Self-diffusion Data Research Articles

Release of Solubilizate from Micelle upon Core Freezing.

By combining NMR (yielding 1H chemical shift, spin relaxation, and self-diffusion data) and small-angle X-ray scattering experiments, we investigate the complex temperature dependence of the molecular and aggregate states in aqueous solutions of the surfactant [CH3(CH2)17(OCH2CH2)20OH], abbreviated as C18E20, and hexamethyldisiloxane, HMDSO. The latter molecule serves as a model for hydrophobic solubilizates. Previously, the pure micellar solution was demonstrated to exhibit core freezing at approximately 7-8 °C. At room temperature, we find that HMDSO solubilizes at a volume fraction of approximately 10% in the core of the C18E20 micelles, which consists of molten and thereby highly mobile alkyl chains. Upon lowering the temperature, core freezing is found, just like in pure micelles, but at a temperature shifted significantly to 3 °C. The frozen cores contain immobile alkyl chains and exhibit a higher density but are essentially devoid (volume fraction below 1%) of the solubilizate. The latter molecules are released, first gradually and then rather steeply, from the core in the temperature range that is roughly delimited by the two core freezing temperatures, one for pure micelles and one for micelles with solubilizates. The release behavior of systems with different initial HMDSO loading follows the same master curve. This feature is rationalized in terms of loading capacity being strongly temperature dependent: upon lowering the temperature, release commences once the loading capacity descends below the actual solubilizate content. The sharp release curves and the actual release mechanism with its molecular features shown in rich detail have some bearing on a diverse class of possible applications.

Mass transfer in polycrystalline ytterbium disilicate under oxygen potential gradients at high temperatures

To elucidate the mass transfer mechanism in polycrystalline Yb2Si2O7 at high temperatures, the oxygen permeability of Yb2Si2O7 wafers was evaluated under various oxygen potential gradients (dμO) at temperatures up to 1673 K, using 18O2. The 18O was found to concentrate at grain boundaries (GBs), indicating that oxygen preferentially diffuses along the wafer GBs. It was also determined that oxygen permeation is controlled by the mutual GB diffusion of ytterbium and oxide ions, and that ytterbium and oxide ions interdiffuse along the GBs without experiencing any acceleration or retardation effects. The lattice and GB diffusion coefficients for oxygen were directly determined from secondary ion mass spectrometry (SIMS). The oxygen GB diffusion coefficients determined from SIMS-18O line profiles along cross-sections of individual GBs were almost the same as those obtained from SIMS-18O depth profiles. The oxygen GB diffusion coefficient under a dμO was clearly smaller than that in the absence of a dμO (representing self-diffusion data). This work also determined the electronic transference numbers for Yb2Si2O7 with and without the application of a dμO, on the basis of the oxygen GB diffusion coefficients predicted using oxygen permeation data.

First-principles investigation of intrinsic defects and self-diffusion in ordered phases of V2C

The self-diffusion behavior of vanadium subcarbide (V2C) is investigated using density functional theory calculations, owing to its potential application as a diffusion barrier in nuclear applications. Three ordered V2C structures, two of which correspond to experimentally observed phases, are characterized in terms of their equilibrium structural, electronic and elastic properties. Our model for self-diffusion in V2C considers diffusion of carbon and vanadium to occur separately on each sublattice. Two sets of self-diffusion coefficients are calculated for each structure: one for vacancy-mediated diffusion of vanadium and the other for interstitial diffusion of carbon. Calculated activation energies and diffusion prefactors are compared to experimental data for the cubic transition metal carbides as there is no experimental self-diffusion data for any of the hexagonal subcarbides.

Diffusion coefficients of transition metals in fcc cobalt

Using first-principles density functional theory (DFT), we calculate the diffusivities of 32 different solute elements—all transition metals, together with Al and Si—in fcc cobalt within the formalism of the five-frequency model. For self-diffusion in fcc cobalt, we compare the accuracy of various approximations to the exchange-correlation energy functional of DFT in estimating the activation energy, and find that only the Perdew-Burke-Ernzerhof (PBE) approximation agrees well with experimental reports and all other functionals largely overestimate it. Our calculations also show that an accurate estimation of the self-diffusion coefficient requires explicit calculation of the effective jump frequency and vacancy formation entropy via phonons. Using accurate self-diffusion data and scaling all solute-related attempt frequencies with respect to the attempt frequency for self-diffusion using a simple relation involving the atomic mass and melting temperature of the solute yields solute diffusivities in excellent agreement with experiments, where such data is available. We find that large solutes spontaneously relax toward the nearest neighbor vacancy to relieve the misfit strain, and the extent of this relaxation correlates negatively with the migration energy. Thus, in general, larger solutes have lower migration energies and diffuse faster than smaller solutes in fcc cobalt. However, extremely large solutes, e.g., group III elements Sc, Y, Lu, tend to be trapped in an energy valley located halfway toward the vacancy, and monovacancy mediated diffusion may no longer be valid in such cases. Finally, for all the solutes considered, we systematically tabulate the diffusion-related quantities calculated—diffusion prefactors, migration and activation energies—constructing an extensive and accurate first-principles database for solute diffusion in fcc cobalt.

Inter-diffusion and its correlation with dynamical cross correlation in liquid Ce80Ni20

We reported the inter-diffusion coefficients in liquid Ce $$_{80}$$ Ni $$_{20}$$ measured by the sliding cell technique. Combined with the self-diffusion data of Ni measured by quasi-elastic neutron scattering in the literature, it was found that the relationship between inter-diffusion and self-diffusion in liquid Ce $$_{80}$$ Ni $$_{20}$$ was strongly deviated from the standard Darken equation with an abnormally small dynamical cross correlation factor S (the so called Manning factor) in a range of 0.6–0.8, less than unity in standard systems. Through the calculated distinct diffusion coefficient and its deviation from the standard one, it was discovered that the small S value was directly originated from enhanced distinct diffusion between Ce and Ni atoms and reduced distinct diffusion between Ni and Ni atoms. Because the inter-atomic interaction was not considered in the standard liquids, the present small S factor and intrinsic distinct diffusion coefficients were believed to be resulted from the chemical interaction between Ce and Ni in the liquid. The results provide new evidence of the dynamic cross correlation in liquid diffusion, and thus shed light on the understanding of the correlation between dynamics and structure in liquid alloys.

Revised and Extended Values for Self-Diffusion Coefficients of 1-Alkyl-3-methylimidazolium Tetrafluoroborates and Hexafluorophosphates: Relations between the Transport Properties.

Earlier measurements of the self-diffusion coefficients of 1-alkyl-3-methylimidazolium (or [RMIM], R = alkyl) tetrafluoroborates and hexafluorophosphates have been revised and extended to 90 °C. The main changes are to DS+ and DS- for [HMIM][PF6] ([C6C1Im][PF6]) and DS- for [OMIM][BF4] ([C8C1Im][BF4]). New atmospheric pressure self-diffusion, density, and conductivity data are provided for [HMIM][BF4] ([C6C1Im][BF4]). Velocity cross-correlation, distinct diffusion, and Laity resistance coefficients have been calculated. There is no evidence for ion association. A new relation between the Nernst-Einstein deviation parameter (Δ) and resistance coefficients (rij) is derived; Δ tends toward 0.5 when the like-ion rii are much smaller than the unlike-ion rij, i.e., when the counterion interactions dominate. [OMIM]+ ion salts approach this limit. Stokes-Einstein-Sutherland and Walden plots overlap almost quantitatively for [BF4]-, [PF6]-, and Cl- salts with a common [RMIM]+ cation. That is, in thermodynamic states that have the same viscosity, the salt molar conductivities and hence ionic electrical mobilities of, say, [BMIM][BF4] and [BMIM][PF6] are almost equal, as are the corresponding Brownian or diffusive mobilities, (DSi/RT), for the cation, and also for these three small anions.

A Monte Carlo study of ionic transport in a simple cubic random alloy via the interstitialcy mechanism: effects of non-collinear and direct interstitial jumps

Self-diffusion and ionic conduction via the interstitialcy mechanism in a simple cubic, binary random alloy AB were investigated as a function of composition using Monte Carlo simulation. It was found that allowance for non-collinear jumps (partly) replacing concurrent collinear site exchanges leads to a reduction in diffusion correlation effects. This goes along with a shift of the diffusion percolation threshold to lower concentrations of the (more) mobile component B. Even stronger changes of mass and charge transport compared to an exclusively collinear interstitialcy scheme are observed for additional contributions of direct interstitial jumps. It is remarkable that for both extensions of interstitialcy mediated diffusion, the Haven ratio appears to be greater than unity in certain composition ranges poor in B. All results rely on the calculation of tracer and interstitialcy correlation factors in the simplest possible three-dimensional lattice structure. Yet they may have more general relevance to the interpretation of tracer self-diffusion data and ionic conductivity measurements on crystalline materials.

A Method for Estimating Transport Properties of Concentrated Electrolytes from Self-Diffusion Data

A theoretical method is introduced that calculates the electrolyte-transport properties using Onsager–Stefan–Maxwell (OSM) theory (concentrated-solution theory) and the generalized-Darken relation. OSM theory is used to relate binary diffusivities to the transport properties of the electrolyte, including transference number, ionic conductivity, and Fickian diffusivity. The generalized-Darken relation is proposed to calculate the binary diffusivities of multicomponent systems from self-diffusivities. Finally, an example is demonstrated to show the details of how this method can be used to estimate transport properties. The calculated properties were reasonably close to the previously reported experimental values.

First-principles calculation of defect free energies: General aspects illustrated in the case of bcc Fe

The first-principles calculation of contributions of phonon and electron excitations to free formation, binding, and migration energies of defects is illustrated in the case of bcc-Fe. First of all, the ground state properties of the vacancy, the foreign atoms Cu, Y, Ti, Cr, Mn, Ni, V, Mo, Si, Al, Co, O, and the O-vacancy pair are determined under constant volume (CV) as well as zero pressure (ZP) conditions. Second, the phonon contribution to defect free energies is calculated within the harmonic approximation using the equilibrium atomic positions determined in the ground state under CV and ZP conditions. Additionally, quasi-harmonic corrections are applied to the ZP-based data. A simple transformation similar to the quasi-harmonic approach is found between the CV- and ZP-based frequencies. Therefore, it is not necessary to calculate these quantities and the corresponding defect free energies separately. In contrast to ground state energetics the CV- and ZP-based defect free energies do not become equal with increasing supercell size. Third, it was found that the contribution of electron excitations to the defect free energy can lead to an additional deviation of the total free energy from the ground state value or can compensate the deviation caused by the phonon contribution. Finally, self-diffusion via the vacancy mechanism is investigated. The ratio of the respective CV- and ZP-based results for the vacancy diffusivity is nearly equal to the reciprocal of that for the equilibrium concentration. This behaviour leads to almost identical CV- and ZP-based values for the self-diffusion coefficient. Obviously, this agreement is accidental. The consideration of the temperature dependence of the magnetization yields self-diffusion data in very good agreement with experiments.

Novel dicationic pyrimidinic surfactant: Self-assembly and DNA complexation

Novel pyrimidinic surfactant with two morpholinium head groups and two decyl tails has been synthesized. As determined by breakpoints on concentration dependences of surface tension and conductivity, the pyrimidinic amphiphile forms aggregates beyond critical micelle concentration of 3.4 mM, which is supported by fluorescence ratiometry, dye solubilization technique and dynamic light scattering data (DLS). The NMR self-diffusion data testify that different types of aggregates are probably formed in the solution above 12 mM. The dual structural behavior is in line with fluorescence anisotropy results and packing parameter calculations. The complexation ability of the pyrimidinic amphiphile toward plasmid DNA pK18 is supported by DLS and zeta potential measurements indicating the occurrence of the compaction and charge neutralization effect. The lipoplex formation is also supported by ethidium bromide exclusion data. The ability of the amphiphile of integrating with lipid bilayer is revealed by measurements of the temperature of main phase transition.

Reply to “Comment on ‘Contributions of vacancies and self-interstitials to self-diffusion in silicon under thermal equilibrium and nonequilibrium conditions’ ”

Suezawa et al. [Phys. Rev. B 90, 117201 (2014)] claim in their Comment that the data reported by Shimizu et al. [ Phys. Rev. Lett. 98, 095901 (2007)] and Kube et al. [Phys. Rev. B 88, 085206 (2013)] on silicon self-diffusion for temperatures between 900 and 735 \ifmmode^\circ\else\textdegree\fi{}C are affected by carbon and vacancy clusters and, accordingly, do not reflect self-diffusion under thermal equilibrium conditions. We demonstrate in our Reply that an impact of carbon on self-diffusion can definitely be excluded. In addition it is rather unlikely that the self-diffusion data reported by Shimizu et al. [Phys. Rev. Lett. 98, 095901 (2007)] and Kube et al. [Phys. Rev. B 88, 085206 (2013)] are affected by the dissolution of vacancy clusters since strong differences exist not only in the preparation of the samples used for the experiments, but also in the time of diffusion. Finally, the vacancy formation enthalpy deduced by Suezawa et al. [J. Appl. Phys. 110, 083531 (2011)] from quenching experiments is consistent with the value obtained from the temperature dependence of the vacancy formation enthalpy reported by Kube et al. [Phys. Rev. B 88, 085206 (2013)]. Overall we conclude that the quenching experiments of Suezawa et al. [J. Appl. Phys. 110, 083531 (2011)] cannot disprove the interpretation of the low-temperature self-diffusion data reported by Shimizu et al. [ Phys. Rev. Lett. 98, 095901 (2007)] and Kube et al. [Phys. Rev. B 88, 085206 (2013)].

Overview of SIMS-Based Experimental Studies of Tracer Diffusion in Solids and Application to Mg Self-Diffusion

Tracer diffusivities provide the most fundamental information on diffusion in materials, and are the foundation of robust diffusion databases that enable the use of the Onsager phenomenological formalism with no major assumptions. Compared to traditional radiotracer techniques that utilize radioactive isotopes, the secondary ion mass spectrometry (SIMS)-based thin-film technique for tracer diffusion is based on the use of enriched stable isotopes that can be accurately profiled using SIMS. An overview of the thin-film method for tracer diffusion studies using stable isotopes is provided. Experimental procedures and techniques for the measurement of tracer diffusion coefficients are presented for pure magnesium, which presents some unique challenges due to the ease of oxidation. The development of a modified Shewmon-Rhines diffusion capsule for annealing Mg and an ultra-high vacuum system for sputter deposition of Mg isotopes are discussed. Optimized conditions for accurate SIMS depth profiling in polycrystalline Mg are provided. An automated procedure for correction of heat-up and cool-down times during tracer diffusion annealing is discussed. The non-linear fitting of a SIMS depth profile data using the thin-film Gaussian solution to obtain the tracer diffusivity along with the background tracer concentration and tracer film thickness is demonstrated. An Arrhenius fit of the Mg self-diffusion data obtained using the low-temperature SIMS measurements from this study and the high-temperature radiotracer measurements of Shewmon and Rhines (Trans. AIME 250:1021-1025, 1954) was found to be a good representation of both types of diffusion data over a broad range of temperatures between 250 and 627 °C (523 and 900 K).

A first-principles study of self-diffusion coefficients of fcc Ni

Self-diffusion coefficients for fcc Ni are obtained as a function of temperature by first-principles calculations based on density functional theory within the local density approximation. To provide the minimum energy pathway and the associated saddle point structures of an elementary atomic jump, the nudged elastic band method is employed. Two magnetic settings, ferromagnetic and non-magnetic, and two vibrational contribution calculation methods, the phonon supercell approach and the Debye model, create four calculation settings for the self-diffusion coefficient in nickel. The results from these four methods are compared to each other and presented with the known experimental data. The use of the Debye model in lieu of the phonon supercell approach is shown to be a viable and computationally time saving alternative for the finite temperature thermodynamic properties. Consistent with other observations in the literature, the use of the phonon supercell approach for the calculation of the finite temperature thermodynamic properties within the LDA results in an underestimation of the diffusion coefficient with respect to experimental data. The calculated Ni self-diffusion coefficients for all four conditions in the present work are compared to a statistical consensus analysis previously performed on all known experimental self-diffusion data. With the exception of the NM phonon setting, the other three conditions fall within the 95% confidence interval for the consensus analysis.

NMR Studies on Effects of Tetraalkylammonium Bromides on Micellization of Sodium Dodecylsulfate

The effects of tetraalkylammonium bromides (TAABs) on the micellization of sodium dodecylsulfate (SDS) are studied using pyrene solubilization and several nuclear magnetic resonance (NMR) techniques. Two-dimensional nuclear Overhauser effect spectroscopy (2D NOESY) experiments confirm that tetraalkylammonium (TAA(+)) ions associate with SDS to form mixed micelles. TAA(+) ions attach to the surface of the mixed micelles and become inserted into the hydrophobic core of the mixed micelles. Because TAA(+) ions appear in the hydrophobic interior of the TAA-SDS mixed micelles, the micropolarity inside the mixed micelles sensed by pyrene might not reflect the true hydrophobicity of the micellar core. Using proton chemical shift analysis, the degree of hydration on the surface of the mixed micelles is determined from the chemical shift change of SDS α-CH2 protons. The self-diffusion coefficients of SDS and TAA(+) ions in the TAAB/SDS/D2O solutions are measured by using pulse-field gradient NMR, and the fraction of TAA(+) ions associated with the SDS to form the mixed micelles is calculated from the self-diffusion data. Moreover, secondary micelle formation for SDS and TAA(+) ions is observed on the basis of (1)H chemical shift analysis and the self-diffusion data. The 2D NOESY experiments also reveal unusual tumbling behavior of SDS alkyl protons. For Pr4NBr/SDS and Bu4NBr/SDS solutions, positive and negative nuclear Overhauser effects are simultaneously observed among the SDS alkyl protons.

Novel biomimetic systems based on amphiphilic compounds with a diterpenoid fragment: Role of counterions in self-assembly

Novel biomimetic systems are designed based on cationic surfactants composed of an isosteviol moiety and different counterions, namely bromide (S1) and tosylate (S2). The counterion structure is shown to play a crucial role in the surfactant association. A number of methods used provide evidence that only one type of aggregate, i.e., micelles are observed in the S2 systems, while a concentration-dependent association occurs in the case of S1. The DLS and fluorescence anisotropy measurements reveal that the micelle–vesicle–micelle transitions probably occur with the S1 system. The occurrence of small aggregates near the critical micelle concentration with radii of 2.5nm is supported by NMR self-diffusion data. The Orange OT solubilization results strongly support the idea of a second threshold in the S1 system around 0.025mM and provide evidence that hydrophobic domains occur in the aggregates. The latter property and the capacity to integrate with the lipid bilayer make it possible to suggest the newly synthesized surfactants as effective nanocontainers for hydrophobic guests.

A combined quasi-continuum/Langevin equation approach to study the self-diffusion dynamics of confined fluids

In this work, we combine our earlier proposed empirical potential based quasi-continuum theory, (EQT) [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys. 127, 174701 (2007)], which is a coarse-grained multiscale framework to predict the static structure of confined fluids, with a phenomenological Langevin equation to simulate the dynamics of confined fluids in thermal equilibrium. An attractive feature of this approach is that all the input parameters to the Langevin equation (mean force profile of the confined fluid and the static friction coefficient) can be determined using the outputs of the EQT and the self-diffusivity data of the corresponding bulk fluid. The potential of mean force profile, which is a direct output from EQT is used to compute the mean force profile of the confined fluid. The density profile, which is also a direct output from EQT, along with the self-diffusivity data of the bulk fluid is used to determine the static friction coefficient of the confined fluid. We use this approach to compute the mean square displacement and survival probabilities of some important fluids such as carbon-dioxide, water, and Lennard-Jones argon confined inside slit pores. The predictions from the model are compared with those obtained using molecular dynamics simulations. This approach of combining EQT with a phenomenological Langevin equation provides a mathematically simple and computationally efficient means to study the impact of structural inhomogeneity on the self-diffusion dynamics of confined fluids.

Microfluidic preparation and self diffusion PFG-NMR analysis of monodisperse water-in-oil-in-water double emulsions

Monodisperse water-in-oil-in-water (WOW) double emulsions have been prepared using microfluidic glass devices designed and built primarily from off the shelf components. The systems were easy to assemble and use. They were capable of producing double emulsions with an outer droplet size from 100 to 40μm. Depending on how the devices were operated, double emulsions containing either single or multiple water droplets could be produced. Pulsed-field gradient self-diffusion NMR experiments have been performed on the monodisperse water-in-oil-in-water double emulsions to obtain information on the inner water droplet diameter and the distribution of the water in the different phases of the double emulsion. This has been achieved by applying regularization methods to the self-diffusion data. Using these methods the stability of the double emulsions to osmotic pressure imbalance has been followed by observing the change in the size of the inner water droplets over time.

Interdiffusion in the Mg-Al System and Intrinsic Diffusion in β-Mg2Al3

Solid-to-solid diffusion couples were assembled and annealed to examine the diffusion between pure Mg (99.96 pct) and Al (99.999 pct). Diffusion anneals were carried out at 573 K, 623 K and 673 K (300 °C, 350 °C and 400 °C) for 720, 360, and 240 hours, respectively. Optical and scanning electron microscopes were used to identify the formation of the intermetallic phases, γ-Mg17Al12, and β-Mg2Al3, as well as the absence of the e-Mg23Al30 in the diffusion couples. The thicknesses of the γ-Mg17Al12 and β-Mg2Al3 phases were measured and the parabolic growth constants were calculated to determine the activation energies for growth. Concentration profiles were determined with electron microprobe analysis using pure elemental standards. Composition-dependent interdiffusion coefficients in Mg-solid solution, γ-Mg17Al12, β-Mg2Al3, and Al-solid solutions were calculated based on the Boltzmann-Matano analysis. Integrated and average effective interdiffusion coefficients for each phase were also calculated, and the magnitude was the highest for the β-Mg2Al3 phase, followed by γ-Mg17Al12, Al-solid solution, and Mg-solid solution. Intrinsic diffusion coefficients based on Huemann’s analysis (e.g., marker plane) were determined for the ~ Mg-62 at. pct Al in the β-Mg2Al3 phase. Activation energies and the pre-exponential factors for the interdiffusion and intrinsic diffusion coefficients were calculated for the temperature range examined. The β-Mg2Al3 phase was found to have the lowest activation energies for growth and interdiffusion among all four phases studied. At the marker location in the β-Mg2Al3 phase, the intrinsic diffusion of Al was found to be faster than that of Mg. Extrapolations of the impurity diffusion coefficients in the terminal solid solutions were made and compared with the available self-diffusion and impurity diffusion data from the literature. Thermodynamic factor, tracer diffusion coefficients, and atomic mobilities at the marker plane composition were approximated using the available literature values of Mg activity in the β-Mg2Al3 phase.

Measurement of Defect-Mediated Oxygen Self-Diffusion in Metal Oxides

Solid-state diffusion of native defects in some metal oxides takes place via highly mobile intermediate species that periodically exchange with lattice atoms. A mathematical model has been formulated to determine the key diffusion parameters from mesoscopic gas-solid diffusion measurements in the short-time limit. The model provides a straightforward analytical means to utilize standard isotope gas-solid exchange experiments to obtain parameters connected to diffusion length and net rate of defect formation at the surface. Application of the method to experimental data for oxygen self-diffusion in titanium dioxide suggests that under conditions where gas-solid exchange takes place through an especially clean surface, a fast-moving species mediates oxygen self-diffusion.

Temperature dependence and anisotropy of self- and mono-vacancy diffusion in α-Zr

Temperature dependence and anisotropy of self- and mono-vacancy diffusion is important for modeling irradiation-induced microstructure evolution and the concomitant macroscopic deformation in Zr and its alloys. For self-interstitials, direct MD simulation of the diffusion has yielded useful data. Vacancy and self-diffusion, however, proceeds at a much slower rate, so that a direct simulation is not always practicable, particularly in the reactor-operating temperature regime. In this paper, we follow an alternate route based on thermodynamic integration and calculate the enthalpy, entropy and attempt jump frequencies of vacancy migration and formation in α-Zr for various temperatures ranging from 100 K to 1100 K. Their jump-direction and temperature dependencies are examined. The diffusivities so derived compare very well with other calculated results. Comparison with experimental self-diffusion data shows good general agreement except in the temperature regime near the α– β transformation. In this regime, the curvature in the Arrhenius plot of the self-diffusivity obtained is substantially smaller than the corresponding experimental results. Possible reasons are discussed.