Frank's constant in the hexatic phase

Using video-microscopy data of a two-dimensional colloidal system the bond-order correlation function G6 is calculated and used to determine the temperature-dependence of both the orientational correlation length xi6 in the isotropic liquid phase and the Frank constant F_A in the hexatic phase. F_A takes the value 72/pi at the hexatic to isotropic liquid phase transition and diverges at the hexatic to crystal transition as predicted by the KTHNY-theory. This is a quantitative test of the mechanism of breaking the orientational symmetry by disclination unbinding

Conservation of Neutral Substitution Rate and Substitutional Asymmetries in Mammalian Genes

Local variation in neutral substitution rate across mammalian genomes is governed by several factors, including sequence context variables and structural variables. In addition, the interplay of replication and transcription, known to induce a strand bias in mutation rate, gives rise to variation in substitutional strand asymmetries. Here, we address the conservation of variation in mutation rate and substitutional strand asymmetries using primate- and rodent-specific repeat elements located within the introns of protein-coding genes. We find significant but weak conservation of local mutation rates between human and mouse orthologs. Likewise, substitutional strand asymmetries are conserved between human and mouse, where substitution rate asymmetries show a higher degree of conservation than mutation rate. Moreover, we provide evidence that replication and transcription are correlated to the strength of substitutional asymmetries. The effect of transcription is particularly visible for genes with highly conserved gene expression. In comparison with replication and transcription, mutation rate influences the strength of substitutional asymmetries only marginally

Elastic Behavior of a Two-dimensional Crystal near Melting

Using positional data from video-microscopy we determine the elastic moduli of two-dimensional colloidal crystals as a function of temperature. The moduli are extracted from the wave-vector-dependent normal mode spring constants in the limit $q\to 0$ and are compared to the renormalized Young's modulus of the KTHNY theory. An essential element of this theory is the universal prediction that Young's modulus must approach $16 \pi$ at the melting temperature. This is indeed observed in our experiment.Comment: 4 pages, 3 figure

Three- and four-body interactions in colloidal systems

Three-body and four-body interactions have been directly measured in a colloidal system comprised of three (or four) charged colloidal particles. Two of the particles have been confined by means of a scanned laser tweezers to a line-shaped optical trap where they diffused due to thermal fluctuations. By means of an additional focused optical trap a third particle has been approached and attractive three-body interactions have been observed. These observations are in qualitative agreement with additionally performed nonlinear Poissson-Boltzmann calculations. Two configurations of four particles have been studied experimentally as well and in both cases a repulsive four-body interaction term has been observed

Many-body interactions and melting of colloidal crystals

We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids. Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pair-interaction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions

The experimental realization of a two-dimensional colloidal model system

We present the technical details of an experimental method to realize a model system for 2D phase transitions and the glass transition. The system consists of several hundred thousand colloidal super-paramagnetic particles confined by gravity at a flat water-air interface of a pending water droplet where they are subjected to Brownian motion. The dipolar pair potential and therefore the system temperature is not only known precisely but also directly and instantaneously controllable via an external magnetic field B. In case of a one component system of monodisperse particles the system can crystallize upon application of B whereas in a two component system it undergoes a glass transition. Up to 10000 particles are observed by video microscopy and image processing provides their trajectories on all relative length and time scales. The position of the interface is actively regulated thereby reducing surface fluctuations to less than one micron and the setup inclination is controlled to an accuracy of 1 microrad. The sample quality being necessary to enable the experimental investigation of the 2D melting scenario, 2D crystallization, and the 2D glass transition, is discussed.Comment: 13 pages, 11 figure

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

Testing the relevance of effective interaction potentials between highly charged colloids in suspension

Combining cell and Jellium model mean-field approaches, Monte Carlo together with integral equation techniques, and finally more demanding many-colloid mean-field computations, we investigate the thermodynamic behavior, pressure and compressibility of highly charged colloidal dispersions, and at a more microscopic level, the force distribution acting on the colloids. The Kirkwood-Buff identity provides a useful probe to challenge the self-consistency of an approximate effective screened Coulomb (Yukawa) potential between colloids. Two effective parameter models are put to the test: cell against renormalized Jellium models

Measuring the equation of state of a hard-disc fluid

We use video microscopy to study a two-dimensional (2D) model fluid of charged colloidal particles suspended in water and compute the pressure from the measured particle configurations. Direct experimental control over the particle density by means of optical tweezers allows the precise measurement of pressure as a function of density. We compare our data with theoretical predictions for the equation of state, the pair-correlation function and the compressibility of a hard-disc fluid and find good agreement, both for the fluid and the solid phase. In particular the location of the transition point agrees well with results from Monte Carlo simulations.Comment: 7 pages, to appear in EPL, slightly corrected versio