Diffusion in model disordered media

The electroneutrality constraint in nonlocal models

We develop a nonlocal Nernst-Planck model for reaction and diffusion in multicomponent ionic systems. We apply the model to the one-dimensional liquid junction problem, in which two electrolytic solutions of different ionic concentrations are brought into contact via a permeable membrane. Transport of ions through the membrane induces an electric field which is modeled using two separate nonlocal conditions: charge conservation and Gauss' law. We investigate how well they satisfy the criterion of strict electroneutrality which stipulates that the net charge at each point in the domain is zero, by considering four different initial scenarios. Charge conservation and Gauss' law yield similar results for most practical scenarios in which the initial condition satisfies strict electroneutrality. However, Gauss' law has two important advantages over charge conservation: (i) it is numerically more stable and can be applied even when the concentration of all the charged species drops to zero and (ii) computationally, it is significantly cheaper. Further, this study provides insights on the prescription of electroneutrality conditions necessary to handle the physics of evolving charges in nonlocal peridynamic models that are aimed at modeling nonlocal reaction-diffusion or corrosion-type processes.

From self-assembly fundamental knowledge to nanomedicine developments

This review highlights the key role of NMR techniques in demonstrating the molecular aspects of the self-assembly of surfactant molecules that nowadays constitute the basic knowledge which modern nanoscience relies on. The aim is to provide a tutorial overview. The story of a rigorous scientific approach to understand self-assembly in surfactant systems and biological membranes starts in the early seventies when the progresses of SAXRD and NMR technological facilities allowed to demonstrate the existence of ordered soft matter, and the validity of Tanford approach concerning self-assembly at a molecular level. Particularly, NMR quadrupolar splittings, NMR chemical shift anisotropy, and NMR relaxation of dipolar and quadrupolar nuclei in micellar solutions, microemulsions, and liquid crystals proved the existence of an ordered polar-apolar interface, on the NMR time scale. NMR data, rationalized in terms of the two-step model of relaxation, allowed to quantify the dynamic aspects of the supramolecular aggregates in different soft matter systems. In addition, NMR techniques allowed to obtain important information on counterion binding as well as on size of the aggregate through molecular self-diffusion. Indeed NMR self-diffusion proved without any doubt the existence of bicontinuous microemulsions and bicontinuous cubic liquid crystals, suggested by pioneering and brilliant interpretation of SAXRD investigations. Moreover, NMR self-diffusion played a fundamental role in the understanding of microemulsion and emulsion nanostructures, phase transitions in phase diagrams, and particularly percolation phenomena in microemulsions. Since the nineties, globalization of the knowledge along with many other technical facilities such as electron microscopy, particularly cryo-EM, produced huge progresses in surfactant and colloid science. Actually we refer to nanoscience: bottom up/top down strategies allow to build nanodevices with applications spanning from ICT to food technology. Developments in the applied fields have also been addressed by important progresses in theoretical skills aimed to understand intermolecular forces, and specific ion interactions. Nevertheless, this is still an open question. Our predictive ability has however increased, hence more ambitious targets can be planned. Nanomedicine represents a major challenging field with its main aims: targeted drug delivery, diagnostic, theranostics, tissue engineering, and personalized medicine. Few recent examples will be mentioned. Although the real applications of these systems still need major work, nevertheless new challenges are open, and perspectives based on integrated multidisciplinary approaches would enable both a deeper basic knowledge and the expected advances in biomedical field.

Sizing of reverse micelles in microemulsions using NMR measurements of diffusion

This paper reports the size of reverse micelles (RMs) in AOT/octane/H(2)O and CTAB/hexanol/H(2)O microemulsions using magnetic resonance (MR) pulsed field gradient (PFG) measurements of diffusion. Diffusion data were measured using the pulsed gradient stimulated echo (PGSTE) experiment for surfactant molecules residing in the RM interface. Inverse Laplace transformation of these data generated diffusion coefficients for the RMs, which were converted into hydrodynamic radii using the Stokes-Einstein relation. This technique is complementary to those previously used to size RMs, such as dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS), but also offers several advantages, which are discussed. RM sizes, determined using the PGSTE method, in the AOT (sodium bis(2-ethylhexyl) sulfosuccinate) and CTAB (cetyltrimethylammonium bromide) microemulsions were compared with previous DLS and SAXS data, showing good agreement. Methods for determining number distributions from the PGSTE data, through the use of scaling factors, were investigated.

Quantification of specific anion binding to non-ionic Triton X-100 micelles

Anion binding to nonionic micelles was quantified by self-diffusion. Four anions were probed by multinuclear PGSTE NMR measurements in a Triton X-100 micellar aqueous solution. The salt concentration used was sufficiently low to avoid any micellar growth affecting surface curvature. The micellar aggregates that provide a model surface are uncharged with hydrophilic headgroups so that electrostatic ion surface interactions play little or no role in prescribing specific anion binding. Anionic affinity to the micellar surface followed a Hofmeister series, (CH(3))(2)AsO(2)(-) ≫ CH(3)COO(-) > H(2)PO(4)(-) > F(-). The observed ion specificity is rationalized by calling into play the nonelectrostatic interactions occurring between the anions and the micellar surface.

Non-Gaussian diffusion imaging: a brief practical review

The departure from purely mono-exponential decay of the signal, as observed from brain tissue following a diffusion-sensitized sequence, has prompted the search for alternative models to characterize these unconventional water diffusion dynamics. Several approaches have been proposed in the last few years. While multi-exponential models have been applied to characterize brain tissue, several unresolved controversies about the interpretations of the results have motivated the search for alternative models that do not rely on the Gaussian diffusion hypothesis. In this brief review, diffusional kurtosis imaging (DKI) and anomalous diffusion imaging (ADI) techniques are addressed and compared with diffusion tensor imaging. Theoretical and experimental issues are briefly described to allow readers to understand similarities, differences and limitations of these two non-Gaussian models. However, since the ultimate goal is to improve specificity, sensitivity and spatial localization of diffusion MRI for the detection of brain diseases, special attention will be paid on the clinical feasibility of the proposed techniques as well as on the context of brain pathology investigations.

Movement of Proteins in an Environment Crowded by Surfactant Micelles: Anomalous versus Normal Diffusion

Small proteins move in crowded cell compartments by anomalous diffusion. In many of them, e.g., the endoplasmic reticulum, the proteins move between lipid membranes in the aqueous lumen. Molecular crowding in vitro offers a systematic way to study anomalous and normal diffusion in a well controlled environment not accessible in vivo. We prepared a crowded environment in vitro consisting of hexaethylene glycol monododecyl ether (C(12)E(6)) nonionic surfactant and water and observed lysozyme diffusion between elongated micelles. We have fitted the data obtained in fluorescence correlation spectroscopy using an anomalous diffusion model and a two-component normal diffusion model. For a small concentration of surfactant (below 4 wt %) the data can be fitted by single-component normal diffusion. For larger concentrations the normal diffusion fit gave two components: one very slow and one fast. The amplitude of the slow component grows with C(12)E(6) concentration. The ratio of diffusion coefficients (slow to fast) is on the order of 0.1 for all concentrations of surfactant in the solution. The fast diffusion is due to free proteins while the slow one is due to the protein-micelle complexes. The protein-micelle interaction is weak since even in a highly concentrated solution (35% of C(12)E(6)) the amplitude of the slow mode is only 10%, despite the fact that the average distance between the micelles is the same as the size of the protein. The anomalous diffusion model gave the anomaly index (r(2)(t) approximately t(alpha)), alpha monotonically decreasing from alpha = 1 (at 4% surfactant) to alpha = 0.88 (at 37% surfactant). The fits for two-component normal diffusion and anomalous diffusion were of equally good quality, but the physical interpretation was only straightforward for the former.

Nearly space-filling fractal networks of carbon nanopores

Small-angle x-ray scattering, nitrogen adsorption, and scanning tunneling microscopy show that a series of activated carbons host an extended fractal network of channels with dimension D(p) = 2.8-3.0 (pore fractal), channel width 15-20 A (lower end of scaling), network diameter 3000-3400 A (upper end of scaling), and porosity of 0.3-0.6. We interpret the network as a stack of quasiplanar invasion percolation clusters, formed by oxidative removal of walls between closed voids of diameter of approximately 10 A and held in registry by fibrils of the biological precursor, and point out unique applications.