Chapter 1 Introduction Many fundamental issues in classical condensed matter physics such as crystallization, liquid structure, phase separation, glassy states, etc. can be addressed experimentally using model systems of individually visible mesoscopic particles ( grains ) playing the role of proxy atoms. The interaction between such atoms is determined by the properties of the surrounding medium and/or by external tuning. The best known examples of such model systems are two different domains of soft matter complex plasmas and colloidal dispersions. Dusty, or complex plasmas are composed of a weakly ionized gas and charged microparticles. Dust and dusty plasmas are ubiquitous in space they are present in planetary rings, cometary tails, interplanetary and interstellar clouds, the mesosphere, thunderclouds, they are found in the vicinity of artificial satellites and space stations, etc. (Whipple, 1981; Grün et al., 1984; Goertz, 1992; Hartquist et al., 1992). The physics of (such naturally occurring) dusty plasmas has for several decades been a well established research field on its own. Furthermore, the presence of dust particles plays a critical role in many important industrial processes [e.g., plasma vapor deposition, microchip production, etching, where growth of dust occurs as a matter of course during the production process (Selwyn et al., 1989; Bouchoule, 1999)] as well as in plasma fusion [where the possibility of producing radioactive and toxic dust in the plasma-wall interactions is an important design issue (Federici et al., 2001; Smirnov et al., 2007; Castaldo et al., 2007)]. Apart from that, plasmas containing micron-size dust particles individually visible under optical microscopy are actively investigated in many laboratories (Shukla and Mamun, 2001; Vladimirov et al., 2005; Fortov et al., 2005; Morfill and Ivlev, 2009; Bonitz et al., 20). After almost a century of study the first observations of dust in discharges have 1
2 Complex Plasmas and Colloidal Dispersions been reported by Langmuir et al. (1924) the current interest in complex plasmas began in the mid 1990 s, triggered by the laboratory discovery of plasma crystals by Chu and I (1994), Thomas et al. (1994), and Hayashi and Tachibana (1994). Today, the physics of complex plasmas (this term is used to distinguish dusty plasmas specially designed for such investigations, from naturally occurring systems) is a rapidly growing field of research. Colloidal dispersions consist of mesoscopic solid particles with typical sizes ranging from nanometers to micrometers, which are suspended in a molecular fluid solvent (Pusey and van Megen, 1986; Palberg, 1999; Anderson and Lekkerkerker, 2002; Frenkel, 2006). They occur in many everyday environments ranging from paint, ink, or milk to cosmetic products or rheologically modified fluids. Colloidal dispersions belong to the material class of soft matter and are therefore susceptible to external perturbations. Like complex plasmas, trajectories of individual particles can be followed in space and time. These properties make colloids ideal for investigating collective phenomena. Beyond their fundamental importance and current usage, colloids have an enormous potential in emerging and future applications, for example in designing smart materials with novel optical, rheological, electric, or magnetic properties. Particle-resolved studies of both complex plasmas and colloidal dispersions use optical microscopy. This imposes a lower size limit of around 1 µm, which means that particles employed in both systems have no principal difference. An example of such particles is presented in Fig. 1.1. While this image shows particles used in complex plasma experiments, similar images of colloidal particles are indistinguishable. In complex plasmas one can easily change the strength of the electrostatic coupling between particles, Γ (ratio of mean energy of pair Coulomb interaction to the thermal particle energy, the so-called coupling parameter ), by changing plasma parameters (Shukla and Eliasson, 2009; Morfill and Ivlev, 2009). The magnitude of Γ, which is proportional to the squared charge of the microparticles, Q 2, can vary over an extremely wide range: The charge increases linearly with the particle size and can be quite large (e.g., Q 3 3 electron charges for a 1 µm particle). In addition, the shape of the interaction potential can be tuned externally (Kompaneets et al., 2009). These unique features distinguish complex plasmas from many other laboratory plasmas, where the ion charges are low, the interaction potentials are fixed, and the coupling strength is relatively weak. In charged colloidal dispersions the temperature T is typically kept constant (at room temperature), while the magnitude and even the sign of
Introduction 3 Fig. 1.1 Electron microscopy image of particles typically used for complex plasma experiments. Particles used for colloidal experiments appear identical. Courtesy of microparticles GmbH. the particle charge can be varied up to about ± 4 elementary charges (Yamanaka et al., 1997; Royall et al., 2003). Furthermore, the effective interaction range can be easily tuned via the electrolyte screening, by adding salt or by de-ionizing the solution (Palberg, 1999; Royall et al., 2003). These properties allow us to control both the coupling strength Γ and the character of the interparticle interaction, from almost hard-sphere to very soft plasma-like potentials. Figure 1.2 demonstrates the broad range of physical parameters (particle charge Q, number density n and kinetic temperature T ) and the resulting coupling strength Γ accessible in experiments with complex plasmas and charged colloidal dispersions. 1 This illustration is very helpful in understanding why both systems are particularly well suited for investigations of states of matter ranging from disordered gases to liquids and to ordered structures of particles. 1 Here we employ the electronvolt (ev) unit for temperature, which is a natural energy measure for charged particles: By definition, it is equal to the energy gained by the electron charge when it passes through an electric potential difference of one volt, i.e., 1 ev approximately corresponds to 11,600 K.
4 Complex Plasmas and Colloidal Dispersions 6 n (cm 3 ) ( Q / e ) 30 25 20 15 5 Colloidal dispersions Earth ionosphere Flames Complex plasmas High pressure arcs Alkali metal plasma Low pressure RF and glow discharges H II Regions Coupling parameter 1 1 Shock tubes Solar corona ( Q n white dwarfs Focus Laser plasmas Z-pinches Fusion reactor Fusion experiments 6 ) 1/3 Sun (center) /k T 0 Solar wind (1AU) Earth plasma sheet -2-1 0 1 2 3 4 5 T (ev) B Fig. 1.2 Parameter ranges for different laboratory and naturally occurring charged systems. Complex plasmas and charged colloids allow experimental investigations in the strong coupling regime, including liquid and crystalline states. The blue solid line (Γ = 1) marks the transition between strongly and weakly coupled regimes. 1.1 Complementarity and Interdisciplinarity What makes research combining complex plasmas and colloidal dispersions so attractive? The answer is quite simple: In complex plasmas, the overall dynamic timescales associated with microparticles (e.g., the inverse Einstein frequency) are in the range of tens of milliseconds, yet the microparticles themselves are large enough to be visualized. Thus, the individual trajectories can be obtained by recording with usual CCD cameras and, therefore, fully resolved kinetics can be easily reconstructed. Furthermore, the rate of momentum/energy exchange through interactions between the charged microparticles can massively exceed the damping rate due to friction caused by a dilute ambient gas. Therefore, the motion of individual particles in strongly coupled complex plasmas is virtually undamped, which provides a direct analogy to conventional liquids and solids in terms of the atomistic dynamics. Two other important aspects are that the form of the pair interaction potential can be tuned
Introduction 5 externally, and that the complex plasma systems are optically thin (scatter little light), so that thousands of particle layers can be visualized, enabling 3D imaging. In colloidal suspensions, the dynamics of microparticles is fully damped due to the presence of the viscous solvent. Hence the embedding host fluid provides very efficient thermalization of the system, leading to Brownian motion of the individual particles. Therefore, colloidal dispersions can be brought into equilibrium in a very controlled way, complementing the complex plasma approach. Otherwise, the colloidal dispersions have the same advantages as complex plasmas: Fully resolved particle trajectories, both in 2D and 3D, can easily be visualized and the pair interactions are tunable. The defining features of complex plasmas and colloidal dispersion are illustrated in Fig. 1.3, which shows the characteristic length scales and composition of both types of system. complex plasmas m colloidal dispersions 3 m dust particles in a plasma colloidal particles in a liquid solvent Fig. 1.3 Schematic view of complex plasmas and colloidal dispersions. Dust particles are surrounded by a dilute weakly ionized gas (left panel), while colloidal particles are embedded in a molecular liquid containing also microions (right panel). Finally, in both complex plasmas and colloidal dispersions individual particles can be easily manipulated in different ways, so that one can perform active controllable experiments to investigate generic processes
6 Complex Plasmas and Colloidal Dispersions occurring in liquids or solids at the most fundamental (individual-particle) level. Because of these properties, combined studies of complex plasmas and colloidal dispersions promise significant synergy and hence bring us more than the sum of the parts: They provide a unique opportunity to go beyond the limits of continuous media down to the fundamental length scale of classical systems the interparticle distance and thus to investigate all relevant dynamic and structural processes using the fully resolved motion of individual grains (be they microparticles in complex plasmas or colloids), from the onset of cooperative phenomena to large strongly coupled systems. Hence, the principal aim of such interdisciplinary research is to study generic self-organization processes at the most fundamental individual-particle level, covering the whole range of non-equilibrium and equilibrium phenomena, at a detail not possible until now. It is important to stress that such particle-resolved studies do not require the identification of individual atoms/molecules of the surrounding fluid. One resolves the individual trajectories of grains (microparticles or colloids), whereas the fluid can still be treated as a continuum. The effect of the fluid in this case is to provide the thermalization and mediate the interparticle interactions. On the other hand, the fluid naturally exerts friction and hence makes the dynamics of grains non-hamiltonian this principal aspect is discussed in Chapter 4. We also would like to take the opportunity to emphasize that particleresolved studies are not totally limited to colloidal dispersions and complex plasmas. Other systems, notably granular matter, where the strong dissipation of the athermal grains is counteracted by constant driving (such that the system is in a steady state) can provide insight into some phenomena we discuss. In particular, granular matter has been used extensively to study jamming and slow dynamics (see Fig. 9.3). We refer the interested reader to the book by Berthier et al. (2011) for further details. This book represents the first concerted effort to review the current status and discuss the perspectives of the combined interdisciplinary research with complex plasmas and colloidal dispersions, focusing on the complementary approaches developed in these two fields. In Chapters 2 and 3 we summarize basic physical properties which are important for understanding complex plasmas and colloidal dispersions as model systems. Chapter 4 provides a detailed discussion and comparison of the two systems in terms of the individual particle dynamics, illustrating their essential similarities and differences. In Chapter 5 we present a concise summary of experi-
Introduction 7 mental methods and hardware currently used for the interdisciplinary research. Chapters 6-11 comprise the core part of the book, describing recent particle-resolved studies of various generic processes in liquid and solid complex plasmas and colloidal dispersions and demonstrating complementarity of this research. In the concluding Outlook we briefly summarize and discuss current hot topics and outstanding problems of the interdisciplinary research, where the combined particle-resolved studies are expected to provide crucial new insights.