Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session H17: Focus Session: Theory and Simulation - Polyelectrolytes & Brushes |
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Sponsoring Units: DPOLY DCOMP Chair: Kevin Cavicchi, University of Akron Room: Colorado Convention Center 102 |
Tuesday, March 6, 2007 8:00AM - 8:36AM |
H17.00001: BREAK
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Tuesday, March 6, 2007 8:36AM - 8:48AM |
H17.00002: Wigner Crystallization of Chiral Polyelectrolyte Bundles Gregory Grason, Robijn Bruinsma We construct an effective model to describe the thermodynamics of the Wigner- crystalline state of polyvalent counterions absorbed within hexagonal bundles of chiral, rod-like macroions (such as DNA or filamentous actin). We argue that the ground state counterion configuration as well as the associated long-wavelength fluctuations about this state are characterized by a frustrated, antiferromagnetic XY {\it spin} Hamiltonian defined on the kagom\'e lattice. The unusual statistical mechanics associated with this model can be treated within a generalized, dual description of interacting vortices (or screw defects), revealing that generically Wigner-crystalline ground states are constructed of arrays of screw-like configurations of counterions which wind helically around the constitute macroions. Further, the dual description reveals that the ground state admits both {\it integer} and {\it fractional} screw-like defects as well as Ising- like fluctuations between domains of unlike chirality. We find that the molecular chirality of the macroions plays an important role in suppressing these domain fluctuations, and hence chirality itself becomes a critical parameter in melting behavior of the Wigner-crystalline state. [Preview Abstract] |
Tuesday, March 6, 2007 8:48AM - 9:00AM |
H17.00003: Variable length condensing agents in polyelectrolyte condensation Richard Guaqueta, Erik Luijten We use grand-canonical Monte Carlo simulations to study the role of the condensing agent in polyelectrolyte condensation. The rigid polyelectrolytes are modeled on the M13 and fd viruses, and (following recent experiments) the condensing agents are short divalent chains of variable length $\delta$ modeled on diamine molecules. We observe two different regimes of condensation as the length of the condensing agent varies, with the behavior at large $\delta$ characterized by significant alignment of the diamines with the polyelectrolytes. We also study the effect of the polyelectrolyte surface charge density $\sigma$, and find that the stability of the condensed phase varies nonmonotonically with $\sigma$, in accordance with the observation of two \emph{different} trends in experiments. [Preview Abstract] |
Tuesday, March 6, 2007 9:00AM - 9:12AM |
H17.00004: Field Theory of Polyelectrolyte Complexation Yuri Popov, Glenn Fredrickson We study polyanion-polycation solutions using a field-theoretic approach formulated in terms of auxiliary fields (conjugate to mass and charge densities). Within this framework, we derive exact Hamiltonians for a wide variety of systems: with implicit or explicit solvents, for symmetric or asymmetric polyions, with or without salt. By systematic expansion, we analytically obtain one-loop fluctuation corrections to the mean-field results for these systems in arbitrary dimensions. As an example, we study the symmetric salt-free polyanion-polycation mixture in implicit solvent. We demonstrate that this basic system and its phase diagram are described by three universal reduced variables. We obtain simple analytical expressions for thermodynamic quantities and structure factors, including two correlation lengths - Edwards's length and a polymer electrostatic length. We also conduct scaling analysis in dilute and semi-dilute regimes and show that the concentration of pair formation is exponentially small in polymer length. [Preview Abstract] |
Tuesday, March 6, 2007 9:12AM - 9:24AM |
H17.00005: Complexation in poly-electrolyte solutions: field theoretic simulations of fluctuation induced phase transition Jonghoon Lee, Yuri Popov, Glenn Fredrickson We study complexation phenomenon in symmetric poly-electrolyte solutions using field theoretic framework. The mean field approximation is incapable to capture the phase transition in the system. We performed large-scale field theoretic simulations using complex Langevin dynamics algorithm to include the field fluctuation effect. This allows us to study thermodynamics and structural properties of the complexes in detail and, ultimately, construct a phase diagram of the complexation transition, which is compared with the beyond-mean-field (one-loop) analytic result. [Preview Abstract] |
Tuesday, March 6, 2007 9:24AM - 9:36AM |
H17.00006: Rouse Dynamics of Polyelectrolyte Solutions: Molecular Dynamics Study Andrey Dobrynin, Qi Liao, Michael Rubinstein We performed molecular dynamics simulations of dilute and semidilute polyelectrolyte solutions to study Rouse dynamics of polyelectrolytes. Polyelectrolyte solutions are modeled by an ensemble of bead-spring chains of charged Lennard-Jones particles with explicit counterions. We show that the simulations of the Rouse dynamics give qualitatively similar results to the experimentally observed dynamics of polyelectrolyte solutions. Our simulations showed that the chain relaxation time depends nonmonotonically on polymer concentration. The chain relaxation time decreases with increasing polymer concentration in dilute solution. This decrease in the chain relaxation time is due to counterion condensation. In the semidilute solution regime the chain relaxation time decreases with polymer concentration as inverse square root of polymer concentration. In this concentration range the chain relaxation time follows the usual Rouse scaling dependence on the chain degree of polymerization. At very high polymer concentrations the chain relaxation time begins to increase with increasing the polymer concentration. The crossover polymer concentration to the new scaling regime is independent on the chain degree of polymerization. [Preview Abstract] |
Tuesday, March 6, 2007 9:36AM - 9:48AM |
H17.00007: Effect of Interfacial Curvature on the Miscibility of Mixed Charged and Neutral Polymer Brushes You-Yeon Won, Kevin Witte We present a theoretical study of the phase behavior of a mixture of neutral and polyelectrolyte polymers attached to a surface or interface in a brush configuration. The Edward's formalism for the Green's function is extended to incorporate electrostatic effects and allow for mixtures of mutually incompatible brushes. The resultant self-consistent field (SCF) equations are numerically evaluated for spherical and cylindrical geometries within the mean field approximation. Phase behavior of the surface constrained polymer mixture (assuming mobile grafting points) is explored by calculating the system free energy and applying the standard free energy of mixing analysis. The effect on the brush mixture miscibility of varying the surface/interface curvature at constant grafting density is extensively investigated. It is further demonstrated that the correlation between brush miscibility and curvature vary with the charge of the polyelectrolyte brushes. [Preview Abstract] |
Tuesday, March 6, 2007 9:48AM - 10:00AM |
H17.00008: Anisotropic Fluctuation Effects in Polyelectrolyte Adsorption Ying Jiang, Qiang Wang We have examined the fluctuation effects on the adsorption of flexible polyelectrolytes on flat substrates using the theory of anisotropic composition fluctuation. We expand the free energy functional in terms of perturbations around the self-consistent mean-field solution of the inhomogeneous system. Setting the functional derivatives with respect to the perturbations of the field variables to zero produces a set of self-consistent equations; the zeroth-order expansion corresponds to the mean-field result and the 2nd-order expansions represent the Gaussian fluctuations in the system. The composition fluctuations result in stronger charge inversion than obtained in our previous self-consistent field calculations for the same system. Our study shows that the fluctuation and correlation effects in the system give the predominant contributions to charge inversion, in agreement with other theoretical and experimental studies. [Preview Abstract] |
Tuesday, March 6, 2007 10:00AM - 10:12AM |
H17.00009: Local algorithms for Coulomb's law in molecular dynamics Joerg Rottler The computation of Coulombic interactions still forms one of the major bottlenecks in molecular dynamics simulations of soft and biologial materials. Most current fast Coulomb techniques rely on Fourier methods, but their parallel efficiency on standard compute clusters is not always ideal. In addition, they have difficulty dealing with inhomogeneous dielectric environments that one might like to treat in implicit solvent models. We discuss an attractive alternative, real-space approach that does not rely on Poisson's equation, but mediates the Coulomb interaction through a thermalized auxiliary field that is dynamically constrained to obey Gauss' law. Instead of globally optimizing the field configuration as in conventional approaches, the algorithm performs a partial integration over the transverse degrees of freedom of the electric field, which requires only local operations. The locality leads directly to linear (i.e. O(N)) scaling with the number of particles, implies excellent parallelizability and generalizes easily to inhomogenenous dielectrics without substantial overhead. We show that recent implementations of this method can yield an accuracy sufficient for atomistic simulations, calibrate its parallel efficiency and compare to standard Fourier methods. [Preview Abstract] |
Tuesday, March 6, 2007 10:12AM - 10:24AM |
H17.00010: ABSTRACT HAS BEEN MOVED TO N21.00014 |
Tuesday, March 6, 2007 10:24AM - 10:36AM |
H17.00011: Transitions of tethered polymer chains Jutta Luettmer-Strathmann, Federica Rampf, Wolfgang Paul, Kurt Binder Polymer chains near surfaces with attractive monomer surface interactions undergo a transition from three-dimensional to two- dimensional conformations as the temperature is lowered. In good solvent conditions, this is a well-known adsorption transition, which corresponds to a bicritical point in the infinite chain limit; it is continuous and the adsorption temperature is independent of the (net) interaction strength between monomers. In poor solvent, on the other hand, the transition is not well understood. In this work, we present simulation results for a flexible lattice model of a single chain tethered to a surface. A two-dimensional Wang- Landau algorithm was employed to obtain a density of states in the space of surface and monomer-monomer contacts for several chain lengths. The density of states was evaluated with interaction parameters spanning the range from good to poor solvent conditions and from repulsive to strongly attractive surfaces. Our results for good-solvent conditions show the expected adsorption transition. In poor solvent, we find a splitting of the adsorption transition into two main branches, which may be interpreted in terms of a drying and wetting transition, where the wetting transition proceeds through a series of layering transitions. [Preview Abstract] |
Tuesday, March 6, 2007 10:36AM - 10:48AM |
H17.00012: Finite-Stretching Corrections to the Strong-Stretching Theory of Polymer Brushes in Solvent Jaeup Kim, Mark Matsen Grafted polymers in solvent are naturally stretched and form a brush. Earlier theoretical approach known as strong-stretching theory (SST) has been very successful in predicting fundamental properties such as parabolic density profile and broad chain end distribution. A more rigorous self-consistent-field theory (SCFT) has shown good agreement with SST but it also revealed new features. For instance, there exists a proximal layer next to the substrate ($z=0$) where the polymer concentration $\phi(z)$ vanishes. Furthermore, a brush has an exponentially decaying tail region beyond the brush height $h$ predicted by SST. Due to the complexity of numerical approach few previous studies focused on these features. We have made a systematic analysis of the proximal layer shape and its effect on the free energy. The size of the proximal region $\mu$ scales as $1/h$ and the profile has a scaling symmetry. Polymer concentration $\phi(z)$ grows linearly near the grafting surface with a slope $6/Na^2$ when the integral of $\phi(z)$ is normalized to unity. Here $a$ is the statistical segment length and $N$ is its total number of segments per chain. A universal function $\overline{\phi}(x)$ is numerically found so that $\phi(z) \approx \mu \overline{\phi}(z/\mu)$ independent of $h$. We also investigated the shape of the tail region to which entropically excited chains contribute. [Preview Abstract] |
Tuesday, March 6, 2007 10:48AM - 11:00AM |
H17.00013: ABSTRACT WITHDRAWN |
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