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Classics and classicists of colloid and interface science 8. Albert Einstein
HISTORICAL NOTE Classics and Classicists of Colloid and Interface Science 8. Albert Einstein It should not come as a surprise to readers of this journal that Albert Einstein's (1879-1955) contributions to colloid science were immense, including as they do Brownian movement, light scattering, sedimentation equilibrium, and viscosity. Despite their eventual eclipse by his outpourings in quantum theory, in special relativity, and in general relativity, they figured centrally during the first decade of his career; indeed, from that vantage point his contributions to colloid science may have been preeminent. He saw colloids as the vehicle through which the atomickinetic view of nature might be verified, an issue that was hotly contested at the time. Einstein is probably second among scientists only to Isaac Newton in his fame and in the esteem accorded to him by contemporary society, and if he was not universally acclaimed, it is because he did not hesitate to take public stands on issues of great controversy. On the other hand, unlike Isaac Newton, whose work on gravitation was for a generation deemed unacceptable by large sections of the scientific community, Einstein's work was quickly incorporated into the fabric of 20th century physics. He was born in Ulm, Germany, on 14 March 1879, the son of Herman and Pauline (Koch) Einstein, and grew up in Munich (1). Einstein resented what he considered the regimentation of the German school system, preferring to read widely and study on his own. He left school at age 15 in order to tramp about Italy, where his family had moved, and recommenced schooling first at a gymnasium in Arrau, Switzerland, and then at the famous Federal Institute of Technology (ETH) in Zurich, from which he received his diploma in 1900. He was unsuccessful in obtaining an appointment at ETH or with Ostwald in Leipzig or Kammerlingh-Onnes in Leiden (2), and accepted some temporary school teaching positions until being appointed as examiner at the Swiss patent office in Bern in 1902. There he spent what he considered 7 very happy years, during the evenings and Sundays of which he wrote the scientific papers that contributed centrally to the foundations of modern physics. He married a fellow student of his ETH days, Mileva Maric, to whom his sons Hans Albert ( 1904-1973 ) and Edward ( 1910- i 965 ) were born. Einstein's miracle year occurred in 1905, when he published three remarkable papers in volume I7 of Annalen der Physik ( 3 ): one each on the nature of light, on Brownian motion, and on special relativity. At the time, he considered the paper on the nature of light the most revolu-
tionary (4). This was also the year that his Ph.D. thesis was accepted by ETH. The subject of the thesis, published in 1906, treated the viscosity and diffusion of colloidal suspensions. The Brownian motion paper was its sequel. It was not until 1909 that Einstein received an academic appointment at the University of Zurich. This was followed by appointments at the German University of Prague in 1911 and the ETH in 1912. In 1914 he moved to Berlin as a member of the Prussian Academy of Sciences and Director of the Kaiser Wilhelm Institute of Physics. He separated from his wife in 1914, was divorced in 1919, and then married his divorced cousin Elsa Einstein Lowenthal. He was awarded the Nobel Prize in 1921 for his work on the nature of light. Einstein became world-famous in t919 when a total solar eclipse provided the opportunity for verifying his general theory of relativity by measuring the bending of light due to the sun's gravity (5). He became increasingly involved in public affairs, particularly as a forceful proponent of pacifism and of Zionism. He had renounced German citizenship upon becoming a Swiss citizen in his youth, had refused to accept German citizenship upon returning to Berlin in 19t4 even when this was initially made a condition of his appointment, and he was almost unique among intellectuals on both sides during World War I in denouncing that war. He became the target of antisemitic attacks in Germany after the war; and upon the accession of Hitler in 1933, resigned his Berlin posts and accepted a position at the Institute for Advanced Studies in Princeton. He became an American citizen in 1940. In t939 he sent his famous letter to President Roosevelt suggesting the possibility of utilizing atomic energy for military purposes. Obviously his pacifism had waned. In 1952 he was offered, but declined, the presidency of Israel. He died in Princeton on April 18, 1955. Einstein's interests in colloids arose in connection with the question of the reality of atoms. Polemics must have followed shortly after the formulation of atomism in antiquity by Leucippos (6) and they raged with renewed virulence upon publication of John Dalton's System of Chemical Philosophy in 1808. By the end of the 19th century, the success of thermodynamics and electromagnetism in viewing matter as a continuum underlay the polemics by opponents of the atomic theory such as Ernst Mach and Wilhelm Ostwald against those such as Boltzmann who championed the kinetic molecular view. Ostwald,
291 0021-9797/89 $3.00 Journal of Colloid and Interface Science, Vol, 129, No. 1, April 1989
Copyright © I989 by Academic Press, Inc. All rights of reproduction in any form reserved.
292
HISTORICAL NOTE
undoubtedly the most influential chemist of the age, "who was one of Boltzmann's most vociferous o p p o n e n t s . . . became more and more convinced that molecules, atoms and ions were only mathematical and a priori fictions, and that the underlying component of the universe was energy in its various arrays" (7). The acceptance of atomism by most of these combatants was to come only after Jean Perrin's verification of Einstein's theory of Brownian motion. Ernst Mach never relented. The origin of Brownian motion had been debated throughout the 19th century (8). The crux of the matter was posed succinctly by G. Gouy: The Brownian movement shows us, therefore, assuredly not the movements of the molecules, but something derived closely from these and furnishes proof of the exactness of the hypothesis on the nature of heat. If one adopts these views, then the phenomenon, the study of which is far from being terminated, takes on assuredly an importance for molecular physics of the first order. (9) The same volume in which the above statement is found also contains an article by Ostwald (10) emitled "The Rout of Contemporary Atomism," in which he protests that "an immediate consequence of this theory has never been verified" and that the imaginary concepts of imagined entities were "disturbing us with forces, the existence of which we cannot demonstrate, acting between atoms we cannot see." This is the fray into which young Einstein, patent examiner, entered. He noted (11) that despite the achievement of the kinetic theory of gases, "in chemistry only the ratios of the atomic masses played any role, not their absolute magnitudes, so that atomic theory could be viewed more as a visualizing symbol than as knowledge concerning the factual structure of matter . . . . My major aim in this was to find facts which would guarantee as much as possible the existence of atoms of definite size." Einstein focused on statistical mechanics; he wrote (11) of his earliest work (1902-1904): Not acquainted with the earlier investigations of Boltzmann and Gibbs, which had appeared earlier and actually exhausted the subject, I developed the statistical mechanics and the molecular-kinetic theory of thermodynamics which was based on the former. My major aim in this was to find facts which would guarantee as much as possible the existence of atoms of definite finite size. In the midst of this I discovered that, according to atomistic theory, there would have to be a movement of suspended microscopic particles, open to observation, without knowing that observations concerning Brownian motion were already long familiar. In one sense the quest for a manifestation of atomic reality can be reduced to a determination of Avogadro's number since this provides a measure of the mass of an atom. And it was this quest that Einstein took upon him-
Journal of CoUoid and InterfaceScience, VoL 129, No. l, April 1989
self. Within the space of less than 3 months Einstein made three distinct fundamental discoveries which permitted calculation of Avogadros' number. The first, with which we are not concerned here, based upon the blackbody radiation law, is contained in the 1905 paper on the nature of light. The others are in his doctoral thesis and the first Brownian motion paper. In his thesis, which was published in 1906 (12b), Einstein utilized fluid mechanical arguments to derive his famous equation for the viscosity of a suspension of coUoidal spheres by extending Van't Hoff's treatment of osmotic pressure to include particles exhibiting Stokes frictional resistance. He also derived a relation for the diffusion coefficient of a sphere. These two equations permitted calculation of Avogadro's number from experimental values of viscosity, diffusion, and density. An error in the viscosity equation was corrected in 1911 (12e) to give the currently accepted formula n* = 7(1 + 2.5~b) where 7" and ~ are the viscosities of sol and solvent and ~bis the volume fraction of suspended spheres. The 1905 Brownian motion paper (12a) builds upon the solution for the diffusion coefficient obtained in his thesis by treating the solution of Fick's law for a single particle as the probability of finding that particle at a certain distance from an origin after a particular time interval. He then notes that an observable quantity, namely, the mean square displacement of the particle X2 in a particular time interval t, can be used to determine Avogadro's number: --
2
/RT
1
)\
provided the radius and the coefficient of viscosity are also known. In this case there were no available data as in the earlier examples from which to calculate a value of N. Yet what was so exciting was the seeming visualization of atomic motion as one observed colloidal particles being buffeted about within a tumultuous sea of molecules. Einstein appreciates the momentous nature of his result. "It is possible that the movements to be discussed here are identical with the so-called Brownian molecular motion . . . . It is to be hoped that some enquirer may succeed in solving the problem suggested here . . . . If the movement discussed here can actually be observed. . . . then classical thermodynamics can no longer be looked upon as applicable to bodies even of dimensions distinguishable in a microscope: an exact determination of actual atomic dimensions is then possible. On the other hand, had the prediction of this movement proved to be incorrect, a weighty argument would be provided against the molecular-kinetic conception of heat." Shortly thereafter, emboldened to entitle the paper " o n the Theory of Brownian Motion" (12c ), Einstein extended the theory to include rotational Brownian motion and the equilibrium distribution of particles in a gravitational field, which occurs as a result of the Brownian motion.
293
HISTORICAL NOTE For Einstein, the study of Brownian motion had a twofold value, the one in verifying a theoretical construct and the other in illuminating our physical sense of things: Because of the understanding of the essence of Brownian motion, suddenly all doubts vanished about the correctness of Boltzmann's interpretation of the thermodynamic laws . . . . It is of great importance since it permits an exact computation of N . . . . The great significance as a matter of principle is, however, • . . that one sees directly under the microscope part of the heat energy in the form of mechanical energy. The story of Jean Perrin's experimental verification of these results, which led to the final collapse of opposition to the view that molecules are real, has been eloquently told elsewhere (7). Einstein's last foray into the issue of molecular reality was his paper on the "Theory of Opalescence of Homogeneous Liquids and Mixtures of Liquids in the Vicinity of the Critical State" (13). He was stimulated by Smoluchowski's paper (14) in which the scattering of light by fluids near the critical point was attributed to microscopic density (and hence refractive index) fluctuations. These fluctuations constituted irreversible processes whose probability could be calculated with the aid of Boltzmann's entropy-probability theorem. Thus Einstein saw still another opportunity to buttress Boltzmann's views and to determine Avogadro's number. Smoluchowski had not in the first of two papers provided a detailed calculation of the amount of light scattered. There followed a statistical thermodynamic analysis leading to an estimate of the mean square fluctuation of the density and an electromagnetic theory analysis giving the scattered field due to such random fluctuations. For a pure liquid the intensity of scattered light was inversely proportional to the isothermal compressibility. For a solution he found that the corresponding parameter was the concentration dependence of the chemical potential. Finally, by utilizing the Gibbs-Duhem relation, the molecular weights of the two components were incorporated into the expression for the light scattering. Once again Einstein completes his analysis by directing attention to a critical experiment (13). "A quantitative experimental investigation into the phenomenon dealt with here would be of great interest: it certainly would be worthwhile to know whether Boltzmann's principle actually predicts correctly the phenomenon considered and, on the other hand, we could obtain through such investigations exact values for the number, N." This work by Smoluchowski and Einstein was entirely novel. Theretofore light scattering had been attributed to random assemblies of isolated particles. Rayleigh was able to show how in the case of a gas the phenomenological refractive index of the gas might be utilized to supplant what otherwise would have required fictitious values for the molecular radius and refractive index. Indeed, Rayleigh then proceeded to use estimates of the varying brightness
of a star at different altitudes to calculate Avogadro's number within a factor of 3 (15 ). However, the treatment of a condensed phase where correlation among the molecular scattering centers results in strong destructive interferences had not been attempted. Einstein's proposal to calculate N by measurement of the light scattered by condensed systems was carried out in 1923, by which time of course new determinations of N were antielimatic (16 ). However, the 1910 paper was eventually to play an important role in the development of colloid and polymer science. In his treatment of binary solutions, Einstein had incorporated the molecular weights of the solute and solvent so that once the value of N was firmly accepted, his equation could be used directly to estimate molecular weights from light scattering data. Peter Debye (17) utilized Einstein's equation to develop the procedures so well known and widely used today to estimate the molecular weights of polymers and the particle sizes of small colloidal particles. Smoluchowski and Einstein had initially proposed that their theory would account for critical opalescence when in fact it applies to liquids except in those states very close to the critical point. Einstein appreciated that the theory would require retention of higher order terms very close to the critical point. However, he was not aware that additional physical effects would arise near the critical point due to correlations among the fluctuations (18). Pais (1), himself a high energy particle physicist, has commented on the impact of Einstein's work on colloids: The history of Einstein's influence on later works, as expressed by the frequency of citations of his papers, offers several striking examples. Of the eleven scientific articles published by any author before 1912 and cited most frequently between 1961 and 1975, four are by Einstein. Among these four, the thesis (or, rather, the 1906 paper) ranks first; then follows a sequel to i t . . . written in 1911. The Brownian motion paper ranks third, the paper on critical opalescence fourth. At the top of the list of Einstein's scientific articles cited most heavily during the years 1970 to 1974 is the 1906 paper. It was quoted four times as often as Einstein's first survey article of 1916 on general relativity and eight times as often as his 1905 paper on the light-quantum. There can be no argument that Einstein's main interests and contributions were in quantum theory and relativity. Yet even though his output in colloid science, work of his early years, comprised a small part of the final corpus of his work, it has had a major impact upon the development of colloid science. REFERENCES 1. Perhaps the most perspicuous of the many biographies, which also discusses his scientific work in considerable detail, is the one by Abraham Pais, "Subtle
Journal of Colloid and Interface Science, Vol. 129,No. 1, April 1989
294
HISTORICAL NOTE
Is the L o r d . . . " (Oxford Univ. Press, New York, 1982). Unattributed quotations by Einstein given in this paper are cited by Pals. 2. Einstein wrote to Ostwald on 19 March 1901. "Esteemed Herr Professor! Because your work on general chemistry inspired me to write the enclosed article, I am taking the liberty of sending you a copy of it. On this occasion permit me also to inquire whether you might have use for a mathematical physicist familiar with absolute measurements. If I permit myself to make such an inquiry, it is only because I am without means, and only a position of this kind would offer me the possibility of additional education. Respectfully yours." This was followed on 13 April 1901 by a long letter from Einstein's father which reads in part "Esteemed Herr Professor! Please forgive a father who is so bold as to turn to you esteemed Herr Professor, in the interest of his son . . . (who) passed his diploma examinations in mathematics and physics with flying colors. He has been trying unsuccessfully to obtain a position as Assistant, which will enable him to continue his education in theoretical and experimental physics. He is oppressed by the thought that he is a burden on us, people of modest means. . . . . Since it is you, highly honored Herr Professor, whom my son seems to admire and esteem more than any other scholar currently active in physics, it is to you to whom I have taken the liberty of turning with the humble request to read his paper published in the Annalen f'tir (sic) Physik. . . . If, in addition, you could secure him an Assistant's position for now or the next autumn, my gratitude would know no bounds. I am taking the liberty of mentioning that my son does not know anything about my unusual step." On 12 April 1901 he wrote to KammerlinghOnnes, "Esteemed Herr Professor! I have learned through a friend from college that you have a vacancy for an assistant. I am taking the liberty of applying for that position. I studied at the department for mathematics and physics of the Zurich Polytechnikum for 4 years, specializing in physics. I obtained there my diploma last summer. Of course, I will make my grade transcripts available to you with pleasure; I have the honor to submit to you by the same mail a reprint of my article that has appeared recently in Annalen der Physik. Respectfully." This correspondence is reproduced from "The Collected Papers of Albert Einstein" ((John Stachel, Ed.), Vol. 1, Princeton Univ. Press, Princeton, NJ, 1987). 3• Einstein, A., Ann. Phys. 17, 132, 549, 891 (t905). 4. Einstein's fundamental contributions toward our present understanding of the nature of light have •
.
.
Journal of Colloid and Interface Science, Vol. 129, No. 1, April 1989
5.
6.
7. 8. 9.
10. 11.
been discussed by Emil Wolf (Optics News 5, 24 (1979)). These commence with the paper which reintroduced the corpuscular theory of light, a paper which among the three marvelous papers submitred within 3 ½months and published in Volume 17 of Annalen der Physik in 1905, Einstein singled out, in a letter to a friend, as being "very revolutionary." The treatment of the photoelectric effect was among the examples that Einstein gave in support of his view of the corpuscular nature of radiation. Included in his other great papers on radiation is a clear discussion of the wave-particle duality (1909), consideration of the elementary processes of interaction between molecules and radiation (1917), and the quantum theory of an ideal gas (1924, 1925)in which Bose-Einstein statistics was established. That his ideas were both revolutionary and controversial can be judged from Max Planck's letter nominating him for membership in the Prussion Academy of Sciences in 1913 in which Planck said: "That he may sometimes have missed the target of his speculations, as for examples in his hypothesis of light quanta, cannot really be held against him." And yet it was this work, rather than relativity or the mechanics of colloidal particles, for which Einstein received the Nobel Prize in 1921. Therein lies another tale (see Chapt. 30 in Pais' biography, Ref. (1)). Einstein was constantly driven to think about light, as he stated in 1917: "For the rest of my life I will reflect on what light is." And his summation in 195t toward the end of his life was typical of his general view of nature: "All the fifty years of conscious brooding have brought me no closer to the answer to the question, "What are light quanta? Of course today every rascal thinks he knows the answer, but he is deluding himself." Einstein became a world figure through wide press announcements such as the headlines in the London Times, "Revolution in science~New theory of the universe/Newtonian ideas overthrown," and in the New York Times, "Lights all askew in the heavens/Einstein theory triumphs." Leueippos flourished about 440 B.C. He was a disciple of Zeno and the teacher of Democritus who credited him with founding the atomic theory. See World's Who's Whoin Science (A. G. Debus, Ed.), A. N. Marquis, Chicago, 1968. Nye, M. J., "Molecular Reality." American Elsevier, New York, 1972. Kerker, M., J. Chem. Educ. 51,764 (1974). Gouy, G., Rev. Gen. Sci. Pures Appl. 6, 1 (I895). Gouy's other major contribution to colloid science was the idea of a diffuse double layer. J. Phys. 9, 457 (t910). Ostwald, W , Rev. Gen. Sci. Pures Appl. 6, 955 (I895). Einstein, A., Autobiographical notes contributed to
295
HISTORICAL NOTE the volume "Albert Einstein: Philosopher Scientist" (P. A. Schilpp, Ed.). Tudor, New York, 1951. These are retrospective ruminations written by Einstein at age 67. 12. Einstein's papers on Brownian movement have been translated into English and collected and edited with notes by R. Furth, "Investigations on the Theory of Brownian Movement." Dutton, New York, 1926. These consist of (a) Ann. Phys. [4] 17, 549 (1905);(b)Ann. Phys. [4] 19, 289 (1906), (c) Ann. Phys. [4] 19, 371 (1906); Z. Elektrochem. 13, 41 (1907); (d) Z. Elektrochem. 14, 235 (1908); (e)Ann. Phys. 34, 591 (1911). 13. Einstein, A.,Ann. Phys. 33, 1275 (1910). An English translation by O. Y. Rainich may be found in Colloid Chemistry (Jerome Alexander, Ed.), Vol. I,
14. 15. 16. 17. 18.
p. 323. The Chemical Catalog Co., New York, 1926. Smoluchowski, M., Ann. Phys. 25, 205 (1908). Strutt (Lord Rayleigh), W., Phil Mag. 47, 375 (1899). Raman, C. V., and Rao, K. S., Phil. Mag. 45, 625 (1923). Debye, P., J. AppL Phys. 15, 338 (1944). Ornstein, L., and Zernike, F., Proc. Acad. Sci. Amsterdam 17, 793 (1914). MILTON KERKER
Clarkson University Potsdam, New York 13676 Received May 23, 1988; accepted May 23, 1988
JournalofColloMandlnterfaceScience.Vol.129,No. 1, April1989
tionary (4). This was also the year that his Ph.D. thesis was accepted by ETH. The subject of the thesis, published in 1906, treated the viscosity and diffusion of colloidal suspensions. The Brownian motion paper was its sequel. It was not until 1909 that Einstein received an academic appointment at the University of Zurich. This was followed by appointments at the German University of Prague in 1911 and the ETH in 1912. In 1914 he moved to Berlin as a member of the Prussian Academy of Sciences and Director of the Kaiser Wilhelm Institute of Physics. He separated from his wife in 1914, was divorced in 1919, and then married his divorced cousin Elsa Einstein Lowenthal. He was awarded the Nobel Prize in 1921 for his work on the nature of light. Einstein became world-famous in t919 when a total solar eclipse provided the opportunity for verifying his general theory of relativity by measuring the bending of light due to the sun's gravity (5). He became increasingly involved in public affairs, particularly as a forceful proponent of pacifism and of Zionism. He had renounced German citizenship upon becoming a Swiss citizen in his youth, had refused to accept German citizenship upon returning to Berlin in 19t4 even when this was initially made a condition of his appointment, and he was almost unique among intellectuals on both sides during World War I in denouncing that war. He became the target of antisemitic attacks in Germany after the war; and upon the accession of Hitler in 1933, resigned his Berlin posts and accepted a position at the Institute for Advanced Studies in Princeton. He became an American citizen in 1940. In t939 he sent his famous letter to President Roosevelt suggesting the possibility of utilizing atomic energy for military purposes. Obviously his pacifism had waned. In 1952 he was offered, but declined, the presidency of Israel. He died in Princeton on April 18, 1955. Einstein's interests in colloids arose in connection with the question of the reality of atoms. Polemics must have followed shortly after the formulation of atomism in antiquity by Leucippos (6) and they raged with renewed virulence upon publication of John Dalton's System of Chemical Philosophy in 1808. By the end of the 19th century, the success of thermodynamics and electromagnetism in viewing matter as a continuum underlay the polemics by opponents of the atomic theory such as Ernst Mach and Wilhelm Ostwald against those such as Boltzmann who championed the kinetic molecular view. Ostwald,
291 0021-9797/89 $3.00 Journal of Colloid and Interface Science, Vol, 129, No. 1, April 1989
Copyright © I989 by Academic Press, Inc. All rights of reproduction in any form reserved.
292
HISTORICAL NOTE
undoubtedly the most influential chemist of the age, "who was one of Boltzmann's most vociferous o p p o n e n t s . . . became more and more convinced that molecules, atoms and ions were only mathematical and a priori fictions, and that the underlying component of the universe was energy in its various arrays" (7). The acceptance of atomism by most of these combatants was to come only after Jean Perrin's verification of Einstein's theory of Brownian motion. Ernst Mach never relented. The origin of Brownian motion had been debated throughout the 19th century (8). The crux of the matter was posed succinctly by G. Gouy: The Brownian movement shows us, therefore, assuredly not the movements of the molecules, but something derived closely from these and furnishes proof of the exactness of the hypothesis on the nature of heat. If one adopts these views, then the phenomenon, the study of which is far from being terminated, takes on assuredly an importance for molecular physics of the first order. (9) The same volume in which the above statement is found also contains an article by Ostwald (10) emitled "The Rout of Contemporary Atomism," in which he protests that "an immediate consequence of this theory has never been verified" and that the imaginary concepts of imagined entities were "disturbing us with forces, the existence of which we cannot demonstrate, acting between atoms we cannot see." This is the fray into which young Einstein, patent examiner, entered. He noted (11) that despite the achievement of the kinetic theory of gases, "in chemistry only the ratios of the atomic masses played any role, not their absolute magnitudes, so that atomic theory could be viewed more as a visualizing symbol than as knowledge concerning the factual structure of matter . . . . My major aim in this was to find facts which would guarantee as much as possible the existence of atoms of definite size." Einstein focused on statistical mechanics; he wrote (11) of his earliest work (1902-1904): Not acquainted with the earlier investigations of Boltzmann and Gibbs, which had appeared earlier and actually exhausted the subject, I developed the statistical mechanics and the molecular-kinetic theory of thermodynamics which was based on the former. My major aim in this was to find facts which would guarantee as much as possible the existence of atoms of definite finite size. In the midst of this I discovered that, according to atomistic theory, there would have to be a movement of suspended microscopic particles, open to observation, without knowing that observations concerning Brownian motion were already long familiar. In one sense the quest for a manifestation of atomic reality can be reduced to a determination of Avogadro's number since this provides a measure of the mass of an atom. And it was this quest that Einstein took upon him-
Journal of CoUoid and InterfaceScience, VoL 129, No. l, April 1989
self. Within the space of less than 3 months Einstein made three distinct fundamental discoveries which permitted calculation of Avogadros' number. The first, with which we are not concerned here, based upon the blackbody radiation law, is contained in the 1905 paper on the nature of light. The others are in his doctoral thesis and the first Brownian motion paper. In his thesis, which was published in 1906 (12b), Einstein utilized fluid mechanical arguments to derive his famous equation for the viscosity of a suspension of coUoidal spheres by extending Van't Hoff's treatment of osmotic pressure to include particles exhibiting Stokes frictional resistance. He also derived a relation for the diffusion coefficient of a sphere. These two equations permitted calculation of Avogadro's number from experimental values of viscosity, diffusion, and density. An error in the viscosity equation was corrected in 1911 (12e) to give the currently accepted formula n* = 7(1 + 2.5~b) where 7" and ~ are the viscosities of sol and solvent and ~bis the volume fraction of suspended spheres. The 1905 Brownian motion paper (12a) builds upon the solution for the diffusion coefficient obtained in his thesis by treating the solution of Fick's law for a single particle as the probability of finding that particle at a certain distance from an origin after a particular time interval. He then notes that an observable quantity, namely, the mean square displacement of the particle X2 in a particular time interval t, can be used to determine Avogadro's number: --
2
/RT
1
)\
provided the radius and the coefficient of viscosity are also known. In this case there were no available data as in the earlier examples from which to calculate a value of N. Yet what was so exciting was the seeming visualization of atomic motion as one observed colloidal particles being buffeted about within a tumultuous sea of molecules. Einstein appreciates the momentous nature of his result. "It is possible that the movements to be discussed here are identical with the so-called Brownian molecular motion . . . . It is to be hoped that some enquirer may succeed in solving the problem suggested here . . . . If the movement discussed here can actually be observed. . . . then classical thermodynamics can no longer be looked upon as applicable to bodies even of dimensions distinguishable in a microscope: an exact determination of actual atomic dimensions is then possible. On the other hand, had the prediction of this movement proved to be incorrect, a weighty argument would be provided against the molecular-kinetic conception of heat." Shortly thereafter, emboldened to entitle the paper " o n the Theory of Brownian Motion" (12c ), Einstein extended the theory to include rotational Brownian motion and the equilibrium distribution of particles in a gravitational field, which occurs as a result of the Brownian motion.
293
HISTORICAL NOTE For Einstein, the study of Brownian motion had a twofold value, the one in verifying a theoretical construct and the other in illuminating our physical sense of things: Because of the understanding of the essence of Brownian motion, suddenly all doubts vanished about the correctness of Boltzmann's interpretation of the thermodynamic laws . . . . It is of great importance since it permits an exact computation of N . . . . The great significance as a matter of principle is, however, • . . that one sees directly under the microscope part of the heat energy in the form of mechanical energy. The story of Jean Perrin's experimental verification of these results, which led to the final collapse of opposition to the view that molecules are real, has been eloquently told elsewhere (7). Einstein's last foray into the issue of molecular reality was his paper on the "Theory of Opalescence of Homogeneous Liquids and Mixtures of Liquids in the Vicinity of the Critical State" (13). He was stimulated by Smoluchowski's paper (14) in which the scattering of light by fluids near the critical point was attributed to microscopic density (and hence refractive index) fluctuations. These fluctuations constituted irreversible processes whose probability could be calculated with the aid of Boltzmann's entropy-probability theorem. Thus Einstein saw still another opportunity to buttress Boltzmann's views and to determine Avogadro's number. Smoluchowski had not in the first of two papers provided a detailed calculation of the amount of light scattered. There followed a statistical thermodynamic analysis leading to an estimate of the mean square fluctuation of the density and an electromagnetic theory analysis giving the scattered field due to such random fluctuations. For a pure liquid the intensity of scattered light was inversely proportional to the isothermal compressibility. For a solution he found that the corresponding parameter was the concentration dependence of the chemical potential. Finally, by utilizing the Gibbs-Duhem relation, the molecular weights of the two components were incorporated into the expression for the light scattering. Once again Einstein completes his analysis by directing attention to a critical experiment (13). "A quantitative experimental investigation into the phenomenon dealt with here would be of great interest: it certainly would be worthwhile to know whether Boltzmann's principle actually predicts correctly the phenomenon considered and, on the other hand, we could obtain through such investigations exact values for the number, N." This work by Smoluchowski and Einstein was entirely novel. Theretofore light scattering had been attributed to random assemblies of isolated particles. Rayleigh was able to show how in the case of a gas the phenomenological refractive index of the gas might be utilized to supplant what otherwise would have required fictitious values for the molecular radius and refractive index. Indeed, Rayleigh then proceeded to use estimates of the varying brightness
of a star at different altitudes to calculate Avogadro's number within a factor of 3 (15 ). However, the treatment of a condensed phase where correlation among the molecular scattering centers results in strong destructive interferences had not been attempted. Einstein's proposal to calculate N by measurement of the light scattered by condensed systems was carried out in 1923, by which time of course new determinations of N were antielimatic (16 ). However, the 1910 paper was eventually to play an important role in the development of colloid and polymer science. In his treatment of binary solutions, Einstein had incorporated the molecular weights of the solute and solvent so that once the value of N was firmly accepted, his equation could be used directly to estimate molecular weights from light scattering data. Peter Debye (17) utilized Einstein's equation to develop the procedures so well known and widely used today to estimate the molecular weights of polymers and the particle sizes of small colloidal particles. Smoluchowski and Einstein had initially proposed that their theory would account for critical opalescence when in fact it applies to liquids except in those states very close to the critical point. Einstein appreciated that the theory would require retention of higher order terms very close to the critical point. However, he was not aware that additional physical effects would arise near the critical point due to correlations among the fluctuations (18). Pais (1), himself a high energy particle physicist, has commented on the impact of Einstein's work on colloids: The history of Einstein's influence on later works, as expressed by the frequency of citations of his papers, offers several striking examples. Of the eleven scientific articles published by any author before 1912 and cited most frequently between 1961 and 1975, four are by Einstein. Among these four, the thesis (or, rather, the 1906 paper) ranks first; then follows a sequel to i t . . . written in 1911. The Brownian motion paper ranks third, the paper on critical opalescence fourth. At the top of the list of Einstein's scientific articles cited most heavily during the years 1970 to 1974 is the 1906 paper. It was quoted four times as often as Einstein's first survey article of 1916 on general relativity and eight times as often as his 1905 paper on the light-quantum. There can be no argument that Einstein's main interests and contributions were in quantum theory and relativity. Yet even though his output in colloid science, work of his early years, comprised a small part of the final corpus of his work, it has had a major impact upon the development of colloid science. REFERENCES 1. Perhaps the most perspicuous of the many biographies, which also discusses his scientific work in considerable detail, is the one by Abraham Pais, "Subtle
Journal of Colloid and Interface Science, Vol. 129,No. 1, April 1989
294
HISTORICAL NOTE
Is the L o r d . . . " (Oxford Univ. Press, New York, 1982). Unattributed quotations by Einstein given in this paper are cited by Pals. 2. Einstein wrote to Ostwald on 19 March 1901. "Esteemed Herr Professor! Because your work on general chemistry inspired me to write the enclosed article, I am taking the liberty of sending you a copy of it. On this occasion permit me also to inquire whether you might have use for a mathematical physicist familiar with absolute measurements. If I permit myself to make such an inquiry, it is only because I am without means, and only a position of this kind would offer me the possibility of additional education. Respectfully yours." This was followed on 13 April 1901 by a long letter from Einstein's father which reads in part "Esteemed Herr Professor! Please forgive a father who is so bold as to turn to you esteemed Herr Professor, in the interest of his son . . . (who) passed his diploma examinations in mathematics and physics with flying colors. He has been trying unsuccessfully to obtain a position as Assistant, which will enable him to continue his education in theoretical and experimental physics. He is oppressed by the thought that he is a burden on us, people of modest means. . . . . Since it is you, highly honored Herr Professor, whom my son seems to admire and esteem more than any other scholar currently active in physics, it is to you to whom I have taken the liberty of turning with the humble request to read his paper published in the Annalen f'tir (sic) Physik. . . . If, in addition, you could secure him an Assistant's position for now or the next autumn, my gratitude would know no bounds. I am taking the liberty of mentioning that my son does not know anything about my unusual step." On 12 April 1901 he wrote to KammerlinghOnnes, "Esteemed Herr Professor! I have learned through a friend from college that you have a vacancy for an assistant. I am taking the liberty of applying for that position. I studied at the department for mathematics and physics of the Zurich Polytechnikum for 4 years, specializing in physics. I obtained there my diploma last summer. Of course, I will make my grade transcripts available to you with pleasure; I have the honor to submit to you by the same mail a reprint of my article that has appeared recently in Annalen der Physik. Respectfully." This correspondence is reproduced from "The Collected Papers of Albert Einstein" ((John Stachel, Ed.), Vol. 1, Princeton Univ. Press, Princeton, NJ, 1987). 3• Einstein, A., Ann. Phys. 17, 132, 549, 891 (t905). 4. Einstein's fundamental contributions toward our present understanding of the nature of light have •
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5.
6.
7. 8. 9.
10. 11.
been discussed by Emil Wolf (Optics News 5, 24 (1979)). These commence with the paper which reintroduced the corpuscular theory of light, a paper which among the three marvelous papers submitred within 3 ½months and published in Volume 17 of Annalen der Physik in 1905, Einstein singled out, in a letter to a friend, as being "very revolutionary." The treatment of the photoelectric effect was among the examples that Einstein gave in support of his view of the corpuscular nature of radiation. Included in his other great papers on radiation is a clear discussion of the wave-particle duality (1909), consideration of the elementary processes of interaction between molecules and radiation (1917), and the quantum theory of an ideal gas (1924, 1925)in which Bose-Einstein statistics was established. That his ideas were both revolutionary and controversial can be judged from Max Planck's letter nominating him for membership in the Prussion Academy of Sciences in 1913 in which Planck said: "That he may sometimes have missed the target of his speculations, as for examples in his hypothesis of light quanta, cannot really be held against him." And yet it was this work, rather than relativity or the mechanics of colloidal particles, for which Einstein received the Nobel Prize in 1921. Therein lies another tale (see Chapt. 30 in Pais' biography, Ref. (1)). Einstein was constantly driven to think about light, as he stated in 1917: "For the rest of my life I will reflect on what light is." And his summation in 195t toward the end of his life was typical of his general view of nature: "All the fifty years of conscious brooding have brought me no closer to the answer to the question, "What are light quanta? Of course today every rascal thinks he knows the answer, but he is deluding himself." Einstein became a world figure through wide press announcements such as the headlines in the London Times, "Revolution in science~New theory of the universe/Newtonian ideas overthrown," and in the New York Times, "Lights all askew in the heavens/Einstein theory triumphs." Leueippos flourished about 440 B.C. He was a disciple of Zeno and the teacher of Democritus who credited him with founding the atomic theory. See World's Who's Whoin Science (A. G. Debus, Ed.), A. N. Marquis, Chicago, 1968. Nye, M. J., "Molecular Reality." American Elsevier, New York, 1972. Kerker, M., J. Chem. Educ. 51,764 (1974). Gouy, G., Rev. Gen. Sci. Pures Appl. 6, 1 (I895). Gouy's other major contribution to colloid science was the idea of a diffuse double layer. J. Phys. 9, 457 (t910). Ostwald, W , Rev. Gen. Sci. Pures Appl. 6, 955 (I895). Einstein, A., Autobiographical notes contributed to
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HISTORICAL NOTE the volume "Albert Einstein: Philosopher Scientist" (P. A. Schilpp, Ed.). Tudor, New York, 1951. These are retrospective ruminations written by Einstein at age 67. 12. Einstein's papers on Brownian movement have been translated into English and collected and edited with notes by R. Furth, "Investigations on the Theory of Brownian Movement." Dutton, New York, 1926. These consist of (a) Ann. Phys. [4] 17, 549 (1905);(b)Ann. Phys. [4] 19, 289 (1906), (c) Ann. Phys. [4] 19, 371 (1906); Z. Elektrochem. 13, 41 (1907); (d) Z. Elektrochem. 14, 235 (1908); (e)Ann. Phys. 34, 591 (1911). 13. Einstein, A.,Ann. Phys. 33, 1275 (1910). An English translation by O. Y. Rainich may be found in Colloid Chemistry (Jerome Alexander, Ed.), Vol. I,
14. 15. 16. 17. 18.
p. 323. The Chemical Catalog Co., New York, 1926. Smoluchowski, M., Ann. Phys. 25, 205 (1908). Strutt (Lord Rayleigh), W., Phil Mag. 47, 375 (1899). Raman, C. V., and Rao, K. S., Phil. Mag. 45, 625 (1923). Debye, P., J. AppL Phys. 15, 338 (1944). Ornstein, L., and Zernike, F., Proc. Acad. Sci. Amsterdam 17, 793 (1914). MILTON KERKER
Clarkson University Potsdam, New York 13676 Received May 23, 1988; accepted May 23, 1988
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