Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session A19: Focus Session: Theory and Simulations of Macromolecules I - Self Consistent Field Theory |
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Sponsoring Units: DPOLY Chair: Roland Faller, University of California, Davis Room: 404 |
Monday, March 3, 2014 8:00AM - 8:12AM |
A19.00001: Fluctuating Field-Theoretic Polymer Simulations of Multispecies Melts and Composites Kris Delaney, Wei Li, Dominik Duechs, Glenn Fredrickson We discuss computational strategies for conducting efficient and stable beyond-mean-field simulations of complex multi-species block polymer melts and composites, with composition fluctuations included through complex Langevin sampling. Our framework is applicable to assemblies of polymer chains of a variety of architectures with interactions introduced through a matrix of Flory-Huggins parameters. We demonstrate the stability, efficiency, and accuracy of a multi-species exchange mapping, and apply the method to the study of fluctuation-induced microphase structures in blends and composites. [Preview Abstract] |
Monday, March 3, 2014 8:12AM - 8:24AM |
A19.00002: Theoretical Basis of Monte-Carlo Field Theoretic Simulations David Morse, Mark Matsen, Pawel Stasiak Monte-Carlo field theoretic simulations (MC-FTS) of incompressible polymer models rely on a rather poorly understood approximation to the complex-Langevin field theoretic simulation (CL-FTS) method of Fredrickson and coworkers, but yield results that appear to be both surprisingly accurate and much more easily interpreted than the results of CL-FTS simulations. Specifically, two of us (Stasiak and Matsen) have shown [1] that results of CL-FT simulations exhibit a simple dependence on spatial resolution (grid-size) that can analytically corrected for to obtain results that are independent of grid spacing, in which the relationship between the effective $\chi$ parameter and the simulation input parameter is given by a simple analytic formula. We give theoretical analysis that explains the accuracy of the method, the nature of its errors, and the reasons for this simple dependence on spatial resolution. We show that a much more complicated dependence on spatial resolution or interaction range is expected in full CL-FT simulations. Our analysis suggests a simple modification of the CL-FT method that should improve its accuracy without effecting its efficiency or other favorable properties. [1] P. Stasiak and M.W. Matsen, {\it Macromolecules} {\bf 46}, 8037 (2013) [Preview Abstract] |
Monday, March 3, 2014 8:24AM - 8:36AM |
A19.00003: Directing the self-assembly of copolymers into a metastable complex network phase via a deep and rapid quench Marcus Mueller, De-Wen Sun The free-energy landscape of self-assembling copolymer systems is characterized by a multitude of metastable minima. Using particle-based simulations of a soft, coarse-grained model we explore opportunities to reproducibly direct the spontaneous ordering of these self-assembling systems into a metastable complex network morphology -- specifically, Schoen's I-WP periodic minimal surface -- starting from a highly unstable state that is generated by a rapid expansion. This process-controlled self-assembly provides an alternative to fine-tuning molecular architecture or blending for fabricating complex network structures. Comparing our particle-based simulation results to recently developed free-energy techniques we critically assess their ability to predict spontaneous formation and highlight the importance of non-equilibrium molecular conformations in the starting state and the local conservation of density. [Preview Abstract] |
Monday, March 3, 2014 8:36AM - 8:48AM |
A19.00004: A massively parallel space-time formulation for SCFT David Ackerman, Baskar Ganapathysubramanian We present a massively parallel, scalable Self Consistent Field Theory framework for modeling multi block copolymers. This is based on a finite-element based real-space implementation - which enables investigating complex, non-periodic domains - integrated into a space-time formulation. A space time formulation allows the implementation of a posteriori error analysis to ensure rigorous error bounds on the propagator. The space-time formulation increases the computation problem size but dramatically enhances the scalability of the problem. We show scaling up to 45,000 processors. The system remains tractable through the use of high order integration schemes which allow a coarser chain model while retaining accuracy of lower order schemes. This framework is applied to rod-coil diblock copolymers utilizing a worm-like chain model. Results of this modeling on complex surfaces (spheres, tori) are presented. [Preview Abstract] |
Monday, March 3, 2014 8:48AM - 9:00AM |
A19.00005: Short Polymer Modeling using Self-Consistent Integral Equation Method Yeongyoon Kim, So Jung Park, Jaeup Kim Self-consistent field theory (SCFT) is an excellent mean field theoretical tool for predicting the morphologies of polymer based materials. In the standard SCFT, the polymer is modeled as a Gaussian chain which is suitable for a polymer of high molecular weight, but not necessarily for a polymer of low molecular weight. In order to overcome this limitation, Matsen and coworkers have recently developed SCFT of discrete polymer chains in which one polymer is modeled as finite number of beads joined by freely jointed bonds of fixed length. In their model, the diffusion equation of the canonical SCFT is replaced by an iterative integral equation, and the full spectral method is used for the production of the phase diagram of short block copolymers. In this study, for the finite length chain problem, we apply pseudospectral method which is the most efficient numerical scheme to solve the iterative integral equation. We use this new numerical method to investigate two different types of polymer bonds: spring-beads model and freely-jointed chain model. By comparing these results with those of the Gaussian chain model, the influences on the morphologies of diblock copolymer melts due to the chain length and the type of bonds are examined. [Preview Abstract] |
Monday, March 3, 2014 9:00AM - 9:12AM |
A19.00006: Liquid-state integral equations via the self-consistent field approach Issei Nakamura, Zhen-Gang Wang We develop liquid-state integral equations via the self-consistent field approach. Taking electrolytes and van der waals fluids as examples, we provide a generic procedure to bridge the longstanding gap between the self-consistent field theory and other multi-scale theories such as the density functional theory and the integral equation theory, and thus a major improvement on the statistical field theory. Our new self-consistent filed theory simultaneously accounts for many important features in soft matters, the molecular interactions at an atomic scale that are expressed beyond a mean-field form, the equation of state, the liquid-vapor phase coexistence, and the oscillatory behavior of the pair distribution function in a liquid phase and the monotonic decay of the pair distribution function in a gas phase. [Preview Abstract] |
Monday, March 3, 2014 9:12AM - 9:24AM |
A19.00007: Effective potentials for multiscale representations of polymer melts Marina Guenza, James McCarty, Jeremy Copperman, Anthony Clark Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. We present an analytical expression for the effective potential between a pair of coarse-grained units, for a polymer liquid where each chain is represented as a collection of interpenetrating soft coarse-grained units, with a variable number of units, $n_b$, of size $N_b$. The potential is characterized by a long tail, slowly decaying with characteristic scaling exponent of $N_b^{1/4}$. This general result applies to any coarse-grained model of polymer melts with units larger than the persistence length. It is our contention that with a reasonable molecular model along with the correct parameters, both structural and thermodynamic properties can be simultaneously preserved in coarse-graining, at variable length of the unit size, without the need of recurring to any numerical re-optimization scheme. The effect of the potential on the structural and dynamical properties of polymer melts will be illustrated. [Preview Abstract] |
Monday, March 3, 2014 9:24AM - 9:36AM |
A19.00008: Coherent States Formulation of Polymer Field Theory Xingkun Man, Kris Delaney, Michael Villet, Henri Orland, Glenn Fredrickson We introduce a stable and efficient complex Langevin scheme to enable the first direct numerical simulations of the coheret-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields and the action of the field theory has a fully explicit, semi-local and finite-order polynomial character. We present the route for deriving CS canonical ensemble theories, and a method for studying asymptotically long polymer chains with composition fluctuations fully included using a simplified field theory in the ground-state-dominance approximation. The formalism is potentially applicable for conducting systematic coarse-graining and numerical renormalization-group studies [Preview Abstract] |
Monday, March 3, 2014 9:36AM - 9:48AM |
A19.00009: Semi-flexible polymer brush confined in a nanoslit: A high performance single chain in mean field simulation study Jiuzhou Tang, Xinghua Zhang, Dadong Yan We develop a single chain in mean field simulation method based on worm-like chain model for investigating the compression effect of semi-flexible polymer brush. For the commonly used self-consistent field theory (SCFT) based on the Gaussian chain model, the compression of the polymer brush leads to an isotropic deformation of the chain. However, for the case of high grafting density, the nematic phase will be formed even in a flexible brush. SCFT with gaussian chain model cannot provide any prediction on this property. Therefore, all the effects from the compression of nematic phase were totally ignored in the previous theoretical studies. In present work, the response of nematic polymer brush to the compression along the nematic axis is studied by applying a high performance single chain in mean field simulation. Our results predict that for the semi-flexible polymer chain under compression, the nematic order director of polymer brush reorient, leading to a XY-model-like lateral rotational symmetry breaking. The quasistatic analysis of the compressing and the relaxing of the confinement indicates that this symmetry breaking corresponds to a first order phase transition. [Preview Abstract] |
Monday, March 3, 2014 9:48AM - 10:00AM |
A19.00010: Exponential Time Differencing Methods for Numerical Self-Consistent Field Theory Yi-Xin Liu, Hong-Dong Zhang We present a fast and accurate numerical method for self-consistent field theory (SCFT) studies of polymer systems. For polymers in bulk, periodic boundary conditions are used. For confined polymers, the confining walls with or without preferential interactions with polymers, are modeled by appropriate non-periodic boundary conditions, which avoids the use of surface field terms and the mask technique in a conventional approach. Then the modified diffusion equations subject to these boundary conditions are solved by an exponential time differencing method with Fourier collocation and Chebyshev collocation for periodic and non-periodic boundary conditions, respectively. It exhibits fourth-order accuracy in time and spectral accuracy in space. The performance of this method is examined in comparison with the operator splitting pseudospectral methods. Numerical experiments show that the time differencing method is more efficient than the operator splitting methods in high accuracy SCFT calculations. Applications of this method to polymer brushes, block copolymers both in bulk and under confinement are demonstrated. [Preview Abstract] |
Monday, March 3, 2014 10:00AM - 10:12AM |
A19.00011: DPD with effective pair potential from integral equation theory of molecular liquids Alexander Kobryn, Dragan Nikoli\'{c}, Olga Lyubimova, Sergey Gusarov, Andriy Kovalenko A coarsening method of soft matter systems in solution is presented, in which the coarse grained (CG) force field is determined based on the statistical mechanical, integral equation theory of molecular liquids in interaction site representation, also known as reference interaction site model (RISM). Coarse graining is accomplished by a structure-matching procedure for solute CG beads without solvent that reproduces the corresponding distribution of all-atom solute in solvent obtained from RISM. Termed as an effective pair potential, the introduced potential of interaction between CG beads includes the effect of solvent and is used in dissipative particle dynamics (DPD) instead of the conservative force potential defined heuristically. It enables high flexibility in specifying the composition of solute CG beads and allows excluding solvent from explicit consideration in DPD. The suggested CG molecular model has been tested computationally and is shown to be a useful tool in investigating both structural and dynamic properties of polymer solutions and a promising platform for studies of macromolecular, supramolecular, and biomolecular systems in solution that require thermodynamic consistency, high accuracy, and computational efficiency. [Preview Abstract] |
Monday, March 3, 2014 10:12AM - 10:24AM |
A19.00012: Coarse-grain Tunable Dissipative Particle Dynamics: Droplet Dynamics in Micro- and Nano-emulsions Arman Boromand, Joao Maia Due to the multiscale phenomena in droplet dynamics from single droplets to highly concentrated emulsions (HCE) on one hand and complexity of the problem on the other hand, there is a need for a mesoscale simulation technique to capture the right underlying physics in these systems. This makes Dissipative Particle Dynamics (DPD) a suitable candidate, since it is capable of capturing microscopic phenomena and provide comparison to macroscopic simulations and experiments, within a reasonable calculation time compared to Molecular Dynamics (MD). In this presentation, we focus on the interplay between droplet size and the stress level in shear flows for three different combinations: Newtonian/non-Newtonian droplet in Newtonian/non-Newtonian matrix. The geometrical changes in these three cases will be compared to macroscopic models and experimental results and the validity of this mesoscopic simulation will be discussed. In addition, the dependency of surface tension to droplet size in the case of Newtonian droplets in Newtonian matrix is shown and the effect of this term on the dynamics of nanoscopic droplets is discussed. For the case of non-Newtonian droplets, their dynamics is studied for polymer chains with different molecular weight and chain characteristics. [Preview Abstract] |
Monday, March 3, 2014 10:24AM - 11:00AM |
A19.00013: Self-consistent field theory of wormlike chains and its applications in polymer physics Invited Speaker: Jeff Z.Y. Chen In recent years, a whole body of knowledge has been built on the structural and conformational properties of polymers, based on the Gaussian description of polymer statistics. Whether we are dealing with a single polymer or spatially inhomogeneous polymer systems, the solution of the self-consistent field theory has been one of the central focuses of theoretical studies. A wormlike-chain model, which differs from a Gaussian-chain model by using a bond-bending energy rather than monomer-monomer stretching energy, is more suitable for dealing with semiflexible polymers; a self-consistent field theory can be built for systems where both spatial inhomogeneity and orientational ordering need simultaneously considered. The wormlike chain model captures a number of physical features of a polymer system that go beyond those described by a Gaussian-chain model. A wormlike-chain based self-consistent field theory can be used to study the structural properties within the length scale smaller than the persistence length and the length scale where the polymer is strongly extended to an almost fully stretched conformation. As well, such a theory can be used to study a system where the orientational properties of polymer segments are important such as a liquid-crystal system. In this talk, we review the progress in solving the self-consistent field theory of wormlike chains for various physical problems and specifically discuss two recent examples of the applications of the theory: (a) the influence of chain rigidity on the phase diagram of AB diblock copolymers [Y. Jiang and J. Z. Y. Chen, Phys. Rev. Lett. \textbf{110}, 138305 (2013); Phys. Rev. E \textbf{88}, 042603 (2013) ]; and (b) liquid-crystal defect structures in confined geometry [J. Z. Y. Chen, Soft Matter \textbf{9}, 10921 (2013)]. As well, we address the question that under what physical conditions, the self-consistent field theory of wormlike chains recovers the theory of Gaussian chains. [Preview Abstract] |
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