Hydrophobic Polyelectrolytes in Better Polar Solvent. Structure and Chain Conformation as seen by Saxs and Sans

We demonstrate in this paper the influence of solvent quality on the structure of the semi-dilute solution of a hydrophobic polyelectrolyte, partially sulfonated Poly-Styrene Sulfonate. Two solvents are used: (i) one mixture of water and an organic solvent: THF, which is also slightly polar; (ii) DMSO, a polar organic solvent. In case (i), it is shown by SAXS study that the structure - namely the scattering from all chains, characterised by a maximum ("polyelectrolyte peak"), of the aqueous hydrophobic polyelectrolyte solutions (PSS) depends on the solvent quality through the added amount of organic solvent THF. This dependence is more pronounced when the sulfonation rate is low (more hydrophobic polyelectrolyte). It is proposed that when THF is added, the chain conformation evolves from the pearl necklace shape already reported in pure water, towards the conformation in pure water for fully sulfonated PSS, which is string-like as also reported previously. On the contrary, for a hydrophilic polyelectrolyte, AMAMPS, no evolution occurs with added THF in the aqueous solution. In case (ii), it is shown directly by SANS study that PSS can behave as a classical solvophilic polyelectrolyte when dissolved in an organic polar solvent such as DMSO: the structure (total scattering) as well as the form factor (single chain scattering measured by SANS using the Zero Average Contrast method) of the PSS chains is independent of the charge content in agreement with Manning condensation, and identical to the one of a fully charged PSS chain in pure water, which has a classical polyelectrolyte behaviour in the semi-dilute regime

Elasticity in strongly interacting soft solids: polyelectrolyte network

This paper discusses the elastic behavior of a very long crosslinked polyelectrolyte chain (Debye-H\"uckel chain), which is weakly charged. Therefore the response of the crosslinked chain (network) on an external constant force $f$ acting on the ends of the chain is considered. A selfconsistent variational computation of an effective field theory is employed. It is shown, that the modulus of the polyelectrolyte network has two parts: the first term represents the usual entropy elasticity of connected flexible chains and the second term takes into account the electrostatic interaction of the monomers. It is proportional to the squared crosslink density and the Debye - screening parameter.Comment: submitted for publication to PR

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied minimizing the free energy $F_N$, depending on $N(N-1)/2$ trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length $2^4<N<2^{16}$ and for an open chain of length $2^4<N<2^9$ in poor and theta solvent conditions, including a Coulomb repulsion between the monomers. In theta solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer--monomer correlation function, reminiscence of necklace formation in poor solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented.Comment: submitted to EPJE (soft matter

Like-Charge Colloid-Polyelectrolyte Complexation

We investigate the complexation of a highly charged sphere with a long flexible polyelectrolyte, \textit{both negatively charged} in salt free environment. Electroneutrality is insured by the presence of divalent counterions. Using molecular dynamics (MD) within the framework of the primitive model, we consider different Coulomb coupling regimes. At strong Coulomb coupling we find that the adsorbed chain is always confined to the colloidal surface but forms different conformations that depend on the linear charge density of the chain. A mechanism involving the polyelectrolyte \textit{overcharging} is proposed to explain these structures. At intermediate Coulomb coupling, the chain conformation starts to become three-dimensional, and we observe multilayering of the highly charged chain while for lower charge density the chain wraps around the colloid. At weak Coulomb coupling, corresponding to an aqueous solvent, we still find like-charge complexation. In this latter case the chain conformation exhibits loops.Comment: 18 pages, 13 (main) eps figures, RevTeX4, submitted to J. Chem. Phy

Simulations and scattering functions of polyelectrolyte-macroion complexes

Using Monte Carlo simulations of complex formation between a polyelectrolyte chain and an oppositely charged macroion, we calculated the scattering function of the polyelectrolyte chain. We investigated the case of the isolated polyelectrolyte chain and studied the effect and influence of key parameters such as the ionic concentration of the solution, polyelectrolyte length and intrinsic rigidity on the scattering function. Then, we focused on the polyelectrolyte-macroion complex by calculating the structure factor S(q) of the adsorbed polyelectrolyte chain. Typical conformations ranging from coils, extended chains to solenoids are revealed and the corresponding S(q) analysed. The effects of ionic concentration, chain length and intrinsic rigidity and relative size ratio between the polyelectrolyte and the macroion are investigated. Important effects on the structure factor of the adsorbed polyelectrolyte are observed when the macroion is partially or totally wrapped by the polyelectrolyte. Distance correlations between the polyelectrolyte monomer positions at the surface of the macroion induce the formation of peaks in the fractal regime of S(q). For semiflexible chains, when solenoid conformations are observed, the position of the peaks in the fractal regime corresponds directly to the separation distance between the turns. The formation of a protruding tail in solution is also observed through the formation in the fractal regime of a linear domai

Radial Distribution Function of Rodlike Polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in a rodlike configuration. We investigate the validity of the concept of electrostatic persistence length for uniformly charged wormlike chains for both screened and unscreened Coulomb interactions. We find that the distribution function of a polyelectrolyte often differs significantly from the distribution function of a wormlike chain.Comment: RevTeX 4, 7 pages, 6 figure

Adsorption and Depletion of Polyelectrolytes from Charged Surfaces

Mean-field theory and scaling arguments are presented to model polyelectrolyte adsorption from semi-dilute solutions onto charged surfaces. Using numerical solutions of the mean-field equations, we show that adsorption exists only for highly charged polyelectrolytes in low salt solutions. Simple scaling laws for the width of the adsorbed layer and the amount of adsorbed polyelectrolyte are obtained. In other situations the polyelectrolyte chains will deplete from the surface. For fixed surface potential conditions, the salt concentration at the adsorption--depletion crossover scales as the product of the charged fraction of the polyelectrolyte f and the surface potential, while for a fixed surface charge density, \sigma, it scales as \sigma^{2/3}f^{2/3}, in agreement with single-chain results.Comment: 12 pages, 8 figures, final version to be published in J. Chem. Phys. 200

Polyelectrolyte Networks: Elasticity, Swelling, and the Violation of the Flory - Rehner Hypothesis

This paper discusses the elastic behavior of polyelectrolyte networks. The deformation behavior of single polyelectrolyte chains is discussed. It is shown that a strong coupling between interactions and chain elasticity exists. The theory of the complete crosslinked networks shows that the Flory - Rehner - Hypothesis (FRH) does not hold. The modulus contains contributions from the classical rubber elasticity and from the electrostatic interactions. The equilibrium degree of swelling is estimated by the assumption of a $c^{*}$-network.Comment: submitted to Computational and Theoretical Polymer Scienc