Shunsuke Sakamoto 1,2 , Yusuke Sanada 1,2 , Mizuha Sakashita 1,2 , Koichi Nishina 1 , Keita Nakai 3 ,
Shin-ichi Yusa 3 and Kazuo Sakurai* 1,2
1 Department of Chemistry and Biochemistry, The University of Kitakyushu,
1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan.
2 Structural Materials Science Laboratory SPring-8 Center, RIKEN Harima Institute Research,
1-1-1 Kouto, Sayo, Sayo, Hyogo 679-5148, Japan.
3 Department of Materials Science and Chemistry, Graduate School of Engineering, University of Hyogo,
2167 Shosha, Himeji, Hyogo 671-2280, Japan.
* Corresponding author: Kazuo Sakurai
E-mail address: sakurai@kitakyu-u.ac.jp (KS)
Contents
I. Fitting Models of SAXS
II. Hydrodynamic radius and TEM image of PICs

According to Pedersen et al 1,2 , the form factor form micelles consisting of spherical core and Gaussian corona chains can be expressed by use of four terms: the self-correlation of the core: , the self-correlation of the corona chains: , the cross term between the core and the corona chains: , and the cross term between different corona chains: S .
F q  N agg
2  2
C
F q  N agg
 2 F q N agg

C
 S q  N agg
( N agg
 1)
 2 S q
(s1)
Here q is the magnitude of the scattering vector, N agg
is the aggregation number, 
C and 
Ch
are the excess scattering lengths of core and corona blocks, respectively. For polymeric micelles, the first term in eq s1 may be regarded as that of homogeneous sphere with radius R
C
:
F q R
C
( ,
C
 A q R s C
)] 2  


3 sin qR  qR cos qR
C C C
( qR
C
) 3



2
(s2)
Here, represents the scattering amplitude of a solid sphere with the radius of R and we assumed that the thickness of the interface between the core and corona region is negligibly small. The second term in eq s1 is the self-correlation of the corona chains, which can be expressed by a Debye function with a radius of gyration ( R g, pMPC
) for the individual corona chain; in the present case the pMPC chain.
F
Ch g, pMPC
)

2
[exp(  q 2 R 2
( q R g, pMPC
) 4 q 2 R 2 ]
(s3)
To eliminate complication and decrease the number of adjustable parameters, we assume that the corona chain density is a constant regardless of the distance from the interface. On this assumption, eq s1 can be rewritten with the corona size of :
 N agg
2

C
A q R
C
)
 
Ch
A q R
Ch
) 
2  N

2 agg Ch Ch
, R g
)
 N

2 agg Ch s
( ,
Ch
)
(s4)
The first term in eq s4 coincides with the scattering intensity from a double layered sphere with and .
In the present case, the first term contributed dominantly at the low q (ca., 0.3 < q ), while the second one became more substantial in the high q in the case of q > 1.0, because the first one decays as while the second one decays as at highq .
3
In the similar manner, the scattering form factor for a mono-layered vesicle consisting of a solid plate and
Gaussian corona chains attached to the plate surface can be expressed by the equation of four-layered spheres with the innermost layer being the same electron density with the solvent:
) 

 i
4 
 1
 i i  1

V A s
( q , R i
)


2
 N agg
 2 F ( q ) (s5)
Where R
2
 R
1
 R
4
 R
3
, which is the thickness of the inner and outer layer of pMPC, ρ i
is the electron density of the i th layer, ρ solv
is the electron density of the solvent and 
1
  
5 solv
,  
1 2
 
4
 
5 due to the same chemical component of pMPC, and N agg
β 2 Ch was given from the total number of the electron of the shell

chains and the aggregation number N agg
β 2 Ch
= ( N agg
β
Ch
) 2 / N agg
= [( ρ
3
– ρ
2
)( V
2
– V
1
) + ( ρ
5
– ρ
4
)( V
4
– V
3
)] 2 / N agg
.
When N agg
> 30, the third term in eq s4 became negligibly small; therefore, we omitted this term in eq s5.
For the case of cylinders with a finite length of L , we used the following equation similar with eq s5, assuming Gaussian chains attaching on the cylinder surface with the radius of R g , pMPC
.


/2
0
N agg
2

  
1 2
 cy
( ,
1
 

 
2 solv
 cy
( ,
2

2
   N agg
 2 F q
(s6)
  j qL 
(
 qR sin

Here, ρ
1
and ρ
2
is the electron densities of the core and shell regions, V
1
and V
2
is the volume of the core and shell cylinders given by V i
= π R i
2 L , N agg
β 2 Ch
was calculated from the same manner of vesicle N agg
β 2 Ch
=
( N agg
β
Ch
) 2 / N agg
= [( ρ
2
– ρ sol
)( V
2
– V
1
)] 2 / N agg
, j and
0
J are the zero-th order of the spherical Bessel function
1 and the 1 st order of the Bessel function, respectively.

Figure S1. (a) Hydrodynamic radius ( R h
) and (b) scattering intensity for the PIC micelles with f + = 0.5 at C p
= 1.0 g/L in 0.1 M NaCl aqueous solutions at 25 °C as a function of sodium chloride concentration ([NaCl]):
P
100
M
96
/P
100
A
99
(C10, ○), P
100
M
48
/P
100
A
45
(C05, ▲), and P
100
M
27
/P
100
A
27
(C03, ◊).

3
Figure S2. Transmission Electron Microscopy (TEM) for C50 and observed short worm-like cylinders
Reference
1 Choi, S.-H., Bates, F. S. & Lodge, T. P. Structure of Poly(styrene-b-ethylene-alt-propylene) Diblock
Copolymer Micelles in Squalane†. The Journal of Physical Chemistry B 113, 13840-13848, doi:10.1021/jp8111149 (2009).
2 Pedersen, J. S., Svaneborg, C., Almdal, K., Hamley, I. W. & Young, R. N. A Small-Angle Neutron and X-ray
Contrast Variation Scattering Study of the Structure of Block Copolymer Micelles:   Corona Shape and
Excluded Volume Interactions. Macromolecules 36, 416-433, doi:10.1021/ma0204913 (2003).
Roe, R. J. Methods of X-ray and Neutron Scattering in Polymer Science . (2000).