Ordered bicontinuous double-diamond

Figure C2.1.11. Morjrhologies of a microphase-separated di-block copolymer as function of tire volume fraction of one component. The values here refer to a polystyrene-polyisoprene di-block copolymer and ( )pg is tire volume fraction of the polystyrene blocks. OBDD denotes tire ordered bicontinuous double diamond stmcture. (Figure from [78], reprinted by pemrission of Annual Reviews.)...

It is well known that block copolymers and graft copolymers composed of incompatible sequences form the self-assemblies (the microphase separations). These morphologies of the microphase separation are governed by Molau s law [1] in the solid state. Nowadays, not only the three basic morphologies but also novel morphologies, such as ordered bicontinuous double diamond structure, are reported [2-6]. The applications of the microphase separation are also investigated [7-12]. As one of the applications of the microphase separation of AB diblock copolymers, it is possible to synthesize coreshell type polymer microspheres upon crosslinking the spherical microdomains [13-16]. 

Winey, K.I., Thomas, E.L., Fetters, L.J. The ordered bicontinuous double-diamond morphology in diblock copolymer/homopolymer blends. Macromolecules 25, 422-428 (1992)... 

Several ordered states distinguished by their symmetries have been identified the preferred one depends primarily on the polymer composition [29,38,39]. Some common patterns are lamellar sheets, ordered bicontinuous double diamond (OBDD), hexagonally packed cylindrical arrays, and body-centered-cubic spherical microstructures. If the volume fractions of the two halves of the polymer chain are similar, the interface between the two regions will be flat and the lamellar phase will form. However, if one block is much smaller than the other, then for packing reasons, the interface will curve toward the smaller half (see Fig. 19b), giving, in order of increasing curvature, the OBDD, cylindrical, and spherical microstructure. 

In the case of microstructures with at least two distinct threefold or greater symmetry axes, symmetry requires the dielectric ellipse to be spherical. The integral of Eq. (22) is therefore isotropic, and the electric field cannot act to align the microstructure. In this class are the spherical and the ordered bicontinuous double diamond microstructures. 

Originally, only the classical set of phases was observed, spheres, cylinders and lamellae. With time and increasing refinement of both theory and experiment other configurations, stable and metastable, were predicted and observed. The ordered bicontinuous double diamond was observed in a star block copolymer (Thomas et al. 1986) and the gyroid in a diblock copolymer (Hajduk et al. 1994). A recent theoretical calculation (Matsen 2012) is shown at left in the figure below, and compared with experimental observations complied from different sources (Matsen 2002) (Figs. 1.12 and 1.13). 

Thomas EL, Alward DB, Kinning DJ, Martin DC, Handlin D Jr, Fetters LJ (1986) Ordered bicontinuous double-diamond stmcture of star block copolymers—a new equilibrium microdomain morphology. Macromolecules 19(8) 2197-2202... 

One of the imique features of phase separated block copolymers involves their ordered morphologies which can include spheres, cylinders, lamellae, bicontinuous as well as ordered bicontinuous doubled diamond and gyroid structures (see Figs. 4.17 and 4.18). Gyroid struc-... 

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