Dilute Limit Research Articles

Bruce-Vincent transference numbers from molecular dynamics simulations.

Transference number is a key design parameter for electrolyte materials used in electrochemical energy storage systems. However, the determination of the true transference number from experiments is rather demanding. On the other hand, the Bruce-Vincent method is widely used in the lab to approximately measure transference numbers of polymer electrolytes, which becomes exact in the limit of infinite dilution. Therefore, theoretical formulations to treat the Bruce-Vincent transference number and the true transference number on an equal footing are clearly needed. Here, we show how the Bruce-Vincent transference number for concentrated electrolyte solutions can be derived in terms of the Onsager coefficients, without involving any extrathermodynamic assumptions. By demonstrating it for the case of poly(ethylene oxide)-lithium bis(trifluoromethane)sulfonimide system, this work opens the door to calibrating molecular dynamics (MD) simulations via reproducing the Bruce-Vincent transference number and using MD simulations as a predictive tool for determining the true transference number.

Measurement of Diffusion of Atmospheric Gases in a Liquid Perfluoro Compound by Means of an Optical Technique

We report on accurate measurements of Fickian diffusion coefficients in binary mixtures consisting of hydrofluoroether (a perfluoro compound of methoxy-nonafluorobutane or HFE-7100) with dissolved atmospheric gases CO2, N2, and O2 in the limit of an infinite dilution of the gas. We show that the use of optical digital interferometry (ODI) allows the determination of diffusion coefficients of dissolved gases with relatively small standard uncertainties for this class of experiments. In addition, we illustrate the ability of an optical approach to determine the gas concentration. We compare the capacity of four mathematical models, singly used in the literature, to obtain diffusion coefficients by applying them to the processing of a large amount of experimental data. We quantify their systematic errors and standard uncertainties. The temperature behavior of the diffusion coefficients measured in the range of 10 to 40 °C is consistent with the behavior of the same gases in other solvents available in the literature.

A smooth transition towards a Tracy–Widom distribution for the largest eigenvalue of interacting k-body fermionic embedded Gaussian ensembles

In spite of its simplicity, the central limit theorem captures one of the most outstanding phenomena in mathematical physics, that of universality. While this classical result is well understood, it is still not very clear what happens to this universal behavior when the random variables become correlated. A fruitful mathematically laboratory to investigate the rising of new universal properties is offered by the set of eigenvalues of random matrices. In this regard, a lot of work has been done using the standard random matrix ensembles and focusing on the distribution of extreme eigenvalues. In this case, the distribution of the largest or smallest eigenvalue departs from the Fisher–Tippett–Gnedenko theorem yielding the celebrated Tracy–Widom distribution. One may wonder, yet again, how robust this new universal behavior captured by the Tracy–Widom distribution is when the correlation among eigenvalues changes. Few answers have been provided to this poignant question, and our intention in the present work is to contribute to this interesting unexplored territory. Thus, we study numerically the probability distribution for the normalized largest eigenvalue of the interacting k-body fermionic orthogonal and unitary embedded Gaussian ensembles in the diluted limit. We find a smooth transition from a slightly asymmetric Gaussian-like distribution, for small , to the Tracy–Widom distribution as , where k is the rank of the interaction and m is the number of fermions. Correlations at the edge of the spectrum are stronger for small values of and are independent of the number of particles considered. Our results indicate that subtle correlations toward the edge of the spectrum distinguish the statistical properties of the spectrum of interacting many-body systems in the dilute limit, from those expected for the standard random matrix ensembles.

Parametric analysis of heat flux inhibition in the solar wind: a macroscopic quasilinear approach

Abstract Magnitudes of electron temperature anisotropy and solar wind heat flux are defined with different physical mechanisms e.g. microinstabilities, interparticle collisions, and adiabatic expansion. In the dilute space plasma limit, the present study assumes the interplay between anisotropic core-halo electron components, their relative drift, and relative density of the halo electrons to determine the dynamics of backward and forward-propagating whistler heat flux instabilities along the ambient magnetic field. To investigate the feedback effects of these micro-instabilities in reshaping solar wind distributions and the total heat flux regulation, we formulate quasilinear kinetic equations on the basis of taking the macroscopic velocity moments. For the same input parameters of linear analysis, numerical solutions of the quasilinear equations indicate the time-scale variations, electrons and protons population, wave intensities, and constraints on the heat flux. In future perspective of the global-kinetic solar wind model, the present formalism may be an important step with the inclusion of radial and nonthermal effects.

Temperature Dependence of Non-Condon Effects in Two-Dimensional Vibrational Spectroscopy of Water.

Non-Condon effects in vibrational spectroscopy refers to the dependence of a molecule's vibrational transition dipole and polarizability on the coordinates of the surrounding environment. Earlier studies have shown that such effects can be pronounced for hydrogen-bonded systems like liquid water. Here, we present a theoretical study of two-dimensional vibrational spectroscopy under the non-Condon and Condon approximations at varying temperatures. We have performed calculations of both two-dimensional infrared and two-dimensional vibrational Raman spectra to gain insights into the temperature dependence of non-Condon effects in nonlinear vibrational spectroscopy. The two-dimensional spectra are calculated for the OH vibration of interest in the isotopic dilution limit where the coupling between the oscillators is ignored. Generally, both the infrared and Raman line shapes undergo red shifts with decrease in temperature due to strengthening of hydrogen bonds and decrease in the fraction of OH modes with weaker or no hydrogen bonds. The infrared line shape is further red-shifted under the non-Condon effects at a given temperature, while the Raman line shape does not show any such red shift due to non-Condon effects. The spectral dynamics becomes slower on decrease of temperature due to slower hydrogen bond relaxation and, for a given temperature, the spectral diffusion occurs at a faster rate upon inclusion of non-Condon effects. The time scales of spectral diffusion extracted from different metrics agree well with each other and also with experiments. The changes in the spectrum due to non-Condon effects are found to be more significant at lower temperatures.

Effects of flexibility in coarse-grained models for bovine serum albumin and immunoglobulin G.

We construct a coarse-grained, structure-based, low-resolution, 6-bead flexible model of bovine serum albumin (BSA, PDB: 4F5S), which is a popular example of a globular protein in biophysical research. The model is obtained via direct Boltzmann inversion using all-atom simulations of a single molecule, and its particular form is selected from a large pool of 6-bead coarse-grained models using two suitable metrics that quantify the agreement in the distribution of collective coordinates between all-atom and coarse-grained Brownian dynamics simulations of solutions in the dilute limit. For immunoglobulin G (IgG), a similar structure-based 12-bead model has been introduced in the literature [Chaudhri et al., J. Phys. Chem. B 116, 8045 (2012)] and is employed here to compare findings for the compact BSA molecule and the more anisotropic IgG molecule. We define several modified coarse-grained models of BSA and IgG, which differ in their internal constraints and thus account for a variation of flexibility. We study denser solutions of the coarse-grained models with purely repulsive molecules (achievable by suitable salt conditions) and address the effect of packing and flexibility on dynamic and static behavior. Translational and rotational self-diffusivity is enhanced for more elastic models. Finally, we discuss a number of effective sphere sizes for the BSA molecule, which can be defined from its static and dynamic properties. Here, it is found that the effective sphere diameters lie between 4.9 and 6.1nm, corresponding to a relative spread of about ±10% around a mean of 5.5nm.

Action at a distance along the microtubule couples kinesin motors.

Coupling of kinesin motors drives flagellar beating and chromosome segregation, among other important biophysical processes. Current models of motor coupling invoke either direct mechanical linkage or protein crowding, which rely on short-range motor-motor interactions. In contrast, coupling mechanisms that act at longer length scales remain largely unexplored. We found that microtubules can physically couple motor movement in the absence of detectable short-range interactions. This occurs for the human kinesin-4 Kif4A, which contributes to the stability of antiparallel microtubule overlaps in the mitotic spindle. In a reconstituted system, Kif4A changes the run length and velocity of other motors on the same microtubule in the dilute binding limit, when approximately 10-nm-sized motors are much farther apart than the motor size. This effect does not depend on specific motor-motor interactions because similar changes in Kif4A motility are induced by kinesin-1 motors. A micrometer-scale attractive interaction potential between motors is sufficient to recreate the experimental results in a biophysical model. Unexpectedly, our theory suggests that long-range microtubule-mediated coupling affects not only binding kinetics but also motor mechanochemistry. Therefore, the model predicts that motors can sense and respond to motors bound several micrometers away on a microtubule. Our results are consistent with a paradigm in which long-range motor interactions along the microtubule enable additional forms of collective motor behavior, possibly due to changes in the microtubule lattice.

Large deviations of a tracer position in the dense and the dilute limits of single-file diffusion.

We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large deviation functions for an initial step density profile with the fluctuating (annealed) and the fixed (quenched) initial conditions. These hydrodynamic results are applicable for a general single-file system and they agree with recent exact results obtained by microscopic solutions for specific model systems.

Operation Cycle Length Extension of a Konvoi PWR: Requirements and Experience from Operator’s Viewpoint

The extension of the operating domain of PreussenElektra’s Konvoi-type pressurized water reactors (PWRs) beyond the natural end of cycle is known as stretch-out operation. A range of possibilities exists to increase nuclear fuel utilization to continue operation after the boron concentration reaches its dilution limit. The most basic option is to continue operation with constant average moderator temperature, which results in a relatively fast decrease in reactor power. From a fuel utilization point of view, this is the least optimal procedure. In PreussenElektra’s PWR fleet, an enhanced operation mode is adopted, leading to a comparatively modest decrease in reactor power and very high utilization of nuclear fuel. Initially, the stretch-out mode provided an option to gain flexibility regarding outage planning. More recently, the stretch-out method has served as a practical approach to optimizing electricity generation costs during the last cycles before the final shutdown as stipulated by law, as operators can extend the cycle length in a range of 30 to 60 days after the natural end of cycle. This paper describes the licensing rationale, the feasibility of this type of operation, and the operating requirements and experience. The system parameters affected by stretch-out operation are discussed. Adjustments of set points of thermal-hydraulic variables in the primary and secondary systems are explained. Licensing requirements for safe reactor operation in stretch-out mode are reviewed. Furthermore, aspects of neutronic and thermal-hydraulic core surveillance are included. After more than 35 years and counting, the methods of increasing fuel utilization are not new, and an evaluation of experience and effectiveness is in order.

Diffusivities in Binary Mixtures of Cyclohexane or Ethyl Butanoate with Dissolved CH4 or R143a Close to Infinite Dilution

This work is part of a series of studies focusing on binary mixtures consisting of a liquid with a dissolved gas close to infinite dilution. A particular focus is on the study of the influence of molecular characteristics on mutual or self-diffusivity. Heterodyne dynamic light scattering (DLS) experiments and equilibrium molecular dynamics (EMD) simulations are applied to determine the Fick diffusion coefficient D11 and the self-diffusion coefficient of the gas solute in the mixture Dself,1. Often, the latter is referred to in the literature as the intradiffusion coefficient, which is equal to D11 in the limit of infinite dilution. Both DLS and EMD simulations are applied in macroscopic thermodynamic equilibrium at or close to saturation conditions. In the present study, mixtures of methane (CH4) or the refrigerant 1,1,1-trifluoroethane (R143a) dissolved in cyclohexane or ethyl butanoate are investigated at temperatures T between 303 and 423 K. The average expanded experimental uncertainty (coverage factor k = 2) of D11 from DLS experiments is 10%, and the average expanded statistical uncertainty (k = 2) of Dself,1 from EMD simulations is 6.4%. Unexpectedly, D11 in mixtures of CH4 dissolved in cyclohexane or ethyl butanoate essentially matches within uncertainties at a given T, and mixtures of cyclohexane with R143a show smaller D11 values in comparison to ethyl butanoate with R143a.

Doping Limits of Phosphorus, Arsenic, and Antimony in CdTe.

Low p-type doping is a limiting factor to increase CdTe thin-film solar-cell efficiency toward the theoretical Shockley-Queisser limit of 33%. Previous calculations predict relatively high ionization energies for group-V acceptors (P, As, and Sb), and they are plagued by self-compensation, forming AX centers, severely limiting hole concentration. However, recent experiments on CdTe single crystals indicate a much more favorable scenario, where P, As, and Sb behave as shallow acceptors. Using hybrid functional calculations, we solve this puzzle by showing that the ionization energies significantly decrease with the supercell size. When including the effects of spin-orbit coupling and extrapolating the results to the dilute limit, we find these impurities behave as hydrogenic-like shallow acceptors, and AX centers are unstable and do not limit p-type doping. We address the differences between our results and previous theoretical predictions and show that our ionization energies predict hole concentrations that agree with recent temperature-dependent Hall measurements.

Free-atom-like d states beyond the dilute limit of single-atom alloys.

Through a data-mining and high-throughput density functional theory approach, we identify a diverse range of metallic compounds that are predicted to have transition metals with "free-atom-like" d states that are highly localized in terms of their energetic distribution. Design principles that favor the formation of localized d states are uncovered, among which we note that site isolation is often necessary but that the dilute limit, as in most single-atom alloys, is not a pre-requisite. Additionally, the majority of localized d state transition metals identified from the computational screening study exhibit partial anionic character due to charge transfer from neighboring metal species. Using CO as a representative probe molecule, we show that localized d states for Rh, Ir, Pd, and Pt tend to reduce the binding strength of CO compared to their pure elemental analogues, whereas this does not occur as consistently for the Cu binding sites. These trends are rationalized through the d-band model, which suggests that the significantly reduced d-band width results in an increased orthogonalization energy penalty upon CO chemisorption. With the multitude of inorganic solids that are predicted to have highly localized d states, the results of the screening study are likely to result in new avenues for heterogeneous catalyst design from an electronic structure perspective.

Coarsening transitions of wet liquid foams under microgravity conditions.

We report foam coarsening studies which were performed in the International Space Station (ISS) to suppress drainage due to gravity. Foams and bubbly liquids with controlled liquid fractions ϕ between 15 and 50% were investigated to study the transition between bubble growth laws previously reported near the dry limit ϕ → 0 and the dilute limit ϕ → 1 (Ostwald ripening). We determined the coarsening rates for the driest foams and the bubbly liquids, they are in close agreement with theoretical predictions. We observe a sharp cross-over between the respective laws at a critical value ϕ*. At liquid fractions beyond this transition, neighboring bubbles are no longer all in contact, like at a jamming transition. Remarkably ϕ* is significantly larger than the random close packing volume fraction of the bubbles ϕrcp which was determined independently. We attribute the differences between ϕ* and ϕrcp to a weakly adhesive bubble interaction that we have studied in complementary ground-based experiments.

Strain stiffening elastomers with swelling inclusions.

Inhomogeneously swollen elastomers are an emergent class of materials, comprising elastic matrices with inclusion phases in the form of microgel particles or osmolytes. Inclusion phases can undergo osmotically driven swelling and deswelling over orders of magnitude. In the swollen state, the inclusions typically have negligible Young's modulus, and the matrix is strongly deformed. In that regime, the effective mechanical properties of the composite are governed by the matrix. Laying the groundwork for a generic analysis of inhomogeneously swollen elastomers, we develop a model based on incremental mean-field homogenization of a hyperelastic matrix. The framework allows for the computation of the macroscopic effective stiffness for arbitrary hyperelastic matrix materials. For an in-depth quantification of the local effective stiffness, we extend the concept of elastic stiffness maps to incompressible materials. For strain-stiffening materials, stiffness maps in the swollen state highlight pronounced radial stiffening with a non-monotonic change in stiffness in the hoop direction. Stiffening characteristics are sensitive to the form of constitutive models, which may be exploited in the design of hydrated actuators, soft composites and metamaterials. For validation, we apply this framework to a Yeoh material, and compare to recently published data. Model predictions agree well with experimental data on elastomers with highly swollen embedded microgel particles. We identify three distinct regimes related to an increasing degree of particle swelling: first, an initial decrease in composite stiffness is attributed to particle softening upon liquid intake. Second, dilute particle swelling leads to matrix stiffening dominating over particle softening, resulting in an increase in composite stiffness. Third, for swelling degrees beyond the dilute limit, particle interactions dominate further matrix stiffening.

Dioctyl sodium sulfosuccinate surfactant self-assembly dependency of solvent hydrophilicity: a modelling study.

The self-assembly of dioctyl sodium sulfosuccinate (AOT) model surfactant in solvent environments of differing polarity is examined by means of dissipative particle dynamics (DPD) bead model parametrized against Hildebrand solubility parameters from atomistic molecular dynamics (MD) simulations. The model predicts that in hydrophobic solvents (e.g. dodecane) the surfactant forms small (Nagg ∼ 8) reverse micellar aggregates, while in a solvent corresponding to water lamellar assembly takes place, in good agreement with literature structural parameters. Interestingly, solvents of intermediate polarity lead to formation of large, internally structured aggregates. In these, the surfactant headgroups cluster within the aggregate, surrounded by a continuous phase formed by the hydrocarbon tails. We show that the partitioning of the headgroups between the aggregate surface layer and the inner clustered phase depends primarily on solvent polarity, and can be controlled by the solvent, but also system composition. Finally, we compare the DPD assembly response to simplified effective interaction potentials derived at dilute concentration limit for the interactions. The comparison reveals that the simplified effective potential descriptions provide good level of insight on the assembly morphologies, despite drastic, isotropic interactions simplification involved.

Imperfections are not 0 K: free energy of point defects in crystals.

Defects determine many important properties and applications of materials, ranging from doping in semiconductors, to conductivity in mixed ionic-electronic conductors used in batteries, to active sites in catalysts. The theoretical description of defect formation in crystals has evolved substantially over the past century. Advances in supercomputing hardware, and the integration of new computational techniques such as machine learning, provide an opportunity to model longer length and time-scales than previously possible. In this Tutorial Review, we cover the description of free energies for defect formation at finite temperatures, including configurational (structural, electronic, spin) and vibrational terms. We discuss challenges in accounting for metastable defect configurations, progress such as machine learning force fields and thermodynamic integration to directly access entropic contributions, and bottlenecks in going beyond the dilute limit of defect formation. Such developments are necessary to support a new era of accurate defect predictions in computational materials chemistry.

The preparation of silica supported, dilute limit PdAu alloys via simultaneous strong electrostatic adsorption

Supported, dilute Pd-in-Au alloyed nanoparticles might possess enhanced reactivity due to the altered structural and electronic properties of the Pd atoms isolated in an Au nanoparticle matrix.

The effective shear modulus of a random isotropic suspension of monodisperse liquid n-spheres: from the dilute limit to the percolation threshold.

A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid n-spherical inclusions (n = 2, 3), each having identical initial radius A, in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension γ. For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus n in terms of the shear modulus μ of the elastomer, the initial elasto-capillary number eCa = γ/2μA, the volume fraction c of inclusions, and the space dimension n. This paper presents numerical solutions-generated by means of a recently introduced finite-element scheme-for n over a wide range of elasto-capillary numbers eCa and volume fractions of inclusions c. Complementary to these, a formula is also introduced for n that is in quantitative agreement with all the numerical solutions, as well as with the asymptotic results for n in the limit of dilute volume fraction of inclusions and at percolation . The proposed formula has the added theoretical merit of being an iterated-homogenization solution.

Microrheology of a thermosensitive gelling polymer for cell culture.

We investigate the rheo-mechanical properties of Mebiol Gel®, a thermosensitive gel-forming polymer extensively used as a medium for cellular culture, using passive microrheology made either by standard dynamic light scattering or by photon correlation imaging. In the dilute limit, Mebiol displays a Newtonian behavior with an effective viscosity that decreases with temperature, consistent with a peculiar aggregation mechanism characterized by an increase of the molecular weight with a simultaneous reduction of the aggregate size. By increasing concentration and approaching gelation, both the storage and loss moduli show a nonmonotonic dependence with temperature, with a pronounced maximum around Tm ≃ 28-30 °C, the value above which, in the dilute limit, the individual Mebiol chains are fully compacted. Such a distinctive trend of the elastic and viscous properties persists within the gel, which, therefore, becomes "softer" above Tm. Although when temperature changes are performed adiabatically, the transition from the fluid to the gel phase takes place without any apparent discontinuity, a rapid T-jump leads to the formation of a hard gel at a concentration where a low heating rate conversely yields a fluid phase. This is a visible manifestation of the nonequilibrium nature of these physical gels.

Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit

Kinetic and hydrodynamic theories are widely employed for describing the collective behavior of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each particle interacts weakly with many others, so that the total forces and torques exerted on each of them is of order unity at all times. Such limit is however not relevant for dilute systems that mostly interact via alignment; there, collisions are rare and make the self-propulsion direction to change abruptly. We derive a fluctuating kinetic theory, and the corresponding fluctuating hydrodynamics, for aligning self-propelled particles in the limit of dilute systems. We discover that fluctuations at kinetic level are not Gaussian and depend on the interactions among particles, but that only their Gaussian part survives in the hydrodynamic limit. At variance with fluctuating hydrodynamics for weakly interacting particles, we find that the noise variance at hydrodynamic level depends on the interaction rules among particles and is proportional to the square of the density, reflecting the binary nature of the aligning process. The results of this paper, which are derived for polar self-propelled particles with polar alignment, could be straightforwardly extended to polar particles with nematic alignment or to fully nematic systems.