Journal of Colloid and Interface Science 317 (2008) 501–506
www.elsevier.com/locate/jcis

Surface activity of solid particles with extremely rough surfaces
Yoshimune Nonomura a,∗ , Shigeyuki Komura b
a Department of Chemistry and Chemical Engineering, Faculty of Engineering, Yamagata University, 4-3-16, Jonan, Yonezawa, Yamagata 992-8510, Japanb Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi,

Tokyo 192-0397, Japan
Received 19 July 2007; accepted 20 September 2007
Available online 29 September 2007

Abstract
The solid particles are adsorbed at liquid–liquid interfaces and form self-assembled structures when the particles have suitable wettability toboth liquids. Here, we show theoretically how the extreme roughness on the particle surface affects their adsorption properties. In our previous
work, we discussed the adsorption behavior of the solid particles with microstructured surfaces using the so-called Wenzel model [Y. Nonomura
et al., J. Phys. Chem. B 110 (2006) 13124]. In the present study, the wettability and the adsorbed position of the particles with extremely roughsurfaces are studied based on the Cassie–Baxter model. We predict that the adsorbed position and the interfacial energy depend on the interfacial
tensions between the solid and liquid phases, the radius of the particle, and the fraction of the particle surface area that is in contact with theexternal liquid phase. Interestingly, the initial state of the system governs whether the particle is adsorbed at the interface or not. The shape of
the particle is also an important factor which governs the adsorbed position. The disk-shaped particle and the spherical particle which is partiallycovered with the extremely rough surface, i.e. Janus particle, are adsorbed at the liquid–liquid interface in an oriented state. We should consider
not only the interfacial tensions, but also the surface structure and the particle shape to control the adsorption behavior of the particle.
© 2007 Elsevier Inc. All rights reserved.
Keywords: Solid particle; Surface activity; Adsorption; Surface roughness; Wettability

1. Introduction
Interfaces adsorbing solid particles have recently attracted
great attentions in the field of materials science [1,2]. The solid
particles are adsorbed at the interfaces and form self-assembled
structures, i.e. emulsions, ball-like aggregates and foams, when
the particles have suitable wettability to both liquids [3–5]. In
recent years, some scientists have used the emulsions as a template of functional composite materials [6–8]. The mechanism
for the adsorption of the surface-active particle has been discussed based on the interfacial energy argument [9]. The particle is adsorbed at the interface when the interfacial tensions
among the three phases are balanced according to the Young’s
equation. The effects of the particle shape and the curvatureof the liquid–liquid interface on the adsorption were also described elsewhere [10–12].
* Corresponding author. Fax: +81 238 26 3414.

E-mail address: nonoy@yz.yamagata-u.ac.jp (Y. Nonomura).
0021-9797/$ – see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcis.2007.09.066

The interfacial properties of particles with a rough surface
are interesting, because complicated rough structures existingon the solid surfaces change their wettability drastically [13].
For example, Tsujii et al. showed that fractal surfaces are super water-repellent [14,15]. It is then natural to expect that theroughness might affect the behavior of surface-active particles.
Here, we show theoretically how the extreme roughness on
the particle surface affects their adsorption properties. The extreme roughness changes drastically the wettability and the adsorbed position of the particle. In the present work, we consider
the interfacial energy of the liquid–liquid interface adsorbing
spherical particles with an extremely rough surface as illustrated in Fig. 1a. In many cases, wettability of the rough surface
has been discussed using the so-called Wenzel model [16–18].
In this model, the interfacial energy is considered to be proportional to the effective surface area. However, the Wenzel model
is not appropriate for extremely rough surfaces and the Cassie–
Baxter model is more suitable, because the liquid in holes on
the particle surfaces is not replaced by another liquid [19]. We
assume that the holes on the surface are filled by the liquid and502

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the rough surface consists of two parts, i.e., the particle surface
and the liquid in the holes. We predict the adsorbed position
and the energy of the interface based on the Cassie–Baxter
model. In addition, we discuss the effect of the asymmetry of
the particle shape on the surface activity. The disk-shaped particles are widely used in various industrial fields, while the Janus
particles which are partially covered with the extremely roughsurface are expected as building blocks for supraparticular assemblies and dual-functionalized devices [20]. In general, thedisk shape of the particle and the partial modification of theparticle surface cause the particle to be adsorbed with a fixedorientation at the liquid–liquid interface [10,11]. The interfacial
energy of the liquid–liquid interface adsorbing the disk-shaped
particle, and the Janus particle is derived in the present study.
We demonstrate here that the asymmetry of the particle surface
is one of the most effective factors to control the adsorbed stateof the particle.
This paper is organized as follows. We first discuss the effectof the surface roughness on the surface activity. We calculated

the interfacial energy of the liquid–liquid interface adsorbing
the spherical particle with extremely rough surfaces. The effectof the asymmetry of the particle on the adsorbing behavior isconsidered in the next section. The interfacial energy of the interface adsorbing the disk-shaped particle and the Janus particle
is calculated. In the discussion, we predict the requirements forthe adsorption of the particle with extremely rough surface.
2. Results
2.1. The adsorption energy of a solid particle with extremelyrough surface
We now discuss the adsorption of a spherical particle P at
an interface between liquids A and B as shown in Fig. 1a
Scheme 1. We assume that there are many tube-like holes on
the particle surface. The particle P which has higher affinity
with the liquid A than the liquid B is adsorbed at the interface
between the liquids A and B. When the particle is adsorbed toFig. 1. The schematic illustrations of the interface adsorbing (a) a spherical particle, (b) a disk-shaped particle, and (c) a partially rough particle. The particles P areadsorbed at the interfaces between liquids A and B. In the illustrations, R is the radius of the spherical particle and the disk-shaped particle. The length h is the
thickness of the disk-shaped particle, whereas z is the immersion depth of the particle. The angle θ is the contact angle at the three phase contact line.

Y. Nonomura, S. Komura / Journal of Colloid and Interface Science 317 (2008) 501–506

the A/B interface from the liquid A side, the liquid A is not replaced by the liquid B, and it remains in the holes. Let F be theinterfacial energy per particle when it is adsorbed at the interface between liquids A and B. Now, we consider the case when
the particle is originally immersed in the liquid A. The interfacial energy F is defined as
F = F1 + F2 + F3 + F4 .

(1)

Here, F1 is the energy when the whole particle is immersed in
the liquid A and is given by F1 = 4πrR 2 γAP . In this equation,
R is the radius of the particle and γij is the interfacial tension
between the phases i and j . The surface area of the sphericalparticle is r times larger than that of the spherical particle having a smooth surface. The energies F2 , F3 , and F4 are energychanges with the contact of the particle surface with the liquid B, the elimination of the interface between the liquids A
and B, and the formation of the interface between the liquids A
and B at the holes, respectively. In this case, the energies F2 ,F3 , and F4 are given by F2 = −2πφR(2R − z)(γAP − γBP ),F3 = −π(2Rz − z2 )γAB , F4 = 2π(1 − φ)R(2R − z)γAB . Here,the quantity z is the depth of immersion into the liquid A, andφ is the fraction of the particle surface area that is in contact
with the external liquid phase. The interfacial energy for the interface adsorbing the spherical particle is given by
F = F1 + 4πR 2 γAB 1 − φ(1 + Σ)
− 2πRγAB 2 − φ(1 + Σ) z + πγAB z2(2)
with Σ = (γAP − γBP )/γAB . In this equation, the second and thethird terms are multiplied by φ, not by r. This result shows that
φ affects the energy change due to the particle adsorption. On
the other hand, the surface magnification r does not affect theenergy change, because the increase of the surface corresponds
to the side surface of the tube-like holes which are covered withthe liquid A. We plot the dimensionless quantity F /(πR 2 γAB )against z/R when γAP /γAB = 0.4, γBP /γAB = 0.5, r = 30, and
φ = 0.3 in Fig. 2a. The above energy F attains a minimum(a)at zmin :zmin = 2 − φ(1 + Σ) R.

503

(3)

The corresponding minimized energy Fmin is given by
Fmin = F1 − πφ 2 R 2 γAB (1 + Σ)2 ,(4)

where the first term is the energy when the particle is immersedin the liquid A, and the second term is the energy change due tothe adsorption of a particle at the liquid–liquid interface. Here,
we define the energy gap between Fmin and the energy when
the particle is immersed in the liquid B [A] as F1 [F2 ]. For aspherical particle, they are given by F1 = 4πR 2 γAB (1 − φ −φΣ) + πφ 2 R 2 γAB (1 + Σ)2 and F2 = πφ 2 R 2 γAB (1 + Σ)2 .
The quantities F1 , F2 , and zmin are plotted against 1 − φ in
Fig. 2b. Note that F1 and F2 are proportional to φ 2 , whereas
zmin is linear in φ. The particle is adsorbed at the liquid–liquidinterface when F1 , F2 > 0.
Next, we consider the case when the particle is originally
immersed in the liquid B. The schematic illustration is shownin Fig. 1a Scheme 2. When the particle has a higher affinity withthe liquid A than with the liquid B, the liquid B in the holes isreplaced by the liquid A. In this case, the adsorbed state can be
described by the Wenzel model [16,17]. Then, F is given by
F = 4πrR 2 γBP − 2πRγAB (1 − rΣ)z + πγAB z2 .

(5)AB ) against z when γAP /γAB = 0.4, γBP /γAB = 0.5, and r = 30 in Fig. 2a. The energy F decreases withincreasing z, and the minimum does not exist. This means thatthe particle is not adsorbed at the interface and is dispersed in
the liquid A.

We plot F /(πR 2 γ

2.2. The effect of asymmetry of the particle with extremelyrough surface
We discuss the adsorption of the disk-shaped particle at theliquid–liquid interface as shown in Fig. 1b. The interfacial energy F is given by F1 = 2πrR(R + h)γAP when the whole particle is immersed in the liquid A. Here, R and h are the radius(b)Fig. 2. Adsorbed state of the spherical particle P. (a) The dimensionless adsorption energy F /(π R 2 γAB ) against immersion depth z/R for the particle P at constantradius R of the particle and the interfacial tensions γij . The parameters are as follows, γAP /γAB = 0.4, γBP /γAB = 0.5, r = 30, and φ = 0.3. (b) The energy gaps
F1 and F2 and the adsorbed position of the particle zmin against the ratio of the particle surface area φ when the particle is adsorbed at the A/B interface fromthe liquid A side. The parameters are as follows, γAP /γAB = 0.4, γBP /γAB = 0.5.

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(a)

(b)

Fig. 3. Adsorbed state of the disk-shaped particle P. (a) The dimensionless adsorption energy F /(π R 2 γAB ) against immersion depth z/ h at constant radius R andheight h of the particle and the interfacial tensions γij . The parameters are as follows, γAP /γAB = 0.4, γBP /γAB = 0.5, r = 20, h/R = 0.1, and φ = 0.3. (b) The
energy gaps F1 and F2 and the adsorbed position of the particle zmin against the ratio of the particle surface area φ when the particle is adsorbed at the A/Binterface from the liquid A side. The parameters are as follows, γAP /γAB = 0.4, γBP /γAB = 0.5, and h/R = 0.1.

and the thickness of the particle, respectively. When the particle
is in contact with the liquid–liquid interface, the energy changes
F2 , F3 , and F4 are given by F2 = −πφR(R + 2h − 2z)(γAP −γBP ), F3 = −πR 2 γAB and F4 = π(1 − φ)R(R + 2h − 2z)γAB .
The interfacial energy for the interface adsorbing the diskshaped particle is given by(6)This interfacial energy changes with z as shown in Fig. 3a. We
note that the energy changes discontinuously at z = 0, that is,when the plane surface of the particle contacts with the liquid–
liquid interface. The energy changes linearly with z as a resultof the contact of the side surface of the particle with the liquid
B and attains the minimum at z = h. The corresponding minimized energy is given by
Fmin = F1 − πφR γAB (Σ + 1).
2

F = F1 − 4πR 2 γAB Σ − 2πRγAB (1 − Σ)z+ πγAB z2 ,R  z  2R,

F = F1 + 2πR γAB 1 − φ − (1 + φ)Σ

(7)

For the disk-shaped particle, the energy changes F1 and F2
are given by F1 = πφR 2 γAB (Σ + 1) − 2πR(R + h)γAB Σand F2 = πφR 2 γAB (Σ + 1), respectively. They are proportional to φ, whereas zmin does not depend on φ, because theinterfacial energy is minimized when the plane surface is incontact with the liquid–liquid interface irrespective of the surface roughness.
We now discuss the adsorption of a Janus particle at aninterface between liquids A and B as shown in Fig. 1c. The
hemisphere of the particle PR is covered with many tube-likeholes, while the other hemisphere PS is covered with a smoothone. The surface area of the PR region is r times larger thanthat of the smooth one, and the particle is more wettable to theliquid A than to the liquid B. Here, we assume that the liquid
A is not replaced with the liquid B, and it remains in the holes
when the particle is adsorbed to the A/B interface from the liquid A side. The interfacial energy per particle F is given by
F1 = 2π(r + 1)R 2 γAP when the whole particle is immersed in
the liquid A. When the particle approaches to the interface from

(8)2

− 2πRγAB (2 − φ − φΣ)z + πγAB z2 ,F = F1 + 2πRhγAB − πφR(R + 2h)γAB (Σ + 1)
+ 2πRγAB (φΣ + φ − 1)z.

the PS side, F is given as follows:

0 < z < R. (9)In the Eq. (8), φ and r do not affect the second and third terms.
On the other hand, these terms are multiplied by φ in Eq. (9).
We plot the dimensionless quantity F /(πR 2 γAB ) against z/Rwhen γAP /γAB = 0.4, γBP /γAB = 0.5, r = 20, and φ = 0.3 inFig. 4a. The above energy F attains a minimum at zmin = (1 −Σ)R and the corresponding energy is given as follows:
Fmin = F1 − πR 2 γAB (1 + Σ)2 ,(10)

where the first term is the energy when the particle is immersedin the liquid A, and the second term is the energy change dueto the adsorption of the particle at the liquid–liquid interface.
Here, zmin and Fmin are determined only by γij and R. This
result shows that the degree of the surface roughness does notaffect the adsorbed state, because PR region does not contact toliquid B in the energy minimized state.
We consider the case when the particle approaches to theinterface from the PR side. The energy F is given as follows:
F = F1 + 4πR 2 γAB (1 − φ − φΣ) − 2πRγAB (2 − φ − φΣ)z
+ πγAB z2 ,R  z  2R,(11)
F = F1 + 2πR γAB 1 − φ − (1 + φ)Σ − 2πRγAB (1 − Σ)z2+ πγAB z2 ,0 < z < R.

(12)

We plot the dimensionless quantity F /(πR 2 γAB ) againstz/R when γAP /γAB = 0.4, γBP /γAB = 0.5, r = 20, and φ = 0.3
in Fig. 4b. The energy F attains a minimum at zmin = (2 − φ −φΣ)R and the corresponding energy is given as follows:
Fmin = F1 − πR 2 φ 2 γAB (1 + Σ)2 .

(13)

Y. Nonomura, S. Komura / Journal of Colloid and Interface Science 317 (2008) 501–506

(a)

505

(b)

Fig. 4. The dimensionless adsorption energy F /(π R 2 γAB ) against immersion depth z/R at constant radius R of the particle and the interfacial tensions γij for
the Janus particle. We show when the particle approaches to the A/B interface from PS side (a) or PR side (b). In these figures, the parameters are as follows,γAP /γAB = 0.4, γBP /γAB = 0.5, r = 20, and φ = 0.3. The adsorption energies are derived based on Cassie–Baxter model when the particle is adsorbed at the A/Binterface from the liquid A side (—), while they are derived based on the Wenzel model when the particle is adsorbed from the liquid B side (- - -).

Here, the second term contains φ and represents the energychange due to the particle adsorption.
Next, we consider the case when the particle is originally
immersed in the liquid B. In this case, the adsorbed state canbe described by the Wenzel model, because the liquid B in theholes is replaced by the liquid A [16,17]. When the particle approaches to the interface from the PR side, F is given as follows:
F = F1 − 4πR 2 γAB Σ − 2πRγAB (1 − Σ)z+ πγAB z2 ,R  z  2R,(14)

F = F1 − 2πRγAB (1 − rΣ)z + πγAB z2 ,0 < z < R.

(15)

AB ) against z when γAP /γAB = 0.4, γBP /γAB = 0.5, and r = 30 in Fig. 4a. The energy F attains aminimum at zmin = (1 − Σ)R. The adsorbed position and theminimized interfacial energy agree with them when the wholeparticle is immersed in the liquid A at the initial state, because
the PR region is not in contact with the liquid A in these conditions.
When the particle approaches to the interface from the PS
side, F is given as follows:

We plot F /(πR 2 γ

F = F1 − 4πrR 2 γAB Σ − 2πRγAB (1 − rΣ)z
+ πγAB z2 ,R  z  2R,(16)

F = F1 − 2πRγAB (1 − rΣ)z + πγAB z ,2

0 < z < R.

(17)

We plot F /(πR 2 γAB ) against z when γAP /γAB = 0.4, γBP /γAB = 0.5, and r = 30 in Fig. 4b. The energy F decreases withincreasing z, and the minimum does not exist. This means thatthe particle is not adsorbed at the interface and is dispersed in
the liquid A.
3. Discussion
The adsorbed position of a particle and the adsorption energy are determined not only by the interfacial tension, butalso the surface roughness. Equations (3) and (4) show thatthe adsorbed position zmin shifts to the liquid A side, while theFig. 5. The state diagram of the particle against the interfacial tensions γij andthe ratio of the particle surface area φ when the particle is adsorbed at the A/Binterface from the liquid A side.

energy gaps F1 and F2 decrease when φ become smaller(Fig. 2b). These results indicate that the particle with a roughsurface is more weakly held at the interface than that with asmooth surface. The wettability and the surface roughness ofthe particle determine whether it exhibits the surface activity
or not. The spherical particle is adsorbed at the interface when0 < zmin < 2R. The required condition to be adsorbed at theinterface is derived from Eq. (4) and shown as equation:−1 < Σ < 2/φ − 1.

(18)

The above condition is drawn in Fig. 5. The particle is adsorbed
at the liquid–liquid interface when the values φ and γij satisfy
the above condition. The particles are dispersed in the liquid
A [B] if Σ is smaller than −1 (larger than 2/φ − 1). The allowed range of the interfacial tension extends with the increaseof 1 − φ. For example, it is −1 < Σ < 1 when 1 − φ = 0,
whereas it is −1 < Σ < 5.666 when 1 − φ = 0.7. Hence, weshould consider not only the wettability, but also the surface
structure in order to control the adsorption behavior of the particles with rough surfaces.

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A contact angle hysteresis is expected for the surface-active
particle. Here we consider how the contact angle θ varies as theparticle is moved from the liquid A to the liquid B through theliquid–liquid interface. The contact angle is constant cos θ =−Σ when the three phase contact line is on the normal particle surface. On the other hand, discontinuous change is expected at the edges of the holes. At these special positions,the contact angle can be an arbitrary value in the range ofarccos(−Σ) < θ < arccos(−Σ) + π/2, and it changes discontinuously due to the pinning effect at the edge. This uniquebehavior is characteristic of the particles with extremely roughsurfaces and is not expected for the particle with smooth or microstructured surfaces.
We have shown that the adsorbed state of a particle with anextremely rough surface depends on the initial state of the system. The adsorbed position of the particle depends on whether
the particle was in the liquid A or B in the initial state. Thismeans that the system can be in a kinetically stable state, but
not in a thermodynamically stable state. In the case of Fig. 2,
the particle is dispersed in the liquid A if it was originally in theliquid B, although the interfacial energy is the lowest when theparticle is adsorbed at the liquid–liquid interface. This is also
important in the preparation of emulsions stabilized by the particles with rough surfaces. In the preparation of emulsions, weshould be careful with the choice of the liquid to which we add
the particles, because the mixed state can be different depending on the initial state.
The oriented adsorption is one of characteristic behaviors ofJanus-particles. The second term of Eq. (13) is multiplied by
the square of φ. Therefore, the energy Fmin is always larger
than that obtained by Eq. (10). This indicates that the PS regionis oriented to the liquid B side at the liquid–liquid interface.
The energy profile based on the Wenzel model is also shownin Fig. 4a. The adsorbed position and the corresponding energy
coincide with those derived from the Wenzel model. When R <z < 2R, the profile overlaps with that of Cassie–Baxter modeland F attains a minimum at zmin = (1 − Σ)R.
The present theory is valid only when the particle has an extremely rough surface. The assumption that the rough surface
consists of two parts does not work when the roughness is below a critical value rc [19]. When r < rc , the wettability of theparticle can be described by the Wenzel model as in our previous study [16,17]. We obtain the critical value for the sphericalparticle rc from the energy derived from Eq. (6) and the energy derived from the Wenzel model [16,17]. This examinationshows rc = φ − (φ − 1)/Σ which is close to 1/Σ [21,22]. For
example, rc = 10 when γAP = 16 mN m−1 , γBP = 20 mN m−1 ,and γAB = 40 mN m−1 .
4. Conclusions
In the present study, we examined the energy of the interface adsorbing the particle with extremely rough surfaces basedon the Cassie–Baxter model. The results predict that the adsorbed state at the liquid–liquid interface depends on the roughness of the particle surface. The shape of the particle is also
an important factor which governs the adsorbed position. The
disk-shaped particle and the Janus particle are adsorbed at theliquid–liquid interface in an oriented state.
The present theory is suitable to explain the behavior of theparticles in nano or micro meter scale, and is not suitable forthe particles whose size is above 100 µm. Because the effectof gravity on the shape of the liquid–liquid interface is neglected in this work. It has been difficult to check the validityof the present theory by experimental works. However, we caninscribe the structure on the particle surface [23]. Further experimental and theoretical studies are necessary to understandthe behavior of the surface-active particles.
Acknowledgments
This work was supported by Grant-in-Aid for Young Scientists (Start-up) 19810001 from the Ministry of Education,
Culture, Sports, Science and Technology, Japan. The authors
would like to thank Dr. Kaoru Tsujii for his kind and useful
discussions.
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