Haim Diamant

From random walk to single-file diffusion.

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. The ansatz asserts that the inverse mean squared displacement is the sum of the inverse mean squared displacement for short time normal diffusion (random walk) and the inverse mean squared displacement for asymptotic single-file diffusion (SFD). The dependence of the 1D mobility in the SFD on the concentration of the colloids agrees quantitatively with that derived for a hard rod model, which confirms for the first time the validity of the hard rod SFD theory. We also show that a recent SFD theory by Kollmann leads to the hard rod SFD theory for a Tonks gas.

Kinetics of surfactant adsorption: the free energy approach

Abstract We review the free energy approach to the kinetics of surfactant adsorption at fluid–fluid interfaces. The formalism is applied to several systems. For non-ionic surfactant solutions, the results coincide with earlier models while indicating their limits of validity. We study the case of surfactant mixtures, focusing on the relation between the mixture kinetics and the properties of its individual constituents. Strong electrostatic interactions in salt-free ionic surfactant solutions drastically modify the adsorption kinetics. In this case the theory accounts for experimental results, which could not be earlier understood. The effect of screening by added salt is studied as well. Our theoretical predictions are compared with available experiments.

Compression Induced Folding of a Sheet: An Integrable System

The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wave vector set by the bending stiffness of the film and the weight of the substrate fluid. Our solution describes the entire progression from a weakly displaced sinusoidal buckling to a single large fold that contacts itself. The pressure decrease is exactly quadratic in the lateral displacement. We identify a complex wave vector whose magnitude remains invariant with compression.

Screened Hydrodynamic Interaction in a Narrow Channel

We study experimentally and theoretically the hydrodynamic coupling between Brownian colloidal particles diffusing along a linear channel. The quasi-one-dimensional confinement, unlike other constrained geometries, leads to a sharply screened interaction. Consequently, particles move in concert only when their mutual distance is smaller than the channel width, and two-body interactions remain dominant up to high particle densities. The coupling in a cylindrical channel is predicted to reverse sign at a certain distance, yet this unusual effect is too small to be currently detectable.

Self-Assembly in Mixtures of Polymers and Small Associating Molecules

The interaction between a flexible polymer in a good solvent and smaller associating solute molecules such as amphiphiles (surfactants) is considered theoretically. Attractive correlations, induced in the polymer because of the interaction, compete with intrachain repulsion and eventually drive a joint self-assembly of the two species, accompanied by partial collapse of the chain. Results of the analysis are found to be in good agreement with experiments on the onset of self-assembly in diverse polymer−surfactant systems. The threshold concentration for self-assembly in the mixed system (critical aggregation concentration, cac) is always lower than the one in the polymer-free solution (critical micelle concentration, cmc). Several self-assembly regimes are distinguished, depending on the effective interaction between the two species. For strong interaction, corresponding experimentally to oppositely charged species, the cac is much lower than the cmc. It increases with ionic strength and depends only weak...

Soft quasicrystals–Why are they stable?

In the last two years we have witnessed the exciting experimental discovery of soft matter with nontrivial quasiperiodic long-range order–a new form of matter termed a soft quasicrystal. Two groups have independently discovered such order in soft matter: Zeng et al. in a system of dendrimer liquid crystals; and Takano et al. in a system of ABC star-shaped polymers. These newly discovered soft quasicrystals not only provide exciting platforms for the fundamental study of both quasicrystals and of soft matter, but also hold the promise for new applications based on self-assembled nanomaterials with unique physical properties that take advantage of the quasiperiodicity, such as complete and isotropic photonic band-gap materials. Here we provide a concise review of the emerging field of soft quasicrystals, suggesting that the existence of two natural length-scales, along with three-body interactions, may constitute the underlying source of their stability.

Increased Concentration of Polyvalent Phospholipids in the Adsorption Domain of a Charged Protein

We studied the adsorption of a charged protein onto an oppositely charged membrane, composed of mobile phospholipids of differing valence, using a statistical-thermodynamical approach. A two-block model was employed, one block corresponding to the protein-affected region on the membrane, referred to as the adsorption domain, and the other to the unaffected remainder of the membrane. We calculated the protein-induced lipid rearrangement in the adsorption domain as arising from the interplay between the electrostatic interactions in the system and the mixing entropy of the lipids. Equating the electrochemical potentials of the lipids in the two blocks yields an expression for the relations among the various lipid fractions in the adsorption domain, indicating a sensitive dependence of lipid fraction on valence. This expression is a result of the two-block picture but does not depend on further details of the protein-membrane interaction. We subsequently calculated the lipid fractions themselves using the Poisson-Boltzmann theory. We examined the dependence of lipid enrichment, i.e., the ratio between the lipid fractions inside and outside the adsorption domain, on various parameters such as ionic strength and lipid valence. Maximum enrichment was found for lipid valence in the range between -3 and -4 in physiological conditions. Our results are in qualitative agreement with recent experimental studies on the interactions between peptides having a domain of basic residues and membranes containing a small fraction of the polyvalent phosphatidylinositol 4,5-bisphosphate (PIP2). This study provides theoretical support for the suggestion that proteins adsorbed onto membranes through a cluster of basic residues may sequester PIP2 and other polyvalent lipids.

Hydrodynamic Interaction in Confined Geometries

This article gives an overview of recent theoretical and experimental findings concerning the hydrodynamic interaction between liquid-embedded particles in various confined geometries. A simple unifying description emerges, which accounts for the various findings based on the effect of confinement on conserved fields of the embedding liquid. It shows, in particular, that the hydrodynamic interaction under confinement remains long-ranged, decaying algebraically with inter-particle distance, except for the case of confinement in a rigid linear channel.

Wrinkle to fold transition: influence of the substrate response

Spatially confined rigid membranes reorganize their morphology in response to imposed constraints. Slight compression of a rigid membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad spatial distribution of energy. For larger compression, the deformation energy is progressively localized in small regions which ultimately develop sharp folds. We review the influence of the substrate on this wrinkle to fold transition by considering two models based on purely viscous and purely elastic foundations. We analyze and contrast the physics and mathematics of both systems.

Dynamic Surface Tension of Aqueous Solutions of Ionic Surfactants: Role of Electrostatics

The adsorption kinetics of the cationic surfactant dodecyltrimethylammonium bromide at the air-water interface has been studied by the maximum bubble pressure method at concentrations below the critical micellar concentration. At short times, the adsorption is diffusion-limited. At longer times, the surface tension shows an intermediate plateau and can no longer be accounted for by a diffusion-limited process. Instead, adsorption appears kinetically controlled and slowed down by an adsorption barrier. A Poisson-Boltzmann theory for the electrostatic repulsion from the surface does not fully account for the observed potential barrier. The possibility of a surface phase transition is expected from the fitted isotherms but has not been observed by Brewster angle microscopy.