No Arabic abstract
A coarse-grained model is developed to allow large-scale molecular dynamics (MD) simulations of a branched polyetherimide derived from two backbone monomers [4,4-bisphenol A dianhydride (BPADA) and m-phenylenediamine (MPD)], a chain terminator [phthalic anhydride (PA)], and a branching agent [tris[4-(4-aminophenoxy)phenyl] ethane (TAPE)]. An atomistic model is first built for the branched polyetherimide. A systematic protocol based on chemistry-informed grouping of atoms, derivation of bond and angle interactions by direct Boltzmann inversion, and parameterization of nonbonded interactions by potential of mean force (PMF) calculations via gas-phase MD simulations of atomic group pairs, is used to construct the coarse-grained model. A six-pair geometry, with one atomic group at the center and six replicates of the other atomic group placed surrounding the central group in a NaCl structure, has been demonstrated to significantly speed up the PMF calculations and partially capture the many-body aspect of the PMFs. Furthermore, we propose a correction term to the PMFs that can make the resulting coarse-grained model transferable temperature-wise, by enabling the model to capture the thermal expansion property of the polymer. The coarse-grained model has been applied to explore the mechanical, structural, and rheological properties of the branched polyetherimide.
The nucleation of cavities in a homogenous polymer under tensile strain is investigated in a coarse-grained molecular dynamics simulation. In order to establish a causal relation between local microstructure and the onset of cavitation, a detailed analysis of some local properties is presented. In contrast to common assumptions, the nucleation of a cavity is neither correlated to a local loss of density nor, to the stress at the atomic scale and nor to the chain ends density in the undeformed state. Instead, a cavity in glassy polymers nucleates in regions that display a low bulk elastic modulus. This criterion allows one to predict the cavity position before the cavitation occurs. Even if the localization of a cavity is not directly predictable from the initial configuration, the elastically weak zones identified in the initial state emerge as favorite spots for cavity formation.
A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is transferable. It is here applied to determine the structure of several polymeric systems, which have different parameter values, such as molecular length, monomeric structure, local flexibility, and thermodynamic conditions. When the pair distribution function obtained from this procedure is compared with the results from a full atomistic simulation, it shows quantitative agreement. Moreover, the multiscale procedure accurately captures both large and local scale properties while remaining computationally advantageous.
Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multi-body terms that emerge from the dimensionality reduction.
Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master Equation that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We show that the corresponding coarse-grained entropy production contains information on microscopic currents that are not captured by the Fokker-Planck equation and thus cannot be deduced from it. We study a discrete-state and a continuous-state system, deriving in both the cases an analytical expression for the coarse-graining corrections to the entropy production. This result elucidates the limits in which there is no loss of information in passing from a Master Equation to a Fokker-Planck equation describing the same system. Our results are amenable of experimental verification, which could help to infer some information about the underlying microscopic processes.
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the elastic distortion and stress regularization at a dislocation core and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are then supplemented with non-singular displacements to enforce mechanical equilibrium. This allows for the consistent separation of plastic and elastic time scales in this framework. A finite element method is introduced to solve the combined amplitude and elasticity equations, which is applied to a few prototypical configurations in two spatial dimensions for a crystal of triangular lattice symmetry: i) the stress field induced by an edge dislocation with an analysis of how the amplitude equation regularizes stresses near the dislocation core, ii) the motion of a dislocation dipole as a result of its internal interaction, and iii) the shrinkage of a rotated grain. We also compare our results with those given by other extensions of classical elasticity theory, such as strain-gradient elasticity and methods based on the smoothing of Burgers vector densities near defect cores.