Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session Q18: Theory and Simulation I |
Hide Abstracts |
Sponsoring Units: DPOLY Chair: August Bosse, National Institute of Standards and Technology Room: 319 |
Wednesday, March 18, 2009 11:15AM - 11:27AM |
Q18.00001: Design of Thermoplastic Elastomers with Self-Consistent Mean Field Theory: Radial (ABA)$_n$ and A(BA)$_n$ Miktoarm Architectures Nathaniel Lynd, Folusho Oyerokun, Donal O'Donoghue, Dale Handlin, Glenn Fredrickson Two thermoplastic elastomer designs were evaluated using self-consistent mean field theory. The phase diagram of a radial (A$_1$BA$_2$)$_n$ block copolymer was calculated at $ \chi N$ = 40 per arm as a function of composition ($\emph{f}_A$) and asymmetry between the A end-blocks ($\tau = N_{A1}/(N_{A1}+N_{A2})$). Significant deflection of the phase boundaries towards larger $\emph{f}_A$ occurred for asymmetric triblock copolymers ($\tau\approx 0.15$ and $ \tau\approx 0.90$) due to the interplay between bidispersity and chain-pullout of the A-blocks. The phase diagram of an A$_1$(BA$_2$)$_n$ miktoarm star triblock copolymer was also investigated as a function of $\emph{f}_A$ and $\tau$ at $\chi N$ = 40 per A$_1$BA$_2$ unit. Similar deflections in phase boundaries towards higher $\emph{f}_A$ resulted. [Preview Abstract] |
Wednesday, March 18, 2009 11:27AM - 11:39AM |
Q18.00002: Unified mathematical model for linear viscoelastic predictions of linear monodisperse and polydisperse and branched polymers. Renat Khaliullin, Jay Schieber We present an application of a single-chain mean-field model for entangled linear blends and star-branched systems. Slip-links instead of tubes are employed. The entanglements on a chain are destroyed by two coupled relaxation processes: so-called sliding dynamics; and relaxation of the environment, so-called constraint dynamics. The constraint dynamics are implemented by destruction and creation of the entanglements in the middle of the chain in a way statistically self consistent with sliding dynamics. In contrast to previous tube models, Rouse dynamics is completely avoided. Nonetheless, the implementation of constraint dynamics in tube models is different for linear and branched chains; the slip-link model shows no need for modification of constraint dynamics. Moreover, our slip-link model requires a single fitting parameter $\tau_{\rm K}$ that depends on the temperature of the melt, but not on chain length. The parameter can be fixed from a single fit to linear viscoelastic data. In addition, for branched polymers the branch point movements are determined by the free energy, so that its position is allowed to fluctuation, and even slide through the slip-links. The resulting model exhibits primitive-path fluctuations and chain stretching, so could be applied to flow and generalized to more complicated branches or cross-linked networks without significant modifications. [Preview Abstract] |
Wednesday, March 18, 2009 11:39AM - 11:51AM |
Q18.00003: Self-assembly of rod coil block copolymers under confinement Manas Shah, Venkat Ganesan The interplay of microphase separation and liquid crystalline ordering in rod-coil block copolymers leads to formation of complex morphologies distinct from that of conventional flexible block copolymer phases. In order to be used for organic electronic applications such as photovoltaic cells, rod-coil block copolymers must be patterned into thin films. The final morphology and the nature of orientation of rod units would now depend (in addition to the constituent interactions) on the interactions of the blocks with the confining surfaces. We combine the self-consistent field theory models of rod-coil block copolymers in a thin film framework to understand the effect of confinement on the morphology and the nature of orientation of rod-units. Also for nearly symmetric rod-coil copolymers, we analyze the parallel -- perpendicular lamellae transitions using a free energy framework. Also, we consider morphologies of such block copolymers (and blends) which can be utilized for higher device efficiency in photovoltaic cells. [Preview Abstract] |
Wednesday, March 18, 2009 11:51AM - 12:03PM |
Q18.00004: Theoretically Informed Particle-Based Simulations of Polymers in Arbitrary Ensembles Darin Pike, Francois Detcheverry, Marcus Mueller, Juan de Pablo A new, particle-based formalism is proposed for simulation of polymeric materials, where the interaction energy is given by the standard functional employed in field-theoretic models. The main features of the proposed formalism reside in its ability to enable simulations at constant stress or constant pressure, thereby permitting accurate estimation of free energies and phase boundaries. The usefulness of the proposed approach is illustrated in a series of thermodynamic property calculations from Monte Carlo simulations in the nVT, nPT, semi-grandcanonical and Gibbs ensembles. In particular, we consider the phase separation of a binary homopolymer blend and a symmetric diblock copolymer. For the blend, we present results for the phase diagram and the critical point of the model. For symmetric copolymers, we study the distribution of local stress in lamellae and the location of the first-order transition from a disordered to a lamellar phase. [Preview Abstract] |
Wednesday, March 18, 2009 12:03PM - 12:15PM |
Q18.00005: Fields Help Particles -- Fast Off-Lattice Monte Carlo Simulations of Soft Materials Yuhua Yin, Qiang Wang Conventional molecular simulations of multi-chain systems are hindered by ``hard'' excluded-volume interactions (e.g., the Lennard-Jones potential in off-lattice simulations and the self- and mutual-avoiding walks in lattice simulations). Although such interactions are necessary for obtaining realistic dynamics, they significantly slow down the chain relaxation towards equilibrium configurations and efficient sampling of the configurational space. The idea of fast off-lattice Monte Carlo (FOMC) simulations is to perform particle-based Monte Carlo simulations in continuum with a Hamiltonian commonly used in polymer field theories, where individual polymer segments are modeled as ``soft'' particles whose interaction energy is finite when they overlap. This leads to much faster chain relaxation and better sampling of the configurational space. Furthermore, using the same Hamiltonian in both polymer field theories and FOMC simulations enables quantitative comparisons between them without any parameter-fitting to unambiguously reveal the effects of fluctuations and correlations in the system. Here we demonstrate these great advantages of FOMC simulations using several model systems. [Preview Abstract] |
Wednesday, March 18, 2009 12:15PM - 12:27PM |
Q18.00006: Particles vs. Fields -- Finite-Range Interactions in Polymer Field Theories Qiang Wang Recently, we proposed a particle-based, fast off-lattice Monte Carlo (FOMC) simulation that uses the same Hamiltonian as in polymer field theories, which has great advantages over conventional molecular simulations. However, the continuous Gaussian chain model and $\delta$-function interactions widely used in polymer field theories (such as the self-consistent field theory) cannot be directly used in FOMC simulations. We therefore extend the field theories to the discrete Gaussian chain model and finite-range interactions. Taking the microphase separation of diblock copolymers as an example, a finite interaction range increases the order-disorder transition from the well-known result of $\chi N \approx 10.5$, as well as the bulk lamellar period. More importantly, this work allows direct comparisons between the polymer field theories and FOMC simulations without any parameter-fitting to unambiguously and quantitatively reveal the effects of fluctuations and correlations in the system. [Preview Abstract] |
Wednesday, March 18, 2009 12:27PM - 12:39PM |
Q18.00007: Mean Field Theory for Ionomer Melts Erica Saltzman, Sanat Kumar Single Chain Mean Field theory is applied to melts of charged polymers. Control parameters include temperature, chain length, and monomer density. Equilibrium variations of polymer conformational, translational, and rotational degrees of freedom and counterion translational degrees of freedom are studied; in particular we are interested in conformational and morphological transitions which occur in ionomers with changes in temperature and apparently dominate their macroscale behavior. The equilibrium theoretical results, which are compared to simulation findings of low temperature condensation of chains and counterions to form ordered sheets of charges, form the basis for stochastic theories which model the temporal evolution of these structures, with immediate relevance to measurable dynamic properties. [Preview Abstract] |
Wednesday, March 18, 2009 12:39PM - 12:51PM |
Q18.00008: Equilibrium and Beyond Equilibrium Properties of Polyelectrolytes - Ewald-Like Approach for Fluctuating Hydrodynamic and Electrostatic Interactions Juan P. Hernandez-Ortiz, Michael D. Graham, Juan J. de Pablo A method is proposed for self consistent simulations of the equilibrium and beyond equlibrium structures and transport properties of polyelectrolytes in solution. The method incorporates solution of the Nernst-Planck diffusion equation for ions and counter-ions within the solvent, and simultaneous description of fluctuating hydrodynamic interactions by means of a Green's function formalism. The proposed approach generalizes our $O(N)$ general geometry Ewald-like method to simultaneous treatment of hydrodynamics and electrostatics. With this method, we examine the transport properties of polyelectrolytes solutions at rest and in various flow fields, and we make direct comparisons to results from explicit ion Brownian dynamics simulations and experimental observations. [Preview Abstract] |
Wednesday, March 18, 2009 12:51PM - 1:03PM |
Q18.00009: Self Consistent Field Theory Study of the Effect of Grafting Density on the Height of a Weak Polyelectrolyte Brush Kevin Witte, You-Yeon Won The height of weakly basic polyelectrolyte brushes in the osmotic brush regime is studied as a function of the grafting density using a numerical self-consistent field (SCF) theory derived from the (semi-) grand canonical partition function. The theory is shown to properly account for the local nature of the charge equilibrium and to be able to capture the basic behaviors of polyelectrolyte brushes, including brush height variation with salt concentration and scaling with respect to degree of polymerization. However, we find, in agreement with recent experiments, that the scaling of brush height with grafting density is qualitatively different than that predicted by basic scaling arguments. This difference is attributed to the relative strength of electrostatic type interactions compared to finite segment size packing constraints. [Preview Abstract] |
Wednesday, March 18, 2009 1:03PM - 1:15PM |
Q18.00010: Adsorption and depletion of polyelectrolytes in charged Dadong Yan, Xingkun Man, An-Chang Shi Self-consistent field theory is presented to study the adsorption of flexible polyelectrolytes (PE) onto uniformly oppositely charged cylinders. We focus on the curvature effect of adsorbing surface on the adsorption-depletion phase- transition-like behavior. In terms of the scaling expression of the critical quantities, i.e., the salt concentration, the charge fraction of PE chain and the area density of surface charge, at the adsorption-depletion transition point have been obtained. Moreover, we find a critical line for the dependence of the critical radius of cylinder on the salt concentration, which separates the adsorption and depletion states. The theoretical results are in good agreement with the Monte Carlo simulations and the experimental results. [Preview Abstract] |
Wednesday, March 18, 2009 1:15PM - 1:27PM |
Q18.00011: Field-Based Modeling and Simulation of Interfacial Fluctuations in Block Copolymers August Bosse The Edwards-model-based, field-theoretic simulation framework of Fredrickson is the cutting edge methodology in coarse-grained, field-based simulation of fluctuating copolymer systems [V. Ganesan and G.H. Fredrickson, \textit{Europhys. Lett.} \textbf{55}, 814 (2001); G.H. Fredrickson, V. Ganesan, and F. Drolet, \textit{Macromolecules} \textbf{35}, 16 (2001)]. Coarse graining the standard Edwards model yields the classic phenomenological ``phase field'' model of Ohta and Kawasaki [T. Ohta and K. Kawasaki, \textit{Macromolecules} \textbf{19}, 2621 (1986)]. Further coarse graining, coupled with the assumption of weak segregation, yields the ubiquitous Leibler-Brazovskii-Fredrickson-Helfand model [G.H. Fredrickson and E. Helfand, \textit{J. Chem. Phys.} \textbf{87}, 697 (1987)]. Each of these field-based models is capable of capturing thermodynamic fluctuations; however, the applicability of each model depends on the quench depth, the molecular weight, and the composition of the constituent copolymers, among other variables. Here we examine fluctuation effects in, and limitations of field-based models in the context of measuring interfacial fluctuations in a two dimensional diblock copolymer melt. [Preview Abstract] |
Wednesday, March 18, 2009 1:27PM - 1:39PM |
Q18.00012: Variational Coarse-Graining of Discretized Field Theories of Fluids Michael Villet, Glenn Fredrickson Statistical field theory models have proven to be valuable tools for studying the equilibrium behavior of polymeric fluids, but direct simulation of these field theories without use of the mean field approximation is computationally demanding. Computational resources can be extended to simulate larger systems by discretizing the field variables with a coarsely spaced lattice, but indelicate coarse graining risks truncation of important short-wavelength physics. We introduce a variational method for systematically coarse-graining discretized field theoretic models of fluids while minimizing this truncation error. [Preview Abstract] |
Wednesday, March 18, 2009 1:39PM - 1:51PM |
Q18.00013: Simulation of Fluctuations in Diblock Copolymer Melts: Testing an Alternative to the Fredrickson-Helfand Theory Jian Qin, David Morse Simulations of a bead-spring model of disordered diblock copolymer melts have been conducted to test a renormalized one-loop (ROL) theory of composition fluctuations recently proposed by the authors. The simulations use hybrid Monte Carlo (MC) / Molecular Dynamics (MD), reptation and double-rebriding moves, combined with replica exchange, to relax chain conformations. The quantitative comparison of simulation results with theory relies on a procedure that uses perturbation theory to independently identify the self-consistent-field (or RPA) interaction parameter. For the modest chain lengths accessible to simulations ($N \leq 64$ here), results for the maximum $S(q^{*})$ of the structure factor are quite different from both RPA and Fredrickson-Helfand predictions, but agree very well with renormalized one-loop predictions. [Preview Abstract] |
Wednesday, March 18, 2009 1:51PM - 2:03PM |
Q18.00014: Microphase Separation Induced by the Differential Monomer-Monomer Interactions in Diblock Copolymer/Homopolymer Blends Jiajia Zhou, An-Chang Shi Phase diagrams of blends composed of diblock copolymer (AB) and homopolymer (C) are obtained using the random phase approximation and self-consistent field theory. Emphasis is placed on the special case where all three monomer pairs, A/B, B/C and C/A, are miscible. Despite the miscibility of the binary pairs, a close-loop immiscible region exists in the AB/C blends when the pair interaction parameters are sufficiently different. Inside the close-loop, the system undergoes microphase separation, exhibiting different morphologies. This phenomenon is enhanced when the homopolymer interacts much strongly to one of the blocks of the diblock copolymer. The theoretical results are used to explain some recent experiments. [Preview Abstract] |
Wednesday, March 18, 2009 2:03PM - 2:15PM |
Q18.00015: Study on the strength of intermonomer interactions for PS-b-PMMA using compressible RPA Hyungju Ahn, Du Yeol Ryu, Youngmin Kim, Kwang Hyun Song, Kyung Wook Kwon, Junhan Cho PS-$b$-PMMA copolymer is one of the most useful nanoscopic materials that can be used as passive electronic materials, and also as templates and scaffolds. It is then clear that the better knowledge on the strength of intermonomer interactions for the PS-$b$-PMMA is of great importance in fabricating nanomaterials from it. Using a compressible random-phase approximation (RPA) theory, we discuss mainly the second-order vertex function in the compressible Landau free energy. This vertex function is involved in the exchange energy between self and cross interactions along with the self interaction difference. Ordering transition temperatures are predicted and compared with experimental measurements using small-angle X-ray scattering (SAXS) and depolarized light scattering. A close relationship between barotropicity (ordering upon pressurization) and the energetic vertex term for the copolymer is argued. [Preview Abstract] |
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