Composition-dependent Diffusivity Research Articles

Hydrogen Bonding Strength Determines Water Diffusivity in Polymer Ionogels.

Polymeric ionogels, cross-linked gels swollen by ionic liquids (ILs), are useful vehicles for the release and storage of molecular solutes in separation, delivery, and other applications. Although rapid solute diffusion is often critical for performance, it remains challenging to predict diffusivities across multidimensional composition spaces. Recently, we showed that water (a neutral solute) diffuses through alkyl-methylimidazolium halide ILs by hopping between hydrogen bonding sites on relatively immobile cations. Here, we expand on this activated hopping mechanism in two significant ways. First, we demonstrate that water diffuses through poly(ethylene glycol)diacrylate ionogels via the same mechanism at a reduced rate. Second, we hypothesize that the activation energy barrier can be determined from relatively simple 1H NMR chemical shift measurements of the proton responsible for H-bonding. This relationship enables water's diffusivity in ionogels of this class to be predicted quantitatively, requiring only (1) the composition-dependent diffusivity and Arrhenius behavior of a single IL and (2) 1H NMR spectra of the ionogels of interest. High-throughput microfluidic Fabry-Perot interferometry measurements verify prediction accuracy across a broad formulation space (four ILs, 0 ≤ xH2O ≤ 0.7, 0 ≤ ϕPEGDA ≤ 0.66). The predictive model may expedite IL-material screening; moreover, it intimates a powerful connection between solute mobility and hydrogen bonding and suggests targets for rational design.

Quantitative spatiotemporal Li profiling using nanoindentation

The rate capability and lifetime of Li-ion batteries is largely dictated by the composition dynamics of the electrodes. We set forth a nanoindentation approach to probe the spatiotemporal Li profile using the functional dependence of the mechanical properties on Li composition. This mechanics-informed material dynamics allows us to measure the composition-dependent diffusivity, assess the rate-limiting process in Li reactions, and quantitatively evaluate the stress regulation on Li transport. The experiments show that Li diffusivity in amorphous Si varies exponentially by three orders of magnitude from the pristine to the fully lithiated state. Lithiation in amorphous Si is limited by diffusion at the micron scale. We further evaluate the thermodynamic driving force for Li diffusion by including the material non-ideality and mechanical stresses. Through computational modeling, we find that the composition dependence of the Li diffusivity in general creates an asymmetry on the rate capability during lithiation versus delithiation. In Si, the exponential dependence results in a fast lithiation that proceeds via a steep concentration gradient compared to a slow and relatively smooth delithiation. This asymmetric behavior appears to be a root cause of Li trapping and loss of the deliverable capacity in Si. This work sheds light on the thermodynamics of Li transport and the lithiation kinetics of amorphous Si. It demonstrates the potential of operando nanoindentation in the mechanics-informed understanding of Li chemistry and aiding battery research beyond mechanical measurement.

Composition-dependent multicomponent diffusivity of 2,5-lutidine with acetonitrile in polyurethane

Evaluation and prediction of multicomponent diffusion in polymers is an important area of research since it occurs in several fields associated with mass transport including membrane separations, preparation of polymer films, and material decontamination. The functional dependence of the diffusivity on the composition in a multicomponent system is critical for accurately predicting transport in these processes. Here, the composition dependent diffusivity of 2,5-lutidine in polyurethane with acetonitrile as a co-penetrant was experimentally determined using Fourier transform infrared spectroscopy (FTIR) to acquire differential sorption curves for lutidine across the composition space and fitting a multicomponent diffusion model to the data. The free volume theory of diffusion was used to develop a mathematical expression for the composition-dependent diffusivity, and shows good agreement with the experimental data for both single and multicomponent cases. The lutidine diffusivity was found to vary up to two orders of magnitude with ACN concentration, and the importance of capturing this dependence quantitatively is highlighted by applying the multicomponent diffusion model with the best-fit values to predict previously published data for lutidine desorption from polyurethane.

A minimal model for solvent evaporation and absorption in thin films

We present a minimal model of solvent evaporation and absorption in thin films consisting of a volatile solvent and non-volatile solutes. An asymptotic analysis yields expressions that facilitate the extraction of physically significant model parameters from experimental data, namely the mass transfer coefficient and composition-dependent diffusivity. The model can be used to predict the dynamics of drying and film formation, as well as sorption/desorption, over a wide range of experimental conditions. A state diagram is used to understand the experimental conditions that lead to the formation of a solute-rich layer, or “skin”, at the evaporating surface during drying. In the case of solvent absorption, the model captures the existence of a saturation front that propagates from the film surface towards the substrate. The theoretical results are found to be in excellent agreement with data produced from dynamic vapour sorption experiments of ternary mixtures comprising an aluminium salt, glycerol, and water. Moreover, the model should be generally applicable to a variety of practical contexts, from paints and coatings, to personal care, packaging, and electronics.

Elastic, dielectric and electromechanical properties of (Bi0.5Na0.5)TiO3-BaTiO3 piezoceramics at the morphotropic phase boundary region

A systematic study of the functional properties of the (1-x)(Bi0.5Na0.5)TiO3–xBaTiO3 (BNT-xBT) piezoceramic system for 0.05 ≤ x ≤ 0.07 is performed. The samples are obtained through the conventional solid-state route. The expected microstructure for these compounds, with no significant dependence on the composition, is verified by field-emission scanning electron microscopy. The morphotropic phase boundary (MPB) is detected for x = 0.06–0.07 by means of the Rietveld analysis of X-ray diffraction data. The dielectric spectra show a frequency-independent, completely diffuse phase transition with a composition-dependent diffusivity coefficient. The depolarization temperature is effectively evaluated from pyroelectric measurements, the value being strongly dependent on the composition. A significant contribution of the extrinsic effect to elastic, dielectric and electromechanical properties is revealed for MPB BNT-xBT. The Bi3+ substitution by Ba2+ leads to the formation of A-site vacancies, which give rise to the enhancement of domain wall motion, as occurs in other perovskite-type piezoelectrics. Good functional properties are achieved for x = 0.07 (d33 = 180 pC/N), which are similar or even better than those obtained by complex synthesis routes. This system exhibits a remarkable stability in the permittivity that has hitherto not been reported. This fact may open the way for BNT-BT compositions to be used in specific applications in which lead-free piezoceramics have previously been employed with little success, e.g. in high power devices.

Phase Field Approach to Multiphase Flow Modeling

We review the phase field (otherwise called diffuse interface) model for fluid flows, where all quantities, such as density and composition, are assumed to vary continuously in space. This approach is the natural extension of van der Waals’ theory of critical phenomena both for one-component, two-phase fluids and for partially miscible liquid mixtures. The equations of motion are derived, assuming a simple expression for the pairwise interaction potential. In particular, we see that a non-equilibrium, reversible body force appears in the Navier-Stokes equation, that is proportional to the gradient of the generalized chemical potential. This, so called Korteweg, force is responsible for the convection that is observed in otherwise quiescent systems during phase change. In addition, in binary mixtures, the diffusive flux is modeled using a Cahn-Hilliard constitutive law with a composition-dependent diffusivity, showing that it reduces to Fick’s law in the dilute limit case. Finally, the results of several numerical simulations are described, modeling, in particular, a) mixing, b) spinodal decomposition, c) nucleation, d) enhanced heat transport, e) liquid-vapor phase separation.

Mixing It Up: Measuring Diffusion in Supercooled Liquid Solutions of Methanol and Ethanol at Temperatures near the Glass Transition

How do liquid mixtures cooled to temperatures below their freezing point behave? We address this question using nanoscale films of methanol and ethanol supercooled liquid solutions of varying composition (0−100% methanol) at temperatures near their glass transition, Tg. The permeation of Kr through these films is used to determine the diffusivities of the supercooled liquid mixtures. We find that the temperature-dependent diffusivities of the mixtures are well-fit by a Vogel−Fulcher−Tamman equation, indicating that the mixtures exhibit fragile behavior at temperatures just above their Tg. Further, for a given temperature, the composition-dependent diffusivity is well-fit by a Vignes-type equation, that is, the diffusivity of any mixture can be predicted using an exponential weighting of the pure methanol and ethanol diffusivities. These results show that deeply supercooled liquid mixtures can be used to provide valuable insight into the properties of normal liquid mixtures.

Experimental Determination of Composition-Dependent Diffusivity of Carbon Dioxide in Polypropylene

This work provides the experimentally determined composition-dependent diffusivity of environmentally benign plasticizer such as carbon dioxide in polypropylene. For this purpose, a pressure decay system is employed to determine composition-dependent diffusivity of carbon dioxide in polypropylene at isothermal conditions. On the basis of a detailed mass transfer model, variational calculus is used to establish the conditions necessary to yield the composition-dependent diffusivity that enables the model-predicted mass of absorbed gas in polymer to match with the experimental counterpart. The experimental solubility and composition-dependent diffusivity of carbon dioxide in polypropylene are obtained at (170, 180, and 190) °C for pressures up to 7.32 MPa.

Precipitate growth with composition-dependent diffusivity: Comparison between theory and phase field simulations

We consider the growth of an isolated precipitate when the matrix diffusivity depends on the composition. We have simulated precipitate growth using the Cahn-Hilliard model, and find good agreement between our results and those from a sharp interface theory for systems with and without a dilatational misfit. With misfit, we report (and rationalize) an interesting difference between systems with a constant diffusivity and those with a variable diffusivity in the matrix.

Abnormal Li diffusion in β-LiGa by the formation of defect complex

The diffusion coefficients of Li in the NaTl-type Li intermetallic compound of β-LiGa have been measured by using a short-lived radioactive diffusion tracer. As the tracer, the α-emitting radioisotope of 8Li delivered as the energetic and pulsed beam from Tokai Radioactive Ion Accelerator Complex (TRIAC) was implanted into the β-LiGa compounds with the composition in the range of about 43 to 54 at.% Li. By analyzing the time-dependent yields of the α-particles measured according to the repetition cycle of the beam, the tracer diffusion coefficients were extracted over the wide range of Li composition. Abnormal composition-dependence of Li diffusion coefficients in β-LiGa was observed; the stoichiometric β-LiGa showed the highest diffusivity of Li. By referring to the composition-dependent diffusivity of Li in the iso-structural β-LiAl and β-LiIn, we could identify the abnormal diffusion of Li in very Li-poor composition of β-LiGa. The anomaly has been discussed qualitatively in terms of the formation of defect complex and the interaction between the constitutional defects.

Determination of Concentration Dependent Diffusion Coefficients of Carbon in Expanded Austenite

In the present paper various experimental procedures to experimentally determine the concentration dependent diffusion coefficient of carbon in expanded austenite are evaluated. To this end thermogravimetric carburization was simulated for various experimental conditions and the evaluated composition dependent diffusivity of carbon derived from the simulated experiments was compared with the input data. The most promising procedure for an accurate determination is shown to be stepwise gaseous carburizing of thin foils in a gaseous atmosphere; the finer the stepsize, the more accurate the approximation of the diffusivity. Thermogravimetry was applied to continuously monitor the weight change of thin foils of AISI 316 during carburizing in CO-H2 gas mixtures for one of the simulated experimental procedures.

Modeling of the transport processes in electrodes showing composition-dependent diffusivity

The work is concerned with the numerical analysis of kinetics and thermodynamics of lithium insertion into electrode materials. The two methods for simulating diffusion in electrode material are shown. The Nernst–Planck flux formula and the law of mass conservation were chosen as the governing equations in a variable diffusivity model (VDM). These equations were solved for the planar electrode and for the different initial and boundary value conditions by means of the finite difference method. The distribution of lithium in the electrode material and the change of the Li +/Li y M half-cell potential are computed. The VDM is compared with a constant diffusivity model (CDM), the results confirm that dependence of the chemical diffusivity of Li on thermodynamics in binary system, M-Li y M, cannot be neglected in practical computations.

Calculating the composition-dependent diffusivity matrix along a diffusion path in ternary systems: Application to β-(Ni, Pt)Al

A numerical inverse analysis has been developed to extract the composition-dependent interdiffusion coefficients from a single diffusion couple in ternary systems. Its application to various diffusion couples at 1100 ∘C in β-(Ni, Pt)Al shows that in the composition domain investigated: • The direct interdiffusion coefficient D AlAl Ni increases as the platinum content increases. • A concentration gradient of platinum has no influence on the diffusion of aluminium, and the corresponding coefficient D AlPt Ni is zero. • The cross coefficient D PtAl Ni is constant and very small except for a deep minimum at an aluminium content of 50 at.%. These results are briefly discussed in relation with diffusion mechanisms in β-(Ni, Pt)Al.

Extension of the High Temperature Limit of Cooling Geospeedometry.

Geospeedometer proposed so far to estimate cooling history of rocks has a limit in terms of the maximum temperature above which we cannot deduce the history. The limit is governed by kinetic processes for geospeedometry and cooling rates; for example the olivine-spinel geospeedometry based on kinetics of Mg-Fe2+ exchange between olivine and spine! with the maximum grain size of a few millimeters cannot record any cooling history above 800°C if the cooling rate is <∼10-4°C/year. In order to extend the limit, a larger distance scale for geospeedometry is needed. By using mineralogical variations forming rock structures, whose distance scale is up to a meter order or more, we can in principle estimate thermal history of rocks up to their so!idus temperatures, if effects of polycrystalline and multi-phase nature and the initial conditions for a large scale rock system are correctly assessed. The olivine-spinel geospeedometry was extended to deduce high temperature thermal history of a dunite-chromitite layer sampled from the Iwanai-lake peridotite mass, Hokkaido. The Fe-Mg variation over 6 cm in dunite from the contact is analyzed by a 1-D diffusion model with a composition-dependent diffusivity and a changeable cooling rate. The dunite-chromitite geospeedometry indicates that the Iwanai-lake mass was cooled from ∼1000°C to 900°C with increasing cooling rate from <0.01°C/year to -0.3°C/year. This suggests that the slower cooling after the melting event was followed by the ascent of the mass that resulted in the inferred rapid cooling at ∼900°C.

The diffusion of carbon in iron-carbon alloys at 1560°C

Measurements have been made of the rate of absorption of carbon from CO-CO2 mixtures into stagnant liquid iron and of the rate of unidirectional dissolution of graphite into stag-nant liquid iron and iron-carbon alloys at 1560°C. Total absorptions and concentration pro-files were found to be consistent with a composition dependent chemical diffusivity given byD = 1.1 (1 + wt pct CJ5.3) X 10∼4 cm2Js with an uncertainty of about ±0.2 x 10-4. It is shown that many of the previous determina-tions of the chemical and self-diffusivity are consistent with this suggested dependence.