Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

A molecular dynamics study of the influence of chain branching on the properties of polymer systems

Die vorliegende Arbeit beschäftigt sich mit dem Einfluß von Kettenverzweigungen unterschiedlicher Topologien auf die statischen Eigenschaften von Polymeren. Diese Untersuchungen werden mit Hilfe von Monte-Carlo- und Molekular-Dynamik-Simulationen durchgeführt.Zunächst werden einige theoretische Konzepte und Modelle eingeführt, welche die Beschreibung von Polymerketten auf mesoskopischen Längenskalen gestatten. Es werden wichtige Bestimmungsgrößen eingeführt und erläutert, welche zur quantitativen Charakterisierung von Verzweigungsstrukturen bei Polymeren geeignet sind. Es wird ebenso auf die verwendeten Optimierungstechniken eingegangen, die bei der Implementierung des Computerprogrammes Verwendung fanden. Untersucht werden neben linearen Polymerketten unterschiedliche Topolgien -Sternpolymere mit variabler Armzahl, Übergang von Sternpolymeren zu linearen Polymeren, Ketten mit variabler Zahl von Seitenketten, reguläre Dendrimere und hyperverzweigte Strukturen - in Abhängigkeit von der Lösungsmittelqualität. Es wird zunächst eine gründliche Analyse des verwendeten Simulationsmodells an sehr langen linearen Einzelketten vorgenommen. Die Skalierungseigenschaften der linearen Ketten werden untersucht in dem gesamten Lösungsmittelbereich vom guten Lösungsmittel bis hin zu weitgehend kollabierten Ketten im schlechten Lösungsmittel. Ein wichtiges Ergebnis dieser Arbeit ist die Bestätigung der Korrekturen zum Skalenverhalten des hydrodynamischen Radius Rh. Dieses Ergebnis war möglich aufgrund der großen gewählten Kettenlängen und der hohen Qualität der erhaltenen Daten in dieser Arbeit, insbesondere bei den linearen ketten, und es steht im Widerspruch zu vielen bisherigen Simulations-Studien und experimentellen Arbeiten. Diese Korrekturen zum Skalenverhalten wurden nicht nur für die linearen Ketten, sondern auch für Sternpolymere mit unterchiedlicher Armzahl gezeigt. Für lineare Ketten wird der Einfluß von Polydispersität untersucht.Es wird gezeigt, daß eine eindeutige Abbildung von Längenskalen zwischen Simulationsmodell und Experiment nicht möglich ist, da die zu diesem Zweck verwendete dimensionslose Größe eine zu schwache Abhängigkeit von der Polymerisation der Ketten besitzt. Ein Vergleich von Simulationsdaten mit industriellem Low-Density-Polyäthylen(LDPE) zeigt, daß LDPE in Form von stark verzweigten Ketten vorliegt.Für reguläre Dendrimere konnte ein hochgradiges Zurückfalten der Arme in die innere Kernregion nachgewiesen werden.

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

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.

Computer simulations of charged systems in partially periodic geometries

This work presents algorithms for the calculation of the electrostatic interaction in partially periodic systems. The framework for these algorithms is provided by the simulation package ESPResSo, of which the author was one of the main developers. The prominent features of the program are listed and the internal structure is described. In the following, algorithms for the calculation of the Coulomb sum in three dimensionally periodic systems are described. These methods are the foundations for the algorithms for partially periodic systems presented in this work. Starting from the MMM2D method for systems with one non-periodic coordinate, the ELC method for these systems is developed. This method consists of a correction term which allows to use methods for three dimensional periodicity also for the case of two periodic coordinates. The computation time of this correction term is neglible for large numbers of particles. The performance of MMM2D and ELC are demonstrated by results from the implementations contained in ESPResSo. It is also discussed, how different dielectric constants inside and outside of the simulation box can be realized. For systems with one periodic coordinate, the MMM1D method is derived from the MMM2D method. This method is applied to the problem of the attraction of like-charged rods in the presence of counterions, and results of the strong coupling theory for the equilibrium distance of the rods at infinite counterion-coupling are checked against results from computer simulations. The degree of agreement between the simulations at finite coupling and the theory can be characterized by a single parameter gamma_RB. In the special case of T=0, one finds under certain circumstances flat configurations, in which all charges are located in the rod-rod plane. The energetically optimal configuration and its stability are determined analytically, which depends on only one parameter gamma_z, similar to gamma_RB. These findings are in good agreement with results from computer simulations.

Application of reactive fluid transport modeling to hydrothermal systems

A one-dimensional multi-component reactive fluid transport algorithm, 1DREACT (Steefel, 1993) was used to investigate different fluid-rock interaction systems. A major short coming of mass transport calculations which include mineral reactions is that solid solutions occurring in many minerals are not treated adequately. Since many thermodynamic models of solid solutions are highly non-linear, this can seriously impact on the stability and efficiency of the solution algorithms used. Phase petrology community saw itself faced with a similar predicament 10 years ago. To improve performance and reliability, phase equilibrium calculations have been using pseudo compounds. The same approach is used here in the first, using the complex plagioclase solid solution as an example. Thermodynamic properties of a varying number of intermediate plagioclase phases were calculated using ideal molecular, Al-avoidance, and non-ideal mixing models. These different mixing models can easily be incorporated into the simulations without modification of the transport code. Simulation results show that as few as nine intermediate compositions are sufficient to characterize the diffusional profile between albite and anorthite. Hence this approach is very efficient, and can be used with little effort. A subsequent chapter reports the results of reactive fluid transport modeling designed to constrain the hydrothermal alteration of Paleoproterozoic sediments of the Southern Lake Superior region. Field observations reveal that quartz-pyrophyllite (or kaolinite) bearing assemblages have been transformed into muscovite-pyrophyllite-diaspore bearing assemblages due to action of fluids migrating along permeable flow channels. Fluid-rock interaction modeling with an initial qtz-prl assemblage and a K-rich fluid simulates the formation of observed mineralogical transformation. The bulk composition of the system evolves from an SiO2-rich one to an Al2O3+K2O-rich one. Simulations show that the fluid flow was up-temperature (e.g. recharge) and that fluid was K-rich. Pseudo compound approach to include solid solutions in reactive transport models was tested in modeling hydrothermal alteration of Icelandic basalts. Solid solutions of chlorites, amphiboles and plagioclase were included as the secondary mineral phases. Saline and fresh water compositions of geothermal fluids were used to investigate the effect of salinity on alteration. Fluid-rock interaction simulations produce the observed mineral transformations. They show that roughly the same alteration minerals are formed due to reactions with both types of fluid which is in agreement with the field observations. A final application is directed towards the remediation of nitrate rich groundwaters. Removal of excess nitrate from groundwater by pyrite oxidation was modeled using the reactive fluid transport algorithm. Model results show that, when a pyrite-bearing, permeable zone is placed in the flow path, nitrate concentration in infiltrating water can be significantly lowered, in agreement with proposals from the literature. This is due to nitrogen reduction. Several simulations investigate the efficiency of systems with different mineral reactive surface areas, reactive barrier zone widths, and flow rates to identify the optimum setup.

Numerical and analytical approaches to strongly correlated electron systems

In this thesis we consider three different models for strongly correlated electrons, namely a multi-band Hubbard model as well as the spinless Falicov-Kimball model, both with a semi-elliptical density of states in the limit of infinite dimensions d, and the attractive Hubbard model on a square lattice in d=2. In the first part, we study a two-band Hubbard model with unequal bandwidths and anisotropic Hund's rule coupling (J_z-model) in the limit of infinite dimensions within the dynamical mean-field theory (DMFT). Here, the DMFT impurity problem is solved with the use of quantum Monte Carlo (QMC) simulations. Our main result is that the J_z-model describes the occurrence of an orbital-selective Mott transition (OSMT), in contrast to earlier findings. We investigate the model with a high-precision DMFT algorithm, which was developed as part of this thesis and which supplements QMC with a high-frequency expansion of the self-energy. The main advantage of this scheme is the extraordinary accuracy of the numerical solutions, which can be obtained already with moderate computational effort, so that studies of multi-orbital systems within the DMFT+QMC are strongly improved. We also found that a suitably defined Falicov-Kimball (FK) model exhibits an OSMT, revealing the close connection of the Falicov-Kimball physics to the J_z-model in the OSM phase. In the second part of this thesis we study the attractive Hubbard model in two spatial dimensions within second-order self-consistent perturbation theory. This model is considered on a square lattice at finite doping and at low temperatures. Our main result is that the predictions of first-order perturbation theory (Hartree-Fock approximation) are renormalized by a factor of the order of unity even at arbitrarily weak interaction (U->0). The renormalization factor q can be evaluated as a function of the filling n for 00, the q-factor vanishes, signaling the divergence of self-consistent perturbation theory in this limit. Thus we present the first asymptotically exact results at weak-coupling for the negative-U Hubbard model in d=2 at finite doping.

Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.

Interactive simulation of flexible parts

Computer simulations play an ever growing role for the development of automotive products. Assembly simulation, as well as many other processes, are used systematically even before the first physical prototype of a vehicle is built in order to check whether particular components can be assembled easily or whether another part is in the way. Usually, this kind of simulation is limited to rigid bodies. However, a vehicle contains a multitude of flexible parts of various types: cables, hoses, carpets, seat surfaces, insulations, weatherstrips... Since most of the problems using these simulations concern one-dimensional components and since an intuitive tool for cable routing is still needed, we have chosen to concentrate on this category, which includes cables, hoses and wiring harnesses. In this thesis, we present a system for simulating one dimensional flexible parts such as cables or hoses. The modeling of bending and torsion follows the Cosserat model. For this purpose we use a generalized spring-mass system and describe its configuration by a carefully chosen set of coordinates. Gravity and contact forces as well as the forces responsible for length conservation are expressed in Cartesian coordinates. But bending and torsion effects can be dealt with more effectively by using quaternions to represent the orientation of the segments joining two neighboring mass points. This augmented system allows an easy formulation of all interactions with the best appropriate coordinate type and yields a strongly banded Hessian matrix. An energy minimizing process accounts for a solution exempt from the oscillations that are typical of spring-mass systems. The use of integral forces, similar to an integral controller, allows to enforce exactly the constraints. The whole system is numerically stable and can be solved at interactive frame rates. It is integrated in the DaimlerChrysler in-house Virtual Reality Software veo for use in applications such as cable routing and assembly simulation and has been well received by users. Parts of this work have been published at the ACM Solid and Physical Modeling Conference 2006 and have been selected for the special issue of the Computer-Aided-Design Journal to the conference.

Spectroscopic properties from hybrid QM, MM molecular dynamics simulation

The central aim of this thesis work is the application and further development of a hybrid quantum mechanical/molecular mechanics (QM/MM) based approach to compute spectroscopic properties of molecules in complex chemical environments from electronic structure theory. In the framework of this thesis, an existing density functional theory implementation of the QM/MM approach is first used to calculate the nuclear magnetic resonance (NMR) solvent shifts of an adenine molecule in aqueous solution. The findings show that the aqueous solvation with its strongly fluctuating hydrogen bond network leads to specific changes in the NMR resonance lines. Besides the absolute values, also the ordering of the NMR lines changes under the influence of the solvating water molecules. Without the QM/MM scheme, a quantum chemical calculation could have led to an incorrect assignment of these lines. The second part of this thesis describes a methodological improvement of the QM/MM method that is designed for cases in which a covalent chemical bond crosses the QM/MM boundary. The development consists in an automatized protocol to optimize a so-called capping potential that saturates the electronic subsystem in the QM region. The optimization scheme is capable of tuning the parameters in such a way that the deviations of the electronic orbitals between the regular and the truncated (and "capped") molecule are minimized. This in turn results in a considerable improvement of the structural and spectroscopic parameters when computed with the new optimized capping potential within the QM/MM technique. This optimization scheme is applied and benchmarked on the example of truncated carbon-carbon bonds in a set of small test molecules. It turns out that the optimized capping potentials yield an excellent agreement of NMR chemical shifts and protonation energies with respect to the corresponding full molecules. These results are very promising, so that the application to larger biological complexes will significantly improve the reliability of the prediction of the related spectroscopic properties.

Monte-Carlo simulation of hard spherocylinders under confinement

When a liquid crystal is confined to a cavity its director field becomes subject to competing forces: on the one hand, the surface of the cavity orients the director field (``surface anchoring''), on the other hand deformations of the director field cost elastic energy. Hence the equilibrium director field is determined by a compromise between surface anchoring and elasticity. One example of a confined liquid crystal that has attracted particular interest from physicists is the nematic droplet. In this thesis a system of hard rods is considered as the simplest model for nematic liquid crystals consisting of elongated molecules. First, systems of hard spherocylinders in a spherical geometry are investigated by means of canonical Monte Carlo simulations. In contrast to previous simulation work on this problem, a continuum model is used. In particular, the effects of ordering near hard curved walls are studied for the low-density regime. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We study how the surface order, the adsorption and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall in a cavity is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations. As a next step, an extension of the Asakura-Oosawa-Vrij model for colloid-polymer mixtures to anisotropic colloids is considered. By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or ``tactoids'' that so form are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we estimate the surface anchoring strength.

Characterization of structure and dynamics of submicrometric systems via fluorescence correlation spectroscopy

The presented thesis revolves around the study of thermally-responsive PNIPAAm-based hydrogels in water/based environments, as studied by Fluorescence Correlation Spectroscopy (FCS).rnThe goal of the project was the engineering of PNIPAAm gels into biosensors. Specifically, a gamma of such gels were both investigated concerning their dynamics and structure at the nanometer scale, and their performance in retaining bound bodies upon thermal collapse (which PNIPAAm undergoes upon heating above 32 ºC).rnFCS’s requirements, as a technique, match the limitations imposed by the system. Namely, the need to intimately probe a system in a solvent, which was also fragile and easy to alter. FCS, on the other hand, both requires a fluid environment to work, and is based on the observation of diffusion of fluorescents at nanomolar concentrations. FCS was applied to probe the hydrogels on the nanometer size with minimal invasivity.rnVariables in the gels were addressed in the project including crosslinking degree; structural changes during thermal collapse; behavior in different buffers; the possibility of decreasing the degree of inhomogeneity; behavior of differently sized probes; and the effectiveness of antibody functionalization upon thermal collapse.rnThe evidenced results included the heightening of structural inhomogeneities during thermal collapse and under different buffer conditions; the use of annealing to decrease the inhomogeneity degree; the use of differently sized probes to address different length scale of the gel; and the successful functionalization before and after collapse.rnThe thesis also addresses two side projects, also carried forward via FCS. One, diffusion in inverse opals, produced a predictive simulation model for diffusion of bodies in confined systems as dependent on the bodies’ size versus the characteristic sizes of the system. The other was the observation of interaction of bodies of opposite charge in a water solution, resulting in a phenomenological theory and an evaluation method for both the average residence time of the different bodies together, and their attachment likelihood.

Numerical study of homogeneous and heterogeneous crystal nucleation in colloidal systems

Im Rahmen dieser Arbeit wurden Computersimulationen von Keimbildungs- und Kris\-tallisationsprozessen in rnkolloidalen Systemen durchgef\"uhrt. rnEine Kombination von Monte-Carlo-Simulationsmethoden und der Forward-Flux-Sampling-Technik wurde rnimplementiert, um die homogene und heterogene Nukleation von Kristallen monodisperser Hart\-kugeln zu untersuchen. rnIm m\"a\ss{ig} unterk\"uhlten Bulk-Hartkugelsystem sagen wir die homogenen Nukleationsraten voraus und rnvergleichen die Resultate mit anderen theoretischen Ergebnissen und experimentellen Daten. rnWeiterhin analysieren wir die kristallinen Cluster in den Keimbildungs- und Wachstumszonen, rnwobei sich herausstellt, dass kristalline Cluster sich in unterschiedlichen Formen im System bilden. rnKleine Cluster sind eher l\"anglich in eine beliebige Richtung ausgedehnt, w\"ahrend gr\"o\ss{ere} rnCluster kompakter und von ellipsoidaler Gestalt sind. rn rnIm n\"achsten Teil untersuchen wir die heterogene Keimbildung an strukturierten bcc (100)-W\"anden. rnDie 2d-Analyse der kristallinen Schichten an der Wand zeigt, dass die Struktur der rnWand eine entscheidende Rolle in der Kristallisation von Hartkugelkolloiden spielt. rnWir sagen zudem die heterogenen Kristallbildungsraten bei verschiedenen \"Ubers\"attigungsgraden voraus. rnDurch Analyse der gr\"o\ss{ten} Cluster an der Wand sch\"atzen wir zus\"atzlich den Kontaktwinkel rnzwischen Kristallcluster und Wand ab. rnEs stellt sich heraus, dass wir in solchen Systemen weit von der Benetzungsregion rnentfernt sind und der Kristallisationsprozess durch heterogene Nukleation stattfindet. rn rnIm letzten Teil der Arbeit betrachten wir die Kristallisation von Lennard-Jones-Kolloidsystemen rnzwischen zwei ebenen W\"anden. rnUm die Erstarrungsprozesse f\"ur ein solches System zu untersuchen, haben wir eine Analyse des rnOrdnungsparameters f\"ur die Bindung-Ausrichtung in den Schichten durchgef\"urt. rnDie Ergebnisse zeigen, dass innerhalb einer Schicht keine hexatische Ordnung besteht, rnwelche auf einen Kosterlitz-Thouless-Schmelzvorgang hinweisen w\"urde. rnDie Hysterese in den Erhitzungs-Gefrier\-kurven zeigt dar\"uber hinaus, dass der Kristallisationsprozess rneinen aktivierten Prozess darstellt.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Modeling and simulation of fibrinogen and its adsorption behavior

In this thesis different approaches for the modeling and simulation of the blood protein fibrinogen are presented. The approaches are meant to systematically connect the multiple time and length scales involved in the dynamics of fibrinogen in solution and at inorganic surfaces. The first part of the thesis will cover simulations of fibrinogen on an all atom level. Simulations of the fibrinogen protomer and dimer are performed in explicit solvent to characterize the dynamics of fibrinogen in solution. These simulations reveal an unexpectedly large and fast bending motion that is facilitated by molecular hinges located in the coiled-coil region of fibrinogen. This behavior is characterized by a bending and a dihedral angle and the distribution of these angles is measured. As a consequence of the atomistic detail of the simulations it is possible to illuminate small scale behavior in the binding pockets of fibrinogen that hints at a previously unknown allosteric effect. In a second step atomistic simulations of the fibrinogen protomer are performed at graphite and mica surfaces to investigate initial adsorption stages. These simulations highlight the different adsorption mechanisms at the hydrophobic graphite surface and the charged, hydrophilic mica surface. It is found that the initial adsorption happens in a preferred orientation on mica. Many effects of practical interest involve aggregates of many fibrinogen molecules. To investigate such systems, time and length scales need to be simulated that are not attainable in atomistic simulations. It is therefore necessary to develop lower resolution models of fibrinogen. This is done in the second part of the thesis. First a systematically coarse grained model is derived and parametrized based on the atomistic simulations of the first part. In this model the fibrinogen molecule is represented by 45 beads instead of nearly 31,000 atoms. The intra-molecular interactions of the beads are modeled as a heterogeneous elastic network while inter-molecular interactions are assumed to be a combination of electrostatic and van der Waals interaction. A method is presented that determines the charges assigned to beads by matching the electrostatic potential in the atomistic simulation. Lastly a phenomenological model is developed that represents fibrinogen by five beads connected by rigid rods with two hinges. This model only captures the large scale dynamics in the atomistic simulations but can shed light on experimental observations of fibrinogen conformations at inorganic surfaces.