An extension to the ${\text{P}}^3\text{M}$ algorithm for electrostatic interactions is presented that allows to efficiently compute dipolar interactions in periodic boundary conditions. Theoretical estimates for the root-mean-square error of the forces, torques, and the energy are derived. The applicability of the estimates is tested and confirmed in several numerical examples. A comparison of the computational performance of the new algorithm to a standard dipolar-Ewald summation methods shows a performance crossover from the Ewald method to the dipolar ${\text{P}}^3\text{M}$ method for as few as 300 dipolar particles. In larger systems, the new algorithm represents a substantial improvement in performance with respect to the dipolar standard Ewald method. Finally, a test comparing point-dipole-based and charged-pair based models shows that point-dipole-based models exhibit a better performance than charged-pair based models.

We introduce a regularization procedure to define electrostatic energies and forces in a slab system of thickness h that is periodic in two dimensions and carries a net charge. The regularization corresponds to a neutralization of the system by two charged walls and can be viewed as the extension to the two-dimensional (2D)+h geometry of the neutralization by a homogeneous background in the standard three-dimensional Ewald method. The energies and forces can be computed efficiently by using advanced methods for systems with 2D periodicity, such as MMM2D or P3M/ELC, or by introducing a simple background-charge correction to the Yeh–Berkowitz approach of slab systems. The results are checked against direct lattice sum calculations on simple systems. We show, in particular, that the Madelung energy of a 2D square charge lattice in a uniform compensating background is correctly reproduced to high accuracy. A molecular dynamics simulation of a sodium ion close to an air/water interface is performed to demonstrate that the method does indeed provide consistent long-range electrostatics. The mean force on the ion reduces at large distances to the image-charge interaction predicted by macroscopic electrostatics. This result is used to determine precisely the position of the macroscopic dielectric interface with respect to the true molecular surface.

In the past decades, ferrofluids have become relevant in many applications ranging from engineering to medicine, and have attracted the interest of scientists from many fields. To understand the physical mechanisms serving as a basis for these applications, over the last decades, many of the properties of ferrofluids have been studied and can now be controlled. However, in order to fine-tune various aspects of the interactions in the system and hopefully – in the long run – to build tailored structures, in recent years, magnetic nanoparticles and colloids that deviate from the model of a spherical particle with a dipole moment at its center were examined. Among them are dumbbells, magnetic core-shell particles, elongated ferro-particles, and colloidal particles with a magnetic cap. In this paper, we introduce and examine – using analytical calculations and Monte Carlo simulations – one such model system, namely, magnetic particles in which the dipole moment is shifted from the center of mass towards the particle's surface. In this way, an additional anisotropy is introduced to the particles, which results in quite different and surprising microscopic properties of suspensions. Here, we mainly concentrate on ground states of small clusters of shifted-dipole particles, but also take a first glance on suspensions at finite temperature.

We will review the sparse attempts to model the structure and dynamics of polyelectrolyte multilayers with coarse-grained bead–spring models within a continuum solvent approach. Due to the inherent complexity and size of the system an all-atom modelling approach is not feasible. Even coarse-grain models face serious problems in reproducing the many experimental observations such as stability under many parameter combinations, and linear film growth in aqueous solutions. We will review current models, point out their shortcomings, and discuss possible extensions.

We try to elucidate the microstructure formation in a monodisperse ferrofluid monolayer. The system under study consists of soft sphere magnetic dipolar particles confined to a thin fluid layer. The positions of the particles are constrained to a 2D geometry, whereas the particle magnetic dipole moments are not fixed to the body systems, and are free to rotate in 3 dimensions, hence forming in what we call a quasi-2D geometry. Using a combination of analytical density functional theory and molecular dynamics (MD) simulations, we find that for the studied range of parameters the majority of aggregates might be divided into two types: chains and rings. Their sizes and area fractions are strongly influenced by the geometrical constraints. We show that for quasi-2D systems the excluded area effects play one of the most important parts in the microstructure formation. The simulation technique and the theoretical model put forward in the present paper agree qualitatively with the results of recent in situ observations of the microstructures observed in ferrofluid monolayers [M. Klokkenberg, R. P. A. Dullens, W. K. Regel, B. H. Erné, A. P. Philipse, Phys. Rev. Lett., 2006, 96, 037203].