Session Y25: Charged and Ion-Containing Polymers: Computation

A New Necklace Model

We have developed a necklace model of hydrophobic polyelectrolytes in which the necklace structure consisting of polymeric globules (beads) connected by extended sections of the chain (strings of monomers) appears as a result of the counterion condensation and is caused by the balance of the correlation-induced attraction of condensed counterions to charged monomers and electrostatic repulsion between uncompensated charges. The size of the beads increases with polymer concentration while their number per chain decreases. We predict coexistence of necklaces with different number of beads on a polymer backbone at any polymer concentration. To test this necklace model we performed molecular dynamics simulations of polyelectrolyte chains with degree of polymerization N varying from 25 to 373 and with fraction of charged monomers f=1/3, 1/2 and 1 in poor solvent conditions for polymer backbone. The observed concentration dependence of the bead size supports the assumption of the counterion condensation origin of the necklace structure. The overlap concentration is almost independent of the degree of polymerization for weakly charged chains (f=1/3). For strongly charged chains with f=1 the overlap concentration follows the normal N-dependence observed for polyelectrolyte solutions in q and good solvent regimes for polymer backbone. In semidilute solutions the correlation length of fully charged chains is inversely proportional to square root of polymer concentration.   

Electrostatic Complexation between Membrane and Colloid

As a primary model of endocytosis, the electrostatic complexation between membrane and colloid is studied. Using a simple approximation, the membrane shape can be determined easily without solving the nonlinear differential shape equation, which facilitates the consideration of electrostatic effects. The phase diagram for the electrostatic complexes can be constructed in terms of the rescaled stretching tension, adhesion strength, and the screening length. By referring to the phase diagram, the possible phase transitions due to the variations of the electrostatic factors (including the charge density, and the screening length) are discussed.   

Molecular Dynamics Simulations of Multilayer Polyelectrolyte Films

We have performed molecular dynamics simulations of multilayer assembly of oppositely charged polyelectrolytes at charged surfaces. The multilayer build-up was achieved through sequential adsorption of charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The strong electrostatic attraction between oppositely charged polyelectrolytes at each deposition step is a driving force behind the nanometer-scale multilayer growth. Our simulations have shown that a charge reversal after each deposition step is critical for steady multilayer growth and that there is a linear increase in amount of polymer adsorbed after the first few deposition steps. There is substantial intermixing between chains adsorbed during different deposition steps within multilayer film. Despite significant chain intermixing, however, there are almost perfect periodic oscillations in local composition of positively and negatively charged polymers in the adsorbed film. We show that the film thickness, polymer surface coverage exhibit strong correlation with the strength of electrostatic and short-range interactions.   

Langevin dynamics simulations of dsDNA translocation through synthetic nanopores

We have modeled dsDNA using a coarse-grained bead-spring method to study its behavior as it is driven by a potential gradient through a nanoscopic pore located in a rigid membrane. Using the Poisson-Nernst-Plank formalism, we calculate traces of the ionic current corresponding to the translocation process and compare our findings with experimental results. In agreement with recent experiments, we find that the dsDNA frequently translocates in a folded configuration. We explore the role of chain length, potential difference and pore diameter on the frequency of translocation events, average residence time, electrophoretic mobility and percentage of unfolded events.   

Modeling Layer-by-Layer Assembly of Flexible Polyelectrolytes

Using a continuum self-consistent field theory, we have modelled the sequential process of layer-by-layer assembly of flexible polyelectrolytes on flat surfaces as a series of kinetically trapped states. Up to 60 depositions of oppositely charged polyelectrolytes are performed, each followed by a washing step. The multilayer has a three-zone structure. An exponential growth is found for the first several layers, followed by a linear growth for subsequent layers evolving towards a steady state. Each layer inverts the total charge of the multilayer film (including the bare substrate charge). While adjacent layers are highly interpenetrating, stratification can be seen for every four or more layers. We have also examined the effects of surface charge density, bulk salt concentration, and solvent quality on the thickness and internal structure of the multilayer. Our results agree with most experimental findings on polyelectrolyte layer-by-layer assembly.   

Simulations of comb polyelectrolytes

Using Langevin dynamics, we have characterized the effects on backbone stretching by systematically varying grafting density, grafted-chain length, and backbone length. Chain persistence length, conformational asphericity, and counterion and monomer density profiles were determined. We have found that increasing grafting density leads to increases in both chain persistence length and overall asphericity. Increasing the length of side chains also creates a stiffer backbone, but overall asphericity is decreased. Simulation results will be compared with theory.   

Spanning the gap between strong and weak-coupling electrostatics for charged rods

I present a method to compute the distribution of counterions near a charged macromolecule at intermediate coupling. The procedure involves decomposing the Coulomb interaction into a separate short and long distance piece. The long distance piece is treated within mean-field theory and a strong-coupling expansion is performed for the long distance part. The theory recovers both the strong and weak coupling results in the appropriate limit for charged surfaces. Furthermore, it is accurate for describing the density at intermediate coupling. I derive from this a two-fluid model for a charged rod with discrete charges along its center axis, making contact with previous models of discretely-charged rods.   

Electrostatic attraction between cationic-anionic assemblies with surface compositional heterogeneities

Biological assemblies of heterogenous cationic and anionic molecules with hydrophobic groups have important functional properties controlled by interdependencies of the architectures and the intermolecular interactions. The net incompatibility among chemically different charged components, which in water can be due to different degrees of hydrophobicity, promotes macroscopic segregation, while electrostatics promotes mixing of the charges into ionic crystal structure. This competition results in formation of surface charge domains. We analyze attractions among two cylindrical assemblies with surface charge heterogeneities. The compositional heterogeneities are correlated and strongly polarized in the presence of the second assembly. This leads to a strong attraction. The strength of the effective attraction is studied as a function of the distance for different values of the net incompatibility. We compare results of computer simulations and theory.   

Relevance of Solvent Characteristics on Ion-Binding and the Structure Formation of Neutral Polymers in Electrolyte Solutions

Polymers carrying functional groups constituted of heteroatoms are omnipresent in biology and polymer technology, for example in the development of solid state polymer electrolytes. When dissolved in polar solvents, these polymers can coordinate ions that result in an effective transformation of the neutral polymer into a weakly charged polyelectrolyte as indicated by the characteristic changes in the polymers solution characteristics. In our contribution we discuss the implications of solvent characteristics -- i.e. dielectric constant and hydrogen bonding capacity -- and the ion-strength of the added electrolyte on the polymer-ion coordination as well as polymer solution characteristics. A mean-field model to predict the amount of ion-coordination is presented and validated for the particular case of poly(oxy ethylene)/salt solutions. The Random Phase Approximation (RPA) is applied to extract quantitative information about the coordination of ions to the polymer in solution from small-angle neutron scattering (SANS) data.   

Conformational Properties and Phase Behavior of Mixed Brushes between Charged and Neutral Polymers: SCF Modeling Using the Edwards Hamiltonian Approach

We present a theoretical study of the single-chain statistics and two-dimensional (2-D) phase behavior of mixed brushes composed of charged and non-charged polymers. We extend the Edwards Hamiltonian formulation for the Green function to investigation of mixed brushes containing a polyelectrolyte species through the incorporation of the combined electrostatic effects as an additional external field which can be self-consistently computed by a corresponding Poisson-Boltzmann-like equation. The resultant SCF equations were numerically analyzed to achieve results that are exact within the assumption of mean field. The 2-D phase behavior of the mixed brushes (assuming that the brushes are laterally mobile) was examined using the conventional free energy of mixing analysis. The predictions on the effects of such control variables as the brush hydrophilicity/hydrophobicity, surface grafting density, charge content of the polyelectrolyte species, and ionic strength of the medium on the conformation properties and phase behavior of the mixed brushes will be discussed.   

Electrostatic Origin of Single-Stranded Genome Packing in Viruses

We develop an electrostatic model for single-stranded RNA/DNA viruses that bind their genome via highly basic semiflexible peptide arms. We show that genome-capsid binding is dominated by non-specific electrostatic interactions, rather than actual amino-acid content. Proposed model explains many universal features of the viral genome. Good agreement is found with wide range of qualified wild-type and mutant viruses.   

Regimes of Conformational Transitions of Diblock Polyampholytes

Regimes of electrostatically-driven conformational transitions of diblock polyampholytes are investigated by scaling theory and molecular dynamics simulations. The coil-globule transition of a symmetric diblock polyampholyte is found to consist of three regimes identified with increasing interaction strength: (i) the folding regime where the electrostatic attraction causes the diblock chain to to fold through the overlap of the two blocks, while each block is slightly stretched by self-repulsion; (ii) the weak association regime which is the classical collapse of the chain into a globule dominated by the fluctuation-induced attractions between oppositely charged chain sections; (iii) the strong association regime that starts with direct binding of oppositely charged monomers (dipole formation), followed by a cascade of multipole formation leading to multiplets. The conformation of a charge-asymmetric diblock polyampholyte changes from extended polyelectrolyte structure, to tadpole-shape with a globular head and a polyelectrolyte tail, and then to polyelectrolyte structure with the variation of the ratio between the charges of the two blocks.   

Polyelectrolyte condensation by linear molecules of variable length: a grand-canonical Monte Carlo study

The condensation of like-charged polyelectrolytes has been observed to occur under the addition of a variety of oppositely-charged species, such as multivalent counterions, charged globular proteins, and even short chain molecules with monovalent end groups. Inspired by the latter, we study via computer simulations a prototypical polyelectrolyte bundle where condensation is induced by dumbbell-like charged molecules of variable length. We present results from a systematic investigation into the effects of the concentration of bundling agent on the stability of the system. We also consider the effect of changing the length of the dumbbells, as well as the surface charge density of the polyelectrolytes. Recent work\footnote{L. K. Sanders, C. Gu\'aqueta \emph{et al.}, Phys.\ Rev.\ Lett.\textbf{95}, 108302 (2005).} has illustrated the important role of the osmotic pressure exerted by the excess solution. In order to take this effect directly into account, we perform simulations in the grand-canonical ensemble, which allows us to equilibrate the bundle with an excess solution of dumbbell molecules at fixed chemical potential.