David Turnbull’s experiments and theoretical insights paved the way for much of our modern understanding of phase transitions in materials. In recognition of his contributions this lecture will concentrate on phase transitions in a material system not considered by Turnbull, thin diblock copolymer films. Well ordered block copolymer films have attracted increasing interest as we attempt to extend photolithography to smaller dimensions. In the case of diblock copolymer spheres an ordered monolayer is hexagonal but the ordered bulk is body centered cubic. There is no hexagonal plane in the BCC so a phase transition must occur as n, the number of layers of spheres in the film, increases. How this phase transition occurs with n and how it can be manipulated is the subject of the first part of my lecture. In the second part I show that monolayers of diblock copolymer spheres and cylinders undergo order to disorder transitions that differ greatly from those of the bulk. These ordered 2D monolayers are susceptible to phonon generated disorder as well as to thermal generation of defects, such as dislocations and disclinations, which while they are line defects in 3D, are point defects in 2D. The results are compared to the KTHNY theory of melting of 2D crystals (spheres) and to the theory of 2D smectic liquid crystals (cylinders)1-6, a comparison that will allow us to understand most, but not all, of the features of these order-disorder transitions (ODT) that occur as the temperature is increased. The theories fail to predict that the ODT of the monolayer occurs 10 to 20K below that of the bulk copolymer. We believe this is because these theories do not take into account the corona chains of the block copolymer. In the cylinder monolayer the corona chains must stretch to fill a nearly square cross-section domain rather than a hexagonal one in the bulk, while the corona chains in a sphere monolayer must stretch to fill a hexagonal prism rather than an octahedron in the bulk. The more non-uniform stretching or “packing frustration” of the chains in the monolayer should increase its free energy and decrease its ODT. 1 J.M. Kosterlitz, D.J. Thouless, “Long-range order and metastability in 2-dimensional solids and superfluids”, J. Phys. C – Solid State, 5, L124-126 (1972). 2 J.M. Kosterlitz, D.J. Thouless, “Ordering, metastability and phase transitions in 2 dimensional systems”, J. Phys. C – Solid State, 6, 1181-1203 (1973).3 B.I. Halperin, D.R. Nelson, “Theory of 2-dimensional melting”, Phys. Rev. Lett., 41, 121-124 (1978).4 D.R. Nelson and B.I. Halperin, “Dislocation-mediated melting in 2 dimensions”, Phys. Rev. B, 19, 2457-2484 (1979). 5 A.P. Young, “Melting and the vector coulomb gas in 2 dimensions”, Phys. Rev. B, 19, 1855-1866 (1979).6 J. Toner, D.R. Nelson, “Smectic, cholesteric and Rayleigh-Bernard order in two dimensions”, Phys. Rev. B, 23, 316-334 (1981).BIOGRAPHYProfessor Kramer received a B.Ch.E. Degree in Chemical Engineering from Cornell University in 1962 and a Ph.D. in Metallurgy and Materials Science from Carnegie-Mellon University in 1966. He was a NATO Postdoctoral Fellow at Oxford with Sir Peter Hirsch, FRS, before joining the faculty of Cornell University in 1967 where he rose through the ranks and was appointed the Samuel B. Eckert Professor of Materials Science and Engineering in 1988. At Cornell his initial research focused on understanding of flux lattice pinning by dislocations, small precipitates, grain boundaries and surfaces in model superconductors. His paper in J. Appl. Phys. 1973, which showed that while at low reduced magnetic fields (H/Hc2) the pinning force on the flux lattice was controlled by the interactions of this lattice with the defects in the superconductor, at high H/Hc2 it was controlled primarily by the deformation and flow of the flux lattice itself, is one of the most highly cited in this field.Already in the 1970’s Kramer had developed a program of research on polymers and he became a pioneering advocate of including the structure-properties-processing of polymers as part of the developing field of Materials Science. At Cornell he began research on the microscopic aspects of crazing, a pre-fracture cavitational mode of plastic deformation, which controls the fracture behavior of glassy polymers. He discovered the mechanisms by which crazes increase in width ("surface drawing"), increase in length (Taylor meniscus instability) and break down to form true cracks ("fibril breakdown"). He was the first to demonstrate experimentally that the formation of crazes can be inhibited by the network of entangled polymer chains inherited from the melt. Using ion beam techniques he was able to measure the diffusion of long polymer molecules in the melt. He pioneered the use of marker techniques to measure mass flows during polymer-polymer interdiffusion; these measurements revealed that the then dominant theory, which required cancellation of diffusion fluxes so that the slower moving polymer species controls the interdiffusion, could not be correct. He also made the first measurements of both the interdiffusion and tracer diffusion in a polymer blend (or alloy). These demonstrated that chemically different molecules of the same length could diffuse at vastly different rates in the same melt and that the thermodynamic interaction between polymer segments in such blends can lead to large enhancement in the rate of interdiffusion.In 1997 Kramer joined the faculty of UCSB where he holds a joint appointment in Materials and Chemical Engineering. Here he has emphasized the lateral organization of block copolymers on chemically and topologically patterned substrates, which recently has led to the discovery that spherical domain block copolymers can be induced to form single crystal layers using small surface steps to template the order. His experimental studies of melting of these 2D arrays, of both spheres and cylinders, have provided critical tests of 25 year old theories of 2D melting and have led to optimum methods for processing these block copolymer films to achieve highly ordered nanostructures. His work has been influential in establishing block copolymer lithography as a potential method to extend optical lithography to smaller feature sizes. His research probing the fundamentals of the interaction of polymer-coated nanoparticles with the interfaces of block copolymers has led to the discovery that these nanoparticles can behave as surfactants, leading to dramatic changes in block copolymer morphology at even small volume fractions. Kramer is a Fellow of the American Physical Society, the Materials Research Society and the American Association for the Advancement of Science. He was a Guggenheim Fellow in 1988 and was awarded a Senior Scientist Award of the Alexander von Humboldt Stiftung in 1987. In 1989 he was elected to the National Academy of Engineering. In 1995 he was awarded the Docteur honoris causa by L’Ecole Polytechnique Fédérale de Lausanne. He won the Polymer Physics prize of the American Physical Society in 1985, the Swinburne Medal of the Institute of Materials in 1996, the Polymeer Technologie Nederland Medema Award of the Dutch Polymer Society in 2007, and the American Chemical Society Polymer Materials: Science and Engineering, Cooperative Research Award in 2008.