The ground state of a two-dimensional ionic mixture composed of oppositely charged spheres is determined as a function of the size asymmetry by using a penalty method. The cascade of stable structures includes square, triangular and rhombic crystals
as well as a dipolar pair gas and a gas of one-dimensional crystalline chains. Thereby we confirm the square structure, found experimentally on charged granulates, and predict new phases detectable in experiments on granular and colloidal matter.
The phase diagram of Yukawa particles confined between two parallel hard walls is calculated at zero-temperature beyond the bilayer regime by lattice-sum-minimization. Tuning the screening, a rich phase behavior is found in the regime bounded by stab
le two-triangular layers and 3-square layers. In this regime, alternating prism phases with square and triangular basis, structures derived from a hcp bulk lattice, and a structure with two outer layers and two inner staggered rectangular layers, reminiscent of a Belgian waffle iron, are stable. These structures are verifiable in experiments on charged colloidal suspensions and dusty plasma sheets.
Recent progress in the understanding of the effect of electrostatics in soft matter is presented. A vast amount of materials contains ions ranging from the molecular scale (e.g., electrolyte) to the meso/macroscopic one (e.g., charged colloidal parti
cles or polyelectrolytes). Their (micro)structure and physicochemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular theoretical and simulational aspects, including the experimental motivations, will be discussed.
The zero-temperature phase diagram of binary mixtures of particles interacting via a screened Coulomb pair potential is calculated as a function of composition and charge ratio. The potential energy obtained by a Lekner summation is minimized among a
variety of candidate two-dimensional crystals. A wealth of different stable crystal structures is identified including $A,B,AB_2, A_2B, AB_4$ structures [$A$ $(B)$ particles correspond to large (small) charge.] Their elementary cells consist of triangular, square or rhombic lattices of the $A$ particles with a basis comprising various structures of $A$ and $B$ particles. For small charge asymmetry there are no intermediate crystals besides the pure $A$ and $B$ triangular crystals.
The adsorption of charged colloids (macroions) onto an oppositely charged planar substrate is investigated theoretically. Taking properly into account the finite size of the macroions, unusual behaviors are reported. It is found that the role of the
coions (the little salt-ions carrying the same sign of charge as that of the substrate) is crucial to understand the mechanisms involved in the process of macroion adsorption. In particular, the coions can accumulate near the substrates surface and lead to a counter-intuitive {it surface charge amplification}.
The phase diagram of binary mixtures of particles interacting via a pair potential of parallel dipoles is computed at zero temperature as a function of composition and the ratio of their magnetic susceptibilities. Using lattice sums, a rich variety o
f different stable crystalline structures is identified including $A_mB_n$ structures. [$A$ $(B)$ particles correspond to large (small) dipolar moments.] Their elementary cells consist of triangular, square, rectangular or rhombic lattices of the $A$ particles with a basis comprising various structures of $A$ and $B$ particles. For small (dipolar) asymmetry there are intermediate $AB_2$ and $A_2B$ crystals besides the pure $A$ and $B$ triangular crystals. These structures are detectable in experiments on granular and colloidal matter.
