Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session V29: Polymer Theory and Simulation I: General |
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Sponsoring Units: DPOLY Chair: Cameron Abrams, Drexel University Room: LACC 504 |
Thursday, March 24, 2005 11:15AM - 11:27AM |
V29.00001: Assessing the Application of the Flory Interaction Parameter Michael Tambasco, Jane Lipson, Julia Higgins The Flory-Huggins interaction parameter is the most commonly implemented tool for describing binary interactions of polymer blends, yet to what extent does this widespread method of analysis yield valuable thermodynamic insight? Making use of an alternate simple theory, we follow a different, less ambiguous route, with the goal of achieving richer connections between the microscopic theoretical description and macroscopic thermodynamic behavior. To this end we analyze experimental data, including results from neutron scattering experiments, cloud point curves and solubility analysis, with the goal of understanding the effects of deuteration as well as the consequences of altering molecular weight, composition and pressure. [Preview Abstract] |
Thursday, March 24, 2005 11:27AM - 11:39AM |
V29.00002: Optimizing a Mesoscale Model for Polyisoprene-Polystyrene Melts Qi Sun, Roland Faller Coarse-graining, the systematic mapping from the atomistic to meso-scale has made significant progress in pure polymers or polymers in solution. However, it has not yet been attempted in melts of polymer mixtures. Our project is aiming at building a multiscale model of Polyisoprene (PI) and Polystyrene (PS) mixtures. The positions of the meso-scale interaction centers (superatoms) are chosen in order to produce a single peaked bond distribution on the meso-scale as well as a harmonic bond stretching potential. For PI, twelve atoms are joined into one superatom positioned in the middle of the single carbon-carbon bond. The superatom center for PS is at the backbone carbon connected to the side ring and represents sixteen atoms. We apply the newly developed ``Inverted Boltzmann Method'' to derive numerical potentials from atomistic models where the interaction potential is iteratively optimized against the atomistic structure using potentials of mean force. We optimize the iteration process and analyze the concentration and temperature dependencies of the evolving potential, investigating further what parameters induce the phase separation in longer chains and miscibility in shorter chains. All the work eventually leads to a better understanding of the mechanisms governing material properties. [Preview Abstract] |
Thursday, March 24, 2005 11:39AM - 11:51AM |
V29.00003: Chemical structure-optical property understanding in bisphenyls and substituted polycarbonates by molecular simulations: Role of polarizabilities and conformations Upendra Natarajan, M.S. Sulatha We present calculations of polarizability tensors, optical anisotropy of organic molecules, repeating units and polymer chains of several bisphenyls, bisphenol carbonates and polycarbonates with a variety of chemical substitutions.$^{1,2}$ Theoretical calculations of polarizabilities and optical birefringence of several newer structures having specific side-group substitutions which render low birefringence, not previously reported, is also shown here. Our method combines VOSRIS scheme$^{3}$, molecular geometry and conformations from force-field simulations and accurate anisotropic polarizability tensors. Aliphatic, aliphatic aromatic and cycloaliphatic substitutions reduce optical anisotropy in relation to bisphenol A polycarbonate. Calculated $\langle $\textit{$\gamma $}$^{2}\rangle $/$x$ of these structurally modified polycarbonates$^{2}$ follows linear behavior with respect to experimentally observed melt stress-optical coefficient ($C_{m})$. \begin{enumerate} \item \textit{J. Phys. Chem. A}, \textbf{107}, 97 (2003) \item \textit{Macromolecules}, \textbf{36}, 2944 (2003) \item P.J. Flory, \textit{Statistical Mechanics of Chain Molecules}, Wiley Interscience, New York (1969) \end{enumerate} [Preview Abstract] |
Thursday, March 24, 2005 11:51AM - 12:03PM |
V29.00004: Semiflexible chain statistics with fixed end orientations Andrew Spakowitz, Lei Zhang, Niles Pierce, Zhen-Gang Wang The simplest model of a semiflexible polymer is the wormlike chain model, which describes the chain as a deformable thread whose bending energy is quadratic in the chain curvature. Using the wormlike chain model to predict polymer behavior in a number of scenarios requires the end-to-end distribution function, which gives the statistics for the position of the end of the chain. We find exact expressions for this fundamental solution incorporating the end positions and the tangent orientations of the end points. Our results for the end-to-end distribution function in Fourier-Laplace space adopt the form of infinite continued fractions, which emerge upon noting the hierarchical structure of the moment-based expansion. We use these results to view the end-to-end distribution function for a wormlike chain in two dimensions with one end pointed in a fixed direction and the other end free. As we progress from high to low rigidity, the end-to-end distribution function shifts from being peaked at a location pointed along the end tangent vector, implying a straightened chain, to the peak being located at zero end separation, as in the Gaussian limit. The crossover between these limiting behaviors exhibits a double- peaked end-to-end distribution function. We discuss our results in the context of looping of a semiflexible polymer, which is relevant in a number of DNA-related phenomena. [Preview Abstract] |
Thursday, March 24, 2005 12:03PM - 12:15PM |
V29.00005: Characterizing knots in polymer coil and globule phases Peter Virnau, Mehran Kardar, Yacov Kantor We examine the statistics of knots with numerical simulations of a model polymer, spanning high temperature (coil) and low temperature (globule) phases. All monomers in the model interact via a Lennard-Jones potential, while adjacent beads are connected by flexible springs. Although relatively simple, this model provides a realistic description of polyethylene, thus relating the simulation results to specific polymers. Equilibrated configurations are generated by a combination of pivot, ``slithering snake'' and local Monte Carlo moves. The knot type is determined by applying Taylor's reduction method$^{1}$ and calculating the Alexander polynomial after connecting the end monomers (of an open polymer). We find that knots are common in the globule phase and under confinement, but rare in coils. We also associate a typical size with the knots, and find knots to be small (tight) in the swollen phase, and large (loose) in the dense phase. $^{1}$ W.R. Taylor, Nature \textbf{406}, 916 (2000) [Preview Abstract] |
Thursday, March 24, 2005 12:15PM - 12:27PM |
V29.00006: Cyclization of Rouse Chains at Long and Short Time Scales Chuck Yeung, Barry Friedman We have investigated cyclization of a Rouse chain at long and short times by a Langevin dynamics simulation method. We measure $S(t)$, the fraction of non-reacted chains, for chains lengths ranging from $Z=5$ to $Z=800$. Comparison is made with the closure approximations of Wilemski and Fixman and Doi and the renormalization group (RG) arguments of Friedman and O'Shaughnessy. The ratio of the long time reaction time scale to the Rouse time, $T= \tau/\tau_R$ is predicted to approach a constant value for long chains independent of the reaction capture range. However, the two theoretical approaches predict different values for $T^{*}$ the long chain limit of $T$. Our simulations find that $T^{*} \approx 1.75$ much closer to the RG prediction of $\pi^3/16=1.94$ than the Wilemski-Fixman-Doi prediction of $T^{*} = 2.17$. More convincing evidence for the RG analysis is obtained by comparing the short time decay of $S(t)$ to long time results. The RG analysis predicts that $S(t)$ should decay as a power law at early times and that the exponent in the power law $\alpha$ is related to $T$ by simple expression with no free parameters. Our simulations find remarkable agreement with this parameter free prediction even for relatively short chains. [Preview Abstract] |
Thursday, March 24, 2005 12:27PM - 12:39PM |
V29.00007: A Minimal Model for the Helix-Coil Transition of Worm-like Polymers Gustavo A. Carri, Vikas Varshney, Taner E. Dirama, Taner Z. Sen We present a geometric approach to the simulation of the Helix-Coil transition in wormlike polymers. In our model, the polymer is treated as a Freely Rotating Chain with hard-core repulsion between beads. The conformational state (helix or coil) of each bead is determined by the value of its torsion. If the difference between the torsion of a bead and the one of the perfect helix is less than a cutoff value, then the bead is part of a helical domain and carries a negative energy, otherwise it is part of a random coil. We have simulated these concepts using the Wang-Landau algorithm where the density of states depends on two parameters: the number of beads in the helical state and the number of interfaces. In this talk I show that these simple ideas can account for the cooperativity of the transition explicitly and capture the known conformational, configurational and thermodynamic properties correctly. Moreover, these concepts have important theoretical implications since they lead naturally to a field-theoretic Hamiltonian of the Edwards' type that might be useful for problems of current experimental interest. [Preview Abstract] |
Thursday, March 24, 2005 12:39PM - 12:51PM |
V29.00008: Solvent-induced collapse of a helical semiflexible polymer Vikas Varshney, Gustavo A. Carri It has been stated that ``the class of materials richest in the occurrence of phase transitions are polymers'' (E. A. Di Marzio, \textit{Prog. Polym. Sci}. \textbf{24}, 329 (1999)). This wealth of phase transitions is unique to polymers and is a consequence of the myriad of possible ways of coupling the basic ten classes of polymeric phase transitions into pairs, triplets and so forth. Two of these transitions are the helix-coil and coil-globule transitions. In this talk we explore the coupling of these two transitions, its molecular origins and physical consequences. For this purpose, we extend a recently developed model of helical polymers to describe the effect of solvent quality and solve it using Monte Carlo simulations based on the Wang and Landau algorithm. We find a very rich phase diagram consisting of 6 phases characterized by very specific conformations of the chain, i.e., a perfect helix, a random coil, a globule or other globular states with residual helical strands. We study the phase boundaries and provide further insight into the physics of the problem with a detailed analysis of the conformational and thermodynamic properties of the polymer chain. [Preview Abstract] |
Thursday, March 24, 2005 12:51PM - 1:03PM |
V29.00009: Long Range Bond-Bond Correlations in Polymer Melts Sergei Obukhov, Joachim Wittmer, Hendrick Meyer, Jorg Baschnagel, Albert Johner, Letitia Mattioni, Marcus M\"uller, Alexander Semenov It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long range memory between subsequent bonds. This has been anticipated already in the 1950s by Flory in his famous ``ideality hypothesis.'' The absence of memory means that the correlation function, $C(n)$, of two bonds separated by $n$ monomers along the chain should exponentially decay with $n$. This is the standard basis for defining an important experimental measure of chain stiffness, the persistence length. In our work we present numerical results and theoretical arguments, demonstrating a non-exponential, long ranged decay of $C(n)$ (see figure). Suggesting a profound analogy with the well-known long range velocity correlations in liquids and granular materials we find $C(n)$ to decay algebraically as $n^{-3/2}$. As a consequence, the operational definition of the persistent length should be carefully revisited. [Preview Abstract] |
Thursday, March 24, 2005 1:03PM - 1:15PM |
V29.00010: Hydrodynamic Self Consistent Field Theory David Hall, Turab Lookman, Sanjoy Banerjee We have developed a new computational technique used to model the flow of polymeric fluids that combines the strongest features of self consistent field theory and viscoelastic hydrodynamics. We will demonstrate the utility of this approach by applying it to the phase separation of block copolymer melts. [Preview Abstract] |
Thursday, March 24, 2005 1:15PM - 1:27PM |
V29.00011: Variable Cell Shape Methods in Polymer Field Theory Simulations Glenn Fredrickson, Jean-Louis Barrat, Scott Sides We present a new method for carrying out field-theoretic simulations of inhomogeneous polymeric fluids under conditions of prescribed external stress, allowing for shape changes of the simulation cell. A compact expression for the deviatoric stress tensor is derived in terms the chain propagator, and is used to drive changes in cell shape according to a simple relaxation scheme. The method allows fully relaxed, stress-free configurations to be obtained, even in non-trivial morphologies, and enables the study of morphology transitions induced by external stresses. [Preview Abstract] |
Thursday, March 24, 2005 1:27PM - 1:39PM |
V29.00012: Unit cell relaxation with the SCFT of block copolymers Eric Cochran, Scott Sides, Dave Morse, Glenn Fredrickson We employ the pseudo-spectral implementation of the self-consistent field theory (SCFT) of linear block copolymer melts to model their equilibrium phase behavior. Here we focus on \textit{unit cell} calculations in which saddle-point configurations are determined iteratively through the simultaneous relaxation of the potential fields and the shape of the simulation volume, which is a parallelepiped of arbitrary dimension. The former is accomplished through either an explicit Euler or semi-implicit Seidel type relaxation of the potential fields. Relaxational cell shape dynamics are dictated by the deviatoric stress tensor, which we compute according to the Parrinello-Rahman-Ray technique recently adapted to SCFT by Barrat and coworkers. Defect-free structures may be obtained by using an initial configuration that is constrained to a particular crystallographic symmetry. [Preview Abstract] |
Thursday, March 24, 2005 1:39PM - 1:51PM |
V29.00013: Novel Approach to Study of the Localization of Plastic Relaxation Events in Plastic Deformation of Amorphous Polymers Qing Peng, Marcel Utz The length scale of the elementary processes of plastic relaxation of amorphous polymers is still an open question. The computer simulation of plastic deformation gives the details of the plastic relaxation events. To study the localization of these events, a novel approach based on Delaunay tesselation and Fast Fourier Transforms techniques is invented. Using this novel approach we have studied the localization of atomic strain in discrete relaxation events during plastic deformation of amorphous polymers. The strain in such relaxation events is highly localized in regions of atomic dimensions. The implications of the novel approach and our simulation results for a universal theory of plasticity of amorphous polymers will be discussed. [Preview Abstract] |
Thursday, March 24, 2005 1:51PM - 2:03PM |
V29.00014: Defect Diffusion, Free Volume and Positron Annihilation Spectroscopy Michael Shlesinger, John Bendler, John Fontanella, J. Bartos, O. Sausa, J. Kristiak Employing an anomalous defect diffusion theory that was devised to explain stretched exponential relaxation and the accompanying Vogel type law, a new theory of free volume in glasses and glass-forming liquids is developed assuming a temperature/pressure dependent population of mobile single defects and immobile defects clusters. The defects encapsulate free volume and a defect cluster is found to possess less free volume than its separated constituent defect parts. The theory is applied to free volumes obtained from positron annihilation lifetime spectroscopy (PALS) studies of poly(propylene glycol) (PPG) 4000 over the wide temperature range from 15 K to 320 K and gives a good description of the free volume vs. temperature. The theory also reasonably predicts the variation of the ortho-positronium (o-Ps) intensity. [Preview Abstract] |
Thursday, March 24, 2005 2:03PM - 2:15PM |
V29.00015: Dynamic Heterogeneity and Glassy Dynamics of Polymer Melts Erica Saltzman, Kenneth Schweizer A statistical mechanical theory of collective dynamic barriers, slow segmental relaxation and the glass transition of polymer melts is developed by combining and extending methods of mode coupling, density functional and activated hopping transport theories. Analytic and numeric results are obtained for the crossover temperature, collective barrier, segmental relaxation time and glass transition temperature, and their relation to structural and thermodynamic properties of the polymer melt is established. A Gaussian ``trap model'' is constructed for the consequences of nanometer scale density fluctuations and barrier fluctuations. It predicts nonexponential relaxation with material and temperature dependent stretching exponents and decoupling of translational and relaxational processes. Correlations between the dynamic fragility, stretching exponent and degree of decoupling are emerge which are consistent with experiments. Heterogeneity effects are much smaller for chain level properties thereby providing a basis for the failure of time-temperature superposition for polymer melts close to T$_{g}$. [Preview Abstract] |
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