Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules. II. Experimental results with synthetic polyelectrolytes

The electric permittivity of aqueous solutions of different synthetic polyelectrolytes have been measured as a function of frequency in the range 5 kHz up to 100 MHz in the absence of added salt. Solutions of polymethacrylic acid and polyacrylic acid of different degrees of polymerization, both partially neutralized with NaOH, were investigated as well as solutions of Na-polystyrenesulphonate at different concentrations.For all systems a dispersion profile with two separated dispersion regions was obtained with a molecular weight dependent value of the static electric permittivity. The low frequency dispersion region was found to be characterized by a molecular weight dependent mean relaxation time while for the high frequency dispersion region both the mean relaxation time and the dielectric increment are molecular weight independent. It is shown that the reciprocal values of the specific increments and of the relaxation times depend linearly on the macromolecular concentration. Extrapolation of the corresponding quantities to infinite dilution was found to be possible. A comparison of these extrapolated values with calculated ones according to the previously derived theory also applicable to flexible macromolecules establishes that this theory describes satisfactorily the dielectric behaviour of the systems investigated.The conclusion is reached that the high frequency dispersion and relaxation can be attributed to fluctuations in the distribution of bound counterions along limited parts of the macromolecule. The relaxation time of the low frequency dispersion region seems to be essentially determined by the rotation of the complete molecule and the static electric permittivity can he explained in terms of fluctuations in the counterion density extending over the whole macromolecule.     

Dielectric studies of aqueous solutions of poly(L-glutamic acid)

The dielectric features of poly(L -glutamic acid) are studied by the Fourier synthesized pseudorandom noise method in a time domain combined with a four-electrode cell. Polymer concentration dependence, the effect of the solvent viscosity, salt effects, and pH dependence are studied concomitantly with measurements of CD. A helix-to-coil transition occurs near pH 5.6 for a salt-free solution; at higher pH values, the polymer has an ionized random-coil conformation, and at lower pH, it has a deionized α-helical conformation. When it is in the ionized random-coil conformation, with the usual features of an electrolytic polymer, the solution shows a relaxation spectrum with a large dielectric increment at low frequencies. In the deionized α-helical state, no distinct relaxation curves are obtained, which does not deny the existence of a permanent peptide dipole. The pH dependence of the dielectric increment does not mainly correspond to the conformational change from helix to coil, but rather corresponds to the change of chain expansion on account of a charge–charge interaction under low ionic strength, which is conceived of by a viscosity measurement.     

Structural flexibility and fast proton transfer reflected by the dielectric properties of poly-L-proline in aqueous solution

Dielectric dispersion curves for the helix-11 form of poly-L-proline in aqueous solution have been determined for various pH in the acid range of zwitterion formation. The results could be excellently described by means of a Cole-Cole dispersion function involving the three parameters Δ?⁰ (total dielectric increment), τ_r (effective rotational relaxation time) and h (characterizing the width of the dispersion region). The quantities τ_r, and h were found to be clearly independent of pH and added inert electrolyte. An analysis of the data permits an evaluation of the dipole moments and leads to the conclusion that the molecule cannot be considered to be a completely stretched rigid rod but must be more or less bent. Addition of formic acid slightly below pH 4 caused a distinct broadening of the experimental curves which could be quantitatively interpreted by a second dielectric relaxation process due to orientation of zwitterions by means of fast proton transfer.     

Dielectric relaxation of DNA in aqueous solutions.

Using a four-electrode cell and a new electronic system for direct detection of the frequency differences specturm of solution impedance, the complex dielectric constant of calf thymus DNA (M_r = 4 × 10⁶) in aqueous NaCl at 10°C is measured at frequencies ranging from 0.2 Hz to 30 kHz. The DNA concentrations are C_p = 0.01% and 0.05%, and the NaCl concentrations are varied from C_s = 10^?4 M to 10^?3 M. A single relaxation regions is found in this frequency range, the relaxation frequency being 10 Hz at C_p = 0.01% and C_s = 10^?3 M. At C_p = 0.05% it is evidenced that the DNA chains have appreciable intermolecular interactions. The dielectric relaxaton time τ_d at C_p = 0.01% agrees well with the rotational relaxation time estimated from the reduced visocisty on the assumption that the DNA is not representable as a rigid rod but a coiled chain. It is concluded that the dielectric relaxiatioinis ascribed to the rotation of the molecule. Observed values of dielectric increment and other experimental findings are reasonably explained by assuming that the dipole moment of DNA results from the slow counterion fluctuation which has a longer relaxation time than τ_d.     

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

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 of alfalfa mosaic virus in aqueous solutions

The electric permittivity of alfalfa virus particles in buffer solutions of three different concentrations at pH 7 was studied between 10 kHz and 100 MHz. The experimental results could be described with one single dispersion curve of the Cole-Cole type characterized by a concentration independent specific dielectric increment and mean relaxation time. The results were interpreted semi-quantitatively in terms of counterions–atmosphere polarizability, neglecting counterion repulsion.     

Dielectric relaxation of collagen in aqueous solutions

The complex dielectric constant of collagen in aqueous solutions (polymer concentration, C_p = 0.02–0.2%) was measured at 10°C in the frequency range from 3 Hz to 30 kHz. The loss peak for C_p = 0.02% is located at 90 Hz and the dielectric relaxation time τ_D is estimated to be 1.8 ± 0.3 msec. The τ_D agrees well with the rotational relaxation time estimated from the reduced viscosity, and the relaxation is ascribed to the end-over-end rotation of the molecule. The C_p dependence of τ_D and the dielectric increment Δε are interpreted in terms of the aggregation of molecules. The dipole moment of a molecule, obtained from Δε at C_p = 0.02% and pH 6.5, is (5.2 ± 0.2) × 10⁴D, which is explained by the asymmetrical distribution of the ionized side chains of the molecule.     

Dielectric properties of polyelectrolytes. III. Effect of divalent cations on dielectric increment of polyacids

Dielectric dispersion of polyacrylic acid (PAA) and polystyrene sulfonic acid (PSS) was measured in the presence of divalent cations. Effects of divalent ions were studied by neutralization with varying ratios of sodium hydroxide and divalent base concentration, addition of salts of divalent cations, and neutralization with divalent bases only. Two dispersion regions were observed in all cases, i.e., low-frequency dispersion (10²–10⁴ Hz) and high-frequency dispersion (10⁵–10⁶ Hz). The dielectric increment increases in the presence of sodium and alkaline earth metal ions together, but not with sodium and transition metal ions. This is due to the increment of low-frequency dispersion and is attributable to the fluctuation of bound counterions which is explained by our theory previously reported.¹ In the case of PAA neutralized with large fractions of divalent ions, or with divalent ions only, the increment is very small because of reduction of the fluctuation by interaction between bound ions at the neighboring sites and reduction of the effective length of polyion probably due to chelation by divalent ions. There are some differences among the effects of Mg⁺⁺, Ca⁺⁺, and Ba⁺⁺ on dielectric increment which may result from affinity or chelating ability of these ions.     

Dielectric properties of hydrated collagen

Dielectric measurements have been carried out on partially hydrated collagen in the frequency ranges 100 kHz–5 MHz, 100 MHz–1 GHz, and 8–23 GHz. In the low-frequency range, a dispersion was observed around 100 kHz which results from inhomogeneous conductivity of the samples. A dielectric relaxation was observed aroud 0.3 GHz using time-domain-spectroscopy techniques. This relaxation can be considered to originate from mobile side chains. Microwave measurements indicate that the water relaxation may extend into the 10-GHz region. An apparent discrepancy between the main water relaxation time and the average rotational correlation time of water as measured by nmr line widths was resolved by the assumption that a fraction of the water molecules is bound to the collagen with residence times on the order of 10^?6 sec, whereas the remainder of the water is only weakly bound and exhibits rotational rates on the order of 10^?10 sec.     

Dielectric relaxation of DNA solutions. II

Real and imaganiry parts of complex dielectric constant of dilute solutions of DNA in 10^?3M NaCl with molecular weight ranging from 0.4 × 10⁶ to 4 × 10⁶ were measured at frequencies from 0.2 Hz to 30 kHz. Dielectric increments Δε were obtained from Cole-Cole plots and relaxation times τ_D from the loss maximum frequency. The τ_D of all samples agrees well with twice of the maximum viscoelastic relexation time in the Zimm theory, indicating that the low-frequency dielectric relaxiation should be ascribed to be the rotation of DNA. The rms dipole moment, which was obtained from Δε, agree well with that calculated from the counterion fluctuation theory. The dielectric increment was found to be greatly depressed in MgCl₂, which is resonably interpreted in terms of a strong binding of Mg⁺⁺ ions with DNA.     

Molecular-weight dependence of the low-frequency dielectric properties of aqueous solutions of gel-fractionated DNA

Combined three- and four-terminal AC bridge measurements have been made at frequencies from 10 Hz to 100 KHz on samples of DNA with different molecular weight in aqueous solution under varying conditions of DNA concentrations and added salt. A method is described for the separation of large quantities of DNA fractionated according to size. A complicated pattern of dependence of the specific dielectric increment on concentration is found, and the difficulties of comparing the results from sample to sample are discussed. The dielectric properties of the fractionated samples of DNA in aqueous solution are reported for solutions sufficiently dilute that specific dielectric increment is independent of concentration. The specific dielectric increment of the solutions (with concentration measured in moles of DNA molecules/liter) is found to increase as the square of the molecular weight. The results are compared with results of polyelectrolyte theories which deal explicitly with counterion fluctuations and interactions. The frequency dependence of the dispersion is much broader than for simple Debye relaxation. It is satisfactorily fitted by the empirical Cole–Cole circular are function and the breadth of the dispersion is found to be, if anything, less for the fractionated samples than for native DNA in solution.     

Dielectric properties of developing rabbit brain at 37 degrees C

The dielectric properties of developing rabbit brain were measured at 37 degrees C between 10 MHz and 18 GHz using time domain and frequency domain systems. The results show a variation with age of the dielectric properties of brain. An analysis of the data suggests that the water dispersion in the brain of newly born animals can be represented by a Debye equation. This dispersion increases in complexity with age, and there is evidence of a smaller additional relaxation process centered around 1 GHz. It is concluded that the principal contribution to this subsidiary dispersion region arises from water of hydration.     

Dielectric studies of electrolytic poly(α-amino acid)s in aqueous solutions

The dependence of the dielectric constant and dielectric loss of aqueous solutions of poly-ε, N-succinyl-L -lysine on its degree of polymerization, degree of neutralization, concentration of the polymer, and counterion type was studied in a frequency range from 300 Hz to 5 MHz. Regardless of the conformation, a low-frequency dispersion in a frequency range lower than 10 kHz and a high-frequency dispersion in a range higher than 100 kHz were found. The large value of the dielectric increment, its nonlinear dependence on concentration, its remarkable dependence on counterion type, and its dependence on the degree of polymerization suggest that the low-frequency dispersion is mainly due to the polarization of loosely bound counterions. These data were found for both the helical and coiled forms. The rotational motion of the electric dipole on the molecule could not have been primarily responsible for these results. On the other hand, the high-frequency dispersions may be attributable to the Maxwell–Wagner-type effect. The results were compared with the dispersions of poly(L -glutamic acid), poly(L -lysine), and their salts reported previously.     

Dielectric dispersion of alternating copolymers of maleic acid

Dielectric dispersions of three kinds of copolymers of maleic acid, poly (maleic acid-co-methyl vinyl ether) (PMAMVE), poly(maleic add-co-ethyl vinyl ether) (PMAEVE) and poly (maleic acid-co-styrene) (PMAST), were measured by use of a pseudorandom noise dielectric spectrometer. A large dielectric increment was observed in the low frequency region (10-20 Hz), and was explained in terms of our theory of ion fluctuation. When these copolymers were neutralized with mixtures of NaOH and Ca(OH)2 by changing their ratio, enhancement of the static dielectric increment was observed in the intermediate ratios of both ion species. This phenomenon was analyzed by modifying our. theory of ion fluctuation to the case of alternating copolymers. Quantitative agreement with experimental results was obtained by using values of parameters representing binding energies and mutual repulsion, which are chosen to fit the calculated degree of ion binding to the experimental data on activities of Na+ and Ca2+ ions. At large fractions of divalent ions, the increment, relaxation time and specific viscosity were found to decrease sharply due to chelation by divalent ions.     

On the electric polarization of DNA

Dielectric dispersion of DNA was studied in the frequency range 100 Hz–100 kHz at four different temperatures (6–30°C). The dielectric increment ε₀–ε_∞ increased with the rise of temperature. The relaxation time, on the other hand, decreased. Both the increase in dielectric increment and the decrease in relaxation time could not be explained on the basis of the counterion polarization theory. Dipole moment was estimated from Kirkwood theory. It was found to decrease systematically with temperature. Even at 0°C there was a dipole moment of 10⁴D.     

Dielectric relaxation of DNA solutions. III. Effects of DNA concentration, protein contamination, and mixed solvents

As a continuation of previous papers [Biopolymers (1976) 15 , 879; (1978) 17 , 1508], the low-frequency dielectric relaxation of DNA solutions was studied with a four-electrode cell and the simultaneous two-frequency measurement. Below a critical concentration, the dielectric relaxation time agrees with the rotational relaxation time estimated from the reduced viscosity and is almost independent of DNA concentration C_p, and the dielectric increment is proportional to C_p. The critical concentration is approximately 0.02% of DNA for molecular weight M_r 2 × 10⁶ and 0.2% for M_r 4.5 × 10⁵ in 1 mM NaCl. Dielectric relaxations are compared for samples before and after deproteinization, and the protein contamination is found to have a minor effect on the dipole moment of DNA. The effect of a mixed solvent of water and ethanol on the dielectric relaxation of DNA is well interpreted in terms of changes in viscosity and the dielectric constant of the solvent, assuming that the relaxation arises from rotation of the molecule with a quasi-permanent dipole due to counterion fluctuation.     

Dielectric dispersion in aqueous solutions of oxyhaemoglobin and carboxyhaemoglobin

The relative permittivity and conductivity of aqueous solutions of oxyhaemoglobin and carboxyhaemoglobin were measured over the frequency range 150kHz-100MHz. To minimize errors of measurement the investigations were carried out with three different samples of each type of haemoglobin, independent apparatus being used in two different laboratories. The dielectric increment and relaxation time were calculated at each of several temperatures from the results. These lead to a dipole moment of 400 Debyes and an activation enthalpy of 17.6+/-1.4kJ.mol(-1), both of which were found to be independent of temperature to within experimental error over the range 3-35 degrees C. The value of the dipole moment shows that the distribution of charge throughout the haemoglobin molecule is nearly symmetrical with respect to the centre of charge. The magnitude of the activation enthalpy is similar to that of the viscosity of water, in accord with the common observation that dielectric relaxation and viscosity are related phenomena. No significant differences are found between the dielectric parameters of oxyhaemoglobin and carboxyhaemoglobin. Combining the results with those obtained from X-ray diffraction of the solid a hydration value of 0.45g of water/g of protein is suggested, subject to the limitations of the model used. Finally, the results indicate the presence of a subsidiary dispersion, which could be attributed to the above quantity of bound water having a static permittivity of about 100 and a relaxation frequency in the region 100-200MHz.     

Dielectric properties of polyelectrolytes. I. A study on tetra-n-butyl ammonium polyacrylate

Dielectric constant and loss of aqueous solutions of tetra-n-butyl ammonium polyacrylate ((Bu)₄NPA) were measured in the frequency range from 300 Hz to 6 MHz as compared with sodium and other salts at various conditions. Our results show that there are two dispersions observed in the low-frequency range (LFD, several ten kHz to MHz), respectively, both of which are roughly expressed as the Cole-Cole dispersion formula with Cole parameters about 0.3. The large values of dielectric increment, its nonlinear concentration dependence, and other features suggest that both dispersions are explained by relaxations of two different ionic processes. For HFD, experimental results were qualitatively similar to those have been reported and compared with theories of the Maxwell-Wagner-type effect. On the other hand, LFD may be attributable to the polarization of loosely bound counterions. A model available for LFD was presented on the basis of counterion fluctuation.     

Dielectric disperison of linear polyelectrolytes

A three-dimensional (gaussian) model is formulated that permits evaluation of the one-dimensional fourier cosine transform of the counterion-counterion coulombic interaction energy ?_k. It is shown that ?_kis much larger for small k than was assumed by Oosawa; consequently, the magnitude of his dielectric increment, and also his relaxation time, must be drastically revised to smaller values. Evidently, the self-field of the fluctuation is large enough to seriously depress the amplitude of the spontaneous fluctuations, and to force Ohmic conduction of the ions at a rate far in excess of the rate of translational diffusion. Finally, it is noted that in highly conducting bulk solvents, where both positive and negative counterfoils coexist in the ion-atmosphere, one might expect to observe a low-frequency component of the dielectric relaxation arising from unequal rates of diffusion of the positive and negative species, in analogy with the situation for spherical colloidal particles. In such a circumstance, the basic counterfoil fluctuation mechanism proposed by Oosawa would acquire a new validity.     

Dielectric relaxation in synthetic melanin

The charging and discharging currents were investigated in a synthetic melanin sample. The presence of long-lasting dielectric relaxation was established. The steady state was reached after a long time, from 10³ to 10⁵ s, which depends both on temperature and voltage. The temperature dependence of polarization was of an activation character (E_α = 0.67 eV). The kind of electrode material did not influence the current curves.