Supplemental Information for Dynamic orientation transition of lyotropic lamellar phase at high shear rate

Typical SAXS profiles and lamellar spacing d as a function of shear rate for the system with B/H=0.30 at T=25◦C are shown in fig. 1. This systems shows the orientation transition at γ̇c/a=300s −1 (see Fig. 6 in the main text). Lamellar spacing d at B/H=0.30 slightly decreases with increase in the shear rate, while at B/H=0.32 it slightly reduces at low shear rate and stays almost constant at high shear rate. Reduction in the lamellar spacing d with the shear rate was also reported for the hyper swollen lamellar phase. Ratio of the reduction at B/H=0.30 is only a few % which is the same order as that observed in dilute lamellar system [1]. We did not see obvious reduction of d at the orientation transition point as expected from theoretical argument. Kato et al. found that the lamellar spacing drastically changes as the shear rate is approached to a specific value where the segregation of the lamellae occurs [2, 3]. Slight decrease in d with the shear rate may indicate that the suppression of the undulation fluctuation is gradually induced but not suddenly at the critical shear rate. However, almost constant value at high shear rate indicates that the suppression of the undulation fluctuation is not only the driving source for the orientation transition.