RETROSPECTIVE RETROSPECTIVE

Samuel Frederick Edwards: Founder of modern polymerandsoftmattertheory

Nigel Goldenfelda,1

This year marks the 50th anniversary of the seminal renormalization group ideas (2). This approach would paper by Sam Edwards on the statistical mechanics of be refined in great detail by subsequent studies, allow- a single polymer chain in dilute solution, a paper that ing accurate computation of universal scaling functions in one stroke founded the modern quantitative un- governing the physical chemistry of all polymers in derstanding of polymer matter, and vaulted soft solution and providing excellent agreement with ex- condensed matter on to the stage of theoretical periment. de Gennes would be awarded the 1991 physics (1). Sir Samuel Frederick Edwards, universally Nobel Prize in physics for his many contributions to known as “Sam,” was a giant of theoretical physics; he soft matter, but many believed that Edwards’ contri- passed away in Cambridge, England on May 7, 2015. butions, so frequently linked with de Gennes’,de- The problem solved in his 1965 paper (1) addresses served similar recognition. the simplest question that one can ask at a fundamen- In establishing the deep connections between tal level about polymeric matter: given the number of quantum field theory and the configurations of monomers in a chain, how big is the polymer itself in a polymer chain, Edwards inaugurated a new and 3D space? It is also an extraordinarily difficult prob- sophisticated way of looking at matter that was not lem: a polymer chain is almost a random configuration simply point-like but extended. He was fond of telling in space, yet it has to respect the constraint that atoms prospective students that “polymers are their own cannot overlap, restricting the positions of the mono- Feynman diagrams,” a single sentence that both en- mers in a nonlocal way and generally resulting in tranced and bewildered the listener. Indeed, the a polymer chain that is somewhat expanded com- Edwards style was articulated in an interview given in pared with a random walk. Paul Flory, the great poly- 1973: “If you can manage to study several subjects, mer chemist, had provided an you find there are fruitful relations between them ... ingenious heuristic solution to and you can solve the same problems in a different the problem of one chain, but subject... One can be a very good entrepreneur in a detailed and systematic un- this business” (3). Edwards’ acts of intellectual arbi- derstanding remained out of trage brought powerful methods from many-body reach. Edwards formulated the theory, statistical mechanics, and quantum field to problem in terms of path inte- bear on a multitude of “dirty” problems that had pre- grals, and solved it in an excel- viously been unjustly dismissed by as out- lent approximation using self- side their purview and perhaps not worthy of consistent field theory. Edwards’ consideration. Edwards did not have any such delicate method would, in time, become sensibilities. During his career, through courageous the basis for a complete attack and sometimes prodigious efforts, Edwards would on all phases of polymeric mat- make seminal contributions to our understanding of ter, not only single chains but di- such systems as granular materials, liquid crystals, lute and concentrated solutions, polymer melts, glasses, turbulent fluids, disordered disordered phases such as rub- electronic phases of matter, colloids, gels ... even ber and gels, charged phases the physics of food! The breadth of his interests was such as polyelectrolytes, and so wide that workers in different fields would some- even dynamical properties. A times express amazement that “their Edwards” was decade after Edwards’ work, one and the same person as another Edwards in Pierre-Gilles de Gennes would a completely different field. However, all of his contri- show that Edwards’ ideas could butions showed a common touch: a dazzling mastery Samuel Frederick Edwards. Image courtesy be extended to take into ac- of functional methods, which he wielded with aban- of the . count critical fluctuations using don and scarce respect for rigor, a powerful intuition

aDepartment of Physics, University of Illinois at Urbana–Champaign, Urbana, IL 61801 Author contributions: N.G. wrote the paper. The author declares no conflict of interest. 1Email: [email protected].

10–11 | PNAS | January 5, 2016 | vol. 113 | no. 1 www.pnas.org/cgi/doi/10.1073/pnas.1523001113 Downloaded by guest on September 29, 2021 for the right and physically correct answer, and a seem- Edwards began his career as a student of Julian ingly boundless mathematical creativity. Schwinger, working on quantum electrodynamics and Of Edwards’ many contributions, arguably the the high energy physics problems of the day. Follow- most enduring is his theory of the viscoelasticity of ing a postdoctoral year at the Institute for Advanced polymer melts, delivered as a series of papers (and Study in Princeton, his first academic position was at eventually a book) with Masao Doi. The Doi–Edwards the University of Birmingham, where he was part of theory was based on the notion that a polymer in a distinguished group around Sir Rudolph Peierls. a melt is effectively confined by a “tube” formed by Later Edwards moved to Manchester, before joining the other polymers in its vicinity, and explored the the , where he eventually held dynamical consequences of this seemingly innocuous the Cavendish Chair. idea with great precision and detail. The tube idea During the 1970s Edwards became increasingly originated in Edwards’ work on rubber (4), and had active in scientific policy and administration in the been famously adopted by de Gennes in his ground- United Kingdom, eventually heading up the Science breaking work on reptation (5), which established the Research Council, the United Kingdom counterpart to background to the Doi–Edwards theory. the National Science Foundation in the . For a different community, Edwards’ most influen- Edwards received many awards and honorary degrees tial work was perhaps the formulation and mean field during his lifetime, including the Boltzmann Medal, solution of the statistical mechanics of disordered the Davy Medal, and the of the Royal magnets (or spin glasses as they came to be known) Society (of which he was a Fellow). Edwards was (6) using the replica method that he had invented to knighted by Queen Elizabeth in 1975. Despite the solve the problem of rubber elasticity. Both problems administrative demands on his time, Edwards were difficult because of the presence of hard con- remained defiantly active and creative in science, straints—random impurities in the former and random deftly wielding his apparatus, “a pencil and paper, cross-links in the latter—but could be treated as the and a telephone,” and supervising graduate students “N→ 0 limit” of the thermodynamics of N copies of on the Cambridge-London train. the original system. This idea has been used in fields Sam Edwards leaves behind a remarkable legacy. as diverse as disordered metals, combinatorial optimi- His students rank among the leaders of condensed zation, and theoretical neuroscience. matter physics in Europe, the United States, and In another famous paper (7), Edwards initiated Japan, many of whom are perpetuating his virtuosity the study of growing interfaces, deriving the general and free-wheeling approach to applying theoretical statistical properties of interfacial fluctuations. Near physics in unconventional areas of science. Edwards’ the end of his career, Edwards developed statistical penetrating and creative insights into science remain mechanical formulations for the properties of granu- a dazzling inspiration to those who would expand the lar materials, introducing a characteristic temper- domain of theoretical physics, without condescension, ature that bears his name despite considerable into practical problems with an underpinning of deep initial skepticism. intellectual challenge.

1 Edwards SF (1965) The statistical mechanics of polymers with excluded volume. Proc Phys Soc 85(4):613–624. 2 de Gennes P-G (1972) Exponents for the excluded volume problem as derived by the Wilson method. Phys Lett A 38(5):339–340. 3 Sherwood M (November 22, 1973) A man for difficult problems: Professor Sam Edwards talks to Dr Martin Sherwood. New Scientist 60(873):538–539. 4 Edwards SF (1967) The statistical mechanics of polymerized material. Proc Phys Soc 92(1):9–16. 5 de Gennes P-G (1971) Reptation of a polymer chain in the presence of fixed obstacles. J Chem Phys 55(2):572–579. 6 Edwards SF, Anderson PW (1975) Theory of spin glasses. J Phys F Met Phys 5:965–974. 7 Edwards SF, Wilkinson DR (1982) The surface statistics of a granular aggregate. Proc R Soc Lond A 381:17–31.

Goldenfeld PNAS | January 5, 2016 | vol. 113 | no. 1 | 11 Downloaded by guest on September 29, 2021