The ionic composition and pair correlations in fluid phases of realistically salt-free charged colloidal sphere suspensions are calculated in the primitive model. We obtain the number densities of all ionic species in suspension, including low-molecu
lar weight microions, and colloidal macroions with acidic surface groups, from a self-consistent solution of a coupled physicochemical set of nonlinear algebraic equations and non-mean-field liquid integral equations. Here, we study suspensions of colloidal spheres with sulfonate or silanol surface groups, suspended in demineralized water that is saturated with carbon dioxide under standard atmosphere. The only input required for our theoretical scheme are the acidic dissociation constants pKa, and effective sphere diameters of all involved ions. Our method allows for an ab initio calculation of colloidal bare and effective charges, at high numerical efficiency.
The pair-correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model, all ions are approximated as non-overlapping hyperspheres with Coulomb interactions
. Our spectral HNC solver is based on a Fourier-Bessel transform introduced by Talman [J. Comput. Phys., 29, 35 (1978)], with logarithmically spaced computational grids. Numeric efficiency for arbitrary spatial dimensions is a commonly exploited virtue of this transform method. Here, we highlight another advantage of logarithmic grids, consisting in efficient sampling of pair-correlation functions for highly asymmetric ionic mixtures. For three-dimensional fluids, ion size- and charge-ratios larger than one thousand can be treated, corresponding to hitherto computationally not accessed micrometer-sized colloidal spheres in 1-1 electrolyte. Effective colloidal charge numbers are extracted from our primitive model results. For moderately large ion size- and charge-asymmetries, we present Molecular Dynamics simulation results that agree well with the approximate HNC pair correlations.
For sedimenting colloidal hard spheres, the propagation and broadening of the crystal-fluid interface is studied by Brownian dynamics computer simulations of an initially homogeneous sample. Two different types of interface broadenings are observed:
the first occurs during growth and is correlated with the interface velocity, the second is concomitant with the splitting of the crystal-fluid interface into the crystal-amorphous and amorphous-liquid interfaces. The latter width is strongly peaked as a function of the gravitational driving strength with a huge amplitude relative to its equilibrium counterpart.
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.
We have performed simulations to study how increasing humidity affects the structure of Nafion-like ionomers under conditions of low sulfonate concentration and low humidity. At the onset of membrane hydration, the clusters split into smaller parts.
These subsequently swell, but then maintain constant the number of sulfonates per cluster. We find that the distribution of water in low-sulfonate membranes depends strongly on the sulfonate concentration. For a relatively low sulfonate concentration, nearly all the side-chain terminal groups are within cluster formations, and the average water loading per cluster matches the water content of membrane. However, for a relatively higher sulfonate concentration the water-to-sulfonate ratio becomes non-uniform. The clusters become wetter, while the inter-cluster bridges become drier. We note the formation of unusual shells of water-rich material that surround the sulfonate clusters.
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.
The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are con
sidered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady-state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady-state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.
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.
