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Paper

Soft Matter

2 Experimental and
theoretical methods
2.1

Preparation of block copolymer nanoparticles

Diblock copolymers composed of polystyrene (PS) and polyisoprene (PI) segments with similar segment volumes of PS and PI
were purchased from Polymer Source, Inc. (Dorval, Quebec,
Canada). The molecular characteristics of these copolymers are
summarized in Table 1. The block copolymers were dissolved in
tetrahydrofuran (THF, with stabilizer, Wako Pure Chemical
Industries, Ltd, Japan) at concentrations of 0.1 g L 1. Deionized
water (2 mL) was then added to 1 mL of each block copolymer
solution with stirring. THF was gradually evaporated at constant
temperatures ranging from 10 1C to 25 1C for over 2 days, and the
block copolymer precipitated as nanoparticles in water.
2.2 TEM, STEM, and TEMT observation of block copolymer
nanoparticles

Fig. 1 (a1–a3) STEM images of confined block copolymer nanoparticles.
(a4) A three-dimensional reconstructed image of PS component in a helix
nanostructure (STEM image of helix is not shown). (b1–b4) Isosurfaces of
the numerical solution of coupled Cahn–Hilliard eqn (3) and (4) with the PS
and PI phases shown in blue and green, respectively. The PS (c1–c4) and PI
(d1–d4) PS phases of the particles are shown separately. (c2) A transparency
value in the blue domain has been added to show the inner structure of the
particle. (a4) Is adapted from ref. 60. Simulation parameters of (b–d) can be
found in the ESI.†

particles. This situation is illustrated in Fig. 1(a1), in which the
nanoparticle acquires a unidirectionally stacked lamellar structure because the PS and PI segments are equally attracted
to water. When the preference of one polymer segment for
water increases, the lamellar layers curl over the particle surface
(Fig. 1(a2)). A different situation occurs when one polymer
segment (PI in this case) interacts strongly with water. This
results in the assembly of nanoparticles with an onion-like
structure (Fig. 1(a3)). Interestingly, the three-dimensional confinement of particles induces the formation of frustrated phases when
the particle diameter is sufficiently small in comparison to the
period of lamellar structures in bulk. Transmission electron
microtomography (TEMT) reveals a nanoparticle possessing
a PS phase composed of a helical structure at the surface and
a spherical core (Fig. 1(a4)). In this paper we propose a theoretical model that successfully reproduces the experimental
results when the appropriate values of parameters are selected
(Fig. 1(b1–d4)).
This work is organized as follows. Section 2 outlines the
experimental methods, theoretical model and numerical details.
Free energy and phase diagrams for different systems along with
comparison between experiments and simulation results are
presented in Section 3. We close with some concluding remarks.

5906 | Soft Matter, 2016, 12, 5905--5914

Block copolymer nanoparticles were stained with OsO4 for several
hours. After staining, the nanoparticles were collected by centrifugation (12 000 rpm, 5 1C, 15 min) and washed three times with
water. Then, the stained nanoparticles were redispersed in water by
ultrasonication and drops of the dispersion were placed onto Cu
grids with elastic carbon membranes (Okenshoji Co., Ltd, Japan).
Phase-separated structures in nanoparticles were observed using
a transmission electron microscope (TEM) (JEM-2200FS, JEOL Co.
Ltd, Japan) and a STEM (HD-2000, Hitachi High-Technologies
Corporation, Japan) operated at 200 kV. TEMT of block copolymer
nanoparticles was carried out using a JEM-2200FS. A series of TEM
images were acquired by tilting from 751 at 11 angular intervals.
TEM images were aligned by the fiducial marker method using Au
nanoparticles deposited on a supporting membrane. After aligning,
the series of the TEM images was reconstructed using a filtered
back projection algorithm (FBP).74,75
2.3

Model and numerical details

Here we give a summary of the theoretical model. The details of
the derivation are available in the ESI.† To describe confined
copolymers, let us consider the mixture of two systems. The first
system is a blend of an AB diblock copolymer and a homopolymer defined throughout the spatial domain by order parameter
u, which acquires values from the interval [ 1,1]. The ending
points of this interval correspond to a homopolymer rich domain
( 1) and a copolymer rich domain (+1). Order parameter u
represents the macrophase separation with a phase boundary
that can be understood as a confining surface. This confining
surface arises naturally to separate the homopolymer phase
from the copolymer phase.

Table 1

Molecular characteristics of polymers

Name

Mn(PS) [kg mol 1]

Mn(PI) [kg mol 1]

Mw/Mn

fPI

PS–PI-1
PS–PI-2
PS–PI-3
PS–PI-4

45
201.8
135
700

31
210
131
850

1.05
1.13
1.10
1.15

0.44
0.54
0.52
0.58

This journal is © The Royal Society of Chemistry 2016