Fickian Diffusion Coefficients Research Articles

Improving the Gas Barrier Properties of Nafion via Thermal Annealing: Evidence for Diffusion through Hydrophilic Channels and Matrix

Oxygen diffusion through commercial Nafion films is investigated using a transient electrochemical reduction method. Direct experimental evidence is found for two Fickian diffusion coefficients corresponding to oxygen permeation through the hydrophilic channels and fluorocarbon matrix. The diffusion coefficient and solubility of oxygen in each phase, which controls the overall permeability, can be tuned via thermal annealing where films annealed at 160 °C have a substantially reduced oxygen permeability relative to the as-received material. Films annealed at 200 °C show intermediate oxygen permeation to the as-received and 160 °C annealed samples. Differential scanning calorimetry and wide-angle X-ray scattering are employed to demonstrate that increasing crystallinity reduces the oxygen solubility and diffusion coefficient through the Nafion matrix. The two oxygen diffusion coefficients are discussed in the context of literature values which span more than an order of magnitude. It is found that the time...

Model of chloride ingress into concrete in cold regions

Chloride ingress and freeze-thaw cycles are the most important mechanisms for deterioration of concrete in cold areas. In this study, chloride ingress into concrete that has been exposed to freeze-thaw cycles was investigated. Data demonstrated that freeze-thaw cycles allow for a larger effective diffusion coefficient. Based on our findings, the concept of a developing coefficient was defined to obtain the evolution equation of the effective diffusion coefficient. Together with considering the effect of aging of concrete on the effective diffusion coefficient, the time-dependent diffusion coefficient was also obtained. Based on Fick's second law and time-dependent diffusion coefficient, chloride ingress model of concrete in cold regions was derived. Finally, the model was tested by comparing predicted results, lab results, and in situ inspection data.

Contribution to the benchmark for ternary mixtures: Measurement of diffusion and Soret coefficients of ternary system tetrahydronaphtalene-isobutylbenzene-n-dodecane with mass fractions 80-10-10 at 25 °C.

This paper provides the molecular diffusion and Soret coefficients of the ternary system 1,2,3,4-tetrahydronaphtalene, isobutylbenzene, n -dodecane system at mass fractions 0.8-0.1-0.1 and temperature 25 (°)C for implementation into the benchmark presented in this topical issue. The Soret coefficients are determined by digital interferometry using the data of DSC-DCMIX microgravity experiment. The method used takes into account the influence of the thermal field on the Soret separations and the selection of the image processing techniques results in reproducible Soret coefficients.The diffusion coefficients are obtained by the Open Ended Capillary technique The fitting of the data collected through a set of two complementary experimental runs allows retrieving the four Fickian diffusion coefficients.

The studies of particle diffusion on a heterogeneous one-dimensional lattice

Abstract Diffusion of particles adsorbed on a heterogeneous one-dimensional chain is investigated using the theoretical approach and Kinetic Monte Carlo simulations. The concentration dependencies of the center-of-mass and Fickian diffusion coefficients are calculated for some representative values of the lateral interaction between the adsorbed particles. We thoroughly compared the analytical dependencies with the numerical data. The perfect coincidence of the data obtained by the two different methods clearly demonstrates that the analytical expressions obtained for the diffusion coefficients exactly describe the particle migration in the heterogeneous lattice gas systems.

Investigation of Fickian diffusion in the ternary mixtures of water-ethanol-triethylene glycol and its binary pairs.

We present a comprehensive experimental study of isothermal Fickian diffusion in the ternary and binary liquid mixtures of water, ethanol, and triethylene glycol over the entire ternary composition space. 21 ternary mixtures inside the composition triangle have been investigated by means of the Taylor dispersion technique and 30 binary mixtures by Taylor dispersion and/or optical beam deflection in a Soret cell. The scalar binary diffusion coefficient has been determined along all three binary boundaries of the composition space and compared with estimations based on the Stokes-Einstein relation using stick or slip boundary conditions. The four elements of the ternary diffusion matrix and the diffusion eigenvalues were determined over a large portion of the composition triangle. The pseudo-binary diffusion coefficients obtained in Taylor dispersion experiments with either one of the two independent concentrations kept constant are comparable to the two diffusion eigenvalues. One of the two off-diagonal elements of the diffusion matrix is of the same order as the diagonal ones and, hence, not negligible, whereas the other one is approximately one order of magnitude smaller. Where available, our results compare well with literature data. The investigated compositions also comprise the five compositions that are scheduled for microgravity experiments in the ESA DCMIX3 project.

Revisiting polymer surface diffusion in the extreme case of strong adsorption.

Revisiting polymer surface adsorption with a level of quantification not possible at the time of earlier seminal contributions to this field, we employ fluorescence microscopy to quantify the in-plane diffusion of end-labeled polystyrene adsorbed onto quartz and mica from cyclohexane solution, mostly at 25 °C. Care is taken to prohibit a surface-hopping mechanism, and the experimental techniques are adapted to measurements that persist for up to a few days. The main conclusion is that we fail to observe a single Fickian diffusion coefficient: instead, diffusion displays a broad multicomponent spectrum, indicating that the heterogeneity of surface diffusion fails to average out even over these long times and over distances (∼600 nm, the diameter of a diffraction-limited spot) greatly exceeding the size of the polymer molecules. This holds generally when we vary the molecular weight, the surface roughness, and the temperature. It quantifies the long-believed scenario that strongly adsorbed polymer layers (monomer-surface interaction of more than 1k(B)T) intrinsically present diverse surface conformations that present heterogeneous environments to one another as they diffuse. Bearing in mind that in spite of adsorption from dilute solution the interfacial polymer concentration is high, ramifications of these findings are relevant to the interfacial mobility of polymer glasses, melts, and nanocomposites.

Diffusion of particles on the patchwise bivariate surfaces

The diffusion of particles adsorbed on patchwise surfaces is investigated in the framework of a lattice-gas model. We propose the analytical expressions for the center-of-mass and Fickian diffusion coefficients. The theoretical dependencies are compared with the numerical data obtained by the kinetic Monte Carlo simulations for three different patchwise lattices. The good coincidence of the theoretical dependencies and the numerical data corroborates the validity of the approach developed to describe the particle migration on such lattices.

Controlled release of thiamin in a glassy κ-carrageenan/glucose syrup matrix

The work dealt with the diffusional mobility of thiamin embedded in a high-solid matrix of κ-carrageenan with glucose syrup. It utilized thermomechanical analysis in the form of modulated differential scanning calorimetry and small-deformation dynamic oscillation in shear, Fourier transform infrared spectroscopy, wide angle X-ray diffraction, scanning electron microscopy and UV–vis spectrophotometry. The structural properties of the matrix were assessed in a temperature induced rubber-to-glass transformation. A thiamin-dye binding assay was employed to monitor the diffusion process of the vitamin from the high-solid preparation to ethylene glycol. The relationship between mechanical properties of the carbohydrate matrix and vitamin mobility was assessed via the application of the combined framework of the free volume theory and the predictions of the reaction rate theory. Results argue that the transport of the micronutrient is governed by the structural relaxation of the high-solid matrix. These were further treated with the concept of Fickian diffusion coefficient to provide the rate of the bioactive compound mobility within the present experimental settings.

Insight on Pure vs Air Exposed Hydroxide Ion Conductivity in an Anion Exchange Membrane for Fuel Cell Applications

Understanding the role of water in anion exchange membrane (AEM) used in fuel cells is essential for commercial application.1 Many literatures published have emphasized the important of water to optimize membrane properties such as ionic conductivity, ion transport, and mechanical and chemical stability.1-3 Recently, the idea of using thin layers of catalyst and solubilized ionomer is very common and demands the greater understanding of hydration behavior of AEMs.4 Several techniques have been used to understand the diffusion of water in membranes. Elabd et al5 have summarized the diffusion coefficient values from different methods and mentioned the in-consistency among different methods. A time resolved Fourier transform infrared- attenuated total reflectance (FTIR-ATR) spectroscopy is a less common method to measure the water diffusion through AEMs although this method has been recently used in other materials.6, 7 FTIR-ATR spectra were collected using Nexus 4700 (Thermo-fisher) with an ATR accessory (Specac, Inc). A liquid nitrogen cooled mercury cadmium telluride (MCT) detector was used to collect a spectrum with 128 scans every 25 seconds with a resolution of 4 cm-1. A custom built design was used to control RH of the membrane sample during experiments. In order to verify the experimental setup, the diffusion coefficient of water through Nafion 117® membrane was observed at the same order of magnitude (1.63±0.27 x 10-7 cm2/s vs 3.71x 10-7 cm2/s observed by Elabd et al7) when the relative humidity of the sample was changed from 0 to 100 %RH. Water diffusion coefficient was then measured for AEMs as a function of temperature and RH. The Fickian water diffusion coefficient for AEMs was observed to be lower than proton exchange membranes by one order of magnitude. Figure 1 shows the comparison of water diffusion kinetics between one of the anion exchange membranes and Nafion 117® at 30 oC.In this work, water behavior of different AEMs as a function of temperature and RH will be presented, the energy barrier for the water diffusion through these membrane will be discussed and the science behind a slow water diffusion through AEMs will be explored.Figure 1. Time-resolved normalized absorbance for O-H stretching vibration collected using FTIR-ATR at 30oC when RH was increased from 0 to 100%. Acknowledgement The authors would like to thank the US Army Research Office for the funding under the MURI #W911NF-10-1-0520and the purchase of FTIR microscope from ARO DURIP #W911NFNF-0462 References Merle, G.; Wessling, M.; Nijmeijer, K., Anion exchange membranes for alkaline fuel cells: A review. Journal of Membrane Science 2011, 377, 1-35.Duan, Q. J.; Ge, S. H.; Wang, C. Y., Water uptake, ionic conductivity and swelling properties of anion-exchange membrane. Journal of Power Sources 2013, 243, 773-778.Myles, T. D.; Kiss, A. M.; Grew, K. N.; Peracchio, A. A.; Nelson, G. J.; Chiu, W. K. S., Calculation of Water Diffusion Coefficients in an Anion Exchange Membrane Using a Water Permeation Technique. Journal of the Electrochemical Society 2011, 158, B790-B796.Mehta, V.; Cooper, J. S., Review and analysis of PEM fuel cell design and manufacturing. Journal of Power Sources 2003, 114, 32-53.Hallinan, D. T.; Elabd, Y. A., Diffusion of Water in Nafion Using Time-Resolved Fourier Transform Infrared−Attenuated Total Reflectance Spectroscopy. The Journal of Physical Chemistry B 2009, 113, 4257-4266.Sundfors, F.; Lindfors, T.; Hofler, L.; Bereczki, R.; Gyurcsanyi, R. E., FTIR-ATR Study of Water Uptake and Diffusion through Ion-Selective Membranes Based on Poly(acrylates) and Silicone Rubber. Analytical Chemistry 2009, 81, 5925-5934.Hallinan, D. T.; Elabd, Y. A., Diffusion and Sorption of Methanol and Water in Nafion Using Time-Resolved Fourier Transform Infrared−Attenuated Total Reflectance Spectroscopy. The Journal of Physical Chemistry B 2007, 111, 13221-13230.

Water/Methanol Transport in Polyethylene Based Block Copolymers as Anion Conductors for Applications in Fuel Cells

Anion exchange membranes have been a central point of focus for the low temperature fuel cell application. The primary goal of AEMs in fuel cells is to transport hydroxide (OH-) ions from cathode to anode and to act as a separator between the electrodes. In this work we have studied a block copolymer of polyethylene and polyvinyl benzyl trimethyl ammonium bromide (PE-b-PVBTMA[Br], Fig. 1) for various transport properties. By using the dynamic vapor sorption apparatus we were able to study water and methanol uptake dynamics for this AEM. Fickian diffusion coefficients for both water and methanol were calculated during this study giving idea about the solvent uptake kinetics.We also measured the conductivity of the AEM under 95% relative humidity (Figure 2). It was found that the AEM followed VFT theory behavior for transporting ions through it as opposed to the classical Arrhenius behavior. VFT behavior suggests that ion transport in the membrane is facilitated by the polymer chain motion as opposed to ion transport in water which is governed mainly by the Arrhenius type of behavior.We also report methanol/water ion transport using the pulse gradient stimulated spin echo (PGSTE) NMR technique to determine the tortuosity of the membrane along with self diffusion of each species. Acknowledgements: We would like to thank the Army Research Office for funding this Multidisciplinary University Research Initiative under contract #W911NF-10-1-0520 and the Colorado School of Mines NMR facility, funded by National Science Foundation under the grant CHE-0923537. We would like to thank Yifan Li, D M Knauss for providing with the polymer for this study.

Analytical approach for collective diffusion: one-dimensional homogeneous lattice.

Diffusion of particles adsorbed on the homogeneous one-dimensional chain was investigated using a theoretical approach and kinetic Monte Carlo simulations. The concentration dependencies of the center-of-mass and Fickian diffusion coefficients have been calculated for some representative values of lateral interactions between adsorbed particles. The analytical dependencies have been compared with the numerical data. The perfect coincidence of the data obtained by the two quite different methods clearly demonstrates that the analytical expressions for the diffusion coefficients derived in the framework of the approach based on the non-equilibrium statistical operator exactly describe the particle migration in the lattice gas systems.

Determination of the thermodynamic correction factor of fluids confined in nano-metric slit pores from molecular simulation.

The multi-component diffusive mass transport is generally quantified by means of the Maxwell-Stefan diffusion coefficients when using molecular simulations. These coefficients can be related to the Fick diffusion coefficients using the thermodynamic correction factor matrix, which requires to run several simulations to estimate all the elements of the matrix. In a recent work, Schnell et al. ["Thermodynamics of small systems embedded in a reservoir: A detailed analysis of finite size effects," Mol. Phys. 110, 1069-1079 (2012)] developed an approach to determine the full matrix of thermodynamic factors from a single simulation in bulk. This approach relies on finite size effects of small systems on the density fluctuations. We present here an extension of their work for inhomogeneous Lennard Jones fluids confined in slit pores. We first verified this extension by cross validating the results obtained from this approach with the results obtained from the simulated adsorption isotherms, which allows to determine the thermodynamic factor in porous medium. We then studied the effects of the pore width (from 1 to 15 molecular sizes), of the solid-fluid interaction potential (Lennard Jones 9-3, hard wall potential) and of the reduced fluid density (from 0.1 to 0.7 at a reduced temperature T* = 2) on the thermodynamic factor. The deviation of the thermodynamic factor compared to its equivalent bulk value decreases when increasing the pore width and becomes insignificant for reduced pore width above 15. We also found that the thermodynamic factor is sensitive to the magnitude of the fluid-fluid and solid-fluid interactions, which softens or exacerbates the density fluctuations.

Unraveling Diffusion and Other Shape Selectivity Effects in ZSM5 Usingn-Hexane Hydroconversion Single-Event Microkinetics

Potentially dominant factors governing the shape selectivity in n-hexane hydroconversion over a Pt/H-ZSM5 catalyst were evaluated by means of single-event microkinetic (SEMK) model regression against experimental data. The observed product distribution could be adequately modeled, and a corresponding physically meaningful interpretation could be made only when accounting for intracrystalline diffusion limitations for each hexane isomer involved in the reaction network, rather than considering physisorption effects or transition-state shape selectivity. Simultaneous diffusion and reaction inside the catalyst crystallites were expressed via Fick’s second law, while the alkane Fick diffusion coefficients were assessed by explicitly accounting for mixture nonideality effects. A 3-fold lower diffusion coefficient was found to be required for 3-methylpentane compared with 2-methylpentane to explain the typically high selectivity toward the latter alkane. Once formed inside the catalyst crystallite, dimethylbuta...

Evolution of particle structure during water sorption observed on different size fractions of durum wheat semolina

This work examines the effect of the particle size of durum wheat semolina on the water diffusion coefficient and the evolution of the microstructure during hydration. Durum wheat semolina was sieved in 5 size categories. Water–particle interaction of powders (5 fractions and raw semolina) was studied using dynamic vapour sorption. Water sorption isotherms were fitted to G.A.B.. and Y&N models. Monolayer values as well as multilayer properties were calculated and compared. Absorption properties were determined by Y&N model. A sorption curve was modelled with the Fickian diffusion equation adapted to water diffusion into solid particles. A dynamic Fickian water diffusion coefficient was calculated for each particle size after conditioning at different RHs. The surface structure of conditioned fractions was observed by ESEM. The microstructure of semolina presented an evolution with the increase of size and RH. Starch grains presented an increased size and protein matrix had a different texture. After correlation of isotherm data and microstructure, the resulting state and properties of the components were a key to understand diffusion on food powder systems.

Measurement of Soret and Fickian diffusion coefficients by orthogonal phase-shifting interferometry and its application to protein aqueous solutions

We have developed a method to measure thermodiffusion and Fickian diffusion in transparent binary solutions. The measuring instrument consists of two orthogonally aligned phase-shifting interferometers coupled with a single rotating polarizer. This high-resolution interferometer, initially developed to measure isothermal diffusion coefficients in liquid systems [J. F. Torres, A. Komiya, E. Shoji, J. Okajima, and S. Maruyama, Opt. Lasers Eng. 50, 1287 (2012)], was modified to measure transient concentration profiles in binary solutions subject to a linear temperature gradient. A convectionless thermodiffusion field was created in a binary solution sample that is placed inside a Soret cell. This cell consists of a parallelepiped cavity with a horizontal cross-section area of 10 × 20 mm(2), a variable height of 1-2 mm, and transparent lateral walls. The small height of the cell reduces the volume of the sample, shortens the measurement time, and increases the hydrodynamic stability of the system. An additional free diffusion experiment with the same optical apparatus provides the so-called contrast factors that relate the unwrapped phase and concentration gradients, i.e., the measurement technique is independent and robust. The Soret coefficient is determined from the concentration and temperature differences between the upper and lower boundaries measured by the interferometer and thermocouples, respectively. The Fickian diffusion coefficient is obtained by fitting a numerical solution to the experimental concentration profile. The method is validated through the measurement of thermodiffusion in the well-known liquid pairs of ethanol-water (ethanol 39.12 wt.%) and isobutylbenzene-dodecane (50.0 wt.%). The obtained coefficients agree with the literature values within 5.0%. Finally, the developed technique is applied to visualize biomolecular thermophoresis. Two protein aqueous solutions at 3 mg∕ml were used as samples: aprotinin (6.5 kDa)-water and lysozyme (14.3 kDa)-water. It was found that the former protein molecules are thermophilic and the latter thermophobic. In contrast to previously reported methods, this technique is suitable for both short time and negative Soret coefficient measurements.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell–Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Thermoresponsive biodegradable PEG‐PCL‐PEG based injectable hydrogel for pulsatile insulin delivery

An injectable biodegradable hydrogel was prepared for temperature-responsive pulsatile release of insulin. Triblock copolymer of poly(ethylene glycol)-poly(ε-caprolactone)-poly(ethylene glycol) (PEG-PCL-PEG, PECE) was prepared by ring opening bulk copolymerization and characterized using FT-IR, (1) HNMR, and gel permeation chromatography. Aqueous solution of PECE formed an injectable hydrogel, which was solution at room temperature and transformed into gel at 37°C. The temperature-responsive sol-gel transition and crystallinity of PECE hydrogel was studied and compared with pluronic, a well-studied nonbiodegradable injectable hydrogel. In vitro release study revealed that insulin release profile of PECE was similar to pluronic, and its viscosity was 1/30(th) of pluronic sol at 10,000 s(-1) shear rate. Release behavior of insulin from PECE hydrogels followed Fickian diffusion of first order. Insulin retained its secondary structure after release as confirmed by circular dichroism spectrum. A threefold increase in Fickian diffusion coefficient was evidenced when temperature was increased from 34 to 40°C because of crystalline melting of PCL part of PECE. Pulsatile release of insulin showed a correlation coefficient of 0.90 with the change of temperature.

A simple thermodynamic approach to predict responses from polymer-coated quartz crystal microbalance sensors exposed to organic vapors

As of lately, the demand for developing artificial sensors with improved capabilities for the detection of explosives, toxics or drugs has increased. Ideally, sensor devices should provide high sensitivity and give a response that is specific to a given target molecule without being influenced by possible interfering molecules in the atmosphere. These properties strongly depend on the structure of the chemical compound used as a sensitive material. It is thus crucial to select the right compound and this step would be facilitated with the aid of predictive tools. The present investigations have been focused on a family of functionalized polysiloxane polymers deposited on a QCM device, producing only weak interactions compatible with reversible sensors. The quartz frequency variation at equilibrium has been linked to the partition coefficient that was evaluated using a thermodynamic description of the adsorption process. We have shown that the relative responses of two polymers can be directly determined from the Gibbs free enthalpy of mixing as determined from NMR measurements performed on neat liquid mixtures. An equivalence of this term—including both enthalpy and entropy contributions—to the energy interaction term calculated using Hansen solubility coefficients, has been demonstrated previously. These results constitute a basis for the development of a numerical program for calculating equilibrium sensor responses. For small molecules, the adsorption kinetics can be easily accounted for by a Fick diffusion coefficient estimated from the Van der Waals volume.

Development of a Unifying Framework for the Restrictions in Multi-component Diffusion Close to Equilibrium

In this work a unifying framework is developed for multi-component diffusion close to equilibrium by proposing additional restrictions for the Fickian diffusion coefficients such as the Onsager reciprocal relations. Moreover, it is shown that these additional restrictions can explain the discrepancy, reported in the literature, of calculating negative concentrations in Fickian ternary free diffusion observed even if the second thermodynamic law constraints and the phase stability criteria are satisfied. It is believed that this work could be used to further investigate multi-component diffusion.

Calculating thermodynamic factors of ternary and multicomponent mixtures using the Permuted Widom test particle insertion method

We present an approach to calculate thermodynamic factors for multicomponent liquid mixtures from molecular simulations by the Permuted Widom test particle insertion method. The thermodynamic factors relate experimentally obtained Fick diffusion coefficients and the Maxwell–Stefan diffusion coefficients computed from molecular simulations/theory. In our earlier work, we presented the Permuted Widom test particle insertion method (Balaji et al. in Mol Phys 2012) for calculating thermodynamic factors for binary systems from a single simulation. In this paper, we have extended this approach to ternary systems consisting of Lennard–Jones particles. The thermodynamic factors computed from the simulations and from numerically differentiating the activity coefficients obtained from the conventional Widom single test particle insertion method were compared. An excellent agreement was observed.