Session Y25: Focus Session: Multiscale Modeling

The heterogeneous multiscale method: A ten-year review

The heterogeneous multiscale method (HMM) was proposed 10 years ago, as a unified framework for designing multiscale algorithms in different applications. It is a top-down strategy in the sense that it relies on a preconceived form of macroscale model. Missing data in the macroscale model are estimated on the fly using a reliable microscale model. In this talk, we will take a critical look at HMM. We will discuss applications to various problems, including dynamic fracture, complex fluids, transition pathways in complex systems and stochastic simulation algorithms. We will also examine areas where improvement are needed in order to make HMM more successful. ~   

Progress Towards Atomistic Simulations that Reach Anthropological Timescale and Beyond

Atomistic and first-principles modeling, which describe the world as assembly of atoms and electrons, provide the most fundamental answer to problems of materials. However, they also suffer the most severe timescale limitations. For instance, in molecular dynamics (MD) simulations, in order to resolve atomic vibrations, the integration time step is limited to hundredth of a picosecond, and therefore the simulation duration is limited to sub-microsecond due to computational cost. Although a nanosecond simulation is often enough (surprisingly) for many physical and chemical properties, it is usually insufficient for predicting microstructural evolution and thermo-mechanical properties of materials. In this invited talk I will discuss recent attempts at overcoming the timescale challenges of atomic-resolution simulations: (a) strain-boost hyperdynamics [Phys. Rev. B 82 (2010) 184114] for simulating primarily displacive events and associated issues of activation entropy and the Meyer-Neldel compensation rule, (b) diffusive molecular dynamics (DMD) [Phys. Rev. B 84 (2011) 054103] for microstructural evolution driven by repetitive diffusion events and coupled displacive-diffusive processes, and (c) a Markovian network statistical mechanical treatment of the energy-landscape basin connectivity and a formula for the viscosity of supercooled liquid and glass [PLoS ONE 6 (2011) e17909]. Challenges and future directions are discussed.   

Adaptation of multiscale thermal modeling methods to general crystalline solids

From the nano- to micro-scale, phonons act as the primary mechanism for energy transport and storage in most non-metalic, crystalline materials. While phonon properties are determined by interatomic interactions on the scale of the atomistic unit cell, phenomena and microstructures of interest are often at length and time scales that are too large for atomistic simulations. The phonon Boltzmann transport equation (pBTE) enables continuum-scale calculations that capture both atomistic- and continuum-scale thermal behavior, though so far pBTE-based methods have been limited primarily to silicon [1]. We have developed a pBTE-based method for general crystaline materials with up to hundreds of atoms per unit cell. We demonstrate its applicability in silica (9-atom unit cell) and RDX (168-atom unit cell), though presently limited to one dimension in k-space. We discuss the main challenges when moving to larger unit cells, including the automated untangling of phonon dispersion data, discretization of phonon modes and the treatment of high energy modes, including the omission and/or lumping of modes and the use of reservoir modes. \\[4pt] [1] Chunjian Ni and J. Murthy, in \textit{11th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, ITHERM}, 2008, 1097   

Extended Lagrangian Born-Oppenheimer Molecular Dynamics: quantum mecahnical molecular dynamics for extended time and length scales

Born-Oppenheimer molecular dynamics (BOMD) based on density functional theory offers a very accurate quantum mechanical approach to atomistic simulations that is more reliable and general compared to classical MD. Unfortunately, BOMD simulations are often limited by a high computational cost or by problems such as unbalanced phase space trajectories, numerical instabilities and a systematic long-term energy drift. These problems become particularly severe in combination with reduced complexity or linear scaling algorithms that are necessary for the study of large systems. We have recently taken some steps toward a new generation of first principles MD, which combines some of the best features of regular BOMD and Car-Parrinello MD, while avoiding their most serious shortcomings. The new dynamics is given in terms of an extended Lagrangian (XL), where auxiliary extended electronic degrees of freedom are added to the nuclear part. Our framework enables accurate geometric integration of both the nuclear and electronic degrees of freedom that provide a time-reversible and energy conserving dynamics on the ground state BO potential energy surface that is stable also under approximate SCF convergence. XL-BOMD provides a surprisingly simple and general framework for atomistic simulations   

Multi scale modeling of atomic layer deposition

Atomic layer deposition (ALD) is one of the techniques now used to grow conformal nanometer thin films with the quality required for electronic devices. ALD is a type of chemical vapor deposition that depends on self-limiting surface chemistry. Many aspects of chemical reactions and their effect on the stoichiometry of the film remain unclear. We have used therefore density functional theory (DFT) to explore those reactions. The growth of HfO$_{2}$ from H$_{2}$O and Hf(N(CH$_{3}$)$_{2}$)$_{4}$ was regarded as a sample ALD system. The process of densification was explained accurately. A new mechanism of multiple proton diffusion was propounded and DFT energetics showed it to be the most favourable path way. We also found that reaction rates are strongly coupled with the coordination number of Hf atoms at the surface. Then this complex chemistry was implemented in kinetic Monte-Carlo (KMC). The KMC calculation showed the effect of intermediate reactions on the growth rate. Furthermore the morphology of the film and the growth rate under different reaction conditions were compared with experimental data.   

A unified approach to preserve structure and thermodynamics in a coarse-grained model of aqueous mixtures

Biological organizations depend on a sensitive balance of noncovalent interactions, in particular also those involving interactions of small molecules, including inorganic salts and urea, with biomolecules in aqueous solution. Computer simulations of these types of systems require simple-yet-specific models in order to cover all relevant time and length scales. We present a method to systematically coarse-grain liquid mixtures using Kirkwood-Buff theory of solution combined with an iterative Boltzmann inversion technique that infers single-site interaction potentials for the solution components from the pair correlation functions. Our method preserves both the solution structure at pair level and variations of solution components' chemical potentials with compositions within a unified coarse-graining framework. To test the robustness of our approach, we simulated urea-water and benzene-water systems over a wide-range of concentrations. We also observe the coarse-grained potentials to be reasonably transferable with varying concentrations.   

Novel mesoscopic approach for modeling Carbon Nanotube System

We present a distinct spherical element concept for simulating morphologies and mechanical properties of carbon nanotube systems. The important interactions present at the microscopic level are encapsulated into two types of contact models that act simultaneously. Each individual nanotube is coarse-grained into a chain of spherical elements interacting by parallel contact bonds, representing the microscopic covalent bonding. An anisotropic model with aligning moments acts at the contact between elements located in different tubes to represent the van der Waals long-ranged interactions. The accuracy, computational efficiency, and capabilities of the created mesoscopic model are discussed along with illustrative examples, including self-folding of individual nanotubes, mechanical testing of nanotube ropes, self-assembly of a high-porosity nanotube paper, and mechanical testing of a low-porosity nanotube paper.   

Structure formation of toluene around C60: Application of the Adaptive Resolution Scheme

In the adaptive resolutions scheme (AdResS) a local, typically all-atom cavity is coupled to a surrounding medium of coarse grained, simplified molecules. This methodology cannot only be used to reduce the CPU time demand of atomistic simulations but also to systematically investigate the relative influence of different interactions on structure formation. For this, we vary the thickness of the all atom layer of toluene around a C60, analyze the first toluene layers and compare the result to a full resolution simulation. With this system, we also introduce the implementation of AdResS for molecular simulations into GroMaCS.   

Characterization of phase behavior in assemblies of colloidal nanoparticles

We report results of a systematic investigation of the phase behavior of clusters of colloidal nanoparticles, which interact via a hard core and depletion attraction potential, as a function of system size and inter-particle interaction strength. To describe the various phases that may be present in such nanoparticle assemblies, we carry out a set of windowed Monte Carlo umbrella sampling (MC-US) simulations to generate free energy landscapes (FELs). For the MC-US generation of the FELs, we use the diffusion mapping method to identify the system's underlying dimensionality and define the dynamically relevant coarse variables. The resulting set of FELs samples broad ranges of the system size and interaction potential strength. These computed FELs describe the phase behavior of the nanoparticle assemblies and allow us to analyze the effects of interaction strength and system size as these assemblies approach the bulk thermodynamic limit. In very small clusters, only a single stable liquid-like phase exists. However, as the number of nanoparticles in the cluster increases, a second crystalline phase emerges in coexistence with the liquid-like phase. The corresponding critical cluster size marks the onset of nucleation of crystalline assemblies of colloidal nanoparticles.   

New algorithms for field-theoretic block copolymer simulations: Progress on using adaptive-mesh refinement and sparse matrix solvers in SCFT calculations

Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.   

Concurrent multiscale modeling of 3D granular systems

Large-scale granular mechanics simulations are often based on continuum approaches such as the finite element method (FEM). However, these approaches require continuum descriptions of the constitutive relationship between stresses and strains. As a result, grain-scale dynamics are not explicitly considered. Therefore, modeling of large-scale history dependent phenomena due to grain-scale rearrangement and strain localization remains a long-standing challenge. For small-scale studies, discrete element method (DEM) simulations model grain-scale interactions and thus capture history dependent phenomena. However, the application of this approach to large-scale systems is computationally expensive and impractical. We demonstrate a scalable multiscale approach where large-scale granular systems are discretized with the classical FEM simulation, while the necessary constitutive relation is calculated concurrently from DEM simulations of representative volume elements of grains subject to the loading and deformation prescribed by each finite element.