Lars Onsager

Lars Onsager (1903-1976) made significant contributions to chemistry, including his developments in the Debye-Hückel theory of electrolytic dissociation and his work with non-reversable systems. He received the 1968 Nobel Prize in Chemistry.

Born in Norway, Lars Onsager received his early education there before coming to the United States in 1928 to do graduate work at Yale University. After receiving his Ph.D. in theoretical chemistry he stayed on at Yale and ultimately spent nearly all of his academic career at that institution. Onsager's first important contribution to chemical theory came in 1926 when he showed how improvements could be made in the Debye-Hückel theory of electrolytic dissociation. His later (and probably more significant) work involved non-reversible systems —systems in which differences in pressure, temperature, or some other factor are an important consideration. For his contributions in this field, Onsager received a number of important awards including the Rumford Medal of the American Academy of Arts and Sciences, the Lorentz Medal of the Royal Netherlands Academy of Sciences, and the 1968 Nobel Prize in Chemistry.

Lars Onsager was born in Oslo (then known as Christiania), Norway, on November 27, 1903. His parents were Erling Onsager, a barrister before the Norwegian Supreme Court, and Ingrid Kirkeby Onsager. Onsager's early education was somewhat unorthodox as he was taught by private tutors, by his own mother, and at a somewhat unsatisfactory rural private school. Eventually he entered the Frogner School in Oslo and did so well that he skipped a grade and graduated a year early. Overall, his early schooling provided him with a broad liberal education in philosophy, literature, and the arts. He is said to have become particularly fond of Norwegian epics and continued to read and recite them to friends and family throughout his life.

In 1920, Onsager entered the Norges Tekniski Hoslashgskole in Trondheim where he planned to major in chemical engineering. The fact that he enrolled in a technical high school suggests that he was originally interested in practical rather than theoretical studies. Onsager had not pursued his schooling very long, however, before it became apparent that he wanted to go beyond the everyday applications of science to the theoretical background on which those applications are based. Even as a freshman in high school, he told of making a careful study of the chemical journals, in order to gain background knowledge of chemical theory.

One of the topics that caught his attention concerned the chemistry of solutions. In 1884, Svante Arrhenius had proposed a theory of ionic dissociation that explained a number of observations about the conductivity of solutions and, eventually, a number of other solution phenomena. Over the next half century, chemists worked on refining and extending the Arrhenius theory.

The next great step forward in that search occurred in 1923, when Onsager was still a student at the Tekniski Hoslashgskole. The Dutch chemist Peter Debye and the German chemist Erich Hückel, working at Zurich's Eidgenössische Technische Hochschule, had proposed a revision of the Arrhenius theory that explained some problems not yet resolved—primarily, whether ionic compounds are or are not completely dissociated ("ionized") in solution. After much experimentation, Arrhenius had observed that dissociation was not complete in all instances.

Debye and Hückel realized that ionic compounds, by their very nature, already existed in the ionic state before they ever enter a solution. They explained the apparent incomplete level of dissociation on the basis of the interactions among ions of opposite charges and water molecules in a solution. The Debye-Hückel mathematical formulation almost perfectly explained all the anomalies that remained in the Arrhenius theory.

Almost perfectly, but not quite, as Onsager soon observed. The value of the molar conductivity predicted by the Debye-Hückel theory was significantly different from that obtained from experiments. By 1925, Onsager had discovered the reason for this discrepancy. Debye and Hückel had assumed that most—but not all—of the ions in a solution move about randomly in "Brownian" movement . Onsager simply extended that principle to all of the ions in the solution. With this correction, he was able to write a new mathematical expression that improved upon the Debye-Hückel formulation.

Onsager had the opportunity in 1925 to present his views to Debye in person. Having arrived in Zurich after traveling through Denmark and Germany with one of his professors, Onsager is reported to have marched into Debye's office in Zurich and declared, "Professor Debye, your theory of electrolytes is incorrect." Debye was sufficiently impressed with the young Norwegian to offer him a research post in Zurich, a position that Onsager accepted and held for the next two years.

In 1928, Onsager emigrated to the United States where he became an associate in chemistry at Johns Hopkins University. The appointment proved to be disastrous: he was assigned to teach the introductory chemistry classes, a task for which he was completely unsuited. One of his associates, Robert H. Cole, is quoted in the Biographical Memoirs of Fellows of the Royal Society: "I won't say he was the world's worst lecturer, but he was certainly in contention." As a consequence, Onsager was not asked to return to Johns Hopkins after he had completed his first semester there.

Fortunately, a position was open at Brown University, and Onsager was asked by chemistry department chairman Charles A. Krauss to fill that position. During his 5-year tenure at Brown, Onsager was given a more appropriate teaching assignment, statistical mechanics. His pedagogical techniques apparently did not improve to any great extent, however; he still presented a challenge to students by speaking to the blackboard on topics that were well beyond the comprehension of many in the room.

A far more important feature of the Brown years was the theoretical research that Onsager carried out in the privacy of his own office. In this research, Onsager attempted to generalize his earlier research on the motion of ions in solution when exposed to an electrical field. In order to do so, he went back to some fundamental laws of thermodynamics, including Hermann Helmholtz's "principle of least dissipation." He was eventually able to derive a very general mathematical expression about the behavior of substances in solution, an expression now known as the Law of Reciprocal Relations.

Onsager first published the law in 1929, but continued to work on it for a number of years. In 1931, he announced a more general form of the law that applied to other non-equilibrium situations in which differences in electrical or magnetic force, temperature, pressure, or some other factor exists. The Onsager formulation was so elegant and so general that some scientists now refer to it as the Fourth Law of Thermodynamics.

The Law of Reciprocal Relations was eventually recognized as an enormous advance in theoretical chemistry, earning Onsager the Nobel Prize in 1968. However, its initial announcement provoked almost no response from his colleagues. It is not that they disputed his findings, Onsager said many years later, but just that they totally ignored them. Indeed, Onsager's research had almost no impact on chemists until after World War II had ended, more than a decade after the research was originally published.

The year 1933 was a momentous one for Onsager. It began badly when Brown ended his appointment because of financial pressures brought about by the Great Depression. His situation improved later in the year, however, when he was offered an appointment as Sterling and Gibbs Fellow at Yale. The appointment marked the beginning of an affiliation with Yale that was to continue until 1972.

Prior to assuming his new job at Yale, Onsager spent the summer in Europe. While there, he met the future Mrs. Onsager, Margarethe Arledter, the sister of the Austrian electrochemist H. Falkenhagen. The two apparently fell instantly in love, became engaged a week after meeting, and were married on September 7, 1933. The Onsagers later had three sons, Erling Frederick, Hans Tanberg, and Christian Carl, and one daughter, Inger Marie.

Onsager had no sooner assumed his post at Yale when a small problem arose: the fellowship he had been awarded was for postdoctoral studies, but Onsager had not as yet been granted a Ph.D. He had submitted an outline of his research on reciprocal relations to his alma mater, the Norges Tekniski Hoslashgskole, but the faculty there had decided that, being incomplete, it was not worthy of a doctorate. As a result, Onsager's first task at Yale was to complete a doctoral thesis. For this thesis, he submitted to the chemistry faculty a research paper on an esoteric mathematical topic. Since the thesis was outside the experience of anyone in the chemistry or physics departments, Onsager's degree was nearly awarded by the mathematics department, whose chair understood Onsager's findings quite clearly. Only at the last moment did the chemistry department relent and agree to accept the judgment of its colleagues, awarding Onsager his Ph.D. in 1935.

Onsager continued to teach statistical mechanics at Yale, although with as little success as ever. (Instead of being called "Sadistical Mechanics," as it had been by Brown students, it was now referred to as "Advanced Norwegian" by their Yale counterparts.) As always, it was Onsager's theoretical—and usually independent—research that justified his Yale salary. In his nearly four decades there, he attacked one new problem after another, usually with astounding success. Though his output was by no means prodigious, the quality and thoroughness of his research was impeccable.

During the late 1930s, Onsager worked on another of Debye's ideas, the dipole theory of dielectrics . That theory had, in general, been very successful, but could not explain the special case of liquids with high dielectric constants. By 1936, Onsager had developed a new model of dipoles that could be used to modify Debye's theory and provide accurate predictions for all cases. Onsager was apparently deeply hurt when Debye rejected his paper explaining this model for publication in the Physikalische Zeitschrift, which Debye edited. It would be more than a decade before the great Dutch chemist, then an American citizen, could accept Onsager's modifications of his ideas.

In the 1940s, Onsager turned his attention to the very complex issue of phase transitions in solids. He wanted to find out if the mathematical techniques of statistical mechanics could be used to derive the thermodynamic properties of such events. Although some initial progress had been made in this area, resulting in a theory known as the Ising model, Onsager produced a spectacular breakthrough on the problem. He introduced a "trick or two" (to use his words) that had not yet occurred to (and were probably unknown to) his colleagues—the use of elegant mathematical techniques of elliptical functions and quaternion algebra. His solution to this problem was widely acclaimed.

Though his status as a non-U.S. citizen enabled him to devote his time and effort to his own research during World War II, Onsager was forbidden from contributing his significant talents to the top-secret Manhattan Project, the United State's research toward creating atomic weapons. Onsager and his wife finally did become citizens as the war drew to a close in 1945.

The postwar years saw no diminution of Onsager's energy. He continued his research on low-temperature physics and devised a theoretical explanation for the superfluidity of helium II (liquid helium). The idea, originally proposed in 1949, was arrived at independently two years later by Princeton University's Richard Feynman. Onsager also worked out original theories for the statistical properties of liquid crystals and for the electrical properties of ice. In 1951 he was given a Fulbright scholarship to work at the Cavendish Laboratory in Cambridge; there, he perfected his theory of diamagnetism in metals.

During his last years at Yale, Onsager continued to receive numerous accolades for his newly appreciated discoveries. He was awarded honorary doctorates by such noble universities as Harvard (1954), Brown (1962), Chicago (1968), Cambridge (1970), and Oxford (1971), among others. He was inducted to the National Academy of Sciences in 1947. In addition to his Nobel Prize, Onsager garnered the American Academy of Arts and Sciences' Rumford Medal in 1953 and the Lorentz Medal in 1958, as well as several medals from the American Chemical Society and the President's National Medal of Science. Upon reaching retirement age in 1972, Onsager was offered the title of emeritus professor, but without an office. Disappointed by this apparent slight, Onsager decided instead to accept an appointment as Distinguished University Professor at the University of Miami's Center for Theoretical Studies. At Miami, Onsager found two new subjects to interest him, biophysics and radiation chemistry. In neither field did he have an opportunity to make any significant contributions, however, as he died on October 5, 1976, apparently the victim of a heart attack.

Given his shortcomings as a teacher, Onsager still seems to have been universally admired and liked as a person. Though modest and self-effacing, he possessed a wry sense of humor. In Biographical Memoirs, he is quoted as saying of research, "There's a time to soar like an eagle, and a time to burrow like a worm. It takes a pretty sharp cookie to know when to shed the feathers and … to begin munching the humus." In a memorial some months after Onsager's death, Behram Kursunoglu, the director of the University of Miami's Center for Theoretical Studies, described him as a "very great man of science—with profound humanitarian and scientific qualities."

Further Reading on Lars Onsager

Biographical Memoirs of Fellows of the Royal Society, Volume 24, Royal Society (London), 1978.

Current Biography 1958, H. W. Wilson, 1958.

Nobel Lectures in Chemistry, 1963-1970, [Amsterdam], 1972.