Cylindrical phases

Transition from a cylindrical phase to a lamellar phase induced by addition of homopolymer... 

UsingTEM to identify blend morphology, two diblocks with/ps 0.8 that form cubic-packed spherical phases and cylindrical phases respectively in the pure copolymer were found not to macrophase separate in a blend with d = 2.2, but to form single domain structures (cylinders or spheres) in the blend (Koizumi et al. 1994c). Similarly, blending a diblock with fK = 0.26 with one with fK = 0.64 (d = 1.2) led to uniform microphase-separated structures, with a lamellar phase induced in the 50 50 blend. Vilesov et al. (1994) also observed that blending two PS-PB diblocks with approximately inverse compositions (i.e. 22wt% PS and 72 wt% PS) induces a lamellar phase in the 50 50 blend. These examples all correspond to case (i). 

Figure 13.6 Transmission electron micrographs of thin-sectioned PS-PI block copolymer phases (a) lamellar phase, (b) hexagonal cylindrical phase. (Reprinted with permission from Forster et al.. Macromolecules 27 6922. Copyright 1994, American Chemical Society.)...

ABC-type triblock copolymers, in which A, B, and C are all chemically distinct from each other, can form a variety of additional structures, such as a cylindrical phase ordered on a square lattice, a tricontinuous diamond phase (Mogi et al. 1992 Nakazawa and Ohta 1993), and some exquisitely delicate structures, such as cylinders decorated by rings (see Fig. 13-8) or by strands winding around them in helieal fashion (Stadler et al. 1995 Krappe et al. 1995). Recent findings have greatly expanded the known types of ordered block copolymer phases. 

Since the system is 27r-periodic in 0, it may be considered as a vector field on a cylinder. (See Section 6,1 for another vector field on a cylinder.) The x-axis runs along the cylinder, and the 0-axis wraps around it. Note that the cylindrical phase space is finite, with edges given by the circles x = 0 and x = 1. 

Fig. 12 Two-dimensional density plots for the diblock/particle systems obtained from the SCFT/DFT theory. Plots are for abN = 20, Xlss = Xbp = 0.02, N = 1000, / = 0.35, and 0p = 0.15. Plots on the left represent the distribution of the A blocks and plots on the right represent the distribution of the centers of mass of the particles. Light regions indicate a high density, while dark regions indicate low densities. The image in part (a) shows that the system displays a cylindrical phase when Rp = OARq and the image in part (b) shows that the mixture forms a lamellar phase when the particle size is increased to Rp = 03Rq. Reprinted with permission from Macromolecules [77]. Copyright (2002) American Chemical Society...

In 1986, Thomas et al. were the first to discover the double-gyroid IMDS in multiarm star diblock copolymers of poly(isoprene) and poly(styrene), but incorrectly identified the new morphology, lying between the lamellar and cylindrical phase, as the... 

The theoretically calculated phase diagrams of the mid 1990s agree remarkably well with the experimentally observed phase behavior of diblock copolymers. Figure4.2b shows the almost symmetric phase diagram of PS-fc-PI measured by Khandpur et al. in 1995 [10]. At that time it was still believed, that the semi-continuous hexagonally perforated lamellar phase, a combination of the lamellar and cylindrical phase, is a stable equilibrium phase. Later experimental and theoretical studies showed, that the HPL is a metastable structure or long-lived transition, but not an equilibrium structure [11]. Similarly, the Fddd was believed to exists as a metastable structure [12]. 

Figure 6.12 Top iown and 70° tilt scanning electron microscopy (SEM) images of thin-film blends of 67-kg/mol cylindrical phase and 74-kg/mol lamellar phase polystyrene-b-poly(methyl methacrylate). The ratio of the blend components is Af (cyl)/...

Each microphase has its own symmetry and unit cell, and a full solution to the NSCF problem must be consistent with them. For example, the unit cell for the cylindrical phase is hexagonal, that for bcc is the appropriate Wigner-Seitz cell, and so on. The early NSCFT calculations approximated the unit cells for the latter two phases by cylinders and spheres, respectively. Matsen and Schick eliminated this unit cell approximation (UCA), by expanding each function of position in a series of orthonormal basis functions, each of which has the full symmetry of the phase under consideration. This provides a more accurate description of the C and S phases and, most importantly, permits the treatment of the more complex, nonclassical phases. 

Figure 6 demonstrates the formation of a perfectly aligned hexagonal cylindrical phase in aqueous solution of 55% triblock copolymer Pluronic L64 (cf. Figs. Ic and 2c). 

The gemini surfactant (CH2)6-l,6-bis[NCPhPhO(CH2)5N" (0113)2, Br ] forms no cylindrical phases but gives rise to two lamellar phases at appropriate temperature and concentration [138]. 

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