Rheologica Acta Rheol Acta 32:245-253 (1993) The rheology of layered liquids: lamellar block copolymers and smectic liquid crystals R.G. Larson 1, K.I. Wineyl*), S.S. Patel 1, H. Watanabe 2 and R. Bruinsma 3 1AT&T Bell Laboratories, Murray Hill 2 Department of Macromolecular Science, Osaka University, Toyonaka, Osaka, Japan 3Department of Physics, University of California, Los Angeles Abstract: The frequency-dependence of the viscoelastic shear modulus at low frequencies in a lamellar polystyrene-polyisoprene block copolymer is quali- tatively identical to that measured in small-molecule smectics, namely, the rod- like 4-cyano-4'-octylbiphenyl and the flexible n-nonyl-l-O-fl-D-glucopyranoside. All three materials were studied after quenching from the isotropic state, and during and after alignment by large-amplitude oscillatory shearing. The kinetics of aligning, as measured by changes in moduli during shearing, are similar, despite great differences in molecular characteristics. These moduli and the aligning process are evidently controlled by smectic fluctuations and defects, the dynamics of which have universal features. Key words: Block copolymers - smectics - liquid crystals - lamellar structure 1. Introduction Block copolymers are useful as adhesives, disper- sants, and impact modifiers; the simplest of them contain two chemically distinct linear polymers covalently bonded into a single linear chain. When neat, or mixed with one or more polymeric or non- polymeric liquids, the chemically dissimilar blocks microseparate at low temperature. The micro- separated domains are most cc,mmonly spherical, cylindrical, or lamellar in shape and these often take on cubic, hexagonal or smectic order. Because of topological defects, this order is often only local and not global, although global order can be produced, for example, by carefully controlled deformations (Keller et al., 1970; Keller and Odell, 1985; Had- ziioannou et al., 1979, 1982; Bates et al., 1990; Koppi et al., 1993; Winey et al., 1993a, 1993b). The usefulness of block copolymers in the applica- tions above is affected by their flow properties, and although the ordered materials flow under large enough mechanical stresses, many of these materials are not fully fluid even when both blocks are well *) Present address: Mat. Sci. and Eng. Dept., Univ. of Pennsylvania, Philadelphia, PA, 19104. above their crystalline or glass transitions. Thus, in the locally ordered state, block copolymers seem to possess no longest, relaxation time, but are viscoelastic even at very low frequencies (Gouinlock and Porter, 1977; Lyngaae-Jorgensen, 1985). This low-frequency viscoelastic behavior is especially in- teresting near the order-disorder transition tempera- ture, as has been explored by Bates and coworkers, for neat lamellae-forming diblock copolymers (Koppi et al., 1993; Bates, 1984; Rosedale and Bates, 1990; Almdal et al., 1992b). In the high-temperature disordered state, there is a longest relaxation time r, and the material is a fluid with a low-frequency viscosity t/, as evidenced by the "terminal" behavior of the complex modulus, G*=G'+iG", with G'~/ro~ 2 and G"~tle). Here, e) is the frequency of an oscillatory shearing flow, and G' and G" are, respectively, the storage and loss moduli. When the material is cooled into the locally ordered phase, the simple fluid-like terminal behavior disappears and is not recovered, even at frequencies that are decades below those for which terminal behavior exists in the disordered state (Gouinlock and Porter, 1977; Watanabe et al., 1984; Bates, 1984; Lyngaae-Jorgen- son, 1985; Rosedale and Bates, 1990; Morrison et al., 1990; Han et al., 1990; Koppi et al., 1993; Winey et al., 1993b, 1993c).