Slow Diffusion Process Research Articles

Multi-Directional 3D Laser Scanning of Lithium-Ion Cells to Detect Inhomogeneity during Cycling and Aging

Introduction Measuring the thickness of lithium-ion batteries is a reliable method to detect the intercalation stages of the electrodes, the state of charge and irreversible effects during aging [1]. When using tactile high-precision displacement sensors, the measurement is limited to only a few positions of the cell at the same time [2]. Experimental In this work, we developed a test stand, which enables simultaneous precise thickness measurement at 100 positions of the cell. This allows for investigations of the homogeneity of mechanical expansion during charging and discharging, as well as non-destructive state-of-health (SOH) mapping. In a first step, inhomogeneity of mechanical expansion during cycling is studied. In a second step, the effects of expansion inhomogeneity during cycling on the aging behavior of the cells are investigated by determining the irreversible and reversible thickness change at each of the 100 positions every 100th cycle. Results We found that the cell contracts homogeneously during discharge, whereas a significant overshoot in the thickness increase during high-rate charging at the current collector tabs is observed at 25 °C. When the ambient temperature is increased to 40 °C, this inhomogeneity is no longer observable. This effect has been ascribed in literature to non-homogeneous intercalation of Li-ions due to the interplay of fast and slow Li ion diffusion processes [3]. The SOH distributions reveal a homogeneous aging of the cells cycled at low charging rate and high charging rate at 40 °C. Compared to that, the cells cycled at high charging rate at 25 °C show inhomogeneous degradation in areas close to the current collector tabs which show the largest degradation. Literature [1] J. Cannarella, C.B. Arnold, Journal of Power Sources 269 (2014) 7–14. [2] K.-Y. Oh, J.B. Siegel, L. Secondo, S.U. Kim, N.A. Samad, J. Qin, D. Anderson, K. Garikipati, A. Knobloch, B.I. Epureanu, C.W. Monroe, A. Stefanopoulou, Journal of Power Sources (2014). [3] L.W. Sommer, P. Kiesel, A. Ganguli, A. Lochbaum, B. Saha, J. Schwartz, C.-J. Bae, M. Alamgir, A. Raghavan, Journal of Power Sources 296 (2015) 46–52. Figure 1

Application of physical–empirical models to calculate a fragment of the phase diagram and the physical properties of bcc Fe–Cr alloys: II. Calculation of phase boundaries, spinodal, and the temperature dependence of the heat capacity of an alloy

The contributions at a temperature of 500 and 600 K of the chemical, elastic, vibrational, magnetic, electronic, and configurational energies to the Gibbs energy of mixing of bcc alloys without regard for the contribution of a short-range order are calculated as functions of composition and temperature using physical–empirical models. The temperature dependences of the heat capacity of an alloy in both one- and twophase states are calculated. The heat capacity jumps calculated for alloys of various compositions can be used to estimate the equilibrium solubility boundaries of Fe–Cr alloys, which can hardly be found from experimental data because of the slow diffusion processes that occur when an equilibrium state is reached. The calculated solubility boundary of bcc solid solutions and the spinodal and the heat capacity of Fe–Cr alloys are compared with the experimental data and the calculation results obtained in other works. The agreement and discrepancy between these data are discussed.

Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Spectral diffusion arising from $^{29}$Si nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on $^{31}$P nuclear spin coherence is measured as a function of $^{29}$Si concentration using X-band pulsed electron nuclear double resonance (ENDOR). The $^{31}$P nuclear spin echo decays show that decoherence is controlled by $^{29}$Si flip-flops resulting in both fast (exponential) and slow (non-exponential) spectral diffusion processes. The decay times span a range from 100 ms in crystals containing 50% $^{29}$Si to 3 s in crystals containing 1% $^{29}$Si. These nuclear spin echo decay times for neutral donors are orders of magnitude longer than those reported for ionized donors in natural silicon. The electron spin of the neutral donors `protects' the donor nuclear spins by suppressing $^{29}$Si flip-flops within a `frozen core', as a result of the detuning of the $^{29}$Si spins caused by their hyperfine coupling to the electron spin.

Polymer inclusion membrane containing a tripodal diglycolamide (T-DGA): Characterization and sorption isotherm studies

Polymer inclusion membranes (PIMs) of the composition, 25.6% T-DGA (tripodal diglycolamide), 53.9% NPOE (2-nitrophenyloctyl ether), and 20.5% CTA (cellulose triacetate) were prepared and characterized using thermogravimetric analysis, X-ray diffraction, scanning electron microscopy (SEM), atomic force microscopy (AFM), and transmission infrared mapping microscopy (TIMM) using Fourier transform infrared (FT-IR) spectroscopy. Uptake of Am3+ was found to be higher than that of Eu3+ and >82% uptake of Am3+ was seen with the PIM of the composition mentioned above. The batch sorption study of Eu3+ (used as a surrogate of Am3+) by this PIM was investigated in 1 M HNO3 and the data were fitted with different conventional kinetic and isotherm model equations. The sorption followed pseudo-second order (Ho) kinetic model suggesting a two-step uptake process, a fast chemical reaction followed by a slow diffusion process. The experimental data were best fitted with a three-parameter model, i.e., the Redlich-Peterson isotherm model. A comparison is made with results obtained with T2EHDGA-based PIMs reported earlier.

Protein Entrapment in Polymeric Mesh: Diffusion in Crowded Environment with Fast Process on Short Scales

The natural environment of proteins is a crowded environment as in cells, extracellular fluids, or during processing. Semidilute polymer solutions have been a source of rich structural and dynamical properties and mimic a crowded environment, but a proper understanding of protein dynamics in the crowded environment is far lagging. Such a study not only realizes protein’s natural environment in a crowded solution in the cell or during processing but also manifests the underlying protein–polymer interaction. By dispersing model globular proteins like α-lactalbumin (La) and hemoglobin (Hb), in aqueous solution of poly(ethylene oxide) (PEO) we mimic a crowded environment and use state-of-the-art neutron spin echo (NSE) and small-angle neutron scattering (SANS) techniques to observe the corresponding protein dynamics in semidilute polymer solution. NSE can access the fast diffusion process (Dfast) prior to the slow diffusion process on long times and length scales (Dγ). The protein dynamics in a crowded enviro...

New effects in Langmuir and Langmuir-Blodgett monolayers from fluorescently labelled phospholipids and their possible use for water quality control

Secondary water contamination poses significant challenges to the sensitivity and selectivity of sensors used for its detection and monitoring. Currently only lab tests can detect these contaminants and by the time this happens the contaminated water has entered the city water supply system. Fluorescent chromophore NitroBenzoxaDiazole (NBD) is very suitable and had been successfully used in biosensor applications due to its high sensitivity to close proximity polarity of the medium. Over the years we have discovered 3 new effects in NBD- labelled phospholipids which can significantly improve the performance of biosensors. The phospholipid matrix provides flexible biocompatible environment for immobilization of selectively reacting enzymes, microorganisms, DNA, immunoagents, whole cells. Use of single layer (3.1 nm thickness) films at the air-water interface (Langmuir films) or deposited on solid support as Langmuir-Blodgett (LB) film gives fast response times for real time monitoring (no slow diffusion processes) and precise molecule ordering and orientation. The first new effect was fluorescence self-quenching in Langmuir and LB films. In the liquid phase films exhibit normal fluorescence. Upon transition to solid phase fluorescence intensity is almost completely self-quenched and fluorescence lifetimes in the nanosecond region decrease 2 times. This is easily measured. Usually large heavy metal atoms quench fluorescence. We observed the opposite new effect when LB film is deposited in the solid phase from a subphase containing heavy metals. The third new effect is the obtaining of nanosized cylinders with bilayer thickness, which remain stable at least for months, when LB monolayer is deposited in the phase coexistence region at thermodynamic equilibrium. This greatly increases reacting surface and sensitivity of possible sensors. Almost all possible optical experimental methods were used for this research. This includes polarized ATR FTIR and polarized UV-VIS spectroscopies, Fluorescence Lifetime Imaging Microscopy (FLIM), Scanning Near-field Optical Microscopy (SNOM).

Multi-scale modelling of moisture diffusion coupled with stress distribution in CFRP laminated composites

Laminated composite structures operating in a marine environment are subject to moisture ingress. Due to the slow diffusion process of moisture, the distribution of moisture is not uniform so that the laminates can develop hygrothermal stresses. An accurate prediction of the moisture concentration and the associated hygrothermal stress is vital to the understanding of the effect of marine environment on failure initiation. The present paper investigates the time-dependent moisture diffusion and the stress distribution in carbon fibre reinforced polymeric (CFRP) composites by means of experimental study and Finite Element Analysis (FEA). Samples were made from CFRP pre-preg autoclave-cured, and then immersed in fresh water and sea water at a constant 50°C for accelerated moisture diffusion. Laminates with [0]16, [90]16, [±45]4s lay-up sequences were investigated. A multiscale 3D FEA model was developed to evaluate the interfacial stresses between polymer matrix and carbon fibre and the stress distribution in the composite laminates. The analysis revealed that both the stress distribution and stress level are time-dependent due to moisture diffusion, and the interphase between fibres and matrix plays an important role in both the process of moisture diffusion and the stress/strain transfer. The interlaminar shear stresses of the laminates induced by hygrothermal expansion exhibited a significant specimen edge effect. This is correlated with the experimental observations of the flexural failure of laminates.

Fast and slow ion diffusion processes in lithium ion pouch cells during cycling observed with fiber optic strain sensors

Cell monitoring for safe capacity utilization while maximizing pack life and performance is a key requirement for effective battery management and encouraging their adoption for clean-energy technologies. A key cell failure mode is the build-up of residual electrode strain over time, which affects both cell performance and life. Our team has been exploring the use of fiber optic (FO) sensors as a new alternative for cell state monitoring. In this present study, various charge-cycling experiments were performed on Lithium-ion pouch cells with a particular class of FO sensors, fiber Bragg gratings (FBGs), that were externally attached to the cells. An overshooting of the volume change at high SOC that recovers during rest can be observed. This phenomenon originates from the interplay between a fast and a slow Li ion diffusion process, which leads to non-homogeneous intercalation of Li ions. This paper focuses on the strain relaxation processes that occur after switching from charge to no-load phases. The correlation of the excess volume and subsequent relaxation to SOC as well as temperature is discussed. The implications of being able to monitor this phenomenon to control battery utilization for long life are also discussed.

Modeling Diffusion of Linear Hydrocarbons in Silica Zeolite LTA Using Transition Path Sampling

The diffusivities of linear hydrocarbons (CH4, C2H6, C2H4, C3H8, C3H6, and C4H10) in pure silica zeolite LTA (ITQ-29) are computed at 300 K and infinite dilution. To overcome the time scale problem arising from the slow diffusion process at room temperature, we used transition path sampling (TPS). The influence of framework flexibility on diffusion is investigated by combining TPS simulations with fully flexible molecular dynamics performed in the NpT ensemble. The ensemble of the collected reactive trajectories was used to characterize sets of transition states, and the corresponding configurations were analyzed to construct window size distributions during the molecular hopping events. The diffusion process is affected by framework flexibility, and the influence of framework flexibility on diffusion of propane and butane is much larger than for methane and ethane.

Step-Flow Kinetics Model for the Vapor–Solid–Solid Si Nanowires Growth

Vapor-solid-solid (VSS) process has recently received continued attention as an alternative to grow Si nanowire. In comparison with common vapor-liquid-solid (VLS) growth with liquid catalyst, VSS growth can prevent the catalyst species from incorporating into nanowires with deep-level impurity, and achieve the compositionally abrupt interfaces by restraining the so-called "reservoir effect". However, despite the huge advances in experimental observations with in situ electron microscopy, VSS growth still remains much less understood in theory. Here, we developed a general mass-transport-limited kinetic model to describe the VSS growth process of Si nanowires by considering three surface diffusion processes and a slow interface diffusion process, where the former determines the atoms supplies way, while the latter dominates the growth of nanowires. The present model is not only well consistent with the available experimental data of Si nanowire, but also gives a clear physical image for the successive side-to-side ledge flow VSS growth.

Oxygen Diffusion in Mayenite

Oxygen transport in mayenite single crystals was studied by means of 18O/16O isotope exchange experiments and time-of-flight secondary ion mass spectrometry (ToF-SIMS). Oxygen tracer diffusion coefficients D* and oxygen surface exchange coefficients k* were determined as a function of temperature, 773 ≤ T/K ≤ 1273, at an oxygen activity of aO2 = 0.1, and as a function of oxygen activity, 0.01 ≤ aO2 ≤ 0.9, at a temperature of T = 1123 K. Two diffusion processes were observed: a fast diffusion process that is attributed to the interstitialcy diffusion of free oxygen ions (O2–) and a slow diffusion process that is attributed to the interstitialcy diffusion of superoxide ions (O2–).

Lidocaine permeation from a lidocaine NaCMC/gel microgel formulation in microneedle-pierced skin: vertical (depth averaged) and horizontal permeation profiles.

Common local anaesthetics such as lidocaine are administered by the hypodermic parenteral route but it causes pain or anxiety to patients. Alternatively, an ointment formulation may be applied which involves a slow drug diffusion process. In addressing these two issues, this paper aims to understand the significance of the 'poke and patch' microneedle (MN) treatment on skin in conjunction to the lidocaine permeation, and in particular, the vertical (depth averaged) and horizontal (e.g. lateral) permeation profiles of the drug in the skin. The instantaneous pharmacokinetics of lidocaine in skin was determined by a skin denaturation technique coupled with Franz diffusion cell measurements of the drug pharmacokinetics. All pharmacokinetic profiles were performed periodically on porcine skin. Three MN insertion forces of 3.9, 7.9 and 15.7N were applied on the MN to pierce the skin. For the smaller force (3.9N), post MN-treated skin seems to provide an 'optimum' percutaneous delivery rate. A 10.2-fold increase in lidocaine permeation was observed for a MN insertion force of 3.9N at 0.25h and similarly, a 5.4-fold increase in permeation occurred at 0.5h compared to passive diffusional delivery. It is shown that lidocaine permeates horizontally beyond the area of the MN-treated skin for the smaller MN insertion forces, namely, 3.9 and 7.9N from 0.25 to 0.75h, respectively. The lateral diffusion/permeation of lidocaine for larger MN-treated force (namely, 15.7N in this work) seems to be insignificant at all recorded timings. The MN insertion force of 15.7N resulted in lidocaine concentrations slightly greater than control (passive diffusion) but significantly less than 3.9 and 7.9N impact force treatments on skin. We believe this likelihood is due to the skin compression effect that inhibits diffusion until the skin had time to relax at which point lidocaine levels increase.

Effects of Ninetyeast Ridge Magmatism and Pre India-Eurasia Collision Dynamics on Basement and Crust-lithospheric Structures of the Northeastern Indian Ocean

Abstract: The coexistence of multifaceted geodynamical situation in the Northeastern Indian Ocean (Bay of Bengal) lithosphere inspires to investigate the origin, present day orientation and gravitational stability of its basement, crust and lithospheric structures. The origin, evolution and the present day configuration of these structures such as the northward down dipping of the Bay of Bengal basement and its lithosphere, the Moho of the 85°E ridge, the formation of the Ninetyeast ridge median graben and ridge normal faults and their interaction with slow convergence and stress diffusion processes in the north Andaman trench, remain conspicuous. In this paper, we explain the above mentioned processes and the existence of the Bay of Bengal basement features through plausible tectonic scenarios that related with past time dynamics of the Indian Plate prior to the India-Eurasia collision and lithospheric thermal perturbation due to the Ninetyeast Ridge magmatism. Our analysis on the basis of satellite altimeter-derived geoid, gravity, sediment thickness, basement undulation, isostatic and prospecting geoid anomaly; suggests apart from the enhanced Oligocene Himalayan erosion and subsequent increased sediment load, the gravitational stability of the basin load (like formation of ridge graben) was also affected by altering the basin rheology to inelastic, owing to the enhanced thermal perturbation by the ninetyeast ridge magma. This made the Bay of Bengal lithosphere rheologically weak. Pre India-Eurasia collision, fast movement and fast convergence of the Indian plate at erstwhile north Andaman subduction zone made the lithosphere relatively stretchable due to the prevalence of intra-plate extensional stresses. The NE-SW orientation of the Central basin depression and the northward (NE-SW) dipping of the Bay of Bengal (BOB) lithosphere are pointing to such a stretchable lithosphere and its remnants are present at the northeast of the northern Ninetyeast ridge, as observed from the low prospecting geoid anomaly. The presence of such a thermally altered, weak lithosphere as a subducting slab at the north Andaman trench caused the present day observed low convergence rate, lack of seismicity, as well as the cessation of fault rupture followed by the Great Sumatra Andaman earthquake of Mw (9.1) on 26 December 2004. The Ninetyeast ridge oblique collision with the north Andaman trench was presumed around Pleistocene based on the timing of abandonment of the Nicobar fan from the Bengal head fan. The discontinuity of the ridge along the oblique convergence zone of the north Andaman and its isostatic stability are mainly controlled by the subduction zone dynamics, unlike the 85°E ridge.

Effect of CO2 sorption-induced anisotropic swelling on caprock sealing efficiency

Caprock sealing integrity is a key issue to CO2 sequestration in a saline aquifer over a long period. Caprock as a sealing layer is defined as water-saturated formation with a sufficient capillary entry pressure to prevent the upward migration of a buoyant fluid. Most caprocks are naturally anisotropic, hence the effect of CO2 sorption-induced anisotropic swelling may heavily impact their sealing efficiency.This paper proposes a numerical model based on a conceptual model for the investigation of the sealing efficiency of anisotropic caprocks, where caprock is a composite body of fracture network and shale matrix. Two-phase flow of brine water and CO2 is observed only in the fracture network but the CO2 in the fractures further diffuses into shale matrix through a much slower diffusion process and makes the shale matrix anisotropically swell or shrink, thus significantly altering the directional porosity and permeability of the fracture network. This numerical model is verified by a storage reservoir and applied to a caprock layer to explore the mechanism for self-enhancement or self-limiting in the CO2–brine mixing zone if anisotropic swelling is considered. These examples demonstrate that this model is able to numerically simulate the CO2 storage relevant geological systems within anisotropic shale. The sorption-induced anisotropic swelling of shale matrix has significant impacts on the caprock sealing efficiency. This work provides an alternative tool to enrich the numerical modeling for the assessment of CO2 caprock sealing efficiency in natural shale caprocks.

Fourier regularization for a final value time-fractional diffusion problem

The evolution process of fractional order describes some phenomenon of anomalous diffusion and transport dynamics in complex system. The equation containing time-fractional derivative provides a suitable mathematical model for describing such a process. The backward problem for this system, which means to recover the initial state for some slow diffusion process from its present status, is very hard to solve due to the nonlocal property of fractional derivative and the irreversibility of time. For this ill-posed problem, we construct a regularizing solution using the Fourier transform method. Both the a-priori choice strategy and the a-posteriori choice strategy for the regularizing parameter are given, with the convergence analysis on the regularizing solution. Numerical implementations are presented to show the validity of the proposed scheme.

Pulsating instability in H2–air partially premixed flames

Steady/unsteady hydrogen–air partially premixed flames (PPFs) in a counterflow configuration were computationally studied with detailed chemistry and transport, and the pulsating instability of PPFs was observed. During PPFs oscillation, the pulsating instability for the premixed flame is caused by a large overall activation energy (Ea) and a slow O2 diffusion process (Le >1). The nonpremixed flame undergoes forced oscillation caused by oscillated H2 diffusion flux from the premixed flame zone. In H2–air PPFs, premixed/nonpremixed flame structures and the interactions between them are controlled by the equivalence ratio (ϕ) and global strain rate (a). These factors also control the stability boundary. Large ϕ and/or a values retard pulsating instability, because increases in ϕ and/or a cause the two flames to move closer to each other, thereby intensifying the conduction heat flux from nonpremixed flame to premixed flame. The temperature in strengthened premixed flame is insensitive to the perturbation of chemical heat release, on the other hand, the competition between H+O2↔OH+O (R1) and H+O2+M↔HO2+M (R9) decreases, which leads to smaller Ea. Thus, the chemical reactions are also insensitive to the perturbation of flame temperature.

Determination and Prediction of the Lag Times of Hydrocarbons through a Polyethylene Terephthalate Film

Polymeric materials can be used as functional barriers to prevent contamination of food from the environment or from other packaging components, e.g. mineral oil hydrocarbons from printing inks. Polyethylene terephthalate (PET) is such a promising barrier material. From permeation studies found in the scientific literature lag times, diffusion coefficients or permeation rates towards organic chemicals could not derived because of the slow diffusion process of the permeants in PET. Knowledge about lag times or diffusion coefficients for different permeants, however, is essential for the evaluation of the barrier properties of PET films towards organic contaminants, e.g. mineral oil hydrocarbons. The aim of the study was to develop automated permeation testing method in order to determine the lag times of high-barrier films. From the lag times, the diffusion coefficients as well as the partition coefficients of the alkanes were calculated. In addition, the permeated amounts were simulated by use of diffusion models. Therefore, the lag times can be predicted under different experimental conditions as used in the current study. The results of this study show that the investigated 12 µm PET film is an effective barrier towards mineral oil hydrocarbons. For example, the predicted lag time for n-octane or n-dodecane at 40°C is 8.8 and 210 years respectively. Copyright © 2014 John Wiley & Sons, Ltd.

Existence of nonnegative nontrivial periodic solutions to a doubly degenerate parabolic equation with variable exponent

The authors investigate a degenerate parabolic equation with delay and nonlocal term, which describes slow diffusive processes in physics or biology. The existence of a nonnegative nontrivial periodic solution is obtained through the use of the Leray-Schauder degree method. MSC:35D05, 35K55.

FEM analysis of magnetic agitation for tagging biomolecules with magnetic nanoparticles in a microfluidic system

In a microfluidic system, magnetic nanoparticles (MNPs) tagged with biomolecules can be efficiently used for separation and detection. Tagging various fluid contents continuously in the micro-scale is often difficult due to slow diffusion process. Therefore, enormous time is needed for biomolecules to be thoroughly mixed and combined with MNPs. In this work, we report a finite-element COMSOL-based model to demonstrate the novel method of tagging biomolecules with MNPs on-chip using time-dependent magnetic field. The oscillating magnetic body forces that act on MNPs cause agitation in the surrounding fluid that otherwise follow laminar profile and overall speed up the reaction kinetics of the tagging process. Based on results, magnetic actuation is a strong function of both magnetic nanoparticle size and switching frequency of magnetic field and for the studied geometrical configuration and flow condition 100nm MNPs together with 0.1Hz switching frequency bring out optimum mixing condition. Effect of flow velocity is also studied and from the analysis MNPs actuated tagging process seems to be more profound at an optimum inlet velocity of 50μm/s. Electrode current and electrode separation are also critical parameters and need to be optimized. For the given configuration, larger separation and higher current produce less agitation effect. Furthermore, magnetic actuation scheme is compared with passive mixing strategy. A 49% increase in tagging performance is observed when MNPs together with magnetic actuation scheme is used as compared to passive method consisting of barriers which only increases the tagging performance by 20%. The strategy demonstrated here is easy to implement and can be integrated on a lab-on-a-chip system. Overall, the developed COMSOL model demonstrates that time-dependent magnetic actuation is an efficient tool to tag MNPs with biomolecules in situ for the development of efficient point-of-care microfluidic systems.

Microgel-like aggregates of isotactic and atactic poly(methacrylic acid) chains in aqueous alkali chloride solutions as evidenced by light scattering.

A comparative light-scattering study of isotactic and atactic poly(methacrylic acid), iPMA and aPMA, respectively, in aqueous solutions with added alkali chlorides, XCl (X = Li, Na, Cs), at 25 °C and XCl concentration of 0.1 mol L(-1), demonstrates that both PMA isomers are strongly associated at low degrees of neutralization, αN (= 0 for aPMA and 0.25 for iPMA), in the presence of all XCls. The shape parameter ρ and the scattering functions suggest that aggregates have the characteristics of microgel particles, with a dense core surrounded by a less dense shell. The extent of aggregation depends on the stereoregular structure of the polymer and on the type of the added cation. Li(+) and Na(+) ions support aggregation better than Cs(+) ions. Besides, iPMA chains are more strongly aggregated than aPMA chains and form particles with a denser core. A model of the aggregation process is suggested for iPMA. At high αN, a slow diffusive process (so-called extraordinary or anomalous mode in diffusion of polyelectrolytes), arising from electrostatic interactions between charged chains, is observed for both PMAs. Results suggest that under the same experimental conditions iPMA is effectively more charged than aPMA. The role of ions in the slow-mode phenomenon is less pronounced than in aggregation.