Martin Goldstein

Martin Goldstein, whose 1969 paper caused a paradigm shift in the physics of viscous liquids and glass, died of complications from cancer on 23 April 2014, at his home in New York. Only weeks earlier, he was working on a paper on the specific heat of glasses and participated in a symposium on the physics of glassy state at Yeshiva University, where he had taught from 1965 to 1987.

Marty, as most of us knew him, was born on 18 November 1919 in Bronx, New York. He served in the US army during World War II, then obtained his Ph.D. from Columbia University in 1950 and did post-doctorates at Harvard and the Brooklyn Polytechnic Institute. After spending five years at Mellon Institute, Pittsburgh, PA, where he developed an interest in the properties of glass and the glassy state itself, he spent one year working on solar energy projects at Israel’s National Physical Laboratory, and then four years on the basic research staff of the Ford Motor Company in Dearborn, MI, before joining Yeshiva’s Belfer Graduate School of Science. In 1954 he married Inge (née Futter), now a special lecturer in environmental epidemiology at Columbia University, and had three children, Eric, Michael, and Aviva.

A modest man of great scientific depth and compassion, Marty profoundly influenced the thinking of a large community of scientists interested in the consequences of molecular diffusion on properties of condensed matter. He made many contributions to help us understand how a glass forms when a liquid is cooled below its freezing point, or pressurized above its freezing pressure, focusing on its configurational thermodynamics and density and structure fluctuations. To the community of physicists and chemists, Marty is most known by his very influential paper on the role of multiplicity of the potential energy barriers in determining the molecular motions in viscous liquid which form glasses, published in 1969. In it, he described his theory based on his intuition that there is not one structure of a liquid but numerous, and a liquid is randomly changing its structure even when its volume and other properties do not change. He modestly called it “A Potential Energy Barrier Picture.” In this picture, each of the minima separated by the barriers on a potential energy surface represented a specific three-dimensional structure of a liquid. A liquid flows, he argued, because its structure can move from one minimum to another without a change in volume or energy. He concluded that when a liquid being cooled becomes a rigid glass, its structure becomes trapped in one deep minimum, but still some molecular mobility in the form of a distribution of relaxation times persists in the rigid glassy state. In this entirely new concept, the potential energy, U, of a system is plotted as a function of 3N atomic coordinates in a 3N + 1 dimensional space, and the state of a system is represented by a point moving on the surface with a 3N dimensional velocity whose average value is temperature dependent. It required one to envisage a hypersurface in which each minimum represents the state point of a liquid, with the structure of the liquids fluctuating between different state points without a change in volume and energy. U itself is not a function of temperature, only of coordinates, but the probability distribution for potential energy of a state point of course is, through the Boltzmann factor, exp(-U/kT), whose integral over all coordinates is the configuration integral.

That picture changed the way we thought about glass formation and the nature of the glassy state. It became known as the potential energy landscape, which bears Marty’s name, and which is now used to quantify the statistical properties by using the number and the energy distribution of these minima in the potential energy surface for bulk systems. Scientists working in diverse disciplines have used the potential energy landscape to describe: diffusion-controlled chemical reaction kinetics, rheology, nucleation and crystallization of liquids, change in properties of an aging glass, atomic clusters, spin glasses, nanoparticles, and configuratonal fluctuations in real crystals containing point defects. Some groups have devoted decades of their research on computational prediction based on his landscape, and written numerous original articles and reviews. To mention only a few of these: Frank Stillinger and Thomas Weber in 1984 described this classification of potential energy minima —mechanically stable molecular packings — as a unifying principle for understanding condensed phase properties, and they regarded these as inherent structures of a liquid; Hans Frauenfelder expressed fluctuations of structure of hydrated proteins in their active states and the process of ligand binding with proteins in terms of the energy landscape; and, when faster computers became available David Wales did computational simulation of the landscape necessarily limited to a tractable number of atoms and its application to a host of phenomena and wrote a monograph on it. In the future, even faster computing would make it possible to simulate an increasingly larger part of the landscape (Marty’s potential energy surface also known as hypersurface) by including more atoms, but it remains to be seen if the entire landscape could be simulated.

The potential energy hypersurface in configuration space is the best attempt yet to put into the physics of liquids what Born and Debye put into the physics of solids when they developed the concepts of collective vibrational modes (with their great range of wavelengths and energies, from macroscopic down to molecular dimensions) to replace the single Einstein oscillator treatments of earlier times. The liquid state is more complex but the “energy landscape” concept, with its e ^N distinct energy states (N is the number of rearrangeable elements of the liquid structure, or number of atoms in the simplest cases), has provided a similar basis for understanding where the energy and, particularly, the entropy of melting of crystals comes from, and how we can begin to understand why the viscosity of liquids changes in such striking ways as temperature is lowered until the structure becomes kinetically arrested at a “glass transition” for each cooling rate. Many workers, including one of the authors (Austen Angell), have since invoked features of Marty’s energy landscape in the search for understanding of such important aspects of the viscous liquid problem as the wide spectrum of viscosity temperature dependences observed for glass-forming liquids, and the very different configurational entropy variations that are associated with them.

His second contribution is the discovery in 1970 of localized molecular mobility in the glassy state, an effect that also bears his name. He initiated the experiments and helped ascertain the accuracy of the results that showed that molecular motions in the glassy state do not require intramolecular degrees of freedom. These fast modes of motions, which Sid Nagel named as the JG relaxation, occur also in ultraviscous liquids, and can be expressed in terms of the potential energy landscape. But their molecular origin remains a mystery. The subject is of practical interest in preventing the leakage current in glassy insulators and for improving the toughness of amorphous polymers. Christoph Schick found that nucleation and crystal growth in some glasses occur at the sites of these fast motions. That made the JG relaxation relevant to the formation of glass ceramics. Similarity between the relaxation features of soft polymers, ultraviscous rigid-molecular liquids, and metal alloy melts led to an inference that segmental motions of a polymer chain occur in an intermolecular environment, and hence involve overcoming intermolecular barriers. Kia Ngai wrote a monograph on the JG relaxations and their role in determining the viscosity’s variation with temperature. Marty himself returned to look into it in his 2011 paper.

Later in his career, Marty developed a second professional vocation: helping the public understand the methods and processes of science. He and Inge co-authored four books elucidating to lay readers the methodology shared by scientists working in fields as disparate as thermodynamics, epidemiology, and psychiatry: How We Know: An Exploration of the Scientific Process (1978), The Experience of Science: An Interdisciplinary Approach (1984), The Refrigerator and the Universe : Understanding the Laws of Energy (Harvard University Press, 1993), and How Much Risk? A Guide to Understanding Environmental Health Hazards (Oxford University Press, 2002). But his proudest publication may have been the comic book he wrote and illustrated for his grandchildren using the concept of infinity to showcase the beauty and use of mathematics. All who knew Marty also knew his passion for fine prose, poetry, and wit. He published articles on Dostoevsky, Trollope, and Shakespeare, and outperformed all his progeny in limerick slams.

Marty was a life-long teacher whose style in the classroom, in the living room or on a log along a trail in the woods was to raise stimulating questions about how things work that inspired his students, children and friends. Marty approached hard questions as if they were puzzles and enjoyed the struggle to find solutions and to share them.

One of us, Gyan Johari, who worked with him as a post-doctoral fellow during 1969-1970, remembered him at “A celebration of the life of Martin Goldstein” on 21 June 2014:

“During much of 1969, he spent hours for many days writing on the black board, explaining to me in his office not only the nature of the glassy state but also how to think about it. That changed my life. His enthusiasm for providing insightful explanations never diminished. He knew how to enter one’s mind through another door, when the first door seemed shut. He cheerfully accepted when there was a need to refine some of his views, and he graciously respected the views of others, howsoever conflicting with his own. As a life-long friend, Marty communicated with me by email about the subject of glass relaxation almost every week since 2001, and wrote about his travels to different parts of the world until late January this year. He sent to me his manuscripts for critical review, wrote about the new ideas he was pursuing, and he was very kind to have read my manuscripts and provide criticism. Once he wondered how much more could have been done if contemporary computer facilities had been available to us in 1969.

Even in poor health, Marty was writing a scientific paper, reading old and relevant results, thinking about glass relaxation, asking questions, and inquiring about new scientific papers. In his last email to me he wrote, ‘I would like to see your paper on the torpid state when you have finished it.’ Unfortunately, that did not happen. I owe an enormous debt of gratitude to Marty for teaching me how to think about scientific problems without bias, and to look at the solutions offered through the eyes of others who may know more. His professional help has meant a lot for my scientific career.”

We believe Marty’s potential energy barrier description will be seen as an improvement on the two-site models in the same way as the collective modes of atomic motions (phonons) are seen as an improvement on the isolated vibrational motions of atoms. As computing becomes faster, it will reveal more on how the distribution of the width and of the depth of energy minima determines molecular transport involved in both the viscous flow and localized motions, and it will help obtain an eagerly sought causative relation between the viscous flow and localized motions.

Those who use Marty’s scientific ideas to explain their findings celebrate his life in their own way, and this celebration will go on.

Gyan Johari¹ and Austen Angell²

¹ Gyan Johari is Professor Emeritus at McMaster University, Hamilton, Canada.

² Austen Angell is Regents Professor of Chemistry at Arizona University State University, Tempe, AZ.