Supporting material
1) Comparison of diffracted intensities for three-phase lamellar structures formed by
ISP triblock terpolymer system with slightly different volume fractions.
Figure S1 compares the calculated diffracted intensities at (h00) plane, where h denotes
Miller index for ISP triblock copolymer blends assuming the volume fractions shown in
Table S1, which are calculated from the blend ratios using the bulk densities of three
polymers, i.e., 0.926, 1.05 and 1.14 for I, S and P, respectively. It is evident that even
ordered peaks are suppressed if volume fractions of center S block is low. This result is
quite consistent with the observed results performed by SAXS experiments.
2) Figure S2 schematically shows cross section of the present undulated lamellar
structure, which includes a lamellar repeating unit in y direction and one frequency
length in x direction. As shown in Figure S2,sine curves are assumed for domain
interfaces drawn by solid lines. Diffracted intensities should be given by executing the
following integrations within the range 0< x, y<1.
I=
ρ ,
sin 2
+
ρ ,
cos 2
eq. S1
In eq. S1, ρ(x,y) denotes electron density of either one of three components, I or S or P,
in bulk at a coordinate (x,y). One lamellar repeating unit in y-direction can be divided
into 9 sections, fiveAm(m=1-5)regions are for pure polymer domains, while Bn(n=1-4)
region sinclude two polymers along x direction within the range 0<x<1. For region A,
obviously the integralare all zero because electron density is constant throughout the
integral period, and hence both the integrals of sin(2πhx) and cos(2πhx) vanish in this
frequency range. For region B, the situation is somewhat complicated. In Figure S2, two
lines aty=αand y=β, are drawn, their heights are complemental in terms of the sine
function for S/P interface. The probable partial scattering intensities can be obtained by
integrating electron densities along two “imaginary” lines, α and β, and summing them
as eq. S2
,
ρ ,
ρ ,
cos 2
sin 2
ρ ,
ρ ,
sin 2
cos 2
eq.S2
Since the sine curve has the nature of rotational symmetry, the lines α and β can be
chosen as complemental ones in height each other. If we take out integrations for sine
and cosine terms for lines α and β in eq. S2 as
S
ρ ,
sin 2
C
ρ ,
cos 2
ρ ,
ρ ,
sin 2
cos 2
eq.S3-1
eq.S3-2
we notice that S and C are both constantly zero, and hence the total intensities along two
lines are zero according to eq. S2. The region B2 can be conceived as the assembly of
infinite numbers α-β pairs, so that the intensities from whole B2 region should be
expressed as eq. S4.
I
lim
∑
∞
∑
,
,
cos 2
sin 2
,
,
cos 2
sin 2
⁄
⁄
eq. S4
Interestingly, we can safely say that IB2=0 because integration for every pair is zero
according to eq. S3 and eq.S2. By applying this procedure for the region B2 to the other
Bns, it is apparent intensities from all Bns vanish. As a result, the diffracted intensities
along equatorial line, i.e., (h00)s should be constantly zero.
Figure S1. Calculated diffracted intensities at (h00) for lamellar structures formed by
ISP triblock terpolymers with various PDI.
Figure S2. Schematic representation of cross sections one-dimensionally undulated
lamellar structures assuming sine functions for domain interfaces.
This figure includes
one lamellar repeating unit in y-direction and unit sine frequency length in x-deirection.