Transverse polarizability of an aligned assembly of charged rods

Electro-optic Kerr effect in the study of mixtures of oppositely charged colloids. The case of polymer-surfactant mixtures in aqueous solutions

In this review I highlight a very sensitive experimental technique for the study of polymer-surfactant complexation: The electro-optic Kerr effect. This review does not intend to be exhaustive in covering the Kerr Effect nor polymer-surfactant systems, instead it aims to call attention to an experimental technique that, even if applied in a qualitative manner, could give very rich and unique information about the structures and aggregation processes occurring in mixtures of oppositely charged colloids. The usefulness of electric birefringence experiments in the study of such systems is illustrated by selected results from literature in hope of stimulating the realization of more birefringence experiments on similar systems. This review is mainly aimed at, but not restricted to, researchers working in polyelectrolyte-surfactant mixtures in aqueous solutions, Kerr effect is a powerful experimental tool that could be used in the study of many systems in diverse areas of colloidal physics.

An electric-field induced dynamical state in dispersions of charged colloidal rods

The response of concentrated dispersions of charged colloids to low-frequency electric fields is governed by field-induced inter-colloidal interactions resulting from the polarization of electric double layers and the layer of condensed ions, association and dissociation of condensed ions, as well as hydrodynamic interactions through field-induced electro-osmotic flow. The phases and states that can be formed by such field-induced interactions are an essentially unexplored field of research. Experiments on concentrated suspensions of rod-like colloids (fd-virus particles), within the isotropic-nematic phase coexistence region, showed that a number of phases/states are induced, depending on the field amplitude and frequency [Soft Matter, 2010, 6, 273]. In particular, a dynamical state is found where nematic domains form and melt on a time scale of the order of seconds. We discuss the microscopic origin of this dynamical state, which is attributed to the cyclic, electric-field induced dissociation and association of condensed ions. A semi-quantitative theory is presented for the dynamics of melting and formation of nematic domains, including a model for the field-induced dissociation/association of condensed ions. The resulting equation of motion for the orientational order parameter is solved numerically for parameters complying with the fd-virus system. A limit-cycle is found, with a cycling-time that diverges at the transition line in the field-amplitude versus frequency plane where the dynamical state first appears, in accord with experimental findings.

Low-frequency collective exchange mode in the dielectric spectrum of salt-free dilute polyelectrolyte solutions

We study the frequency-dependent dielectric response of flexible polyelectrolyte chains in aqueous salt-free dilute solution as a function of polymer concentration and length by means of Brownian dynamics simulations including hydrodynamic interactions. We show that condensed and uncondensed counter ions are characterized by different dielectric response spectra and thus confirm long-held scaling assumptions used for the interpretation of experimental data. In addition to the well-known relaxation modes of condensed and uncondensed counter ions we observe for a single polyelectrolyte chain, we find in many-chain simulations a novel spectral feature at low frequencies that essentially corresponds to an exchange of counter ions between neighboring polyelectrolytes. Our results suggest that the experimental low-frequency dielectric mode might not be due to condensed counter ions, as is commonly assumed, but rather due to a collective many-chain process. This could resolve a long-standing puzzle in the comparison of experimental results and scaling predictions.

Counterion condensation theory of attraction between like charges in the absence of multivalent counterions

There is abundant experimental evidence suggesting the existence of attractive interactions among identically charged polyelectrolytes in ordinary salt solutions. The presence of multivalent counterions is not required. We review the relevant literature in detail and conclude that it merits more attention than it has received. We discuss also some recent observations of a low ionic strength attraction of negatively charged DNA to the region of a negatively charged glass nanoslit where the floor of the nanoslit meets the walls, again in the absence of multivalent ions. On the theoretical side, it has become clear that purely electrostatic interactions require the presence of multivalent counterions if they are to generate like-charge attraction. Any theory of like-charge attraction in the absence of multivalent counterions must therefore contain a non-electrostatic component. We point out that counterion condensation theory, which has predicted like-charge polyelectrolyte attraction in an intermediate range of distances in ordinary 1:1 salt conditions, contains both electrostatic and non-electrostatic elements. The non-electrostatic component of the theory is the modeling constraint that the counterions fall into two explicit populations, condensed and uncondensed. As reviewed in the paper, this physically motivated constraint is supported by strong experimental evidence. We proceed to offer an explanation of the nanoslit observations by showing in an idealized model that the line of intersection of two intersecting planes is a virtual polyelectrolyte. Since we have previously developed a counterion condensation theory of attraction of two like-charged polyelectrolytes, our suggestion is that the DNA is attracted to the virtual polyelectrolytes that may be located in the nanoslit where floor meets walls. We present the detailed calculations needed to document this suggestion: an extension of previous theory to the case of polyelectrolytes with like but not identical charges; the demonstration of counterion condensation on a plane with bare charge density greater than an explicitly exhibited critical value; a calculation of the free energy of the plane; a calculation of the interaction of a line charge polyelectrolyte with a like-charged plane; and the detailed demonstration that the line of intersection of two planes is a virtual polyelectrolyte.

A counterion condensation theory for the relaxation, rise, and frequency dependence of the parallel polarization of rodlike polyelectrolytes

We calculate the relaxation, rise, and frequency dependence of the parallel polarization of counterions condensed on rodlike polyelectrolytes and charged colloids. Emphasis is placed on an effective counterion mobility along the rod as strongly influenced by electrostatic interactions.

Electric-field-induced polarization and interactions of uncharged colloids in salt solutions

The electric-field-induced charge distribution and potential around a colloidal sphere and rod in salt solutions are analyzed. The resulting field-induced colloid-colloid interactions are calculated for specific orientations. The colloids are assumed to be uncharged (or very weakly charged), such that the deflection of ion fluxes by the cores of the colloids is the dominant polarization mechanism (which is referred to as volume-polarization). Explicit expressions are derived for the frequency-dependent charge distribution and the potential in case of a symmetric electrolyte. It is shown that colloid-colloid interactions due to the induced charge distributions can be much larger than the thermal energy, and are therefore sufficiently strong to give rise to electric-field-induced phase transitions. The present study is a first step towards a quantitative description of field-induced transitions for systems where volume-polarization is the dominant polarization mechanism.