Dynamics, rheology and critical properties of colloidal fluid mixtures

Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.

Realisierung einer 3D-Kreuzkorrelationsanlage zur Untersuchung von Struktur und Dynamik hochkonzentrierter Kolloide

Realisierung einer 3D-Kreuzkorrelationsanlage zur Untersuchung von Struktur und Dynamik hochkonzentrierter Kolloide Im Rahmen dieser Arbeit wird eine neuartige 3D-Kreuzkorrelationsanlage zur mehrfachstreufreien Untersuchung des diffusiven Verhaltens hochkonzentrierter kolloidaler Suspensionen vorgestellt. Hierzu werden zwei Lichtstreuexperimente gleichzeitig am gleichen Streuvolumen und mit dem gleichen Streuvektor durchgeführt. Aus der so gewonnenen Kreuzkorrelationsfunktion kann das dynamische Verhalten der Kolloide bestimmt werden. Für die Diffusion der Partikel spielen neben der direkten Wechselwirkung elektroviskoser Effekt und die hydrodynamische Wechselwirkung eine entscheidende Rolle. Insbesondere bei hohen Konzentrationen kann keiner der drei Effekte vernachlässigt werden. Die zu messenden Unterschiede in den Diffusionskoeffizienten sind sehr klein. Daher wurde der experimentelle Aufbau detailliert charakterisiert. Hierbei konnten theoretische Überlegungen hinsichtlich des Nachpulsens und der Totzeit der verwendeten Si-Avalanche-Photodioden überprüft werden. Der Kurzzeitselbstdiffusionskoeffizient hochkonzentrierter geladener kolloidaler Suspensionen wurde gemessen. Um die Daten bei hohen Konzentrationen korrekt zu normieren, wurde der elektroviskose Effekt bei geringen Konzentrationen ausführlich untersucht. Hierbei zeigte sich, dass der elektroviskose Einzelteilcheneffekt zu einer monotonen Abnahme des Diffusionskoeffizienten bei abnehmender Ionenstärke führt. Anhand der volumenbruchabhängigen Daten des Kurzzeitselbstdiffusionskoeffizienten konnte zum ersten Mal gezeigt werden, dass die hydrodynamische Wechselwirkung einen geringeren Einfluss auf die Diffusion hat, falls das direkte Wechselwirkungspotential ein Coulomb-Potential anstelle eines Harte-Kugel-Potentials ist.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.