Dielectric behavior of polyelectrolytes. VI. Dynamic response of cylindrical biopolymers to electric fields

Nonlinear response of the electric birefringence of polyelectrolyte solutions

A theoretical approach for the nonlinear ac electro-optical response in polyelectrolytes is developed in the case where a weak ac electric field superimposed on a strong dc bias electric field is applied to these electrically charged systems. By restricting ourselves to an assembly of noninteracting and nonpolar rodlike macroions, we use a perturbation procedure and establish expressions for the first two harmonic components of the electric birefringence up to the second order in the electric field strength. An attempt is also made to extend this theory to the (non-Markovian) subdiffusive regime based on a fractional kinetic equation written in a configuration space where angular and linear displacements are taken into account. The results obtained are illustrated by three-dimensional dispersion and absorption plots together with Cole-Cole-like diagrams to show the importance of the coupling effect between translation and rotation. Besides considering the stationary ac response, we have also derived, in the context of subdiffusion, new expressions for the transient electric birefringence in the presence of a constant electric field, both for the buildup and the reversing pulse. All these results are illustrated by plots demonstrating the effect of the coupling (rotation-translation) parameter a and the critical exponent α (subdiffusion). A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a polyelectrolyte solution of NaCMC appears to be quite satisfactory.

Nonlinear harmonic components in dielectric relaxation of polyelectrolytes

The problem of the nonlinear ac dielectric response in polyelectrolytes is carried out by considering these electrically charged systems acted on by a strong dc bias electric field superimposed on a weak ac field. An infinite set of coupled (translation-rotation) kinetic equations is derived, and by using a perturbation procedure, we establish a new expression for the complex dielectric increment of an assembly of nonpolar rodlike macroions surrounded by small counterions. By considering the stationary regime, we show that the electric polarization of the nonpolar macroion is given by calculating the expectation value of P(1)(cos theta)H(1)(x), where P(1) and H(1) stand for the first Legendre and Hermite polynomials, respectively. The results so obtained provide new relaxation features, which are presented in the form of analytic expressions and illustrated by Cole-Cole-like diagrams and three-dimensional dispersion and absorption plots in order to show the influence of the coupling parameter a measuring the importance of the rotational motion over the translational one.

Dielectric dispersion for short double-strand DNA

A complex dielectric constant for double-strand DNA molecules with a length of not greater than 120 base pairs in an aqueous solution containing 30 mM NaCl was systematically measured as a function of chain length in such a way that experimental uncertainties associated with the molecular-weight distribution of specimens were virtually excluded. In contrast to the past experimental and theoretical studies for much longer DNA molecules, both the molar specific dielectric increment and the relaxation time are proportional to the chain length. These scaling rules cannot be accounted for by any theory so far proposed that gives analytical expressions for those two quantities in the long-chain limit.

Temperature dependence of DNA dielectric dispersion at radiofrequency

We have studied the dielectric behavior of DNA aqueous solutions at various ionic strengths and in the presence of the specific DNA ligand ethidium bromide, in the frequency range 1 MHz-1 GHz, at different temperatures ranging from 5 to 40 degrees C. The activation enthalpies of the dielectric relaxations studied were obtained by Arrhenius plots of In(tau T)-1 vs. T-1. The results are consistent with a counterion fluctuation model as previously developed by Mandel and colleagues.