Effective Hydrodynamic Radius Research Articles

Self-diffusion and shear viscosity of pure 1-alkanol unary system: molecular dynamics simulation and review of experimental data.

Self-diffusion coefficients and shear viscosity coefficients of pure 1-alkanol liquids from methanol to 1-hexanol were predicted using molecular dynamics (MD) simulations. These coefficients have been calculated using the Green-Kubo and Einstein methods at a range of temperatures of 200-330 K with increments of 10 K. Two force fields, TraPPE-UA and OPLS-AA were applied. The predicted results were compared to the experimental data, and the activation energies for self-diffusion and shear viscosity were calculated using the Arrhenius equation. The Stokes-Einstein equation was used to examine its capability in predicting the relationship between self-diffusion and shear viscosity, and the effective hydrodynamic radius was determined using both the experimental data and the results from MD simulations. The TraPPE-UA force field showed better results for the transport properties of methanol, while the OPLS-AA force field performed well for predicting shear viscosity but weakly for self-diffusion, particularly at low temperatures and for 1-alkanol with higher methylene numbers. Using the mean squared displacement method for self-diffusion was found to be more accurate than the Green-Kubo method, while the Green-Kubo method was slightly better for calculating shear viscosity. The Stokes-Einstein equation is valid for pure 1-alkanol liquids with temperature-dependent effective hydrodynamic radius.

Short-Time Transport Properties of Bidisperse Suspensions of Immunoglobulins and Serum Albumins Consistent with a Colloid Physics Picture.

The crowded environment of biological systems such as the interior of living cells is occupied by macromolecules with a broad size distribution. This situation of polydispersity might influence the dependence of the diffusive dynamics of a given tracer macromolecule in a monodisperse solution on its hydrodynamic size and on the volume fraction. The resulting size dependence of diffusive transport crucially influences the function of a living cell. Here, we investigate a simplified model system consisting of two constituents in aqueous solution, namely, of the proteins bovine serum albumin (BSA) and bovine polyclonal gamma-globulin (Ig), systematically depending on the total volume fraction and ratio of these constituents. From high-resolution quasi-elastic neutron spectroscopy, the separate apparent short-time diffusion coefficients for BSA and Ig in the mixture are extracted, which show substantial deviations from the diffusion coefficients measured in monodisperse solutions at the same total volume fraction. These deviations can be modeled quantitatively using results from the short-time rotational and translational diffusion in a two-component hard sphere system with two distinct, effective hydrodynamic radii. Thus, we find that a simple colloid picture well describes short-time diffusion in binary mixtures as a function of the mixing ratio and the total volume fraction. Notably, the self-diffusion of the smaller protein BSA in the mixture is faster than the diffusion in a pure BSA solution, whereas the self-diffusion of Ig in the mixture is slower than in the pure Ig solution.

The effective hydrodynamic radius in the Stokes–Einstein relation is not a constant

Variants based on the assumption of effective hydrodynamic radius being a constant are usually adopted to test the Stokes–Einstein (SE) relation. The rationality of the assumption is examined by performing molecular dynamics simulations with the truncated Lennard-Jones-like (TLJ) model, Kob–Andersen model and ortho-terphenyl (OTP) model. The results indicate the assumption is generally not established except for special case. The effective hydrodynamic radius is observed to increase with decreasing temperature for TLJ model but is decreased for Kob–Andersen and OTP model; and which is almost a constant for TLJ particle with enough rigidity. The variant of SE relation is invalid for the three models except for the TLJ particle with enough rigidity. We propose similar inconsistency may be also existed in other liquids and the assumption should be critically evaluated when adopted to test the SE relation.

Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove.

Advanced carbon microelectrodes, including many carbon-nanotube (CNT)-based electrodes, are being developed for the in vivo detection of neurotransmitters such as dopamine (DA). Our prior simulations of DA and dopamine-o-quinone (DOQ) on pristine, flat graphene showed rapid surface diffusion for all adsorbed species, but it is not known how CNT surfaces affect dopamine adsorption and surface diffusivity. In this work, we use molecular dynamics simulations to investigate the adsorbed structures and surface diffusion dynamics of DA and DOQ on CNTs of varying curvature and helicity. In addition, we study DA dynamics in a groove between two aligned CNTs to model the spatial constraints at the junctions within CNT assemblies. We find that the adsorbate diffusion on a solvated CNT surface depends upon curvature. However, this effect cannot be attributed to changes in the surface energy roughness because the lateral distributions of the molecular adsorbates are similar across curvatures, diffusivities on zigzag and armchair CNTs are indistinguishable, and the curvature dependence disappears in the absence of solvent. Instead, adsorbate diffusivities correlate with the vertical placement of the adsorbate’s moieties, its tilt angle, its orientation along the CNT axis, and the number of waters in its first hydration shell, all of which will influence its effective hydrodynamic radius. Finally, DA diffuses into and remains in the groove between a pair of aligned and solvated CNTs, enhancing diffusivity along the CNT axis. These first studies of surface diffusion on a CNT electrode surface are important for understanding the changes in diffusion dynamics of dopamine on nanostructured carbon electrode surfaces.

A molecular simulation study on transport properties of FAMEs in high-pressure conditions

Transport property prediction of fatty acid methyl esters (FAMEs) is essential to its utilisation as biodiesel and biolubricant which can work under high-pressure conditions. Equilibrium molecular simulation is performed to study the viscosity, diffusivity, density and molecular structure dynamics at conditions up to 300 MPa. Among the transport properties, convergence of the viscosity needs a sufficiently large number of independent replications of the simulation. The system size effect on diffusion coefficient should be taken into consideration in fitting the Stokes-Einstein relation. The capability of three different force fields on predicting transport properties is evaluated in terms of the united-atom molecular model and all-atom molecular model. The solidification of FAMEs under high pressure occurs with parallel molecular alignment. The spatial inhomogeneity results in the breakdown of Stokes-Einstein relation. A hybrid effective hydrodynamic radius is established on the linear relation between experimental viscosity and diffusion coefficient in molecular simulation. This provides a predictive method to estimate viscosity from molecular diffusion coefficient over a broad range of conditions provided that Stokes-Einstein relation applies.

Concentration- and Temperature-Driven Evolution of V5+ Solution Structure in Redox-Flow Battery Electrolytes Studied By Multinuclear NMR

The ongoing implementation of renewable energy generation systems into worldwide electrical grids increasingly demands additional energy storage platforms to maintain stability through their associated intermittency, with vanadium redox-flow batteries being a forefront solution owing to the decoupling of energy- and power-density that they afford.1 However, a lingering performance issue associated with this chemistry in its conventional format, with the vanadium ions dissolved in concentrated aqueous sulfuric acid, is the poor thermal stability of the V5+ cation in solution. This leads to precipitation as the hydrated penta-coordinated vanadate complex, stable at room temperature, is deprotonated and converted to insoluble V2O5 by a condensation reaction induced at elevated temperature.2 This process ultimately limits the concentration of the electrolyte – adversely impacting the available energy density – and its operation at temperatures above ~310 K. While alternatives to this relatively simple electrolyte composition have shown great promise in rectifying this thermal- and concentration-induced instability of the solvated V5+, via the introduction of mixed acid solvent systems3 or stabilizing additives,4 a complete understanding in the original formulation at a range of length- and time-scales and across a multitude of conditions will aid the further development of alternative systems, and provide a means to benchmark their performance at a very fundamental level.This study therefore aims to greatly expand on previous multinuclear NMR work2,5 on the elucidation of this precipitation mechanism by combining a thorough exploration of concentration effects on V5+ solvation structure and dynamics in conjunction with an investigation of their thermal behavior. Ten samples spanning the concentration range of 0 M to 1.7 M V5+ (all with 5 M H2SO4) were examined over temperatures from 298 K to 383 K ascending, and subsequently likewise descending. Combining 1H, 17O, 33S, and 51V linewidth and shift measurements, the evolving solution structure with increasing temperature – and the associated hysteresis on again decreasing it – is mapped as a function of the V5+ concentration. In particular, the extent of the thermal hysteresis previously established with 17O and 51V linewidth and shift measurements at high V5+ concentration2 is quantitatively examined as the concentration is lowered. This spectroscopic analysis is complemented by a similar variable-concentration and variable-temperature study of the 1H self-diffusivity via pulsed-field gradient (PFG) NMR and by 17O longitudinal (T1) relaxation measurements, to determine both the effect of this evolving solution structure on the dynamics and transport, and how they are impacted by increasing V5+ concentration via the associated activation energy trends. The 1H PFG-NMR measurements, coupled with high-accuracy dynamic viscosity measurements via the falling-ball method, are also used to examine the evolution of the effective proton hydrodynamic radius as the V5+ aggregation reaction occurs. The totality of the data, collected across such a wide range of concentration and temperature conditions, yields an unprecedented map of the V5+ solvation phenomena and solution dynamics which spans molecular to bulk length- and time-scales, and which will serve as a useful platform of comparison for analyzing the effectiveness of alternative solvent systems and stabilizing agents presently undergoing development. References M. Skyllas-Kazacos, M. H. Chakrabarti, S. A. Hajimolana, F. S. Mjalli, and M. Saleem, J. Electrochem. Soc., 158, R55 (2011) https://iopscience.iop.org/article/10.1149/1.3599565.M. Vijayakumar et al., J. Power Sources, 196, 3669–3672 (2011) http://dx.doi.org/10.1016/j.jpowsour.2010.11.126.L. Li et al., Adv. Energy Mater., 1, 394–400 (2011) http://doi.wiley.com/10.1002/aenm.201100008.N. Kausar, A. Mousa, and M. Skyllas-Kazacos, ChemElectroChem, 3, 276–282 (2016) http://doi.wiley.com/10.1002/celc.201500453.M. Vijayakumar et al., Chempluschem, 80, 428–437 (2015) http://doi.wiley.com/10.1002/cplu.201402139.

Self-Diffusion Coefficients, Aggregation Numbers and the Range of Existence of Spherical Micelles of Oxyethylated Alkylphenols

Aggregation numbers were calculated based on measurements of the self-diffusion coefficients, the effective hydrodynamic radii of micelles and aggregates of oxyethylated alkylphenols in aqueous solutions. On the assumption that the radii of spherical micelles are equal to the lengths of fully extended neonol molecules, the limiting values of aggregation numbers corresponding to spherically shaped neonol micelles were calculated. The concentration and temperature ranges under which spherical micelles of neonols are formed were determined.

Molecular dynamics simulation of Brownian diffusion boundary condition for nanoparticles

Brownian motion refers to the endless random motion of nanometer-to-micron particles suspended in a fluid. It widely exists in nature, and is applied to energy, biology, chemical industry, environment and other industries. As the Brownian motion of the object decreases from the micron level to the nanometer level, the boundary conditions of the particle motion no longer strictly follow the stick hydrodynamic boundary conditions, but are closer to the slip boundary theory, meanwhile, the interaction between particles and solvents has increasingly important influence on particle dynamics. Molecular dynamics simulation is an important means to study nanofluids, which can not only capture the microscopic details of the interactions between particles and solvent molecules in nanofluids, but also have high potential function accuracy. In this paper, an all-atom model of the diffusion of Cu nanoparticles of different sizes in water is established by using the rigid TIP4P/2005 water molecule model as solvent, the dynamic viscosity from the TIP4P/2005 model is in good agreement with the experimental result, which is verified by the Green-Kubo formula. The FCC lattice structure is used to construct Cu particles of 0.5 nm, 1.0 nm, 1.5 nm, 2.0 nm in size, and the interaction between atoms in the particle is described by the EAM potential. The translational diffusion coefficient of particles is fitted by the single particle tracking algorithm and the least square method, the rotational diffusion coefficient of particles is obtained by quaternion transformation. The diffusion coefficient and friction factor of the particles are calculated, and the friction factor is compared with the result under the stick hydrodynamics boundary conditions and the result under the slip boundary conditions. It is found that the frictional factors of translation and rotation of nano-particles lie between the theoretical values predicted by the two boundary conditions. The radial distribution functions of water molecules around nanoparticles of different sizes are calculated, we find that the smaller the particle size, the more obvious the adsorption of solvent molecules will be, and the water molecular layer on the particle surface will increase the effective volume of particles and make the calculation result of friction factor larger. The effect of solvent adsorption on the effective hydrodynamic radius of particles cannot be ignored when calculating the friction coefficient of Brownian motion of nano-particles, especially when the particle radius is close to the solvent radius. In Brownian dynamics, viscous resistance and stochastic force are constrained by fluctuation dissipation theorem, and a reasonable selection of particle friction factor can provide theoretical basis for the improvement of Brownian dynamics.

Diffusion Coefficients of Methane in Methylbenzene and Heptane at Temperatures between 323\xa0K and 398\xa0K at Pressures up to 65\xa0MPa

We reported experimental measurements of the diffusion coefficient of methane at effectively infinite dilution in methylbenzene and in heptane at temperatures ranging from (323 to 398) K and at pressures up to 65 MPa. The Taylor dispersion method was used and the overall combined standard relative uncertainty was 2.3%. The experimental diffusion coefficients were correlated with a simple empirical model as well as the Stokes–Einstein model with the effective hydrodynamic radius of methane depending linearly upon the solvent density. The new data address key gaps in the literature and may facilitate the development of an improved predictive model for the diffusion coefficients of dilute gaseous solutes in hydrocarbon liquids.

Toward Diffusion Measurements of Colloidal Nanoparticles in Biological Environments by Nuclear Magnetic Resonance.

Protein corona formation on the surface of nanoparticles (NPs) is observed in situ by measuring diffusion coefficients of the NPs under the presence of proteins with a 19 F nuclear magnetic resonance (NMR) based methodology. Formation of a protein corona reduces the diffusion coefficient of the NPs, based on an increase in their effective hydrodynamic radii. With this methodology it is demonstrated that the apparent dissociation constant of protein-NP complexes may vary over at least nine orders of magnitude for different types of proteins, in line with the Vroman effect. Using this methodology, the interaction between one type of protein and one type of nanoparticle can be studied quantitatively. Due to the NMR-based detection, this methodology has no interference by absorption/scattering effects, by which optical detection schemes are affected. By using the potential of the NMR chemical shift, the detection of multiple 19 F signals simultaneously opens the possibility to study the diffusion of several NPs at the same time. The 19 F labeling of the NPs has negligible effect on their acute toxicity and moderate effect on NPs uptake by cells.

Microscopic origin of breakdown of Stokes-Einstein relation in binary mixtures: Inherent structure analysis.

Aqueous binary mixtures often exhibit dramatic departure from the predicted hydrodynamic behavior when transport properties are plotted against composition. We show by inherent structure (IS) analysis that this sharp composition dependent breakdown of the Stokes-Einstein relation can be attributed to the non-monotonic variation in the average inherent structure energy of these mixtures. Further IS analysis reveals the existence of a unique ground state, stabilized by both the formation of an optimum number of H-bonds and a favorable hydrophobic interaction at this composition. The surprisingly sharp turnaround behavior observed in the effective hydrodynamic radius also owes its origin to the same combination of these two factors. Interestingly, the temperature dependence of isothermal compressibility shows a minimum at the particular composition. Extensive studies on water-dimethyl sulfoxide and water-ethanol mixtures using two different force-fields of water reveal many features that are nearly universal. A justification of this quasi-universal behavior is provided in terms of a mode-coupling theory (MCT) of viscosity, which can serve as the starting point of a remarkable correlation observed with the nearest neighbor structure, as captured by the first peaks of the radial distribution function, and the slowdown in the intermediate scattering function at intermediate wavenumbers. Therefore, the formation of the local structure captured through IS analysis can be correlated with the MCT.

Unusual behavior of Stokes–Einstein relation in liquid mixtures

The Stokes–Einstein (S–E) relation is well studied for pure liquids. Here, we report the applicability of the S–E relation in liquid mixtures. The breakdown of the S–E relation in organic and aqueous liquid mixtures might be attributed to the self-diffusion coefficient, shear viscosity, or the hydrodynamics radius of the solute–solvent species, which are strongly correlated. The hydrodynamic radius must be adjusted with an effective radius that accounts for the size of the diffusing solute wetted by the solvent molecules. Furthermore, the mutual diffusivity could be the correct option instead of self-diffusivity for the prediction of hydrodynamic radius using the S–E relation, as the mobility of the solute is strongly coupled with the mobility of the solvent molecules. The theoretical hydrodynamic radius obtained from the S–E relation is predicted to be well correlated with the distance between the solute and solvent center of mass calculated from molecular dynamics simulations. The acceptance of this effective hydrodynamic radius is ensured by testing its applicability for a large collection of liquid mixtures.

Dynamic and structural properties, cloud point of mixed micelles of oxyethylated isononylphenols

We measured the self-diffusion coefficients of mixed micelles formed in binary mixtures of oxyethylated isononylphenols (neonols) AF9-2,3,4,6,8,9,10,12 by NMR diffusometry in aqueous 1 wt% solutions. The effective hydrodynamic radii of the micelles were calculated using the Stokes-Einstein relation. Cloud points of these solutions were determined visually and the relation between the cloud point and the composition of the mixture was suggested. Extraction of phenol from the solutions at their cloud points was also studied.

Dynamic cluster formation determines viscosity and diffusion in dense protein solutions

We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the Kd ≈ 10-mM regime.

Diffusion of Gold Nanorods Functionalized with Thermoresponsive Polymer Brushes

Understanding the diffusion of gold nanorods (AuNRs) and their composites in dispersion is important at fundamental level and in fields as diverse as material science, nanobiotechnology to drug delivery. The translational and rotational diffusion of AuNRs decorated with thermoresponsive poly(N-isopropylacrylamide) brushes having hydrophilic and hydrophobic end groups was investigated in the dilute regime by dynamic light scattering. The same series of functionalized AuNRs were studied in the isotropic concentrated dispersions by high-resolution NMR diffusometry. The dependence of translational and rotational diffusivity upon molecular weight and polymer end group were measured as a function of temperature in the region of the brush phase transition. The effective hydrodynamic radius of AuNR composites proved to be the most sensitive quantity to the temperature-induced phase transition of brushes, allowing the evaluation of the brush thickness in the swollen and collapsed states.

YAG Ceramic Nanocrystals Implementation into MCVD Technology of Active Optical Fibers

Nanoparticle doping is an alternative approach the conventional solution doping method allowing the preparation of active optical fibers with improved optical and structural properties. The combination of the nanoparticle doping with MCVD process has brought new technological challenges. We present the preparation of fiber lasers doped with Er-doped yttrium aluminum garnet (Er:YAG) nanocrystals. These nanocrystals, prepared by a hydrothermal reaction, were analyzed by several structural methods to determine the mean nanocrystal size and an effective hydrodynamic radius. The nanocrystals were incorporated into silica frits with various porosity made by the conventional MCVD process. The Er:YAG-doped silica frits were processed into preforms, which were drawn into optical fibers. We studied the effect of the nanocrystal size and frit’s porosity on the final structural and optical properties of prepared preforms and optical fibers. Selected optical fibers were tested as an active medium in a fiber ring laser setup and the characteristics of the laser were determined. Optimal laser properties were achieved for the fiber length of 7 m. The slope efficiency of the fiber laser was about 42%. Presented method can be simply extended to the deposition of other ceramic nanomaterials.

Cluster Size and Quinary Structure Determine the Rheological Effects of Antibody Self-Association at High Concentrations.

The question of how nonspecific reversible intermolecular protein interactions affect solution rheology at high concentrations is fundamentally rooted in the translation of nanometer-scale interactions into macroscopic properties. Well-defined solutions of purified monoclonal antibodies (mAbs) provide a useful system with which to investigate the manifold intricacies of weak protein interactions at high concentrations. Recently, characterization of self-associating IgG1 antibody (mAb2) solutions has established the direct role of protein clusters on concentrated mAb rheology. Expanding on our earlier work with three additional mAbs (mAb1, mAb3, and mAb4), the observed concentration-dependent static light scattering and rheological data present a substantially more complex relationship between protein interactions and solution viscosity at high concentrations. The four mAb systems exhibited divergent correlations between cluster formation (size) and concentrated solution viscosities dependent on mAb primary sequence and solution conditions. To address this challenge, well-established features of colloidal cluster phenomena could be applied as a framework for interpreting our observations. The initial stages of mAb cluster formation were investigated with small-angle X-ray scattering (SAXS) and ensemble-optimized fit methods, to uncover shifts in the dimer structure populations which are produced by changes in mAb interaction modes and association valence under the different solution conditions. Analysis of mAb average cluster number and effective hydrodynamic radii at high concentrations revealed cluster architectures can have a wide range of fractal dimensions. Collectively, the static light scattering, SAXS, and rheological characterization demonstrate that nonspecific and anisotropic attractive intermolecular interactions produce antibody clusters with different quinary structures to regulate the rheological properties of concentrated mAb solutions.

External Potential Modifies Friction of Molecular Solutes in Water

Stokes’s law for the friction of a sphere in water has been argued to work down to molecular scales, provided the effective hydrodynamic radius includes the hydration layer. In interpretations of experiments and in theoretical models, it is tacitly assumed that the solvent friction experienced by a solute does not depend on whether an external confinement potential acts on the solute. Using a novel method to extract the friction memory function from molecular dynamics simulations, we show that the solvent friction of a strongly harmonically confined methane molecule in water increases by 60% compared to its free-solution value, which is caused by an amplification of the slowest component of the memory function. The friction enhancement occurs for potential strengths typical of physical and chemical bonds and is accompanied by a significant slowing-down of the hydration water dynamics. Thus, the solvent friction acting on molecular solutes is not determined by solvent properties and solute-solvent interactions alone but results from the coupling between solute and solvent dynamics and thereby can be tuned by an external potential acting on the solute. This also explains why simulations of positionally constrained solutes do not reproduce free-solution diffusivities. Dynamic scaling arguments suggest similar effects also for macromolecular solutes provided the solution viscosity is sufficiently enhanced.

The Stokes-Einstein equation and the diffusion of ferrocene in imidazolium-based ionic liquids studied by cyclic voltammetry: Effects of cation ion symmetry and alkyl chain length

The diffusion of ferrocene (Fc) molecules in ionic liquids (ILs) was studied using cyclic voltammetry. The symmetric ILs 1,3-dialkylimidazolium bis[(trifluoromethane)sulfonyl]amide ([(CN/2)2im][NTf2] with N = 4, 6, 8, and 10) and non-symmetric ILs 1-alkyl-3-methylimidazolium bis[(trifluoromethane)sulfonyl]amide ([CN−1C1im][NTf2] with N = 3, 4, 6, 8, and 10) were used to examine the effect of the symmetry of alkyl substitution on the cation and the role of alkyl chain length on the diffusion of Fc. The diffusion coefficient D of Fc was determined by applying the Randles-Sevcik equation to the peak current in the cyclic voltammograms. The diffusion coefficient was found to be higher in a symmetric IL than in a non-symmetric IL with the same number of alkyl carbon atoms N, with the difference decreasing with increasing N. The diffusion of Fc in these ILs is well described by the Stokes-Einstein equation with slip boundary conditions, but with an effective hydrodynamic radius of 0.23 ± 0.01 nm, which is less than the 0.27 nm crystallographic radius of Fc, in agreement with previous studies of the diffusion of solutes in ILs that show the hydrodynamic radius to be less than the van der Waals radius of the solute.

Electrochemical and Spectroscopic Measurements of Diffusion of Vanadium Species in Ionomer Membranes

The vanadium redox flow battery (VRFB) is a tool for energy storage that has been promising in applications of large grid storage. Two cells are separated by an ion exchange membrane, which allows proton conduction to preserve electrical balance during the charge/discharge cycles1. The battery is composed of positive and negative cells operating with VO2+/VO2 + and V(II)/V(III) redox couples, respectively. The membrane also allows water, vanadium and acid to crossover from one cell to the other, this can lead to concentration imbalances and self-discharge, ultimately decreasing the efficiency of the battery.2 , 3 The focus of this investigation is on measurements of diffusive properties of ionomer films. Perfluorinated ionomers (e.g. Nafion®) have been extensively studied owing to the application of Nafion in fuel cells and electrolyzers. Electron paramagnetic resonance (EPR) enables the measurement of diffusion in of a spin probe or EPR active metal. Rotational diffusion, R, is obtained from analyzing the EPR line shape of the probe.4 , 5 This illustrates the local viscosity in the diffusion pathway, i.e. the hydrated channels. In turn, Rmay be related to the effective local viscosity by the Stokes-Einstein equation (see attached image), where a is an effective hydrodynamic radius of the probe, s is an anisotropy factor, and i labels the axis. These values are probe dependent, for the Tempone spin probe, a = 4.2 Å, s || = 0.402 and s^ = 0.543. EPR has also previously been used to further understand the environment of absorbed species in the membrane, including alternative hydrocarbon membranes.6 , 7 Previous studies have shown the VO2+ ion permeability to have a dependence on acid concentration in solution.8 In addition, translational diffusion in hydrated membranes can be measured with UV/vis or EPR by allowing the vanadium permeants to diffuse through the membrane in a cell designed for this purpose where concentrated solution is in contact with one side of the membrane and concentration increase is monitored in a blank solution in contact with the opposite side. A recent paper has shown a more significant discrepancy in comparisons of rotational diffusion and translational diffusion in aromatic hydrocarbon membranes than in perfluorinated ionomer membranes, suggesting a different diffusion pathway in the hydrocarbon based membranes. 9 To further characterize the diffusion of vanadium ions in ionomer membranes electrochemical methods are be used. Two separate measurements determine the diffusion of the redox active species through a membrane cast onto a glassy carbon rotating disc electrode (RDE). By taking detailed voltammetric RDE and chronoamperometric measurements at varying film thicknesses and diffusant concentrations, considerable information about the diffusion of different species in the membrane. The effects of backbone architecture and ionization level on the diffusion and solubility of migrant species can be further elucidated. References (1) Rychcik, M.; Skyllas-Kazacos, M. Journal of Power Sources 1988, 22, 59. (2) Xi, J.; Wu, Z.; Teng, X.; Zhao, Y.; Chen, L.; Qiu, X. Journal of Materials Chemistry 2008, 18, 1232. (3) Weidmann, E.; Heintz, E.; Lichtenthaler, R. N. J. Mem. Sci 1998, 141, 207. (4) Lawton, J.; Smotkin, E.; Budil, D. J. Phys. Chem. B 2008, 112, 8549. (5) Lawton, J.; Budil, D. J. Phys. Chem. B 2009, 10679. (6) Lawton, J.; Budil, D. J. Mem. Sci 2010, 357, 47. (7) Lawton, J.; Budil, D. Macromolecules 2010, 43, 652. (8) Lawton, J. S.; Jones, A.; Zawodzinski, T. Journal of The Electrochemical Society 2013, 160, A697. (9) Lawton, J.; Jones, A.; Tang, Z.; Lindsey, M.; Fujimoto, C.; Zawodzinski, T. J. Electrochem. Soc. 2016, 163, A5229. Figure 1