Effective Self-diffusion Coefficient Research Articles

Physicochemical Analysis of Chloride Diffusion and Adsorption in Water-saturated Concrete: Theory and Measurement

The theory of ionic diffusion in water-saturated concrete accompanying ion exchange with mobile or immobile adsorbed ions was constructed by using the general theory of diffusion and the condition of electrical neutrality. Analysis of the diffusion profile of chloride (Cl−) ions in concrete with the theory revealed that adsorbed Cl− ions in AFm and C-S-H are as mobile as free Cl− ions in the pore solution, so that the adsorption does not retard the ingress of Cl− ions. The existing test methods for determining the effective or apparent diffusion coefficient of Cl− ions were evaluated on the bases of the present theory and new experimental findings. It was revealed that steady-state electrochemical methods such as NTBUILD-355 and ASTM C1202 are not suitable for determining the diffusion coefficient, because the steady state methods expel preexisting diffusible ions which strongly affect the diffusion of Cl− ions. Moreover, the steady state methods overestimate the diffusion rate because the methods assume that adsorbed Cl− ions are immobile. The electrochemically-accelerated method NT BUILD 443 is also unsuitable for the diffusion test, because the acceleration is induced by the electro-osmotic flow of the external solution into concrete. The present diffusion theory necessitates the effective self-diffusion coefficient of not only Cl− ions but also all the other diffusible ions in concrete. A simple method of determining the effective self-diffusion coefficients of arbitrary ions in concrete from the diffusion profile of Cl− ions was presented.

Direct observation of ion dynamics in supercapacitor electrodes using in situ diffusion NMR spectroscopy

Ionic transport inside porous carbon electrodes underpins the storage of energy in supercapacitors and the rate at which they can charge and discharge, yet few studies have elucidated the materials properties that influence ion dynamics. Here we use in situ pulsed field gradient NMR spectroscopy to measure ionic diffusion in supercapacitors directly. We find that confinement in the nanoporous electrode structures decreases the effective self-diffusion coefficients of ions by over two orders of magnitude compared with neat electrolyte, and in-pore diffusion is modulated by changes in ion populations at the electrode/electrolyte interface during charging. Electrolyte concentration and carbon pore size distributions also affect in-pore diffusion and the movement of ions in and out of the nanopores. In light of our findings we propose that controlling the charging mechanism may allow the tuning of the energy and power performances of supercapacitors for a range of different applications. It is challenging to probe ion dynamics in supercapacitor electrodes, which has significant implications in optimizing their performance. Here, the authors develop in situ diffusion NMR spectroscopy to measure and illustrate the diffusion of the charge-storing ions in working supercapacitors.

Diffusion of water inside carbon nanotubes studied by pulsed field gradient NMR spectroscopy.

Diffusion dynamics of guest molecules in nanopores has been studied intensively because diffusion is center on a number of research fields such as separation, drug delivery, chemical reactions, and sensing. In the present work, we report an experimental investigation of the self-diffusion of water inside carbon nanotube (CNT) channels using a pulsed field gradient (PFG) NMR method. The dispersion of CNTs homogeneously in water and cooling to temperatures below the melting point of bulk water allow us to probe the translational motion of confined water molecules. The results demonstrate that the self-diffusion coefficient of water in CNTs is highly dependent on the diffusion time and CNT diameter. In particular, the diffusivity of water in double-walled carbon nanotubes (DWNTs) with an average inner diameter of 2.3 ± 0.3 nm is twice that in multiwalled carbon nanotubes (MWNTs) with an average inner diameter of 6.7 ± 0.8 nm in the temperature range of 263-223 K. In addition, the effective self-diffusion coefficient in DWNTs is 1 order of magnitude higher than that reported for mesoporous silica materials with a similar pore size. The faster diffusivity of water in CNTs could be attributed to the ordered hydrogen bonds formed between water molecules within the confined channels of CNTs and the weak interaction between water and the CNT walls.

Anisotropic hole growth during solid-state dewetting of single-crystal Au–Fe thin films

Thin Fe–Au bilayers were deposited on c-plane sapphire substrates. The layers were found to be quasi-single crystalline, with a 〈111〉 texture and strong heteroepitaxy to the substrate. When annealed, these films dewetted from the substrate via the formation of faceted hexagonally shaped holes, which grow anisotropically with increasing annealing time. The studied Fe–Au films exhibited significantly higher thermal stability against dewetting than polycrystalline Au films prepared and annealed under identical conditions. We developed a thermodynamic diffusion model describing the growth kinetics of an individual hole. This model, in conjunction with experimental results, allows estimation of the effective surface self-diffusion coefficient.

The effect of evaporation on size and shape evolution of faceted gold nanoparticles on sapphire

We studied the size and shape evolution of about 180 faceted gold nanoparticles attached to a sapphire substrate during annealing at 950 °C in air. We employed the scanning force microscopy and interrupted annealing techniques to track the changes in size and shape of individual nanoparticles. The height of all single-crystalline nanoparticles was constant up to the longest cumulative annealing time of 65 h. The lateral dimensions of ∼20% of all nanoparticles shrunk during anneals, while all three dimensions of the remaining 80% of nanoparticles remained constant. Only the nanoparticles with the height below the average (for all particles) were laterally shrinking. We formulated a kinetic model relating the lateral shrinkage of the nanoparticles to the evaporation of Au atoms adsorbed on sapphire. We also assumed that the process controlling particles shrinkage is the slow self-diffusion of Au atoms along the lateral facets of the nanoparticles toward the substrate. The model predicted a power law dependence of the shrinkage rate on the particle height, with the exponent n = 3. The corresponding exponent determined from the experimental data was n = −2.9 ± 0.3, in excellent agreement with the theory. The low value of the effective self-diffusion coefficient along the lateral facets determined with the aid of our model (3.2 ± 0.2 × 10 −17 m 2 s −1) was attributed to the difficulties of step nucleation on atomically flat facets.

Effective self-diffusion coefficients of ions in sodium dodecyl sulfate micellar solutions

The effective self-diffusion coefficients of ions in premicellar and micellar solutions of sodium dodecyl sulfate are measured by the NMR self-diffusion method at 40°C. The obtained regularities are explained using a proposed model that takes into account the possible surface diffusion of counterions bound with micelles. This effect is shown to markedly influence the charge transfer in micellar solutions. Based on the results obtained, the self-diffusion coefficients of bound Na+ counterions are estimated and the causes and ranges of their variations are indicated.

Effect of temperature on water transport through aquaporins

The mean effective water self-diffusion coefficient in maize root segments under the effect of aquaporin blocker (mercuric chloride, 0.1 mM) was measured using the spin-echo NMR method with pulsed magnetic field gradient within the temperature range from 10 to 35 °C. HgCl2 caused the reduction in water diffusion by 30 % as compared to the control samples. Temperature dependences of water self-diffusion coefficients showed two linear regions with different values of Q10 and activation energy, Ea. As the temperature reduced from 20 to 10 °C, Ea values calculated from the Arrhenius plots were close to those of bulk water (20 ± 3 kJ mol−1) and slightly changed for the sample pretreated HgCl2. Within the temperature range from 25 to 35 °C the slope of temperature dependences became steeper and Ea values were 31 ± 3 kJ mol−1 for the control and 40 ± 4 kJ mol−1 for the treated sample. In the vicinity of 20 °C, the temperature dependence of water diffusion via the mercury-sensitive water channels showed extreme value. In the region, the specific area of the mercury-sensitive aquaporins was 0.004 % of the total cell surface area. The data indicate that water transfer via aquaporins is sensitive to temperature, and the contributions of the transmembrane pathways (aquaporins, lipid bilayer) differ in different temperature ranges.

PFG NMR investigation of hydrocarbon diffusion in large NaX zeolite crystals: Effect of internal field gradients on diffusion data

Self-diffusion coefficients for intracrystalline diffusion of hydrocarbon molecules adsorbed in large crystals of NaX zeolite have been measured by the pulsed field gradient (PFG) NMR technique, at ambient temperature and at different diffusion times (from 6 to 12 ms). Two NMR pulse sequences, stimulated and 13-interval bipolar spin echo, were used to examine the influence of internal field gradients on diffusion data. For both sequences the effective self-diffusion coefficient of the guest molecules was found to decrease with increasing observation times. The extrapolated intracrystalline diffusion coefficient is independent of the NMR sequence. In contrast, the estimated extent of molecular diffusion depends strongly on the pulse program. For the small molecules (butane to hexane), the domain size, R, of restricted diffusion obtained with the stimulated spin-echo sequence is smaller than the crystal dimension whereas R is always comparable to it when the 13-interval pulse sequence is used. This shows the effect of internal field gradients on the diffusion data leading to wrong values of R if the stimulated pulse sequence is used. The light hydrocarbons diffuse freely inside the zeolite particles whereas the crystal boundaries act as reflecting surfaces, as previously observed. On the other hand, even with the 13-interval pulse sequence, the smaller values of R obtained for large molecules as n-heptane and octane shows that their displacement is hindered by restrictions in the NaX macro-crystals.

Concentration-dependent self-diffusion of adsorbates in mesoporous materials

The pulsed-field gradient NMR method has been applied to study self-diffusion of liquids in mesoporous materials with different pore sizes and morphologies as a function of pore loading. It is found that the effective diffusivities of adsorbate molecules in mesopores at partial loadings are related to two mechanisms, the Knudsen diffusion through the gaseous phase in the pore space and the diffusion within the layer of molecules adsorbed on the pore walls. The relative contributions of these modes, which are determined by the details of the interphase equilibrium, change with variation of the pore loading, leading to a complex behavior of the effective self-diffusion coefficient. The impact of the pore size and the adsorbate-surface interaction on self-diffusion is elucidated. Possible reasons for an experimentally obtained hysteresis in the diffusivities measured on adsorption and desorption in mesopores are discussed.

Inverse analyses of diffusion processes in type 13X zeolite particles

To determine effective surface self-diffusion coefficients of CO 2 within type 13X zeolite particles, at various temperatures (25–70 °C), inverse analyses of observed CO 2-uptake curves were successfully performed. The obtained effective surface self-diffusion coefficients increase with both the amount adsorbed and the temperature and ranged from 7.8 × 10 −10 to 1.95 × 10 −9 m 2/s under the present experimental conditions.

Concentration-dependent self-diffusion of liquids in nanopores: a nuclear magnetic resonance study.

Nuclear magnetic resonance has been applied to study the details of molecular motion of low-molecular-weight polar and nonpolar organic liquids in nanoporous silicon crystals of straight cylindrical pore morphology at different pore loadings. Effective self-diffusion coefficients as obtained using the pulsed field gradient nuclear magnetic resonance method were found to pass through a maximum with increasing concentration for all liquids under study. Taking account of a concentration-dependent coexistence of capillary condensed, adsorbed and gaseous phases a generalized model for the effective self-diffusion coefficient was developed and shown to satisfactorily explain the experimental results. An explicit use of the adsorption isotherm properties within the model extends its applicability to the mesoporous range and highlights the role of surface interaction for the transport of molecules in small pores. The problem of surface diffusion and diffusion of multilayered molecules is also addressed.

Determination of Some Parameters of a Porous Medium–Liquid System by the Pulsed Field Gradient NMR

A possibility was considered to estimate the parameter of a porous medium S/Vp, whereSand Vp are the surface area and the volume of pores, respectively, as well as the power of nuclear magnetic energy sinks ρ of a porous medium–liquid system by the example of randomly packed glass spheres 53–63 μm in diameter and acetone, water, or decane as a liquid medium. Estimates were made by analyzing the time dependences of the effective self-diffusion coefficient D(t ) and P(t ), the probability of return of a molecule to its initial position by time t. It was shown that the short-time parts of D(t ) dependence allow us to obtain parameters S/Vp and ρ, whereas those of P(t ), only the S/Vp parameter. The values of ρ, obtained from D(t ), and from the time of relaxation of longitudinal nuclear magnetization, differ from each other by an order of magnitude. As expected, the value of S/Vp, obtained for a given porous medium, is independent of the nature of introduced liquid.

Space-dependent self-diffusion processes in molten copper halides: A molecular dynamics study

This work is concerned with single ion dynamics in molten copper halides (CuI and CuCl) which exhibit fast ionic conduction before melting. The self-dynamic structure factor of the two ionic species in each melt have been calculated by molecular dynamics simulations and the corresponding effective wavelength-dependent self-diffusion coefficients have been studied. The results have been compared with those obtained for molten alkali halides (KCl and RbCl).

Study of Self-Diffusion ofn-Decane in NaX Zeolite by the Pulsed Magnetic-Field Gradient NMR Method

Translational mobility of n-decane molecules in a porous space of NaX zeolite was studied within the wide ranges of diffusion times and temperatures. The dependence of the effective self-diffusion coefficient on diffusion time was established. Confined mobility of diffusant molecules inside the crystallite was observed both for complete and partial filling of NaX pores with a liquid, when the adsorption barrier was absent at the interface between intra- and intercrystallite regions. It was suggested that obstacles are present at the surface of NaX crystallites complicating the transfer of liquid molecules from crystallite channels to intercrystallite space. True value of self-diffusion coefficient ofn-decane in the itracrystallite space of NaX was determined and its dependence on the concentration of liquid molecules in zeolite channels was considered. A special attention was paid to the study of molecular exchange between intra- and intercrystallite-confined liquids.

Regulation of transmembrane water transfer by rotational motion of plant cell protoplasm

By changing the velocity of protoplasm motion, a plant cell with a membrane permeability coefficient of 10−3 cm/s is able to control the intensity of transmembrane water exchange. The data were obtained by synchronous tracking, with the effective water self-diffusion coefficients measured by pulsed nuclear magnetic resonance.

Concentration dependence of diffusion–adsorption rate in activated carbon

A new method based on transfer rate measurements of a radioactive solute inside activated carbon grains is presented which allows to isolate the relative contributions of the chemical (reversible adsorption) and geometrical (tortuous diffusion paths) effects on the overall effective diffusion coefficient. Transfer rate measurements were performed with two different initial conditions: carbon grains either initially saturated with a solution of the same concentration as the bath ( self-diffusion) or free of solute. In the self-diffusion case the adsorption equilibrium for the solute is undisturbed during the process and the adsorption dynamics for tracer particles becomes linear. These processes can be analyzed in terms of an effective self-diffusion coefficient ( D eff). The concentration dependence of the transfer rate is shown to be controlled by nonlinearities of the adsorption isotherm. We also show that the self-diffusion coefficient ( D s ) is one order of magnitude lower than in free bulk diffusion. Finally, in the second case (grains initially free of solute) we predict satisfactorily sorption rate curves, as well as the dependence of the transfer rate on the initial concentration, using results obtained in the self-diffusion case.

Measurements of Effective Self-diffusion Coefficients in a Gel-Type Cation Exchanger by the Zero-Length-Column Method

The zero-length column (ZLC), conventionally developed for measuring the diffusivity of gases and liquids in zeolite crystals, has been extended to the measurement of intraparticle diffusivities in ion exchangers. A theoretical model which considers the ZLC cell as a continuous stirred tank reactor is developed. The model allows the use of nonlinear ion-exchange equilibrium isotherms, describes ion fluxes with Nernst-Planck equations, and includes the resistances to mass transfer both in the particle and in the film. Simulations have been carried out to analyze the effect of model parameters on the system response and to choose experimental operating conditions. The model validity has been tested by comparison with the experimental results of the ZLC for a step perturbation in the binary systems Na + -H + , K + -H + , and Na + -K + .

Molecular dynamics simulations of passive transport in two-dimensional Rayleigh-Bénard convection.

We use the molecular dynamics technique to study the enhancement of the self-diffusive transport of particles in a two-dimensional Rayleigh-B\'enard convective fluid. The effective self-diffusion coefficient ${\mathit{D}}^{\mathrm{*}}$ can be computed from the simulations performed with 5 to 10 000 particles. The enhancement of diffusion with respect to molecular self-diffusion is shown to scale as ${\mathrm{Pe}}^{1/2}$, where Pe is the P\'eclet number, which characterizes the ratio of the diffusive to the advective time. This behavior is in agreement with previous theoretical and experimental results. The simulation technique, however, permits us to explore domains of intermediate P\'eclet numbers around 100, where experiments are knowledgeably difficult to perform.

Effective self-diffusion coefficients of 14C-urea in a polyphenolsulfonic acid cation exchange membrane in the presence of different counterions

Effective self-diffusion coefficients of the polar non-electrolyte urea were obtained from tracer experiments with 14C-urea. For a membrane loaded with Na+ the tracer-diffusion coefficient was investigated as a function of the total urea concentration. Also tracer-diffusion was observed for membranes loaded with different counterions at constant urea concentration in solution.

The Effective Translational Self-Diffusion Coefficient of Small Molecules in Colloidal Crystals of Spherical Particles

The effective translational self-diffusion coefficient of small molecules in colloidal crystals of spherical particles is calculated. The colloidal crystal is modeled as a two-phase system. The colloidal particles are treated as immobile spheres with their centers located on the lattice points of cubic array. The diffusing molecule under consideration is characterized by both a self-diffusion coefficient and a concentration inside the colloidal particle as well as a self-diffusion coefficient and a concentration in the continuous phase. We have analyzed the results for three different cubic lattice types. For low volume fractions of colloidal particles (<0.3) the calculated self-diffusion coefficient is found to be independent of the lattice type and shows quantitative agreement with a simple cell model. (B. Jonsson, H. Wennerstrom, P.G. Nilsson, and P. Linse, Colloid Polym. Sci. 264, 77, 1986). The results of this study therefore support the analysis of experimental data on self-diffusion of small hydrophobic molecules in latex dispersions for low-volume fractions by the cell model (M. H. Blees and J. C. Leyte, J. Colloid Interface Sci. 157, 355, 1993). For higher volume fractions the behavior is found to be rather different. The self-diffusion coefficient is found to depend on the specific lattice structure of the colloidal particles, and significant deviations from the cell model result are found. Both sign and magnitude of the deviations are found to depend on the ratio of the transport coefficient of the diffusing molecule in the colloidal particles and the transport coefficient in the continuous phase.