A Re-Evaluation of the Morphology of a Bicontinuous Block Copolymer-Ceramic Material Gilman E. S. Toombes, ² Adam C. Finnefrock, ²,‡ Mark W. Tate, ² Ralph Ulrich, ‡,⊥ Ulrich Wiesner, § and Sol M. Gruner* ,², | Department of Physics, Department of Materials Science and Engineering, and Cornell High Energy Synchrotron Source (CHESS), Cornell UniVersity, Ithaca, New York 14853, and Max-Planck-Institute for Polymer Research, Postfach 3148, D-55021 Mainz, Germany ReceiVed July 11, 2007; ReVised Manuscript ReceiVed September 7, 2007 ABSTRACT: The structures of a poly(isoprene-block-ethylene oxide) (PI-b-PEO) block copolymer-directed aluminosilicate mesostructure and the resulting ceramic material obtained from calcination were studied via small- angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). The PI minority phase (volume fraction 0.36) formed a continuous network of channels, previously reported 1,2 to be consistent with the plumber’s nightmare 3 morphology. The solvent casting process used to form the material caused it to shrink uniaxially by ∼30%, deforming the network structure within it. Calculated structure factors for constant-curvature and constant- thickness models of a distorted double gyroid structure are consistent with SAXS from the material, while [100] and [111] projections of the distorted double gyroid structure match the TEM data. Because the structural data from the material is most consistent with a distorted version of the double gyroid morphology, the previous assignment of the plumber’s nightmare morphology must be reconsidered. Approaches for structural assignment are also discussed. Introduction A number of bicontinuous network structures have been identified in soft-condensed matter systems including the double gyroid 4,5 (G), double diamond 6,7 (D), plumber’s nightmare 3,6 (P), and I-WP 4,8 morphologies illustrated in Figure 1. Identifica- tion of these complex structures can be challenging, 9 and a combination of characterization techniques is frequently re- quired. Many bicontinuous materials lack long-range periodic- ity 10,11 and single-crystal specimens are certainly the exception. 9 Space-group assignment is difficult when dynamic and static disorder smear out all but a handful of diffraction peaks. 2,9 Furthermore, some 2-D projections of different network struc- tures are quite similar in appearance. 12-14 Consequently, in some instances further study of a material has led to a revision of an earlier structural assignment. 12,15,16 This report describes such a re-evaluation for a solvent-cast poly(isoprene-block-ethylene oxide) (PI-b-PEO) copolymer/ aluminosilicate composite material and the resulting ceramic obtained from calcination. The thickness of the solvent-cast film was approximately 0.5-1.0 mm while the volume fraction of the PI minority phase was 0.36. In an earlier study, 1,2 some of us reported the material’s structure to be consistent with the plumber’s nightmare (P) morphology and excluded the double gyroid (G) structure because small-angle X-ray scattering (SAXS) from the material showed {110} and {200} Bragg reflections forbidden by the symmetries of the double gyroid structure (G, space group Ia3d,Q 230 ). 17 However, the solvent- casting process uniaxially compressed the film along the film normal by ∼30%, as illustrated in Figure 2. Compression of a cubic lattice breaks the screw-axis and glide-plane symmetries of the Ia3d space-group and {110} and {200} reflections are no longer forbidden. 18,19 Thus, the observation of {110} and {200} reflections does not rigorously exclude a double gyroid structure distorted by lattice compression (distorted-G). To determine if a distorted double gyroid (distorted-G) structure was consistent with the experimental data, the structural deformations caused by lattice contraction were calculated for models of the double gyroid structure with elastic (G el ), constant- thickness 20 (G CT ), and constant-curvature 20 (G CC ) material properties. Structure factors for these three distorted double * Corresponding author. E-mail: smg26@cornell.edu. ² Department of Physics. ‡ Present addresses: Merck Research Laboratories, WYN-2, 466 Devon Park Drive, Wayne, PA 19087 (A.C.F.); Lanxess Deutschland GmbH, Geba ¨ude G17, 41539 Dormagen, Germany (R.U.). § Department of Materials Science and Engineering. | Cornell High Energy Synchrotron Source (CHESS). ⊥ Max-Planck-Institute for Polymer Research. Figure 1. Unit cells of the (a) double gyroid (G) structure, space group Ia3d,Q 230 ; (b) double diamond (D) structure, Pn3m,Q 224 ; (c) plumber’s nightmare (P) structure, Im3m,Q 229 ; and (d) I-WP network structure, Im3m,Q 229 . The green IPMS divides space between the gold and blue skeletal frames, each of which forms a continuous network in all three spatial directions. Skeletal frames and IPMS were calculated using the level-set approximation. 48 8974 Macromolecules 2007, 40, 8974-8982 10.1021/ma0715369 CCC: $37.00 © 2007 American Chemical Society Published on Web 11/10/2007