Supplementary Information

Chain Length Dependence of Polyion Complex Architecture Bearing Phosphobetaine Block Explored with SAXS and FFF/MALS

Shunsuke Sakamoto 1,2,Yusuke Sanada 1,2,Mizuha Sakashita 1,2, Koichi Nishina 1,Keita Nakai 3,

Shin-ichi Yusa 3and Kazuo Sakurai*1,2

1Department of Chemistry and Biochemistry, The University of Kitakyushu,

1-1 Hibikino, Kitakyushu, Fukuoka 808-0135, Japan.

2Structural Materials Science Laboratory SPring-8 Center, RIKEN Harima Institute Research,

1-1-1 Kouto, Sayo, Sayo, Hyogo679-5148, Japan.

3Department 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: (KS)

Contents

I. Fitting Models of SAXS

II. Hydrodynamic radius and TEM image of PICs

I. Fitting Models of SAXS

According to Pedersen et al1,2, 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:.

(s1)

Here q is the magnitude of the scattering vector, Nagg is the aggregation number, Cand 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 ofhomogeneous sphere with radius RC:

(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 (Rg, pMPC) for the individual corona chain; in the present case the pMPC chain.

(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 :

(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., 0.3q), while the second one became more substantial in the high q in the case of q1.0, because the first one decays as while the second one decays as at high-q.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:

(s5)

Where, which is the thickness of the inner and outer layer of pMPC, ρiis the electron density of theith layer, ρsolv is the electron density of the solvent and , due to the same chemical component of pMPC, and Naggβ2Chwas given from the total number of the electron of the shell chains and the aggregation number Naggβ2Ch= (NaggβCh)2/Nagg= [(ρ3– ρ2)(V2– V1) + (ρ5– ρ4)(V4– V3)]2/Nagg. When Nagg30, 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 Rg,pMPC.

(s6)

Here, ρ1 and ρ2 is the electron densities of the core and shell regions, V1 and V2 is the volume of the core and

shell cylinders given by Vi = πRi2L, Naggβ2Ch was calculated from the same manner of vesicle Naggβ2Ch= (NaggβCh)2/Nagg= [(ρ2– ρsol)(V2– V1)]2/Nagg, and are the zero-th order of the spherical Bessel function and the 1st order of the Bessel function, respectively.

II. Hydrodynamic radius and TEM image of PICs

Figure S1. (a) Hydrodynamic radius (Rh) and (b) scattering intensity for the PIC micelles with f+ = 0.5 at Cp = 1.0 g/L in 0.1 M NaCl aqueous solutions at 25 °C as a function of sodium chloride concentration ([NaCl]): P100M96/P100A99 (C10, ○), P100M48/P100A45 (C05, ▲), and P100M27/P100A27 (C03, ◊).

Figure S2. Transmission Electron Microscopy (TEM) for C50 and observed short worm-like cylinders

Reference

1Choi, 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 B113, 13840-13848, doi:10.1021/jp8111149 (2009).

2Pedersen, 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. Macromolecules36, 416-433, doi:10.1021/ma0204913 (2003).

3Roe, R. J. Methods of X-ray and Neutron Scattering in Polymer Science. (2000).