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Anomalous bending of a polyelectrolyte.

We report on a study of the shape of a stiff, charged rod that is subjected to equal and opposite force couples at its two ends. Unlike a neutral elastic rod, which forms a constant curvature configuration under such influences, the charged rod tends to flatten in the interior and accumulate the curvature in the end points, to maximally reduce the electrostatic self-repulsion. The effect of this nonuniform bending on the effective elasticity and on the statistical conformations of a fluctuating charged rod is discussed. An alternative definition for the electrostatic persistence length is suggested. This definition is found to be consistent with a corresponding length that can be deduced from the end-to-end distribution function of a fluctuating polyelectrolyte.

Journal Article↗

Computer simulation study on the swelling of a polyelectrolyte gel by a Stockmayer solvent.

The swelling of a model polyelectrolyte gel is studied via three-dimensional molecular dynamics simulations, taking into account the counterions and the solvent explicitly. Each network bead carries a charge q(*). The counterion charge is -q(*), and thus the total system is neutral. The solvent is modeled via a Stockmayer fluid, i.e., each solvent particle is a point dipole plus a Lennard-Jones interaction center. A "two-box--particle transfer" simulation method is applied to calculate the swelling ratio of the network as well as the counterion mobility. The swelling of the network shows a broad maximum as a function of q(*) at T(*)(r)=T(*)/T(*)(c)=1.05 and P(*)(r)=P(*)/P(*)(c)=1.0. Here, T(*)(c) and P(*)(c) are the critical temperature and the critical pressure of the pure Stockmayer solvent, respectively, with dipole moments given by mu(*2)=1.0, 2.0, 3.0, and 4.0. The residence time of the counterions is calculated, showing a strong coupling to the charged network beads (condensation) as q(*) increases. Additional simulations at three different charge strengths (i.e., q(*)=0.5, 3.5, and 8.6) illustrate the complicated swelling behavior of the network under supercritical and subcritical conditions.

Journal Article↗

Electrical conductivity of polyelectrolyte solutions in the presence of added salt: The role of the solvent quality factor in light of a scaling approach.

The effects of added salt on the electrical conductivity behavior of a polyelectrolyte solution are described in light of the scaling approach recently proposed by Dobrynin and Rubinstein [Macromolecules 28, 1859 (1995); 32, 915 (1999)], taking into account the influence of the solvent quality factor. The coupling between the conformation of the chain and the local charge distribution, giving rise to different conductometric behaviors, has been investigated under different conditions, in a wide concentration range of added salt. The polyion equivalent conductances lambda(p) have been evaluated in different concentration regimes for a hydrophilic polyion in good solvent condition and compared with the experimental values obtained from electrical conductivity measurements. The agreement is rather good in the wide range of concentration of the added salt investigated. In the case of poor solvent conditions, we find the appropriate expressions for the electrical conductivity when the polyion chain consists into collapsed beads alternating with stretched segments in the framework of the necklace globule model.

Electric Conductivity↗

Cohesive energy, stability, and structural transitions in polyelectrolyte bundles.

A lattice of uniformly charged, infinitesimally thin rods decorated with an ordered array of counterions exhibits anomalous behavior as the spacing between the rods is varied. In particular, the counterion lattice undergoes a sequence of structural shearing or "tilting," phase transformations as the spacing between the rods decreases. The potential implications of this behavior with respect to the packaging of biologically relevant polyelectrolytic molecules are commented upon.

Biophysical Phenomena↗

Theory of polyelectrolytes in solvents.

Using a continuum description, we account for fluctuations in the ionic solvent surrounding a Gaussian, charged chain and derive an effective short-ranged potential between the charges on the chain. This potential is repulsive at short separations and attractive at longer distances. The chemical potential can be derived from this potential. When the chemical potential is positive, it leads to a meltlike state. For a vanishingly low concentration of segments, this state exhibits scaling behavior for long chains. The Flory exponent characterizing the radius of gyration for long chains is calculated to be approximately 0.63, close to the classical value obtained for second order phase transitions. For short chains, the radius of gyration varies linearly with N, the chain length, and is sensitive to the parameters in the interaction potential. The linear dependence on the chain length N indicates a stiff behavior. The chemical potential associated with this interaction changes sign, when the screening length in the ionic solvent exceeds a critical value. This leads to condensation when the chemical potential is negative. In this state, it is shown using the mean-field approximation that spherical and toroidal condensed shapes can be obtained. The thickness of the toroidal polyelectrolyte is studied as a function of the parameters of the model, such as the ionic screening length. The predictions of this theory should be amenable to experimental verification.

Journal Article↗

Mechanism of protein binding to spherical polyelectrolyte brushes studied in situ using two-photon excitation fluorescence fluctuation spectroscopy.

We used two-photon excitation fluorescence fluctuation spectroscopy with photon counting histogram (PCH) analysis as a new tool to study the binding of globular proteins to colloidal particles in situ. Whereas fluorescence fluctuations are traditionally evaluated by calculating the autocorrelation function (fluorescence correlation spectroscopy), a complementary PCH analysis has been performed in this study which is advantageous when particle concentrations of a multicomponent system are of interest and the particles can be distinguished through particle brightness differences. The binding of two proteins, staphylococcal nuclease (SNase) and bovine serum albumin (BSA), to spherical polyelectrolyte brushes (SPB) was measured as a function of protein concentration and ionic strength of the solution at pH-values where SNase and BSA are positively and negatively charged, respectively. It has been found that SNase and BSA strongly bind to the SPB regardless of the protein charge. When the ionic strength of the solution is raised to 100 mM, the SPB become resistant to both proteins. These findings provide further evidence for a binding mechanism where the proteins are mainly driven to the SPB by the "counterion evaporation" force, while Coulomb interactions play a minor role. The results of this study characterize the potential of SPB as a new class of carrier particles for proteins whose use in biotechnological applications appears to be rewarding.

Acrylic Resins↗

Invariance of density correlations with charge density in polyelectrolyte solutions.

We present a theory for the equilibrium structure of polyelectrolyte solutions. A simple and general optimization method is introduced that enables theories such as the random phase approximation to handle the strong repulsive forces present in such systems. Quantitative comparison is made with data from recent neutron-scattering experiments of randomly charged, hydrophilic polymers in salt-free, semidilute solution at various charge densities. We show that the invariance observed at high charge fraction may be the result of polymer-polymer correlations, rather than the conventional explanations involving counterion condensation.

Journal Article↗

Electrophoresis of large polyelectrolyte-coated colloidal particles.

We perform electrophoretic mobility mu measurements of spherical colloidal particles coated with a charged polyelectrolyte shell versus 1:1 electrolyte concentration c. Instead of the expected Smoluchowski scaling law mu approximately c(- 1 / 2) for large kappaa, with kappa the inverse of the Debye length, we find that mu scales as mu approximately c(- 1 / 3). We account for this result using a general theory for the electrophoresis of soft particles [H. Ohshima, Adv. Colloid Interface Sci. 62, 189 (1995)] combined with the salt concentration dependence of the shell thickness, as described by Pincus [P. Pincus, Macromolecules 24, 2912 (1991)].

Journal Article↗

Large equilibrium clusters in low-density aqueous suspensions of polyelectrolyte-liposome complexes: a phenomenological model.

In this paper, we revisit some of our previous results together with further experimental evidences for the existence of large equilibrium clusters in low-density aqueous colloidal suspensions, resulting from the screening of charged spherical macroions by oppositely charged linear polyelectrolytes. The aggregation process is described by a simple phenomenological model where aggregates interact via a long-range repulsion Yukawa potential and some supports to the equilibrium properties of the resulting aggregates, on the basis of dynamic light scattering, zeta potential, and transmission electron microscopy techniques, have been provided.

Colloids↗

Boundary condition of polyelectrolyte adsorption.

The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.

Journal Article↗

Lattice-gas model of DNA charge inversion by a positively charged polyelectrolyte.

The model of DNA charge inversion by Nguyen and Shklovskii [T. T. Nguyen and B. I. Shklovskii, Phys. Rev. Lett. 89, 018101 (2002)] is extended. A single double-helix strand of DNA is represented by a lattice of negative charges at the positions of the protruding oxygens of the phosphates along the DNA backbone, and the adsorbed polyelectrolyte molecules are represented by charged dimers. A lattice-gas model is used in which dimers adsorbing either parallel or perpendicular to the lattice are treated as separate species, and the model allows for vacancies between adsorbed species. The mean field theory used is formulated as a saddle-point approximation of the exact functional integral representation of the grand canonical partition function, opening the way for the inclusion of the effects of charge fluctuation corrections.

Computer Simulation↗

Electrophoresis of a polyelectrolyte through a nanopore.

A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and that classical continuum electrostatics and hydrodynamics may be considered applicable. An explicit formula for the translocation speed as a function of the pore geometry and other physical parameters is obtained and is shown to be consistent with experimental measurements on DNA translocation through nanopores in silicon membranes. Experiments also show a weak dependence of the translocation speed on polymer length that is not accounted for by the present model. It is hypothesized that this is due to secondary effects that are neglected here.

Computer Simulation↗

Adsorption of polyelectrolytes at an oppositely charged surface

We develop a scaling theory of polyelectrolyte adsorption at an oppositely charged surface. At low surface charge densities, the thickness of the adsorbed layer is determined by the balance between electrostatic attraction to the charged surface and chain entropy. At high surface charge densities, it is determined by the balance between electrostatic attraction and short-range monomer-monomer repulsion. These different stabilizing mechanisms result in the nonmonotonic dependence of the layer thickness on the surface charge density.

Journal Article↗

Conformations and interactions of star-branched polyelectrolytes.

Combining monomer-resolved molecular dynamics simulations with a theory based on a variational free energy, we calculate the conformational properties and the effective interactions of star-branched polyelectrolytes for a large variety of arm numbers, degrees of polymerization, and charge fractions, with and without added salt. We find quantitative agreement between theory and simulation and put forward analytical expressions that allow the calculation of the interaction between such macromolecules.

Journal Article↗

Stretching single stranded DNA, a model polyelectrolyte.

The elastic properties of single stranded (ss)DNA, studied by pulling on an isolated molecule, are shown to agree with a recent model of ssDNA that takes into account base pairings and screened electrostatic repulsion of the phosphodiester backbone. By an appropriate physicochemical treatment, the pairing interactions were suppressed and ssDNA used as an experimental model for a generic polyelectrolyte. The elastic behavior of such an altered ssDNA deviates strongly from the behavior of an ideal polymer. This deviation is shown to result from the elasticity of the chain and its electrostatic self-avoiding interactions.

DNA, Single-Stranded↗

Polyelectrolytes in the presence of multivalent ions: gelation versus segregation.

We analyze solutions of strongly charged chains bridged by linkers such as multivalent ions. The gelation induced by the strong short range electrostatic attractions is dramatically suppressed by the long range electrostatic correlations due to the charge along the non-cross-linked monomers and ions. A modified Debye-Hückel approach of cross-linked clusters of charged chains is used to determine the mean field gelation transition self-consistently. Highly dilute polyelectrolyte solutions tend to segregate macroscopically. Semidilute solutions can form gels if the Bjerrum length l(B) and the distance between neighboring charged monomers along the chain b are both greater than the ion size a.

Electrolytes↗

Thickness and density profiles of polyelectrolyte brushes: dependence on grafting density and salt concentration.

We have performed neutron reflectivity measurements on a monolayer of charged diblock copolymers in a Langmuir trough, and determined precise density profiles of the polyelectrolyte brush at different densities. We obtain profiles in good agreement with existing self-consistent field computations, both for the osmotic and the salted brush regime. We show that the osmotic brush's thickness increases with density.

Biomimetic Materials↗

Do spherical polyelectrolyte brushes interdigitate?

The structure of spherical micelles of the diblock copolymer poly(styrene-block-acrylic acid) in water was investigated with small angle neutron scattering and contrast matching. We have monitored intermicelle correlation and the extension of the polyelectrolyte chains in the coronal layer through the overlap concentration. Irrespective of ionic strength, the corona shrinks with increasing packing fraction. Furthermore, at high charge and minimal screening conditions, the corona layers interpenetrate once the volume fraction exceeds the critical value 0.53+/-0.02.

Journal Article↗