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November 17, 2003
Volume 81, Number 46
CENEAR 81 46 p. 70
ISSN 0009-2347

Correction of Debye theory to predict dielectric constants of polar liquids had far-reaching effect


Yale University professor Lars Onsager first sent his paper on electric moments of molecules in liquids to Physikalische Zeitschrift, a journal edited by Petrus J. W. (Peter) Debye, but Debye turned it down. John G. Kirkwood, then a research fellow with Debye in Leipzig, convinced Onsager to write an English version and submit it to the Journal of the American Chemical Society, which published it [J. Am. Chem. Soc., 58, 1486 (1936)] (PDF file).

NEW CONCEPT Onsager showed how Debye's theory of dipoles could be extended to polar solvents. COURTESY OF YALE UNIVERSITY NEWS BUREAU
The paper, which is the sixth most highly cited JACS paper, corrected Debye's formula relating the dielectric constant of a polar substance to the molecular dipole moment. Debye's formula includes the polarizability of the molecule, its permanent electric moment, the dielectric constant, and the energy of thermal agitation. Onsager served as a research assistant for Debye from 1926 to 1928.

"Debye's original theory is still used today to determine dipole moments of molecules dissolved in nonpolar solvents by measuring the dielectric constant of the solution," says John F. Kauffman, a chemistry professor at the University of Missouri, Columbia.

The problem was that Debye's formula didn't work for polar liquids. "At the time," Kauffman says, "a common explanation was that 'association effects' due to dipole-dipole interactions could not be properly accounted for in the Debye theory. Onsager sought to correct this misconception by performing an analysis of the interaction of a dipolar solute molecule with the electric field that is produced as the result of the polarization of the surrounding solvent by the solute molecule."

Debye's theory predicted a "ferroelectric Curie point," a temperature below which the molecule would be in a stable state of permanent electric polarization, much like the permanent magnetic polarization of iron. In his paper, Onsager pointed out that such electric polarization states are actually quite rare.

Onsager introduced the concept of a "reaction field" to deal with the problem. This reaction field is the electric field experienced by a polar molecule when it's surrounded by oriented polar solvent molecules. Onsager showed that with this correction the Debye theory properly predicts dielectric constants of pure polar liquids from their dipole moments.

"Onsager single-handedly reversed the pessimism regarding the ability to understand polar liquid behavior," says Patrik R. Callis, a chemistry professor at Montana State University.

"The theory had far-reaching influence on the field of solvent effects on chemical reactions," Kauffman says. "Any time a polar solute exists in a polar solvent, which of course occurs often, the energy of the solute is affected by the reaction field."

Theoretical chemist Jacopo Tomasi of the University of Pisa, in Italy, wrote about Onsager's article in a special "New Century Issue" of Theoretical Chemistry Accounts [103, 196 (2000)]. Tomasi indicated that several characteristics have contributed to the longevity of Onsager's paper, including the mathematical simplicity and physical robustness of the model. "It may be modified with little effort and adapted to many different problems," Tomasi wrote.

"The original theory by Onsager only applies to a spherical molecule and cavity, and many modern implementations allow more complex shapes," says Paul R. Rablen, associate chemistry professor at Swarthmore College, in Pennsylvania. "However, authors who develop or use continuum solvation models still frequently cite Onsager, since he did lay out the original theoretical framework."

The paper eventually opened new avenues of research. For example, Onsager's equation was adapted in the 1950s to solvatochromism, the study of solvent effects on electronic spectra of molecules in solution.

Onsager's model is also relevant for studying the time dependence of the polarization process. "Imagine a nonpolar molecule which becomes polar upon absorption of a photon of light," Kauffman says. "In the ground state, there is no reaction field (no oriented molecules surrounding the solute), but upon excitation a polar molecule is created and now we expect polarization. The time-dependent process of polarization is known as solvent relaxation, and it is a very active field of research currently."

"Like Onsager's more important contribution--the Onsager reciprocal relations, for which he was awarded the Nobel Prize--I believe this one was ahead of its time as regards applications by the chemical community as a whole," Callis says. "Its importance rose for a while and is now declining in terms of being cited or direct use of the equations. However, applications of the concept of reaction field are probably growing, especially as the use of fluorescent dyes in biology increases exponentially."

"Onsager's paper had far-reaching consequences for essentially all of solution-phase chemistry with respect to the fundamental physics that underlies chemical reactions," Kauffman says. "The reaction field is a fundamental aspect of any solution. Onsager was the first to recognize its significance, and now everyone concerned with solvent effects must include the reaction field in their picture of chemical reaction dynamics in solution. I would have to conclude that this will never diminish in importance because it is so fundamental."

Onsager received the 1968 Nobel Prize in Chemistry for other work on the thermodynamics of irreversible processes, which was published in two papers in 1931. He died in 1976 at the age of 72.

C&EN is celebrating the 125th volume of the Journal of the American Chemical Society by featuring selected papers from the list of its 125 most cited. Onsager's paper ranks sixth on the list.


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Copyright © 2003 American Chemical Society

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