Samuel Frederick Edwards: Founder of modern polymer and soft matter theory

Abstract

This year marks the 50th anniversary of the seminal paper by Sam Edwards on the statistical mechanics of a single polymer chain in dilute solution, a paper that in one stroke founded the modern quantitative understanding of polymer matter, and vaulted soft condensed matter on to the stage of theoretical physics (1). Sir Samuel Frederick Edwards, universally known as “Sam,” was a giant of theoretical physics; he passed away in Cambridge, England on May 7, 2015. The problem solved in his 1965 paper (1) addresses the simplest question that one can ask at a fundamental level about polymeric matter: given the number of monomers in a chain, how big is the polymer itself in 3D space? It is also an extraordinarily difficult problem: a polymer chain is almost a random configuration in space, yet it has to respect the constraint that atoms cannot overlap, restricting the positions of the monomers in a nonlocal way and generally resulting in a polymer chain that is somewhat expanded compared with a random walk. Paul Flory, the great polymer chemist, had provided an ingenious heuristic solution to the problem of one chain, but a detailed and systematic understanding remained out of reach. Edwards formulated the problem in terms of path integrals, and solved it in an excellent approximation using self-consistent field theory. Edwards’ method would, in time, become the basis for a complete attack on all phases of polymeric matter, not only single chains but dilute and concentrated solutions, disordered phases such as rubber and gels, charged phases such as polyelectrolytes, and even dynamical properties. A decade after Edwards’ work, Pierre-Gilles de Gennes would show that Edwards’ ideas could be extended to take into account critical fluctuations using renormalization group ideas (2). This approach would be refined in great detail by subsequent studies, allowing accurate computation of universal scaling functions governing the physical chemistry of all polymers in solution and providing excellent agreement with experiment. de Gennes would be awarded the 1991 Nobel Prize in physics for his many contributions to soft matter, but many believed that Edwards’ contributions, so frequently linked with de Gennes’, deserved similar recognition.