We describe recent efforts to improve our predictive modeling of rate-dependent behavior at, or near, a phase transition using molecular dynamics simulations. Cadmium sulfide (CdS) is a well-studied material that undergoes a solid-solid phase transition from wurtzite to rock salt structures between 3 and 9 GPa. Atomistic simulations are used to investigate the dominant transition mechanisms as a function of orientation, size and rate. We found that the final rock salt orientations were determined relative to the initial wurtzite orientation, and that these orientations were different for the two orientations and two pressure regimes studied. The CdS solid-solid phase transition is studied, for both a bulk single crystal and for polymer-encapsulated spherical nanoparticles of various sizes.
Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning or twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling, and twisting. Only when the particle model includes rolling and twisting friction were experimental volume fractions reproduced.
Using random walk analyses we explore diffusive transport on networks obtained from contacts between isotropically compressed, monodisperse, frictionless sphere packings generated over a range of pressures in the vicinity of the jamming transition pā0. For conductive particles in an insulating medium, conduction is determined by the particle contact network with nodes representing particle centers and edges contacts between particles. The transition rate is not homogeneous, but is distributed inhomogeneously due to the randomness of packing and concomitant disorder of the contact network, e.g., the distribution of the coordination number. A narrow escape time scale is used to write a Markov process for random walks on the particle contact network. This stochastic process is analyzed in terms of spectral density of the random, sparse, Euclidean and real, symmetric, positive, semidefinite transition rate matrix. Results show network structures derived from jammed particles have properties similar to ordered, euclidean lattices but also some unique properties that distinguish them from other structures that are in some sense more homogeneous. In particular, the distribution of eigenvalues of the transition rate matrix follow a power law with spectral dimension 3. However, quantitative details of the statistics of the eigenvectors show subtle differences with homogeneous lattices and allow us to distinguish between topological and geometric sources of disorder in the network.
The role of an external field on capillary waves at the liquid-vapor interface of a dipolar fluid is investigated using molecular dynamics simulations. For fields parallel to the interface, the interfacial width squared increases linearly with respect to the logarithm of the size of the interface across all field strengths tested. The value of the slope decreases with increasing field strength, indicating that the field dampens the capillary waves. With the inclusion of the parallel field, the surface stiffness increases with increasing field strength faster than the surface tension. For fields perpendicular to the interface, the interfacial width squared is linear with respect to the logarithm of the size of the interface for small field strengths, and the surface stiffness is less than the surface tension. Above a critical field strength that decreases as the size of the interface increases, the interface becomes unstable due to the increased amplitude of the capillary waves.
We present a review and critique of several methods for the simulation of the dynamics of colloidal suspensions at the mesoscale. We focus particularly on simulation techniques for hydrodynamic interactions, including implicit solvents (Fast Lubrication Dynamics, an approximation to Stokesian Dynamics) and explicit/particle-based solvents (Multi-Particle Collision Dynamics and Dissipative Particle Dynamics). Several variants of each method are compared quantitatively for the canonical system of monodisperse hard spheres, with a particular focus on diffusion characteristics, as well as shear rheology and microstructure. In all cases, we attempt to match the relevant properties of a well-characterized solvent, which turns out to be challenging for the explicit solvent models. Reasonable quantitative agreement is observed among all methods, but overall the Fast Lubrication Dynamics technique shows the best accuracy and performance. We also devote significant discussion to the extension of these methods to more complex situations of interest in industrial applications, including models for non-Newtonian solvent rheology, non-spherical particles, drying and curing of solvent and flows in complex geometries. This work identifies research challenges and motivates future efforts to develop techniques for quantitative, predictive simulations of industrially relevant colloidal suspension processes.
The most feasible way to disperse particles in a bulk material or control their packing at a substrate is through fluidization in a carrier that can be processed with well-known techniques such as spin, drip and spray coating, fiber drawing, and casting. The next stage in the processing is often solidification involving drying by solvent evaporation. While there has been significant progress in the past few years in developing discrete element numerical methods to model dense nanoparticle dispersion/suspension rheology which properly treat the hydrodynamic interactions of the solvent, these methods cannot at present account for the volume reduction of the suspension due to solvent evaporation. As part of LDRD project FY-101285 we have developed and implemented methods in the current suite of discrete element methods to remove solvent particles and volume, and hence solvent mass from the liquid/vapor interface of a suspension to account for volume reduction (solvent drying) effects. To validate the methods large scale molecular dynamics simulations have been carried out to follow the evaporation process at the microscopic scale.
In this presentation we examine the accuracy and performance of a suite of discrete-element-modeling approaches to predicting equilibrium and dynamic rheological properties of polystyrene suspensions. What distinguishes each approach presented is the methodology of handling the solvent hydrodynamics. Specifically, we compare stochastic rotation dynamics (SRD), fast lubrication dynamics (FLD) and dissipative particle dynamics (DPD). Method-to-method comparisons are made as well as comparisons with experimental data. Quantities examined are equilibrium structure properties (e.g. pair-distribution function), equilibrium dynamic properties (e.g. short- and long-time diffusivities), and dynamic response (e.g. steady shear viscosity). In all approaches we deploy the DLVO potential for colloid-colloid interactions. Comparisons are made over a range of volume fractions and salt concentrations. Our results reveal the utility of such methods for long-time diffusivity prediction can be dubious in certain ranges of volume fraction, and other discoveries regarding the best formulation to use in predicting rheological response.
Nanoparticles are now more than ever being used to tailor materials function and performance in differentiating technologies because of their profound effect on thermo-physical, mechanical and optical properties. The most feasible way to disperse particles in a bulk material or control their packing at a substrate is through fluidization in a carrier, followed by solidification through solvent evaporation/drying/curing/sintering. Unfortunately processing particles as concentrated, fluidized suspensions into useful products remains an art largely because the effect of particle shape and volume fraction on fluidic properties and suspension stability remains unexplored in a regime where particle-particle interaction mechanics is prevalent. To achieve a stronger scientific understanding of the factors that control nanoparticle dispersion and rheology we have developed a multiscale modeling approach to bridge scales between atomistic and molecular-level forces active in dense nanoparticle suspensions. At the largest length scale, two 'coarse-grained' numerical techniques have been developed and implemented to provide for high-fidelity numerical simulations of the rheological response and dispersion characteristics typical in a processing flow. The first is a coupled Navier-Stokes/discrete element method in which the background solvent is treated by finite element methods. The second is a particle based method known as stochastic rotational dynamics. These two methods provide a new capability representing a 'bridge' between the molecular scale and the engineering scale, allowing the study of fluid-nanoparticle systems over a wide range of length and timescales as well as particle concentrations. To validate these new methodologies, multi-million atoms simulations explicitly including the solvent have been carried out. These simulations have been vital in establishing the necessary 'subgrid' models for accurate prediction at a larger scale and refining the two coarse-grained methodologies.
We have enhanced our parallel molecular dynamics (MD) simulation software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator, lammps.sandia.gov) to include many new features for accelerated simulation including articulated rigid body dynamics via coupling to the Rensselaer Polytechnic Institute code POEMS (Parallelizable Open-source Efficient Multibody Software). We use new features of the LAMMPS software package to investigate rhodopsin photoisomerization, and water model surface tension and capillary waves at the vapor-liquid interface. Finally, we motivate the recipes of MD for practitioners and researchers in numerical analysis and computational mechanics.
Using molecular dynamics simulations, a constitutive model for the chemical aging of polymer networks was developed. This model incorporates the effects on the stress from the chemical crosslinks and the physical entanglements. The independent network hypothesis has been modified to account for the stress transfer between networks due to crosslinking and scission in strained states. This model was implemented in the finite element code Adagio and validated through comparison with experiment. Stress relaxation data was used to deduce crosslinking history and the resulting history was used to predict permanent set. The permanent set predictions agree quantitatively with experiment.
The Independent Network Model (INM) has proven to be a useful tool for understanding the development of permanent set in strained elastomers. Our previous work showed the applicability of the INM to our simulations of polymer systems crosslinking in strained states. This study looks at the INM applied to theoretical models incorporating entanglement effects, including Flory's constrained junction model and more recent tube models. The effect of entanglements has been treated as a separate network formed at gelation, with additional curing treated as traditional phantom contributions. Theoretical predictions are compared with large-scale molecular dynamics simulations.
Constitutive models for chemically reacting networks are formulated based on a generalization of the independent network hypothesis. These models account for the coupling between chemical reaction and strain histories, and have been tested by comparison with microscopic molecular dynamics simulations. An essential feature of these models is the introduction of stress transfer functions that describe the interdependence between crosslinks formed and broken at various strains. Efforts are underway to implement these constitutive models into the finite element code Adagio. Preliminary results are shown that illustrate the effects of changing crosslinking and scission rates and history.