Session Z31: New Computational Methods in Polymer & Soft Matter Physics

Simulations of Coarse Grain Entangled Polymeric Systems: From Thermodynamics to Rheology

Coarse-grained models have been proposed for description of soft materials over length and time scales unattainable by using atomistic models. Polymeric materials present particular challenges, because characteristic length and time scales generally span several orders of magnitude. Most coarse-grained models resort to soft effective interaction potentials, with the result that important effects are lost, including those created by the non-crossability of long polymer chains. In this work we generalize a particle-based coarse-grained approach, which has been successfully used in the past to describe the structure and thermodynamics of homopolymers and block polymers, to the study of linear and non-linear rheology in polymer melts well above the entanglement molecular weight. Entanglements are represented by slip-springs introduced at the two-chain level, as fluctuating interactions between neighboring pairs of polymeric molecules. The model is shown to exhibit scaling laws for the mean square displacement and shear viscosity that are consistent with those observed in tube theories and in experiments. Comparison between simulation and experimental results shows that the model is capable of describing quantitatively the linear and non-linear rheology of homopolymer melts and blends   

Model for the shear viscosity of suspensions of star polymers and other soft particles

We propose a model to describe the concentration dependence of the viscosity of soft particles. We incorporate in a very simple way the softness of the particles into expressions originally developed for rigid spheres. This is done by introducing a concentration-dependent critical packing, which is the packing at which the suspension looses fluidity. The resultant expression reproduces with high accuracy the experimental results for suspensions of star polymers in good solvents. The model allows to explain a weak increase of the viscosity observed in the case of diblock copolymer stars suggesting that the reason for this peculiar behavior is mainly a consequence of the softness of the particles. In the semi-dilute regime, suspensions of star polymers are modeled using the Daoud-Cotton picture to complete the description in the whole concentration regime.   

Systematic and Simulation-Free Coarse-Graining of Polymer Melts using Soft Potentials

Full atomistic simulations of many-chain systems such as polymer melts are not feasible at present due to their formidable computational requirements. Coarse-grained models have to be used instead, where the segments interact with soft potentials that allow complete overlapping. This enables systematic coarse-graining with different $N$ (number of segments on each chain) at constant invariant degree of polymerization controlling the system fluctuations. In this work we use integral-equation theories and a relative entropy framework for coarse-graining to investigate how the soft potential varies with $N$ and how well the coarse-grained models can reproduce both structural and thermodynamic properties of the original system. This will provide us with a quantitative basis for choosing small $N$-values that can still capture the chain conformational entropy, a characteristics of polymers.   

Solvent Entropy in and Coarse-Graining of Polymer Lattice Models

In conventional lattice models for polymeric systems, each lattice site is occupied by at most one polymer segment, and an unoccupied lattice site is often treated as a solvent molecule. This self- and mutual-avoiding walk requires that all lattice sites, polymer segments, and solvent molecules have the same volume. Since a polymer segment here is the coarse-grained representation of a group of real monomers, this incorrectly accounts for the solvent entropy (i.e., size ratio between polymer segments and solvent molecules). It also limits the coarse-graining capability of such models, where the invariant degree of polymerization controlling the system fluctuations is too small (thus exaggerating the fluctuations) compared to that in most experiments. Here we show how to properly account for the solvent entropy in new lattice models with multiple occupancy of lattice sites [Q. Wang, \textbf{Soft Matter 5}, 4564 (2009); \textbf{6}, 6206 (2010)], and present a quantitative coarse-graining strategy that ensures both the solvent entropy and fluctuations in experimental systems are properly accounted for using the new lattice models.   

Recent developments in the VOTCA package for coarse-graining

Coarse-graining is a systematic way of reducing the number of degrees of freedom used to represent a system of interest. The Versatile Object-oriented Toolkit for Coarse-graining Applications (VOTCA) provides a uniform interface to commonly used coarse-graining techniques such as iterative Boltzmann inversion, force-matching, and inverse Monte Carlo. Further, it provides a flexible modular platform for the further development of new coarse-graining techniques. Recently two new methods for coarse-graining have been added to the package and got tested on SPC/E water and methanol-water mixtures. We will discuss these results in comparison to earlier structure-based studies, but also talk about the development of non-structure-based model.   

Coarse-graining of Polystyrene in Various Environments by Iterative Boltzmann Inversion

We have developed mesoscale models for polystyrene (PS) oligomers in various environments following the Iterative Boltzmann Inversion Technique for polymer coarse--graining with and without confinement. Bond, bending angle, torsion angle distributions and radial distribution functions between PS monomers show that local structures were reproduced very well, while a small discrepancy remained in the reproduction of global structures (radii of gyration and end--to--end distances), which is probably due to end effects. Speed--up in polymer dynamics with each model was monitored by scaling factors calculated based on characteristic relaxation times of the end monomers as well as diffusivities of the chains. Results show that coarse--graining is most successful for the highest concentration system (melt) and least for the lowest concentration (dilute solution) due to the stronger slowdown of diffusive and rotational dynamics in atomistic simulations with concentration. The speed--up in the confined solution system was found to be greater than in the unconfined solution system due to the same reason except that confinement slows down the dynamics in that situation. We also characterize the limits to which extent the same models can be used for different degrees of confinement.   

Complex Langevin Simulation of the Coherent States Formulation of Polymer Field Theory

In 1969, Edwards and Freed adapted the ``coherent state'' methods employed in the second quantization formalism of quantum many-body theory to study polymer networks. Since its introduction into polymer science, this formalism has been largely neglected and to our knowledge, has never been applied as a basis for numerical simulations, even for linear polymers. However, in contrast to the Edwards auxiliary-field framework, this alternative polymer field theory has several attractive features, including an action or effective Hamiltonian with an explicit, finite-order, and semi-local polynomial character. We thus revisited the CS formalism and show that these characteristics have advantages both for analytical and numerical studies of linear polymers at equilibrium. For this purpose, we developed a new Complex Langevin sampling scheme that allows for simulations within the CS formalism with stable and efficient numerical characteristics. We anticipate that this methodology will facilitate efficient simulations of a wide range of systems, including complicated branched and networked polymers and liquid crystalline polymers.   

Using adaptive-mesh refinement in SCFT simulations of surfactant adsorption

Adsorption of surfactants at interfaces is relevant to many applications such as detergents, adhesives, emulsions and ferrofluids. Atomistic simulations of interface adsorption are challenging due to the difficulty of modeling the wide range of length scales in these problems: the thin interface region in equilibrium with a large bulk region that serves as a reservoir for the adsorbed species. Self-consistent field theory (SCFT) has been extremely useful for studying the morphologies of dense block copolymer melts. 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. However, even SCFT methods can be difficult to apply to systems in which small spatial regions might require finer resolution than most of the simulation grid (eg. interface adsorption and confinement). We will present results on interface adsorption simulations using PolySwift++, an object-oriented, polymer SCFT simulation code aided by the Tech-X Chompst library that enables via block-structured AMR calculations with PETSc.   

Embedding methods: application and development

Correlated-wavefunction/density functional theory (CW/DFT) embedding methods aim to combine the formally exact correlation treatment in CW methods with the high efficiency of DFT. By partitioning a system into a cluster and its environment, each part can be treated independently. Different embedding schemes have been proposed. The density-based scheme searches for a global embedding potential mediating the interaction on the DFT level. The potential can then be used in CW calculations, e.g., to investigate hot-electron assisted H$_{\mathrm{2}}$ dissociation on Al and Au surfaces. Experimentally, optical excitations of plasmons efficiently create the required hot electrons. The embedded CW calculations validates that the hot electrons play a key role. However, this method neglects the back-action of the cluster on the environment. To solve this problem, a potential-based scheme has been proposed [\textit{J. Chem. Phys.},~135, 194104 (2011)] that allows for a self-consistent combination of different ab-initio methods. Such an embedding potential thus goes beyond the DFT level. The heterogeneity involved poses various numerical challenges. We report on efforts to construct appropriate basis sets and pseudopotentials as well as to optimize the numerical procedure.   

Ion distributions near dielectric interfaces from Car-Parrinello molecular dynamics

Free charges in media characterized by different dielectric constants and separated by thin boundaries are basic models for studying phenomena in both biological and synthetic materials. Knowing the distributions of ions near the dielectric interfaces between these media is crucial towards understanding the structural and physical properties of these systems. We present a new Car-Parrinello molecular dynamics method for simulating charges in heterogeneous media and computing such distributions. This method is founded on a true energy functional of induced charge density which enables the replacement of the expensive solution of the Poisson equation at each simulation step with an on-the-fly computation of polarization effects. Our simulations track the exact induced density at all times and demonstrate excellent energy conservation. The method is applied to study models of a charged colloid in polar solvent, ions near a liquid-liquid emulsion droplet, and charged biological macromolecule in aqueous solution. Results for ionic density profiles for different dielectric contrasts, ion concentrations, ion valencies, and different interfacial shapes are presented.   

Monte Carlo approaches for a particle at a diffusivity interface and the ``Ito-Stratonovich dilemma''

Diffusion of a particle in a fluid is often described by the overdamped Langevin equation (OLE). However, when the fluid is inhomogeneous, the stochastic term in the OLE is ambiguous (the ``Ito-Stratonovich dilemma''). Different interpretations of this term correspond to different stochastic calculi that may be appropriate in different physical situations. Concentrating on the case when two fluids with different viscosities are separated by a sharp interface, we develop two lattice Monte Carlo algorithms, both giving the choice between calculi (including Ito, Stratonovich, and ``isothermal''). We validate the algorithms considering a 1D system with the interface in the middle between two walls and particles starting at the interface and comparing the simulation results to both theory and molecular dynamics simulations, with Langevin Dynamics corresponding to isothermal and Brownian Dynamics to Ito calculi. This simple system turns out to have surprisingly rich behavior. The algorithms have also been applied to a model of polymer translocation.   

Application of atomic-orbital projections to the study of the electronic properties of metal-organic frameworks

Metal-organic frameworks (MOF) are a new class of artificial crystalline materials. Because of their flexibility for synthesis and instrinsic ultrahigh surface area and porosity, MOFs show superior performance in gas storage, catalysis, and sensing applications. We use an efficient projection of plane-wave wavefunctions onto atomic orbitals for studying the electronic properties of these intriguing materials. The present scheme harnesses the robust periodic algorithms and systematic convergence of the plane-wave method for an atomistic electronic (Landauer conductance) and chemical (charge transfer, bond and atomic charge) analysis that provides guidelines for the design of MOF electronic materials.