Spherical microdomains

As with cylinder- and lamellae-forming block copolymers, the rheological behavior of block copolymers that form spherical domains depends on whether or not the domains possess macrocrystalline order. If the domains are disordered, then the low-frequency moduli show terminal behavior typical of ordinary viscoelastic liquids that is, G and G fall off steeply as the frequency becomes small (Watanabe and Kotaka 1983, 1984 Kotaka and Watanabe 1987). When the spherical domains are ordered, however, elastic behavior is observed at low frequency that is, G approaches a constant at low frequency, and a yield stress is observed in steady shearing. 

---

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]. 

The core-shell type polymer microspheres were synthesized upon the chemical crosslinking of the spherical microdomains in the microphase separated films. The block copolymers were dissolved in 1,1,2-trichloroeth-... 

Figure 14 Radius distribution functions (a) between the P4VP cores of the microspheres, (b) from P4VP core to P2VP spherical microdomains, (c) from P2VP spherical microdomain to P4VP core, and (d) between P2VP spherical microdomains [37].

Fig. 8 Schematic representation of block copolymer nanolithography process, a Schematic cross-sectional view of a nanolithography template consisting of a uniform mono-layer of PB spherical microdomains on silicon nitride. PB wets the air and substrate interfaces, b Schematic of the processing flow when an ozonated copolymer film is used as a positive resist, which produces holes in silicon nitride, c Schematic of the processing flow when an osmium-stained copolymer film is used as a negative resist, which produces dots in silicon nitride, (taken from [44])...

In the earliest studies, so-called core-shell morphologies were identified, where the core of the minority end-component is separated from the other endblock by a shell of the midblock (B). Spherical microdomains surrounded by a shell of the midblock have been observed using TEM for a number of polymers (Arai et al. 1980 Riess et al. 1989). Mogi et al. (1992a) studied a series of PI-PS-P2VP triblocks where the volume fraction of the PS middle block was varied from 0.3 to 0.8, whilst the volume fractions of the endblocks were kept equal to each other. On increasing the PS volume fraction a core-shell lamellar... 

Cohen et al. (1990) studied a poly(styrene)-poly(ethylene) (PS-PE) diblock that was solvent cast from toluene. Crystallization within microphase-separated PE spheres occurred when solvent-casting was done above the PE block melting temperature, Tm (see Fig. 5.2). When solvent was removed below Tm crystallization did not occur within spherical microdomains, instead TEM and SANS experiments suggested an irregular structure. Nojima et al. (1994) suggest that crystallization from the melt in this sample occurred within the microphase-separated block in the former case due to the high molecular weight of the... 

Hashimoto T., Fujimura M. and Kawai H., Domain-boundary structure of styrene-isoprene block copolymer films cast from solutions 5. molecular-weight dependence of spherical microdomains. Macromolecules 13 (1980) pp. 1660-1669. 

Fig. 7. Prediction of the cavitation model (full curves) and the meniscus instability model (broken tine) for the dependence of craze velocity on applied stress for a block copolymer containing 18 vol. % PB spherical microdomains...

Of course the modulus of a block copolymer with ordered spherical microdomains is much lower than that of a crystalline solid. Near the disordering transition, the potential energy holding each domain or atom in place is of order ksT, and the modulus is roughly vksT, where v is the number of domains or atoms. This gives an elastic modulus 10 -10 dyn/cm for typical block copolymers with spherical domains, as opposed to 10 -10 dyn/cm for atomic crystals. Ordered spherical diblock copolymers are therefore soft solids. They deflect under an imposed shear stress, but do not flow continuously unless that stress exceeds a critical value, the yield stress (Watanabe and Kotaka 1984). 

Also in bulk block copolymers microphase-separate into ordered liquid crystalline phases. A variety of phase morphologies such as lamellae (LAM), hexagonally ordered cylinders (HEX), arrays of spherical microdomains (BCC, FCC), modulated (MLAM) and perforated layers (FLAM), ordered bicontinuous structures such as the gyroid, as well as the related inverse structures have been documented. The morphology mainly depends on the relative block length. If, for instance, both blocks are of identical length, lamellar structures are preferred. 

The scaling described in Equation 2 indicates that the modulus is a strong function of the hybrid loading and is consistent with the data obtained for other filled polymer systems as well as the scaling observed for block copolymers with spherical microdomains. ... 

An isothermal morphology diagram of poly(styrene-fe/oc -butadiene) is shown in Fig. 19 as a function of molecular weight and copolymer composition the classic morphologies include spherical microdomains (0< a<0.15) packed in a body-centered cubic lattice, hexagonally packed cylindrical microdomains (0.15 <( a-0-3), and alternating lamellae of approximately symmetric diblocks (0.3 <0 -0-5). Sever-... 

---