M. Mandel

Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules: I. Theory

Abstract A theory is derived for the static and frequency dependent value of the electric permittivity for model systems representing a solution of a macromolecule bearing a large number of identical charges. The polyion is represented either as a charged rigid rod (A) or as a sequence of charged rodlike subunits in an arbitrary but fixed configuration (B) and it is assumed that a certain fraction of the counterions is closely associated to the macromolecule. The dielectric properties are described in terms of fluctuations in the distribution of the associated counterions along the polyion. These fluctuations can occur locally between potential barriers marking the ends of the subunits (if considered) but can also extend over the whole molecule. Neglecting correlations between different associated counterions expressions for the static value of the dielectric increment are obtained which reveal its dependence on the fraction of bound ions, on the charge of the counterions and on the length of the molecule for model A or the radius of gyration for model B. The dynamic behaviour of A is distinguishable from that of B as the former will present one single dispersion curve of the frequency dependent electric permittivity while the latter may give rise to two different dispersion regions. This will be the case if both the exchange between bound and free ions and the rotation of the complete molecule are relatively slow in comparison to the local bound counterion density fluctuations and if these fluctuations occur on a much shorter time scale than the ion density fluctuations extending over the complete macromolecule.

Dielectric properties of poly-L-glutamic acid in salt-free aqueous solutions

Abstract The electric permittivity of poly-L-glutamic acid (PGA) in salt-free aqueous solutions was measured in the frequency range 2.5 kHz – 100 MHz at different concentrations and degrees of ionization. Two samples of different molecular weight were investigated. The experimental results could under most circumstances be described by a superposition of two dispersion curves of the Cole-Cole type. The low-frequency dielectric parameters were strongly molecular weight dependent, the high-frequency ones not. Strong concentration effects were observed resulting in increasing specific dielectric increments and relaxation times with decreasing concentration. Using the theory proposed by Van der Touw and Mandel to interpret the experimental results these concentration effects could be ascribed to the influence of the polyion interactions on the average dimensions and the rigidity of the polyelectrolyte chains. The change in the total dielectric increment and low-frequency relaxation time with degree of ionization correctly reflects the helix-coil transition of PGA occurring in ths region α = 0.3–0.5. The effect of counterion size and charge on the dielectric behaviour was also found to be consistent with the theoretical model.

Electric permittivity and dielectric dispersion of low-molecular weight DNA at low ionic strength

The dielectric properties of sonicated calf-thymus DNA (MW approximately 3 X 10(5) g mol-1) have been investigated in a frequency range between a few kHz and 100 MHz. Two samples, sonicated in a different way were used after proper characterization including light-scattering, viscometry and contour length distribution by electron microscopy. Dielectric measurements were performed at several concentrations between 10(-4) and 3 X 10(-3) monomol 1-1 and 22 degrees C. Under all circumstances two separated dispersion regions were observed, the corresponding specific increments of which decreased with increasing concentration. The same was observed with the mean relaxation time of the high frequency dispersion. Both the frequency and concentration dependence was largely analogous to what is observed with other polyelectrolytes. Values of the dielectric parameters extrapolated to infinite dilution could also be interpreted in the same manner as for more simple, charged macromolecules and no specific effects had to be taken into account.

The dielectric increments of aqueous polyelectrolyte solutions: a scaling approach

This paper deals with dielectric dispersion curves (covering a frequency range from a few Hz to 100 MHz) of Na-poly(styrene-sulfonate) of 65,000 < or = Mw < or = 1,060,000 g mol(-1) in aqueous solutions. The values of the low frequency (dielectric increment1) and high frequency (dielectric increment2) dielectric increments, obtained from the experimental curves matched to a superposition of two Cole-Cole equations, have been analyzed in terms of their concentration and molar mass dependence. The concentrations C (g l(-1)) of the various solutions were mostly situated in the transition regime defined by Odijk [T. Odijk, Macromolecules 12 (1979) 688] between the dilute regime (C < Cg*) and the semi-dilute one (C > C**), and wherein the characteristic concentration C* marks the onset of flexibility effects on the polyion behavior. It has been shown that in the concentration range Cg* < C < C** the increments in both frequency domains satisfy a scaling relation dielectric increment(j) = Bj M(nu j) (C/C*)(mu j) with molar mass independent exponents nu j and mu j changing around C*. Their values are different for dielectric increment1 and dielectric increment2, except for mu above C* where both increments appear to become concentration-independent. Below Cg*, in the dilute regime, the two dispersion domains seem to merge. The increment dielectric increment = relative permittivity (0) - high frequency limit of relative permittivity is molar mass independent if scaled to (C/Cg*). The molar mass dependence of the increments as a function of the macromolecular concentration rhoP, dielectric increment or dielectric increment(j) approximately Mgamma (rhoP)mu, also reveals differences between the different concentration regimes. Extrapolation from above Cg* to zero concentration is thus unjustified.

Plane-parallel condenser with variable electrode-spacing for determination of electric permittivity of highly conducting liquids below 1 MHz. Part 2.—Experimental approach

The theoretical expressions for the capacitance Cx and conductance Gx of a plane parallel-plate condenser as series expressions in negative powers of the electrode spacing, are submitted to experimental verification. Using cells, differing in the dimensions of the electrodes, the measured values of Cx and Gx verify these expressions within experimental accuracy, and that neither the influence of electrode nor edge effects can be neglected for liquids of large conductivity. A semi-empirical approach to the theoretical equations of part 1, devised to increase the accuracy for the computation of the relative electric permittivity, is also presented and tested experimentally.

Plane-parallel condenser with variable electrode spacing for determination of electric permittivity of highly conducting liquids below 1 MHz. Part 1.—Theoretical considerations

A method is described for the determination of the relative electric permittivity Iµx of highly conducting liquids below 1 MHz with a measuring cell consisting of a plane-parallel-plate condenser with variable electrode spacing. Both the electrode effects (due to the impedance of the diffuse double layer at the electrodes) and the edge effects (due to the perturbation of the uniform electric field near the edges of the plates) are taken into account in the expressions for the total capacitance and conductance of the cell. Using a series expression of the measured capacitance in negative powers of the spacing between the electrodes, Iµx can be computed from the coefficient of the linear term, if certain conditions are fulfilled. The correction methods for electrode effects only, as proposed previously by Fricke and Curtis or Shaw may lead to erroneous results.

A measuring device for the determination of the electric permittivity of conducting liquids in the frequency range 2-500 kHz. II: The measuring cell

For pt.I see ibid., vol.8, p.840 (1975). The cell is, in principle, a plane parallel plate capacitor in which the spacing between the electrodes is variable and determined by gauge blocks. The special construction is prerequisite for the use of a correction procedure for electrode polarization and edge effects.

Dielectric Properties of Polyelectrolytes in Solution

Dielectric measurements belong to the oldest techniques used by physical chemists to gain information about molecular properties and molecular behaviour. Dielectric investigations are generally focused on two main aspects: (1) the equilibrium value of the electric permittivity (or dielectric constant) e which is related to the equilibrium polarization of the system under the influence of an external field; (2) the dispersion or frequency dependence of s which is related to the change in time of the polarization when the external field is established or switched off. Both the equilibrium or static electric permittivity and the dielectric dispersion of polyelectrolyte solutions have been subjects of experimental investigations of which Oncley’s pioneering work on protein solutions should be mentioned [1]. Owing to experimental difficulties measurements in the past have often been limited to a small frequency range but more recently experiments covering a much broader domain have become available. (In our own laboratory experiments are performed between 2.5 kFlz and 100 MHz; Minakata and Irnai [2] claim to have measured between 30 Hz and 6 MHz). Although it should be ideal to measure dielectric properties at frequencies as low as possible, determinations of s below 50 kHz become increasingly difficult for two different reasons: (1) the conductivity contribution of the solution admittance becomes predominant; (2) the effects of electrode polarization which has to be corrected for increase very rapidly with decreasing frequency. Special experimental equipment is necessary and correction methods must be devised to take care of the influence of the electrode effects.

A measuring device for the determination of the electric permittivity of conducting liquids in the frequency range 2-500 kHz. I. The bridge

A measuring bridge is described which is in particular applicable in the kHz region to the determination of the components of an impedance characterized by a very high loss factor. Calibration of the bridge can be performed empirically using special standards. Frequency limits and accuracy are discussed.

Static relative permittivity of some electrolyte solutions in water and methanol

Experimental results are presented for the relative permittivity of several chlorides in water and methanol at 25°C measured at 5–20 MHz up to concentration of 0.1 mol dm–3. These permittivities are interpreted as the static values Iµ° and show in general an initial increase with concentration, followed by a decrease below the static value of the relative permittivity Iµ°s of the solvent. The changes in Iµ° with respect to Iµ°s are of comparable magnitude for all chlorides in water at equal equivalent concentration, with a noticeable exception for HCl which exhibits much larger decrements. The decrements in methanol relative to Iµ°s are larger than in water. These results for the static relative permittivity of the electrolyte solutions have been shown to be interpretable in terms of a superposition of the Debye–Falkenhagen effect and the kinetic depolarization deficiency recently proposed by Hubbard and Onsager. At concentrations ⩽2.5 × 10–2 mol dm–3 the observed increments are in fair agreement with the theoretical values according to Debye and Falkenhagen.At higher concentrations the experimental decrements seem to follow the theoretical relation proposed by Hubbard and Onsager, at least semi-quantitatively, and after correction for the former effect. The dependence of the relative decrements on the specific conductivity of the solution and the dielectric relaxation time of the solvent, predicted by Hubbard and Onsager, has been confirmed. No definite conclusion could be reached as to whether or not the dielectric saturation effect has some influence on the observed decrements.