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Computer simulations are an indispensable tool for the exploration of material properties in and out of equilibrium. They reveal quantities that are difficult or impossible to obtain in experiments, test theories, provide hints to new unexpected behaviour and greatly help reduce the effort to engineer new functional materials. We seek to understand the molecular level mechanisms that govern the structural and mechanical behaviour of complex materials. To this end, we employ a host of simulation techniques that range from ab-initio (density functional theory) methods, atomistic molecular dynamics and Monte Carlo simulations to field theoretic (phase field) methods on the continuum scale.

Mechanical behavior of amorphous solids
 Electrostatic effects in complex fluids

 Microstructure evolution in metals
Epitaxial growth at surfaces
Diffusion in alloys
  

  • Mechanical behavior of amorphous solids
    A majority of materials that surround us and that we use in everyday life are noncrystalline or glassy and include for instance polymer and metallic glasses, colloidal glasses, foams, emulsions and granular media. Physicists have been fascinated by trying to rationalize the common behavior of such diverse solids in a unifying framework. Understanding the mechanical properties of glasses is particularly challenging, because unlike in crystalline materials, where the motion of topological defects such as dislocations represent the basic ingredient to models of plasticity, no such counterpart can be identified easily in amorphous materials with no long-range order. "Shear transformation zones" have become a popular concept, in which one tries to identify small groups of molecular constituents that rearrange in a characteristic manner under an applied stress.  Based on these ideas, pheonomenological theories can be formulated that reproduce macroscopic stress-strain curves, but the microscopic processes underlying yield in glassy materials remain largely not understood.

    We are interested in the molecular level and statistical properties of glasses that determine their macroscopic behavior, in particular their response to external stresses. In the absence of a true microscopic theory, molecular dynamics simulations of simple glass-forming models can provide useful insight.      In glassy solids, relaxation times are much longer than observation times, which leads to slow dynamics, history dependence, and other nonequilibrium phenomena.  A focus of our recent work has been to better understand slow structural relaxation or physical aging, which occurs universally in all structural glasses, magnetic (spin) glasses as well as related disordered systems and has significant implications for the material lifetime to failure. Through molecular simulations, mean field rate theory and stochastic models, we recently proved that molecular mobility controls macroscopic mechanical response, analyzed the interplay between relaxation and deformation
    which leads to reduced (rejuvenation) or accelerated (overaging) dynamics, and identified an atomistic level mechanism of aging and memory in glassy solids.

    Students: Anton Smessaert, Amanda Parker:
  • Electrostatic effects in complex fluids
    Electrostatic interactions dominate many of the properties of soft condensed matter systems such as polyelectrolytes, proteins and DNA. They are, however, difficult to treat numerically due to their long range forces. Conventional algorithms based on the electrostatic potential perform poorly in Monte Carlo (MC) simulations, have difficulty treating inhomogeneous dielectric media and can be difficult to implement on large parallel computers.We recently developed a novel class of fast electrostatic algorithms for (bio)molecular Monte Carlo and molecular dynamics simulations. Based on a constrained electrostatic functional, our algorithms use a purely local formulation that allow a calculation of Coulombic interactions with an effort that scales as O(N) with the number of particles N, a substantial improvement over classic Ewald sums. In addition, the mathematical underpinnings of the constrained statistical mechanics and their relationship to the theory of electromagnetism are very elegant.  The characteristic feature of these algorithms is that the speed of light c is reintroduced into the algorithms (with great similarity to plasma physics codes).  This leads to a diffusive dynamics in MC, while in MD the speed of light can be used as a dynamical optimization parameter very similar to the electron mass in Car-Parinello (ab-initio) molecular dynamics.  Recent offlattice implementations show that the speed of the algorithm is competitive with other fast electrostatic methods in MD and dramatically improves MC simulations, where no O(N) electrostatic algorithm has been available to date. In addition to it's efficiency, the algorithm is much more easily generalizable to inhomogeneous dielectric environments, which occur regularly in solutions of biopolymers.

    Our new algorithms are particularly suited to describe the dielectric behavior of water, which displays many unusual features. Due to correlations between water molecules, the dielectric function is not constant as usually assumed in continuum electrostatics, but is in general nonlocal. Specifically, there is a band of wavevectors where the dielectric function is negative, leading to a so-called overscreening effect that implies oscillatory interaction potentials between charges on the nanoscale. We have recently extented our local electrostatic algorithm to treat such spatial dependencies by including gradient terms of the polarization. Our results showed that these nonlocal terms can have strong effect on the dielectric barrier for ion translocation through low-dielectric molecular pores. Presently we are conducting a series of atomistic MD simulations with realistic water models to obtain direct information about the nonlocal dielectric response between solvated ions and rigid polyelectrolytes. This information will be used as input and benchmark to the development of implicit solvent models that describe these nanoscale solvation effects without explicit representation of the solvent.

    Students: Matthew Badali, Shahzad Ghanbarian
    Collaborator: Prof. Mona Berciu, UBC
  • Microstructure evolution in metals
    The structural properties of metals are determined by how they were formed. However, the phenomena of solidification and grain growth involve complex structural
    changes between parent and daughter phases and couple atomic-scale elastic and plastic effects with diffusional processes. They take place on length and time scales     that are inaccessible with conventional molecular dynamics methods. In materials science, coarse-grained field theoretic methods (phase fields) elegantly describe the relaxation dynamics of order parameters, but are devoid of any atomistic features. We are using the formalism of classical dynamic density functional theory (DDFT) to develop a computational tool that acts as a bridge between atomistic particles and continuum fields, the so called Phase Field Crystal model. In DDFT, the time evolution of the fields is purely diffusive and governed by a free energy that can systematically be expanded in interaction terms. In recent contributions we developed free energies that reflect the crystal symmetries of solid state structures and used them to study phase transformations and defect dynamics in multigrain systems. We analyzed the elastic properties of the phase field crystal and extended the formalism to binary alloys. Current efforts are dedicated towards developing a concurrent multiscale method that links the phase field crystal to phase field models via amplitude expansions.

    Postdoctoral fellow: Joel Berry
    Collaborator: Prof. Nikolas Provatas, McMaster University
  • Epitaxial growth at surfaces
    Thin films grown by     Molecular Beam Epitaxy (MBE) are of great technological importance and can display an amazing variety of shapes. During epitaxy, adatoms are deposited onto a surface, where they diffuse and aggregate at islands or steps. One important parameter is the ability of the film to grow in a smooth layer by layer fashion, or a rough multilayer mode where new layers start to grow before lower layers are complete. The occurence of a particular growth mode is a consequence of kinetics, not thermodynamics. Other interesting phenomena can occur when growth takes place on vicinal (stepped) surfaces. A highly vicinal surface can grow in a so-called step flow mode, where all deposited adatoms attach to existing steps. By contrast, adatoms deposited onto a flat surface frequently nucleate new islands that grow and eventually merge. We showed using kinetic Monte Carlo simulations that the transition between these two growth modes leads to the formation of kinetic facets with a special slope when regrowth is performed on prepatterned surfaces.

    In more recent work, we employed the Phase Field Crystal model described above to simulate the growth of quasicrystalline surfaces. Quasicrystals are ordered but aperiodic solids, and their surfaces have generated much interest due to low friction coefficients and applications in catalysis. Using again the Phase Field Crystal technique we studied the morphology of adsorbed monolayers for different interaction parameters and predict a wide range of pseudomorphic structures. Since the model operates on diffusive timescales it is much more efficient than particle based Monte Carlo simulations. Current we are working on extending our studies to three-dimensional growth in order to better understand the transition from pseudomorphic growth to regular crystal growth.

    Collaborator: Prof. Mikko Haataja, Princeton University
  • Biomolecular systems
    Although DNA is perhaps the best studied biopolymer, many of its properties are still poorly understood and very difficult to simulate on the computer. So-called all atom simulations explicitly account for every atom and chemical interaction, but can only study about 50 basepairs on timescales less than 100 nanoseconds. In order to be able to reach the much longer biologically relevant timescales, it is necessary to use simpler or coarse-grained models, where some degrees of freedom have been integrated out but key physical properties of the DNA are preserved. We have constructed such a model, where we replace the complexity of the DNA backbone with a bead-spring system and model the four bases ACTG with ellipsoidal objects. The goal is to still be able to differentiate in the shape and chemical specificity of the base molecules while benefitting from large computational savings. The model provides insight into the origion of important biopolymer quantities such as persistence length, twist and stacking, and chirality. Future applications of this model will include detailed studies of DNA translocation through molecular pores.

    Collaborator: Prof. Steven Plotkin, UBC
  • Diffusion in alloys
    The design of multicomponent alloys requires knowledge of the transport properties of the alloying elements. Although the basic transport mechanism of diffusion via impurity-vacancy exchange is well understood, accurate predictions of the diffusivity requires in general a quantum level calculation that captures chemical detail. We used Density Functional Theory (DFT) to calculate the activation energies for diffusion of various alloying elements, in particular rare earths, in magnesium. For these atoms we found strong correlation effects that substantially alter the diffusivities obtained from transition state energies alone. Presently we are extending these calculations to diffusion near high-symmetry grain boundaries.

    Students: Liam Huber
    Collaborators: Prof. Matthias Militzer, UBC, Dr. Ilya Elfimov, UBC