Biographical Memoirs Volume 60 (1991) / Chapter Skim
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12. Lars Onsager
12. Lars Onsager
Pages 182-233
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From page 183... ...
The young man's name was Lars Onsager.2 Forty-three years later Onsager was awardect the Nobel Prize in Chemistry for the "discovery of the reciprocal relations bearing his name, which are fundamental for the thermoclynamics of irreversible processes." A group of physicists and chemists at Cornell had written of him: "We believe that his work is unique for its penetration, breadth, and influence in the development of theoretical and experimental studies of condenser! matter.
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From page 184... ...
In 1920 Lars was admitted to the Norges Tekniske Hogskole in Trondheim to study chemical engineering in preparation for a technical career. But his inclinations were mainly intellectual; he had already bought a copy of Whittaker and Watson's classic monograph, Modern Analysis,3 and he worked through most of the (notoriously ctifficult)
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From page 185... ...
It was his own Pleas about these processes that ultimately led him to the reciprocal relations that now bear his name; but a parallel influence on his thinking was the experimental work of C
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From page 186... ...
Debye and his assistant Erich Huckel had put forward a new theory of electrolyte solutions founded on the idea that the electrostatic field of a dissolved ion is screened by an "atmosphere" of opposite net charge, the effective screening distance being inversely proportional to the square root of the ionic strength c, defined as ~ 2 C = ~,CiZi (1) where ci Is the concentration of ion i, and zi is its electric charge in elementary units.
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From page 187... ...
had evaluated Al by assuming one particular ion to move uniformly in a straight line but allowing the other ions to undergo Brownian motion subject to the fields of their clistortec3 atmospheres. All that was requires!
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From page 188... ...
Onsager would have been the first to admit that he stood on Debye's shoulders both in his work on electrolytes and in his later investigations of the dielectric constants of polar liquids and solutions of polar molecules. During the next few years the meticulous experimental work of ShedIovsky6 confirmed the Limiting Law to a high degree of accuracy, and Onsager was to continue to develop his theory of electrolytic transport especially in collaboration with Raymonc!
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From page 189... ...
with him as a postdoctoral associate, recalls a lecture to the Kapitza Club in Cambridge, many years later, at which Onsager was explaining his joint work with Bruria Kaufman on the Ising lattice.
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From page 190... ...
Conf. Irreversible Thermodynamics and the Statistical Mechanics of Phase Transitions (Onsager Symposium)
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From page 191... ...
Claesson, "The Nobel Prize for Chemistry" (presentation speech) , Les Prix Nobel en 1968, p.
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From page 192... ...
in conducting this experiment until more than a decade later, when it was needed as part of the Manhattan Project for the atomic bomb." ~i Onsager's pedagogic encleavours at Brown were hardly more effective than at Johns Hopkins, but they resulted! in one major conversion.
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From page 193... ...
Admittedly, I did assume some consistent scheme of Brownian motion kinetics; but even that seemed non-essential." At this point his thoughts returned to the precise experimental work of Riiber on the mutarotation of sugars. Riiber had discovered that galactose existec!
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From page 194... ...
According to a principle formulated by Boltzmann, the nature of thermal (and chemical) equilibrium is statistical, and the statistics of spontaneous deviation is determined by the associated changes of the thermodynamic master function that is, the entropy.
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From page 195... ...
With characteristic simplicity and depth of physical insight he chose for his non-equilibrium parameters the displacements Hi of certain centres of mass and energy from their equilibrium positions. Thus a small temperature gradient in a solid body could be represented by assigning a small finite value to the vector displacement of the center of energy from its equilibrium position, and the consequent flow of heat would appear as a regression of this displacement towards the value zero.
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From page 196... ...
with great care, and a complete exposition clid not appear until 193 I." The claims were general incleecI, and the Reciprocal Relations are now often referred to as the Fourth Law of Thermodynamics. Like the other equations of thermodynamics, they are at the same time mathematically simple and physically deep.
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From page 197... ...
G Miller, "Thermodynamics of irreversible processes: the experimental verification of the Onsager reciprocal relations," Chem.
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From page 198... ...
Having awarded him a postdoctoral fellowship, the Chemistry Department was embarrassed to discover that he had no Ph.D. The Reciprocal Relations had been published two years before, but an outline of his results, submitted to his alma mater in Trondheim, had been judged unacceptable for a doctorate as it stood.
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From page 199... ...
He suggester} to Professor Hill, chairman of chemistry, that if the Chemistry Department felt uneasy at doing so, the Mathematics Department wouIc! be happy to recommend the award of the degree.
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His best-known papers of that period! were a paper on the Wien effect and one on the dipole moments of molecules in solution.
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disturbecl a number of chemists because it called into question the Debye formula relating the dielectric constant of a polar substance to the molecular dipole moment. The formula had been widely used for determining dipole moments from the temperature variation of gaseous dielectric constants but was known to fad!
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Two papers on the separation of isotopes by thermal diffusion (1939,2,3) foreshaclowecl the use of this technique in the Manhattan Project for extracting the fissile isotope 235U from natural uranium, which is mostly MU.
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From page 203... ...
the reach of human intelligence. The problem was this: Can the funciamental postulates of statistical mechanics account for the distinct phases of matter, and more specifically, do they imply the occurrence of a sharp phase transition in a regular array of particles that interact only with their nearest neighbors in the array?
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From page 204... ...
"With fascination, Onsager examined their methods and saw that he could add a trick or two, then followed up one encouraging lead after another until he had computed the partition function, which determines the thermodynamic properties. The result was obtained in 1942; he took time to tidy up various details and published it in 1944."~9 Onsager, in fact, utilized the transfer matrix method intro(luced by Kramers and Wannier in which the partition function of a square lattice of m rows, each containing n particles or spins, is expressed as a trace; explicitly one has ~9 L
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From page 205... ...
TncleecI, Onsager's work proved that a sharp phase transition occurs only when the lattice becomes infinite in both dimens~ons. Onsager has related how he first attacked the problem by solving the two-row case (m = 2)
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From page 206... ...
Onsager's solution of the Ising problem was first revealed as a discussion remark following a paper by Gregory Wannier at a meeting of the New York Academy of Sciences on February IS, 1942. It took the world of theoretical physics by storm: "The partition function for the Ising model of a two-dimensional 'ferromagnetic' has been evaluated in closed form.
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From page 207... ...
. But as he once remarked to Joseph Hubbard, "Obsession with partition functions maketh a dull man," and he was soon on the track of the other properties of the two-dimensional Ising ferromagnet.
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22(1969) :720-22; "Neutron scattering investigation of phase transitions and magnetic correlations in the two-dimensional antiferromagnets K2NiF4, Rb2MnF4, Rb2FeF4," Phys.
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From page 209... ...
E Fisher, "The susceptibility of the plane Ising model," Physica 25 (1959)
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C Ward, "Correlations and spontaneous magnetization of the two-dimensional Ising model," [.
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. ,,28 Joseph Hubbard reports that Onsager could not be persuadecl to give his opinion of Feynman's theory of liquid helium, but Richard Feynman has given us a vivid account of some personal encounters with Onsager.
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From page 212... ...
Frisch, F.R.S., is reproduced by permission of the Biographical Memoirs of Fellows of the Royal Society, London. Feynman was quick to recognize, behind Onsager's habit of talking in ricicIles, a kindly ant]
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From page 213... ...
the contribution of his experimental colleagues at the Mond: "Within a few years, D Shoenberg rose to the challenge and applied intense magnetic fields by a pulse technique, then picked up the fine ripples of the magnetic response as the field changed." During the same year he gave a seminar in Oxford about his ideas on liquid helium, but on this occasion even the theorists were baffled.
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From page 214... ...
Technicae in 1960 from the Norwegian Institute of Technology, his penitent alma mater; and in 1962 no fewer than three more honorary doctorates (one of them from Brown University)
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From page 215... ...
Kirkwood and Onsager had been at Yale together for some years, and though both men added lustre to the Sterling Chemical Laboratory, they were a study in contrasts. Kirkwood had a passion for formal rigor but less of a taste for bold simplifying physical assumptions.
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From page 216... ...
Eventually, just before he left, Onsager was prevailed upon to return the paper. His report consisted of the single word "Somehow." It is hardly surprising that the journals eventually stopped asking him to act as a referee.
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From page 217... ...
In 1966 he received the Belfer Awarcl at Yeshiva University, and in 1968 he was nominated—not for the first time— for the Nobel Prize. The faculty at Cornell nominated him both for the Physics and the Chemistry prize, mentioning especially his fundamental work on phase transitions; in the 32 M
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From page 218... ...
By the time others in the University discovered the situation and protested to President Kingman Brewster, fir., it was too late. Onsager had, in the meanwhile, accepted an appointment as Distinguished University Professor at the University of Miami, Coral Gables, and joined the University's Center for Theoretical Studies directed by Behram Kursunoglu, where his research was generously funded by national agencies.
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From page 219... ...
(He was a regular attender at conferences of all sorts, but his interventions were few and far between; he preferre(1 listening, usually with his eyes closed, to hoIcling forth.) But he never underestimated the task of understancIing the brain, of the electroencephalogram he once remarkecl: `6lt is like trying to discover how the telephone system works by measuring the fluctuations in the electric power used by the telephone company." Joseph Hubbard, who first met Onsager at Yale as a postdoctoral fellow in 1971 and accompanied him to Coral Gables, has given us a number of personal glimpses of the last few years.
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From page 220... ...
" 1975. The Royal Society elected Onsager a Foreign Member in In the autumn of 1976, Lars went to a conference in Canacla on radiation chemistry a relatively new interest, but touching on some of his early Pleas ~ ~ 974,31.
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From page 221... ...
A service in his memory was held ten days later, on October I5, in the Dwight Memorial Chapel at Yale University, and tributes were paid him by Henry Margenau, Platonia Kirkwoo(l, anti Manfred Eigen. RETROSPECT Lars Onsager was not altogether of this world, though he had a creep unclerstanding of its fundamental laws.
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From page 222... ...
Feynman, Joseph Hubbard, Oliver Penrose, Michael Stephen, and Julian Sturtevant for valuable sidelights on Onsager's life, Benjamin Widom for a critical reading of the manuscript, and the Kline Science Library at Yale University for material assistance in the preparation of the bibliography, which we believe to be essentially complete.33 We are also particularly indebted to Otto Frisch for his drawing of Onsager reproduced here. 33 For a list compiled by the Kline Science Library of the biographies of Lars Onsager that appeared from 1938 to 1963, see Biographical Memoirs, Royal Society (London)
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From page 223... ...
LARS ONSAGER APPOINTMENTS 223 1926-1928 Research Assistant, Eidgenossische Technische Hoch schule, Zurich, Switzerland 1928 Associate in Chemistry, Johns Hopkins University 1928-1933 Instructor in Chemistry, Brown University 1933-1934 Sterling and Gibbs Fellow, Yale University 1934-1940 Assistant Professor of Chemistry, Yale University 1940-1945 Associate Professor of Chemistry, Yale University 1945-1973 I Willard Gibbs Professor of Theoretical Chemistry, Yale University 1951-1952 Fulbright Scholar, Cambridge University 1961 Visiting Professor, University of California, San Diego 1967-1968 Visiting Professor, Rockefeller University 1968 Visiting Professor, University of Gottingen 1970 Visiting Professor, University of Leiden 1972-1976 Distinguished University Professor, University of Miami, Coral Gables DEGREES 1925 Ch.E., Norges Tekniske Hogskole, Trondheim, Norway 1935 Ph.D., Yale University HONORARY DEGREES 1954 D.Sc., Harvard University 1960 Dr Technicae, Norges Tekniske Hogskole 1962 D.Sc., Brown University D.Sc., Rensselaer Polytechnic Institute Dr Naturwissenschaften, Rheinisch-Westfalisch Technische Hochschule, Aachen 1968 D.Sc., The University of Chicago 1969 D.Sc., Ohio State University 1970 Sc.D., Cambridge University 1971 D.Sc., Oxford University MEDALS AND PRIZES 1953 Rumford Gold Medal, American Academy of Arts and Sciences
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From page 224... ...
W Debye Award in Physical Chemistry, American Chemical Society 1966 Belfer Award in Pure Science, Yeshiva University 1968 Nobel Prize in Chemistry President's National Medal of Science ACADEMIC AFFILIATIONS AND DISTINCTIONS FELLOW American Physical Society (1933)
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(1974) ASSOCIATE Neurosciences Research Program, U.S.A.
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From page 226... ...
37: 405-26. Reciprocal relations in irreversible processes.
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Clark Jones. On the theory of isotope separation by thermal diffusion.
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Zucker. Apparatus for isotope separation by thermal diffusion.
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From page 229... ...
Kim. The relaxation effect in mixed strong electrolytes.
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Liu. Zur Theorie des Wiene~ekts in schwachen Elektrolyten.
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From page 231... ...
1971 The Ising model in two dimensions. In: Critical phenomena in alloys, magnets and superconductors (Report on the Battelle Symposium)
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From page 232... ...
227-79. In: Quantum statistical mechanics in the natural sciences, Coral Gables Conf., 1973, eds.
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