Abstract.
A mesoscopic model for diblock copolymers is combined with a simple rheological description of the viscoelastic contrast of its two phases. Under oscillatory shear the contrast generates secondary velocity fields and substantial deviations of volume-averaged flow parameters. The validity of our analytical findings is tested with three-dimensional numerical simulations. Furthermore, we consider the effect of advection by the generated flows on the stability of ordered lamellar states and propose a new criterion for the selection of orientations.
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References
I.W. Hamley, The Physics of Block Copolymers (Oxford University Press, 1998).
G.H. Fredrickson, J. Rheol. 38, 1045 (1994).
M. Goulian, S.T. Milner, Phys. Rev. Lett. 74, 1775 (1995).
R.G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, 1999).
A.K. Khandpur, S. Förster, F.S. Bates, A.I. Hamley, A.J. Ryan, W. Bras, K. Almdal, K. Mortensen, Macromolecules 28, 8796 (1995).
K.A. Koppi, M. Tirrell, F.S. Bates, Phys. Rev. Lett. 70, 1449 (1993).
V.K. Gupta, R. Krishnamoorti, J.A. Kornfield, S.D. Smith, Macromolecules 28, 4464 (1995).
D. Maring, U. Wiesner, Macromolecules 30, 660 (1997).
U. Wiesner, Macromol. Chem. Phys. 198, 3319 (1997).
V.K. Gupta, R. Krishnamoorti, J.A. Kornfield, S.D. Smith, M.M. Satkowski, J.T. Grothaus, Macromolecules 29, 875 (1996).
A.N. Morozov, J.G.E.M. Fraaije, Phys. Rev. E 65, 031803 (2002).
G.H. Fredrickson, J. Chem. Phys. 117, 6810 (2002).
H. Kodama, M. Doi, Macromolecules 29, 2652 (1996).
F. Drolet, P. Chen, J. Viñals, Macromolecules 32, 8603 (1999).
P. Chen, J. Viñals, Macromolecules 35, 4183 (2002).
G.K. Auernhammer, H.R. Brand, H. Pleiner, Phys. Rev. E 66, 061707 (2002).
M. Cross, P. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
G. Fredrickson, F. Bates, Annu. Rev. Mater. Sci. 26, 501 (1996).
L. Leibler, Macromolecules 13, 1602 (1980).
T. Ohta, K. Kawasaki, Macromolecules 19, 2621 (1986).
S.R. Ren, I.W. Hamley, G.J.A. Sevink, A .V. Zvelindovsky, J.G.E.M. Fraaije, Macromol. Theory Simul. 11, 123 (2002).
D.D. Joseph, Fluid Dynamics of Viscoelastic Fluids (Springer, New York, 1990).
H.J. Wilson, M. Renardy, Y. Renardy, J. Non-Newt. Fluid Mech. 80, 251 (1999).
P.N. Brown, G.D. Byrne, A.C. Hindmarsh, SIAM J. Sci. Stat. Comput. 10, 1038 (1989).
The instantaneous diffusion terms in equation (ns4) have been used to simplify the algebraic equations. In principle, the system can be solved without these terms, but we have performed this alternative calculation only for the base state. We did not find significant changes to the solution.
S.S. Patel, R.G. Larson, K.I. Winey, H. Watanabe, Marcomolecules 28, 4313 (1995).
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Rüdiger, S. Viscoelastic response of diblock copolymers to oscillatory shear. Eur. Phys. J. E 17, 45–52 (2005). https://doi.org/10.1140/epje/i2004-10103-4
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DOI: https://doi.org/10.1140/epje/i2004-10103-4