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OSCAR KNEELER RICE February 12, 1903May 7, 1978 BY BENJAMIN WIDOM AND RUDOLPH A. MARCUS WITH THE DEATH of Oscar Rice at Chapel Hill, North Carolina, in the spring of 197S, physical chemistry lost one of its foremost practitioners, a man who for more than half a century had been a leacler and an inspiration in the clevelopment of that science. For the last forty-two of those years he tract been a member of the chemistry faculty of the University of North Carolina, as Kenan Professor from 1959 and as Kenan Professor Emeritus from 1975. He died the week before he was to have been awarclec! an Sc.D. degree by his university. The degree was awarded posthumously; he was cited as "very likely the most clistinguished chemist ever to have lived in North Carolina." ~ Oscar Rice was born in Chicago on February 12, 1903. His parents, Oscar Guiclo Rice and Thekla Knefler Rice, had been married only six months when his father ctiec! of ty- phoic! fever. His mother never remarried, and Oscar never knew a father. He was brought up by his mother and her sister, Amy Knefler, who joined them as homemaker while Thekla Rice supported the househoIc! as a secretary. Al- though the financial resources of the family were strained, ' Maurice M. Bursey, Carolina Chemists: Sketches from Chapel Hill (Department of Chemistry, University of North Carolina at Chapel Hill, 1982), p. 153. 425

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426 BIOGRAPHICAL MEMOIRS Oscar's mother anct aunt made the sacrifices necessary to en- able him to complete his education.2 Oscar attenclec} what was then San Diego Junior College (now San Diego State University) from 1920 to 1922, then transferred to the University of California, Berkeley, where he was awarcled the B.S. degree in 1924. He stayed on at Berkeley for his graduate studies and by 1926he was then only 23 years old tract earned his Ph.D. (Two of his contem- poraries as graduate students at Berkeley were Henry Eyring anti Joseph E. Mayer, also to become important figures in physical chemistry.) After one more year at Berkeley (1926- 27) as an Associate in Chemistry, Rice became a National Re- search Fellow.3 He spent the first two years of his fellowship, 1927 to 1929, at the California Institute of Technology (with brief stays again in Berkeley); the thircl, 1929-30, was spent . . . In . _elpzlg. On his return from :Leipzig, Rice was appointed Instruc- tor in Chemistry at Harvard. He had by then aIreacly com- pleted the early versions of his great work on the theory of unimolecular reactions, written at Berkeley and Caltech, so it can harcIly have been a surprise when, in 1932 after hav- ing been at Harvard for two years he was given the second American Chemical Society Award in Pure Chemistry. (The first winner, in 1931, was Linus Pauling.) For some years while at Harvard, Rice gave a course of lectures entitled "A(1- vancect Inorganic Chemistry" on which he later based his book Electronic Structure and Chemical Binding. The book was not completect, however, until 1939, after Rice's first three years in Chapel Hill. It was published in 1940. Rice's Harvarc! period was highly productive on the re- search side. He studiecl energy exchange in inelastic molec- 2 From a letter by his wife, Hope Sherfy Rice, to their friend "sally" (the Reverend Ann Calvin Rogers-Witte), written May 10, 1978, three days after Oscar Rice's death. 3 In later years called a National Research Council Fellow.

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OSCAR KNEELER RICE 427 ular collisions, using creatively the methods of what was then the new quantum mechanics. He continued the work on un- imolecular reaction-rate theory and on preclissociation and diffuse spectra, which he had begun earlier at Caltech and Leipzig. He wrote his noted papers with Gershinowitz (a Har- varct gracluate student and a Parker Traveling Fellow at Princeton) on reaction-rate theory, and he pursued his im- portant experimental work on thermal decompositions with the collaboration of D. V. Sickman (a postdoctoral associate), A. O. Allen (his first graduate student), and H. C. Campbell. Although those years at Harvard could hardly have been more fruitful, Rice seemed not to be very happy there. A. O. Allen believes that the social sophistication of Harvard may not have been well suited to Rice's quiet, solitary, and contem- plative style. Later, at Chapel Hill, he found him to be more relaxed and at peace" although otherwise unchanged.4 On leaving Harvard in 1935, Rice returned briefly (1935- 36) to the Berkeley chemistry department as a research as- sociate. In 1936, with an appointment as associate professor, he began his long and illustrious career at the University of North Carolina at Chapel Hill. He was promoted to full pro- fessor in 1943. Rice was to remain at Chapel Hill, although he traveled widely for conferences and lectures and took an occasional leave of absence. Just after the Seconc} World War, from ~ 946 to 1947, Rice took a position as Principal Chemist at the Oak Ricige National Laboratory. "The story goes that the Army officer in charge of the laboratory was much concerned about the productivity of this man who sat all clay in an armchair thinking. When it was time to review what had been pro- clucecT, the quality of the work that Dr. Rice had generated in the armchair was so impressive that the officer recom- 4 Letter of November 8, 1982, by A. O. Allen to the authors.

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428 BIOGRAPHICAL MEMOIRS mended stuffed armchairs for every scientist whom he su- pervisecI."5 Before that, at Chapel Hill, under contract to the Office of Scientific Research anc} Development, Rice hac! workoc! on the problem of the burning of rocket powders (1950g).6 In 1947 he was awarded a U.S. Army and Navy Certificate of Appreciation for his war research. It was at Oak Ridge that Oscar Rice met Hope Ernestyne Sherfy, whom he asked to join him as his wife when he re- turnect to Chapel Hill. They were married in 1947. Hope Rice was Oscar's constant companion and a source of joy, comfort, anc! support for their more than thirty years to- gether. They adoptecl two slaughters, Margarita and Pamela, both born in Germany. The Rices adopter! them on two sepa- rate trips Oscar Accompanied by Hope on the first one) macle to Germany to attend! scientific congresses. After the death of Oscar's Aunt Amy, his agec! mother came to live with them in a new and larger house they built in Chapel Hill. The only substantial time Rice spent away from the Uni- versity of North Carolina, except for his year at Oak Ridge, was in 196S, when he was a visiting professor at the Virginia Polytechnic Institute (now the Virginia Polytechnic Institute and State University) in Blacksburg, anct in 1969, when he was Seyclel-Woolley Visiting Professor of Chemistry at the Georgia Institute of Technology. Those physical scientists who, like Oscar Rice, were born in the first half of the century's first decacle, reacher! scientific maturity along with the new quantum theory and wave me- chanics. They couIcl thus, still as young men, participate in the glorious crusade that causect one after another famous problem of physics or chemistry to yield to the power of the new ideas ant! techniques. Writing of the time he began re- 5 Bursey, Carolina Chemists, p. 151. 6 Here and hereafter, years and letters in parentheses refer to entries in the ap- pended bibliography; thus, (1950g) means the seventh entry for 1950.

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OSCAR KNEFLER RICE 429 search with Rice at Harvard, A. O. Allen says: "Oscar hacI just recently published his epochal paper with Ramsperger on the theory of unimolecular reactions, which played an important role in the expansion of physical chemistry cluring what ~ later heard H. S. Taylor refer to as the 'glorious thir- ties.' Incleed, a time when the rest of the florid was clepressed ant! fearful was just when the physical sciences were most exciting anct hopeful. ~ asked for nothing better than to join the exciting revolution in chemical dynamics under Oscar's tutelage."7 Rice's first work at Berkeley was not with quantum me- chanics, for the new theory had hardly been born. Instead, he investigates! those aspects of colloid stability and surface tension that could be treated by classical methods. In his first publisher! paper (1926a), he acknowledges help from R. C. Tolman of Caltech ant! I. H. Hildebranct of Berkeley, who were, or were soon to be, recognized as two of the most prom- inent physical chemists and inspiring teachers in this country. At Berkeley, Rice also knew G. N. Lewis, who hem the prom- ising young student in high regarc! ant! later recommended him for the faculty position at Harvard.8 Rice's early work on surface tension was to have important echoes later in his ca- reer. IncleecI, the combining of microscopic with macro- scopic, largely thermodynamic, ideas to create a phenome- nological theory or description the process one sees in these early papers was also to be the style of much of his later work from the 1940s on. His great work on unimolecular reactions was also, at first (1927b), non-quantum mechanical. It followed ancI was in- tended to explain the measurements of H. C. Ramsperger (also then in the Berkeley chemistry departments on the de- 7 A. O. Allen letter. ~ As attested by a longtime friend, Professor Milton Burton of Notre Dame, in a letter of November 4, 1983, to the authors.

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430 BIOGRAPHICAL MEMOIRS composition of azomethane. Presumably, it was cluring Rice's first postcloctoral year, when he was still at Berkeley as an Associate in Chemistry, that he and Ramsperger formulated the theory.9 The general problem was accounting for the rates of unimolecular decompositions or isomerizations, particularly for the observed fall-off of the rate at low pressures. Earlier ideas of Linclemann, later elaborated by Hinshe~wood (both worker! in Englancl), yielder! some important clues. A prim- itive version of that early theory is the following: Suppose A is the molecule that will react to form product P. and that it does so through a high-energy intermediate A* that is former] by the collision of A with some species M that could be either A or some chemically inert gas with which A is dilutect. The reaction scheme is then: Al k2 A + M=A* + M, A* ~ P. k - I characterizes} by activation and deactivation rate constants kit and k_~ ant] by the rate constant k2 for reaction of the acti- vatecl species. If the population of the latter is assumed to vary only slowly during the reaction (the "steacly-state" ap- proximation), the apparent rate coefficient k for the observed reaction A ~ P is k = k~k2 (M) / Ok_ (M) + k2], where (M) is the concentration of M. Thus k decreases as (M) decreases, which is the characteristic low-pressure fallow of the rate coefficient. This scheme accounted qualitatively for what was ob- 9 The paper was received by the Journal of the American Chemical Society in January 1927 so the work was probably done mainly during the latter half of 1926.

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OSCAR KNEELER RICE 431 served in experiment but not quantitatively: experimentally, I/k floes not vary linearly with I/(M). Rice recognized that a proper theory would have to be more explicit about the meaning of A* anc! k2. He envisaged the complex molecule A as a collection of couplet! oscillators and the activated mol- ecules A* as all those that tract a great enough total energy to react. However, it was only if that energy were correctly ap- portioned particularly, only if some required minimum amount of it founcT its way into a crucial one of the molecule's vibrational degrees of freedomthat reaction would occur. Rice saw the mean time that hacl to elapse between the initial energization of A ancT the favorable reapportionment of that energy as what the primitive versions of the theory tract been trying to express as the time lag to reaction, I/k2. He could now, however, relate that time explicitly to the complexity of the molecule: the greater the number of active vibrational degrees of freedom, the longer wouIct it take for the requirec! energy to fins! its way into a particular one of them. The result was not only a theory in better accord with experiment than its predecessors, but a much more detailed ant! reveal- ing picture of the dynamics of polyatomic molecules. It is a picture that continues to excite the imagination of scientists. The issues raised by itcentral to the study of regular versus stochastic behavior of complex mechanical systems are the object of much current research. When Rice left Berkeley and went to Caltech as a National Research Fellow, one of his first concerns (192Sb) was to re- phrase the unimolecular reaction-rate theory, where neces- sary, in the language of the (older, pre-wave-mechanical) quantum theory. At Caltech he met Louis S. Kassel, who was working on the same problem along similar lines. (In his 1928 paper, Rice expressed his inclebtedness to Kasse} for discus- sions of the problem.) Their names were soon to be linkect permanently, when the theory came to be known to all cbem-

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432 . BIOGRAPHICAL MEMOIRS fists first as the RRK (Rice-Ramsperger-Kassel) theory, then later as the RRKM theory (after later work with tI95la] and bye R. A. Marcus). It was also at Caltech that Rice diet his first landmark work on predissociation anc! diffuse spectra (1929a,b). The phe- nomenon of prectissociation has much in common with that of unimolecular decomposition, and Rice eluciciated the con- nection. Some of this work was apparently done during a temporary return to Berkeley (for his 1929 paper, "On the Quantum Mechanics of Chemical Reactions," has a Berkeley byline). It is clear from the papers of this perioc! that Rice was aIrea(ly mastering and applying the ideas and methods of the new quantum theory originates] primarily by German phys- icists. Since, at that time, the Germans were applying the theory most rapidly and widely, the next major step in his studies a year at the Institute for Theoretical Physics of the University of Leipzig was a natural one. While he was there he met ant! benefittec! from discussions with Werner Heis- enberg, Michael Polanyi, Eugene Wigner, Felix Bloch, and Hartmut KalImann. During his stay in Leipzig, Rice worked on problems of inelastic atomic and molecular collisions (1930a,193la) and extended his earlier work (1929a,b,e) on predissociation. On his return to the United States, he continued his studies of inelastic collisions at Harvard. Referring to Rice's papers (193Ib,c) on that subject, L. lLanclau, writing in 1932, said that until then only Rice had correctly recognized the fun- damental role that the crossing of potential-energy curves played in those processes. Landau remarked that previous work had impliecl a strange disappearance of energy. In an- ' R. A. Marcus,./ournal of Chemical Physics 20(1952):359. " L. Landau, Physikalische Zeitschrift der Sowjetunion I(1932):~.

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OSCAR KNEFLER RICE 433 other direction, Rice's method for treating problems in which the collision partners approach slowly but interact strongly (193le) anticipated what later came to be called the "method of perturbed stationary states." Recent evaluations have also recognized the perceptive- ness of Rice's pioneering work on predissociation ( 1929a,b,e, 1930c).~3 Wilse Robinson, referring to Rice's work of this pe- riocI, noted: "Many persons, myself inclucled, working on ra- cliationIess transitions in large molecules 30 years later un- fortunately were not fully aware, even though we should have been, of the beautiful physical insight into this problem al- reacly recorclect, dust-covered and forgotten, in the library. Who would guess that one of the best intuitive descriptions of the process whereby a discrete state 'prepared by the ab- sorption of light' interacts with a continuum is contained in that great paper of September ~ 0, ~ 929 . . . ?" 14 In collaboration with Harold Gershinowitz at Harvard, Rice also macle an early contribution toward the now famous transition-state theory of chemical reactions (1934c). In ad- dition, he mastered the new ideas of valency and molecular structure that arose from the quantum theory. His course in advanced inorganic chemistry at Harvard must have been one of the first in the country to give a systematic presenta- tion of those ideas for young students; now such courses are stanciarct in the chemistry curriculum. Rice's influential book, Electronic Structure and Chemical Binding (1940a), which was basect on his Harvard lectures, has come to be regarded as a highly original contribution to the pedagogy of chemistry. After moving to Chapel Hill, Rice continued to pursue his i2 N. F. Mott and H. S. W. Massey, The Theory of Atomic Colli ions, 2d ed. (Oxford, 1949), pp. 153-57. 13 R. A. Harris, Journal of Chemical Physics 39(1963):978; G. W. Robinson, in Excited States, vol. 1, ed. E. C. Lim (New York: Academic Press, 1974), p. 1. 14 G. W. Robinson, in Excited States, p. 1.

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434 BIOGRAPHICAL MEMOIRS interests in chemical reaction kinetics (both its theoretical and experimental aspects) with vigor. In the early 1960s, he again took up the problem of the kinetics and mechanism of atomic recombination (anct its inverse, diatomic dissociation, to which he hacI been giving intermittent attention since 1941. He presented arguments of great subtlety and generality (196Ib) to clarify the question of equality between the equi- librium constant in a reaction anct the ratio of forward and reverse rate constants (the "rate-quotient land. These can be best appreciated in a simple example. In the kinetic scheme k, ko kit A = A* = B* = B. k6 k5 k4 with A* and B* being transient high-energy intermediates, the concentrations of which can be treater} in steady-state approximation, the rate constants kf and kr for the forward and reverse reactions A > B and B ~ A are: kf= k~k2k3/(k3k6 + k5k6 + kSk3) kr = k4k5k6/(k3k6 + k5k6 + k2k3) The "equilibrium" approximations to these rate constants (obtained for the forward reaction as k2 times the ratio of the concentrations of A* and A at equilibrium, and analogously for the reverse reaction) are kfq = k~k2/k6 and kreq = k5k4/k3. These exceec} the true (i.e., the steady-state) rate constants by the common factor ~ + k5/k3 + k2/k6. Thus, although the true rate constants kf and kr are less than they are estimated to be by the equilibrium approximation, they deviate from the latter by identical factors, so that kf/kr, like kfq/kreq, is just k~k2k3/k4k5k6, which is the equilibrium constant for the reac- tion A = B. This illustrates what Rice found to be a general phenom-

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OSCAR KNEELER RICE 447 1936 On the zero-point energy of an activated complex and the reaction 2NO + O`: > KNOB. }. Chem. Phys., 4:53-59. With D. V. Sickman. Studies on the decomposition of azomethane. I. Description of the apparatus. J. Chem. Phys., 4:239-41. With D. V. Sickman. Studies on the decomposition of azomethane. II. Pure azomethane and azomethane in the presence of he- lium. I. Chem. Phys., 4:242-51. On the thermodynamic properties of nitric oxide. An example of an associated liquid. l. Chem. Phys., 4:367-72. With G. E. Gibson. The electric moment of the 'l; + to O+ transition in the continuum of Cat. Phys. Rev., 50:380 (erratum 50:8711. With D. V. Sickman. Studies on the decomposition of azomethane. III. Effect of various inert gases. I. Chem. Phys., 4:608-13. 1937 With R. A. Ogg, Jr. Factors influencing rates of reaction in solution. J. Chem. Phys., 5:140-43. Internal volume and the entropy of vaporization of liquids. J. Chem. Phys., 5:353-58. On transitions in condensed systems. I. Chem. Phys., 5:492-99. 1938 The solid-liquid equilibrium in argon. J. Chem. Phys., 6:472-75. On communal entropy and the theory of fusion. I. Chem. Phys., 6:476-79. 1939 Further remarks on the solid-liquid equilibrium in argon. }. Chem. Phys.,7:136-37. With H. C. Campbell. The explosion of ethyl azide in the presence of diethyl ether. J. Chem. Phys., 7:700-709. The nature of the fusion process in argon. J. Chem. Phys., 7:883- 92. 1940 Electronic Structure and ChemicalBonding: With SpecialReference to Inorganic Chemistry. New York: McGraw-Hill Book Company. (Reprinted with corrections, Mineola, N.Y.: Dover, 1969~.

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448 BIOGRAPHICAL MEMOIRS The role of heat conduction in thermal gaseous explosions. I. Chem. Phys., 8:727-33. With W. L. Haden, tr., and E. P. H. Meibohm. Note on the chain photolysis of acetaldehyde in intermittent light. I. Chem. Phys., 8:998. 1941 A note on tne entropy of fusion of argon. }. Chem. Phys., 9: 121. The interatomic potential curve and the equation of state for ar- gon. I. Am. Chem. Soc., 63:3-11. On the recombination of iodine and bromine atoms. l. Chem. Phys., 9:258-62. With C. V. Cannon. The photolysis of azomethane. I. Am. Chem. Soc., 63:2900. 1942 The effect of intermittent light on a chain reaction with bimolec- ular and unimolecular chain-breaking steps. J. Chem. Phys., 10:440-44. With W. L. Haden, Jr. The chain photolysis of acetaldehyde in in- termittent light. l. Chem. Phys., 10:445-60 [erratum 12~19441:5211. With C. V. Cannon. A monochromator using a large water prism. Rev. Sci. Instrum., 13:513 - 14. The partition function of a gas of hard elastic spheres. l. Chem. Phys., 10:653-54. The partition function of a simple liquid. I. Chem. Phys., 10:654. 1944 On the statistical mechanics of liquids, and the gas of hard elastic spheres. I. Chem. Phys., 12: 1-18 terrata 12:521 l. The thermodynamic properties and potential energy of solid ar- gon. J. Chem. Phys., 12:289-95. 1946 The thermodynamic properties and potential energy of solid ar- gon. II. l. Chem. Phys., 14:321-24. The thermodynamic properties of liquid argon. J. Ghem. Phys., 14:324-38.

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OSCAR KNEELER RICE 449 A note on communal entropy. Remarks on a paper by Henry S. Frank. J. Chem. Phys., 14:348-50. With G. W. Murphy. Corresponding states in the frozen rare gases. J. Chem. Phys., 14:518-25. Review of Photosynthesis and Related Processes, vol.1, Chemistry of Pho- tosynthes~s, Chemosynthes~s, and Related Processes in Vitro and in Vivo, by Eugene I. Rabinowitch. Rev. Sci. Instrum., 17:145-46. 1947 With L. White, Jr. The thermal reaction of hexafluoroethane with quartz. I. Am. Chem. Soc., 69:267-70. On the behavior of pure substances near the critical point. l. Chem. Phys., 15:314-32 Lerrata 15:6151. The effect of pressure on surface tension. }. Chem. Phys., 15:333- 35. Activation in unimolecular reactions. I. Chem. Phys., 15:689-90. A note on the relation between entropy and enthalpy of solution. J. Chem. Phys., 15:875-79. 1948 Quantum corrections to the thermodynamic properties of liquids, with application to neon. I. Chem. Phys., 16:141-47. With F. London. On solutions of He3 in He4. Phys. Rev., 73:1188- 93. 1949 Critical phenomena in binary liquid systems. Chem. Rev., 44:69- 92. The thermodynamics of liquid helium on the basis of the two-fluid theory. Phys. Rev., 76:1701-7. 1950 Effect of He3 on the A-point of He4. Phys. Rev., 77: 142-43. With O. G. Engel. Lambda-temperatures of solutions of He3 in He4. Phys. Rev., 78:55-57. The partial molal entropy of superfluid in pure He4 below the A- point. Phys. Rev., 78:182-83. With O. G. Engel. Thermodynamics of He3-He4 solutions..Phys. Rev., 78:183.

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450 BIOGRAPHICAL MEMOIRS The thermodynamics of liquid helium and of He3-He4 solutions. Phys. Rev., 79: 1024-25. With V. E. Lucas. The chain-breaking process in acetaldehyde pho- tolysis. J. Chem. Phys., 18:993-94. With R. Ginell. The theory of the burning of double-base rocket powders. I. Phys. Colloid Chem., 54:885-917. Introduction to the symposium on critical phenomena. I. Phys. Colloid Chem., 54: 1293 -1305. 1951 With R. A. Marcus. The kinetics of the recombination of methyl radicals and iodine atoms. I. Phys. Colloid Chem., 55:894-908. With R. W. Rowden. Critical phenomena in the cyclohexane- aniline system. I. Chem. Phys., 19: 1423-24. The solid-liquid transition in argon. In: Phase Transformations in Solids (Proceedings of a symposium at Cornell University, Au- gust 1948), ed. R. Smoluchowski, I. E. Mayer, and W. A. Weyl. New York: John Wiley & Sons. 1952 With R. W. Rowden. Phenomene critique dans le systeme cyclo- hexane-aniline. In: Changements de Phases. Comptes Rendus de la Deuxieme Reunion Annuelle de la Societe de Chimie Phy- sique, Paris, tune 2-7, 1952. With I. L. Weininger. The photolysis of azoethane. I. Am. Chem. Soc., 74:6216-19. 1953 Reply to Careri's "Note on the rate of recombination of free atoms." I. Chem. Phys., 21:750-51. Irreversible processes with application to helium II and the Knud- sen effect in gases. Phys. Rev., 89:793-99. With B. Widom. The thermodynamics of the helium film. Phys. Rev., 90:987. With D. Atack. The interracial tension and other properties of the cyclohexane-aniline system near the critical solution tempera- ture. Discuss. Faraday Soc., 15:210-18. Contributions to the discussion. Discuss. Faraday Soc.,15:110,276, 286, 287.

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OSCAR KNEELER RICE 1954 451 With }. C. Morrow. Solutions of nonelectrolytes. Annul Rev. Phys. Chem., 5:71. With D. Atack. Critical phenomena in the cyclohexane-aniline system. J. Chem. Phys., 22:382-85. The nature of higher-order phase transitions with application to liquid helium. Phys. Rev., 93:1161-68. Thermodynamics of phase transitions in compressible solid lat- tices. I. Chem. Phys., 22:1535-44. With D. Atack. Thermodynamics of vapor-phase mixtures of io- dine and benzene, with application to the rate of recombination of iodine atoms. T Phys. Chem., 58: 1017-23. Statistical mechanics of helium II near INK. Phys. Rev., 96: 1460- 63. Heat and entropy of mixing of He3 and Her on the basis of the two-fluid theory of He4. Phys. Rev., 96: 1464-65. 1955 Shape of the coexistence curve near the critical temperature. i. Chem. Phys., 23:164-68. Relation between isotherms and coexistence curve in the critical region. J. Chem. Phys., 23:169-73. Interpretation of the magnetic behavior of liquid helium-3. Phys. Rev., 97:263-66. Can helium-3 be expected to exhibit superfluidity at sufficiently low temperatures? Phys. Rev., 97 :558-59. Energy levels in liquid He3. Phys. Rev., 97: 1176. Comparison of the energy excitations in liquid He3 and Her. Phys. Rev., 98:847-51. With B. Widom. Critical isotherm and the equation of state of liquid-vapor systems. }. Chem. Phys., 23:1250-55. With H. A. Hartung. Some studies of spontaneous emulsification. J. Colloid Sci., 10:436-39. With R. Gopal. Shape of the coexistence curve in the perfluoro- methylcyclohexane-carbon tetrachloride system. J. Chem. Phys., 23:2428-31. Critical phenomena. In: High Speed Aerodynamics and Jet Propulsion, vol. 1, Thermodynamics and Physics of Matter, ed. F. D. Rossini, pp. 419 - 500. Princeton: Princeton University Press.

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452 BIOGRAPHICAL MEMOIRS 1956 Elementary theory of the excitations in liquid helium: New model for rotors. Phys. Rev., 102:1416. Reversible flow phenomena and thermodynamic properties of liquid helium and the two-fluid hypothesis. Phys. Rev., 103: 267-74. 1957 A kinetic approach to the thermodynamics of irreversible pro- cesses. I. Phys. Chem., 61:622-29. With F. Kohler. Coexistence curve of the triethylamine-water sys- tem. J. Chem. Phys., 26: 1614-18. Some remarks on solutions of He3 in He4. In: Proceedings of the Symposium on Liquid and Solid Helium Three. on. 173-80. Colum- bus: Ohio State University Press. Elementary theory of liquid helium: Refinement of the theory and comparison with Feynman's theory. Phys. Rev., 108:551-60. ' 1 ~ 1958 Energy fluctuations in liquid helium and its flow properties. Nuovo Cimento Suppl., 9(ser. 10~:267 - 85. 1959 With F. R. Meeks and R. Gopal. Critical phenomena in the cyclo- hexane-aniline system: Effect of water at definite activity. I. Phys. Chem., 63:992-94. Reaktionen mit intermolekularem Energieaustausch. Monatsh. Chem., 90:330-56. The recombination of atoms, and other energy-exchange reac- tions. In: Proceedings of the Ninth International Astronautics Con- gress, Amsterdam, 1958, pp.9 - 19. Vienna: Springer-Verlag KG. Gas of hard nonattracting spheres. J. Chem. Phys., 31:987-93. 1960 Note on the equation of state for hard spheres. J. Chem. Phys., 32: 1277-78. With M. E. Jacob and I. T. MacQueen. A dilatometric study of the cyclohexane-aniline system near its critical separation temper- ature. J. Phys. Chem., 64:972-75.

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OSCAR KNEELER RICE 453 The thermodynamics of non-uniform systems, and the interracial tension near a critical point. I. Phys. Chem., 64:976-84. Conditions for a steady state in chemical kinetics. i. Phys. Chem., 64: 1851-57. The principle of minimum entropy production and the kinetic ap- proach to irreversible thermodynamics. I. Phys. Chem., 64: 1857-60. Clausius-Clapeyron equation. In: Encyclopaedic Dictionary of Physics, vol. 1, pp. 695 - 96. London: Pergamon Press. Continuity of state. In: Encyclopaedic Dictionary of Physics, vol. 2, pp. 71 - 72. London: Pergamon Press. 1961 With }. T. MacQueen and F. R. Meeks. The effect of an impurity on the phase transition in a binary liquid system as a surface phenomenon. l. Phys. Chem., 65:1925-29. On the relation between an equilibrium constant and the non- equilibrium rate constants of direct and reverse reactions. }. Phys. Chem., 65:1972-76. Effects of quantization and of anharmonicity on the rates of dis- sociation and association of complex molecules. l. Phys. Chem., 65: 1588-96. 1962 With I. T. MacQueen. The effect of an impurity on the phase tran- sition in a binary liquid system. II. I. Phys. Chem., 66:625-31. With W. Forst. Entropy of activation in the thermal decomposition of azomethane. Ann. Assoc. Can.-Fr. Av. Sci. Montreal, 28:47. 1963 Further remarks on the "rate-quotient law." l. Phys. Chem., 67: 1733-35. Non-equilibrium effects in the dissociation of diatomic molecules by a third body. J. Phys. Chem., 67:6-11. With W. Forst. The thermal decomposition of azomethane. I. Effect of added olefin and nitric oxide. Can. l. Chem., 41 :562-85. With A. W. Loven. Coexistence curve of the 2,6-lutidine + water system in the critical region. Trans. Faraday Soc., 59:2723-27.

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454 BIOGRAPHICAL MEMOIRS 1964 Some problems in energy exchange related to chemical kinetics. In: Transfert d'Energae dans les Gaz, Douzieme Conseil de Chimie Solvay, Brussels, November 1962, pp. 17-86. New York: Inter- science Publishers. With D. R. Thompson. Shape of the coexistence curve in the per- fluoromethylcyclohexane-carbon tetrachl:~ride system. II. Mea- surements accurate to 0.0001. l. Am. Chem. Soc., 86:3547-53. The thermodynamic properties and interatomic potential energy of solid argon. I. Elisha Mitchell Sci. Soc., 80: 120. 1965 Energy fluctuations and the nature of the rotons in helium II. In: Proceedings of the Ninth International Conference on Low Temperature Physics, p. 88. New York: Plenum Press. 1966 With W. C. Worsham and M. T. ~aquiss. High pressure capillary thallium-amalgam arc for use in ultraviolet. Rev. Sci. Instrum., 37: 1084-85. 1967 Statistical Mechanics, Thermodynamics, and Kinetics. San Francisco: W. H. Freeman and Company. Statistical thermodynamics of A-transitions, especially of liquid helium. Phys. Rev., 153:275 -79. With N. F. Irani. Coexistence curve of the cyclohexane + methylene iodide system in the critical region. Trans. Faraday Soc., 63:2158-62. Possible relation between phase separation and the A-transition in 3He-4He mixtures. Phys. Rev. Lett., 19:295-97. With W. C. Worsham. Deactivation by collision in the photolysis of azoethane. J. Chem. Phys., 46:2021. With B. W. Davis. Thermodynamics of the critical point: Liquid- vapor systems. J. Chem. Phys., 47 :5043-53. 1968 With E-C. Wu. The photolysis of perfluoroazomethane. l. Phys. Chem., 72:542-46.

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OSCAR KNEFLER RICE 455 On charge-transfer complexes in the vapor phase. Int. J. Quantum Chem. Symp., 2:219-24. 1969 Some remarks on the foundations of thermodynamics and statis- tical mechanics. J. Phys. Soc. Jpn., 26(suppl.~:219. With D. R. Chang. The thermal decomposition of azomethane-d6. Int. I. Chem. Kinet., 1:171-91. On the motion of a sphere in a perfect fluid with application to liquid helium. Proc. Natl. Acad. Sci. USA, 63:1055-62. Statistical thermodynamics of the A transition in liquid helium. I. Am. Chem. Soc., 91:7682-84. Melting phenomena in simple solids. Physikertag. Phys. Ges. (Salz- burg), Vorabdrucke Kurzfassungen Fachber., 34:73-78. 1971 With D. R. Chang. Secondary variables in critical phenomena, with application to A transition in liquid helium. In: Critical Phenom- ena in Alloys, Magnets, and Superconductors, ed. R. E. Mills, E. Ascher, and R. I. Jaycee, pp. 105-24. New York: McGraw-Hill Book Company. On the relation between unimolecular reaction and predissocia- tion. I. Chem. Phys., 55:439-46. 1972 Secondary variables in critical phenomena. Acc. Chem. Res., 5:112-20. With D. R. Chang. Thermodynamic relationship at the tricritical point in 3He-4He mixtures. Phys. Rev. A, 5: 1419-22. With D. R. Chang. Some thermodynamic relations at the critical point in liquid-vapor systems. Proc. Natl. Acad. Sci. USA, 69:3436-39. 1973 On the relation between A lines and phase separations. Proc. Natl. Acad. Sci. USA, 70:1241-45. Foreword. In: Theory of Unimolecular Reactions, by W. Forst: New York: Academic Press.

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456 BIOGRAPHICAL MEMOIRS 1974 With D. R. Chang. Density fluctuations and the specific heat near the critical point. Physica, 74:266 -76. With D. R. Chang. Density fluctuations and the specific heat near the critical point. II. Physica, 78:490-99. With D. R. Chang. The effect of density-gradient terms in the free energy on density fluctuations near the critical point. Physica, 78:500-504. Critical Phenomena and Liquid Helium, National Technical Infor- mation Service AD Report no. 783381/7GA. Washington, D.C.: National Technical Information Service. 1976 With D. R. Chang. Thermodynamic properties of fluids near the critical point, as interpreted by a simplified renormalization theory and the self-limitation of fluctuations. Physica, 83A: 18-32. With D. R. Chang. Effect of the density-gradient term in the free energy expression on critical exponents. Physica, 83A:609-14. The effect of an impurity on the critical point of a binary liquid system as a surface phenomenon. I. Chem. Phys., 64:4362-67. Effect of an impurity on the critical point of a binary liquid system as a surface phenomenon. In: Colloid and Interface Science, vol. 5, ed. M. Kerker, pp. 405-9. New York: Academic Press. 1977 Interfacial tension near the critical point and the density-gradient term in the free energy. J. Phys. Chem., 81:1388-92. Interfacial tension near the tricritical point of 3He-4He solutions. I. Low Temp. Phys., 29:269-73. 1979 Fluctuations, density gradients, and interfaces near the critical point of one-component fluids. J. Phys. Chem., 83: 1859-1863. Existence of two characteristic lengths in determining the thickness of an interface near the critical point, and the interface profile. J. Phys. Chem., 83:1863-1865.

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