Linear Melt Rheology and Small-Angle X-ray Scattering of AB Diblocks vs A 2 B 2 Four Arm Star Block Copolymers D. M. A. Buzza,* ,†,‡ A. H. Fzea, §,| J. B. Allgaier, | R. N. Young, | R. J. Hawkins, ‡ I. W. Hamley, ⊥ T. C. B. McLeish, ‡ and T. P. Lodge # Department of Physics and Astronomy & Polymer IRC, University of Leeds, Leeds LS2 9JT, U.K.; Department of Chemistry, University of Sheffield, Sheffield S3 7HF, U.K.; School of Chemistry, University of Leeds, Leeds LS2 9JT, U.K.; and Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 Received March 2, 2000; Revised Manuscript Received August 9, 2000 ABSTRACT: The frequency dependent viscoelastic properties and lamellar spacing of three symmetric styrene-isoprene (PS-PI) diblock copolymers are compared to those of their hetero-four-arm star counterparts. The PS and PI arm molecular weights of the three linear and three star samples are 10, 20, and 60 kg/mol, respectively. All six samples were unoriented and had lamellar morphology for temperatures less than T ODT, the order-disorder temperature for each molecular weight. The lamellar spacing D at the same temperature was found to scale with overall molecular weight N according to D ∼ N δ , with δ ≈ 0.7 for both linear and stars. However, the star chains were consistently 5-10% more strongly stretched compared to their linear counterparts. For the 10K arm materials, the critical frequency for the onset of mesophase relaxations (ω c) for the stars was found to be about 20 times smaller compared to the linears. This difference correlated very well with quantitative estimates of the inverse layer hopping time of the chains, suggesting that mesophase relaxations for the 10K arm materials may be controlled by layer hopping of chains. For the 10K and 20K arm materials, relaxation of the PS chain deformations are dominant for ω . ω term PS , whereas nonclassical terminal scaling of G′, G′′ ∼ ω 1/2 was observed for ω , ω term PS and T < TODT due to mesophase relaxations (ω term PS is the PS block terminal relaxation frequency). In addition, the linear rheology of the linear and star analogues coincide for ω . ω term PS , but an additional shoulder emerges in the star materials for ω ≈ ω term PS . By fitting to a simple model incorporating free chain Rouse dynamics and mesophase relaxations, we were able to obtain excellent quantitative fits to the 20K materials across the whole frequency range and conclude that the observed shoulder in the star materials was due to differences in the linear and star mesophase relaxations. The fitted ω c and GM0 (the mesophase modulus) values are in good agreement with Kawasaki-Onuki theory indicating that the mesophase relaxations of the 20K arm materials may be controlled by collective hydrodynamic layer fluctuations rather than layer hopping of chains. For the 60K arm materials, qualitatively different behavior compared to the lower molecular weight samples was observed: PI rate controlled relaxation with G′, G′′ ∼ ω 1/2 was observed for ω . ω term PS . We identify this relaxation as a PI controlled mesophase relaxation. Theoretical estimates of ωc for this mechanism using Kawasaki-Onuki theory yield ωc . ω term PS in support of our suggestion. I. Introduction Block copolymers are macromolecules where se- quences, or blocks, of chemically distinct repeat units are covalently bonded together within the same mol- ecule. One of the most striking features of these macromolecules is that, in the melt phase, the distinct chemical units microphase separate at low enough temperatures to form ordered microdomains whose length scale is of the order of the size of a molecule. This transition is called the order-disorder transition (ODT) and the temperature at which it occurs is known as the order-disorder transition temperature (T ODT ). For T > T ODT , the system is in the disordered state and its rheology is similar to that of homopolymer melts. However, qualitatively different behavior is observed for T < T ODT for frequencies below the terminal frequency for molecular relaxations. Because of formation of microdomains, nonclassical terminal behavior, sensitive to the symmetry of the microdomain morphology, is observed. 1 Until relatively recently, most rheological studies on block copolymers have tended to focus on block copolymers with simple linear architecture, no- tably on diblocks and triblocks. 1-10 However, advances in synthetic chemistry, especially in the area of anionic polymerization, have allowed block copolymers with more complex molecular architectures, specifically those with branched architecture, to be synthesized. This has opened up a whole new dimension in block copolymer research, namely the influence of molecular architecture and topology on solution and melt properties of block copolymers. For some examples of studies on the dynamical properties of block copolymers with complex molecular architecture, see refs 11-13. For well entangled homopolymers, the presence of long chain branching has a dramatic effect on dynamical and rheological behaviors. The theory is particularly well-developed for the rheology of homopolymers with the simplest branched architecture, namely that of † E-mail: dmabuzza@leeds.ac.uk. ‡ Department of Physics and Astronomy & Polymer IRC, University of Leeds. § Present address: Department of Chemistry, University of Dundee, Dundee DD1 4HN, U.K. | University of Sheffield. ⊥ School of Chemistry, University of Leeds. # University of Minnesota. 8399 Macromolecules 2000, 33, 8399-8414 10.1021/ma000382t CCC: $19.00 © 2000 American Chemical Society Published on Web 10/14/2000