Bridging Properties of Multiblock Copolymers
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A4.3.1
Bridging Properties of Multiblock Copolymers
K.Ø. Rasmussen, E.M. Kober, T. Lookman, and A. Saxena Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, U.S.A. ABSTRACT
Using self-consistent field theory, we attempt to elucidate the links between microscopically determined properties, such as the bridging fraction of chains, and mechanical properties of multiblock copolymer materials. We determine morphological aspects such as period and interfacial width and calculate the bridging fractions, and compare with experimental data. INTRODUCTION
Block copolymers exhibit a fascinating variety of structured mesoscale phases when the different blocks are sufficiently incompatible. Most work [1] has focused on diblock copolymers AnBm. The chemical dissimilarity between the A and B species (quantified through the segmentsegment Flory-Huggins interaction parameter, χ) produces periodic mesoscale morphologies [2-4] with symmetries determined by the overall volume fraction, f, of the A block and by the degree of immiscibility, χN, (where N=n+m is the total number of segments). The lowest degree of immiscibility (χ N ≈ 10.5) leading to mesoscale morphologies occurs for symmetric systems (f ≈ 0.5 or n ≈ m) where a lamellar structure emerges. Other equilibrium structures [2] established to date include spheres of A (B) arranged on a body-centered cubic lattice in a B (A) matrix, cylinders of A (B) arranged on a hexagonal lattice in a B (A) matrix, and bicontinuous gyroid channels. Multiblock copolymers [(AnBm)p or (AnBm)pAn], on the other hand, have received considerably less attention, although many commercial applications requiring mechanical strength rely on these systems [5]. It has been established that the mesoscopic phases of the multiblock systems are indistinguishable from those formed by diblocks. The onset of microsegregation, i.e. the disorderorder transition, however, occurs at increasingly higher χ N as the diblock unit is repeated (larger p) [6, 7, 8]. The period of the segregated structures has similarly been found to decrease with p. The most comprehensive theoretical study of linear multiblock copolymers has been published by Matsen and Schick [9] in the many-block (p >> 1) limit using the self-consistent mean-field theory (SCFT) initially developed by Helfand [10]. Matsen and Schick theoretically established the morphological phase diagram and found that the periodicity D ~ χ 1 / 6 N 2 / 3 and the interfacial width w ~ χ −1/ 2 scale with the same exponents as for diblock systems. The principal feature that makes the multiblock copolymers more attractive for commercial applications is the double tethered central portion of the molecule. In contrast to diblock copolymers, this tethering allows blocks in the central portions of a multiblock copolymer to bridge their respective domains. Bridging blocks are thought to provide multiblock copolymers with superior mechanical properties, relative to their diblock analogs, as they provide a physically cross-linked network. Several theoreti
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