315 PERIODIC AREA MINIMIZATION SURFACES IN MICROSTRUCTURAL SCIENCE EDWIN L. THOMAS and SAMUEL P. GIDO Department of Materials Science and Engineering, and Program in Polymer Science and Technology, Massachusetts Institute of Technology, Cambridge, MA 02139 Abstract An A/B block copolymer consists of two macromolecules bonded together. In forming an equilibrium structure, such a material may separate into distinct phases, creating domains of component A and of component B. A dominant factor in the determination of the domain morphology is area-minimization of the intermaterial surface, subject to fixed volume fractions. Surfaces that satisfy this mathematical condition are said to have constant mean curvature. The geometry of such surfaces strongly influences material physical properties. We have discovered domain structures in microphase-separated diblock copolymers that closely approximate periodic surfaces of constant mean curvature. Transmission electron microscopy and computer-simulation are used to deduce the three dimensional microstructure by comparison of tilt series with two-dimensional image projection simulations of three-dimensional mathematical models. Two structures are discussed: First is the double diamond microdomain morphology, associated with a newly discovered family of triply periodic constant mean curvature surfaces. Second, a doubly periodic boundary between lamellar microdomains, corresponding to a classically known minimal surface (Scherk's First Surface), is described. Introduction Most multifuctional materials are multiphased; comprised of two or more phases whose simultaneous presence and mutual arrangement lead to unique properties. Emphasis in multiphased materials research in recent years has been concerned with the production of microphase textures of ever finer scale, since novel macroscopic properties can arise from materials with nanoscale structure. As the size scale of the phase domains decreases, an increasing percentage of the material is at or near an intermaterial interface. Surface phenomena which are absent or negligible in the bulk materials then begin to dominate the physics. Materials which have extremely high interphase surface area per unit volume can exhibit entirely new physical properties. In order to exploit such materials we need to learn how to control the size and mutual arrangement of the microphases. A commonly used route to such ordered micro and nanocomposites involves directly building up the structure via microlithographic processes. With this approach process control is critical. An alternative approach is that of self assembly - the ability of amphiphilic molecules to organize themselves into nanoscale patterns in response to thermodynamic driving forces[1,2,3]. In our work we employ very large amphiphiles: diblock copolymers consisting of two chemically different polymer segments. The mutual repulsion of these segments leads to the formation of periodic nanoscale structure. This self repulsion arises due to the positive enthalpy of interaction between the different block monomer units, and is not significantly resisted by the loss of entropy because of the long chain nature of the molecules. The local segregation of the A and B segments into microphases occurs in spatially periodic patterns, due to the covalent link between the two types of segments. Area-minimization of the A-B intermaterial interface is a dominant factor in determining the specific microdomain geometry which forms for a particular ratio of A and B block lengths. Area minimization subject to fixed volume fraction (fixed composition) is the mathematical Mat. Res. Soc. Symp. Proc. Vol. 175. ©1990 Materials Research Society