Cylindrical microstructure

X — A/T + B (where A and B are constants) however, the parameters from the fit cannot straightforwardly be interpreted on a molecular basis (Almdal et al. 1996). A transition from shear-induced order to shear-induced disorder on increasing the shear rate has recently been reported in an asymmetric PS-PI diblock in concentrated solution (Balsara and Dai 1996). The low-shear rate ordering was consistent with the suppression of fluctuations, and the high-shear rate disordering was interpreted as arising from fluctuations of the ordered (cylindrical) microstructure (Balsara and Dai 1996). 

The orientation of crystalline stems with respect to the interface of the microstructure in block copolymers depends on both morphology and the speed of chain diffusion, which is controlled by block copolymer molecular weight and the crystallization protocol (i.e. cooling rate). In contrast to homopolymers, where folding of chains occurs such that stems are always perpendicular to the lamellar interface, a parallel orientation was observed for block copolymers crystallized from a lamellar melt phase perpendicular folding was observed in a cylindrical microstructure. Both orientations are shown in Fig. 8. Chain orientation can be probed via combined SAXS and WAXS on specimens oriented by shear or compression. In PE, for example, the orientation of (110) and (200) WAXS reflections with respect to Bragg peaks from the microstructure in the SAXS pattern enables the unit cell orientation to be deduced. Since PE stems are known to be oriented along the c axis, the chain orientation with respect to the microstructure can be determined. 

Let us halt for a moment and consider the relationship between block copolymer materials and liquid crystals. A block copolymer exhibiting a lamellar microstructure can be classified as a smectic A liquid crystal because it has positional disorder in two dimensions and a periodic pattern in the third. Here, the periodic pattern can be identified with the variation in the local monomer compo,sition. In small-molecule smectics, the analogous periodicity arises from the molecular center-of-mass distribution. A block copolymer exhibiting a cylindrical microstructure is analogous to a columnar liquid crystal. The OBDD and spherical microstructures have three-dimensional order and have no liquid cry.stal analogs. 

FIGURE 21 The dielectric tensor represented as an ellipse. A general ellipse is shown in (a) with the three eigenvalues e, e, and e, in (b) an oblate ellipsoid for a block copolymer with a lamellar microstructure, in (c) a prolate ellipsoid for a block copolymer with a cylindrical microstructure, and in (d) a sphere for a spherical or OBDD microstructure. 

Wang [81] and Hamley [82] considered this instability more extensively in block copolymers with lamellar and cylindrical microstructures, respectively, under uniaxial extension. Onuki and Fukuda [78,83] developed a theory for this instability induced by an electric field. This is considered next. 

Figure 2. TEM of cylindrical microstructures formed from a 1 1 ratio of 1 and 2.

Several additional, non-microstructural, inputs are required for the fracture model (i) Particle critical stress intensity factor, KIc. Here, the value determined in a previous study (Klc = 0.285 MPa in )[3] was adopted for all four graphites studied. This value is significantly less than the bulk Klc of graphites (typically -0.8-1.2 MPa rn). However, as discussed in the previous section, when considering fracture occurring in volumes commensurate in size with the process zone a reduced value of Klc is appropriate (ii) the specimen volume, taken to be the stressed volume of the ASTM tensile test specimens specimen used to determine the tensile strength distributions and (iii) the specimen breadth, b, of a square section specimen. For cylindrical specimens, such as those used here, an equivalent breadth is calculated such that the specimen cross sectional area is identical, i.e.,... 

Tubules have also been prepared by swelling thin films of polymerizable diacetylenic phosphatidylhydroxyethanol (choline functionally in 21 is replaced by hydroxyethanol) in aqueous metal ion solutions above the phase transition temperature of the lipid. Various cylindrical structures were observed upon swelling the lipid in the presence of mono- and divalent cations. In contrast, no definable microstructures were noted in the absence of cations [362],... 

One can have the same type of situation in a blend of two mutually immiscible polymers (e.g., polymethylbutene [PMB], polyethylbutene [PEB]). When mixed, such homopolymers form coarse blends that are nonequilibrium structures (i.e., only kinetically stable, although the time scale for phase separation is extremely large). If we add the corresponding (PEB-PMB) diblock copolymer (i.e., a polymer that has a chain of PEB attached to a chain of PMB) to the mixture, we can produce a rich variety of microstructures of colloidal dimensions. Theoretical predictions show that cylindrical, lamellar, and bicontinuous microstructures can be achieved by manipulating the molecular architecture of block copolymer additives. 

FIG. 1.7 Some of the microstructures produced by the self-association behavior of diblock copolymer solutions. The figure illustrates the (a) spherical, (b) cylindrical, and (c) lamellar structures (among others) that are possible in such solutions. Each diblock polymer chain consists of strings of white beads (representing one type of homopolymer) and strings of black beads (representing the second type of homopolymer). (Redrawn from A. Yu. Grosberg and A. Khokhlov, Statistical Physics of Macromolecules, AIP Press, New York, 1994.)... 

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