Joerg Rottler

Microstructure evolution of materials is derived by kinetic processes that are atomistic in nature. Phenomena like grain boundary migration, the formation and growth of crystalline phases in bulk metallic glasses and structural relaxation in amorphous materials are examples of microstructural phenomena that are derived from atomic scale dynamics. Probing such processes in disordered atomic environments is challenging experimentally since they operate at small length scales (nanometers) and time scales (nanoseconds). In this work, we employ molecular dynamics simulations and a variety of dynamical coarse-graining methods to bridge the gap between microscopic processes and macroscopic observables. First, the diffusion kinetics of carbon in Fe-C glasses is studied. By detecting individual atomic hops, we quantify the parameters that control the diffusivity, namely jump length, residence time and correlation factor. Our results help explain the experimentally observed increase in stability of metal-metalloid glasses against crystallization with increasing carbon concentration. Next, the dynamical processes and structural relaxations in a model glassy system are explored using a machine learning algorithm involving neural networks combined with Markov State Models with the aim of identifying previously unexplored dynamical processes that may be crucial for understanding the complex behaviour of metallic glasses. Finally, the kinetic processes governing grain boundary (GB) motion are studied using the same approach as was used for the glasses. The GB mobility is extracted from three GBs in iron using both conventional techniques as well as Markov State Models. The Markov State Model is shown to also provide insights into the intra-GB processes that govern the temperature dependence of GB motion.

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Heat conduction phenomena of carbon nanotubes (CNTs) have attractedgreat interest both from the viewpoint of engineering applications andfundamental science, but the thermal conductivity of individualsingle-walled CNTs remains a rather controversial topic. Starting froman empirical, realistic atomic interaction potential, we study thelattice thermal conductivity (LTC) of single-walled CNTs by employingtwo approaches: quantum mechanical calculations of three-phononscattering rates in the framework of the Peierls-Boltzmann transporttheory (PBTT) and classical molecular dynamics (MD) simulations.First, we compare the system-size and temperature dependence of theLTC determined from an iterative solution of the linearized phonontransport equation in the framework of the PBTT and from anonequilibrium MD (NEMD) approach. At room temperature, qualitativelysimilar trends for the tube-length dependence are found in the limitof short tubes, where an extensive regime of ballistic heat transportprevailing in CNTs of lengths L ≲ 1 µm is independently confirmed. In the limit of long tubes, the PBTT-derivedLTC diverges. Using PBTT and equilibrium MD approaches, we performnumerical calculations of acoustic phonon lifetimes to clarify thesource of divergence. NEMD-derived temperature dependencies obtainedfor micrometer-long CNTs and temperatures T ≤ 800 K confirmthe 1/T behavior of the LTC at moderately high temperatures.Next, we revisit the tube-length dependence of the LTC by use of therelaxation time approximation in the PBTT. Through a combination ofnumerics and analytical considerations, we derive exact asymptoticscaling laws of the LTC. In particular, we demonstrate the importanceof tensile lattice strain, previously overlooked in the long-standingdispute over tube-length convergence vs divergence of the LTC. Namely,it is proved that, in the long-tube limit, the relaxation timeapproximation yields a finite value for stress-free but an infinitevalue of the LTC in any stretched tube configuration.Lastly, we pursue a matrix inversion approach to solve the linearizedphonon transport equation in the framework of the PBTT. Here, it isshown that violations of acoustic sum rules cause spurious convergentbehaviors of a length-dependent LTC.

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We present a molecular dynamics (MD) and experimental study of polyelectrolyte (PE) gel based electronic devices such as sensors and diodes. We first perform an MD study of two PE gels with different degrees of ionization coupled in a slab geometry. Our simulations show that a pressure gradient emerges between the two gels that results in the buildup of a Nernst-Donnan potential. The Nernst-Donnan potential at the interface is found to scale linearly with temperature with the coefficient of proportionality given by the fraction of concentrations of the uncondensed counterions. We show that the potential difference can also be expressed as a linear function of the lateral pressure, thus providing a molecular interpretation of the piezo-ionic effect. These findings provide further insight onto the behaviour of soft-sensors in the equilibrium regime with no salt ion/solvent fluxes.We also perform an MD study of a junction of two oppositely charged PE networks, and compare the ion densities and electrostatic field to a corresponding continuum Poisson-Boltzmann (PB) model. At low electrostatic coupling strength, the PB model reproduces the MD simulation results for density and electric field throughout the gel very well. At higher electrostatic coupling and higher degrees of ionization, the standard PB fails to predict the MD profiles at the diode interface due to counterion condensation, network collapse and field-induced gel deformation. In fact, MD simulations predict that the rectifying behavior of diodes operating in such regimes will be much reduced. We develop a modified PB model that accounts for these effects, show that it produces better agreement with the MD results, and can be used for improved modeling of Polyelectrolyte Gel Diodes (PGDs).Additionally, we perform a systematic stress-test of the predictions of the (Yamamoto and Doi 2014) theory of the PGDs under linear sweep and step bias. We have found that the predictions of the functional forms of current-voltage (I-V) curves of the Yamamoto theory hold well. They predict an exponential increase in the regime of the forward bias as well as the square-root dependency for the regime of the reverse voltage.

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We use a molecular dynamics (MD) framework to study the mechanical propertiesof triblock copolymer materials which form thermoplastic elastomers (TPEs). Thesematerials form physical, rather than chemical, cross-links as a result of their phaseseparatednano-structure. It is difficult, or impossible, to measure the details ofnetwork chains and monomers experimentally. However, it is these microscopicfeatures that give rise to the material’s elastomeric properties. We use a coarsegrainedbead-spring model which retains the vital details of the chain network andthe nano-structured regions while removing unnecessary atomistic detail.We first present a simulation strategy for the equilibration of nano-structuredcopolymer melt morphologies. MD simulations with a soft pair potential that allowsfor chain crossing result in efficient modelling of phase segregation. We successfullyreintroduce excluded volume pair interactions with only a short re-equilibration ofthe local structure, allowing configurations generated (with this method) to be usedfor studies of structural and mechanical properties.We then study the plastic deformation of triblock TPEs, probing the microscopicmechanisms operative during deformation and how they connect to the macroscopicstress response. We compare two deformation modes, uniaxial stress and strain,which emulate experimental tests and conditions around material failure. We findthat triblocks’ stress response exhibits a significant increase in strain hardeningcompared to homopolymeric chains. We analyse several microscopic properties,including: the chain deformation, monomer displacement, deformation and divisionof glassy domains, and void formation.We introduce an entropic network model for the stress response utilising microscopicinformation about chain configurations and their topological constrains.The model assumes additive contributions from chain stretch and the stretch betweenchain entanglement points and results in quantitative prediction of the stressresponse. Only one parameter fit is required to describe both triblock and homopolymerssystems. We compare our model to recent entropic models developedfor vulcanised rubbers and probe its limitations and more general applicability. Extensionsto more complicated architectures are possible (e.g. stars).

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This thesis presents a computational study of the interaction between solute atoms and defects in the crystal lattice of metals at low solute concentrations. To accurately capture the electronic behaviour of these solutes in complex environments, we use density functional theory calculations. We begin by examining the diffusion of technologically relevant rare earth solutes in Mg. The calculated activation energies agree qualitatively with experimental values. This work also demonstrates that the existing 8-frequency model for diffusion in hexagonally close-packed metals can be improved with the consideration of an additional vacancy jump frequency. We calculate the binding energies of solute atoms to a Ʃ7 grain boundary in Mg. These energies are dominated by elastic effects for many important alloying species, and we develop a computationally efficient model for predicting the binding energies for these elastically dominated solutes. These results agree well with the findings of other experimental and computational studies of Mg boundaries. Using molecular statics calculations of general high-angle grain boundaries in combination with our binding energy model, we predict binding energies for boundaries not accessible by quantum calculations. In addition to providing a better understanding of solute-grain boundary interaction in Mg, binding energies for use in models at higher length scales, and a new, efficient model for predicting binding energy, we also show the importance of using segregation models which utilize multiple binding energies to predict segregation levels. We develop an improved multiscale method for embedding quantum mechanical density functional theory calculations in much larger classical simulations. This method removes the constraints on structure size usually imposed by the high cost of quantum calculations by treating a small region of interest (e.g. a solute and its neighbourhood) with quantum accuracy while coupling the quantum domain to a much larger classical system. The method is developed and tested using solute binding energies to a vacancy and to sites at a special, high-symmetry grain boundary in Al, for which purely quantum mechanical evaluations are also possible, providing a reliable benchmark. We then apply this method to find solute binding energy to a general, low-symmetry grain boundary in Al.

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This thesis aims to understand the nanoscale effects of water as a structured solvent on the phenomenon of counterion-induced DNA condensation. We present results of molecular dynamics simulations of the electrostatic interaction between two DNA molecules in the presence of divalent counterions in different solvation models. We also develop a coarse-grained implicit solvent model for investigating the dynamics on long time and length scales. In the first project, we investigate the role of the solvation effects on the interaction between like-charged cylindrical rods as simplified model for DNA molecules. We obtain the average force between two parallel charged rods in simulations that differ only by their representation of water as a implicit or explicit solvent, but have otherwise identical parameters. We find that the presence of water molecules changes the structure of the counterions and results in both qualitative and quantitative changes of the force between highly charged polyelectrolytes. In the second project, we explore the importance of the DNA geometry on the electrostatic forces by considering two rigid helical models. The simulation results indicate that the DNA shape is an essential contributor to the interaction. A regime of attractive interaction, which disappeared in the cylindrical model, is recovered in the explicit solvent model in both types of helical models. The results also confirm that the behaviour of the interactions between two DNA molecules in the explicit solvent model are different from the implicit solvent models. In the third project, we develop a coarse-grained (CG) representation of these solvation effects. This CG model is constructed from explicit simulations and significantly reduces the computational expense. Short-ranged corrections are added to the pair-wise interaction potentials in the implicit solvent model such that the structure of counterions in the system is consistent with the results from the explicit solvent simulations. This CG model succeeds in reproducing the like-charge attraction effect between DNA molecules in explicit simulations.In a final project, we apply the CG model developed previously to study three DNA strands in the presence of divalent counterions as a starting point for investigating many-body effects in the mechanism of DNA bundling.

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Microscopic dynamics and mechanical response of polymer glasses are studied in four projects using molecular dynamics simulations of a simple bead-spring model. The first project studies the interplay between physical aging and mechanical perturbation. Structural, dynamical and energetic quantities are monitored in the recovery regime following aging and uniaxial tensile deformation periods. The total engineering strain is found to control a continuous transition from transient to permanent mechanical rejuvenation: After deformation in the pre-yield regime all quantities quickly reset to pre-deformation values, while deformation around the yield point results in the erasure of aging history. Deformation in the post-yield regime, however, drives the system into a distinct thermodynamic state.In the second project, I introduce an efficient algorithm that detects microscopic relaxation events, which are the basis of aging dynamics and plasticity. I use this technique to calculate the density-density correlations from the spatio-temporal distribution of so called hops in quiescent polymer glasses at different temperatures and ages. Correlation ranges are extracted and I analyze the size distributions of collaboratively rearranging groups of particles. Furthermore, I spatially resolve dynamical heterogeneity (DH) as hop-clusters, and I compare cluster growth, as well as volume distribution during aging with the four-point dynamical susceptibility Χ₄ as the established measure of DH.The third and fourth project use the hop detection technique to investigate the link between relaxation events and local structure. Quasi-localized low-energy vibrational modes, called soft modes, are found to correlate with the location and direction of hops. In the third project, I analyze the temperature- and age-dependence of this correlation in quiescent polymer glasses, and I show that the soft modes are long lived structural features. The fourth project extends the analysis to mechanically deformed polymer glasses. I find that the spatial correlation of hops and soft modes is reduced to pre-aging values after deformation in the strain softening regime. This reveals an additional perspective on mechanical rejuvenation and substantiates the findings from the first project. In the strain hardening regime the correlation increases, and this novel effect is linked to a growing localization of the soft modes.

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Non-equilibrium dynamics in the glassy state lead to interesting aging and memory effects. In this dissertation, extensive computer simulations are performed in order to determine the microscopic origin of these phenomena. Molecular dynamics simulations show all of the qualitative characteristics of real glasses and additionally provide microscopic information that is not typically available to experiments. After a rapid quench to the glassy state, particle correlation functions exhibit dynamical rescaling: all of the relaxation times increase identically with the age of the sample. To investigate the microscopic origins of this behaviour, a new numerical analysis technique is developed to identify structural relaxations on the single particle level. The full distribution of relaxation times and displacements is obtained and used to parametrize a continuous time random walk, which reproduces all features of the dynamics, including dynamical rescaling. These results demonstrate that aging is primarily a kinetic phenomenon, due to the wide distribution of relaxation times. So far, neither the average nor the local structural order can explain the aging dynamics.Variations in temperature and deformation can modify the aging dynamics, causing both rejuvenation and overaging (an apparent increase/decrease in the dynamics compared to simple aging). Non-linear creep is shown to accelerate the dynamics and cause an apparent reversal of aging, whereas a temperature step has complex effects on the relaxation times that are impossible to describe as simple rejuvenation or overaging. The effects of parameters such as the temperature, stress, strain, strain rate, and quench history on the apparent age of the sample are investigated through stochastic simulation of the soft glassy rheology model. In this model, rejuvenation due to load predominates, and overaging is observed only under specific conditions of low temperatures, small strains, and high initial energies. Comparison with molecular dynamics simulations shows qualitative agreement, but also identifies several limitations to the model. Investigating the single particle relaxation dynamics under deformation and at different temperatures may enable further improvements of models of plasticity in amorphous solids.

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