Translational Diffusion Coefficient Research Articles

In situ pulmonary mucus hydration assay using rotational and translational diffusion of gold nanorods with polarization-sensitive optical coherence tomography.

Assessing the nanostructure of polymer solutions and biofluids is broadly useful for understanding drug delivery and disease progression and for monitoring therapy. Our objective is to quantify bronchial mucus solids concentration (wt. %) during hypertonic saline (HTS) treatment in vitro via nanostructurally constrained diffusion of gold nanorods (GNRs) monitored by polarization-sensitive optical coherence tomography (PS-OCT). Using PS-OCT, we quantified GNR translational () and rotational () diffusion coefficients within polyethylene oxide solutions (0 to 3wt. %) and human bronchial epithelial cell (hBEC) mucus (0 to 6.4wt. %). Interpolation of and data is used to develop an assay to quantify mucus concentration. The assay is demonstrated on the mucus layer of an air-liquid interface hBEC culture during HTS treatment. In polymer solutions and mucus, and monotonically decrease with increasing concentration. is more sensitive than to changes above 1.5wt. % of mucus and exhibits less intrasample variability. Mucus on HTS-treated hBEC cultures exhibits dynamic mixing from cilia. A region of hard-packed mucus is revealed by measurements. The extended dynamic range afforded by simultaneous measurement of and of GNRs using PS-OCT enables resolving concentration of the bronchial mucus layer over a range from healthy to disease in depth and time during HTS treatment in vitro.

Solvation dynamics on the diffusion timescale elucidated using energy-represented dynamics theory.

Photoexcitation of a solute alters the solute-solvent interaction, resulting in the nonequilibrium relaxation of the solvation structure, often called a dynamic Stokes shift or solvation dynamics. Thanks to the local nature of the solute-solvent interaction, the characteristics of the local solvent environment dissolving the solute can be captured by the observation of this process. Recently, we derived the energy-represented Smoluchowski-Vlasov (ERSV) equation, a diffusion equation for molecular liquids, which can be used to analyze the solvation dynamics on the diffusion timescale. This equation expresses the time development for the solvent distribution on the solute-solvent pair interaction energy (energy coordinate). Since the energy coordinate can effectively treat the solvent flexibility in addition to the position and orientation, the ERSV equation can be utilized in various solvent systems. Here, we apply the ERSV equation to the solvation dynamics of 6-propionyl-2-dimethylamino naphthalene (Prodan) in water and different alcohol solvents (methanol, ethanol, and 1-propanol) for clarifying the differences of the relaxation processes among these solvents. Prodan is a solvent-sensitive fluorescent probe and is thus widely utilized for investigating heterogeneous environments. On the long timescale, the ERSV equation satisfactorily reproduces the relaxation time correlation functions obtained from the molecular dynamics (MD) simulations for these solvents. We reveal that the relaxation time coefficient on the diffusion timescale linearly correlates with the inverse of the translational diffusion coefficients for the alcohol solvents because of the Prodan-solvent energy distributions among the alcohols. In the case of water, the time coefficient deviates from the linear relationship for the alcohols due to the difference in the extent of importance of the collective motion between the water and alcohol solvents.

Measuring nanoparticles shape by structured illumination

Exploiting the size and shape of nanoparticles is critical for engineering the optical and mechanical properties of nanoparticle systems that are ubiquitous in everyday life. However, accurate determination of nanoparticle morphology usually requires elaborated methods such as XRD or TEM, which are not suitable for non-invasive and rapid control. Dynamic light scattering on the other hand, relies on the motion of nanoparticles and mixes different rotational and translational diffusion coefficients to infer synthetic information about the shape in terms of effective hydrodynamic characteristics. Here, we introduce a new scattering approach for measuring shape. We demonstrate analytically, numerically, and experimentally that the contrast of low-intensity fluctuations arising from the scattering of classically entangled optical fields allows determining the polarimetric anisotropy of nanoparticles. By leveraging the active variation of illumination structuring, we control the non-Gaussian statistics of the measured fluctuations, which, in turn, provides means to improve the measurement sensitivity. This technique offers practical opportunities for applications ranging from molecular chemistry to drug delivery to nanostructures synthesis where the real-time, quantitative assessment of nanoparticles shapes is indispensable.

Dynamics of anisotropic colloidal systems: What to choose, DLS, DDM or XPCS?

Investigation of the dynamics of colloids in bulk can be hindered by issues such as multiple scattering and sample opacity. These challenges are exacerbated when dealing with inorganic materials. In this study, we employed a model system of Akaganeite colloidal rods to assess three leading dynamics measurement techniques: 3D-(depolarized) dynamic light scattering (3D-(D)DLS), polarized-differential dynamic microscopy (P-DDM), and x-ray photon correlation spectroscopy (XPCS). Our analysis revealed that the translational and rotational diffusion coefficients captured by these methods show a remarkable alignment. Additionally, by examining the q-ranges and maximum volume fractions for each approach, we offer insights into the best technique for investigating the dynamics of anisotropic systems at the colloidal scale.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity v 0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of v 0 polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Методический подход к исследованию магнитного взаимодействия тонкодисперсных частиц в водной суспензии методом компьютерного моделирования

The need to increase the efficiency of mining operations determines the relevance of studying the properties of fine mineral particles for their extraction and reduction of environmental pollution. The development of approaches to studying magnetic interaction of fine particles is of scientific and practical importance and is associated with the complexity of calculating the superposition of their fields when solving the problem of controlling the magnetic properties of a suspension. A computer model of the dynamics of magnetic particle interaction was developed with account for their aggregation under the impact of the magnetic dipole-dipole interaction and the destruction of aggregates during thermal (Brownian) motion in order to predict the magnetic properties of the suspension using the example of magnetite deposits of the Zaimandrovsky iron ore region. The calculation shows that the electrostatic and dispersion interactions do not have a significant effect on the interaction dynamics of micron and submicron particles of magnetite with account of the experimentally measured zeta potential and the Hamaker's constant. A procedure has been developed for calibrating a computer model of the interaction dynamics of magnetic particles using the temperature dependence of the coefficient of translational diffusion of magnetite particles and the concentration dependence of the magnetic susceptibility of a suspension. An array of calculated values of the diffusion coefficient of the model particles and the initial magnetic susceptibility of their system is formed in a wide range of computer model parameters. A procedure has been developed for linking the calculated and experimental data by varying the normalization parameters of the particle size, viscosity of the medium, and thermal energy in order to minimize the maximum discrepancy between the values. The necessity is established of taking into account the change in magnetic properties with a decrease in the size of magnetite particles during the calibration of the magnetic susceptibility of a model system. The developed methodological approach ensures good convergence of the calculated and experimental data and makes it possible to visualize the aggregation of the model particles as the result of dipole-dipole interactions. The developed computer model of the interaction dynamics of magnetic particles can be used to study the effect of an external magnetic field on the aggregation ability of fine magnetite particles in order to control their extraction in separation processes.

First coarse grain then scale: How to estimate diffusion coefficients of confined molecules.

An approach for approximating position and orientation dependent translational and rotational diffusion coefficients of rigid molecules of any shape suspended in a viscous fluid under geometric confinement is proposed. It is an extension of the previously developed scheme for evaluating near-wall diffusion of macromolecules, now applied to any geometry of boundaries. The method relies on shape based coarse-graining combined with scaling of mobility matrix components by factors derived based on energy dissipation arguments for Stokes flows. Tests performed for a capsule shaped molecule and its coarse-grained model, a dumbbell, for three different types of boundaries (a sphere, an open cylinder, and two parallel planes) are described. An almost perfect agreement between mobility functions of the detailed and coarse-grained models, even close to boundary surfaces, is obtained. The proposed method can be used to simplify hydrodynamic calculations and reduce errors introduced due to coarse-graining of molecular shapes.

Understanding the influence of ethylene glycol on the microscopic behavior of imidazolium-based monocationic and dicationic ionic liquid

In the present work, the influence of a molecular co-solvent, ethylene glycol (EG) on the microscopic behaviour of an imidazolium-based dicationic ionic liquid (DIL) is analysed by employing time-resolved fluorescence anisotropy (TRFA) and nuclear magnetic resonance (NMR) spectroscopic techniques. In order to have a clear understanding of the specific role of DIL, a mono-cationic ionic liquid (MIL) containing an alkyl side chain unit, same as the alkyl spacer chain length of DIL, has also been investigated. The rotational diffusion of two fluorescent probes 9-PA and R110 have been carried out in both neat MIL and DIL and their mixtures with various fractions of EG. The analysis of the results has demonstrated that, within the studied concentration range, the microstructure of MIL encompassing both polar and nonpolar domains gets disrupted as the mole fraction of EG increases. However, a similar investigation in DIL has revealed that the micro-structure of DIL gets affected slightly when similar proportions of EG are added to DIL. This behaviour of DIL is attributed to the enhanced rigidity of the DIL structure due to its folded structural arrangements. Furthermore, NMR studies have provided additional insights into the interactions between the components of ILs and the added solvent. It has been observed that EG can form strong hydrogen-bonding interactions with the imidazolium-ring and alkyl chain protons of MIL. However, such interaction has not been observed in DIL. Moreover, the translational diffusion coefficient (Dt) value for the cationic moiety of both MIL and DIL, measured through NMR, has depicted that in the presence of EG, the change in Dtvalue is much higher for MIL than that for DIL. Overall, the outcome of the combined fluorescence and NMR studies have pointed out that the behaviour of DIL and MIL in the presence of a co-solvent is very different from one another and thus the individual mixture (IL+solvent) can be used for various targeted industrial applications.

Identical Diffusion Distributions and Co-Cluster Formation Dictate Azeotrope Formation: Microscopic Evidences and Experimental Signatures.

What selects azeotropic pairs and governs the azeotropic conditions (composition and temperature) is an open and intriguing question. A combined simulation and experimental work presented here investigates this by considering ethanol-water mixtures. We find identical distributions of center-of-mass diffusion coefficients for ethanol and water molecules under the azeotropic condition (95.5 wt % ethanol +4.5 wt % water, Tazeo = 351.1K). Moreover, the particle displacements show strong interspecies correlations at Tazeo. Interestingly, simulated reorientation time distributions become identical at Tazeo but at a composition different from that at which the translational diffusion distributions overlapped. Cluster analyses indicate that solutions at Tazeo with xwater ≤ 15 wt % are more microheterogeneous than those with higher water content, although no anomaly in the composition-dependent solution structural properties was detected. Ethanol-water and ethanol-ethanol interaction energies show pronounced nonideal composition dependence, but the size of the relative fluctuations in them remained small (∼0.5kBT). Rare water-water H-bonding, predominant water-ethanol H-bonding, and a sizable population of "free" water molecules characterize the azeotropic solutions. The red edge excitation spectroscopic (REES) measurements with a dissolved anionic fluorescent dye, coumarin343 (C343), support the predicted solution microheterogeneity by showing a nonmonotonic composition dependence of the excitation energy-induced changes in the fluorescence emission spectral frequencies and bandwidths, the largest changes being under the azeotropic condition. Subsequent dynamic anisotropy measurements reveal a nonmonotonic composition dependence of C343 rotation times with a peak under the azeotropic condition. In summary, equalization of the component translational diffusion coefficients and solution microheterogeneity with regular composition dependence of the solution structure appear to characterize the ethanol-water azeotrope.

The influence of thermodynamic qualities of a solvent on the physicochemical properties of lentil protein concentrate – Second virial coefficient study

A protein concentrate (75.2%) was obtained from some Lens culinaris L. seeds. The osmotic, hydrodynamic and surface properties of protein concentrate aqueous solutions were studied with the help of membrane osmometry, dynamic light scattering, ζ-potential and the pendant drop method, in a wide range of protein concentrate concentrations and pH conditions. The second virial coefficient was determined in the range of pH 2–9. Two theta points (pH∼ 5 and pH∼ 8) were found. The change of the hydrodynamic radii as a function of pH and scattering vector was analysed. It was found that the change of the solvent parameters (pH) has a significant influence on the surface tension value. This phenomenon was related to the values of the second virial coefficient and the translational diffusion coefficient. The increase in the value of the diffusion coefficient (smaller hydrodynamic radius) resulted in faster interface formation at the gas–liquid interface.

Stationary states of an active Brownian particle in a harmonic trap.

We study the stationary states of an overdamped active Brownian particle (ABP) in a harmonic trap in two dimensions via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with a certain velocity, whose magnitude is constant, but its direction is subject to Brownian rotation. In the limit where translational diffusion is negligible, the stationary distribution of the particle's position shows a transition between two different shapes, one with maximum and the other with minimum density at the center, as the trap stiffness is increased. We show that this nonintuitive behavior is captured by the relevant Fokker-Planck equation, which, under minimal assumptions, predicts a continuous phase transition-like change between the two different shapes. As the translational diffusion coefficient is increased, both these distributions converge into the equilibrium, Boltzmann form. Our simulations support the analytical predictions and also show that the probability distribution of the orientation angle of the self-propulsion velocity undergoes a transition from unimodal to bimodal forms in this limit. We also extend our simulations to a three-dimensional trap and find similar behavior.

Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides a Fast but Still Accurate Treatment of Hydrodynamic Interactions in Brownian Dynamics Simulations of Biological Macromolecules.

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HIs). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here, we explore the use of an alternative way to accelerate the calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA-RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA-RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast, approximate way of including HIs in BD simulations of intermediate-scale systems.

Retrospective rationalization of disparities between the concentration dependence of diffusion coefficients obtained by boundary spreading and dynamic light scattering.

This study establishes the existence of substantial agreement between published results from traditional boundary spreading measurements (including synthetic boundary measurements in the analytical ultracenrifuge) on two globular proteins (bovine serum albumin, ovalbumin) and the concentration dependence of diffusion coefficient predicted for experiments conducted under the operative thermodynamic constraints of constant temperature and solvent chemical potential. Although slight negative concentration dependence of the translational diffusion coefficient is the experimentally observed as well as theoretically predicted, the extent of the concentration dependence is within the limits of experimental uncertainty inherent in diffusion coefficient measurement. Attention is then directed toward the ionic strength dependence of the concentration dependence coefficient ([Formula: see text]) describing diffusion coefficients obtained by dynamic light scattering, where, in principle, the operative thermodynamic constraints of constant temperature and pressure preclude consideration of results in terms of single-solute theory. Nevertheless, good agreement between predicted and published experimental ionic strength dependencies of [Formula: see text] for lysozyme and an immunoglobulin is observed by a minor adaptation of the theoretical treatment to accommodate the fact that thermodynamic activity is monitored on the molal concentration scale because of the constraint of constant pressure that pertains in dynamic light scattering experiments.

Experimental support for reclassification of the light scattering second virial coefficient from macromolecular solutions as a hydrodynamic parameter.

This investigation examines the source of the disparity between experimental values of the light scattering second virial coefficient [Formula: see text] (mL.mol/g2) for proteins and those predicted on the statistical mechanical basis of excluded volume. A much better theoretical description of published results for lysozyme is obtained by considering the experimental parameters to monitor the difference between the thermodynamic excluded volume term and its hydrodynamic counterpart. This involves a combination of parameters quantifying concentration dependence of the translational diffusion coefficient obtained from dynamic light scattering measurements. That finding is shown to account for observations of a strong correlation between [Formula: see text] (mL/g), where M2 is the molar mass (molecular weight) of the macromolecule and the diffusion concentration parameter [Formula: see text] (mL/g). On the grounds that [Formula: see text] is regarded as a hydrodynamic parameter, the same status should be accorded the light scattering second virial coefficient rather than its current incorrect thermodynamic designation as [Formula: see text] (mL.mol/g2), or just B, the osmotic second virial coefficient for protein self-interaction.

Anomalous Dependence of Translational Diffusion on the Water Mole Fraction for Solute Molecules Dissolved in a 1-Butyl-3-methylimidazolium Tetrafluoroborate/Water Mixture.

Translational diffusion coefficients of carbon monoxide (CO), diphenylacetylene (DPA), and diphenylcyclopropenone (DPCP) were determined in mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate ([C4mim]BF4) and water using transient grating spectroscopy at different mole fractions of water (xw). While DPA exhibited a larger diffusion coefficient than DPCP at low water mole fractions (xw < 0.7), as observed for conventional liquids and ionic liquids (ILs), it was smaller at high mole fractions (xw > 0.9). The apparent molecular radius of DPA determined using the Stokes-Einstein equation at xw > 0.9 is close to the radius of an IL cluster in a water pool as determined from small-angle neutron scattering experiments (J. Bowers et al., Langmuir, 2004, 20, 2192-2198), suggesting that the DPA molecules are trapped in IL clusters in the water pool and move together. The solvation state of DPCP in the mixture was studied using Raman spectroscopy. Dramatically strong water/DPCP hydrogen bonding was observed at higher water mole fractions, suggesting that DPCP is located near the cluster interfaces. The large diffusion coefficient of DPCP suggests that hopping of DPCP between IL clusters occurs through hydrogen bonding with water.

Unwrapping NPT Simulations to Calculate Diffusion Coefficients.

In molecular dynamics simulations in the NPT ensemble at constant pressure, the size and shape of the periodic simulation box fluctuate with time. For particle images far from the origin, the rescaling of the box by the barostat results in unbounded position displacements. Special care is thus required when a particle trajectory is unwrapped from a projection into the central box under periodic boundary conditions to a trajectory in full three-dimensional space, e.g., for the calculation of translational diffusion coefficients. Here, we review and compare different schemes in use for trajectory unwrapping. We also specify the corresponding rewrapping schemes to put an unwrapped trajectory back into the central box. On this basis, we then identify a scheme for the calculation of diffusion coefficients from NPT simulations, which is a primary application of trajectory unwrapping. In this scheme, the wrapped and unwrapped trajectory are mutually consistent and their statistical properties are preserved. We conclude with advice on best practice for the consistent unwrapping of constant-pressure simulation trajectories and the calculation of accurate translational diffusion coefficients.

Near-infrared light-propelled Janus metal-phenolic@Au micromotors for enhanced removal of organic pollutants

Metal-phenolic particles (MPPs) have received increasing attention due to their excellent physicochemical properties (e.g., high porosity, high stability, versatile coordination chemistry) for molecular adsorption. Herein, we constructed NIR light-propelled Janus MPPs@Au (JMPPs@Au) micromotors by depositing Au nanoparticles (NPs) onto the half surface of MPPs, to achieve the active molecular adsorption. Due to excellent photothermal conversion efficiency of Au half nanoshells and its asymmetrical Janus distribution, JMPPs@Au micromotors can make directional movement under the NIR-light irradiation. The translational diffusion coefficient of JMPPs@Au is 5.0 μm2/s and their velocity can reach 8.5 μm/s under NIR laser irradiation (808 nm, 3 W/cm2). Noteworthily, JMPPs@Au micromotors show the enhanced removal efficiency of 10.2 % for methylene blue (MB) dye under NIR light irradiation.

Unified description for the temperature dependence of mobility in liquids.

The physical mechanisms governing molecular mobility in liquids remain unresolved. Whether distinct mechanisms govern mobility in the Arrhenian and super-cooled regions, and whether the mobility in these regions can be unified remain open questions. Here, molecular dynamics simulations were used to search for a structural property with a temperature dependence related by a simple functional form to the temperature dependent translational diffusion coefficient, Dtrans. The logarithm of Dtrans was found to be a two-parameter function of F2, where F2 is the mean squared-force per molecule. The relationship is demonstrated for all systems investigated: a three-bead model of ortho-terphenyl, an 80:20 binary mixture of Lennard-Jones spheres, and a system of Lennard-Jones dumbbells. For each system, the relationship holds for the entire range of temperatures under both constant pressure and constant density conditions. The same F2-based expression describes the translational diffusion coefficient in the Arrhenian, crossover, and super-Arrhenian regions.

Effect of curvature on the diffusion of colloidal bananas.

Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods-also known as colloidal bananas-as a function of their opening angle α. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from 0^{∘} (straight rods) to nearly 360^{∘}(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when α>180^{∘}. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.

Correlating the diffusion of water to performance in model reverse osmosis polyamides with controlled crosslink densities

We systematically reduce the crosslink density of a PA network based on m-phenylene diamine by substituting a fraction of the trifunctional trimesoyl chloride crosslinking agent with a difunctional isophthaloyl analog that promotes chain extension, in order to elucidate robust design cues for improving the polyamide (PA) separation layer in reverse osmosis (RO) membranes for desalination. Thin films of these model PA networks are fully integrated into a composite membrane and evaluated in terms of their water flux and salt rejection. By incorporating 15 mol % of the difunctional chain extender, we reduce the crosslink density of the network by a factor of two, which leads to an 80% increase in the free or unreacted amine content. The resulting swelling of the PA network in liquid water increases by a factor of two accompanied by a 30% increase in the salt passage through the membrane. Surprisingly, this leads to a 30% decrease in the overall permeance of water through the membrane. This conundrum is resolved by quantifying the microscopic diffusion coefficient of water inside the PA network with quasi-elastic neutron scattering. In the highest and lowest crosslink density networks, water shows strong signatures of confined diffusion. At short length scales, the water exhibits translational diffusion that is consistent with the jump-diffusion mechanism. This translational diffusion coefficient is approximately five times slower in the lowest crosslinked density network, consistent with the reduced water permeance. This is interpreted as water molecules interacting more strongly with the increased free amine content. Over longer length scales the water diffusion is confined, exhibiting mobility that is independent of length scale. The length scales of confinement from the quasi-elastic neutron scattering experiments at which this transition from confined to translational diffusion occurs is on the order of (5–6) Å, consistent with complementary X-ray scattering, small angle neutron scattering, and positron annihilation lifetime spectroscopy measurements. The confinement appears to come from heterogeneities in the average inter-atomic distances, suggesting that diffusion occurs by water bouncing between chains and occasionally sticking to the polar functional groups. The results obtained here are compared with similar studies of water diffusion through both rigid porous silicates and ion exchange membranes, revealing robust design cues for engineering high-performance RO membranes.