Synthetic Chemotaxis and Collective Behavior in Active Matter

Conspectus: The ability to navigate in chemical gradients, called chemotaxis, is crucial for the survival of microorganisms. It allows them to find food and to escape from toxins. Many microorganisms can produce the chemicals to which they respond themselves and use chemotaxis for signalling which can be seen as a basic form of communication. Remarkably, the past decade has let to the development of synthetic microswimmers like e.g. autophoretic Janus colloids, which can self-propel through a solvent, analogously to bacteria and other microorganims. The mechanism underlying their self-propulsion involves the production of certain chemicals. The same chemicals involved in the self-propulsion mechanism also act on other microswimmers and bias their swimming direction towards (or away from) the producing microswimmer. Synthetic microswimmers therefore provide a synthetic analogue to chemotactic motile microorganisms. When these interactions are attractive, they commonly lead to clusters, even at low particle density. These clusters may either proceed towards macrophase separation, resembling Dictyostelium aggregation, or, as shown very recently, lead to dynamic clusters of self-limited size (dynamic clustering) as seen in experiments in autophoretic Janus colloids. Besides the classical case where chemical interactions are attractive, this Account discusses, as its main focus, repulsive chemical interactions, which can create a new and less known avenue to pattern formation in active systems leading to a variety of pattern, including clusters which are surrounded by shells of chemicals, travelling waves and more complex continously reshaping patterns. In all these cases `synthetic signalling' can crucially determine the collective behavior of synthetic microswimmer ensembles and can be used as a design principle to create patterns in motile active particles

Phase-field-crystal model for liquid crystals

Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases. As far as the dynamics is concerned, the translational density is a conserved order parameter while the orientational ordering is non-conserved. The derived phase-field-crystal model can serve for efficient numerical investigations of various nonequilibrium situations in liquid crystals

DDFT calibration and investigation of an anisotropic phase-field crystal model

The anisotropic phase-field crystal model recently proposed and used by Prieler et al. [J. Phys.: Condens. Matter 21, 464110 (2009)] is derived from microscopic density functional theory for anisotropic particles with fixed orientation. Further its morphology diagram is explored. In particular we investigated the influence of anisotropy and undercooling on the process of nucleation and microstructure formation from atomic to the microscale. To that end numerical simulations were performed varying those dimensionless parameters which represent anisotropy and undercooling in our anisotropic phase-field crystal (APFC) model. The results from these numerical simulations are summarized in terms of a morphology diagram of the stable state phase. These stable phases are also investigated with respect to their kinetics and characteristic morphological features.Comment: It contain 13 pages and total of 7 figure

Colloidal crystal growth at externally imposed nucleation clusters

We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian dynamics simulations are applied to a two-dimensional colloidal system with dipolar interactions. The externally imposed nucleation clusters involve colloidal particles either on a rhombic lattice or along two linear arrays separated by a gap. Crystal growth occurs after the peaks of the nucleation cluster have first relaxed to a cutout of the stable bulk crystal.Comment: 4 pages, accepted for publication in Phys. Rev. Let

Effect of many-body interactions on the solid-liquid phase-behavior of charge-stabilized colloidal suspensions

The solid-liquid phase-diagram of charge-stabilized colloidal suspensions is calculated using a technique that combines a continuous Poisson-Boltzmann description for the microscopic electrolyte ions with a molecular-dynamics simulation for the macroionic colloidal spheres. While correlations between the microions are neglected in this approach, many-body interactions between the colloids are fully included. The solid-liquid transition is determined at a high colloid volume fraction where many-body interactions are expected to be strong. With a view to the Derjaguin-Landau-Verwey-Overbeek theory predicting that colloids interact via Yukawa pair-potentials, we compare our results with the phase diagram of a simple Yukawa liquid. Good agreement is found at high salt conditions, while at low ionic strength considerable deviations are observed. By calculating effective colloid-colloid pair-interactions it is demonstrated that these differences are due to many-body interactions. We suggest a density-dependent pair-potential in the form of a truncated Yukawa potential, and show that it offers a considerably improved description of the solid-liquid phase-behavior of concentrated colloidal suspensions

Soft repulsive mixtures under gravity: brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

A binary mixture of particles interacting via long-ranged repulsive forces is studied in gravity by computer simulation and theory. The more repulsive A-particles create a depletion zone of less repulsive B-particles around them reminiscent to a bubble. Applying Archimedes' principle effectively to this bubble, an A-particle can be lifted in a fluid background of B-particles. This "depletion bubble" mechanism explains and predicts a brazil-nut effect where the heavier A-particles float on top of the lighter B-particles. It also implies an effective attraction of an A-particle towards a hard container bottom wall which leads to boundary layering of A-particles. Additionally, we have studied a periodic inversion of gravity causing perpetual mutual penetration of the mixture in a slit geometry. In this nonequilibrium case of time-dependent gravity, the boundary layering persists. Our results are based on computer simulations and density functional theory of a two-dimensional binary mixture of colloidal repulsive dipoles. The predicted effects also occur for other long-ranged repulsive interactions and in three spatial dimensions. They are therefore verifiable in settling experiments on dipolar or charged colloidal mixtures as well as in charged granulates and dusty plasmas.Comment: 10 pages, 11 figure

Attraction between like-charged colloidal particles induced by a surface a density - functional analysis

We show that the first non-linear correction to the linearised Poisson-Boltzman n (or DLVO) theory of effective pair interactions between charge-stabilised, co lloidal particles near a charged wall leads to an attractive component of entro pic origin. The position and depth of the potential compare favourably with rec ent experimental measurementsComment: 12 pages including 2 figures. submitted to physical review letter

Tension and stiffness of the hard sphere crystal-fluid interface

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kT/\sigma^2 with a small anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\sigma^2 for the (001) orientation and 1.03 kT/\sigma^2 for the (111) orientation. Here kT is denoting the thermal energy and \sigma the hard sphere diameter. We compare our results with existing experimental findings

Field theory fo charged fluids and colloids

A systematic field theory is presented for charged systems. The one-loop level corresponds to the classical Debye-H\"uckel (DH) theory, and exhibits the full hierarchy of multi-body correlations determined by pair-distribution functions given by the screened DH potential. Higher-loop corrections can lead to attractive pair interactions between colloids in asymmetric ionic environments. The free energy follows as a loop-wise expansion in half-integer powers of the density; the resulting two-phase demixing region shows pronounced deviations from DH theory for strongly charged colloids.Comment: 4 pages, 2 ps figs; new version corrects some minor typo