Ali Naji

Statics and dynamics of strongly charged soft matter

Abstract Soft matter materials, such as polymers, membranes, proteins, are often electrically charged. This makes them water soluble, which is of great importance in technological application and a prerequisite for biological function. We discuss a few static and dynamic systems that are dominated by charge effects. One class comprises complexation between oppositely charged objects, for example the adsorption of charged ions or charged polymers on oppositely charged substrates of different geometry. Here the main questions are whether adsorption occurs and what the effective charge of the resulting complex is. We explicitly discuss the adsorption behavior of polyelectrolytes on substrates of planar, cylindrical and spherical geometry with specific reference to DNA adsorption on supported charged lipid layers, DNA adsorption on oppositely charged cylindrical dendro-polymers, and DNA binding on globular histone proteins, respectively. In all these systems salt plays a crucial role, and some of the important features can already be obtained on the linear Debye–Huckel level. The second class comprises effective interactions between similarly charged objects. Here the main theme is to understand the experimental finding that similarly and highly charged bodies attract each other in the presence of multi-valent counterions. This is demonstrated using field-theoretic arguments as well as Monte-Carlo simulations for the case of two homogeneously charged bodies. Realistic surfaces, on the other hand, are corrugated and also exhibit modulated charge distributions, which is important for static properties such as the counterion-density distribution, but has even more pronounced consequences for dynamic properties such as the counterion mobility. More pronounced dynamic effects are obtained with highly condensed charged systems in strong electric fields. Likewise, an electrostatically collapsed highly charged polymer is unfolded and oriented in strong electric fields. All charged systems occur in water, and water by itself is not a very well understood material. At the end of this review, we give a very brief and incomplete account of the behavior of water at planar surfaces. The coupling between water structure and charge effects is largely unexplored, and a few directions for future research are sketched. On an even more nanoscopic level, we demonstrate using ab initio methods that specific interactions between oppositely charged groups (which occur when their electron orbitals start to overlap) are important and cause ion-specific effects that have recently moved into the focus of interest.

Electrostatic Interactions in Strongly-Coupled Soft Matter

Charged soft-matter systems—such as colloidal dispersions and charged polymers—are dominated by attractive forces between constituent like-charged particles when neutralizing counterions of high charge valency are introduced. Such counter-intuitive effects indicate strong electrostatic coupling between like-charged particles, which essentially results from electrostatic correlations among counterions residing near particle surfaces. In this paper, the attraction mechanism and the structure of counterionic correlations are discussed in the limit of strong coupling based on recent numerical and analytical investigations and for various geometries (planar, spherical and cylindrical) of charged objects.

Perspective: Coulomb fluids—Weak coupling, strong coupling, in between and beyond

We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counterion-only system in the presence of macroscopic, uniformly charged boundaries, where they can be derived systematically. Later we show how this formalism can be generalized to the cases with additional characteristic length scales that introduce new coupling parameters into the problem. These cases most notably include asymmetric ionic mixtures with mono- and multivalent ions that couple differently to charged surfaces, ions with internal charge (multipolar) structure and finite static polarizability, where weak and strong coupling limits can be constructed by analogy with the counterion-only case and lead to important new insights into their properties that cannot be derived by any other means.

Theoretical approaches to neutral and charged polymer brushes

Neutral or charged polymers that are densely end-grafted to surfaces form brush-like structures and are highly stretched under good-solvent conditions. We discuss and compare relevant results from scaling models, self-consistent field methods and MD simulations and concentrate on the conceptual simple case of planar substrates. For neutral polymers the main quantity of interest is the brush height and the polymer density profile, which can be well predicted from self-consistent calculations and simulations. Charged polymers (polyelectrolytes) are of practical importance since they are soluble in water. Counterion degrees of freedom determine the brush behavior in a decisive way and lead to a strong and nonlinear swelling of the brush.

Attraction and unbinding of like-charged rods

We investigate the effective interaction between two like-charged rods in the regime of large coupling parameters using both Molecular Dynamics simulation techniques and the recently introduced strong-coupling theory. We obtain attraction between the rods for elevated Manning parameters accompanied by an equilibrium surface-to-surface separation of the order of the Gouy-Chapman length. A continuous unbinding between the rods is predicted at a threshold Manning parameter ξc = 2/3.

Strong-Coupling Electrostatics in the Presence of Dielectric Inhomogeneities

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the intersurface space upon increasing the solvent-membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.

Non-linear osmotic brush regime: simulations and mean-field theory.

Abstract.We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and is controlled by the counterion-condensation process around polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.

Many-body effects in the van der Waals–Casimir interaction between graphene layers

Van der Waals-Casimir dispersion interactions between two apposed graphene layers, a graphene layer and a substrate, and in a multilamellar graphene system are analyzed within the framework of the Lifshitz theory. This formulation hinges on a known form of the dielectric response function of an undoped or doped graphene sheet, assumed to be of a random phase approximation form. In the geometry of two apposed layers the separation dependence of the van der Waals-Casimir interaction for both types of graphene sheets is determined and compared with some well known limiting cases. In a multilamellar array the many-body effects are quantified and shown to increase the magnitude of the van der Waals-Casimir interactions.

Counterion-mediated weak and strong coupling electrostatic interaction between like-charged cylindrical dielectrics

We examine the effective counterion-mediated electrostatic interaction between two like-charged dielectric cylinders immersed in a continuous dielectric medium containing neutralizing mobile counterions. We focus on the effects of image charges induced as a result of the dielectric mismatch between the cylindrical cores and the surrounding dielectric medium and investigate the counterion-mediated electrostatic interaction between the cylinders in both limits of weak and strong electrostatic couplings (corresponding, e.g., to systems with monovalent and multivalent counterions, respectively). The results are compared with extensive Monte Carlo simulations exhibiting good agreement with the limiting weak and strong coupling results in their respective regime of validity.

Weak- and strong-coupling electrostatic interactions between asymmetrically charged planar surfaces.

We compare weak- and strong-coupling theory of counterion-mediated electrostatic interactions between two asymmetrically charged plates with extensive Monte Carlo simulations. Analytical results in both weak- and strong-coupling limits compare excellently with simulations in their respective regimes of validity. The system shows a surprisingly rich structure in terms of interactions between the surfaces as well as fundamental qualitative differences in behavior in the weak- and the strong-coupling limits.