. For the α-process, we find upon cooling a crossover from a fragile behavior to a strong behavior at a temperature which is about five degrees higher than that of bulk water. The long-relaxation time appears strictly connected to the protein motion as it shows upon cooling a temperature crossover from a strong behavior with a lower activation energy to a strong behavior with a higher activation energy. The crossover temperature coincides with the temperature of the protein dynamical transition. These findings can help experimentalists to disentangle the different information coming from total correlators and to better characterize hydration water relaxations in different biomolecules.

The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects

In Part 1 of this study (Ireland et al., J. Fluid Mech., vol. 796, 2016, pp. 617–658), we analysed the motion of inertial particles in isotropic turbulence in the absence of gravity using direct numerical simulation (DNS). Here, in Part 2, we introduce gravity and study its effect on single-particle and particle-pair dynamics over a wide range of flow Reynolds numbers, Froude numbers and particle Stokes numbers. The overall goal of this study is to explore the mechanisms affecting particle collisions, and to thereby improve our understanding of droplet interactions in atmospheric clouds. We find that the dynamics of heavy particles falling under gravity can be artificially influenced by the finite domain size and the periodic boundary conditions, and we therefore perform our simulations on larger domains to reduce these effects. We first study single-particle statistics that influence the relative positions and velocities of inertial particles. We see that gravity causes particles to sample the flow more uniformly and reduces the time particles can spend interacting with the underlying turbulence. We also find that gravity tends to increase inertial particle accelerations, and we introduce a model to explain that effect. We then analyse the particle relative velocities and radial distribution functions (RDFs), which are generally seen to be independent of Reynolds number for low and moderate Kolmogorov-scale Stokes numbers $St$. We see that gravity causes particle relative velocities to decrease by reducing the degree of preferential sampling and the importance of path-history interactions, and that the relative velocities have higher scaling exponents with gravity. We observe that gravity has a non-trivial effect on clustering, acting to decrease clustering at low $St$ and to increase clustering at high $St$. By considering the effect of gravity on the clustering mechanisms described in the theory of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018), we provide an explanation for this non-trivial effect of gravity. We also show that when the effects of gravity are accounted for in the theory of Zaichik & Alipchenkov (2009), the results compare favourably with DNS. The relative velocities and RDFs exhibit considerable anisotropy at small separations, and this anisotropy is quantified using spherical harmonic functions. We use the relative velocities and the RDFs to compute the particle collision kernels, and find that the collision kernel remains as it was for the case without gravity, namely nearly independent of Reynolds number for low and moderate $St$. We conclude by discussing practical implications of the results for the cloud physics and turbulence communities and by suggesting possible avenues for future research.

Structure and collective dynamics of hydrated anti-freeze protein type III from 180 K to 298 K by X-ray diffraction and inelastic X-ray scattering.

We investigated hydrated antifreeze protein type III (AFP III) powder with a hydration level h (=mass of water/mass of protein) of 0.4 in the temperature range between 180 K and 298 K using X-ray diffraction and inelastic X-ray scattering (IXS). The X-ray diffraction data showed smooth, largely monotonic changes between 180 K and 298 K without freezing water. Meanwhile, the collective dynamics observed by IXS showed a strong change in the sound velocity at 180 K, after being largely temperature independent at higher temperatures (298-220 K). We interpret this change in terms of the dynamic transition previously discussed using other probes including THz IR absorption spectroscopy and incoherent elastic and quasi-elastic neutron scattering. This finding suggests that the dynamic transition of hydrated proteins is observable on the subpicosecond time scale as well as nano- and pico-second scales, both in collective dynamics from IXS and single particle dynamics from neutron scattering. Moreover, it is most likely that the dynamic transition of hydrated AFP III is not directly correlated with its hydration structure.

Linking density functional and mode coupling models for supercooled liquids.

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

Consequences of minimising pair correlations in fluids for dynamics, thermodynamics and structure

ABSTRACTLiquid-state theory, computer simulation and numerical optimisation are used to investigate the extent to which positional correlations of a hard-sphere fluid – as characterised by the radial distribution function and the two-particle excess entropy – can be suppressed via the introduction of auxiliary pair interactions. The corresponding effects of such interactions on total excess entropy, density fluctuations and single-particle dynamics are explored. Iso-g processes, whereby hard-sphere-fluid pair structure at a given density is preserved at higher densities via the introduction of a density-dependent, soft repulsive contribution to the pair potential, are considered. Such processes eventually terminate at a singular density, resulting in a state that – while incompressible and hyperuniform – remains unjammed and exhibits fluid-like dynamic properties. The extent to which static pair correlations can be suppressed to maximise pair disorder in a fluid with hard cores, determined via direct functional maximisation of two-body excess entropy, is also considered. Systems approaching a state of maximised two-body entropy display a progressively growing bandwidth of suppressed density fluctuations, pointing to a relation between ‘stealthiness’ and maximal pair disorder in materials.

Criticality and correlated dynamics at the irreversibility transition in periodically driven colloidal suspensions

One possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving force. We consider a simple numerical model for driven suspensions which allows us to characterize in great detail a large body of physical observables that can be experimentally determined to assess the existence and universality class of such a non-equilibrium phase transition. Characterizing the behaviour of static and dynamic correlation functions both in real and Fourier space we determine in particular several critical exponents for our model, which take values that are in good agreement with the universality class of directed percolation. We also provide a detailed analysis of single-particle and collective dynamics of the system near the phase transition, which appear intermittent and spatially correlated over diverging timescales and lengthscales, and provide clear signatures of the underlying criticality.

Driven Liouville von Neumann Equation in Lindblad Form.

The Driven Liouville von Neumann approach [J.Chem. Theory Comput. 2014, 10, 2927-2941] is a computationally efficient simulation method for modeling electron dynamics in molecular electronics junctions. Previous numerical simulations have shown that the method can reproduce the exact single-particle dynamics while avoiding density matrix positivity violation found in previous implementations. In this study we prove that in the limit of infinite lead models the underlying equation of motion can be cast in Lindblad form. This provides a formal justification for the numerically observed density matrix positivity conservation.

A spectral canonical electrostatic algorithm

Studying single-particle dynamics over many periods of oscillations is a well-understood problem solved using symplectic integration. Such integration schemes derive their update sequence from an approximate Hamiltonian, guaranteeing that the geometric structure of the underlying problem is preserved. Simulating a self-consistent system over many oscillations can introduce numerical artifacts such as grid heating. This unphysical heating stems from using non-symplectic methods on Hamiltonian systems. With this guidance, we derive an electrostatic algorithm using a discrete form of Hamilton’s principle. The resulting algorithm, a gridless spectral electrostatic macroparticle model, does not exhibit the unphysical heating typical of most particle-in-cell methods. We present results of this using a two-body problem as an example of the algorithm’s energy- and momentum-conserving properties.

Qualitatively different collective and single-particle dynamics in a supercooled liquid.

The equations of fluctuating nonlinear hydrodynamics for a two component mixture are obtained with a proper choice of slow variables which correspond to the conservation laws in the system. Using these nonlinear equations we construct the basic equations of the mode coupling theory (MCT) and consequent ergodic-nonergodic (ENE) transition in a binary mixture. The model is also analyzed in the one component limit of the mixture to study the dynamics of a tagged particle in the sea of identical particles. According to the existing MCT, dynamics of the single-particle correlation is slaved to that of the collective density fluctuations and, hence, both correlations freeze simultaneously at the ENE transition. We show here from a nonperturbative approach that at the ENE transition, characterized by the freezing of the long time limit of the dynamic correlation of collective density fluctuations to a nonzero value, the tagged-particle correlation still decays to zero. Our result implies that the point at which simulation or experimental data of the self-diffusion constant extrapolate to zero would not correspond to the ENE transition of simple MCT.

Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model

The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger’s theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.

Free volume under shear.

Using an athermal quasistatic simulation protocol, we study the distribution of free volumes in sheared hard-particle packings close to, but below, the random-close packing threshold. We show that under shear, and independent of volume fraction, the free volumes develop features similar to close-packed systems - particles self-organize in a manner as to mimick the isotropically jammed state. We compare athermally sheared packings with thermalized packings and show that thermalization leads to an erasure of these structural features. The temporal evolution in particular the opening-up and the closing of free-volume patches is associated with the single-particle dynamics, showing a crossover from ballistic to diffusive behavior.

Molecular dynamics simulations of the structure and single-particle dynamics of mixtures of divalent salts and ionic liquids.

We report a molecular dynamics study of the structure and single-particle dynamics of mixtures of a protic (ethylammonium nitrate) and an aprotic (1-butyl-3-methylimidazolium hexaflurophosphate [BMIM][PF6]) room-temperature ionic liquids doped with magnesium and calcium salts with a common anion at 298.15 K and 1 atm. The solvation of these divalent cations in dense ionic environments is analyzed by means of apparent molar volumes of the mixtures, radial distribution functions, and coordination numbers. For the protic mixtures, the effect of salt concentration on the network of hydrogen bonds is also considered. Moreover, single-particle dynamics of the salt cations is studied by means of their velocity autocorrelation functions and vibrational densities of states, explicitly analyzing the influence of salt concentration, and cation charge and mass on these magnitudes. The effect of the valency of the salt cation on these properties is considered comparing the results with those for the corresponding mixtures with lithium salts. We found that the main structural and dynamic features of the local solvation of divalent cations in ionic liquids are similar to those of monovalent salts, with cations being localized in the polar nanoregions of the bulk mixture coordinated in monodentate and bidentate coordination modes by the [NO3](-) and [PF6](-) anions. However, stronger electrostatic correlations of these polar nanoregions than in mixtures with salts with monovalent cations are found. The vibrational modes of the ionic liquid (IL) are seen to be scarcely affected by the addition of the salt, and the effect of mass and charge on the vibrational densities of states of the dissolved cations is reported. Cation mass is seen to exert a deeper influence than charge on the low-frequency vibrational spectra, giving a red shift of the vibrational modes and a virtual suppression of the higher energy vibrational modes for the heavier Ca(2+) cations. No qualitative difference with monovalent cations was found in what solvation is concerned, which suggests that no enhanced reduction of the mobility of these cations and their complexes in ILs respective to those of monovalent cations is to be expected.