Continuum modelling of polyelectrolytes in solution

Abstract

A phenomenological model for solutions of polyelectrolytes accounting for electromechanical interactions is proposed within the framework of continuum thermodynamics. The modelling involves the conformation of macromolecules in the form of a tensorial "internal variable" and the electric polarization of the solution. The paper aims to demonstrate the possible competition between flow and electricity effects on rigorous phenomenological grounds. Three kinds of dissipative mechanisms are accounted for: viscosity of the solution, electric relaxation and the relaxation of the conformation of macromolecules. Anisotropic effects induced by the applied electric field and flow-induced polarization through changes in conformation are exhibited. These effects are small. By way of application, the problem of the orientation and conformation taken by macromolecules of polyelectrolytes under the combined influence of a simple shear flow and a longitudinal or orthogonal electric bias field is treated in detail and illustrated graphically. Some optical properties are mentioned.

Behavior of Na+-Polystyrene Sulfonate at the Interface with Single-Walled Carbon Nanotubes (SWNTs) and Its Implication to SWNT Suspension Stability

“…Typically, LbL films comprised of PSS and a polycation (such as polyallylaminehydrochloride, PAH) deposited at the working pH of 3 and with the same abundance of Na + counterions present in solution show a planar polyelectrolyte morphology with each layer having a thickness of 2 nm [14][15][16]. Spherically coiled polyelectrolyte diameters of 40 nm are predicted by continuum models for molecular chains of 250 nm length [17]. Here, the observed PSS spherically coiled diameter varied between ~2 nm (the order of the SWNT diameter) and ~200 nm (for some of the largest PSS coils observed).…”

Optical and hydrodynamical regimes in dilute solutions of polyelectrolytes

“…The basic equations deduced in [1] from a thermodynamical model using the notion of internal variable to account for the conformational changes of macromolecules, consist of a) The equation of motion…”

“…The conformation tensor K considered in this paper is a deviator so that only deviations from spherically coiled conformations are studied, the "molecules" being volume preserving, cf. [1] for this notion. The full conformation tensor C may be thought of as an ensemble average of the dyadic product of the end-to-end directed distance between extreme monomers in the macromolecule.…”

“…In the present work we use the model recently developed by the authors [1] to account for the electromechanical behaviour of dilute solutions of polyelectrolytes, with special attention to dynamical, small amplitude, oscillatory phenomena, among which are optical effects. The latter, i.e., birefringence and absorption of light, allow one to gather informations concerning the structure, dimensions, and overallshapes of macromolecules in solution.…”

“…Flow birefringence is the oldest of these methods [10]. The theoretical basis for these effects is obtained by studying small dynamical solutions of the entire set of electro-magneto-mechanical equations given in [1], and specializing the range of frequencies or characteristic speeds to optical or mechanical ones. This perturbation scheme which is common in fluid-stability theory, thus allows to deduce within the same framework, but for two extreme situations, the set of equations that characterize the passing through of light in the solution and the set of equations corresponding to mechanically induced oscillations.…”