Viscosity of a solution of polyelectrolytes near the rod limit.

Herein, I consider a solution of rodlike polyelectrolytes far from the isotropic-nematic critical concentration and focus on the solution viscosity. Varying the polymer concentration, a series of screening regimes is unveiled with the corresponding effects on the solution rheological behavior. I propose a conformational approach to explain the experimental results: the presence of screened electrostatic interactions modifies the persistence length which induces variable rod bending. A hydrodynamic approach leads to closed expressions for the reduced viscosity in the dilute and semidilute regimes by extending the derivation for the neutral rod case. In my derivation, intermediate results for the rotational diffusion constant and viscous stress are exact while the one for the elastic stress is approximate. The predictions for the reduced viscosity as a function of concentration throughout the dilute and semidilute regimes show a non-monotonic behavior similar to that of flexible polyelectrolytes. Although the final expressions cannot be expressed in terms of scaling laws, a comparison with the experimental results shows very good agreement.

Molecular model for nematic, smectic-A, and smectic-C liquid crystals.

We analyze a molecular model to describe the phase transitions between the isotropic, nematic, smectic-A, and smectic-C phases. The smectic phases are described by the use of a pair potential, which lacks the full rotational symmetry because of the cylindrical symmetry around the smectic axis. The tilt of the long molecules inside the smectic layers is favored by a biquadratic pair potential, which compete with the pair potential of the McMillan model. The part of the phase diagram showing the first three phases is similar to that of the McMillan molecular model. The smectic-C phase is separated from the nematic by a continuous phase transition line along which the tilt angle is nonzero. The tilt angle vanishes continuously when one reaches the line separating the smectic-C and the smectic-A line.

The viscosity of short polyelectrolyte solutions.

We consider the viscosity of solutions of highly charged short polyelectrolytes. Our system is a poly(styrene-maleic acid) copolymer solution (SMA) with various added salt concentrations in dilute and semidilute regimes. The SMA solutions show some particular features: (i) variations of the specific viscosity measured for different values of concentration and ionic strength can be rescaled on two universal curves when plotted as a function of the effective volume fraction; (ii) the reduced viscosity is proportional to the Debye length. In order to describe the viscosity of such a system we model the motion of the charged rods considering a simpler system: we replace each charged rod and its corresponding charge cloud by an effective neutral rod. This modified system is yet below the concentrated regime and, at most, steric interactions are left. In the semidilute regime, we model the rescaled rods moving under a mean field potential and obtain a dynamical equation for the orientational tensor, considered small, and the viscosity is derived from it. Within our mean field approach, the effects due to the rod Brownian motion and due to the potential cancel each other and the behavior of the viscosity is explained in terms of the effective volume fraction only. Our predictions are in good qualitative agreement with the experimental results over a wide range of parameters, and suggest a method for obtaining the rotational diffusion constant in the semidilute regime.