Sabine H. L. Klapp

Dipolar fluids under external perturbations

We discuss recent developments and present new findings on the structural and phase properties of dipolar model fluids influenced by various external perturbations. We concentrate on systems of spherical particles with permanent (point) dipole moments. Starting from what is known about the three-dimensional systems, particular emphasis is given to dipolar fluids in different confining situations involving both simple and complex (disordered) pore geometries. Further topics concern the effect of quenched positional disorder, the influence of external (electric or magnetic) fields, and the fluid–fluid phase behaviour of various dipolar mixtures. It is demonstrated that due to the translational–orientational coupling and due to the long range of dipolar interactions even simple perturbations such as hard walls can have a profound impact on the systems.

Phase transitions in dipolar fluids: An integral equation study

We consider several dipolar fluids in their isotropic phase by integral equations in the reference hypernetted chain approximation. The systems differ in the form of the nondipolar potential. At low temperatures all of these fluids exhibit a spinodal line. Approaching this line from above, several fluctuations strongly increase. We interpret these fluctuations as indications for the low temperature states of the systems. In agreement with simulation results we find that the fluctuations at low densities strongly depend on the form of the nondipolar potential. In the dipolar hard sphere fluid we see a strong tendency that the particles associate into chainlike structures. Considering the same system with an additional Lennard-Jones attraction (Stockmayer fluid), we find that fluctuations of the number density which point to a usual condensation, clearly dominate. By switching off this isotropic attraction gradually, there is a smooth changeover from condensation to dipole clustering. At higher densities the behavior of the fluctuations becomes independent of the nondipolar potential: now the fluctuations indicate a transition into a fluid state with long-ranged ferroelectric order. By minimizing a density functional which has direct correlation functions of the isotropic phase as an input, we find the corresponding coexistence lines. Only at very high densities do the fluctuations point to crystallization.

Mesoscale modeling of complex binary fluid mixtures: towards an atomistic foundation of effective potentials.

This paper is devoted to equilibrium molecular-dynamics (MD) simulations of a fully atomistic model of binary mixtures of water (component 1) and ethanol (component 2). We investigate ways to extract from these simulations effective, pairwise additive potentials suitable to describe the interactions between coarse-grained molecules (i.e., beads) in corresponding mesoscale dissipative particle-dynamics simulations. The fully atomistic model employed in MD simulations is mapped onto an implicit water model, where the internal degrees of freedom of ethanol and all the degrees of freedom of water are integrated out. This gives us an effective one-component system consisting only of ethanol beads. The effective interaction potential between a pair of ethanol beads, Phi(R), is approximated at three levels of sophistication. At the lowest one, we approximate Phi(R) by the potential of mean force between the centers of mass of two ethanol beads calculated in the fully atomistic MD simulations; at the second level, we take Phi(R) to be the potential linked to total and direct correlation functions in the hypernetted-chain closure of the Ornstein-Zernike equation. At the third level we approximate Phi(R) numerically by improving it iteratively through the Boltzmann inversion scheme. Our results indicate that the level-one approach works only at the lowest (8 wt %) concentration; the level-two approach works only up to intermediate ethanol concentrations (ca. 50 wt %). Only the Boltzmann inversion scheme works for all, up to the highest concentration considered (70 wt %).

Unravelling the multilayer growth of the fullerene C60 in real time

Molecular semiconductors are increasingly used in devices, but understanding of elementary nanoscopic processes in molecular film growth is in its infancy. Here we use real-time in situ specular and diffuse X-ray scattering in combination with kinetic Monte Carlo simulations to study C60 nucleation and multilayer growth. We determine a self-consistent set of energy parameters describing both intra- and interlayer diffusion processes in C60 growth. This approach yields an effective Ehrlich–Schwoebel barrier of EES=110 meV, diffusion barrier of ED=540 meV and binding energy of EB=130 meV. Analysing the particle-resolved dynamics, we find that the lateral diffusion is similar to colloids, but characterized by an atom-like Schwoebel barrier. Our results contribute to a fundamental understanding of molecular growth processes in a system, which forms an important intermediate case between atoms and colloids.

Self-assembly of model amphiphilic Janus particles.

We apply molecular dynamics simulations to investigate the structure formation of amphiphilic Janus particles in the bulk phase. The Janus particles are modeled as (soft) spheres composed of a hydrophilic and hydrophobic part. Their orientation is described by a vector representing an internal degree of freedom. Investigating energy fluctuations and cluster size distributions, we determine the aggregation line in a temperature-density-diagram, where the reduced temperature is an inverse measure for the anisotropic coupling. Below this aggregation line clusters of various sizes depending on density and reduced temperature are found. For low densities in the range ρ∗ ≤ 0.3, the cluster size distribution has a broad maximum, indicating simultaneous existence of various cluster sizes between 5 and 10. We find no hint of a condensation transition of these clustered systems. In the case of higher densities (ρ∗ = 0.5 and 0.6), the cluster size distribution shows an extremely narrow peak at clusters of size 13. In these icosahedrons, the particles are arranged in a closed-packed manner, thereby maximizing the number of bonds. Analyzing the translational mean-square displacement we also observe indications of hindered diffusion due to aggregation.

Asymptotic structure of charged colloids between two and three dimensions: the influence of salt

We present theoretical, computer simulation and experimental results for the structural length scales characterizing bulk and confined charged colloidal suspensions. The target quantities are the bulk pair correlation functions on the one hand, and the oscillatory solvation forces of the colloids in films of various thicknesses on the other. Recently we have shown, for a system with very low salt concentration, that these quantities are characterized by the same wavelength in the asymptotic limit, in agreement with predictions from density functional theory. Here we consider systems with larger ionic strengths of added salt. Our results indicate that the wavelength remains essentially unaffected, whereas the correlation length and the amplitude depend significantly on the amount of added salt. Indeed, already at ionic salt strengths as low as 10−3 mol l−1 the force oscillations essentially disappear.

Effect of particle size and Debye length on order parameters of colloidal silica suspensions under confinement

Using atomic force microscopy (AFM) and small angle X-ray scattering (SAXS), we show a full comparison between structuring of nanoparticles in confinement and in bulk in order to explain the effect of confinement on characteristic lengths and the scaling law of the characteristic lengths. Three different-sized particle suspensions are used to check the generalization and the correlation between the characteristic lengths and the system parameters, like particle diameter and Debye length. The two characteristic lengths obtained from AFM force curves, the oscillatory wavelength λ, which is related to the average particle distance, and the decay length ξ, which measures how far particle correlates to obtain periodic oscillations, are in good agreement with the mean particle distance 2π/qmax and the correlation length 2/Δq in bulk, respectively, obtained from the structure peaks of SAXS diagrams. Although confinement causes layering of nanoparticles parallel to the confining surfaces, the characteristic lengths in the direction perpendicular to the confining surfaces follow the bulk behavior. The wavelength scales as ρ−1/3 with the particle number density ρ irrespective of the particle size and the ionic strength and shows a pure volume effect. Upon comparing with literature results, the λ = ρ−1/3 scaling law can be applied more generally for charged particles, as long as the repulsive interaction is sufficiently long-ranged, than the previous expression of λ = 2(R + κ−1), which only approaches the value of average particle distance under specific conditions. The decay length ξ is controlled both by the particle size and the ionic strength of the suspensions, and ξ = R + κ−1 is proposed in the paper. In addition, the interaction strength, the force amplitude and maximum scattering intensity, increases linearly with particle concentration. On the other hand, the Monte Carlo (MC) simulations and approximate hypernetted chain (HNC) closure calculation based on Derjaguin-Landau-Verwey-Overbeek (DLVO) potential are employed to study the characteristic lengths from the theoretical point of view. The experimental wavelengths are in good agreement with the theoretical counterparts and the experimental decay lengths show the same qualitative behavior as theoretical ones on the particle size and ionic strength.

Pattern formation of dipolar colloids in rotating fields: layering and synchronization

We report Brownian dynamics (BD) simulation and theoretical results for a system of spherical colloidal particles with permanent dipole moments in a rotating magnetic field. Performing simulations at a fixed packing fraction and dipole coupling parameter, we construct a full non-equilibrium phase diagram as a function of the driving frequency (ω0) and field strength (B0). This diagram contains both synchronized states, where the individual particles follow the field with (on average) constant phase difference, and asynchronous states. The synchronization is accompanied by layer formation, i.e., by spatial symmetry-breaking, similar to systems of induced dipoles in rotating fields. In the permanent dipole case, however, too large ω0 yields a breakdown of layering, supplemented by complex changes of the single-particle rotational dynamics from synchronous to asynchronous behavior. We show that the limit frequencies ωc can be well described as a bifurcation in the nonlinear equation of motion of a single-particle rotating in a viscous medium. Finally, we present a simple density functional theory, which describes the emergence of layers in perfectly synchronized states as an equilibrium phase transition.

Impact of surface charges on the solvation forces in confined colloidal solutions

Combining computer simulations and experiments we address the impact of charged surfaces on the solvation forces of a confined, charged colloidal suspension (slit-pore geometry). Investigations based on the colloidal-probe atomic-force-microscope technique indicate that an increase in surface charges markedly enhances the oscillations of the force in terms of their amplitude. To understand this effect on a theoretical level we perform grand-canonical Monte-Carlo simulations (GCMC) of a coarse-grained model system. It turns out that various established approaches of the interaction between a charged colloid and a charged wall, such as linearized Poisson-Boltzmann (PB) theory involving the bulk screening length, do not reproduce the experimental observations. We thus introduce a modified PB potential with a space-dependent screening parameter. The latter takes into account, in an approximate way, the fact that the charged walls release additional (wall) counterions which accumulate in a thin layer at the surface(s). The resulting, still purely repulsive fluid-wall potential displays a nonmonotonic behavior as function of the surface potential with respect to the strength and range of repulsion. GCMC simulations based on this potential reproduce the experimentally observed charge-induced enhancement in the force oscillations. We also show, both by experiment and by simulations, that the asymptotic wave- and decay length of the oscillating force do not change with the wall charge, in agreement with predictions from density functional theory.

Phase diagram of two-dimensional systems of dipole-like colloids

Based on Discontinuous Molecular Dynamics (DMD) simulations we present a phase diagram of two-dimensional nano-particles with dipole-like short-ranged interactions. Similar to systems with true, long-ranged dipolar interactions the present system undergoes a transition from an isotropic fluid phase into a polymer-like fluid, characterized by an association of most particles into clusters. Further decrease of the temperature leads to a percolated system which, moreover, displays dynamical properties reminiscent of a gel. Specifically, we find a plateau in the mean-squared displacement and a non-gaussian behavior of the self-part of the van Hove correlation function. In the high density region we observe crystallization from the isotropic fluid into a solid phase with hexagonal order. Surprisingly, the crystallization is accompanied by a global parallel ordering of the dipole moments, i.e., a ferroelectric phase. This behavior is in marked contrast to what is found in 2D systems with long-ranged dipolar interactions. Our results allow insights into the design of gel-like or highly ordered structures at interfaces, shells around droplets and bubbles and new-sheet like materials.