The Journal of
Physical Chemistry
0 Copyright, 1984, by the American Chemical Society
VOLUME 88, NUMBER 26
DECEMBER 20, 1984
Peter Debye (1884-1 966): A Centenary Appreciation “Peter Debye? Yes,” one can hear the young physical chemist saying, “that must be the dipole-moment and strong electrolyte man”. And quite correctly identified, if only by two details in a much larger picture. It. is a sad feature in the hectic pace characterizing even the teaching of science that we have so little, if any, time to consider its development. How can one understand the present, if one has small knowledge of how it has arisen? And yet for an active scientist (Le,, one mainly geared to this year’s research) to spend time on the background and growth of his subject is usually “to go off the boil” or “to waste time on inessentials”. But there is an important sense in which science, as an adequate appreciation of the established facts and their interpretation, is far more than the latest results and their immediate implication. Hence the significance of grasping at least aspects of its growth and, to this, the contributions of its leading exponents provide an introduction of immediate appeal. There can be substantial rewards to such a study. It is now clear that a sufficiently sharp minded reader of Maxwell’s treatment of the field due to a moving charge might have grasped the essentials of Einstein’s special theory of relativity without the subtleties of “simultaneity”: and a footnote in a Debye paper (1913) clarified what was unnecessarily obscure for 45 years, when a widely general far-infrared absorption greatly added to our understanding of molecular motion in liquids. “‘The individual clearly shows the nature of his roots”. Debye certainly had “roots”. His family, for four generations, was established in Maastricht, a city in the southeast corner of The Netherlands, capital of the Limburg province, and distanced even more in character than in space from the Protestant Holland of the north. There, his father was a respected foreman in a metal foundry and his mother, a bright, sharp, numerate person, was the cashier of the Maastricht theatre which doubled as an opera house for touring companies. As a teenager Peter Debye had immense pleasure from the opera performances he well recalled 50 years later. Debye graduated from the Maastricht High School in seventeen subjects (five methematical, four sciences, four languages, history, geography, public administration, and economics) and at the top of the Limburg list. His father insisted he continue his studies, although, lacking Greek and Latin, he could not then enter a Dutch university. The ancient German city of Aachen was some 20 miles away and in its Technische Hochschule he studied for his diploma in electrotechnology. In view of his later more than adequate mathematical ability, it is significant that Debye was immersed from the early stages in applied mathematics. He had two gifted physics professors: Max Wien (experimental) and Arnold Sommerfeld (theoretical). It was Sommerfeld who quickly realized Debye’s outstanding gifts and when, in 1906, Sommerfeld moved 0022-3654/84/2088-6461$01.50/0
to become professor of theoretical physics at the University of Munich, he took Debye with him as his assistant-“a charming boy who looked out on the world and on life with intelligence and curiosity... From here (Munich) he set out on his victorious progress through Physics and Chemistry”.’ Debye’s doctoral thesis (entitled “Concerning the Rainbow”) was completed in Munich. It gave a comprehensive account of the interaction of light with spherical particles of varying refractive index. The thesis showed mathematical ability of a high order (e.g., in the treatment of Hankel and Bessel functions) and it provided a base for much of Debye’s later achievement in evaluating the varied interactions of radiation with matter. Table I provides a listing of Debye’s major published contributions to molecular and physical science. It will be appropriate in this account to give most attention to physicochemical items, although these are by no means the most widely significant. Planck arrived at his famous radiation formula by a series of steps and only subsequently justified it in a treatment which used complete continuity for the energy spectrum in one part, but introduced discontinuous energy values (hv) in the other part ( 1900). Debye ( 1910) first gave a deduction which used quantized radiation throughout: a deduction acclaimed and subsequently used by Planck, who, it is well-known, had for many years (unlike Einstein and Debye) doubts about the reality of quanta of radiation. Debye was firmly convinced of the generality of the quantization condition, and specifically so before Bohr had grasped it.* His clarity of grasp led him to his well-known treatment of lattice specific heats (and the first of so many “Debye equations”) and to the calculation of the temperature effect in X-ray diffraction intensities within only months of the discovery of the diffraction by von Laue’s group. This treatment (experimentally confirmed by W. H. Bragg, 1914), Ewald characterized as “a most impressive one and of great consequence ... also for the first immediate experimental proof of the existence of zero-point en erg^".^ With the same confidence in the character of quantized radiation, Debye later (1923) published a complete, concise and outstandingly clear analysis of what was to be known as the Compton effect, to which he was stimulated by the appearance of a brief preliminary note of Arthur Compton’s experimental results. In 1912, in a paper entitled “A Kinetic Theory of Insulators”, Debye not only invoked, for the first time, permanent electric dipoles in molecules but, much more significantly, he sketched the theory for their measurement. Although adequately applicable only for gases, he ventured (in the absence of appropriate gaseous (1) Sommerfeld, A. Phys. BI. 1950, 6, 509. (2) Davies, M. Biogr. Mem. Fellows R.SOC.1970, 16, 175.
(3) Ewald, P. P. “Fifty Years of X-ray Diffraction”; Oosthoek’s Uitgeversmaatschappij: Utrecht, 1962; p 79.
0 1984 American Chemical Society
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The Journal of Physical Chemistry, Vol. 88. No. 26, 1984
data) to apply his relations to liquids. His values, given in D, Le., the Debye unit = lo-’* esu, included (current values in brackets): diethyl ether, 1.18 (1.16): toluene, 0.51 (0.34): water, 0.57 (1.82). The order of magnitude is all that is correct. The deduction of what became known as the total molar polarization (but is more appropriately the total molar polarizability) is merely sketched on the basis of “the Curie-Langevin form E(a/T)”: a reference to the fact that he was following Langevin’s treatment of paramagnetism (1905). In 1913 a far more impressive paper appeared giving the theory of the frequency dependence of the electric permittivity, Le., the dispersion of the “dielectric constant” (E’) and of the accompanying dielectric absorption (E”). Firstly, Debye shows that the rotation of a dipolar molecular sphere, following a Brownian motion pattern, will lead to an exponential decay of the very slight orientation it would acquire in an electric field when that field is removed. This gives for the time decay of the dipole polarization: P(t) = P(0)e-kr= P(O)d/‘ Here, = l/k, is introduced by Debye as a real time factor to characterize the first molecular relaxation time in physics. H e also deduces, from the Stokes equation, 7 = (3V/kT)v, where Vis the volume of the molecule and 7 is the “viscosity” factor effective at the molecular level. These “Debye equations” include the very simple form of the frequency (w = 2xv) dependence of the dielectric absorption (E”): E”(W) =
(E’O
- E-)-’
TABLE I: Some of Debve’s Maior Contributions Debye’s location contribution and date Munich (1906-10) first consistent deduction Planck radiation formula (19 10) Zurich (1911-12) specific heats for crystalline solids: C, = f(Debye temperature), (1912) defines and evaluates molecular electric dipole moments: 1 X lo-’* esu = 1 D (1912) theory of dielectric dispersion and evaluation Utrecht (1912-14) molecular relaxation times (19 13) calculates influence of lattice temperature on X-ray diffraction intensities: the Debye temperature factor (1913) for crystals, expansion coefficient related to anharmonicity lattice vibrations: conductivity to scattering and decay of phonons ( 1913) Gottingen ( 1914-20) Debye-Scherrer X-ray diffraction powder method (1916-20) uses Hamiltonian as basis theory of atomic spectra ( 1916)
Zurich (1920-27)
W7
1
+ w272
They have provided a remarkably effective basis for the initial valuation of dielectric b e h a ~ i o r . Debye ~ himself, using Drude’s experimental data, applied his relations to liquid water with the results (present values in brackets): E ’ ~= 80 (80.2); dm= 2 (4.5); 7 (ps) = 5 (9.2). Until 1947, it could be said that no published data were certainly nearer the correct values than Debye’s estimates of 1913. A footnote in the 1913 paper explains that Debye’s omission of the inertial term (Z(d20/dt2)) from the equation of molecular rotational motion was justified owing to the smallness of Z (cgs units) for times greater than s or frequencies below 1Olo Hz. This explicit omission led to two significant and concurring forms of correction before 1949 (Rocard: Powles) but despite this, up to 1965 and even later, special deductions were being made in the absence of its appreciation. Eventually, Poley established (1955) and Gebbie and Chamberlain (1 965), using interferometric spectrometry over 10 to 150 cm-l, showed the form of the nonDebye absorption which necessarily comes in from the quasilibrational motion of the dipoles in their real molecular cage. The Debye-Scherrer powder method for X-ray diffraction (1916) was a new method developed by a successful excursion into experimental studies, and of major significance also in foreshadowing later far more detailed treatments in the same area (e.g., the Compton effect and X-ray diffraction by gases and liquids). The Debye-Hiickel electrolyte theory was a new interest, stimulated by Debye hearing an account by Edmond Bauer of Ghosh’s attempt to treat salt solutions using a quasi-lattice distribution of the ions. Milner had more correctly treated the thermodynamic aspects of the system (1909) but, without knowing this, Debye produced clear deductions of both the thermodynamic and the more intricate conductivity behavior. In these papers, as in many others, his mastery is seen in the restriction to the main essentials, their mathematically sound analysis, and the presentation of the results in forms directly useable with experimental data. It is well-known that Onsager corrected the conductivity function: he also extended the Debye evaluation of dipole moments and aspects of the low-temperature work. In 1926 Debye published a remarkably lucid evaluation of the cooling effect on the demagnetization of a paramagnetic salt. A value for the cooling could not be predicted as the necessary physical factors were not then measured-“it appears not to be (4) Davies, M. In “Dielectric Properties and Molecular Behavior”, Hill, N., Vaughan, W. E., Price, A. H., Davies, M., Ed.; Van Nostrand: London,
1969.
Davies
Leipzig (1927-34)
Berlin (1934-40)
Cornell (1940-66)
comprehensive theory of the Compton effect (1923) theory of strong electrolytes-thermodynamic features and conductivities (1923: with Huckel) extended theory of X-ray scattering by gaseous molecules (1925) molecular theory Kerr effect (1925) full theory cooling by adiabatic demagnetization (1926) Experimental studies of the X-ray diffraction of gases and liquids related to molecular structure (1929-33) diffraction of light by ultrasonic waves in liquids (1932) several aspects quasi-crystalline “structure” of liquids (1937-39) Fourier methods in electron diffraction studies (1938) theory thermal diffusion (Clusius) method of isotope separation (1939) light (and, more generally, radiation) scattering related to molecular and media structures (1944-66) many aspects polymer behavior (1945-66) critical state opalescence (1960-66) electric field effects (1960-66)
excluded that this can be large. Only experiments can decide ...” There is reason to believe that this paper (again, somewhat “out of the blue”) was stimulated by Debye hearing at Berkeley a preliminary account of the work he was engaged on by Giauque, who published his own theoretical treatment in 1927, and achieved major practical results in 1933. Debye’s further important activities can only be briefly summarized: he significantly extended both the theory and practice of X-ray diffraction in the gaseous and liquid states; he advanced electron diffraction studies by using Fourier methods in their evaluation; he repeatedly emphasized the local quasi-crystalline “structure” in liquids; he gave the theory for Clusius’s method of isotope separation. At Cornel1 there was a marked preoccupation with the molecular physics of polymers. The basis and limitations of the Staudinger viscosity relation were illuminated. There were many studies of critical opalescence and the critical state. And, perhaps best known, there was the development of the light-scattering method for the evaluation of molecular weights and molecular interactions. Few could have succeeded as well as Debye in the very careful, successful, application of this procedure even down to solutions of sucrose with a molecular weight of only 342. The theory was based on Rayleigh-one of Debye’s favorite physicists-and had earlier been well illustrated by Putzeys and Brosteaux (1935).
