The Polarizability of Rod-Like Polyelectrolytes: An Electric Circuit View
Abstract
In this chapter we use the fluctuation-dissipation theorem (FDT) to estimate the polarizability or dielectric constant as a function of the frequency for low electric field of a polyelectrolyte immersed in an ionic solution; the idea is to consider each charged group within the polyelectrolyte framework and its neighbourhood as a resistor and a capacitor in series. We obtained for the longitudinal polarizability α ∥ (0) = Cδ2, where C is the total polyelectrolyte-ionic capacitance and δ the average displacement of the ‘bound’ ions under the influence of the thermal fluctuating field. Any of the theories which predict α ∥ (0), δ, and the relaxation time τ, can be used to estimate R and C, on the other hand, R, C and δ can be obtained independently by modeling the system. Using Mandel’s results we obtain for the total polyelectrolyte-ionic longitudinal capacitance C = n2C0 where n is the number of condensed but mobile counterions of valence z, and C0 is the elementary capacitance, \(C_{0} = (ze_{0})^{2}/kT\). We obtain results that are consistent with the experimental data of Takashima for the dielectric dispersion of DNA solutions.
Keywords
Polarizability Electrical fluctuations Ionic dielectric relaxation Cylindrical polyelectrolytesReferences
- 1.Allgen, L.G.: A dielectric study of nucleohistone from calf thymus. Acta Physiol. Scand. Suppl. 22 (Suppl. 76), 1–140 (1950)Google Scholar
- 2.Hasted, J.B.: Aqueous Dielectrics, p. 11. Chapman and Hall, London (1973)Google Scholar
- 3.Jerrard, H.G., Simmons, B.A.W.: Dielectric studies on deoxyribonucleic acid. Nature 184, 1715 (1959)CrossRefGoogle Scholar
- 4.Jungner, G., Jungner, I., Allgen, L.G.: Molecular weight determination on thymonuclelc acid compounds by dielectric measurements. Nature 163, 849 (1949)CrossRefGoogle Scholar
- 5.Klug, D., Kranbuehl, D., Vanghau, W.: Molecular correlation functions and dielectric relaxation. J. Chem. Phys. 50, 3904 (1969)CrossRefGoogle Scholar
- 6.Mandel, M.: The electric polarization of rod-like, charged macromolecules. Mol. Phys. 4, 489 (1961)CrossRefGoogle Scholar
- 7.Mandel, M., Jenard, A.: Dielectric behaviour of aqueous polyelectrolyte solutions. Part 1. Trans. Faraday Soc. 59, 2158 (1963)Google Scholar
- 8.Mandel, M., Jenard, A.: Dielectric behaviour of aqueous polyelectrolyte solutions. Part 2. Trans. Faraday Soc. 59, 2170 (1963)Google Scholar
- 9.Manning, G.S.: A condensed counterion theory for polarization of polyelectrolyte solutions in high fields. J. Chem. Phys. 99, 477 (1993)CrossRefGoogle Scholar
- 10.Mohanty, U., Zhao, Y.: Polarization of counterions in polyelectrolytes. Biopolymers 38, 377 (1996)CrossRefGoogle Scholar
- 11.Oncley, J.L.: The investigation of proteins by dielectric measurements. Chem. Rev. 30, 433 (1942)CrossRefGoogle Scholar
- 12.Oosawa, F.: Counterion fluctuation and dielectric dispersion in linear polyelectrolytes. Biopolymers 9, 677 (1970)CrossRefGoogle Scholar
- 13.Oosawa, F.: Polyelectrolytes, Chap. 5 Marcel Dekker, New York (1971)Google Scholar
- 14.O’Konski, C.T.: Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes. J. Phys. Chem. 64, 605 (1960)Google Scholar
- 15.Schwarz, G.: Zur theorie der leitfahigkeitsanisotropie von polyelektrolyten in losung,. Z. Phys. 145, 563 (1956)CrossRefGoogle Scholar
- 16.Schwarz, G.: Dielectric relaxation of biopolymers in solution. Z. Phys. Chem. 19, 286 (1959)CrossRefGoogle Scholar
- 17.Takashima, S.: Dielectric dispersion of DNA. J. Mol. Biol. 7, 455 (1963)CrossRefGoogle Scholar
- 18.Takashima, S.: Dielectric dispersion of deoxyribonucleic acid. J. Phys. Chem. 70, 1372 (1966)CrossRefGoogle Scholar
- 19.Takashima, S.: Effect of ions on the dielectric relaxation of DNA. Biopolymers 5, 899 (1967)CrossRefGoogle Scholar