我們使用小角度X光散射來研究具組態規則性的嵌段共聚物聚丙烯-聚苯乙烯 (syndiotactic polypropylene-block-polystyrene, sPP-b-aPS) 的雙連續網狀奈米結構。我們發現此共聚物呈現一非典型的ordered bicontinuous double-diamond (OBDD)結構，且該結構經升溫會轉化成典型的ordered bicontinuous double-gyroid (OBDG)結構，該有序-有序轉化 (order-order transition, OOT) 伴隨著domain spacing變化。根據體積守恆的假設，我們提出一普遍適用的模型來計算OBDD和OBDG結構中domain spacing和晶格常數 (lattice parameter) 的比例。此外，我們也建構出OBDD結構在實空間中的3D穿透式電子顯微影像。我們認為，在較低溫時，sPP分子鏈會形成不同長度的螺旋片段，該構造可使分子鏈的內能降低，補償packing frustration熵的損失，因而穩定OBDD結構。另外，我們也發現摻混sPP均聚物 (homopolymer) 後，sPP-b-aPS會由OBDD結構轉化成HEX結構，此過程不可逆。我們認為加入sPP均聚物會使OBDD結構的雙曲線域 (hyperbolic domain) 產生膨脹效應(swell effect)，不但降低其表面曲度(interfacial curvature)，影響sPP和PS的構形(conformation)，且使得sPP均聚物的分子鏈分布不均，造成熵的損失變大，在高溫時這些熵的損失會降低雙曲線型曲度的穩定性，促使OBDD結構轉化為較穩定的hexagonally-packed cylinder (HEX)結構。在OBDD結構轉化成HEX結構的過程中，其體積守恆且lattice parameter幾乎維持不變，因此我們也根據此關係提出了一種可能的轉化路徑。

We have investigated the formation of ordered bicontinuous nanostructures in a diblock copolymer composed of a stereoregular block, syndiotactic polypropylene - block-polystyrene (sPP-b-aPS). The temperature-dependent small angle x-ray scattering (SAXS) revealed that the ordered bicontinuous double-diamond (OBDD) structure underwent a thermally reversible order-order transition (OOT) to ordered bicontinuous double gyroid (OBDG) upon heating, and the transition was accompanied with a slight reduction of domain spacing, as demonstrated both experimentally and theoretically. Based on the assumption of volume conservation, the ratio of the lattice parameters of these two bicontinuous structures was derived to be a_G/a_D =1.634, which closely agrees with that prescribed by the assumption of Bonnet transformation for the OOT. The OBDD structure was further confirmed by the reconstruction of 3D image using electron tomography. The thermodynamic stability of the OBDD structure may be attributed to the ability of the configurationally regular sPP block to form helical segments even above its melting point, as the reduction of internal energy associated with the helix formation may effectively compensate the greater packing frustration of sPP blocks in the tetrapod of OBDD relative to that in the tripod of OBDG, making the OBDD the more stable structure at the lower temperature. By blending sPP-b-aPS system with a small amount of sPP homopolymer, a phase transition from the OBDD structure to the hexagonally-packed cylinder (HEX) structure occured on heating. The volume fraction of the homopolymer in the blend affected not only the temperature range of the OOT, but also TOOT. The hyperbolic sPP domain of the OBDD structure is swollen, leading to a reduction of the interfacial curvature and hence a perturbation of sPP and PS conformation. Moreover, the distribution of sPP homopolymer chains in the tetrapod is non-uniform, giving rise to a loss of translational entropy. The loss of these entropies, which becomes important at high temperature destabilizes the OBDD structure and drives transformation into HEX phase. A possible kinetic pathway of the OBDD-to-HEX transition was proposed based on the assumption of volume conservation and constant lattice parameter.

1. Frank S. Bates; Fredrickson, G. H., Block Copolymers - Designer Soft Materials. Physics Today 1999, 52, 32.
2. Hashimoto, T.; Nishikawa, Y.; Tsutsumi, K., Identification of the “Voided Double-Gyroid-Channel”:  A New Morphology in Block Copolymers. Macromolecules 2007, 40 (4), 1066-1072.
3. Leibler, L., Theory of Microphase Separation in Block Copolymers. Macromolecules 1980, 13 (6), 1602-1617.
4. Matsen, M. W.; Bates, F. S., Unifying Weak- and Strong-Segregation Block Copolymer Theories. Macromolecules 1996, 29 (4), 1091-1098.
5. Tanaka, H.; Hasegawa, H.; Hashimoto, T., Ordered structure in mixtures of a block copolymer and homopolymers. 1. Solubilization of low molecular weight homopolymers. Macromolecules 1991, 24 (1), 240-251.
6. Koizumi, S.; Hasegawa, H.; Hashimoto, T., Ordered structure of block polymer/homopolymer mixtures, 4. Vesicle formation and macrophase separation. Makromolekulare Chemie. Macromolecular Symposia 1992, 62 (1).
7. Hajduk, D. A.; Harper, P. E.; Gruner, S. M.; Honeker, C. C.; Kim, G.; Thomas, E. L.; Fetters, L. J., The Gyroid: A New Equilibrium Morphology in Weakly Segregated Diblock Copolymers. Macromolecules 1994, 27 (15), 4063-4075.
8. Matsen, M. W.; Schick, M., Stable and unstable phases of a diblock copolymer melt. Physical Review Letters 1994, 72 (16), 2660.
9. Almdal, K.; Mortensen, K.; Ryan, A. J.; Bates, F. S., Order, Disorder, and Composition Fluctuation Effects in Low Molar Mass Hydrocarbon−Poly(dimethylsiloxane) Diblock Copolymers. Macromolecules 1996, 29 (18), 5940-5947.
10. Avgeropoulos, A.; Dair, B. J.; Hadjichristidis, N.; Thomas, E. L., Tricontinuous Double Gyroid Cubic Phase in Triblock Copolymers of the ABA Type. Macromolecules 1997, 30 (19), 5634-5642.
11. Dair, B. J.; Honeker, C. C.; Alward, D. B.; Avgeropoulos, A.; Hadjichristidis, N.; Fetters, L. J.; Capel, M.; Thomas, E. L., Mechanical Properties and Deformation Behavior of the Double Gyroid Phase in Unoriented Thermoplastic Elastomers. Macromolecules 1999, 32 (24), 8145-8152.
12. Lynd, N. A.; Hillmyer, M. A., Influence of Polydispersity on the Self-Assembly of Diblock Copolymers. Macromolecules 2005, 38 (21), 8803-8810.
13. Nykänen, A.; Nuopponen, M.; Laukkanen, A.; Hirvonen, S. P.; Rytelä, M.; Turunen, O.; Tenhu, H.; Mezzenga, R.; Ikkala, O.; Ruokolainen, J., Phase Behavior and Temperature-Responsive Molecular Filters Based on Self-Assembly of Polystyrene-block-poly(N-isopropylacrylamide)-block-polystyrene. Macromolecules 2007, 40 (16), 5827-5834.
14. Hajduk, D. A.; Harper, P. E.; Gruner, S. M.; Honeker, C. C.; Thomas, E. L.; Fetters, L. J., A Reevaluation of Bicontinuous Cubic Phases in Starblock Copolymers. Macromolecules 1995, 28 (7), 2570-2573.
15. Tselikas, Y.; Hadjichristidis, N.; Lescanec, R. L.; Honeker, C. C.; Wohlgemuth, M.; Thomas, E. L., Architecturally-Induced Tricontinuous Cubic Morphology in Compositionally Symmetric Miktoarm Starblock Copolymers. Macromolecules 1996, 29 (10), 3390-3396.
16. Xu, J. T.; Turner, S. C.; Fairclough, J. P. A.; Mai, S. M.; Ryan, A. J.; Chaibundit, C.; Booth, C., Morphological Confinement on Crystallization in Blends of Poly(oxyethylene-block-oxybutylene) and Poly(oxybutylene). Macromolecules 2002, 35 (9), 3614-3621.
17. Epps, T. H.; Chatterjee, J.; Bates, F. S., Phase Transformations Involving Network Phases in ISO Triblock Copolymer−Homopolymer Blends. Macromolecules 2005, 38 (21), 8775-8784.
18. Thomas, E. L.; Alward, D. B.; Kinning, D. J.; Martin, D. C.; Handlin, D. L.; Fetters, L. J., Ordered bicontinuous double-diamond structure of star block copolymers: a new equilibrium microdomain morphology. Macromolecules 1986, 19 (8), 2197-2202.
19. Hasegawa, H.; Tanaka, H.; Yamasaki, K.; Hashimoto, T., Bicontinuous microdomain morphology of block copolymers. 1. Tetrapod-network structure of polystyrene-polyisoprene diblock polymers. Macromolecules 1987, 20 (7), 1651-1662.
20. Larsson, K., Cubic lipid-water phases: structures and biomembrane aspects. The Journal of Physical Chemistry 1989, 93 (21), 7304-7314.
21. Matsen, M. W.; Schick, M., Stable and Unstable Phases of a Linear Multiblock Copolymer Melt. Macromolecules 1994, 27 (24), 7157-7163.
22. Likhtman, A. E.; Semenov, A. N., Stability of the OBDD Structure for Diblock Copolymer Melts in the Strong Segregation Limit. Macromolecules 1994, 27 (11), 3103-3106.
23. Anderson, D. M.; Thomas, E. L., Microdomain morphology of star copolymers in the strong-segregation limit. Macromolecules 1988, 21 (11), 3221-3230.
24. Matsen, M. W.; Schick, M., Microphase Separation in Starblock Copolymer Melts. Macromolecules 1994, 27 (23), 6761-6767.
25. Peter D. Olmsted; Milner, S. T., Strong-segregation theory of bicontinuous phases in block copolymers. Phys. Rev. Lett. 1994, 72, 936.
26. Thomas, E. L.; Anderson, D. M.; Henkee, C. S.; Hoffman, D., Periodic area-minimizing surfaces in block copolymers. Nature 1988, 334 (6183), 598-601.
27. Matsen, M. W.; Bates, F. S., Origins of Complex Self-Assembly in Block Copolymers. Macromolecules 1996, 29 (23), 7641-7644.
28. Matsen, M. W., Stabilizing New Morphologies by Blending Homopolymer with Block Copolymer. Phys. Rev. Lett. 1995, 74, 4225.
29. Matsen, M. W., Phase Behavior of Block Copolymer/Homopolymer Blends. Macromolecules 1995, 28 (17), 5765-5773.
30. Martínez Veracoechea, F. J.; Escobedo, F. A., Monte Carlo Study of the Stabilization of Complex Bicontinuous Phases in Diblock Copolymer Systems. Macromolecules 2007, 40 (20), 7354-7365.
31. Martínez Veracoechea, F. J.; Escobedo, F. A., Bicontinuous Phases in Diblock Copolymer/Homopolymer Blends: Simulation and Self-Consistent Field Theory. Macromolecules 2009, 42 (5), 1775-1784.
32. Winey, K. I.; Thomas, E. L.; Fetters, L. J., The ordered bicontinuous double-diamond morphology in diblock copolymer/homopolymer blends. Macromolecules 1992, 25 (1), 422-428.
33. Takagi, H.; Yamamoto, K.; Okamoto, S., Ordered-bicontinuous-double-diamond structure in block copolymer/homopolymer blends. EPL (Europhysics Letters) 2015, 110 (4), 48003.
34. Seddon, J. M.; Hogan, J. L.; Warrender, N. A.; Pebay Peyroula, E., Structural studies of phospholipid cubic phases. In Trends in Colloid and Interface Science IV, Zulauf, M.; Lindner, P.; Terech, P., Eds. Steinkopff: 1990; Vol. 81, pp 189-197.
35. Mark F. Schulz; Frank S. Bates; Kristoffer Almdal; Mortensen, K., Epitaxial Relationship for Hexagonal-to-Cubic Phase Transition in a Book Copolymer Mixture. Phys. Rev. Lett. 1994, 73, 86.
36. Matsen, M. W., Cylinder↔Gyroid Epitaxial Transitions in Complex Polymeric Liquids. Phys. Rev. Lett. 1998, 80, 4470.
37. Vigild, M. E.; Almdal, K.; Mortensen, K.; Hamley, I. W.; Fairclough, J. P. A.; Ryan, A. J., Transformations to and from the Gyroid Phase in a Diblock Copolymer. Macromolecules 1998, 31 (17), 5702-5716.
38. Zhu, L.; Huang, P.; Chen, W. Y.; Weng, X.; Cheng, S. Z. D.; Ge, Q.; Quirk, R. P.; Senador, T.; Shaw, M. T.; Thomas, E. L.; Lotz, B.; Hsiao, B. S.; Yeh, F.; Liu, L., “Plastic Deformation” Mechanism and Phase Transformation in a Shear-Induced Metastable Hexagonally Perforated Layer Phase of a Polystyrene-b-poly(ethylene oxide) Diblock Copolymer. Macromolecules 2003, 36 (9), 3180-3188.
39. Park, I.; Lee, B.; Ryu, J.; Im, K.; Yoon, J.; Ree, M.; Chang, T., Epitaxial Phase Transition of Polystyrene-b-Polyisoprene from Hexagonally Perforated Layer to Gyroid Phase in Thin Film. Macromolecules 2005, 38 (25), 10532-10536.
40. Park, H.-W.; Jung, J.; Chang, T.; Matsunaga, K.; Jinnai, H., New Epitaxial Phase Transition between DG and HEX in PS-b-PI. J. Am. Chem. Soc. 2009, 131 (1), 46-47.
41. Honda, T.; Kawakatsu, T., Epitaxial Transition from Gyroid to Cylinder in a Diblock Copolymer Melt. Macromolecules 2006, 39 (6), 2340-2349.
42. Ly, D. Q.; Honda, T.; Kawakatsu, T.; Zvelindovsky, A. V., Kinetic Pathway of Gyroid-to-Cylinder Transition in Diblock Copolymer Melt under an Electric Field. Macromolecules 2007, 40 (8), 2928-2935.
43. Pinna, M.; Zvelindovsky, A. V., Kinetic pathways of gyroid-to-cylinder transitions in diblock copolymers under external fields: cell dynamics simulation. Soft Matter 2008, 4 (2), 316-327.
44. Schmidt, K.; Pester, C. W.; Schoberth, H. G.; Zettl, H.; Schindler, K. A.; Böker, A., Electric Field Induced Gyroid-to-Cylinder Transitions in Concentrated Diblock Copolymer Solutions. Macromolecules 2010, 43 (9), 4268-4274.
45. Rancon, Y.; Charvolin, J., Epitaxial relationships during phase transformations in a lyotropic liquid crystal. The Journal of Physical Chemistry 1988, 92 (9), 2646-2651.
46. Xiuyuan Cheng; Ling Lin; Weinan E; Pingwen Zhang; Shi, A. C., Nucleation of Ordered Phases in Block Copolymers. Phys. Rev. Lett. 2010, 104, 148301.
47. Sugimori, H.; Niihara, K. i.; Kaneko, T.; Miyoshi, W.; Jinnai, H., Direct Three-Dimensional Observations of Order-Order Transition from Gyroid to Cylindrical Structures in a Block Copolymer. Progress of Theoretical Physics Supplement 2008, 175, 166-173.
48. Jung, J.; Lee, J.; Park, H. W.; Chang, T.; Sugimori, H.; Jinnai, H., Epitaxial Phase Transition between Double Gyroid and Cylinder Phase in Diblock Copolymer Thin Film. Macromolecules 2014, 47 (24), 8761-8767.
49. Gilbert, P., Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol. 1972, 36 (1), 105-117.
50. Kremer, J. R.; Mastronarde, D. N.; McIntosh, J. R., Computer Visualization of Three-Dimensional Image Data Using IMOD. J. Struct. Biol. 1996, 116 (1), 71-76.
51. Takenaka, M.; Wakada, T.; Akasaka, S.; Nishitsuji, S.; Saijo, K.; Shimizu, H.; Kim, M. I.; Hasegawa, H., Orthorhombic Fddd Network in Diblock Copolymer Melts. Macromolecules 2007, 40 (13), 4399-4402.
52. Förster, S.; Timmann, A.; Konrad, M.; Schellbach, C.; Meyer, A.; Funari, S. S.; Mulvaney, P.; Knott, R., Scattering Curves of Ordered Mesoscopic Materials. The Journal of Physical Chemistry B 2005, 109 (4), 1347-1360.
53. Natta, G.; Pasquon, I.; Zambelli, A., Stereospecific Catalysts for the Head-To-Tail Polymerization of Propylene to a Crystalline Syndiotactic Polymer. J. Am. Chem. Soc. 1962, 84 (8), 1488-1490.
54. Fetters, L. J.; Lohse, D. J.; Graessley, W. W., Chain dimensions and entanglement spacings in dense macromolecular systems. Journal of Polymer Science Part B: Polymer Physics 1999, 37 (10), 1023-1033.
55. Clancy, T. C.; Pütz, M.; Weinhold, J. D.; Curro, J. G.; Mattice, W. L., Mixing of Isotactic and Syndiotactic Polypropylenes in the Melt. Macromolecules 2000, 33 (25), 9452-9463.
56. Zhu, L.; Cheng, S. Z. D.; Calhoun, B. H.; Ge, Q.; Quirk, R. P.; Thomas, E. L.; Hsiao, B. S.; Yeh, F.; Lotz, B., Phase structures and morphologies determined by self-organization, vitrification, and crystallization: confined crystallization in an ordered lamellar phase of PEO-b-PS diblock copolymer. Polymer 2001, 42 (13), 5829-5839.
57. Benedicto, A. D.; O'Brien, D. F., Bicontinuous Cubic Morphologies in Block Copolymers and Amphiphile/Water Systems:  Mathematical Description through the Minimal Surfaces. Macromolecules 1997, 30 (11), 3395-3402.
58. S. T. Hyde; Andersson, S., A cubic structure consisting of a lipid bilayer forming an infinite periodic minimum surface of the gyroid type in the glycerolmonooleat-water system. Zeitschrift für Kristallographie - Crystalline Materials 1984, 168, 213.
59. S. T. Hyde; Andersson, S., Differential geometry of crystal structure descriptions, relationships and phase transformation. Zeitschrift für Kristallographie - Crystalline Materials 1985, 170, 225.
60. Adam M. Squires; R. H. Templer; J. M. Seddon; J. Woenkhaus; R. Winter; T. Narayanan; Finet, S., Kinetics and mechanism of the interconversion of inverse bicontinuous cubic mesophases. Physical Review E 2005, 72, 011502.
61. Jinnai, H.; Watashiba, H.; Kajihara, T.; Takahashi, M., Connectivity and topology of a phase-separating bicontinuous structure in a polymer mixture: Direct measurements of coordination number, inter-junction distances and Euler characteristic. The Journal of Chemical Physics 2003, 119 (14), 7554-7559.
62. Hiroshi Jinnai; Takashi Kajihara; Hideyuki Watashiba; Yukihiro Nishikawa; Spontak, R. J., Interfacial and topological measurements of bicontinuous polymer morphologies. Physical Review E 2001, 64, 010803.
63. Chu, C. Y.; Jiang, X.; Jinnai, H.; Pei, R. Y.; Lin, W. F.; Tsai, J. C.; Chen, H. L., Real-space evidence of the equilibrium ordered bicontinuous double diamond structure of a diblock copolymer. Soft Matter 2015, 11 (10), 1871-1876.
64. Schröder Turk, G. E.; Fogden, A.; Hyde, S. T., Local v/a variations as a measure of structural packing frustration in bicontinuous mesophases, and geometric arguments for an alternating Im3m (I-WP) phase in block-copolymers with polydispersity. Eur. Phys. J. B 2007, 59 (1), 115-126.
65. Schoen, A. H., Three dimensional Euclidean space partitioned into interpenetrating labyrinths by infinite periodic minimal surfaces without self intersections NASA Tech. Note 1970, D-5541, 1.
66. Chu, C. Y.; Lin, W. F.; Tsai, J. C.; Lai, C. S.; Lo, S. C.; Chen, H. L.; Hashimoto, T., Order–Order Transition between Equilibrium Ordered Bicontinuous Nanostructures of Double Diamond and Double Gyroid in Stereoregular Block Copolymer. Macromolecules 2012, 45 (5), 2471-2477.
67. Kobayashi, M.; Tsumura, K.; Tadokoro, H., Infrared spectra of polymer solutions. I. Conformational stability of isotactic polymer chains in solution. Journal of Polymer Science Part A-2: Polymer Physics 1968, 6 (8), 1493-1508.
68. Lotz, B.; Lovinger, A. J.; Cais, R. E., Crystal structure and morphology of syndiotactic polypropylene single crystals. Macromolecules 1988, 21 (8), 2375-2382.
69. Brookes, A.; Dyke, J. M.; Hendra, P. J.; Meehan, S., The FT-Raman spectroscopic study of polymers at temperatures in excess of 200°C. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 1997, 53 (13), 2313-2321.
70. Rizzo, P.; Lamberti, M.; Albunia, A. R.; Ruiz de Ballesteros, O.; Guerra, G., Crystalline Orientation in Syndiotactic Polystyrene Cast Films. Macromolecules 2002, 35 (15), 5854-5860.
71. Sevegney, M. S.; Parthasarthy, G.; Kannan, R. M.; Thurman, D. W.; Fernandez Ballester, L., Deformation-Induced Morphology Changes and Orientation Behavior in Syndiotactic Polypropylene. Macromolecules 2003, 36 (17), 6472-6483.