0000000000010108
AUTHOR
Leonid Yelash
Towards the Quantitative Prediction of the Phase Behavior of Polymer Solutions by Computer Simulation
The phase diagram of polymer solutions (cf. e.g. alkanes dissolved in supercritical carbon dioxide) is complicated, since there are four control parameters (temperature, pressure, monomer volume fraction, chain length of the polymer) and due to the interplay of liquid-vapor transitions and fluid-fluid unmixing. As a result I very intricate phase diagram topologies can result. An attempt to develop coarse-1 grained models that can deal with this task will be described. As usual, the polymers I will be modelled as off-lattice bead-spring chains, where several chemical monomers I are integrated into one effective bond, torsional degrees of freedom being dis-I regarded. But also a coarse-graine…
Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide.
Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The mode…
Effect of the phase behaviour of the solvent–antisolvent systems on the gas–antisolvent-crystallisation of paracetamol
Abstract The influence of the phase behaviour of the solvent–antisolvent system on the process conditions for the gas–antisolvent process is investigated. The two fluids are modelled by the Peng–Robinson equation of state while the dissolved solid is described by a Clapeyron-type approach. Based on the correlation of the ternary system, a liquid–liquid immiscibility region has been found which hinders the proper crystallisation of the solute. A thorough investigation of the binary solvent–antisolvent system by the global phase diagram methods yields a criterion for the proper choice of the solvent. The crucial property turns out to be the distance of the solvent–antisolvent system from the …
Three-step decay of time correlations at polymer-solid interfaces
Two-step decay of relaxation functions, i.e., time scale separation between microscopic dynamics and structural relaxation, is the defining signature of the structural glass transition. We show that for glass-forming polymer melts at an attractive surface slow desorption kinetics introduces an additional time scale separation among the relaxational degrees of freedom leading to a three-step decay. The inherent length scale of this process is the radius of gyration in contrast to the segmental scale governing the glass transition. We show how the three-step decay can be observed in incoherent scattering experiments and discuss its relevance for the glass transition of confined polymers by an…
Interactions between polymer brush-coated spherical nanoparticles: the good solvent case.
The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to…
A multi-scale method for complex flows of non-Newtonian fluids
We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into acco…
Adaptive discontinuous evolution Galerkin method for dry atmospheric flow
We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realiz…
How Well Can Coarse-Grained Models of Real Polymers Describe Their Structure? The Case of Polybutadiene
Coarse-graining of chemical structure of macromolecules in the melt is investigated using extensive molecular dynamics simulation data which are based on a united atom force-field model of polybutadiene. Systematically increasing the number, n, of the united atoms approximated by an effective coarse-grained monomer, we study the influence of degree of coarse-graining on the structure functions such as the segment-segment intermolecular and intramolecular correlation functions. These results are compared to Monte Carlo simulations of the corresponding coarse-grained bead-spring model and Chen-Kreglewski potential for chain molecules. In contrast to the atomistic chemically realistic model of…
Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization t…
A coarse-graining procedure for polymer melts applied to 1,4-polybutadiene
We present a coarse-graining procedure for homopolymer melts mapping intra- as well as inter-molecular interactions from a chemically realistic united atom description to a bead-spring type molecular model. On the coarse-grained level the repeat units interact through bond-length and bond angle potentials and a non-bonded Lennard-Jones type interaction. The latter one is of the 7,4 form and softer than the typically employed 12,6 interactions. The coarse-graining of the intramolecular interactions follows well developed procedures, however, we point out in which way the non-bonded intramolecular interactions in the chemically realistic model should be treated. The parameters of the non-bond…
Effect of the solvent quality on the structural rearrangement of spherical brushes: coarse-grained models
A coarse-grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various polymer lengths, grafting densities, and nanoparticle sizes by molecular dynamics simulations, considering variable solvent quality in the framework of an implicit solvent treatment. Below the theta point, the tuning of the temperature strongly influences the coverage of the nanoparticle surface by collapsed single chains or clusters of several chains. The shape and size of the aggregates depend on the number of monomers and surface density of the polymers. Specifically we analyzed the effect of the solvent quality on the density profiles and radius of gyration of the single …
Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation bo…
Spherically averaged versus angle-dependent interactions in quadrupolar fluids
Employing simplified models in computer simulation is on the one hand often enforced by computer time limitations but on the other hand it offers insights into the molecular properties determining a given physical phenomenon. We employ this strategy to the determination of the phase behaviour of quadrupolar fluids, where we study the influence of omitting angular degrees of freedom of molecules via an effective spherically symmetric potential obtained from a perturbative expansion. Comparing the liquid-vapor coexistence curve, vapor pressure at coexistence, interfacial tension between the coexisting phases, etc., as obtained from both the models with the full quadrupolar interactions and th…
Molecular Dynamics simulation of evaporation processes of fluid bridges confined in slit-like pore
A simple fluid, described by point-like particles interacting via the Lennard-Jones potential, is considered under confinement in a slit geometry between two walls at distance Lz apart for densities inside the vapor-liquid coexistence curve. Equilibrium then requires the coexistence of a liquid "bridge" between the two walls, and vapor in the remaining pore volume. We study this equilibrium for several choices of the wall-fluid interaction (corresponding to the full range from complete wetting to complete drying, for a macroscopically thick film), and consider also the kinetics of state changes in such a system. In particular, we study how this equilibrium is established by diffusion proces…
Coarse-graining dipolar interactions in simple fluids and polymer solutions: Monte Carlo studies of the phase behavior
In this paper we investigate the phase diagram of pure dipolar substances and their mixtures with short alkanes, using grand canonical Monte Carlo simulations of simplified coarse-grained models. Recently, an efficient coarse-grained model for simple quadrupolar molecules, based on a Lennard-Jones (LJ) interaction plus a spherically averaged quadrupolar potential, has been shown to be successful in predicting single-component and mixture phase diagrams. Motivated by these results, we investigate the phase diagrams of simple dipolar molecules (and their mixtures with alkanes) using a spherically averaged potential. First, we test the model on pure components. A generalized (state-dependent) …
Spinodal decomposition of polymer solutions: A parallelized molecular dynamics simulation
In simulations of phase separation kinetics, large length and time scales are involved due to the mesoscopic size of the polymer coils, and the structure formation on still larger scales of length and time. We apply a coarse-grained model of hexadecane dissolved in supercritical carbon dioxide, for which in previous work the equilibrium phase behavior has been established by Monte Carlo methods. Using parallelized simulations on a multiprocessor supercomputer, large scale molecular dynamics simulations of phase separation following pressure jumps are presented for systems containing $N=435\phantom{\rule{0.2em}{0ex}}136$ coarse-grained particles, which correspond to several millions of atoms…
Computer Simulations and Coarse-Grained Molecular Models Predicting the Equation of State of Polymer Solutions
Monte Carlo and molecular dynamics simulations are, in principle, powerful tools for carrying out the basic task of statistical thermodynamics, namely the prediction of macroscopic properties of matter from suitable models of effective interactions between atoms and molecules. The state of the art of this approach is reviewed, with an emphasis on solutions of rather short polymer chains (such as alkanes) in various solvents. Several methods of constructing coarse-grained models of the simple bead–spring type will be mentioned, using input either from atomistic models (considering polybutadiene as an example) or from experiment. Also, the need to have corresponding coarse-grained models of t…
Artificial multiple criticality and phase equilibria: an investigation of the PC-SAFT approach
The perturbed-chain statistical associating fluid theory (PC-SAFT) is studied for a wide range of temperature, T, pressure, p, and (effective) chain length, m, to establish the generic phase diagram of polymers according to this theory. In addition to the expected gas-liquid coexistence, two additional phase separations are found, termed "gas-gas" equilibrium (at very low densities) and "liquid-liquid" equilibrium (at densities where the system is expected to be solid already). These phase separations imply that in one-component polymer systems three critical points occur, as well as equilibria of three fluid phases at triple points. However, Monte Carlo simulations of the corresponding sys…
Polymer Dynamics in a Polymer-Solid Interphase: Molecular Dynamics Simulations of 1,4-Polybutadiene At a Graphite Surface
A chemically realistic model of 1,4-polybutadiene confined by graphite walls in a thin film geometry was studied by molecular dynamics simulations. The chemically realistic approach allows for a quantitative determination of a variety of experimentally accessible relaxation functions (e.g., dielectric, NMR, or neutron scattering responses). The simulations yield these experimental observables. Additionally, the simulations can be resolved as a function of distance to the solid interface on a much finer scale than experimentally possible, providing a detailed mechanistic picture of the segmental and large scale motions of polymers in the interfacial region between bulk polymer melts and soli…
Phase separation of an asymmetric binary fluid mixture confined in a nanoscopic slit pore: Molecular-dynamics simulations
As a generic model system of an asymmetric binary fluid mixture, hexadecane dissolved in carbon dioxide is considered, using a coarse-grained bead-spring model for the short polymer, and a simple spherical particle with Lennard-Jones interactions for the carbon dioxide molecules. In previous work, it has been shown that this model reproduces the real phase diagram reasonable well, and also the initial stages of spinodal decomposition in the bulk following a sudden expansion of the system could be studied. Using the parallelized simulation package ESPResSo on a multiprocessor supercomputer, phase separation of thin fluid films confined between parallel walls that are repulsive for both types…
Structure and pair correlations of a simple coarse grained model for supercritical carbon dioxide
A recently introduced coarse-grained pair potential for carbon dioxide molecules is used to compute structural properties in the supercritical region near the critical point, applying Monte Carlo simulations. In this model, molecules are described as point particles, interacting with Lennard-Jones (LJ) forces and a (isotropically averaged) quadrupole–quadrupole potential, the LJ parameters being chosen such that gratifying agreement with the experimental phase diagram near the critical point is obtained. It is shown that the model gives also a reasonable account of the pair correlation function, although in the nearest neighbour shell some systematic discrepancies between the model predicti…
Shear-Thinning in Oligomer Melts—Molecular Origins and Applications
We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations …
A slow process in confined polymer melts: layer exchange dynamics at a polymer solid interface
Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.
Dynamics of macromolecules grafted in spherical brushes under good solvent conditions
Spherical polymer brushes have a structure intermediate between star polymers and polymer brushes on flat substrates, and are important building blocks of polymer nanoparticles. Molecular dynamics simulations are presented for isolated spherical polymer brushes under good solvent conditions, varying the grafting density as well as the chain length, using a coarse-grained bead-spring model of flexible chains. We complement previous work on the static properties of the same model by analyzing the chain dynamics, studying the motions of monomers in relation to their position along the grafted chains, and extract suitable relaxation times. A qualitative discussion in terms of the Rouse model is…
Spinodal decomposition of polymer solutions: molecular dynamics simulations of the two-dimensional case.
As a generic model system for phase separation in polymer solutions, a coarse-grained model for hexadecane/carbon dioxide mixtures has been studied in two-dimensional geometry. Both the phase diagram in equilibrium (obtained from a finite size scaling analysis of Monte Carlo data) and the kinetics of state changes caused by pressure jumps (studied by large scale molecular dynamics simulations) are presented. The results are compared to previous work where the same model was studied in three-dimensional geometry and under confinement in slit geometry. For deep quenches the characteristic length scale ℓ(t) of the formed domains grows with time t according to a power law close to [Formula: see…