INSTITUTE OF PHYSICS PUBLISHING

JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 17 (2005) S2929–S2935

doi:10.1088/0953-8984/17/31/020

Surfactant mesophases mediated by colloidal particles
Masayuki Imai1 , Yukiko Suganuma1 , Kaori Nakaya1
and Shigeyuki Komura1,2
1 Department of Physics, Faculty of Science, Ochanomizu University, 2-1-1 Otsuka, Bunkyo,
Tokyo 112-0012, Japan
2 Department of Chemistry, Faculty of Science, Tokyo Metropolitan University,
1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan

E-mail: imai@phys.ocha.ac.jp

Received 22 December 2004, in final form 4 February 2005
Published 22 July 2005
Online at stacks.iop.org/JPhysCM/17/S2929
Abstract
We have investigated effects of guest colloidal particles on the mesoscopic
structures of a surfactant/water system by means of small angle neutron andx-ray scattering techniques. The addition of a small amount of colloidal
particles between lamellar slits reduces the undulational fluctuations of lamellae
and brings about a lamellar to micelle transition. On the other hand, on additionof colloidal particles into a disordered prolate micelle phase, the micelles deform
to a spherical shape. We will discuss these structure changes in terms of thedepletion effects due to the presence of colloidal particles.

1. Introduction
Soft matter forms a variety of mesoscopic structures as a result of a balancing between
entropic interactions and energetic interactions. The balance is easily modified by applying
external fields such as shear flow and electric field, and the original mesoscopic structure isdestabilized. The addition of a small amount of guest particles to the host mesoscopic structure
provides a unique external field for controlling the mesoscopic structure. Thus, on adding
guest particles, the dominant interactions that stabilize the host soft material structure aremodified by an entropic interaction originating from the excluded volume of the guests, whichbrings about characteristic structural changes. The most familiar entropic interaction is thedepletion interaction [1, 2], which is an attractive interaction between host particles caused by
the reduction of the free volume of the guests. Another interesting entropic interaction induced
by guests is reported for lamellar membrane + guest polymer systems [3–6]. Ligoure et al
showed that the addition of polymer chains into the lamellar membranes induces a decrease of
the smectic compressibility and finally brings about a lamellar–lamellar phase separation [5, 6].
Thus the effective inter-lamellar interaction mediated by the presence of polymer chains is
attractive.
0953-8984/05/312929+07$30.00© 2005 IOP Publishing Ltd

Printed in the UK

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M Imai et al

In this study we investigate the structural change of surfactant mesoscopic structuresinduced by the addition of guest hard sphere particles [7]. The excluded volume effect of thehard spheres may bring about another kind of entropic interaction compared with the case ofpolymer chains which have soft nature due to the large internal degrees of freedom. We added
spherical colloidal particles between lamellar membrane slits and into the disordered micelles
phase and followed the change of the mesoscopic structures by means of small angle x-ray
scattering (SAXS) and small angle neutron scattering (SANS) techniques. We will show that
addition of a small amount of guest colloidal particles brings about unique structural changes
due to the excluded volume of the guest particles.
2. Experiments
We investigate ternary mixtures of water, C12 E5 , and spherical colloid particles. The nonionicsurfactant C12 E5 (purity > 98%) was purchased from Nikko Chemicals Inc., and used without
further purification. The colloidal particles used in this study were of polystyrene latex having
the diameter of 160 Å, obtained from Magsphere Inc.
The ternary mixture samples for the scattering measurements were prepared by thefollowing procedure. The surfactant and water mixtures (C12E5 /D2 O for SANS and C12 E5 /H2 O
for SAXS) were homogenized and then the colloidal particles were added to the surfactant
solution (C12E5 = 0.053, C12E5 : volume fraction of C12 E5 ) at room temperature (isotropic
micelle phase). We waited several weeks to examine the stability of the observed phases,
because in the case of lamellar + guest component systems it sometimes takes an extremely
long time to equilibrate the phases. The samples of the lamellar phase without the guests aremonophasic and slightly cloudy and on the addition of the colloidal particles, the samples
became transparent. The homogenized sample was transferred to a cell for scattering
measurements and then annealed at the measurement temperature 57 ◦ C for the lamellar phase
experiment and 30 ◦ C for the disordered micelle phase experiment.
Details of the scattering experiments are given in the preceding paper [7].
3. Results and discussion
3.1. Phase behaviour of the lamellae membranes + colloid particles system
First we show the characteristic phase behaviours of the lyotropic lamellar membranes + colloidal particles system. Figure 1(a) shows a series of SANS profiles as a function of col (col :volume fraction of colloidal particles) at constant C12E5 = 0.053. Unfortunately, there is novisible Bragg peak in the SANS profile of the lamellar phase without guests, because of thelarge amplitude of the membrane fluctuations. Then we evaluate the lamellar repeat distanced from the following relationship from the literature [8]:


kB T
t
ln C12E5
1−(1)d=
C12E54πκ0where t is the thickness of the membrane and κ0 is the bare elastic bending modulus of a single
membrane. Using t = 30 Å and κ0 = 1.3kB T , we obtained d(C12E5 = 0.053) = 666 Å.
Thus the size of the guest colloid particle is much smaller than the lamellar period. On additionof colloidal particles, the first lamellar peak begins to appear at very low colloid concentration
col = 0.01% and the lamellar period estimated from the peak position is ∼630 Å, whichroughly agrees with the value estimated using equation (1). With increasing col , the first Bragg
peak sharpens and the second harmonic emerges. Thus in the presence of colloidal particles,Surfactant mesophases mediated by colloidal particles

S2931

(a)

102

104
Intensity (Arb.)

105

10

Intensity (Arb.)

(b)

3

101

100

Φcol

103

102

0%
0.01%
0.03%
0.3%
3%

10-1
0.001

0.01
-1
q (Å )

0.1

101
0.001

ρPEO (%)
0.0
0.01
0.03
0.05

0.01
-1
q (Å )

0.1

Figure 1. SANS profiles of a lamellar phase confining guest components, colloidal particles (a)and PEO (b), at constant surfactant volume fraction C12E5 = 0.053 as a function of the guest
concentration.

the fluctuation of the lamellar membrane is suppressed and the inter-lamellar interactions
induced by the addition of the guest colloidal particles are repulsive. Similar modificationof inter-lamellar interactions caused by the presence of hard particles has been reported for alyotropic lamellar with colloidal magnetic particles system [9]. With further increase of col ,the lamellar peaks shift to the higher q side at col ∼ 0.3%, which indicates a phase separation
to concentrated and swollen lamellae. At C12E5 = 3%, the scattering profile shows a drasticchange and can be described using the sum of the spherical colloid particle and the spherical
micelle form factors. Thus the addition of colloidal particles brings about a lamellar to micelletransition.
It is quite interesting to note that the addition of polymer chains between the lamellar slits
brings about an attractive interaction, as revealed by Ligoure et al [4–6]. They found that theaddition of the polymer into the smectic bilayer decreases the inter-lamellar repulsive force
and finally brings about the lamellar–lamellar phase separation when the layer compression
modulus vanishes. We show the change of SANS profiles for C12 E5 lamellar phase upon
addition of poly(ethylene oxide) (PEO) at C12E5 = 0.053 in figure 1(b). Upon the addition of
PEO chains the scattering functions keep the initial profile until ρPEO ∼ 0.03% (ρPEO : weightfraction of PEO) and then the scattering intensity in the low q region increases with increaseof ρPEO , which is due to the phase separation. The Ligoure model explains the observed phaseseparation behaviour for the C12 E5 lamellar membrane + polymer system, whereas for themembrane + colloidal particle system the observed strong repulsive force between adjacentlamellar layers and the lamellar–micelle transition cannot be explained by that model. The
difference between the addition of polymer and colloid particles is probably attributable to the
excluded volume effect of added guest particles; thus the polymer chain has flexible entities
and the spherical colloidal particle has rigid entities [7, 9]. In the following we focus on
the morphology transition induced by the addition of hard colloidal particles using a simpler
system, i.e. the micelle + colloid particle system.

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M Imai et al

3.2. Micelle + colloid particle system
Here we investigate the effect of guest colloid particles on the morphology of surfactant
micelles. It is well known that the shape of disordered surfactant micelles strongly depends
on the temperature and concentration of the surfactant solution. In the case of nonionicsurfactant/water systems, the micelles have spherical shape at a certain temperature expressedby Tc −T0 , where Tc is a critical consolution temperature and T0 is the characteristic temperaturedepending on the chemical structure, and above Tc − T0 the micelles grow into prolate
micelles [10]. We added a small amount of colloidal particles into the disordered prolate
micelle phase of the C12 E5 /water system. Figure 2 shows the SAXS profiles as a function ofcol . Without colloidal particles the scattering profile is well described using the form factor
of a prolate core–shell model expressed by [11]
 1
P(q) ≡|F(q, x)|2 dx
(2)
0




4
4
j (u i )j (u o )F(q, x) = (ρc − ρm ) πai Ri3 3+ (ρm − ρs ) πao Ro3 3
(3)
3
ui
3
uo


u o = q Ro ao2 x 2 + (1 − x 2 )(4)
u i = q Ri ai2 x 2 + (1 − x 2 ),where Ro and Ri are the outer and inner radii of the prolate minor axis, ao and ai the ratiosof major to minor axes for outer and inner radius, respectively, and j (x) is the first-order
spherical Bessel function. The electron densities ρc , ρm , ρS correspond to core, membrane,
and solvent, respectively. With increasing col , the scattering intensity of the lower q sideof the form factor peak decreases, indicating that the micelle shape deforms from a prolate
to a spherical shape. The result of fitting using equations (2)–(4) is shown in figure 2 by asolid curve for each scattering profile and the ao and Ro obtained are plotted against col infigure 3. With increasing col the axis ratio decreases monotonically, keeping Ro constant,and at col = 0.01, the micelle has a nearly spherical shape (a0 ∼ 1.5). Thus on addition ofcolloidal particles, the prolate micelle transforms to a nearly spherical micelle.
We interpret the observed prolate to sphere transition induced by the addition of colloidal
particles in terms of the depletion effect [1, 2]. In this case the system can be described as a
mixture of Nc hard sphere colloidal particles with radius Rc and Nm surfactant micelles withthe size δ (Rc > δ). The centre of a micelle is excluded from a ‘depletion zone’ of thickness δmeasured from the surface of a colloidal particle. When the shape of the micelles transforms
from prolate to spherical, the size of the micelle (thickness of the depletion zone) decreases
and the free volume of the micelles increases. When this free energy gain overcomes thefree energy cost of the micelle transformation, the micelles will show the prolate to spheretransition. Thus the total free energy for the micelles + colloidal particles system can be
expressed as
Fm+c = Ftr + n s f mic(5)

where Ftr is the translational entropy contribution of a binary mixture of surfactant micelles
and colloid particles, n s is the number of surfactant molecules in a volume V , and f mic is thefree energy of a surfactant molecule in a micelle. The mixing free energy is expressed as [11]Ftr = Fc (Nc , V ) + Fm (Nm , αV )(6)where Fc and Fm are the free energies due to the translational entropy of the pure colloid
particles system and the pure micelles system, Nc and Nm are the numbers of colloidal particles
and micelles in the volume V . The free volume fraction α is defined by Vfree ≡ αV whereSurfactant mesophases mediated by colloidal particles

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Φcol
0%
0.03%
0.1%
0.3%
1.0%

100
90
Intensity (Arb.)

80
70
60
50
40

30

20
0

0.05

0.1

0.15

0.2

0.25

0.3

-1

q (Å )
Figure 2. SAXS profiles of the disordered micelle phase at constant surfactant volume fraction
C12E5 = 0.053 as a function of the colloidal particle concentration col .

5

30
a0
R0

4.5

28
4

ao

26

3

Ro (Å)

3.5

24

2.5
2

22
1.5
1

0

0.2

0.4
0.6
Φ col (%)

0.8

1

20

Figure 3. Dependences of the outer radius of the prolate minor axis, Ro , and the ratio of major tominor axes for the outer radius, ao , on colloidal particle concentration col .

Vfree is the free volume in which the micelles can move and for simplicity we expressed Vfree
by
Vfree = V − 43 π(Rc + δ)3 Nc .

(7)

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M Imai et al

In order to calculate Vfree , we approximate the value of δ using the outer radius of the major
axis of the prolate micelle; thus
for spherical micelles
Ro
δ=
(8)
for prolate micelles.
a 0 RoWhen we assume that the micelles interact as points with each other, but as hard particles
having size δ with colloidal particles, we can write
Fmic = Nm kB T log(Nm vm /Vfree )(9)where vm is the volume of a surfactant micelle. The free energy of hard colloid particles canbe expressed by [12]
(1 + col + 2col )
3kB T
V

dcol
Fc (Nc , V ) =col
4π Rc3col (1 − col )33= Nc kB T− log(1 − col ) + log col .
(10)2(1 − col )2
Unfortunately we do not have an appropriate theoretical free energy model for describing
the surfactant micelle; thus we adopt a strong segregation theory of diblock copolymers because
the phase behaviour of diblock copolymer is very similar to that of surfactant/water systems.
Olmsted and Milner [13] developed a strong segregation theory of micelles based on wedge
constituents filled with diblock copolymer. According to their theory, the free energies permolecule for the cylinder and sphere are given by
2εφ(1 − φ 1/2 )3 (3 + φ 1/2 ) 2φ 1/3+(11)
fcyl = f 0(1 − φ)2
ε
 4/3

φ 1/3
εφ (1 − φ 1/3 )3 (φ 2/3 + 3φ 1/3 + 6)
fsph = 3 f 0+(12)
10(1 − φ)2
10ε




1/6
27π 2 1/3 1/3 2/3
A B
γ
(13)
f0 =
32
RA2 RB2
where ε is Fredrickson’s asymmetry parameter, is the total volume of the surfactant chain,
A and B are the volumes of hydrophobic chains with end to end distance RA and hydrophilic
chains with end to end distance RB , respectively. The volume fraction of hydrophobic
component φ is expressed by
φ=

A/

.

(14)

We approximate the prolate micelle by a spherocylinder model; then the free energy permolecule for the spherocylinder is expressed by11
f cyl .
fsc =fsph + 1 −
(15)
a0
a0
Then we can calculate the free energy of the ‘micelles having various axis ratios a0 + colloidal
particles’ mixture system, Fmic+c (a0 , col ) = Fm +n s f mic , as a function of the colloidal particle
volume fraction col . Using the values γ = 1.7 mN m−1 , Rc = 80 Å, and Ro = 26 Å, we plot
the normalized free energies, [Fmic+c (a0 , col ) − Fmic+c (1, 0)]/Fmic+c (1, 0), for a0 = 1.0, 1.5,
2.0, 2.5, 3.0, and 3.5 in figure 4, where Fmic+c (1, 0) is the free energy for spherical micelles
without colloidal particles. Here we estimated the molecular volume of the surfactant moleculeusing literature values [14] and RA and RB were assumed to be the surfactant micelle core minor
radius and the hydrophilic layer thickness, respectively. In figure 4 we can see a sequentialSurfactant mesophases mediated by colloidal particles

S2935

(a)

(b)

4 10-50.01

2 10-5

a0
2.0
2.5
3.0
3.5

1.0
0.008
[F(a0,φcol)-F(1,0)]/F(1,0)[F(a0,φcol)-F(1,0)]/F(1,0)

a0

0

1.5
2.0

0.006

0.004

0.002
-2 10-5

0

0.001

0.002

0.003
Φcol

0.004

0.005

0.006

0

0

0.05

0.1
Φcol

0.15

0.2

Figure 4. Normalized free energies of a ‘micelles having various axis ratios a0 ((a) a0 = 3.5,
3.0, 2.5, 2.0 and (b) 2.0, 1.5, 1.0) + colloidal particles’ mixture system, [Fmic+c (a0 , col ) −Fmic+c (1, 0)]/Fmic+c (1, 0), as a function of the colloidal particle concentration col .

transition from the prolate micelles (a0 = 3.5) to spherical micelles (a0 = 1.0) with increasing
col , which agrees with the experimental results. Of course the quantitative behaviour of thetheoretical model strongly depends on the parameter values used, especially the ratio of δ/Rc
and the surface tension γ . In order to analyse the experimental data more quantitatively, weneed a refinement of the theoretical model. We will describe this in a forthcoming paper.
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