13124

J. Phys. Chem. B 2006, 110, 13124-13129

Adsorption of Microstructured Particles at Liquid-Liquid Interfaces
Yoshimune Nonomura,*,† Shigeyuki Komura,‡ and Kaoru Tsujii§
Tokyo Research Laboratories, Kao Corporation, 2-1-3 Bunka, Sumida-ku, Tokyo 131-8501, Japan,
Department of Chemistry, Faculty of Science, Tokyo Metropolitan UniVersity, 1-1 Minami-Osawa, Hachioji-shi,
Tokyo 192-0397, Japan, and Nanotechnology Research Center, Research Institute for Electronic Science,
Hokkaido UniVersity, N21, W10 Kita-ku, Sapporo 001-0021, Japan
ReceiVed: March 19, 2006; In Final Form: May 9, 2006

The solid particles are adsorbed at interfaces and form self-assembled structures when the particles havesuitable wettability to both liquids. Here, we show theoretically how the microstructure on the particle surface
affects their adsorption properties. The physical properties of the interface adsorbing a particle will be describedby taking into account the surface roughness due to the microstructure. The microstructure on the surfacechanges drastically the wettability and the equilibrium position of the adsorbed particle. Therefore, the contact
angle of the particle at the three-phase contact line shifts with the particle surface area, because the surface
roughness enhances the interfacial properties of the particle surface. Moreover, the range of the interfacial
tensions at which the particle is adsorbed becomes narrower with the increase of the surface roughness. The
effect of the particle shape on the adsorption properties is also studied. In the case of disk-shaped particles,
the energy changes discontinuously when the plane surface of the particle contacts the liquid-liquid interface.
The adsorbing position does not change with the surface roughness. The orientation of a parallelepiped particle
at the liquid-liquid interface is governed by the aspect ratio and the surface area of the particle. On the other
hand, the particle which is partially covered with the microstructured surface is adsorbed firmly at the interface
in an oriented state. We should consider not only the interfacial tensions but also the surface structure and theparticle shape to control the adsorption behavior of the particle.

Introduction
The surface-active adsorbed particles align at liquid-liquidinterfaces1,2 and stabilize emulsions and foams.3,4 These emulsions and foams have been applied to food or cosmetic products,
because they are stable due to the adsorption of the particles
on the interfaces.5,6 In recent years, some scientists have focusedon the emulsions as a template of functional composite materials.
A hollow sphere and a ribosome-like nanocapsule were obtained
through the emulsion state.7-9
The mechanism for the adsorption of the surface-active
particle has been discussed on the basis of the interfacial energy
argument.10,11 The equilibrium position of the adsorbed particle
can be predicted from the interfacial energy. When sphericalparticles are adsorbed at an interface, the energy depends on
the three different interfacial tensions, that is, between theparticle-liquid interfaces and a liquid-liquid interface. The
particle is adsorbed at the interface when the interfacial tensions
among the three phases are balanced according to Young’s
equation.
The interfacial properties of the particles with the microstructured surface are interesting due to their great potential as
industrial materials, such as electronic materials, medical
materials, and supported catalysts.12 Moreover, complicatedrough structures exist on the surfaces of natural products, suchas skins, leaves, and biominerals. These structures on the solid
surfaces change their wettability drastically. For example, Tsujii
et al. showed that the fractal surface of a wax, alkylketene dimer,† Kao Corporation.
‡ Tokyo Metropolitan University.
§ Hokkaido University.

is super-water-repellent.13-16 In general, wettability of the
microstructured surface has been discussed on the basis of theWenzel model.17,18 The interfacial energy is proportional to thesurface area. However, the model does not work when thesurface roughness is above a critical value. In such a case, theCassie-Baxter model is more suitable than the Wenzel model.19
In the latter model, it is assumed that the rough surface consistsof more than one component.
In the present work, we have calculated the interfacial energyof the liquid-liquid interface adsorbing a spherical particle witha microstructured surface, as illustrated in Figure 1a. We study
the effect of the microstructured rough surface on the interfacial
energy. The surface area of the particle is assumed to be r times
larger than that of the particle having a smooth surface.20 The
quantity r is designated as the surface area magnification factor.
We can obtain r by measuring the specific surface area or by
analyzing the surface geometry based on the concept of fractal.13
The interfacial energy can be calculated by taking into accountthe increase of the particle surface area.
The interfacial energy of the liquid-liquid interface adsorbing
the disk-shaped particle, the parallelepiped particles, or the
spherical particle which are partially covered with the microstructured surface is also derived to discuss the effect of theparticle shape. In general, asymmetric particle shape and partial
modification of the particle surface cause the particle to beadsorbed with a fixed orientation at the liquid-liquid interface.20-23 Some preparation methods for the asymmetric particle
have been proposed recently.24,25 We demonstrate here that theparticle shape and the partial modification of the particle surface
are the most effective factors for controlling the adsorbing stateof the particle.

10.1021/jp0617017 CCC: $33.50 © 2006 American Chemical Society
Published on Web 06/09/2006

Adsorption of Microstructured Particles

J. Phys. Chem. B, Vol. 110, No. 26, 2006 13125

Figure 1. Schematic illustrations of the interface adsorbing (a) a spherical particle, (b) a disk-shaped particle, (c) a parallelepiped particle, and (d)a partially microstructured particle. The particles P are adsorbed at the interface between liquids A and B. In the illustrations, Rs and Rd are theradius of the spherical particle and the disk-shaped particle, respectively. The length h is the height of the disk-shaped particle. The quantity a isthe length of one side of the square, l is the height of the rectangular parallelepiped particle, and z is the immersion depth of the particle. The angle
θ is the contact angle at the three-phase contact line.

Results(a) Energy of the Liquid-Liquid Interface Adsorbing theSpherical Particle with the Microstructured Surface. We now
discuss the adsorption of spherical particle P at the liquidliquid interface, as shown in Figure 1a. Let F be the interfacial
energy per particle when it is adsorbed at the interface between
liquids A and B. Then, F is given by F ) 4πrRs2γAP or F )4πrRs2γBP when the whole particle is immersed in either liquid
A or liquid B, respectively. Here, Rs is the radius of the particle
and γij is the interfacial tension between phases i and j. Whenthe particle is adsorbed at the interface between liquids A andB, as shown in Figure 1a, F is given by eq 1:

F ) 4πrRs2γBP - 2πRsγAB(1 - rΣ)z + πγABz2(1)where Σ is (γAP - γBP)/γAB and z is the depth of immersion
into liquid A. The symbol Σ is equal to minus cosine of thecontact angle for the particle with the smooth surface. The
derivation of the interfacial energy, F, is presented in the
Supporting Information. In this interfacial energy, we have taken
into account both the contact of the particle surface with liquid
A and the elimination of the interface between liquids A and
B. The surface roughness changes the former factor, and thequantity r is involved in the first and second terms. We plot
dimensionless F/(πRs2γAB) against z/Rs when γAP/γAB ) 0.4,
γBP/γAB ) 0.5, and r ) 3 in Figure 2a. The above energy F
attains a minimum at zmin:

zmin ) (1 - rΣ)Rs(2)

F ) 2πrRd(Rd + h)γBP - πRd2γAB(1 - rΣ) + 2πrRdγABΣz(4)

The corresponding minimized energy, Fmin, is given by

Fmin ) 4πrRs2γBP - πRs2γAB(1 - rΣ)2

the particle is immersed in liquid B (A) as ∆F1 (∆F2) (see Figure2a). These energy changes are important, because the particle
adsorbs at the liquid-liquid interface when ∆F1, ∆F2 > 0. For
the spherical particle, they are given by ∆F1 ) πRs2γAB(1 rΣ)2 and ∆F2 ) 4πrRs2γABΣ + πRs2γAB(1 - rΣ)2, respectively.
The energy changes, ∆F1 and ∆F2, depend on the square of r,
whereas zmin is proportional to r. In Figure 2b, we plot ∆F1,
∆F2, and zmin as a function of r when γAP/γAB ) 0.4 and γBP/
γAB ) 0.5. The energy change ∆F2 decreases with r, while ∆F2and zmin increase. The particle shifts to liquid A with an increaseof r, and it is adsorbed at the liquid-liquid interface when r <10.
The state diagram of the spherical particle against Σ and r isshown in Figure 2c. The spherical particle adsorbs at theinterface when the particle satisfies -r-1 < Σ < r-1. The particle
is dispersed in liquid A (B) if Σ is smaller than -r-1 (larger
than r-1). The above range of the interfacial tensions narrows
with the increase of r. The allowed range for adsorptiopn is-1 < Σ < 1 when r ) 1, whereas it is -0.2 < Σ < 0.2 whenr ) 5.
(b) Energy of the Interface Adsorbing the Disk-Shaped
Particle with the Microstructured Surface. We discuss theadsorption of the disk-shaped particle at the liquid-liquidinterface, as shown in Figure 1b. The interfacial energy, F, isgiven by F ) 2πrRd(Rd + h)γAP or F ) 2πrRd(Rd + h)γBP
when the whole particle is immersed either in liquid A or in
liquid B, respectively. Here, Rd and h are the radius and theheight of the particle, respectively. When the particle is adsorbed
at the interface between liquids A and B, F is given by eq 4:(3)where the first term is the energy when the particle is immersed
in liquid B and the second term is the energy change due to theadsorption of the particle at the liquid-liquid interface. Here,
we define the energy gaps between Fmin and the energy when

The derivation of the interfacial energy, F, is presented in the
Supporting Information. This interfacial energy changes withz, as shown in Figure 3a. We have plotted dimensionless
F/(πRd2γAB) when γAP/γAB ) 0.4, γBP/γAB ) 0.5, h/Rd ) 0.1,
and r ) 3. It is remarkable that the energy changes discontinu-

13126 J. Phys. Chem. B, Vol. 110, No. 26, 2006

Figure 2. Adsorbing state of the spherical particle. (a) The dimensionless adsorption energy, F/(πRs2γAB), against immersion depth, z/Rs, forthe spherical particle P at constant radius Rs of the particle and theinterfacial tensions γij. The parameters are as follows: γAP/γAB ) 0.4,
γBP/γAB ) 0.5, and r ) 3. (b) The energy gaps, ∆F1 and ∆F2, and theequilibrium position of the particle, zmin, against the ratio of the particle
surface area, r, when Σ ) -0.1. (c) The state diagram of the particle
against the interfacial tensions, γij, and the surface area magnification
factor, r.

ously at z ) 0 and h, that is, when the plane surface of theparticle contacts the liquid-liquid interface. The energy changes
linearly with z as a result of the contact of the side surface withliquid A and attains the minimum at z ) h. The corresponding
minimized energy is given by

Fmin ) 2πrRd(Rd + h)γBP - πRd2γAB(1 - rΣ) +2πrRdhγABΣ (5)where the first term is the energy when the particle is immersed
in liquid B and the second and third terms are the energychanges due to the adsorption of the particle at the liquidliquid interface. The energy gaps, ∆F1 and ∆F2, are given by∆F1 ) πRd2γAB - πrRd(Rd + 2h)γABΣ and ∆F2 ) πRd2γAB +πrRd2γABΣ, respectively.
In Figure 3b, we plot ∆F1, ∆F2, and zmin as a function of rwhen γAP/γAB ) 0.4, γBP/γAB ) 0.5, and h/Rd ) 0.1. The energychanges, ∆F1 and ∆F2, are proportional to r, whereas zmin does
not depend on r, because the interfacial energy is minimized
when the plane surface is in contact with the liquid-liquidinterface irrespective of the surface area. The disk-shaped
particle adsorbs at the liquid-liquid interface when r < 10,
because ∆F1, ∆F2 > 0.

Nonomura et al.

Figure 3. Adsorbing state of the disk-shaped particle. (a) The
dimensionless adsorption energy, F/(πRd2γAB), against immersion depth,z/Rd, for the disk-shaped particle at constant radius Rd of the particle
and the interfacial tensions γij. The parameters are as follows: γAP/γAB ) 0.4, γBP/γAB ) 0.5, h/Rd ) 0.1, and r ) 3. (b) The energy gaps,∆F1 and ∆F2, and the equilibrium position of the particle, zmin, against
the ratio of the particle surface area, r. (c) The state diagram of theparticle against the interfacial tensions, γij, and the surface area
magnification factor, r.

The state diagram for the disk-shaped particle is shown in
Figure 3c. The required condition is similar to that for the
spherical particle. The disk-shaped particle adsorbs at theinterface when the particle satisfies -r-1 < Σ1 < r-1. The rangeof the interfacial tensions for the adsorbing state narrows with
the increase of r.
(c) Energy of the Interface Adsorbing the Parallelepiped
Particle with the Microstructured Surface. We calculate theinterfacial energy of the liquid-liquid interface adsorbing theparallelepiped surface-active particle as illustrated in Figure 1c.
Several situations of adsorption seem possible due to its strong
anisotropic shape, and the adsorption energy is important tounderstand the stability of each condition. Here, we discuss threeadsorbing states, that is, (i) state 1, the main axis and the planesurface of the particle are parallel to the interface; (ii) state 2,
the main axis of the particle is perpendicular to the interface;and (iii) state 3, the main axis of the particle is parallel to theinterface and the plane surface of the particle is π/4 rad to theliquid-liquid interface. In the model, F1, F2, and F3 are theadsorption energies per particle for states 1, 2, and 3, respectively. The quantity a is the length of one side of the square,and l is the height of the rectangular parallelepiped particle.

Adsorption of Microstructured Particles

J. Phys. Chem. B, Vol. 110, No. 26, 2006 13127

Figure 4. Adsorbing state of the parallelepiped particle. (a) The
dimensionless adsorption energy, F/(a2γAB), against immersion depth,z/a, for the parallelepiped particle at constant length a and l of theparticle and the interfacial tensions γij. The parameters are as follows:
γAP/γAB ) 0.4, γBP/γAB ) 0.5, h/Rd ) 0.1, and r ) 3. (b) The minimizedenergy, Fmin/(a2γAB), against the surface area magnification factor, r.

In Figure 4a, we have plotted dimensionless F/(a2γAB) whenγAP/γAB ) 0.4, γBP/γAB ) 0.5, l/a ) 10, and r ) 3. For state
1 (state 2), the energy changes discontinuously at z ) 0 and a(l), that is, when the plane surface of the particle contacts theliquid-liquid interface. The energy changes linearly with z asa result of the contact of the side surface with liquid A andattains the minimum at z ) a (l). The corresponding minimizedenergies are given by

F1min ) r{(3al + 2a2)γAP + alγBP} - alγAB(6)F2min ) r{(4al + a2)γAP + a2γBP} - a2γAB(7)

On the other hand, the energy profile of F3 is different from F1and F2. The energy decreases with z gradually and attains theminimum at z ) a/x2. The corresponding minimized energy
is given by

F3min ) r(2al + a2)(γAP - γBP) - x2alγAB +2ra(2l + a)γBP (8)In Figure 4b, we plot F1min/(a2γAB), F2min/(a2γAB), and F3min/(a2γAB) against r. They are proportional to r, and the slopes forthe three states are different from each other. These results
indicate that the surface roughness on the parallelepiped particle
affects the orientation at the interface at the equilibrium.
(d) Energy of the Liquid-Liquid Interface Adsorbing thePartially Microstructured Particle. Let us consider next thespherical particle partially covered with the microstructured
surface, as shown in Figure 1d. We assume here that (i) a partof the particle Pm is covered by the microstructured surface while
the other hemisphere Ps is a smooth one and (ii) the surface
area of the Pm region is r times larger than that of the smoothone, as shown in Figure 1d. The interfacial energy, F, decreases
drastically when the particle in liquid B approaches the interface

Figure 5. Adsorbing state of the partially microstructured particle.
(a) The dimensionless adsorption energy, F/(πRs2γAB), against immersion depth, z/Rs, at constant radius Rs of the particle and the interfacial
tensions γij. The particle approaches from the Pm side (state 1) or fromthe Ps side (state 2). The parameters are as follows: γAP/γAB ) 0.4,
γBP/γAB ) 0.5, r ) 5, and l ) R. (b) The energy gaps, ∆F1 and ∆F2,
and the equilibrium position of the particle, zmin, for the particle against
the ratio of the particle surface area, r. The parameters are as follows:
γAP/γAB ) 0.4, γBP/γAB ) 0.5, and l ) R. (c) The state diagram of theparticle against the interfacial tensions, γij, and the surface area
magnification factor, r.

from the Pm side (Figures 1d and 5a, state 1). In this case, theenergy, F, decreases with the particle adsorption and the cusp
is located at the boundary between the Pm part and the Ps part,that is, z ) R. The energy attains the minimum at 1 - rΣ (0 <
Σ < 1/r) or 1 - Σ (-1 < Σ < 0). The corresponding minimizedenergy is given by

Fmin ) 2(r + 1)πR2γBP - πR2γAB(1 - rΣ)2 (0 < Σ < 1/r)
(9)
Fmin ) 2(r + 1)πR2γBP +2(r - 1)πR2γABΣ - πR2γAB(1 - Σ)2 (-1 < Σ < 0) (10)On the other hand, when the particle contacts the interface fromthe Ps side, the energy change is smaller than the previous case
(Figures 1d and 5a, state 2) The cusp appears also at z ) Rs.
These results indicate that the partial modification of the surface
increases the surface activity and fixes the particle direction at
the liquid-liquid interface, even if the surface composition of
the particle is completely the same.

13128 J. Phys. Chem. B, Vol. 110, No. 26, 2006
When -1 < Σ < 0, the energy gaps, ∆F1 and ∆F2, are given
by ∆F1 ) -2(r -1)πRs2γABΣ + πRs2γAB(1 -Σ)2 and ∆F2 )4πRs2γABΣ + πRs2γAB(1 - Σ)2, respectively. In Figure 5b, weplot ∆F1, ∆F2, and zmin as a function of r when γAP/γAB ) 0.4
and γBP/γAB ) 0.5. The energy gap ∆F1 is proportional to r.
However, zmin and ∆F2 do not depend on r. In the case of Figure
5b, the particle is adsorbed at the interface irrespective of r,
because the particle is adsorbed at the liquid-liquid interface
when ∆F1, ∆F2 > 0.
The state diagram for the partially microstructured particle
is shown in Figure 5c. The particle is adsorbed at the liquidliquid interfaces when -1 < Σ < r-1. The lower value of Σ forthe adsorbing state does not depend on r, because the surface
area of the Ps region is constant irrespective of r.
Discussion
The equilibrium position of the spherical particle is determined not only by the interfacial tension of the particle surface
but also by the surface area of the microstructured particle.
Figure 2b shows that zmin is proportional to r. This can beunderstood by noting that the interfacial energy, F, consists of
two parts. The first one is the surface energy between the particle
P and the liquids. The second one is the energy change due tothe elimination of the interface between liquids A and B. The
effective increment of the particle surface having the microstructured surface influences the first factor directly, although
it does not affect the second one. Therefore, the equilibrium
position shifts to liquid A if the particle has a relatively higher
affinity to liquid A.
In equilibrium, the contact angle, θeq, is related to theinterfacial tensions, γij, and the particle surface area by the
Wenzel equation, cos θeq ) -rΣ. This equation shows that the
microstructure enhances the wetting properties of the particle.17,18 Therefore, the hydrophilic particle having the microstructured surface is more hydrophilic than that having thesmooth surface.
How the microstructure affects the adsorbing state of theparticle depends on the particle shape. The spherical particle
and the disk-shaped particle adsorb at the interface when theparticle satisfies -r-1 < Σ < r-1, as shown in Figure 2c and3c. However, partially microstructured particles are adsorbed
at the liquid-liquid interfaces when -1 < Σ < r-1, as shownin Figure 5c. The lower value of Σ for the adsorbing state is
contact irrespective of r. This required condition is caused by
the two-faced geometry of the particle.
The interfacial energy of the interface adsorbing the parallelepiped particle indicates that the microstructure on the particle
affects the orientation of the anisotropic particle. When γAP/γAB ) 0.4, γBP/γAB ) 0.5, l/a ) 10, and r ) 1, the particle isadsorbed at the liquid-liquid interface in state 3, because theenergy F3min is lower than F1 and F2. This result agrees withthat in the previous study by Dong and Johnson.26 They
investigated the adsorption of prolate and cylindrical particles
at a liquid-liquid interface and showed that the planar configuration (states 1 and 3 in the present study) is most stable inboth cases.26 On the other hand, the particle is adsorbed in state
1 when r ) 5, because F1 is lower than F2 and F3. This showsthat the surface roughness is one of the factors which govern
the orientation of the particle at the liquid-liquid interface.
In general, one might consider not only the wettability andthe surface structure but also the line tension acting on the threephase contact line to control the adsorption behavior of theparticle.26 The line tension arises as a result of the excess free

Nonomura et al.
energy associated with a unit length of the three-phase contact
line. In practice, a line tension of 10-6 N would have quite adrastic effect when the size of the particle is less than 20 nm.
Moreover, the line tension plays a significant role in determining
the adsorption of an acicular particle.26 The present theoretical
study will be extended in the future to take into account theeffect of the line tension.
In this paper, we have shown that the surface activity of thesolid particle can be controlled by the microstructure on theparticle surface. The strength of the adsorption and the directionof the particle at the liquid-liquid interface are governed by
the interfacial tensions and the microstructure of the particle
surface. Binks et al. showed that naturally occurring spore
particles which have microstructure exhibit as a surface-active
agent.27 On the other hand, we can inscribe the microstructureon the particle surface. For example, one of the present authors(K.T.) has succeeded in preparing microstructured particles by
the spray dry method.28 The theoretical results in the present
study are useful to understand the behavior of the solid particles
and design new functional materials. Some predictions in thiswork have not yet been proven by the experiments. Further
experimental and theoretical studies are necessary to understandthe behavior of the surface-active particles.
Acknowledgment. The authors would like to thank Drs. T.
Onda, N. Sato, S. Shibuichi, Y. Murase, and H. Mayama for
their kind and useful discussions.
Supporting Information Available: Derivations of theinterfacial energies. This material is available free of charge
via the Internet at http://pubs.acs.org.
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