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.

Using Monte Carlo simulations, we study the counterion distribution close to planar charged walls in two geometries: i) when only one charged wall is present and the counterions are confined to one half-space, and ii) when the counterions are confined between two equally charged walls. In both cases the surface charge is smeared out and the dielectric constant is the same everywhere. We obtain the counterion density profile and compare it with both the Poisson-Boltzmann theory (asymptotically exact in the limit of weak coupling, i.e. low surface charge, high temperature and low counterion valence) and the strong-coupling theory (valid in the opposite limit of high surface charge, low temperature and high counterion valence) and with previously calculated correction terms to both theories for different values of the coupling parameter, thereby establishing the domain of validity of the asymptotic limits. Gaussian corrections to the leading Poisson-Boltzmann behavior (obtained via a systematic loop expansion) in general perform quite poorly: At coupling strengths low enough so that the Gaussian (or one-loop) correction does describe the numerical deviations from the Poisson-Boltzmann result correctly, the leading Poisson-Boltzmann term by itself matches the data within high accuracy. This reflects the slow convergence of the loop expansion. For a single charged plane, the counterion pair correlation function indicates a behavioral change from a three-dimensional, weakly correlated counterion distribution (at low coupling) to a two-dimensional, strongly correlated counterion distribution (at high coupling), which is paralleled by the specific-heat capacity which displays a rounded hump at intermediate coupling strengths. For the case of counterions confined between two equally charged walls, we analyze the inter-wall pressure and establish the complete phase diagram, featuring attraction between the walls for large enough coupling strength and at intermediate wall separation. Depending on the thermodynamic ensemble, the phase diagram exhibits a discontinuous transition where the inter-wall distance jumps to infinity (in the absence of a chemical potential coupling to the inter-wall distance, as for charged lamellae in excess solvent) or a critical point where two coexisting states with different inter-wall distance become indistinguishable (in the presence of a chemical potential, as for charged lamellae with a finite fixed solvent fraction). The attractive pressure decays with the inter-wall distance as an inverse cube, similar to analytic predictions, although the amplitude differs by an order of magnitude from previous theoretical results. Finally, we discuss in detail our simulation methods and compare the finite-size scaling behavior of different boundary conditions (periodic, minimal image and open).

Similarly and highly charged plates in the presence of multivalent counterions attract each other and form electrostatically bound states. Using Monte-Carlo simulations, we obtain the interplate pressure in the global parameter space. The equilibrium plate separation, where the pressure changes from attractive to repulsive, exhibits a novel unbinding transition. A systematic and asymptotically exact strong-coupling field theory yields the bound state from a competition between counterion entropy and electrostatic attraction, in agreement with simple scaling arguments and simulations.

The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature.In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling. Formally, it corresponds to a standard virial expansion. Long-range divergences, which render the virial expansion intractable for homogeneous bulk systems, are shown to be renormalizable for the case of inhomogeneous distribution functions by a systematic expansion in powers of the fugacity. For a planar charged wall, our analytical results compare quantitatively with extensive Monte Carlo simulations.

PACS. 82.70.-y -Disperse systems; complex fluids. PACS. 61.20.Qg -Structure of associated liquids: electrolytes, molten salts, etc.. PACS. 82.45.+z -Electrochemistry.Abstract. -We consider counterions in the presence of a single planar surface with a spatially inhomogeneous charge distribution using Monte-Carlo simulations and strong-coupling theory. For high surface charges, multivalent counterions, or pronounced substrate charge modulation the counterions are laterally correlated with the surface charges and their density profile deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.Typeset using EURO-T E X

We study the role of flexible spacers in specific adhesion from the point of view of polymer reaction--diffusion theory. By assuming that the interactions between complementary adhesion moieties occur on a length scale much smaller than the size of the polymer spacer, we describe in detail binding and rupture between two opposing surfaces. Predictions are given for the physical properties of interest such as the time evolution of bond density and the ranges of attraction and unbinding. We also discuss the dynamic crossover between reversible and irreversible bridging.

We study theoretically the adhesion between two approaching surfaces, one containing tethered ligands and the other receptors. Using the reaction-diffusion formalism, we show that the range of adhesion ℓr is generally determined by a combination of tether dynamics, ligand-receptor affinity and experimental speed of approach v. Contrary to previous studies, we fully account for back reactions and are thus able to describe the crossover between irreversible adhesion at large affinities or high speed v and reversible adhesion at small affinities or low speed. We also briefly discuss the case of rupture and show that in the limit of irreversible adhesion the rupture occurs always at a larger distance than ℓr determined for approaching surfaces.

We used field-theoretic simulations to study the equilibrium behavior of a polymer solution under good solvent conditions confined to a slit of width L. In particular, we obtained the chemical potential and the density profiles across the slit for different values of the monomer excluded volume over a wide range of concentrations C. We also obtained mean field results for the chemical potential and the density profiles. The effective correlation length ξeff was calculated from the density profiles and compared to the mean field result (valid in the limit of high concentrations). For small excluded volume parameters we found that ξeff is well described by the mean field result for all concentrations. For larger excluded volume parameters the correlation length exhibits a C−3/4 scaling behavior for intermediate concentrations, which is compatible with the behavior expected for this system in the semidilute regime.