Dynamics and interactions of Quincke roller clusters: From orbits and flips to excited states.

Active matter systems may be characterized by the conversion of energy into active motion, e.g., the self-propulsion of microorganisms. Artificial active colloids form models that exhibit essential properties of more complex biological systems but are amenable to laboratory experiments. While most experimental models consist of spheres, active particles of different shapes are less understood. Furthermore, interactions between these anisotropic active colloids are even less explored. Here, we investigate the motion of active colloidal clusters and the interactions between them. We focus on self-assembled dumbbells and trimers powered by an external dc electric field. For dumbbells, we observe an activity-dependent behavior of spinning, circular, and orbital motions. Moreover, collisions between dumbbells lead to the hierarchical self-assembly of tetramers and hexamers, both of which form rotational excited states. On the other hand, trimers exhibit flipping motion that leads to trajectories reminiscent of a honeycomb lattice.

Solid-liquid interfacial free energy of ice Ih, ice Ic, and ice 0 within a mono-atomic model of water via the capillary wave method.

We apply the capillary wave method, based on measurements of fluctuations in a ribbon-like interfacial geometry, to determine the solid-liquid interfacial free energy for both polytypes of ice I and the recently proposed ice 0 within a mono-atomic model of water. We discuss various choices for the molecular order parameter, which distinguishes solid from liquid, and demonstrate the influence of this choice on the interfacial stiffness. We quantify the influence of discretisation error when sampling the interfacial profile and the limits on accuracy imposed by the assumption of quasi one-dimensional geometry. The interfacial free energies of the two ice I polytypes are indistinguishable to within achievable statistical error and the small ambiguity which arises from the choice of order parameter. In the case of ice 0, we find that the large surface unit cell for low index interfaces constrains the width of the interfacial ribbon such that the accuracy of results is reduced. Nevertheless, we establish that the interfacial free energy of ice 0 at its melting temperature is similar to that of ice I under the same conditions. The rationality of a core-shell model for the nucleation of ice I within ice 0 is questioned within the context of our results.

Correction: Folding kinetics of a polymer.

Correction for 'Folding kinetics of a polymer' by Stepán Ruzicka et al., Phys. Chem. Chem. Phys., 2012, 14, 6044-6053.

Testing the transferability of a coarse-grained model to intrinsically disordered proteins.

The intermediate-resolution coarse-grained protein model PLUM [T. Bereau and M. Deserno, J. Chem. Phys., 2009, 130, 235106] is used to simulate small systems of intrinsically disordered proteins involved in biomineralisation. With minor adjustments to reduce bias toward stable secondary structure, the model generates conformational ensembles conforming to structural predictions from atomistic simulation. Without additional structural information as input, the model distinguishes regions of the chain by predicted degree of disorder, manifestation of structure, and involvement in chain dimerisation. The model is also able to distinguish dimerisation behaviour between one intrinsically disordered peptide and a closely related mutant. We contrast this against the poor ability of PLUM to model the S1 quartz-binding peptide.

Monodisperse Clusters in Charged Attractive Colloids: Linear Renormalization of Repulsion.

Experiments done on polydisperse particles of cadmium selenide have recently shown that the particles form spherical isolated clusters with low polydispersity of cluster size. The computer simulation model of Xia et al. ( Nat. Nanotechnol. 2011 , 6 , 580 ) explaining this behavior used a short-range van der Waals attraction combined with a variable long-range screened electrostatic repulsion, depending linearly on the volume of the clusters. In this work, we term this dependence "linear renormalization" of the repulsive term, and we use advanced Monte Carlo simulations to investigate the kinetically slowed down phase separation in a similar but simpler model. We show that amorphous drops do not dissolve and crystallinity evolves very slowly under linear renormalization, and we confirm that low polydispersity of cluster size can also be achieved using this model. The results indicate that the linear renormalization generally leads to monodisperse clusters.

Monte Carlo simulation of kinetically slowed down phase separation.

Supercooled colloidal or molecular systems at low densities are known to form liquid, crystalline or glassy drops, which may remain isolated for a long time before they aggregate. This paper analyses the properties of this large time window, and how it can be tackled by computer simulation. We use single-particle and virtual move Monte Carlo simulations of short-range attractive spheres which are undercooled to the temperature region, where the spinodal intersects the attractive glass line. We study two different systems and we report the following kinetic behavior. A low-density system is shown to exhibit universal linear growth regimes under single-particle Monte Carlo correlating the growth rate to the local structure. These regimes are suppressed under collective motion, where droplets aggregate into a single large disordered domain. It is shown that the aggregation can be avoided and linear regimes recovered, if long-range repulsion is added to the short-range attraction. The results provide an insight into the behavior of the virtual move algorithm generating cluster moves according to the local forcefields. We show that different choices of maximum Monte Carlo displacement affect the dynamical trajectories but lead to the same kinetically slowed down or arrested states.

Propagating director bend fluctuations in nematic liquid crystals.

We show, by molecular simulation, that for a range of standard, coarse-grained, nematic liquid crystal models, the director bend fluctuation is a propagating mode. This is in contrast to the generally accepted picture of nematic hydrodynamics, in which all the director modes (splay, twist, bend, and combinations thereof) are overdamped. By considering the various physical parameters that enter the equations of nematodynamics, we propose an explanation of this effect and conclude that propagating bend fluctuations may be observable in some experimental systems.

Collective translational and rotational Monte Carlo cluster move for general pairwise interaction.

Virtual move Monte Carlo is a cluster algorithm which was originally developed for strongly attractive colloidal, molecular, or atomistic systems in order to both approximate the collective dynamics and avoid sampling of unphysical kinetic traps. In this paper, we present the algorithm in the form, which selects the moving cluster through a wider class of virtual states and which is applicable to general pairwise interactions, including hard-core repulsion. The newly proposed way of selecting the cluster increases the acceptance probability by up to several orders of magnitude, especially for rotational moves. The results have their applications in simulations of systems interacting via anisotropic potentials both to enhance the sampling of the phase space and to approximate the dynamics.

Collective translational and rotational Monte Carlo moves for attractive particles.

Virtual move Monte Carlo is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.

Selective adsorption of lattice peptides on patterned surfaces.

To study the adsorption of individual peptides in implicit solvent, we propose a version of the Wang-Landau Monte Carlo algorithm that uses a single surface, with no need for a confining wall or grafting. Our "wall-free" method is both more efficient than the traditional ones and free of additional assumptions or approximations. We illustrate it by simulating an HP-model lattice peptide on planar surfaces with a variety of patterns of adsorption sites, discovering a temperature-induced switch of surface selection which is due to a balance of energetic and entropic effects.

Phase diagrams of knotted and unknotted ring polymers.

The phase diagram for a lattice ring polymer under applied force, with variable solvent quality, for different topological knot states, is determined for the first time. In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that nontrivial knots result in additional pseudophases under tensile force conditions.

Folding kinetics of a polymer.

We present the results of computer simulations giving a kinetic insight into the liquid-to-solid transition of a homopolymer chain with short-range interactions. By calculating the absolute rates in each direction of the transition, using molecular dynamics employing the forward flux sampling scheme, we provide the phase diagram based on purely kinetic data, and compare it with the results from Monte Carlo simulations. Additionally, we present and discuss a remarkably simple and general relation between the polymer topology and the folding pathway, and show that the eigenvalue spectrum of a matrix defined by non-bonded contacts (the Laplacian matrix) provides an insight into the nonequilibrium ensembles of these trajectories. In particular, the Laplacian matrix seems to identify a large fraction of configurations on the folding pathway at the free energy maximum that have a very low probability of reaching the crystallized state. This implies that the eigenvalues of this matrix may be suitable additional reaction coordinates to describe the folding transition of chain molecules.

Improving the Wang-Landau algorithm for polymers and proteins.

The 1/t Wang-Landau algorithm is tested on simple models of polymers and proteins. It is found that this method resolves the problem of the saturation of the error present in the original algorithm for lattice polymers. However, for lattice proteins, which have a rough energy landscape with an unknown energy minimum, it is found that the density of states does not converge in all runs. A new variant of the Wang-Landau algorithm that appears to solve this problem is described and tested. In the new variant, the optimum modification factor is calculated in the same straightforward way throughout the simulation. There is only one free parameter for which a value of unity appears to give near optimal convergence for all run lengths for lattice homopolymers when pull moves are used. For lattice proteins, a much smaller value of the parameter is needed to ensure rapid convergence of the density of states for energies discovered late in the simulation, which unfortunately results in poor convergence early on in the run.

Improved simulations of lattice peptide adsorption.

We propose several improvements to the Monte Carlo simulation techniques for lattice peptide adsorption on surfaces. Firstly, we examine the implementation of "pull" moves and discuss the most efficient way of selecting them. Secondly, we explicitly show how Wang-Landau sampling may be used to calculate the appropriate density of states for a peptide chain in contact with a single surface, and how the information from such a simulation may be used to calculate results for slit geometry with a range of wall separations. Lastly, we consider further possible modifications of the simulation method and its application to adsorption on structured and patterned surfaces.

Effect of substrate geometry on liquid-crystal-mediated nanocylinder-substrate interactions.

Using classical density functional theory, the liquid crystal (LC)-mediated interaction between a cylindrical nanoparticle and a structured substrate is studied. The surface is structured by cutting a rectangular groove into the surface. In the absence of the nanoparticle, a range of defect structures is formed in the vicinity of the groove. By varying the groove width and depth, the LC-mediated interaction changes from repulsive to attractive. This interaction is strongest when the groove is of comparable size to the nanoparticle. For narrow grooves the nanoparticle is attracted to the center of the groove, while for wider grooves there is a free energy minimum near the sidewalls.

Elastic constants of hard thin platelets by Monte Carlo simulation and virial expansion.

In this paper we present an investigation into the calculation of the Frank elastic constants of hard platelets via molecular simulation and virial expansion beyond second order. Monte Carlo simulations were carried out and director fluctuations measured as a function of wave vector k, giving the elastic constants through a fit in the low-k limit. Additionally, the virial expansion coefficients of the elastic constants up to sixth order were calculated, and the validity of the theory determined by comparison with the simulation results. The simulation results are also compared with experimental measurements on colloidal suspensions of platelike particles.

Structure and stability of isotropic states of hard platelet fluids.

We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.

Structure of molecular liquids: hard rod-disk mixtures.

The structure of hard rod-disk mixtures is studied using Monte Carlo simulations and integral equation theory, for a range of densities in the isotropic phase. By extension of methods used in single component fluids, the pair correlation functions of the molecules are calculated and comparisons between simulation and integral equation theory, using a number of different closure relations, are made. Comparison is also made for thermodynamic data and phase behavior.

Forces between cylindrical nanoparticles in a liquid crystal.

Using classical density functional theory, the forces between two cylindrical nanoparticles in a liquid crystal solvent are calculated. Both the nematic and isotropic phases of the solvent are considered. In the nematic phase, the interaction is highly anisotropic. At short range, changes in the defect structure around the cylinders leads to a complex interaction between them. In the isotropic phase, an attractive interaction arises due to overlap between halos of ordered fluid adsorbed on the surfaces of the cylinders.

Structure of molecular liquids: closure relations for hard spheroids.

We present the results of Monte Carlo simulations of hard spheroids of revolution of different elongations. Both prolate and oblate shapes are examined. A systematic study of the bridge function b(1,2), and direct comparison with the indirect correlation function gamma(1,2)=h(1,2)-c(1,2) at densities spanning the isotropic fluid range, allow us to evaluate the accuracy of various proposed closure relations for integral equations.