arXiv subjects

Gerhard Kahl

Publications and source records attributed to Gerhard Kahl.

At least 37 records · Page 2Linked to original sources

arXiv2019

Controlled self-aggregation of polymer-based nanoparticles employing shear flow and magnetic fields

Star polymers with magnetically functionalized end groups are presented as a novel polymeric system whose morphology, self-aggregation, and orientation can easily be tuned by exposing these macromolecules simultaneously to an external magnetic field and to shear forces. Our investigations are based on a specialized simulation technique which faithfully takes into account the hydrodynamic interactions of the surrounding, Newtonian solvent. We find that the combination of magnetic field (including both strength and direction) and shear rate controls the mean number of magnetic clusters, which in turn is largely responsible for the static and dynamic behavior. While some properties are similar to comparable non-magnetic star polymers, others exhibit novel phenomena; examples of the latter include the breakup and reorganization of the clusters beyond a critical shear rate, and a strong dependence of the efficiency with which shear rate is translated into whole-body rotations on the direction of the magnetic field.

cond-mat.soft↗

arXiv2019

Structure and equation-of-state of a disordered system of shape anisotropic patchy particles

We present a new two dimensional model for elliptic (i.e., shape anisotropic) patchy colloids, where the impenetrable core of the particles is decorated on its co-)vertices by Kern-Frenkel type of patches. Using (i) well-documented criteria for the overlap of the undecorated ellipses and (ii) proposing new criteria that give evidence if the patchy regions of two particles interact we perform extensive Monte Carlo simulations in the NPT ensemble. Considering elliptic particles of aspect ratios \{kappa} = 2, 4, and 6 with two patches located at the co-vertices and choosing representative values for the temperature we study on a semi-quantitative level the emerging disordered phases in terms of snapshots and radial distribution functions and present results for the equation-of-state.

cond-mat.soft↗

arXiv2018

The asymmetric Wigner bilayer

We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates, and form there ordered sublattices. Using complementary tools (analytic and numerical) we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: the desire to guarantee net charge neutrality on each of the plates and the effort of the particles to self-organize into commensurate sublattices. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows to study on a quantitative level phenomena such as over- and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive Monte Carlo simulations, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy.

cond-mat.soft↗

arXiv2018

Structure and stimuli-responsiveness of all-DNA dendrimers: theory and experiment

We present a comprehensive theoretical and experimental study of the solution phase properties of DNA-based family of nanoparticles - dendrimer-like DNA molecules (DL-DNA). These charged DNA dendrimers are novel macromolecular aggregates, which hold high promise in targeted self-assembly of soft matter systems in the bulk and at interfaces. To describe the behavior of this family of dendrimers (with generations ranging from G1 to G7), we use a theoretical model in which base-pairs of a single DL-DNA molecule are modeled by charged monomers, whose interactions are chosen to mimic the equilibrium properties of DNA correctly. Experimental results on the sizes and conformations of DL-DNA are based on static and 1dynamic light scattering; at the same time, Molecular Dynamics simulations are employed to model the equilibrium properties of DL-DNA, which compare favorably with the findings from experiments while at the same time providing a host of additional information and insight into the molecular structure of the nanostructures. We also examine the salt-responsiveness of these macromolecules, finding that despite the strong screening of electrostatic interactions, brought about by the added salt, the macromolecules shrink only slightly, their size robustness stemming from the high bending rigidity of the DNA-segments. The study of these charged dendrimer systems is an important field of research in the area of soft matter due to their potential role for various interdisciplinary applications, ranging from molecular cages and carriers for drug delivery in a living organism to the development of dendrimer- and dendron-based ultra-thin films in the area of nanotechnology. These findings are essential to determine if DL-DNA is a viable candidate for the experimental realization of cluster crystals in the bulk, a novel form of solids with multiple site occupancy.

cond-mat.soft↗

arXiv2016

On the applicability of density dependent effective interactions in cluster-forming systems

We systematically studied the validity and transferability of effective, coarse-grained, pair potentials in ultrasoft colloidal systems. We focused on amphiphilic dendrimers, macromolecules which can aggregate into clusters of overlapping particles to minimize the contact area with the surrounding (implicit) solvent. Simulations were performed for both the monomeric and coarse-grained model in the liquid phase at densities ranging from infinite dilution up to values close to the freezing point. For every state point, each macromolecule was mapped onto a single interaction site and the effective pair potential was computed using a coarse-graining technique based on force-matching. We found excellent agreement between the spatial dendrimer distributions obtained from the coarse-grained and microscopically detailed simulations at low densities, where the macromolecules were distributed homogeneously in the system. However, the agreement deteriorated significantly when the density was increased further and the cluster occupation became more polydisperse. Under these conditions, the effective pair potential of the coarse-grained model can no longer be computed by averaging over the whole system, but the local density needs to be taken into account instead.

cond-mat.soft↗

arXiv2016

Equilibrium structures of anisometric, quadrupolar particles confined to a monolayer

We investigate the structural properties of a two-dimensional system of ellipsoidal particles carrying a linear quadrupole moment in their center. These particles represent a simple model for a variety of uncharged, non-polar conjugated organic molecules. Using optimization tools based on ideas of Evolutionary Algorithms, we first examine the ground state structures as we vary the aspect ratio of the particles and the pressure. Interestingly, we find, besides the intuitively expected T-like configurations, a variety of complex structures, characterized with up to three different particle orientations. In an effort to explore the impact of thermal fluctuations, we perform constant-pressure Molecular Dynamics simulations within a range of rather low temperatures. We observe that ground state structures formed by particles with a large aspect ratio are in particular suited to withstand fluctuations up to rather high temperatures. Our comprehensive investigations allow for a deeper understanding of molecular or colloidal monolayer arrangements under the influence of a typical electrostatic interaction on a coarse-grained level.

cond-mat.soft↗

arXiv2015

Self-assembly of DNA-functionalized colloids

Colloidal particles grafted with single-stranded DNA (ssDNA) chains can self-assemble into a number of different crystalline structures, where hybridization of the ssDNA chains creates links between colloids stabilizing their structure. Depending on the geometry and the size of the particles, the grafting density of the ssDNA chains, and the length and choice of DNA sequences, a number of different crystalline structures can be fabricated. However, understanding how these factors contribute synergistically to the self-assembly process of DNA-functionalized nano- or micro-sized particles remains an intensive field of research. Moreover, the fabrication of long-range structures due to kinetic bottlenecks in the self-assembly are additional challenges. Here, we discuss the most recent advances from theory and experiment with particular focus put on recent simulation studies.

cond-mat.soft↗

arXiv2015

Generalized inverse patchy colloid model

We generalize the inverse patchy colloid model that was originally developed for heterogeneously charged particles with two identical polar patches and an oppositely charged equator to a model that can have a considerably richer surface pattern. Based on a Debye-Hueckel framework, we propose a coarse-grained description of the effective pair interactions that is applicable to particles with an arbitrary patch decoration. We demonstrate the versatility of this approach by applying it to models with (i) two differently charged and/or sized patches, and (ii) three, possibly different patches.

cond-mat.soft↗

arXiv2014

Theoretical and numerical investigations of inverse patchy colloids in the fluid phase

We investigate the structural and thermodynamic properties of a new class of patchy colloids, referred to as inverse patchy colloids (IPCs) in their fluid phase via both theoretical methods and simulations. IPCs are nano- or micro- meter sized particles with differently charged surface regions. We extend conventional integral equation schemes to this particular class of systems: our approach is based on the so-called multi-density Ornstein-Zernike equation, supplemented by the associative Percus-Yevick approximation (APY). To validate the accuracy of our framework, we compare the obtained results with data extracted from $NpT$ and $NVT$ Monte Carlo simulations. In addition, other theoretical approaches are used to calculate the properties of the system: the reference hypernetted-chain (RHNC) method and the Barker-Henderson thermodynamic perturbation theory. Both APY and RHNC frameworks provide accurate predictions for the pair distribution functions: APY results are in slightly better agreement with MC data, in particular at lower temperatures where the RHNC solution does not converge.

cond-mat.soft↗

arXiv2014

Inverse patchy colloids with small patches: fluid structure and dynamical slowing down

Inverse Patchy Colloids (IPCs) differ from conventional patchy particles because their patches repel (rather than attract) each other and attract (rather than repel) the part of the colloidal surface that is free of patches. These particular features occur, .e.g., in heterogeneously charged colloidal systems. Here we consider overall neutral IPCs carrying two, relatively small, polar patches. Previous studies of the same model under planar confinement have evidenced the formation of branched, disordered aggregates composed of ring-like structures. We investigate here the bulk behavior of the system via molecular dynamics simulations, focusing on both the structure and the dynamics of the fluid phase in a wide region of the phase diagram. Additionally, the simulation results for the static observables are compared to the Associative Percus Yevick solution of an integral equation approach based on the multi-density Ornstein-Zernike theory. A good agreement between theoretical and numerical quantities is observed even in the region of the phase diagram where the slowing down of the dynamics occurs.

cond-mat.soft↗

arXiv2014

Explicit spatial description of fluid inclusions in porous matrices in terms of an inhomogeneous integral equation

We study the fluid inclusion of both Lennard-Jones particles and particles with competing interaction ranges --short range attractive and long range repulsive (SALR)-- in a disordered porous medium constructed as a controlled pore glass in two dimensions. With the aid of a full two-dimensional Ornstein-Zernike approach, complemented by a Replica Ornstein-Zernike integral equation, we explicitly obtain the spatial density distribution of the fluid adsorbed in the porous matrix and a good approximation for the average fluid-matrix correlations. The results illustrate the remarkable differences between the adsorbed Lennard-Jones (LJ) and SALR systems. In the latter instance, particles tend to aggregate in clusters which occupy pockets and bays in the porous structure, whereas the LJ fluid uniformly wets the porous walls. A comparison with Molecular Dynamics simulations shows that the two-dimensional Ornstein-Zernike approach with a Hypernetted Chain closure together with a sensible approximation for the fluid-fluid correlations can provide an accurate picture of the spatial distribution of adsorbed fluids for a given configuration of porous material.

cond-mat.dis-nn↗

arXiv2014

Antinematic local order in dendrimer liquids

We use monomer-resolved numerical simulations to study the positional and orientational structure of a dense dendrimer solution, focusing on the effects of dendrimers' prolate shape and deformability on the short-range order. Our results provide unambiguous evidence that the nearest-neighbor shell of a tagged particle consists of a mixture of crossed, side-by-side, side-to-end, and end-to-end pair configurations, imposing antinematic rather than nematic order observed in undeformable rodlike particles. This packing pattern persists even at densities where particle overlap becomes sizable. We demonstrate that the antinematic arrangement is compatible with the A15 crystal lattice reported in several dendrimer compounds.

cond-mat.soft↗

arXiv2014

Taking one charge off a two-dimensional Wigner crystal

A planar array of identical charges at vanishing temperature forms a Wigner crystal with hexagonal symmetry. We take off one (reference) charge in a perpendicular direction, hold it fixed, and search for the ground state of the whole system. The planar projection of the reference charge should then evolve from a six-fold coordination (center of a hexagon) for small distances to a three-fold arrangement (center of a triangle), at large distances $d$ from the plane. The aim of this paper is to describe the corresponding non-trivial lattice transformation. For that purpose, two numerical methods (direct energy minimization and Monte Carlo simulations), together with an analytical treatment, are presented. Our results indicate that the $d=0$ and $d\to\infty$ limiting cases extend for finite values of $d$ from the respective starting points into two sequences of stable states, with intersecting energies at some value $d_t$; beyond this value the branches continue as metastable states.

cond-mat.soft↗

arXiv2014

Crystal phases of soft spheres systems in a slab geometry

We have identified the ground state configurations of soft particles (interacting via inverse power potentials) confined between two hard, impenetrable walls. To this end we have used a highly reliable optimization scheme at {\it vanishing} temperature while varying the wall separation over a representative range. Apart from the expected layered triangular and square structures (which are compatible with the three dimensional bulk fcc lattice), we have identified a cascade of highly complex intermediate structures. Taking benefit of the general scaling properties of inverse power potentials, we could identify -- for a given softness value -- one single master curve which relates the energy to the wall separation, irrespective of the density of the system. Via extensive Monte Carlo simulations, we have performed closer investigations of these intermediate structures at {\it finite} temperature: we could provide evidence to which extent these particle arrangements remain stable over a relatively large temperature range.

cond-mat.soft↗

arXiv2013

Wigner crystals for a planar, equimolar binary mixture of classical, charged particles

We have investigated the ground state configurations of an equimolar, binary mixture of classical charged particles (with nominal charges $Q_1$ and $Q_2$) that condensate on a neutralizing plane. Using efficient Ewald summation techniques for the calculation of the ground state energies, we have identified the energetically most favourable ordered particle arrangements with the help of a highly reliable optimization tool based on ideas of evolutionary algorithms. Over a large range of charge ratios, $q = Q_2 / Q_1$, we identify six non-trivial ground states, some of which show a remarkable and unexpected structural complexity. For $0.59 \lesssim q < 1$ the system undergoes a phase separation where the two charge species populate in a hexagonal arrangement spatially separated areas.

cond-mat.soft↗

arXiv2013

Computing Gibbs free energy differences by interface pinning

We propose an approach for computing the Gibbs free energy difference between phases of a material. The method is based on the determination of the average force acting on interfaces that separate the two phases of interest. This force, which depends on the Gibbs free energy difference between the phases, is computed by applying an external harmonic field that couples to a parameter which specifies the two phases. Validated first for the Lennard-Jones model, we demonstrate the flexibility, efficiency and practical applicability of this approach by computing the melting temperatures of sodium, magnesium, aluminum and silicon at ambient pressure using density functional theory. Excellent agreement with experiment is found for all four elements, except for silicon, for which the melting temperature is, in agreement with previous simulations, seriously underestimated.

cond-mat.stat-mech↗

arXiv2012

Predicting Patchy Particle Crystals: Variable Box Shape Simulations and Evolutionary Algorithms

We consider several patchy particle models that have been proposed in literature and we investigate their candidate crystal structures in a systematic way. We compare two different algorithms for predicting crystal structures: (i) an approach based on Monte Carlo simulations in the isobaric-isothermal ensemble and (ii) an optimization technique based on ideas of evolutionary algorithms. We show that the two methods are equally successful and provide consistent results on crystalline phases of patchy particle systems.

physics.comp-ph↗

arXiv2011

Ultrasoft primitive model of polyionic solutions: structure, aggregation, and dynamics

We introduce an ultrasoft core model of interpenetrating polycations and polyanions with continuous Gaussian charge distributions, to investigate polyelectrolyte aggregation in dilute and semi-dilute, salt-free solutions. The model is studied by a combination of approximate theories (random phase approximation and hypernetted chain theory) and numerical simulations. The calculated pair structure, thermodynamics, phase diagram and polyion dynamics of the symmetric version of the model (the "ultrasoft restricted primitive model" or UPRM) differ from the corresponding properties of the widely studied "restricted primitive model" (RPM) where ions have hard cores. At sufficiently low temperatures and densities, oppositely charged polyions form weakly interacting, polarizable neutral pairs. The clustering probabilities, dielectric behavior and electrical conductivity point to a line of sharp conductor-insulator transitions in the density-temperature plane. At very low temperatures the conductor-insulator transition line terminates near the top of a first order coexistence curve separating a high-density, liquid phase from a low-density, vapor phase. The simulation data hint at a tricritical behavior, reminiscent of that observed of the two-dimensional Coulomb Gas, which contrasts with the Ising criticality of its three-dimensional counterpart, the RPM.

cond-mat.soft↗