Jump Diffusion Coefficients Research Articles

Capturing Hydrated Vanadium Ion Dynamics in Ionomer Nanocomposites Used for Redox Flow Batteries.

Herein, we employed high-flux backscattering spectroscopy to capture for the first time the motions of hydrated vanadyl ions in ionomer nanocomposites prepared by both solution-cast and in situ sol-gel condensation methods. Both local and jump diffusion coefficients of the hydrated vanadyl (VO2+) ions as well as the dynamic length scales of ion motions and the fraction of immobile hydrogen atoms were extracted from the scattering spectra. Notably, for solution-cast membranes, the jump and local diffusion coefficients of hydrated VO2+ ions were seen to decrease by over 10- and 4-fold, respectively, with the introduction of 10 mass % silica nanoparticles (SiNPs) compared to their neat counterparts. Further, the VO2+ diffusion coefficients were observed to decrease with thermal annealing, though the impact of annealing was less significant than that seen with the introduction of SiNPs. Finally, in general, thermal annealing and the introduction of SiNPs had no measurable impact on the fraction of immobile hydrogen atoms in both solution-cast and sol-gel ionomer nanocomposites. The data observed in this work, in conjunction with previous structural and chain dynamics studies on hydrated Nafion-SiNP nanocomposites, suggest that a combination of stiffening of the segmental dynamics as well as a decrease in available sulfonic acid groups facilitating transport leads to an overall decrease in mobility of vanadium ions in these ionomer nanocomposites.

Wasserstein distance estimates for jump-diffusion processes

We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps (Xt)t∈[0,T] and a jump-diffusion process (Xt∗)t∈[0,T]. Our bounds are expressed using the stochastic characteristics of (Xt)t∈[0,T] and the jump-diffusion coefficients of (Xt∗)t∈[0,T] evaluated in Xt, and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and Lp integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation.

Well-posedness and order preservation for neutral type stochastic differential equations of infinite delay with jumps

<abstract><p>In this work, we are concerned with the order preservation problem for multidimensional neutral type stochastic differential equations of infinite delay with jumps under non-Lipschitz conditions. By using a truncated Euler-Maruyama scheme and adopting an approximation argument, we have developed the well-posedness of solutions for a class of stochastic functional differential equations which allow the length of memory to be infinite, and the coefficients to be non-Lipschitz and even unbounded. Moreover, we have extended some existing conclusions on order preservation for stochastic systems to a more general case. A pair of examples have been constructed to demonstrate that the order preservation need not hold whenever the diffusion term contains a delay term, although the jump-diffusion coefficient could contain a delay term.</p></abstract>

Experimental and Modeling Studies of Local and Nanoscale para-Cresol Behavior: A Comparison of Classical Force Fields.

The dynamics of bulk liquid para-cresol from 340-390 K was probed using a tandem quasielastic neutron scattering (QENS) and molecular dynamics (MD) approach, due to its relevance as a simple model component of lignin pyrolysis oil. QENS experiments observed both translational jump diffusion and isotropic rotation, with diffusion coefficients ranging from 10.1 to 28.6 × 10-10 m2s-1 and rotational rates from 5.7 to 9.2 × 1010 s-1. The associated activation energies were 22.7 ± 0.6 and 10.1 ± 1.2 kJmol-1 for the two different dynamics. MD simulations applying two different force field models (OPLS3 and OPLS2005) gave values close to the experimental diffusion coefficients and rotational rates obtained upon calculating the incoherent dynamic structure factor from the simulations over the same time scale probed by the QENS spectrometer. The simulations gave resulting jump diffusion coefficients that were slower by factors of 2.0 and 3.8 and rates of rotation that were slower by factors of 1.2 and 1.6. Comparing the two force field sets, the OPLS3 model showed slower rates of dynamics likely due to a higher molecular polarity, leading to greater quantities and strengths of hydrogen bonding.

Uncovering the hydride ion diffusion pathway in barium hydride via neutron spectroscopy

Solid state materials possessing the ability for fast ionic diffusion of hydrogen have immense appeal for a wide range of energy-related applications. Ionic hydrogen transport research is dominated by proton conductors, but recently a few examples of hydride ion conductors have been observed as well. Barium hydride, BaH2, undergoes a structural phase transition around 775 K that leads to an order of magnitude increase in the ionic conductivity. This material provides a prototypical system to understand hydride ion diffusion and how the altered structure produced by the phase transition can have an enormous impact on the diffusion. We employ quasielastic and inelastic neutron scattering to probe the atomic scale diffusion mechanism and vibrational dynamics of hydride ions in both the low- and high-temperature phases. Jump lengths, residence times, diffusion coefficients, and activation energies are extracted and compared to the crystal structure to uncover the diffusion pathways. We find that the hydrogen jump distances, residence times, and energy barriers become reduced following the phase transition, allowing for the efficient conduction of hydride ions through a series of hydrogen jumps of length L = 3.1 Å.

Translational Jump-Diffusion of Hydroxide Ion in Anion Exchange Membrane: Deciphering the Nature of Vehicular Diffusion.

Earlier, ab initio and reactive force-field-based molecular dynamics (MD) simulation studies suggested an overwhelming contribution of the vehicular diffusion in the total diffusion of hydroxide ions rather than structural diffusion. But does the vehicular diffusion occur via small-step displacement? This question is important to have an understanding of the real characteristics of vehicular diffusion. To answer this question, we perform a classical molecular dynamics simulation of a system containing a hydroxide ion exchange membrane polymer and hydroxide ion at different hydration levels and temperatures using the same molecular force field (Dubey, V. Chem. Phys. Lett. 2020, 755, 137802), which successfully captured the microscopic structure and dynamics of the system. We use the translational jump-diffusion approach, used previously in supercooled water for understanding the origin of breakdown of the Stokes-Einstein relation, to calculate the jump-diffusion coefficient of hydroxide ion and water in the anion exchange membrane. We have seen a significant role of hydration level and temperature in the mechanism of vehicular diffusion. In overhydrated membrane, both hydroxide ions and water molecules diffuse via both small- and large-step displacement. With decreasing hydration level and temperature, the diffusion is increasingly governed by the jump-diffusion mechanism. The larger contribution of jump-diffusion comes from the stronger caging of the diffusing species by the solvent at lower hydration levels and temperature. These results, therefore, suggest that the hydration level and temperature of the hydroxide ion exchange membrane determine the detailed mechanism of the vehicular diffusion of hydroxide ion, especially whether the diffusion follows hydrodynamics or not.

Molecular Dynamics of Lysozyme Amyloid Polymorphs Studied by Incoherent Neutron Scattering.

Lysozyme amyloidosis is a hereditary disease, which is characterized by the deposition of lysozyme amyloid fibrils in various internal organs. It is known that lysozyme fibrils show polymorphism and that polymorphs formed at near-neutral pH have the ability to promote more monomer binding than those formed at acidic pH, indicating that only specific polymorphs become dominant species in a given environment. This is likely due to the polymorph-specific configurational diffusion. Understanding the possible differences in dynamical behavior between the polymorphs is thus crucial to deepen our knowledge of amyloid polymorphism and eventually elucidate the molecular mechanism of lysozyme amyloidosis. In this study, molecular dynamics at sub-nanosecond timescale of two kinds of polymorphic fibrils of hen egg white lysozyme, which has long been used as a model of human lysozyme, formed at pH 2.7 (LP27) and pH 6.0 (LP60) was investigated using elastic incoherent neutron scattering (EINS) and quasi-elastic neutron scattering (QENS). Analysis of the EINS data showed that whereas the mean square displacement of atomic motions is similar for both LP27 and LP60, LP60 contains a larger fraction of atoms moving with larger amplitudes than LP27, indicating that the dynamical difference between the two polymorphs lies not in the averaged amplitude, but in the distribution of the amplitudes. Furthermore, analysis of the QENS data showed that the jump diffusion coefficient of atoms is larger for LP60, suggesting that the atoms of LP60 undergo faster diffusive motions than those of LP27. This study thus characterizes the dynamics of the two lysozyme polymorphs and reveals that the molecular dynamics of LP60 is enhanced compared with that of LP27. The higher molecular flexibility of the polymorph would permit to adjust its conformation more quickly than its counterpart, facilitating monomer binding.

Transport properties of lattice fluid with SALR-potential on a simple square lattice

The transport properties of the lattice fluid with the attraction interaction between the nearest and repulsion interaction between the next-next-nearest neighbours on the square lattice are investigated. Computer simulation by the Monte Carlo method of the diffusion process in the specified system has been realised. The jump and tracer diffusion coefficients were determined. The dependence of the diffusion coefficients versus the concentration of adparticles and the interaction parameter of the model is investigated. The activation energy of jump and tracer diffusion determined. The possibility of estimating the jump diffusion coefficient of the lattice fluid with competing interactions using the Zhdanov’s relation on the base of information on the equilibrium properties of the system and the diffusion coefficient of a Langmuir (non-interacting) lattice gas is shown. In the future, it is planned to use the obtained results to study transport processes in 3D lattice systems which is suitable for describing the processes of mass or charge transfer in the volumes of solids.

Understanding the Origin of the Breakdown of the Stokes-Einstein Relation in Supercooled Water at Different Temperature-Pressure Conditions.

A recent experiment has measured the viscosity of water down to approximately 244 K and up to 300 MPa. The correct viscosity and translational diffusivity data at various temperature-pressure (T-P) state points allowed for checking the validity of the Stokes-Einstein (SE) relation, which accounts for the coupling between translational self-diffusion and medium viscosity. The diffusion-viscosity decoupling increases with decreasing temperature, but the increasing pressure reduces the extent of the decoupling. Earlier simulation studies explained the breakdown of the SE relation in terms of the location of the Widom line, emanating from the liquid-liquid critical point (LLCP). Although these studies made a significant contribution to the current understanding of the above phenomena, a detailed molecular picture is still lacking. Recently, our group has explained the diffusion-viscosity decoupling from a jump-diffusion perspective. The jump-diffusion coefficient, emanating from the jump translation of water molecules, is calculated using a quantitative approach for different temperatures at ambient pressure. It has been observed that jump-diffusion is the key factor for diffusion-viscosity decoupling in supercooled water. The same method is adopted in the present work to estimate the jump-diffusion coefficient for different T-P state points and, thereby, explains the role of jump-diffusion for the different extents of the SE relation breakdown at different pressures. The residual diffusion coefficient, the other component of the total diffusion that originates from small step displacement and that is calculated by subtracting the jump-diffusion coefficient from the total diffusion, is seen to be fairly coupled to the viscosity at the entire range of temperature and pressure. Furthermore, we have calculated the average number of H-bonds per water molecule and the tetrahedral order for different T-P state points and investigated an approximate correlation between the average local structure and the contribution of the jump-diffusion to the total diffusion of water. This study, therefore, puts forward a new perspective for explaining the SE relation breakdown in supercooled water under different pressure conditions.

Strong convergence of compensated split-step theta methods for SDEs with jumps under monotone condition

This paper is concerned with strong convergence of the compensated split-step theta (CSST) method for autonomous stochastic differential equations (SDEs) with jumps under weaker conditions. More precisely, the diffusion coefficient and the drift coefficient are both locally Lipschitz and the jump-diffusion coefficient is globally Lipschitz, while they all satisfy the monotone condition. It is proved that the CSST method is strongly convergent of order 12. Finally, the obtained results are supported by numerical experiments.

A Study of Elliptic Partial Differential Equations with Jump Diffusion Coefficients

As a simplified model for subsurface flows, elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts f...

Effect of particle-hole symmetry on the behavior of tracer and jump diffusion coefficients

This paper analyzes the effect of particle-hole symmetry on the behavior of the tracer diffusion coefficient as well as the jump diffusion coefficient. The coefficients are obtained by performing a random walk of individual atoms in a two-dimensional square lattice at monolayer, using the n-fold way Monte Carlo simulation. Different hopping mechanisms have been introduced to study the effect of particle-hole symmetry. For hopping kinetics where the initial-state interactions are involved, the diffusion coefficient at high coverage falls several orders of magnitude due to the effect of particle-hole symmetry. For hopping kinetics where the final-state interactions are present, the effect is the opposite. For those involving both initial- and final-state interactions, like the so-called interaction kinetics, the effect of particle-hole symmetry is also discussed. This effect seems to be critical for repulsive lateral interactions, for which the behavior of the diffusion coefficients is modified by introducing the particle-hole symmetry condition.

Rigorous Results on Surface Diffusion Coefficients Near a First-Order Phase Transition

We present a microscopic statistical–mechanical approach from which the chemical surface diffusion coefficient can be obtained in the local equilibrium limit, assuming that the system of a finite size undergoes a first-order phase transition between two phases. We also show the behavior of the jump diffusion coefficient and thermodynamic factor near such a transition. Explicit formulas for the dependences of these quantities on the chemical potential, coverage, and size of the system are presented. The general results are applied to a simple two-dimensional lattice model on a regular triangular lattice.

Comparison Theorem for Stochastic Differential Delay Equations with Jumps

In this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function although the jump-diffusion coefficient could contain a delay function. Moreover, another example is established to show that the comparison theorem is not necessary to be true provided that the jump-diffusion term is non-increasing with respect to the delay variable.

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.

Proton dynamics of CsH 2PO 4 studied by quasi-elastic neutron scattering and PFG-NMR

To illuminate ionic conduction behavior of super protonic phase of CsH 2PO 4 (CDP), quasi-elastic neutron scattering (QENS), pulse field gradient nuclear magnetic resonance (PFG-NMR) and 1H NMR spin-lattice relaxation time ( T 1) measurements were carried out. Diffusion coefficient of protons obtained from PFG-NMR reproduced well the electrical conductivity by using Nernst–Einstein equation. Comparison of PFG-NMR and T 1 provided a hopping distance of protons as 2.7 Å, which agreed with the next nearest proton sites in CDP. On the other hand, QENS data was fitted well with a jump-diffusion model. Comparison of the jump diffusion coefficient and the correlation time obtained by QENS provided a librational correlation time of protons in the order of 10 − 12 s. The present investigation suggests that different techniques, QENS and NMR, can observe protonic motions having different time constants including librational and translational motions within the hydrogen bonding network of CDP.

Modeling diffusion on heterogeneous lattices: honeycomb lattice

We investigate diffusion of particles adsorbed on a heterogeneous honeycomb lattice withtwo kinds of non-equivalent sites. General analytical expressions for the chemical and jumpdiffusion coefficients have been derived in the case of strong inhomogeneity. It is shown thatthe character of the particle migration depends crucially on the relative jumpfrequencies of particles occupying deep and shallow sites. In the case of widelydiffering jump frequencies, particles perform pairs of strongly correlated jumps.We have calculated coverage dependencies of the diffusion coefficients and somethermodynamic quantities for attractive and repulsive lateral pairwise interactions andcompared them with the results of the kinetic Monte Carlo simulations of the particlediffusion. Almost perfect agreement between the respective results has been found.

Diffusion characteristics of particles on energetically disordered lattices

The barrier model with random distribution of barrier energies is considered at nonzero particle concentrations. The statistical mechanics expressions for the jump diffusion coefficient that takes into account interparticle interactions are derived for dynamic and static disorder. For the former case the analytical expression for the barrier energy contribution is calculated, while for the latter case the limiting low and high temperature contributions are obtained. The derived expressions are tested by Monte Carlo simulations for uniform and exponential barrier energy distributions for one- and square, triangular and honeycomb two-dimensional lattices.

Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states

The carrier transport properties in nanocrystalline semiconductors and organic materials play a key role for modern organic/inorganic devices such as dye-sensitized (DSC) and organic solar cells, organic and hybrid light-emitting diodes (OLEDs), organic field-effect transistors, and electrochemical sensors and displays. Carrier transport in these materials usually occurs by transitions in a broad distribution of localized states. As a result the transport is dominated by thermal activation to a band of extended states (multiple trapping), or if these do not exist, by hopping via localized states. We provide a general view of the physical interpretation of the variations of carrier transport coefficients (diffusion coefficient and mobility) with respect to the carrier concentration, or Fermi level, examining in detail models for carrier transport in nanocrystalline semiconductors and organic materials with the following distributions: single and two-level systems, exponential and Gaussian density of states. We treat both the multiple trapping models and the hopping model in the transport energy approximation. The analysis is simplified by thermodynamic properties: the chemical capacitance, C(mu), and the thermodynamic factor, chi(n), that allow us to derive many properties of the chemical diffusion coefficient, D(n), used in Fick's law. The formulation of the generalized Einstein relation for the mobility to diffusion ratio shows that the carrier mobility is proportional to the jump diffusion coefficient, D(J), that is derived from single particle random walk. Characteristic experimental data for nanocrystalline TiO(2) in DSC and electrochemically doped conducting polymers are discussed in the light of these models.

Modeling diffusion on heterogeneous lattices: Simple cubic lattice

In our previous work, general analytical expressions for the chemical and jump diffusion coefficients have been derived in the case of strong inhomogeneity for lattices of different symmetries and dimensionalities. It has been shown that the character of the particle migration depends crucially on the relative jump frequencies of particles located in deep and shallow sites. If these frequencies differ insignificantly, particle diffusion proceeds by single uncorrelated jumps, while widely differing jump frequencies result in pairs of strongly correlated jumps. We have checked the expressions for the case of square inhomogeneous lattice using kinetic Monte Carlo simulations. Here, we present results of particle migration over three-dimensional inhomogeneous simple cubic lattice. The density dependences obtained by the analytical expressions for different temperatures and signs of the lateral pairwise interaction are compared with the results of the direct kinetic Monte Carlo simulations of the particle diffusion. Almost perfect agreement between the respective results has been found.