Jörg Rottler

Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations.

We combine molecular dynamics simulations of deformation at the submicron scale with a simple continuum fracture mechanics model for the onset of crack propagation to calculate the macroscopic fracture energy of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length, and polymer rigidity.

Local simulation algorithms for Coulomb interactions.

We consider a problem in dynamically constrained Monte Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.

Free energy functionals for efficient phase field crystal modeling of structural phase transformations.

The phase field crystal (PFC) method is a promising technique for modeling materials with atomic resolution on mesoscopic time scales. While numerically more efficient than classical density functional theory (CDFT), its single mode free energy limits the complexity of structural transformations that can be simulated. We introduce a new PFC model inspired by CDFT, which uses a systematic construction of two-particle correlation functions that allows for a broad class of structural transformations. Our approach considers planar spacings, lattice symmetries, planar atomic densities, and atomic vibrational amplitudes in the unit cell, and parameterizes temperature and anisotropic surface energies. The power of our approach is demonstrated by two examples of structural phase transformations.

Electrostatics in Biomolecular Simulations: Where Are We Now and Where Are We Heading?

Abstract In this review, we discuss current methods and developments in the treatment of electrostatic interactions in biomolecular and soft matter simulations. We review the current ‘work horses’, namely, Ewald summation based methods such the Particle-Mesh Ewald, and others, and also newer real-space methods such as multigrid methods, and local algorithms for Coulombs law. We also pay attention to boundary conditions. Although periodic boundary conditions are used most commonly, it is often desirable to have systems that are confined or have boundaries. Finally, we briefly describe some current and available software for the computation of electrostatics in biomolecular and soft matter simulations.

Fracture in glassy polymers: a molecular modeling perspective

Over the past 25 years, molecular modeling and simulations have provided important insights into the physics of deformation and fracture of glassy polymers. This review presents an overview of key results discussed in the context of experimentally observed polymer behavior. Both atomistic and coarse-grained polymer models have been used in different deformation protocols to study elastic properties, shear yielding, creep, physical aging, strain hardening and crazing. Simulations reproduce most of the macroscopic features of plasticity in polymer glasses such as stress-strain relations and creep response, and reveal information about the underlying atomistic processes. Trends of the shear yield stress with loading conditions, temperature and strain rate, and the atomistic dynamics under load have been systematically explored. Most polymers undergo physical aging, which leads to a history-dependent mechanical response. Simulations of strain hardening and crazing demonstrate the nature of polymer entanglements in the glassy state and the role of local plasticity and provide insight into the origin of fracture toughness of amorphous polymers.

Local Molecular Dynamics with Coulombic Interactions

We propose a local, O(N) molecular dynamics algorithm for the simulation of charged systems. The long ranged Coulomb potential is generated by a propagating electric field that obeys modified Maxwell equations. On coupling the electrodynamic equations to an external thermostat we show that the algorithm produces an effective Coulomb potential between particles. On annealing the electrodynamic degrees of freedom the field configuration converges to a solution of the Poisson equation much like the electronic degrees of freedom approach the ground state in ab initio molecular dynamics.

Jamming under tension in polymer crazes.

Molecular dynamics simulations are used to study a unique expanded jammed state. Tension transforms many glassy polymers from a dense glass to a network of fibrils and voids called a craze. Entanglements between polymers and interchain friction jam the system after a fixed increase in volume. As in dense jammed systems, the distribution of forces is exponential, but they are tensile rather than compressive. The broad distribution of forces has important implications for fibril breakdown and the ultimate strength of crazes.

Nucleation on top of islands in epitaxial growth

We develop a theory for nucleation on top of islands in epitaxial growth based on the derivation of lifetimes and rates governing individual microscopic processes. These in particular include the encounter rate of j atoms in a state, where in total

Defect stability in phase-field crystal models: Stacking faults and partial dislocations

ng~j

Phase field crystal modeling as a unified atomistic approach to defect dynamics

atoms are present on top of the island, and for the lifetime of this state. The latter depends strongly on the additional step edge barrier