EUROPHYSICS LETTERS

1 August 2005

Europhys. Lett., 71 (3), pp. 494–500 (2005)
DOI: 10.1209/epl/i2005-10093-3

Polymer-confinement-induced nematic transitionof microemulsion droplets
K. Nakaya 1 , M. Imai 1 , S. Komura 2 , T. Kawakatsu 3 and N. Urakami 41

Department of Physics, Ochanomizu University
2-1-1, Otsuka, Bunkyo-ku, Tokyo, 112-8610, Japan2
Department of Chemistry, Tokyo Metropolitan University
1-1 Minami-Osawa, Hachioji-shi, Tokyo, 192-0397, Japan3
Department of Physics, Tohoku University
Aoba, Aoba-ku, Sendai, 980-8578, Japan
4
Department of Physics, Yamaguchi University
1667-1 Yoshida, Yamaguchi-shi, Yamaguchi, 753-8512, Japan
received 19 April 2005; accepted in ﬁnal form 1 June 2005
published online 13 July 2005
PACS. 82.70.Uv – Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems (hydrophilic and hydrophobic interactions).
PACS. 36.20.Ey – Conformation (statistics and dynamics).
PACS. 64.70.Nd – Structural transitions in nanoscale materials.

Abstract. – We study a shape change of spherical microemulsion droplets when water-soluble
polymers are conﬁned inside of them. Upon conﬁnement, spherical droplets deform to prolate
ellipsoid droplets while keeping the total surface area and the total enclosed volume of all thedroplets constant. We found that an increase of the degree of polymer conﬁnement causes anincrease in the uniaxial anisotropy of the prolate droplet, which leads to an isotropic-nematictransition in the concentrated droplet region. As a possible origin of this structural transition,
we consider a loss of the conformational entropy of polymer chains due to the conﬁnement.

Nowadays complex systems consisting of various soft materials, such as polymers, colloidal
particles, liquid crystals and amphiphilic membranes, have acquired great interest because
these complex materials are widely observed in biological systems and are extensively used inpharmaceutical, cosmetic, food, and other chemical industries. By doping guest soft materials to a host soft material, the dominant interactions that stabilize the structure of the host
soft material are modiﬁed by additional interactions originated from the restriction of translational degrees of freedom of the guests, which brings characteristic structural transitions.
The most familiar entropic interaction is the depletion interaction [1–3], which is an attractive
interaction between the host soft materials caused by the reduction of the free volume of theguests. Another interesting entropic interaction is expected for conﬁned polymer systems.
For example, when polymer chains are conﬁned between lamellar membrane slits, the membranes exhibit a phase separation between concentrated and swollen lamellae [4, 5]. In thisphenomenon, the restriction of conformational entropy of polymer chains plays a crucial role.
c EDP Sciences
Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.doi.org/10.1209/epl/i2005-10093-3

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The eﬀects of the polymer conﬁnement become more pronounced when polymer chains are
conﬁned inside of a spherically closed membrane. Such conﬁnement reduces the conformational entropy of polymer chains considerably, which may induce new membrane morphologies.
Lal et al. [6] and Javierre et al. [7] have investigated the structural change of the microemulsion
droplets (water/SDS/alcohol/oil system) containing a polymer (polyethylene oxide: PEO) using a small-angle neutron scattering (SANS) technique. Both groups found that by conﬁning
the PEO chains inside the droplets, the size and shape polydispersity of droplets increased.
We also conﬁrmed their results using other conﬁned polymer systems [8]. In these systems
the degree of polymer conﬁnement is not so high and if a polymer is conﬁned in a sphere more
tightly, a drastic morphology transition of enclosing membrane is expected. In this study weshow a series of morphology transitions of microemulsion droplets induced by changing thedegree of polymer conﬁnement.
Since in microemulsion systems the oil and water regions are separated by surfactantmonolayers, the microemulsion droplets can conﬁne the polymer chains inside of the closed
nano-space by selecting the solubility of the polymer to the solvent. As a typical example, we
studied a water-in-oil microemulsion droplet system consisting of water, isooctane, surfactant
AOT (sodium bis (2-ethylhexyl) sulfosuccinate), to which system a gelatin is added as a watersoluble polymer. A gelatin is a linear random-coil molecule and has high solubility to thenano-scale water pool. The gelatin is purchased from Sigma Co. Ltd. It has Bloom strengthof 300 and the z-averaged molecular weight of 96000 with a rather large polydispersity [9].
The interaction between gelatin and AOT monolayers was examined by putting gelatin chains
between AOT lamellar membranes in water. There was no signiﬁcant change in the scattering
proﬁles from the lamellar structure by the addition of gelatin, indicating that the adsorption
or anchoring of gelatin to the AOT monolayers is negligible.
The degree of conﬁnement of the gelatin is characterized by two parameters, i.e., the ratioof the end-to-end distance of a gelatin chain in the bulk state to the diameter of a sphericalwater pool RF /2Rs , and the average polymer weight concentration W in the water pool. The
radius of gyration of a gelatin√molecule Rg obtained by SANS measurements is Rg = 89 Å,and we assumed that RF = 6Rg = 218 Å for simplicity. We controlled the radius of thewater pool, Rs , with keeping the total volume fraction of droplets φ = φsur + φdis constant,where φsur and φdis are the volume fractions of surfactant and dispersed water phase.
The samples of microemulsion droplets containing gelatin were prepared by mixing a solution of AOT in isooctane and a solution of the gelatin in water at 60 ◦ C, and then cooled
to the measurement temperature. In the SANS measurements, we employed the ﬁlm contrast
condition, i.e., we used deuterated oil, water, hydrogenated surfactant and gelatin. SANS
measurements were carried out with the SANS-U instrument of ISSP at the JAERI (Tokai)
and the SWAN instrument of KENS at the KEK (Tsukuba).
We ﬁrst show the change in the scattering proﬁles induced by the conﬁnement of the gelatinchains in the spherical microemulsion droplets in ﬁg. 1. This experiment was performed at adilute solution of droplets, i.e. φ = 0.07. The scattering proﬁle of the microemulsion droplets−1(q is the magnitude ofwithout gelatin has a characteristic maximum at qmax = 0.06 Å
scattering vector) and well ﬁtted by the following expression:
I(q) = nP (q)S(q),(1)

where n is the number density of droplets, P (q) is the form factor for a spherical core-shellstructured particle [10], and S(q) is the structure factor of the Percus-Yevick model [11]. The
ﬁtting result using this model is shown by the solid line with the values of the ﬁtting parameters n = 5.4 × 1016 /cm3 , the length of a surfactant molecule δ = 8 Å, and 2Rs = 119.6 Å.

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Fig. 1 – SANS proﬁles for water-in-oil microemulsion droplet consisting of AOT-isooctane-water at
φ = 0.07 without (circle) and with (triangle) gelatin of W = 9% at 30 ◦ C. The solid and dashedlines are ﬁtting results with the sphere core shell and the prolate core shell model, respectively. The
quantitative S(q) of the prolate model is obtained from our Monte Carlo simulation.

By introducing the gelatin chains inside the droplets, the characteristic maximum shifted to−1
a larger value of qmax = 0.08 Å , and the scattering intensity in the low-q region increased
considerably. In this case, the degree of conﬁnement is RF /2Rs = 1.82 and the gelatin concentration in the water pool is W = 9.1 wt%. In contrast to the pure droplet microemulsion,
several features of the scattering proﬁle of the microemulsion containing the gelatin cannot be
explained by the scattering function of the spherical model. Instead we can ﬁt the observed
proﬁle using a prolate core-shell model for which the following analytical expressions for the
scattering function are available [12], 1|F (q, x)|2 dx,

P (q) =

(2)



4
4
j(uc )j(u)33
F (q, x) = (Bc − Bm ) πac Rc 3
+ (Bm − Bs ) πaR 3
,
3
uc
3
u


u = qR a2 x2 + (1 − x2 ) .
uc = qRc a2c x2 + (1 − x2 ) ,
0





(3)
(4)

Here, R and Rc are the outer and inner radii of the prolate minor axis, a and ac are the axial
ratios of the outer and inner radii, respectively, and j(x) is the ﬁrst-order spherical Bessel
function. The scattering length densities Bc , Bm , Bs correspond to the core, the membrane,
and the solvent, respectively. The above expressions reduce to those of the spherical core-shellmodel when a = ac = 1. The structure factor S(q) for the prolate model was obtained by
the Monte Carlo simulation of hard spherocylinders with corresponding rod size and volume
fraction. In this paper, we used the prolate ellipsoid model to ﬁt the form factor of thescattering proﬁles, whereas we used the spherocylinder model to obtain the structure factor.

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Fig. 2 – The two-dimensional SANS patterns of the microemulsion conﬁning polymer chains at 33 ◦ C.
The volume fraction of the water pool in the microemulsion is ﬁxed to φ = 0.4. Concentrations ofadded polymer are (a) W = 0, (b) 13, (c) 23, and (d) 26 wt%. Inset ﬁgures in (a) and (d) are thecorresponding crossed polarizers photographs.

This is due to the lack of the analytical expression of the form factor for the spherocylinder
shape. To our knowledge the diﬀerence between the prolate ellipsoid model and the spherocylinder model does not make a signiﬁcant change on the ﬁtting results of the experimental
proﬁles. The ﬁtted curve using this model is given in ﬁg. 1 by the dashed line that agrees wellwith the observed proﬁle. The obtained ﬁt parameters are Rc = 41.3 Å, the mean axis ratio
am = (a + ac )/2 ∼ 4 and n = 4.0 × 1016 /cm3 . This means that the averaged number of gelatinchains per droplet is roughly 0.8. Thus, the microemulsion droplet deforms from the sphericalshape to the rod-like one by conﬁning gelatin chains. It is known that the sphere-to-rod transition is achieved by changing the elastic parameters of membrane [13,14]. From neutron spinecho experiments, however, we conﬁrmed that the bending rigidity of AOT microemulsion
membrane is not changed by the conﬁnement of gelatin chains [15]. Then, this result opens
up a new possibility to control the membrane morphologies.
Based on the above experimental results, we expect that the rod-like droplets exhibit anisotropic-nematic transition when droplets are concentrated. Figure 2 shows the evolution of
the 2D scattering patterns of a concentrated solution of droplets (φ = 0.4) as a function of

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the polymer concentration W at 33 ◦ C. Here we ﬁxed RF /2Rs = 1.43. Without gelatin, thescattering pattern shows an isotropic ring arising from the characteristic form factor peak,which is pronounced by the suppression of the scattering intensity in the low-q region due
to the structure factor. By the addition of gelatin up to W = 13 wt%, the scattering ring−1
was shifted toward q ∼ 0.08 Å with the decreased scattering intensity, and the scattering
intensity in the low-q region is increased. This indicates that the droplets start to become arod-like shape, which is consistent with that of the dilute droplet system (ﬁg. 1). At this gelatinconcentration, the scattering pattern was still isotropic. At W = 23%, the scattering pattern
begins to show a slight anisotropy and further increase of the gelatin concentration (W = 26%)
brings a highly oriented rod-like droplet phase. In order to support this assertion, we show
the corresponding crossed polarizers photographs of concentrated (φ = 0.4) microemulsion
droplets without gelatin (inset of ﬁg. 2a) and with strongly conﬁned gelatin (RF /2Rs = 1.43,
W = 26%; inset of ﬁg. 2d) in a vial. Without gelatin the photo image is homogeneously dark,
indicating an isotropic structure. On the other hand, the microemulsion droplets conﬁning
polymer chains show a colored and heterogeneous texture similar to the Schlieren texture ofa nematic phase. These results clearly demonstrate that the isotropic-nematic transition of
the rod-like droplets is induced by the gelatin conﬁnement. The interesting point here is thefact that combining a spherical droplet and a spherical polymer coil spontaneously forms ananisotropic structure.
Here we discuss the geometrical constraints in the sphere-to-rod transition. The radiusof the minor axis of the prolate droplet (Rc = 41.3 Å) was about 2/3 times smaller than theradius of the spherical droplet without gelatin (Rs = 59.8 Å). Using Helfrich’s bending elastic
model of a surfactant monolayer, the equilibrium shape of the droplet is determined by thefollowing Hamiltonian [16]:2κ(H − C0 )2 + κK dS,(5)fmem =
where κ and κ are the bending and Gaussian moduli, H and K the mean and Gaussian
curvatures, C0 the spontaneous curvature, and S the surface area of the droplet. In addition
to this elastic energy, we have the incompressibility condition, i.e., the total surface area ofall droplets and the total enclosed volume of all droplets satisfynSδ = φsur ,nV = φdis ,

(6)
(7)

respectively, where V is the volume of a droplet and n is the number density of droplets.
The morphology of the microemulsion droplet is determined by an optimization of the elastic
energy under the constraints of the incompressibility, eqs. (6) and (7) [14]. When the moststable shape is a sphere, its radius Rs is simply given by
Rs = 3δφdis /φsur ,(8)which means that the radius is ﬁxed so long as the droplets are spherical. Since this constraint
holds very strictly, the size of a spherical droplet containing large polymer chains cannot change
unless it deforms. On the other hand, the incompressibility constraint on the rod-like droplets(for simplicity, we assume a sphero-cylindrical shape) is expressed by
Rc =2 + 2asc
Rs ,2 + 3asc(9)

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Fig. 3 – The relationship between asc and Rc for the diﬀerent conditions of the polymer conﬁnementat φ = 0.07. The experimental values for RF /2Rs = 1.82 (closed circle) and RF /2Rs = 1.43 (closed
triangle), and solid and dashed lines are calculated by eq. (9). The inset ﬁgure shows the relationshipbetween the gelatin concentration W and asc .

where asc is the axis ratio of the sphero-cylinder, asc = am − 1. In the limit of asc → ∞, weobtain Rc = (2/3)Rs from eqs. (8) and (9). Here, the volume fraction of the polymer chains is
included in φdis . It should be noted here that the number of droplets per unit volume should
decrease owing to the conservation law when the transition takes place. We measured thescattering proﬁles of the droplets containing gelatin as a function of the gelatin concentration
W for two samples with RF /2Rs = 1.82 and RF /2Rs = 1.43 at φ = 0.07. We show in ﬁg. 3 therelationship between asc and Rc obtained by the ﬁtting of the scattering proﬁles. The inset
ﬁgure shows the relationship between W and asc . With increasing W , the length of the rodlike droplets increases, which is consistent with the nematic transition induced by the gelatin
conﬁnement (ﬁg. 2). For both samples having diﬀerent RF /2Rs values, the experimentallyobtained relationship between asc and Rc agrees well with eq. (9). Thus we conﬁrmed thatthe size of the droplets after the transition is determined by the incompressibility condition.
Finally, we give some free-energy considerations on the microemulsion droplets containing
polymer chains. The total free energy per unit volume Ftot of the system essentially consistsof the following two terms:(10)
Ftot = ni (fmem + fconf ),where ni (i = s, c) is the number density of spherical (s) and cylindrical (c) droplets. The
morphology of the microemulsion droplets conﬁning polymer chains is determined by minimizing Ftot . The elastic energy per droplet fmem is given by eq. (5), and fconf represents thepolymer conﬁnement energy per droplet. When the self-avoiding polymer chains are conﬁned
inside of either a spherical or a cylindrical space, the corresponding free energy increase is [17]fconf = nip αi kB T



RF
2Ri

 53

,

(11)

where nip is the number of polymer chains per droplet (i = s, c), and αi is an unknown

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numerical constant. Since the total number of polymer chains should be conserved, we have therelation ncp nc = nsp ns . The ﬁrst term in eq. (10) represents the stability of the microemulsion
droplets without polymer. Since the original empty droplets prefer the spherical shape, thesc< nc fmem
holds for the given experimental conditions. Consequently, therelation ns fmemi.
dominant driving force for the transition should be the polymer conﬁnement energy ni fconfcsFrom the relation Rc = (2/3)Rs and the above-mentioned conservation law np nc = np ns , thenecessary (but not suﬃcient) condition for the shape transition to occur is that the numericalcoeﬃcients in eq. (11) satisfy αc /αs ≤ (2/3)5/3 . Unfortunately, we cannot compare thenumerical values of αc and αs , because eq. (11) is obtained only within the scaling argument.
This issue will be discussed in our forthcoming paper [15].
In conclusion, by conﬁning polymer chains inside of the microemulsion droplet, the membrane morphology changes from the spherical shape to the rod-like one, and further increasein the degree of polymer conﬁnement brings the isotropic-to-nematic transition in the concentrated droplet region. We also conﬁrmed that the constraint of the incompressibility is wellsatisﬁed in the morphological transition, and that the necessary condition for this transitionis that the numerical coeﬃcients in eq. (11) satisfy αc /αs ≤ (2/3)5/3 .
∗∗∗The SANS experiments were done under the approval of Neutron Scattering Program Advisory Committee of ISSP and KENS. This work was supported by Grant-in-Aid for Exploratory
Research (No. 15740261) from the Ministry of Education, Sciences, and Culture of Japan.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]

Asakura S. and Oosawa F., J. Chem. Phys., 22 (1954) 1255.
Anderson V. J. and Lekkerkerker H. N. W., Nature, 416 (2002) 811.
Adams M., Dogic Z., Kekker S. L. and Fraden S., Nature, 393 (1998) 349.
Daoud M. and de Gennes P. G., J. Phys. (Paris), 38 (1977) 85.
Ligoure C., Bouglet G. and Porte G., Phys. Rev. Lett., 71 (1993) 3600.
Lal J. and Auvray L., J. Phys. II, 4 (1994) 2119.
Javierre I., Bellocq A. M. and Nallet F., Langmuir, 17 (2001) 5417.
Nakaya K. and Imai M., J. Phys. Soc. Jpn. Suppl. A, 70 (2001) 338.
Pezron I., Djabourov M. and Leblond J., Polymer, 32 (1991) 3201.
Guinier A. and Fournet G., Small-Angle Scattering of X-rays (Wiley, New York) 1995.
Percus J. K. and Yevic G. J., Phys. Rev., 110 (1958) 1.
Kotlarchyk M. and Chen S.-H., J. Chem. Phys., 79 (1983) 2461.
Svergun D. I., Konarev P. V., Volkov V. V., Koch M. H. J., Sager W. F. C., Smeets
J. and Blokhuis E. M., J. Chem. Phys., 113 (2000) 1651.
Safran S. A., Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (AddisonWesley Publishing Company) 1994.
Nakaya K., Imai M., Komura S., Kawakatsu T. and Urakami N., in preparation.
Helfrich W., Z. Naturforsch., 28c (1973) 693.
de Gennes P. G., Scaling Concepts in Polymer Physics (Cornell University Press) 1979.