Macroscopic Transport Coefficients Research Articles

Generation and optimization of cross-sections for electron-C4F7N collisions

Abstract A complete and consistent set of electron-neutral collision cross-sections for the novel insulating gas C4F7N is reported. The set is composed of a combination of cross-sections previously reported in literature, optimized via a genetic algorithm in conjunction with a multi-term Boltzmann equation solver, and calculated ab initio using the R-matrix code Quantemol-EC. The finalized set accurately reproduces reported macroscopic rate and transport coefficients as well as Townsend coefficients and critical electric field strengths in C4F7N and its mixtures with nitrogen, carbon dioxide, and argon.

Pre-asymptotic dispersion of active particles through a vertical pipe: the origin of hydrodynamic focusing

When motile algal cells are exposed to gyrotactic torques, their swimming directions are guided to form radial accumulation, well known as hydrodynamic focusing. The origin of hydrodynamic focusing from the effects of active swimming, ambient flow and particle anisotropy is elucidated in the present study on the pre-asymptotic dispersion of active particles through a vertical pipe. With an extension of the Galerkin method to pipe flows, time-dependent solutions directly from the Smoluchowski equation in the position and orientation space are derived by series expansions of spherical harmonics and Bessel functions. Ballistic and diffusive scaling laws are examined with the predominance of self-propelled swimming, and computation is validated against an explicit benchmark solution and Lagrangian particle simulation. In the limit of extreme shear, the competitive roles of shear dispersion and Brownian rotation are reflected concretely in the pre-asymptotic phase of hydrodynamic focusing. For flows with various shear strengths, a concentration peak in near-wall regions with a smooth transition to hydrodynamic focusing is illustrated with richer phenomena in upwelling and downwelling flows. A newly observed regime through a vertical pipe, named transient effective trapping, is revealed as a transitional mode towards hydrodynamic focusing. The pre-asymptotic approach to hydrodynamic focusing is elaborated intensively through extensive solutions of concentration moments and macroscopic transport coefficients characterised by swimming and flow Péclet numbers. The unique findings for the origin of hydrodynamic focusing could provide insight into related micro-algae reactor technology and contribute to flow control and biomass transfer in confined environments.

Normal-state charge transport in YBa2Cu3O6.67 under uniaxial stress

To provide a foundation for theoretical models of high-temperature superconductivity, experimental research has sought to establish correspondences between macroscopic transport coefficients on the one hand, and atomic-scale correlation functions measured by spectroscopic and scattering probes on the other hand. This research avenue has been confounded by the gradual onset of electronic ordering phenomena and of the corresponding transport anomalies. We report measurements of the uniaxial-stress dependence of the normal-state resistivity and Hall coefficient of the underdoped high-temperature superconductor YBa2Cu3O6.67. We observe a remarkable correspondence between the differential stress responses of the transport coefficients and resonant X-ray diffraction features indicative of charge ordering, which parallels the phenomenology of classical charge-density-wave compounds. However, our observations imply that static charge order is not responsible for a sign reversal of the Hall coefficient, and suggest that the interplay with liquid-like, dynamical charge correlations is essential for the prominent transport anomalies in the underdoped cuprates.

Nonequilibrium Green-Kubo relations for hydrodynamic transport from an equilibrium-like fluctuation-response equality

Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and fluctuations as embodied by the equilibrium fluctuation-dissipation theorem, a connection generically broken far from equilibrium. In this work, we identify a class of perturbations whose response around far-from-equilibrium steady states is linked to steady-state correlation functions via an equilibrium-like fluctuation-response equality. We then utilize this prediction to substantiate linearized hydrodynamic transport equations that describe how spatial inhomogeneities in macroscopic nonequilibrium systems relax. As a consequence, we derive nonequilibrium Green-Kubo relations for the transport coefficients of two types of hydrodynamic variables: local conserved densities and broken-symmetry modes. A byproduct of this work is to provide a theoretical foundation for the validity of Onsager's regression hypothesis around nonequilibrium steady states. Our predictions are analytically and numerically corroborated for two model systems: density diffusion in a fluid of soft, spherical active Brownian particles and phase diffusion in the noisy Kuramoto model on a square lattice.

Microscopic Model to Quantify the Difference of Energy-Transfer Rates between Bonded and Nonbonded Monomers in Polymers

Thermal transport properties often dictate the usefulness of materials in a variety of applications. In this context, polymers are an important material class because they provide different pathways of energy transport due to the distinct microscopic interactions, i.e., via stiff, covalently bonded backbone interactions or via soft, nonbonded interactions, such as van der Waals (vdW) forces and/or hydrogen bonds (H-bond). Therefore, the precise control of the delicate balance between bonded and nonbonded energy transfer rates provides a possible strategy to tailor the thermal conductivity of a material. In this work, we devise a simple analytical model that decouples the microscopic bonded, Gb, and nonbonded, Gnb, contributions to the heat transport in polymeric materials. This model considers the diffusion of energy along the macromolecular backbone, involving multiple transfers before it can hop off to a neighboring chain molecule. We show how these individual microscopic components can be combined to obtain a diffusive contribution to the macroscopic thermal transport coefficient, κ. The ability of the model to describe thermal transport is validated by molecular simulations of one universal polymer model and three, chemically specific, all-atom polymer models. These results suggest strategies for tailoring κ of polymeric materials by macromolecular engineering of molecular architecture and conformations.

Total-transmission and total-reflection of individual phonons in phononic crystal nanostructures

The control of thermal waves by the phononic crystal exhibits peculiar behaviors different from the particle picture of phonons and thus has attracted increasing interest. However, the wave nature of phonons is only indirectly reflected in most studies via the macroscopic thermal transport coefficient, such as thermal conductivity. In this work, we investigate directly the coherent interference effect in a graphene superlattice structure at the microscopic phonon mode level via wave-packet simulations. The constructive interference and destructive interference between the reflected phonons give rise to valleys and peaks in the transmission coefficient, respectively, leading to the periodic oscillation of the transmission function with the variation of the superlattice period length. More importantly, both total-transmission and total-reflection of individual phonons have been clearly demonstrated. The physical conditions for realizing the phonon interference have been proposed, which are quantitatively in good agreement with independent wave-packet simulations. Our study provides direct evidence for the coherent phonon interference effect, which might be helpful for the regulation of phonon transport based on its wave nature.

Ion transport in small-molecule and polymer electrolytes.

Solid-state polymer electrolytes and high-concentration liquid electrolytes, such as water-in-salt electrolytes and ionic liquids, are emerging materials to replace the flammable organic electrolytes widely used in industrial lithium-ion batteries. Extensive efforts have been made to understand the ion transport mechanisms and optimize the ion transport properties. This perspective reviews the current understanding of the ion transport and polymer dynamics in liquid and polymer electrolytes, comparing the similarities and differences in the two types of electrolytes. Combining recent experimental and theoretical findings, we attempt to connect and explain ion transport mechanisms in different types of small-molecule and polymer electrolytes from a theoretical perspective, linking the macroscopic transport coefficients to the microscopic, molecular properties such as the solvation environment of the ions, salt concentration, solvent/polymer molecular weight, ion pairing, and correlated ion motion. We emphasize universal features in the ion transport and polymer dynamics by highlighting the relevant time and length scales. Several outstanding questions and anticipated developments for electrolyte design are discussed, including the negative transference number, control of ion transport through precision synthesis, and development of predictive multiscale modeling approaches.

On the influence of boundary conditions when determining transport coefficients from digital images of heterogeneous media.

Sensitivity to the boundary conditions (BC’s) when determining macroscopic transport coefficients by numerical upscaling in finite domains is a well known methodological issue, explored here with the purpose of: quantifying the influence of the BC’s in relation with the parameters of the system (porosity, characteristic length scale, conductivity contrast); assessing the level of confidence associated with the predictions; devising criteria to anticipate the risk of serious artifacts, and proposing ways to limit them. The terminology of thermal transfer is used but the developments apply to any transport mechanism governed by a diffusion equation, including conduction, mass diffusion or Darcy flow. Quantitative indicators are defined for a rigorous individual or comparative assessment of conductivity tensors, and used in the analysis of extensive numerical data obtained in tomographic images and model materials, with a broad range of properties. Practical criteria are proposed for the a priori and a posteriori detection of at-risk situations, and a self-diagnosing protocol is proposed to screen out the BC’s influence, whenever possible.

Effect of local chemistry and structure on thermal transport in doped GaAs

Using a first-principles approach, we analyze the impact of \textit{DX} centers formed by S, Se, and Te dopant atoms on the thermal conductivity of GaAs. Our results are in good agreement with experiments and unveil the physics behind the drastically different effect of each kind of defect. We establish a causal chain linking the electronic structure of the dopants to the thermal conductivity of the bulk solid, a macroscopic transport coefficient. Specifically, the presence of lone pairs leads to the formation of structurally asymmetric \textit{DX} centers that cause resonant scattering of incident phonons. The effect of such resonances is magnified when they affect the part of the spectrum most relevant for thermal transport. We show that these resonances are associated with localized vibrational modes in the perturbed phonon spectrum. Finally, we illustrate the connection between flat adjacent minima in the energy landscape and resonant phonon scattering through detailed analyses of the energy landscape of the defective structures.

Role of short- and long-range ordering on diffusion in Ni-Al alloys

The varying degrees of short- and long-range order exhibited by multicomponent solids complicates a first-principles calculation of nondilute diffusion coefficients. Temporal and spatial variations in the local degree of order affect the migration barriers of individual hops and can result in strong correlations between successive hops that ultimately affect macroscopic transport coefficients. Here we report on a first-principles study of diffusion in Ni-rich Ni-Al alloys. We used cluster expansion Hamiltonians to describe the energies of the end states and migration barriers of each hop. Kinetic Monte Carlo simulations were performed to calculate macroscopic transport coefficients. Variations in the degree of ordering are shown to play a significant role in affecting diffusion coefficients. While Al has a higher mobility than Ni in the disordered Ni-rich fcc solid solution, it becomes significantly less mobile in the ordered $L{1}_{2}\phantom{\rule{4pt}{0ex}}{\ensuremath{\gamma}}^{\ensuremath{'}}$ phase due to strong thermodynamic tendencies that keep Al trapped to disconnected sublattice sites.

Exotic multifractal conductance fluctuations in graphene

In quantum systems, signatures of multifractality are rare. They have been found only in the multiscaling of eigenfunctions at critical points. Here we demonstrate multifractality in the magnetic field-induced universal conductance fluctuations of the conductance in a quantum condensed matter system, namely, high-mobility single-layer graphene field-effect transistors. This multifractality decreases as the temperature increases or as doping moves the system away from the Dirac point. Our measurements and analysis present evidence for an incipient Anderson-localization near the Dirac point as the most plausible cause for this multifractality. Our experiments suggest that multifractality in the scaling behavior of local eigenfunctions are reflected in macroscopic transport coefficients. We conjecture that an incipient Anderson-localization transition may be the origin of this multifractality. It is possible that multifractality is ubiquitous in transport properties of low-dimensional systems. Indeed, our work suggests that we should look for multifractality in transport in other low-dimensional quantum condensed-matter systems.

Fission observables from 4D Langevin calculations with macroscopic transport coefficients

We have extended the Langevin equations to 4 dimensions (4D) by allowing the independent deformation for the left (δ1) and right fragments (δ2) of the fissioning nucleus. At the moment we are only able to use them in conjunction with the macroscopic transport coefficients. Nevertheless, we can see a considerable improvement in the preliminary results for the fission observables, especially those related to the total kinetic energy (TKE) of fission fragments. By plotting the TKE distributions we have revealed the super-long fission modes in236U and super-short fission modes in257Fm. By plotting the distribution ofδagainst the fragment’s TKE we have noted a correlation between the values ofδand Brosa’s fission modes. We have found that the standard fission modes correspond to prolate tips of the light fragments while the complementary heavy fragments have oblate fission tips. On the other hand, if both fragments were prolate at the tips, we get super-long fission modes. If both fragments were oblate at the tips, we get super-short fission modes.

Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study.

Ionic transport in solid electrolytes can often be approximated as ions performing a sequence of hops between distinct lattice sites. If these hops are uncorrelated, quantitative relationships can be derived that connect microscopic hopping rates to macroscopic transport coefficients; i.e. tracer diffusion coefficients and ionic conductivities. In real materials, hops are uncorrelated only in the dilute limit. At non-dilute concentrations, the relationships between hopping frequency, diffusion coefficient and ionic conductivity deviate from the random walk case, with this deviation quantified by single-particle and collective correlation factors, f and fI, respectively. These factors vary between materials, and depend on the concentration of mobile particles, the nature of the interactions, and the host lattice geometry. Here, we study these correlation effects for the garnet lattice using lattice-gas Monte Carlo simulations. We find that, for non-interacting particles (volume exclusion only), single-particle correlation effects are more significant than for any previously studied three-dimensional lattice. This is attributed to the presence of two-coordinate lattice sites, which causes correlation effects intermediate between typical three-dimensional and one-dimensional lattices. Including nearest-neighbour repulsion and on-site energies produces more complex single-particle correlations and introduces collective correlations. We predict particularly strong correlation effects at xLi=3 (from site energies) and xLi=6 (from nearest-neighbour repulsion), where xLi=9 corresponds to a fully occupied lithium sublattice. Both effects are consequences of ordering of the mobile particles. Using these simulation data, we consider tuning the mobile-ion stoichiometry to maximize the ionic conductivity, and show that the ‘optimal’ composition is highly sensitive to the precise nature and strength of the microscopic interactions. Finally, we discuss the practical implications of these results in the context of lithium garnets and other solid electrolytes.

Rayleigh–Brillouin light scattering spectroscopy of nitrous oxide (N2O)

High signal-to-noise and high-resolution light scattering spectra are measured for nitrous oxide (N2O) gas at an incident wavelength of 403.00 nm, at 90° scattering, at room temperature and at gas pressures in the range 0.5−4 bar. The resulting Rayleigh–Brillouin light scattering spectra are compared to a number of models describing in an approximate manner the collisional dynamics and energy transfer in this gaseous medium of this polyatomic molecular species. The Tenti-S6 model, based on macroscopic gas transport coefficients, reproduces the scattering profiles in the entire pressure range at less than 2% deviation at a similar level as does the alternative kinetic Grad’s 6-moment model, which is based on the internal collisional relaxation as a decisive parameter. A hydrodynamic model fails to reproduce experimental spectra for the low pressures of 0.5-1 bar, but yields very good agreement ( < 1%) in the pressure range 2−4 bar. While these three models have a different physical basis the internal molecular relaxation derived can for all three be described in terms of a bulk viscosity of ηb∼(6±2)×10−5 Pa · s. A ‘rough-sphere’ model, previously shown to be effective to describe light scattering in SF6 gas, is not found to be suitable, likely in view of the non-sphericity and asymmetry of the N-N-O structured linear polyatomic molecule.

Symmetry properties of macroscopic transport coefficients in porous media

We report on symmetry properties of tensorial effective transport coefficients characteristic of many transport phenomena in porous systems at the macroscopic scale. The effective coefficients in the macroscopic models (derived by upscaling (volume averaging) the governing equations at the underlying scale) are obtained from the solution of closure problems that allow passing the information from the lower to the upper scale. The symmetry properties of the macroscopic coefficients are identified from a formal analysis of the closure problems and this is illustrated for several different physical mechanisms, namely, one-phase flow in homogeneous porous media involving inertial effects, slip flow in the creeping regime, momentum transport in a fracture relying on the Reynolds model including slip effects, single-phase flow in heterogeneous porous media embedding a porous matrix and a clear fluid region, two-phase momentum transport in homogeneous porous media, as well as dispersive heat and mass transport. The results from the analysis of these study cases are summarized as follows. For inertial single-phase flow, the apparent permeability tensor is irreducibly decomposed into its symmetric (viscous) and skew-symmetric (inertial) parts; for creeping slip-flow, the apparent permeability tensor is not symmetric; for one-phase slightly compressible gas flow in the slip regime within a fracture, the effective transmissivity tensor is symmetric, a result that remains valid in the absence of slip; for creeping one-phase flow in heterogeneous media, the permeability tensor is symmetric; for two-phase flow, we found the dominant permeability tensors to be symmetric, whereas the coupling tensors do not exhibit any special symmetry property; finally for dispersive heat transfer, the thermal conductivity tensors include a symmetric and a skew-symmetric part, the latter being a consequence of convective transport only. A similar result is achieved for mass dispersion. Beyond the physical mechanisms under consideration in the present work, the reported technique can be viewed as a general methodology applicable to any type of upscaled model obtained by volume averaging.

Effects of microscopic transport coefficients on fission observables calculated by Langevin equation and its systematics

The Langevin dynamical description of fission observables is inspired by the random evolution of shape parameters across the potential surface. In these work, we shall use mass and friction tensors inspired from Linear Response Theory (microscopic transport coefficients) and obtain the fission observables associated with these calculations. We compare these microscopic results with calculations using hydrodynamical mass tensor and wall-window friction tensor (macroscopic transport coefficients). We are able to calculate the fission product yield, Coulomb kinetic energy and prescission kinetic energy from the Langevin calculation. This allows us to observe the systematic of average light and heavy mass fission product yield calculated using both microscopic and macroscopic calculations. We also compare the results of microscopic and macroscopic calculation total kinetic energy (TKE) with Viola's TKE systematics. In the case of 236,239 U compound nucleus, we do the microscopic calculation for several excitation energy up to 30 MeV and afterwards compare it to the TKE of experimental data and corresponding macroscopic TKE. Reasonable agreement of microscopic TKE to experiment is obtained which shows decreasing TKE with increasing excitation energy. Macroscopic TKE however, is independent of excitation energy and thus contrary to experimental data.

Characterizing Structural Complexity in Disordered Carbons: From the Slit Pore to Atomistic Models.

The reliable characterization of nanoporous carbons is critical to the design and optimization of their numerous applications; however, the vast majority of carbons in industrial use are highly disordered, with complex structures whose understanding has long challenged researchers. The idealized slit pore model represents the most commonly used approximation to a carbon nanopore; nevertheless, it has been only partially successful in predicting adsorption isotherms and fails significantly in predicting transport properties because of its inability to capture structural disorder and its effect on fluid accessibility. Atomistic modeling of the structure has much potential for overcoming this limitation, and among such approaches, hybrid reverse Monte Carlo simulation has emerged as the most attractive. This method reconstructs the structure of a carbon based on the fitting of its experimentally measured pair distribution function and appropriate properties such as porosity while minimizing the energy. The method is shown to be best implemented using a multistage strategy, with the first stage used to attain a deep minimum of the energy and subsequent stages to refine the structure based on the fitting of specific properties. Methods to determine the accessibility of gases based on the atomistic structure are outlined, and it is shown that energy barriers are very sensitive to small differences in the sizes of constrictions and pore entries. The ability to accurately predict macroscopic transport coefficients of adsorbates in nanoporous carbons appears to be the greatest limitation of such models. Overcoming this will require the fitting of properties more sensitive to long-range disorder than the currently used pair distribution and the use of a suitable multiscaling strategy, which is suggested as a future direction for advancing atomistic models. The inclusion of heteroatoms in the structure is also an important area requiring further attention, particularly in the development of computationally efficient force fields incorporating their interactions.

Macroscopic Modeling of In Vivo Drug Transport in Electroporated Tissue.

This study develops a macroscopic model of mass transport in electroporated biological tissue in order to predict the cellular drug uptake. The change in the macroscopic mass transport coefficient is related to the increase in electrical conductivity resulting from the applied electric field. Additionally, the model considers the influences of both irreversible electroporation (IRE) and the transient resealing of the cell membrane associated with reversible electroporation. Two case studies are conducted to illustrate the applicability of this model by comparing transport associated with two electrode arrangements: side-by-side arrangement and the clamp arrangement. The results show increased drug transmission to viable cells is possible using the clamp arrangement due to the more uniform electric field.

Determination of macroscopic transport coefficients of a dissipative particle dynamics solvent.

We present an approach to determine macroscopic transport coefficients of a dissipative particle dynamics (DPD) solvent. Shear viscosity, isothermal speed of sound, and bulk viscosity result from DPD-model input parameters and can be determined only a posteriori. For this reason approximate predictions of these quantities are desirable in order to set appropriate DPD input parameters. For the purpose of deriving an improved approximate prediction we analyze the autocorrelation of shear and longitudinal modes in Fourier space of a DPD solvent for Kolmogorov flow. We propose a fitting function with nonexponential properties which gives a good approximation to these autocorrelation functions. Given this fitting function we improve significantly the capability of a priori determination of macroscopic solvent transport coefficients in comparison to previously used exponential fitting functions.

Impact of Non-uniform Properties on Governing Equations for Fluid Flows in Porous Media

The macroscopic governing equations of a compressible multicomponents flow with non-uniform viscosity and with mass withdrawal (due to heterogeneous reactions) in a porous medium are developed. The method of volume averaging was used to transform local (or microscopic) governing equations into averaged (or macroscopic) governing equations. The impacts of compressibility, non-uniform viscosity, and mass withdrawal on the form of the averaged equations and on the value of the macroscopic transport coefficients were investigated. The results showed that the averaged mass conservation equation is significantly affected by mass withdrawal when a specific criterion on the size of the domain is respected. The results also showed that the form of the averaged momentum equations is not affected by mass withdrawal, by compressibility effects or by non-uniform viscosity, provided that the Reynolds number at the pore level is small. Nonetheless, the velocity field is affected by the heterogeneous reaction via the averaged mass conservation equation, and also by viscosity variations due to the presence of the volume-averaged viscosity (which value changes with position) in the averaged momentum equations. A new closure variable definition was proposed to formulate the closure problem, which avoided the need to solve an integro-differential equation in the closure problem. This formulation was used to show that the permeability tensor only depends on the geometry of the porous medium. In other words, that tensor is independent on whether the fluid is compressible/incompressible, has uniform/non-uniform viscosities, and whether mass withdrawal due to heterogeneous reactions is present/absent.