Linear Melt Rheology and Small-Angle X-ray Scattering of AB Diblocks vs A2B2 Four Arm Star Block Copolymers

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 ≫, whereas nonclassical terminal scaling of G ‘, G ‘ ‘ ∼ ω 1/2 was observed for ω ≪ and T < T ODT due to mesophase relaxations ( is the PS block terminal relaxation frequency). In addition, the linear rheology of the linear and star analogues coincide for ω ≫, but an additional shoulder emerges in the star materials for ω ≈ . 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 G M0 (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 ≫ . We identify this relaxation as a PI controlled mesophase relaxation. Theoretical estimates of ω c for this mechanism using Kawasaki−Onuki theory yield ω c ≫ in support of our suggestion.