Juan J. Cerdà

P3M algorithm for dipolar interactions.

An extension to the P(3)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 P(3)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.

Ferrofluids with shifted dipoles: ground state structures

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 particles 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.

How to analyse the structure factor in ferrofluids with strong magnetic interactions: a combined analytic and simulation approach

We present a theoretical model for calculating the structure factor for ferrofluids with strong inter-particle magnetic dipole–dipole interactions, where chain aggregates are known to exist. Our analytical model is based on the minimization of a free energy density functional that allows us to explicitly construct the radial distribution functions of the ferroparticles. Both mono- and bi-disperse model systems have been investigated in the absence of an external magnetic field. We perform an extensive comparison of the theoretical model predictions with the results of molecular dynamic computer simulations for a wide range of ferroparticle densities and coupling parameters, and find encouraging agreement between the simulation data and theory. The behaviour of the structure factor in the region of the first peak and in the region of large wave vectors is studied in detail, and related to the observed microstructure. Our results demonstrate that the combined method developed in the present study is suitable for revealing the connection between microstructure and scattering images, and thus can help to interpret experimental results such as small angle neutron scattering images.

The optimal P3M algorithm for computing electrostatic energies in periodic systems.

We optimize Hockney and Eastwoods particle-particle particle-mesh algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in three-dimensional periodic charged systems. To this end we construct an optimal influence function that minimizes the root-mean-square (rms) errors of the energies. As a by-product we derive a new real-space cutoff correction term, give a transparent derivation of the systematic errors in terms of Madelung energies, and provide an accurate analytical estimate for the rms error of the energies. This error estimate is a useful indicator of the accuracy of the computed energies and allows an easy and precise determination of the optimal values of the various parameters in the algorithm (Ewald splitting parameter, mesh size, and charge assignment order).

Semiflexible magnetic filaments near attractive flat surfaces: a Langevin dynamics study

The adsorption of stiff magnetic filaments close to an attractive surface is studied thoroughly via extensive Langevin dynamics simulations (LD). Magnetic filaments are represented by a coarse-grained bead-spring model where each bead bears a point dipole located at its center and the excluded volume interaction is introduced via a soft-core repulsive potential. We find strong evidence for the existence of two transitions as the temperature is lowered. First, the system undergoes a continuum phase transition from the desorbed to the adsorbed state. This transition is followed by a second structural transition that takes place when the filaments are already adsorbed. The adsorption transition is found to be very similar to the one observed for stiff non-magnetic polymer chains [Sintes et al., Macromolecules 2001, 34, 1352–1357] where the chain bending interaction plays a similar role as the magnetic component of the present case. However, the tendency of the magnetic chains to stretch is reversed by a further reduction in temperature and the chains tend to form closed adsorbed loops leading to a second structural transition. A representation of the phase diagram for the adsorption of magnetic filaments is determined here for the first time. We also present a novel way to determine the temperature at which the chain is adsorbed that is based on the analysis of the change in the number of trains, tails and loops developed by the polymer chain during the adsorption process.

Spherical brushes within spherical cavities: A self-consistent field and Monte Carlo study

We present an extensive numerical study on the behavior of spherical brushes confined into a spherical cavity. Self-consistent field (SCF) and off-lattice Monte Carlo (MC) techniques are used in order to determine the monomer and end-chain density profiles and the cavity pressure as a function of the brush properties. A comparison of the results obtained via SCF, MC, and the Flory theory for polymer solutions reveals SCF calculations to be a valuable alternative to MC simulations in the case of free and softly compressed brushes, while the Florys theory accounts remarkably well for the pressure in the strongly compressed regime. In the range of high compressions, we have found the cavity pressure P to follow a scale relationship with the monomer volume fraction v, P approximately v(alpha). SCF calculations give alpha=2.15+/-0.05, whereas MC simulations lead to alpha=2.73+/-0.04. The underestimation of alpha by the SCF method is explained in terms of the inappropriate account of the monomer density correlations when a mean field approach is used.