Narrow Results

Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics.

First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles).

Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical density functional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations.

Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of density functional theory towards orientational degrees of freedom is proposed and the collective behaviour of “active” (self-propelled) Brownian particles is briefly discussed.

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 …

Plasmas have been systematically investigated in laboratories since the beginning of the 20th century. For most of that time, the presence of dust in a plasma was merely seen as a contamination effect, and dusty plasmas were interesting mainly for astrophysicists who developed early theories for the dust charging, interaction, transport, and other processes occurring in cometary and planetary atmospheres, interstellar matter, planet formation, etc. (Grün et al., 1984; Goertz, 1992; Hartquist et al., 1992). In the late 1980s, laboratory research on dusty plasmas became important for industry, e.g., for the fabrication of microelectronics using plasma processes, where dust particles grew during the manufacture process (Selwyn et al., 1989; Bouchoule, 1999)…

Colloidal dispersions are mesoscopic solid particles suspended in a molecular fluid solvent. The almost complete length-scale separation between the size of the colloidal particle and the solvent molecules makes colloidal dispersions analogous to complex plasmas. In both systems the particles can become highly charged, which results in effective screened Coulomb interactions described in the simplest case by a Yukawa pair potential. Therefore charged colloidal dispersions and complex plasmas share very many similarities in their behavior. However, the embedding medium is different – it is a liquid for colloids and a dilute gas for plasmas, which leads to completely different damping mechanismsoperating in these two systems (see Chap. 4 for detailed discussion)…

In the two preceding chapters we summarized basic properties of complex plasmas and colloidal dispersions, with the primary focus on a variety of processes which determine theinterparticle interactions in these two systems. Some of the interaction mechanisms are common for plasmas and charged colloids (such as the Debye-Hückel screening), some appear to be similar but have very important distinctions in the underlying physics (suchas wake-mediated/hydrodynamic interactions operating in plasmas/colloids), and some are unique for each system (e.g., weak longrange forces due to nonlocality in plasma processes, or depletion forces in colloids)…

The following sections are included:

• Complex Plasmas
  • RF discharges
  • DC discharges
  • Other types of complex plasmas

• Colloidal Dispersions
  • Preparation of colloidal dispersions
  • Optical/confocal microscopy

• Real Space Analysis
  • Spatial particle tracking
  • Tracking in time
  • Non-equilibrium systems
  • Recent developments

Of the three basic states of matter, liquids require far more sophisticated theoretical models than gases or solids. The former may be treated to a first approximation as an ideal gas, the latter by a harmonic bead-spring model. No such straightforward analytical approaches exist for liquids which combine the disorder of gases and the strong correlations of solids. In other words, there is no obvious smallness parameter to be implemented, which makes the description of the liquid state rather challenging (Hansen and MacDonald, 2006)…

Crystal growth is a very important branch of industry, with numerous applications ranging from semiconductors, substrates for high temperature superconductors, piezo sensors, ferroelectric memories, optical elements to nano-structures, quantum dots and organic systems. There are different facets to crystal growth – homogeneous nucleation, heterogeneous nucleation, epitaxial growth, molecular beam epitaxy, chemical vapor deposition, etc. Whilst techniques for visualization (and quality control) of crystal growth have improved greatly, the detailed kinetic understanding of dynamic growth processes is still far from complete. The same holds for nano- and microparticle contamination in production processes…

Both in nature and technological applications, fluid and solid systems are often mixtures of different particles (atoms). Each particle species is generally characterized by its interaction with other particles (e.g., interaction strengths and/or lengths are different), thus providing increasingly rich phenomenology – both in terms of structure and kinetics. Even for binary mixtures, the variety of phase states and structural correlations is very large in comparison with one-component systems. Below we present some truly fascinating examples from binary colloids and complex plasmas.

The slow dynamics associated with the cooling of a liquid (or increasing the density) is undoubtedly one of the major outstanding problems in condensed matter physics. The nature of how the viscosity of a liquid increases with remarkable rapidity upon cooling, and whether this has any thermodynamic origin or is a purely kinetic phenomenon – these basic fundamental issues remain unresolved (Cavagna, 2009)…

Whilst the macroscopic (hydrodynamic) behavior of fluids is well understood, a microscopic theory at the single-particle level is a major outstanding problem, which makes particle-resolved studies tremendously important. Of particular interest is the onset and nonlinear development of hydrodynamic instabilities at the individual particle level. Furthermore, one can address the “discreteness issue” of continuous media which is formulated as follows: “What is the smallest scale at which the conventional hydrodynamic description breaks down?” Apparently, the answer depends on the particular problem under consideration: It is determined by the similarity variables (and hence the related physical parameters) that play the major role in the description of the macroscopic problem – e.g., for a planar shear flow these are, primarily, the Reynolds and Mach numbers.¹ Here we present some recent advances in the particle-resolved studies of driven systems, and focus on examples which enable us to identify generic “atomistic” mechanisms governing numerous non-equilibrium processes in liquids and solids in the presence of external fields (which are essentially different from the equilibrium behavior).

Although the major qualitative properties of many generic processes have no critical dependence on the particular form of the interparticle interaction, a large number of phenomena only occur when the interaction becomes anisotropic. The most striking feature is the appearance of novel phases: From the liquid crystals introduced by the simplest symmetry breaking to exotic “anisotropic” crystal lattices induced with external fields, the richness in behavior is remarkable. Moreover, the effects of anisotropic interactions are not limited to solids – fluid phases also exhibit string formation, which would not be expected a priori…

In this concluding chapter we present a brief summary of critical open issues and discuss some outstanding problems of interdisciplinary research, where particle-resolved studies of complex plasmas and colloidal dispersions can provide crucial new insights into the understanding of generic phenomena in condensed matter. The summary spans a variety of research topics, mainly in the realm of phase transitions as well as equilibrium and nonequilibrium dynamics. In no way does this list intend to be comprehensive and complete – rather it represents a selection of problems which we believe are important for future research.

The following sections are included:

• Appendix A Symbols

• Bibliography

• Index

The following sections are included:

• Foreword

• Preface

• Contents