Gyroid

Another phase which has attracted recent interest is the gyroid phase, a bicontinuous ordered phase with cubic symmetry (space group Ia3d, cf. Fig. 2 (d) [10]). It consists of two interwoven but unconnected bicontinuous networks. The amphiphile sheets have a mean curvature which is close to constant and intermediate between that of the usually neighboring lamellar and hexagonal phases. The gyroid phase was first identified in lipid/ water mixtures [11], and has been found in many related systems since then, among other, in copolymer blends [12]. 

W. Gozdz, R. Holyst. High genus gyroid surfaces of non-positive gaussian curvature. Phys Rev Lett 76 2726-2729, 1996. 

Figure 1. Phase diagrams of the systems M0-H20 (Adapted from ref. 1) and MO-DOPC-H20 (at 28 C, Adapted from ref. 2), respectively. G (gyroid) and D (diamond) are cubic phases with similar structures to the type shown schematically in the figure (Adapted from ref. 18).

The best-known and simplest class of block copolymers are linear diblock copolymers (AB). Being composed of two immiscible blocks, A and B, they can adopt the following equilibrium microphase morphologies, basically as a function of composition spheres (S), cylinders (C or Hex), double gyroid (G or Gyr), lamellae (L or Lam), cf. Fig. 1 and the inverse structures. With the exception of the double gyroid, all morphologies are ideally characterized by a constant mean curvature of the interface between the different microdomains. 

A systematic comparative study of triblock terpolymers in the bulk and thin-film state was carried out on polystyrene-fo-poly(2-vinyl pyridine)-b-poly(ferf-bulyl methacrylate), PS-fr-P2VP-fr-PfBMA. A diblock precursor with a minority of PS leading to a double gyroid structure was used. Upon increase of PfBMA content this morphology changed from lamellae with... 

Fig. 18 Phase space of PI-fc-PS-fc-PEO in vicinity of ODT. Filled and open circles-. ordered and disordered states, respectively, within experimental temperature range 100 < T/° C< 225. Outlined areas compositions with two- and three-domain lamellae (identified by sketches) shaded regions three network phases, core-shell double gyroid (Q230), orthorhombic (O70), and alternating gyroid (Q214). Overlap of latter two phase boundaries indicates high- and low-temperature occurrence, respectively, of each phase. Dashed line condition tfin = 0peo associated with symmetric PI-fc-PS-fc-PEO molecules. From [75]. Copyright 2004 American Chemical Society...

Fig. 38 Milner s diagram for morphologies of A-b-B copolymers as reported in literature [111]. Observed morphologies of linear and miktoarm-star copolymers of BS-b-P2MP system are represented. Lamellar structure, cylinders of P2MP in PS matrix spheres of P2MP in PS matrix, biphasic structure of lamellar/double gyroid microdomains. From [113]. Copyright 2003 American Chemical Society...

The appearance and persistence of core-shell structures as well as the occurrence of phase separation are attributed to a small asymmetry in the X -parameters (xPS-pi = 0.06, xpi-pdms = 0.09 and xps-pdms = 0.20). Hence, a PDMS core surrounded by a PI shell embedded in a PS matrix results in a smaller inner diameter interfacial area, relative to that for the PS-PI case. In a blend of a PS-fo-PI-fc-PDMS triblock with PS and PDMS homopolymers, more PS homopolymer is expected to be found in the corona of the PS block than PDMS homopolymer in the corona of the PDMS block because the penalty for contact between the PI block and PDMS homopolymer is larger. In consequence, the distribution of homopolymers favours an expanded PS-PI interface, making the core-shell morphologies, gyroid and cylinder, more prevalent. 

Addition of the middle B block to an ABC triblock terpolymer has been investigated by Suzuki et al. for the PI- -PS- -P2VP system [ 159]. Starting from the lamellar structure of the unblended triblock (0ps = 0.42) PS homopolymer was subsequently added. At fas 0.50 a morphological transformation into a gryoid structure is observed. Even if the volume fraction of PS is increased up to fas = 0.60, the cell size of the gyroid structure will remain... 

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