Small Diffusion Coefficient Research Articles

Improved applicability of DOSY experiments by high resolution probes combined with gradient amplifiers of diffusion units

Short relaxation times and small diffusion coefficients often impede reliable diffusion experiments due to insufficient signal to noise ratios, especially in low temperature studies, where in the case of small diffusion coefficients in combination with very short T(2) times and substantial convection, double-stimulated-echo experiments are required as last resort of convection-compensating DOSY pulse sequences. Therefore, the combination of a strong gradient amplifier of a diffusion unit with Z-gradient high resolution probes is tested for low temperature applications to combine the advantages of high (1)H resolution, flexible temperature, and multinuclear applications with short gradient durations and diffusion delay. The experimental spectra on phosphoramidite ligands and phosphoramidite-copper complexes show that signal to noise improvements up to 176% were achieved despite longer eddy current delays and increased noise levels. Calculational estimations of the enhancement factors predict special benefits for systems with short transversal relaxation times and small diffusion coefficients and promise even higher enhancement factors for noise level optimized combinations. In addition, an easy way is presented to find fast and effectively relaxation optimized DOSY parameters for the convection-compensated double-stimulated-echo pulse sequence of Jerschow and Müller.

Trajectory attractor for a reaction-diffusion system with a small diffusion coefficient

Trajectory attractor for a reaction-diffusion system with a small diffusion coefficient

Air diffusion biocathode with CueO as electrocatalyst adsorbed on carbon particle-modified electrodes

The current density of biofuel cells which use dissolved O 2 as electron acceptor is limited by O 2 supply to the electrode surface due to the low solubility and small diffusion coefficient of O 2 in the electrolyte solution. In order to increase the current density, we constructed an air diffusion biocathode which uses O 2 directly from the air. As cathodic biocatalyst, we utilized CueO from Escherichia coli, which belongs to the family of multi-copper oxidases. O 2 reduction was catalyzed by CueO adsorbed on Ketjen black-modified carbon paper electrodes. The hydrophobic electrode surface was obtained by optimizing the weight ratio of polytetrafluoroethylene binder to Ketjen black. The current density of O 2 reduction reached values as high as 20 mA cm − 2 at 0 V vs. Ag|AgCl, KCl(sat.) in a citrate buffer (1.0 M, pH 5.0, 25 °C).

Heterogeneous polyvinylchloride blends with chlorinated polyethylene: rheological, diffusion, and gas sorption characteristics

Rheological and diffusion properties of binary PVC–CPE blends were investigated. The blends were obtained in a rather wide composition range (PVC : CPE = 100/0, 90/10, 80/20, 60/40, 40/60, 20/80, 10/90, 0/100 wt./wt.%). It was concluded from the sorption analysis data that for coating and barrier materials systems with higher PVC content should be regarded more appropriate because of their smaller diffusion coefficients. The rheological analysis showed that all the PVC compositions with CPE were thermoplastic in nature and could be processed and recycled with traditional thermoplastic processing equipment.

Physicochemical Properties of Structured Water at Material Surfaces

Physicochemical properties of thin film water on and between material surfaces have been reviewed. Infrared (IR) spectroscopy on thin film water sandwiched between various materials showed shifts of OH stretching vibration frequency maxima from 3400 cm−1 to about 3250 cm−1. These shifts vary with different materials, crystallographic orientations, film thickness (less than about 200 nm), dissolved ions and temperatures. The thin film water is supposed to have constrained structure close to ice and might have smaller diffusion coefficients and larger viscosity than the bulk liquid water. Standard molar volume, specific heat and entropy values for hydration water on some inorganic materials are different from these for the bulk liquid water and close to those for ice polymorphs. Sonic wave velocity measurements on a water-saturating rock suggest a larger P wave velocity for the thin film water than the value for bulk water. These structured thin water films with different properties from those of the bulk water can be present in the earth's interior and also in living materials such as cactus and human skin controlling dynamics of earth and life.

Well‐posed problem of a pollutant model of the Kazhikhov–Smagulov type

AbstractIn this paper, we consider a well‐posed problem of a pollutant model of the Kazhikhov–Smagulov type, which is derived by Bresch et al. (J. Math. Fluid Mech. 2007; 9:377–397). For proper smooth data, existence and uniqueness are stated on a time interval, which become independent of the diffusion coefficient λ when λ goes to zero. A blow‐up criterion involving the norm of the gradient of the velocity in L1(0, T; L∞) is also proved. Besides, we show that if the density‐dependent Euler system has a smooth solution on a given time interval [0, T0] , then the pollutant model of the Kazhikhov–Smagulov type with the same data and small diffusion coefficient has a smooth solution on [0, T0] . The diffusion solution tends to the Euler solution when the diffusion coefficient λ goes to zero. The rate of the convergence in L2 is of order λ . Copyright © 2008 John Wiley & Sons, Ltd.

Reaction Properties and Interfacial Intermetallics for Sn-xAg-0.5Cu Solders as a Function of Ag Content

Wetting and interfacial reactions were investigated for Sn−xAg−0.5Cu alloys, in which the Ag content had a variation from x=1.0 to x=4.0. Differential scanning calorimetry (DSC) was used to investigate the range of the melting temperature and the solidification temperature by measuring the endothermic and the exothermic heat flow, respectively. Low Ag contents increased the melting temperature ranges and deteriorated the wetting properties such as zero cross time and wetting force measured at two seconds. The extent of undercooling increased and the thickness of intermetallic compounds (IMC) decreased as the Ag content decreased. As the Ag content decreased, the initial IMC thickness decreased due to the large undercooling and, during the solid aging at 170°C, the IMC growth slightly decelerated because of the small diffusion coefficient. For the application of good drop shock reliability, Sn−Ag−Cu solder of low Ag content should be beneficial due to the restraint of the IMC growth (Cu6Sn5 and Cu3Sn) and of the coarse plate-like IMC (Ag3Sn).

Control systems of subdifferential type depending on a parameter

In a separable Hilbert space, we consider a control system with a subdifferential operator and a non-linear perturbation of monotonic type. The control is subject to a restriction that is a multi-valued map depending on the phase variables with closed non-convex values in a reflexive separable Banach space. The subdifferential operator, the perturbation, the restriction on the control and the initial condition depend on a parameter. Along with this system we consider a control system with convexified restrictions on the control. By a solution of such a system we mean a pair `trajectory-control'. We prove theorems on the existence of selectors that are continuous with respect to the parameter and whose values are solutions of the control system. We establish relations between the sets of selectors continuous with respect to the parameter whose values are solutions of the original system and solutions of the system with convexified restrictions on the control. We deduce from these relations various topological properties of the sets of solutions. We apply the results obtained to a control system described by a vector parabolic equation with a small diffusion coefficient in the elliptic term. We prove that solutions of the control system converge to solutions of the limit singular system as the diffusion coefficient tends to zero.

Estimation for stochastic differential equations with a small diffusion coefficient

We consider a multidimensional diffusion X with drift coefficient b ( X t , α ) and diffusion coefficient ε a ( X t , β ) where α and β are two unknown parameters, while ε is known. For a high frequency sample of observations of the diffusion at the time points k / n , k = 1 , … , n , we propose a class of contrast functions and thus obtain estimators of ( α , β ) . The estimators are shown to be consistent and asymptotically normal when n → ∞ and ε → 0 in such a way that ε − 1 n − ρ remains bounded for some ρ > 0 . The main focus is on the construction of explicit contrast functions, but it is noted that the theory covers quadratic martingale estimating functions as a special case. In a simulation study we consider the finite sample behaviour and the applicability to a financial model of an estimator obtained from a simple explicit contrast function.

Single or triple gradients?

Pulsed Field Gradients (PFGs) have become ubiquitous tools not only for Magnetic Resonance Imaging (MRI), but also for NMR experiments designed to study translational diffusion, for spatial encoding in ultra-fast spectroscopy, for the selection of desirable coherence transfer pathways, for the suppression of solvent signals, and for the elimination of zero-quantum coherences. Some of these experiments can only be carried out if three orthogonal gradients are available, while others can also be implemented using a single gradient, albeit at some expense of performance. This paper discusses some of the advantages of triple- with respect to single-gradient probes. By way of examples we discuss (i) the measurement of small diffusion coefficients making use of the long spin-lattice relaxation times of nuclei with low gyromagnetic ratios γ such as nitrogen-15, and (ii) the elimination of zero-quantum coherences in Exchange or Nuclear Overhauser Spectroscopy (EXSY or NOESY) experiments, as well as in methods relying on long-lived (singlet) states to study very slow exchange or diffusion processes.

Experimental evidence of diffusion-induced bias in near-wall velocimetry using quantum dot measurements

Near-surface velocity measurements are carried out with quantum dot (QD) nanoparticles using evanescent wave illumination. Relying on the small size of QDs, their correspondingly small hydrodynamic radius and high Brownian diffusion coefficient, we consider the situation where the tracer diffusion length over the inter-frame time Δt is large compared to the size of the interrogation region next to the wall. While keeping all other experimental parameters fixed, we systematically increase Δt by as much as a factor of 25, resulting in an increase of the QD diffusion length by a factor of 5. Data indicate a significant overestimation of the “apparent” mean velocity measured experimentally. These results provide a direct confirmation of the phenomenon of diffusion-induced bias described by the simulations of Sadr et al. (2007).

Detection of active oxygen species dynamics in TiO 2 sol solutions using single-shot near-field heterodyne transient grating method

Active oxygen species generated by photoexcitation of TiO 2 sol solutions were directly observed by the single-shot near-field heterodyne transient grating method. Two kinds of dynamics due to chemical species were observed and their lifetimes and diffusion coefficients were determined. From the dependence of the quantity of dissolved oxygen, it was confirmed that one of the species was generated from dissolved oxygen, such as a superoxide anion. Furthermore, this species was found to have a very small diffusion coefficient compared with other molecules with similar molecular weight, thereby suggesting that it was adsorbed onto TiO 2 particles.

Measurement technique on the diffusion coefficient of powder flow in a screw feeder by X-ray visualization

Measuring the diffusion coefficient of powder flow, which shows the magnitude of mixing, using X-ray visualization has been developed with the help of image processing techniques. Injecting minute metallic tracers into the powder yielded flow characteristics using the X-ray penetration images. The diffusion coefficient of the flow was determined by tracer figure deformation with time. Using this method, we evaluated four kinds of powder flows transported using different shaped screws in a screw feeder unit. The following results were obtained from this investigation: (i) Increasing the pitch width of the screw yielded decreased transport velocity and a larger diffusion coefficient. (ii) Double screw provided the largest transport velocity and the smallest diffusion coefficient. In addition, uncertainty analysis was applied to the method of measuring the diffusion coefficient to achieve greater bias limit.

Operational Limits of Controlled Current Coulometry with Ion‐Selective Polymeric Membranes

AbstractPlasticized polymeric membrane electrodes containing selective chemical receptors (ionophores) that are used in potentiometric and optical sensors have recently been shown to be attractive in controlled current coulometry for calibration free reagent delivery. For this purpose, a galvanostatic pulse of fixed duration is applied across an ion‐selective membrane containing added ion‐exchanger sites, resulting in the release of a calculated amount of ions from the membrane into the sample phase. This paper evaluates the operational limits of such coulometric actuators with chronopotentiometry, using silver‐selective membranes as model systems. Diffusion theory predicts the depletion of ionophore and ion‐exchanger at one of the two interfaces in a matter of minutes, owing to the relatively small diffusion coefficients in such membranes. Chronopotentiometry on membranes containing lipophilic cations at either side of the membrane, rather than silver ions, confirms that the ionophore depletes at the inner side of the membrane. At the sample side, ionophore is expected to increase in concentration and does not result in a loss of selectivity. Chronopotentiometric responses show a drastic transition at long times, typically 30 min, which cannot plausibly be explained by the depletion of added lipophilic ion‐exchanger at the sample side since the diffusion coefficients are similar to that of ionophore. It is postulated that the intrinsic anion‐exchanger sites of the PVC matrix are relatively immobile and do not easily concentration polarize upon application of a transmembrane current pulse, in agreement with Buck's earlier work on fixed site membranes. Indeed, silver and calcium‐selective membranes fabricated with increased concentrations of such fixed sites, by using carboxylated PVC, exhibited chronopotentiometric breakdown times larger than 60 min and no loss in coulometric efficiency. The results obtained here will help in designing coulometric actuators with improved characteristics on the basis of hydrophobic polymeric ion‐selective membranes.

The notion of persistence applied to breathers in thermal equilibrium

We study the thermal equilibrium of nonlinear Klein–Gordon chains at the limit of small coupling (anticontinuum limit). We show that the persistence distribution associated to the local energy density is a useful tool to study the statistical distribution of the so-called thermal breathers, mainly when the equilibrium is characterized by long-lived pinned excitations; in that case, the distribution of persistence intervals turns out to be a power law. We demonstrate also that this generic behaviour has a counterpart in the power spectra, where the high-frequencies domains nicely collapse if properly rescaled. These results are also compared to nonlinear Klein–Gordon chains with a soft nonlinearity, for which the thermal breathers are rather mobile entities. Finally, we discuss the possibility of a breather-induced anomalous diffusion law, and show that despite a strong slowing down of the energy diffusion, there are numerical evidences for a normal asymptotic diffusion mechanism, but with exceptionally small diffusion coefficients.

Effective velocity for transport in heterogeneous compressible flows with mean drift

Solving transport equations in heterogeneous flows might give rise to scale dependent transport behavior with effective large scale transport parameters differing from those found on smaller scales. For incompressible velocity fields, homogenization methods have proven to be powerful in describing the effective transport parameters. In this paper, we aim at studying the effective drift of transport problems in heterogeneous compressible flows. Such a study was done by Vergassola and Avellaneda in Physica D 106, 148 (1997). There, it was shown that for static compressible flow without mean drift, impacts on the large scale drift do not occur. We will first discuss the impact of a mean drift and show that static compressible flow with mean drift can produce a heterogeneity driven large scale drift (or ballistic transport). For the case of Gaussian stationary random processes, we derive explicit results for the large scale drift. Moreover, we show that the large scale or effective drift depends on the small scale diffusion coefficients and thus on the molecular weights of the particles. This study could be applied to weight-based particle separation. Numerical simulations are presented to illustrate these phenomena.

CO2 diffusion in polar ice: observations from naturally formed CO2 spikes in the Siple Dome (Antarctica) ice core

AbstractOne common assumption in interpreting ice-core CO2 records is that diffusion in the ice does not affect the concentration profile. However, this assumption remains untested because the extremely small CO2 diffusion coefficient in ice has not been accurately determined in the laboratory. In this study we take advantage of high levels of CO2 associated with refrozen layers in an ice core from Siple Dome, Antarctica, to study CO2 diffusion rates. We use noble gases (Xe/Ar and Kr/Ar), electrical conductivity and Ca2+ ion concentrations to show that substantial CO2 diffusion may occur in ice on timescales of thousands of years. We estimate the permeation coefficient for CO2 in ice is ∼4 × 10−21 mol m−1 s−1 Pa−1 at −23°C in the top 287 m (corresponding to 2.74 kyr). Smoothing of the CO2 record by diffusion at this depth/age is one or two orders of magnitude smaller than the smoothing in the firn. However, simulations for depths of ∼930–950 m (∼60–70 kyr) indicate that smoothing of the CO2 record by diffusion in deep ice is comparable to smoothing in the firn. Other types of diffusion (e.g. via liquid in ice grain boundaries or veins) may also be important but their influence has not been quantified.

Large time behavior of nonlocal aggregation models with nonlinear diffusion

The aim of this paper is to establish rigorous results on thelarge time behavior of nonlocal models for aggregation, includingthe possible presence of nonlinear diffusion terms modeling localrepulsions. We show that, as expected from the practicalmotivation as well as from numerical simulations, one obtainsconcentrated densities (Dirac $\delta$ distributions) asstationary solutions and large time limits in the absence ofdiffusion. In addition, we provide a comparison for aggregationkernels with infinite respectively finite support. In the firstcase, there is a unique stationary solution corresponding toconcentration at the center of mass, and all solutions of theevolution problem converge to the stationary solution for largetime. The speed of convergence in this case is just determined bythe behavior of the aggregation kernels at zero, yielding eitheralgebraic or exponential decay or even finite time extinction. Forkernels with finite support, we show that an infinite number ofstationary solutions exist, and solutions of the evolution problemconverge only in a measure-valued sense to the set of stationarysolutions, which we characterize in detail.Moreover, we also consider the behavior in the presence of nonlinear diffusion terms,the most interesting case being the one of small diffusion coefficients. Via the implicit function theorem we give aquite general proof of a rather natural assertion for such models, namely that there exist stationary solutionsthat have the form of a local peak around the center of mass. Our approach even yields the order of the size ofthe support in terms of the diffusion coefficients.All these results are obtained via a reformulation of theequations considered using the Wasserstein metric for probabilitymeasures, and are carried out in the case of a single spatialdimension.

Curvature Coupling Dependence of Membrane Protein Diffusion Coefficients

We consider the lateral diffusion of a protein interacting with the curvature of the membrane. The interaction energy is minimized if the particle is at a membrane position with a certain curvature that agrees with the spontaneous curvature of the particle. We employ stochastic simulations that take into account both the thermal fluctuations of the membrane and the diffusive behavior of the particle. In this study, we neglect the influence of the particle on the membrane dynamics, thus the membrane dynamics agrees with that of a freely fluctuating membrane. Overall, we find that this curvature coupling substantially enhances the diffusion coefficient. We compare the ratio of the projected or measured diffusion coefficient and the free intramembrane diffusion coefficient, which is a parameter of the simulations, with analytical results that rely on several approximations. We find that the simulations always lead to a somewhat smaller diffusion coefficient than that from our analytical approach. A detailed study of the correlations of the forces acting on the particle indicates that the diffusing inclusion tries to follow favorable positions on the membrane such that forces along the trajectory are on average smaller than they would be for random particle positions.

Direct measurement of effective diffusion coefficients in nanochannels using steady-state dispersion effects

We present a method to measure effective diffusion coefficients of fluorescently labeled molecules inside a nanofluidic system. Molecules with small diffusion coefficients show a larger lateral dispersion than highly diffusive species, which is counterintuitive. We performed measurements with wheat germ agglutinin proteins and obtained an effective diffusion coefficient which is four orders of magnitude lower than its free diffusion coefficient. Our technique which is a direct and relatively simple measurement of the effective diffusion coefficients inside nanochannels of well controlled dimensions could help fundamental studies in membranes and separation sciences.