The mechanisms underlying triboelectric charging have a stochastic nature. We investigate how this randomness affects the distributions of charges generated on granular particles during either a single or many collisions. The charge distributions we find in our experiments are more heavy-tailed than normal distributions with an exponential decay of the probability, they are asymmetric, and exhibit charges of both signs. Moreover, we find a linear correlation between the width and mean of these distributions. We rationalize these findings with a model for triboelectric charging which combines stochastic charge separation during contact and stochastic charge recombination after separation of the surfaces. Our results further imply that subsequent charging events are not statistically independent.

The dynamic evolution of the microscopic structure of solid and liquid phases of complex plasmas is studied experimentally and by means of molecular dynamics (MD) simulations. In small finite systems, the cooperative motion can be described in terms of discrete modes. These modes are studied with different experimental approaches. Using diffuse scattered laser light, applying laser tweezer forces to individual particles, and periodic laser pulses, the excitation of modes is investigated. The instantaneous normal mode analysis of experimental data from two-dimensional liquid clusters gives access to the local dynamics of the liquid phase. Our investigations shed light on the role of compressional and shear modes as well as the determination of diffusion constants and melting temperatures in finite systems. Special attention is paid to hydrodynamic situations with a stationary inhomogeneous dust flow. MD simulations allow to study the collective motion in the shell of nearest neighbors, which can be linked to smooth and sudden changes of the macroscopic flow. Finally, the observed micro-motion in all situations above allows to shed light on the preference of shear-like over compressional motion in terms of a minimized potential energy and a dynamic incompressibility.

We study the effect of humidity on the charge accumulation of polymer granulates shaken vertically in a stainless steel container. This setup allows us to control the humidity level from 5% to 100%RH while performing automated charge measurements in a Faraday cup directly connected to the shaking container. We find that samples of approximately 2000 polymer spheres become highly charged at low humidity levels (<30%RH), but acquire almost no charge for humidity levels above 80%RH. The transition between these two regimes does depend on the material, as does the sign of the charge. For the latter we find a correlation with the contact angle of the polymer with only very hydrophilic particles attaining positive charges. We show that this humidity dependence of tribo-charging can be used to control segregation in shaken binary mixtures.

Equal volume mixtures of small and large polytetrafluorethylene spheres are shaken in an atmosphere of controlled humidity which allows one to also control their tribocharging. We find that the contact numbers are charge dependent: As the charge density of the beads increases, the number of same-type contacts decreases and the number of opposite-type contacts increases. This change is not caused by a global segregation of the sample. Hence, tribocharging can be a way to tune the local composition of a granular material.

Dynamical properties of colloidal clusters composed of paramagnetic beads are presented. The clusters were trapped either in a parabolic trough or in a hard-wall confinement. In order to access the dynamics of the ensembles, the instantaneous normal mode (INM) approach is utilized, which uses cluster configurations as an input. The peaks in the mode spectra weaken when the system size is increased and when the coupling strength is lowered. The short-time diffusive properties of the clusters are deduced using the INM technique. It is found that angular diffusion is always larger than radial diffusion regardless of the shape of the external trap. Further, short-time diffusion seems to be almost independent of the coupling strength in the solid regime, but decreases with increasing packing fraction and size of the ensembles. In general, it is found that diffusion is larger for parabolically confined than for hard-wall trapped clusters.

The most attractive feature of dusty plasmas is the possibility to create strong correlations at room temperatures. At the same time, these plasmas allow for a precise diagnostics with single-particle resolution. From such measurements, the structural properties of finite two-dimensional (2D) clusters and three-dimensional (3D) spherical crystals in nearly harmonic traps-Yukawa balls-have been explored in great detail. Their structural properties-the shell compositions and the order within the shells-have been investigated and good agreement to theoretical predictions was found. Open questions on the agenda are the excitation behavior, the structural changes, and phase transitions that occur at elevated temperature. In order to increase the dust temperature in the experiment various techniques have been used. Among them, laser heating appears to have unique capabilities because it affects only the dust particles, leaving the lighter plasma components unchanged. Here we report on recent experimental results where laser heating methods were further improved and applied to finite 2D and 3D clusters. Comparing to simulations, we demonstrate that this indeed allows to increase the temperature in a controlled manner. For the analysis of thermodynamics and phase transitions in these finite systems, we present theoretical and experimental results on the basis of the instantaneous normal modes, pair distribution function and the recently introduced center-two-particle distribution function.

The recrystallization process of finite three-dimensional dust clouds after laser heating is studied experimentally. The time-dependent Coulomb coupling parameter is presented, showing that the recrystallization starts with an exponential cooling phase where cooling is slower than damping by the neutral gas friction. At later times, the coupling parameter oscillates into equilibrium. It is found that a large fraction of cluster states after recrystallization experiments is in metastable states. The temporal evolution of the correlation buildup shows that correlation occurs on even slower time scale than cooling.

The method of symbolic transfer entropy has been applied to analyze the behavior of charged-particle systems under the influence of an ion focus (wakefield) in a dusty plasma. Using long-run experiments under various plasma and trapping conditions, it is revealed from the transfer entropy that information is transported from the upper particle in an ion flow to the lower. The information transfer increases with smaller interparticle distance and with reduced height in the sheath. This can be consistently explained by the formation of the ion focus by an ion flow in the sheath. From the analysis of two-particle and many-particle systems, the symbolic entropy transfer can be judged as a reliable measure for information asymmetry, and hence interaction asymmetry, in dusty plasma systems.

The recrystallization process of a finite dust cloud is studied experimentally on the kinetic level. The temporal evolution of the coupling parameter allows to reveal that the cluster is molten while laser heated and recrystallizes when heating is switched OFF. The cooling rate can be deduced from the initial stage of recrystallization.

Like-charged particles usually interact via a repulsive force. However, in streaming dusty plasmas one can observe that two negatively charged dust particles may attract each other. This is explained by accumulation of positive ions below the dust particles (with respect to the streaming direction). In this chapter, we describe the dependence of this ion focus and the resulting wakes on discharge rf-power, pressure and thermophoretic force, as the three key parameters, that can be varied in dusty plasma experiments. Moreover, we discuss the impact of this attractive force on the collective properties of many dust particles, in particular, on the structure and on the dynamics of spherically confined clusters.

The dynamic properties of finite three-dimensional dust clusters in a dusty plasma under the influence of an ion focus are studied by normal modes. The mode analysis has been extended to account for the ion focus using the point-charge model for the horizontal interaction of the dust particles. From that, an analytical model for a few-particle system is derived accounting for three distinct dynamical regimes at different focus strengths, namely, absolutely unstable and fully stable configurations as well as an unstable oscillatory regime. The techniques of normal mode analysis (NMA) and instantaneous normal modes (INM) extended by the ion focus have been applied to dust systems in the experiment and compared to the model. From this, the ion focus strength has been derived. The specific sensitivity of NMA and INM allows one to identify equilibrium configurations in this nonequilibrium environment for these finite clusters.

The liquid state and the freezing transition of finite two-dimensional dust systems are studied using the instantaneous normal mode (INM) analysis. This technique measures the instantaneous unstable modes of a cluster configuration and relates them to the liquid properties of the system. Here, the INM analysis has been applied to experiments on laser-heated dust clusters. From the experiments, diffusion constants and melting temperatures for clusters of different size have been derived. The INM diffusion constants have been compared to those derived from other standard approaches. The scatter of the diffusion constant retrieved by the INM is smaller than that retrieved by other methods, allowing a more reliable determination of melting temperatures. Moreover, the behavior of double-well and escape modes, which reflect certain topological properties of unstable modes, correlates very well with the behavior of the diffusion constant. Further, the dynamic nature of the unstable modes has been determined as mostly shearlike. Finally, the INM results on the experiments are checked against those from Langevin simulations. DOI: 10.1103/PhysRevE.87.033107

The spectral properties of three-dimensional dust clusters confined in gaseous discharges are investigated using both a fluid mode description and the normal mode analysis (NMA). The modes are analysed for crystalline clusters as well as for laser-heated fluid-like clusters. It is shown that even for clusters with low particle numbers and under presence of damping fluid modes can be identified. Laser-heating leads to the excitation of several, mainly transverse, modes. The mode frequencies are found to be nearly independent of the coupling parameter and support the predictions of the underlying theory. The NMA and the fluid mode spectra demonstrate that the wakefield attraction is present for the experimentally observed Yukawa balls at low pressure. Both methods complement each other, since NMA is more suitable for crystalline clusters, whereas the fluid modes allow to explore even fluid-like dust clouds.

The quantities entropy and diffusion are measured for two- and three-dimensional (3D) dust clusters in the fluid state. Entropy and diffusion are predicted to be closely linked via unstable modes. The method of instantaneous normal modes is applied for various laser-heated clusters to determine these unstable modes and the corresponding diffusive properties. The configurational entropy is measured for 2D and 3D clusters from structural rearrangements. The entropy shows a threshold behavior at a critical temperature for the 2D clusters, allowing us to estimate a configurational melting temperature. Further, the entropic disorder increases for larger clusters. Finally, the predicted relation between entropy and unstable modes has been confirmed from our experiments for 2D systems, whereas 3D systems do not show such a clear correlation.

The experimental melting transition of finite two-dimensional dust clusters in a dusty plasma is analyzed using the method of instantaneous normal modes. In the experiment, dust clusters are heated in a thermodynamic equilibrium from a solid to a liquid state using a four-axis laser manipulation system. The fluid properties of the dust cluster, such as the diffusion constant, are measured from the instantaneous normal mode analysis. Thereby, the phase transition of these finite clusters is approached from the liquid phase. From the diffusion constants, unique melting temperatures have been assigned to dust clusters of various sizes that very well reflect their dynamical stability properties.

The melting transition of finite dust clusters in a dusty plasma is studied experimentally. For that purpose, a system of a small number of charged microspheres is trapped in a discharge plasma and subsequently heated by laser manipulation to a liquid state. The fluid properties of the dust cluster such as the diffusion constant are measured from the particle trajectories using the instantaneous normal mode analysis. From that, the freezing temperature of the cluster is derived.

Phase transitions of finite systems of charged microspheres trapped in a gaseous discharge plasma in twodimensional and three-dimensional arrangements are investigated. Novel experimental techniques to drive phase transitions in these dust clusters as well as advanced theoretical concepts to quantitatively characterize these transitions are presented (c) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Yukawa clusters in dusty plasmas have been investigated experimentally with respect to their structural properties when they become elongated. These elongated clusters can be formed by creating an anisotropic confinement potential with changing plasma power. It is observed that increasing deformation of the cluster is accompanied by a vertical alignment of the particles although the alignment is neither seen nor expected for spherical clusters. Simulations of elongated clusters with and without the action of an ion focus have been performed and compared to the experiment. It has been revealed that the structure of spherical clusters is unaffected by the presence of a weak ion focus whereas elongated clusters visibly react to the presence of a weak ion focus.