On the Effective Charge of Hydrophobic Polyelectrolytes

One-dimensional colloidal model with dielectric inhomogeneity

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.

Chain conformation of poly(acrylic acid)-graft-poly(ethylene oxide)-graft-dodecyl in solution: an anomalous counter-ions condensation

A dielectric spectroscopy study on a polyelectrolyte in aqueous solutions, which contains hydrophobic groups in part of the side chains poly(acrylic acid)-graft-poly(ethylene oxide)-graft-dodecyl (PAA-g-PEO-g-dodecyl) is reported. A refined double layer polarization model was proposed to analyze the double dielectric relaxations in the dielectric spectra. Various electrical and structural parameters of the copolymers were obtained. Besides the crossover concentration, another turning point around 4 mg mL^-1 was identified through the analysis of all the dielectrical parameters including dielectric increment, relaxation time and correlation length. According to the scaling relationship between the correlation length and concentration, a necklace-like structure was predicted. In addition, 4 mg mL^-1 was proven to be the transition point between string-controlling with bead-controlling structure of the chains. In addition, the fraction of effective charges on the chains was illustrated by Ito's counter-ions fluctuation theory, as well as its linear dependence relationship with the zeta potential. Meanwhile, the counter-ions condensation behavior was consistent with the avalanche-like trend, which was predicted by theory for a hydrophobic polyelectrolyte with a necklace conformation. The results demonstrated that the electrostatic interactions were the main driving force of the necklace-like structure with pendant globules when the string-controlling structure was below 4 mg mL^-1. While hydrophobic interactions are the main driving force of the structure of bead-controlling above 4 mg mL^-1.

Dendritic polyelectrolytes revisited through the Poisson-Boltzmann-Flory theory and the Debye-Hückel approximation

The properties of a dendritic polyelectrolyte in equilibrium with a reservoir of monovalent salts are investigated using the cell model and the Poisson-Boltzmann-Flory theory. Within this approach we use the Debye-Hückel approximation to solve the Poisson-Boltzmann equation and minimize the semi-grand potential of the system with respect to the size of the molecule which enables us to inspect its conformations as well as the electric field, the ionic density profile, the overall charge density, the effective charge of the dendrimer and the osmotic pressure based on their response to the salt concentration and the dendrimer charge. The model predicts pronounced trapping of salt ions, a local charge neutrality and a zero electric field in the volume of the molecule as well as oscillations of the density profiles and the electric field in the vicinity of the dendrimer-bulk interface. As a result of ion trapping and screening of Coulomb interactions monovalent salts are found to have a minor effect on the size of the dendrimer. Specifically, the dendrimer exists in slightly swollen states as compared to the neutral molecule which indicates that the conformational properties of the polyelectrolyte depend weakly on monovalent salts. These observations harmonise with the equilibrium behavior of the dendrimer pressure, the internal pressure and the bulk pressure, respectively.

Dendritic polyelectrolytes as seen by the Poisson–Boltzmann–Flory theory

The conformational and electrostatic properties of dendritic polyelectrolytes accompanied by counterions are investigated using the Poisson–Boltzmann–Flory theory.

Regimes of electrostatic collapse of a highly charged polyelectrolyte in a poor solvent

We perform extensive molecular dynamics simulations of a highly charged, collapsed, flexible polyelectrolyte chain in a poor solvent for the case when the electrostatic interactions, characterized by the reduced Bjerrum length l_B, are strong. We find the existence of several sub-regimes in the dependence of the gyration radius of the chain R_g on l_B characterized by R_g ∼ l. In contrast to a good solvent, the exponent γ for a poor solvent crucially depends on the size and valency of the counterions. To explain the different sub-regimes, we generalize the existing counterion fluctuation theory by including a more complete account of all possible volume interactions in the free energy of the polyelectrolyte chain. We also show that the presence of condensed counterions modifies the effective attraction among the chain monomers and modulates the sign of the second virial coefficient under poor solvent conditions.

Effect of induced electric field on migration of a charged porous particle

The effect of ambient fluid flow on a charged porous spherical particle suspended in an aqueous medium is analyzed. The porous particle is ion permeable and fluid penetrable. The induced electric field due to the polarization of the particle's electric double layer and counterion condensation leads to a hindrance effect on particle migration by producing an electric force. The influence of this retardation force on the hydrodynamics of the particle is studied through the Nernst-Planck equations, which are coupled with the Stokes-Brinkman equation. The interactions of the double-layer polarization, shielding effect, electroosmosis of unbalanced ions and fluid convection are analyzed. The settling velocity and fluid collection efficiency of the charged aggregate is determined. We have studied the electrokinetics for a wide range of fixed charge density and permeability of the particle with no assumption made on the thickness of the double layer relative to the dimension of the particle.

Size and charge characterization of polymeric drug delivery systems by Taylor dispersion analysis and capillary electrophoresis

In this work, Taylor dispersion analysis and capillary electrophoresis were used to characterize the size and charge of polymeric drug delivery nanogels based on polyglutamate chains grafted with hydrophobic groups of vitamin E. The hydrophobic vitamin E groups self-associate in water to form small hydrophobic nanodomains that can incorporate small drugs or therapeutic proteins. Taylor dispersion analysis is well suited to determine the weight average hydrodynamic radius of nanomaterials and to get information on the size polydispersity of polymeric samples. The effective charge was determined either from electrophoretic mobility and hydrodynamic radius using electrophoretic modeling (three different approaches were compared), or by indirect UV detection in capillary electrophoresis. The influence of vitamin E hydrophobicity on the polymer effective charge has been studied. The presence of vitamin E leads to a drastic decrease in polymer effective charge in comparison to non-modified polyglutamate. Finally, the electrophoretic behavior of polyglutamate backbone grafted with hydrophobic vitamin E (pGVE) nanogels according to the ionic strength was investigated using the recently proposed slope plot approach. It was deduced that the pGVE nanogels behave electrophoretically as polyelectrolytes which is in good agreement with the high water content of the nanogels.

Behavior of hydrophobic polyelectrolyte solution in mixed aqueous/organic solvents revealed by neutron scattering and viscosimetry

We investigate in this paper the influence of the improvement of the solvent quality on the structure and the viscous properties of solutions of an hydrophobic polyelectrolyte, poly(styrene-co-sodium styrenesulfonate): PSS. The solvent used is a mixture of water and an organic solvent, THF, which is also slightly polar. We use small angle neutron scattering in the semidilute regime and viscosimetry as a function of concentration in dilute and semidilute unentangled regime. The structure, namely the scattering from all chains, is characterized by a maximum ("polyelectrolyte peak"). Its position and amplitude depends, at a given sulfonation rate of PSS, on the solvent quality through the added amount of organic solvent (THF). These evolutions with the THF amount are more pronounced when the sulfonation rate f is low (more hydrophobic polyelectrolyte) and the amount of added THF is high. Adding THF to hydrophobic PSS (f = 0.50 or f = 0.38), diminishes also the "shoulder" visible in the log I - log q plot and associated with the pearl size. It is therefore proposed that when THF is added to aqueous polyelectrolyte solutions, the pearls are dissolved and the chain conformation evolves from the pearl-necklace shape already reported in pure water toward the string-like conformation in pure water for fully sulfonated PSS. An addition of THF also reduces the important low q upturn found with hydrophobic polyelectrolyte solutions: the large aggregates are dissolved by THF. The upturn can become for PSSNa f = 0.38, after adding enough THF (50%), even smaller than that for the charged hydrophilic case PSSNa f = 0.82, in water. This can mean that in the quasi-fully charged PSS at f = 0.82 there are still hydrophobic effects in water, which is disagreeing with our recent reports, or that the electrostatics contribution to the upturn is reduced due to a lower dielectric permittivity. Concerning the hydrophilic polyelectrolyte, poly(sodium-2-acrylamido-2-methylpropanesulfonate)-co-(acrylamide): AMAMPS, no evolution in structure occurs until 25% THF. The viscosimetry variation with THF fraction is in good agreement with the scattering one up to 25%: though little dependent on THF for AMAMPS, and for hydrophilic PSSNa, it increases for hydrophobic PSSNa in agreement with the chain expansion signaled by scattering. At 50% THF concentration, the hydrophilic polyelectrolyte shows new surprising behaviors: the scattering of PSSNa is no longer characteristic of polyelectrolytes, and AMAMPS solutions display an unexpected viscosity decrease.

Determination of effective charge of small ions, polyelectrolytes and nanoparticles by capillary electrophoresis

In this paper, a systematic and comparative study related to the effective charge determination of three kinds of solutes (small ions, polyelectrolytes and nanoparticles) was performed. Four approaches were compared regarding their conditions of validity and their advantages/disadvantages. Three of them allow the effective charge determination from the electrophoretic mobility and the hydrodynamic radius of the solutes using electrophoretic mobility modelings based on Nernst-Einstein (NE), O'Brien-White-Ohshima (OWO) and Yoon and Kim (YK) equations. Electrophoretic mobility and hydrodynamic radius were determined by capillary electrophoresis and Taylor dispersion analysis, respectively, using the same instrumentation in similar conditions, on a large set of samples. A fourth experimental approach based on the sensitivity of detection in indirect UV detection mode (IUV) was compared to the previously mentioned methods. OWO and YK modelings are well adapted for the effective charge determination of small ions and nanoparticles, while IUV is the only method adapted for polyelectrolytes.

Energy landscape analyses of disordered histone tails reveal special organization of their conformational dynamics

Histone tails are highly flexible N- or C-terminal protrusions of histone proteins which facilitate the compaction of DNA into dense superstructures known as chromatin. On a molecular scale histone tails are polyelectrolytes with high degree of conformational disorder which allows them to function as biomolecular "switches", regulating various genetic processes. Unfortunately, their intrinsically disordered nature creates obstacles for comprehensive experimental investigation of both the structural and dynamical aspects of histone tails, because of which their conformational behaviors are still not well understood. In this work we have carried out ∼3 microsecond long all atom replica exchange molecular dynamics (REMD) simulations for each of four histone tails, H4, H3, H2B, and H2A, and probed their intrinsic conformational preferences. Our subsequent free energy landscape analysis demonstrated that most tails are not fully disordered, but show distinct conformational organization, containing specific flickering secondary structural elements. In particular, H4 forms β-hairpins, H3 and H2B adopt α-helical elements, while H2A is fully disordered. We rationalized observed patterns of conformational dynamics of various histone tails using ideas from physics of polyelectrolytes and disordered systems. We also discovered an intriguing re-entrant contraction-expansion of the tails upon heating, which is caused by subtle interplay between ionic screening and chain entropy.

Electric-field-induced polarization of the layer of condensed ions on cylindrical colloids

In concentrated suspensions of charged colloids, interactions between colloids can be induced by an external electric field through the polarization of charge distributions (within the diffusive double layer and the layer of condensed ions) and/or electro-osmotic flow. In case of rod-like colloids, these field-induced inter-colloidal interactions have recently been shown to lead to anomalous orientation perpendicular to the external field, and to phase/state transitions and dynamical states, depending on the field amplitude and frequency of the external field. As a first step towards a (semi-) quantitative understanding of these phenomena, we present a linear-response analysis of the frequency-dependent polarization of the layer of condensed ions on a single, long and thin cylindrical colloid. The in-phase and out-phase response functions for the charge distribution and the electric potential are calculated for arbitrary orientation of the cylindrical colloid. The frequency-dependent degree of alignment, which is proportional to the electric-field-induced birefringence, is calculated as well, and compared to experiments on dilute fd virus suspensions.

Effect of counterions on the Rayleigh-Plateau instability of a charged cylinder

The effect of counterions on the instability of a charged cylinder is investigated. Both axisymmetric and asymmetric perturbations are considered. The analysis shows that the Rayleigh-Plateau instability is modified for a charged cylinder in the presence of counterions. For the axisymmetric instability, the counterions have a stabilizing effect at low values of kappa, the inverse Debye layer thickness. However, the effect is destabilizing at higher values of kappa . The asymmetric modes which are stable for an uncharged cylinder are rendered unstable at high values of kappa . The analysis should be important in pearling instability of charged cylindrical vesicles. The expression for the correlation time of thermally induced shape fluctuations of charged cylindrical vesicles is also derived.

Comparison of a hydrogel model to the Poisson-Boltzmann cell model

We have investigated a single charged microgel in aqueous solution with a combined simulational model and Poisson-Boltzmann theory. In the simulations we use a coarse-grained charged bead-spring model in a dielectric continuum, with explicit counterions and full electrostatic interactions under periodic and nonperiodic boundary conditions. The Poisson-Boltzmann hydrogel model is that of a single charged colloid confined to a spherical cell where the counterions are allowed to enter the uniformly charged sphere. In order to investigate the origin of the differences these two models may give, we performed a variety of simulations of different hydrogel models which were designed to test for the influence of charge correlations, excluded volume interactions, arrangement of charges along the polymer chains, and thermal fluctuations in the chains of the gel. These intermediate models systematically allow us to connect the Poisson-Boltzmann cell model to the bead-spring model hydrogel model in a stepwise manner thereby testing various approximations. Overall, the simulational results of all these hydrogel models are in good agreement, especially for the number of confined counterions within the gel. Our results support the applicability of the Poisson-Boltzmann cell model to study ionic properties of hydrogels under dilute conditions.