PAPER www.rsc.org/softmatter | Soft Matter

Particle-stabilised foams: an interfacial study

Antonio Stocco,*a Wiebke Drenckhan,a Emanuelle Rio,a Dominique Langevina and Bernard P. Binksb

Received 20th January 2009, Accepted 19th March 2009

First published as an Advance Article on the web 24th April 2009

DOI: 10.1039/b901180c

In an attempt to elucidate the remarkable stability of foams generated from dispersions of partially

hydrophobic nanoparticles (fumed silica), we present investigations into the static and dilational

properties of the gas–liquid interfaces of such dispersions. By relating the dynamic surface tension g(t)

and the dilational elasticity E measured using an oscillating bubble device, we confirm that the Gibbs

stability criterion E > g/2 against foam coarsening is fulfilled. We complement these studies using

ellipsometry and Brewster angle microscopy, which provide evidence for a pronounced adsorption

barrier for the particles and a network-like structure in the interface at sufficiently high concentrations.

We observe this structure also in freely suspended films drawn from the same particle dispersions.

1. Introduction

It is well known that Pickering emulsions,1,2 i.e. emulsions

stabilized solely by partially hydrophobic particles of nano- or

micrometre size, are remarkably stable. More recently, it has

been demonstrated also that foams can be stabilized by parti-

cles.3,4 Colloidal particles play, in particular, a key role in the

stabilization of metallic foams4 since the more classical foaming

agents, such as surfactants or polymers, degrade at the temper-

atures required for the foaming process.

Several research groups are now working on aqueous foams

stabilized solely by particles3,5–10 or on individual particle-coated

bubbles.11,12 All the existing studies confirm that the particle layer

at the gas–liquid interface forms a ‘‘colloidal armour’’ which

inhibits the two main ageing mechanisms of the foams: bubble

coalescence (film rupture) and coarsening (exchange of gas

between bubbles due to differences in Laplace pressure) which

are often completely stopped. This leads to super-stable foams

(lifetimes of months!), provided that the foaming medium

contains a sufficient amount of particles.5,8–10

The shape and size of the stabilizing particles can vary

significantly, ranging from micrometre sized particles6 to nano-

metric aggregates10 or even rods.7 Recent investigations revealed

a strong correlation between the hydrophobicity of the particles

and foam stability.8,13 For example, in the case of the silica

particles used in this article, a clear maximum in foamability is

found at a particle hydrophobicity of 34%, expressed as the

percentage of unreacted SiOH groups after silanisation.8,10

Previous research indicates that a key physical parameter

underlying the origin of foam stabilization by particles is the

dilational elasticity E of the particle-coated bubble surfaces.8 A

general argument, provided by Cervantes-Martinez et al.8 and

based on an analysis by Gibbs,14 proceeds as follows: foam

coarsening occurs because the derivative of the bubble capillary

pressure P with respect to the bubble radius R is negative

aLaboratoire de Physique des Solides, Universit�e Paris-Sud, F-91405 OrsayCedex, FrancebSurfactant and Colloid Group, Department of Chemistry, University ofHull, Hull, UK, HU6 7RX

This journal is ª The Royal Society of Chemistry 2009

(dP/dR ¼ �2g/R2 < 0). This is generally the case as in mostsystems the surface tension g is independent of the bubble size.

Solid particles at a gas–liquid interface, however, have such high

desorption energies5 that their number can be considered fixed,

meaning that their concentration (and therefore the surface

tension) varies with the interfacial area A (and hence the bubble

size). This provides an interfacial, dilational elasticity E ¼ dg/dln(A), and the derivative of the bubble capillary pressure can

now be written as dP/dR ¼ �2g/R2 +4E/R2. Hence, a bubblebecomes stable against coarsening when E > g/2, which is called

the Gibbs stability criterion.14 Safouane et al.13 and Zang et al.15

measured g and E for particle monolayers obtained by spreading

particles dispersed in alcohol on water surfaces and the

measurements confirm the validity of this criterion.

The behaviour of foams stabilized solely by silica particles was

investigated based on two different aspects: the effect of the particle

hydrophobicity and of the particle concentration on the foam-

ability of the aqueous dispersions.8,10,13 It seems likely that particles

stabilize foams due to the surface elasticity E of the particle-coated

bubble surfaces. Cervantes-Martinez et al. showed that by

increasing the particle concentration from 0.1 to 0.7 wt.%, foam

coarsening could be entirely prevented over the duration of the

experiment, which was attributed to the effect of the surface elas-

ticity. The bubble size of polydisperse foam was monitored by

a multiple light scattering technique, and no significant change was

detected during 10 h for dispersion concentration $0.7 wt%. Also,

photographic and optical images of foam samples left in sealed

containers displayed no remarkable variations in volume and

macroscopic structure over several months.8

The properties of adsorbed particle layers have been investi-

gated both at liquid–liquid and gas–liquid interfaces (ref. 16,17

and references therein). In addition to steric and electrostatic

interactions, colloidal particles at interfaces commonly experi-

ence capillary-mediated interactions which are either induced by

non-spherical colloid shapes, by chemical heterogeneities at the

surface or by ‘‘direct’’ interactions.18 A model using these capil-

lary forces was shown recently to satisfactorily explain the

rupture of particle clusters at the air–water interface upon

application of shear.19 To complement those investigations we

present here studies of the dynamic surface tension g(t) and of

Soft Matter, 2009, 5, 2215–2222 | 2215

the dilational elasticity E, both of which are measured directly on

the gas–liquid interfaces of aqueous particle dispersions. Thus,

we emulate more realistic conditions occurring during foam

generation.

We used dispersions of fumed silica nanoparticles with inter-

mediate hydrophobicity (34% SiOH). Among different % SiOH

contents, those dispersions provide the maximum volume of foam

after production, i.e. maximum foamability.8,10 We present

measurements of the dynamic surface tension g(t) (change of

surface tension with time) and of the dilational elastic modulus E

conducted using an oscillating bubble device, for a range of

particle concentrations previously investigated in a foam stability

study.8,10 We complement these studies by investigations of the

nature of the interfacial particle layer using ellipsometry, Brewster

angle microscopy and observations of free-standing liquid films.

Fig. 1 (a) Zimm plot obtained using static light scattering measurements

for aqueous dispersions of silica nanoparticles at different concentrations

(given). K is an optical constant, Rq is the Rayleigh ratio and a is an

arbitrary constant. (b) Field autocorrelation function fm(q,s) measured atthe scattering angle q ¼ 90� for systems in (a): 0.1 (,), 0.3 (B), 0.5 (O),0.7 (P) wt.%. Solid lines are cumulant fits.

2. Materials and methods

2.1 Materials

Particles. Fumed silica nanoparticles were kindly provided by

Wacker-Chemie (Germany). The particles investigated in this

work were chemically coated with a short-chain silane reagent

(dichlorodimethylsilane) by the manufacturer. The hydrophobic

character of the particles is expressed by the percentage of

surface silanol groups SiOH. We used a 34% grade throughout

our experiments which corresponds to the particle hydropho-

bicity which provides maximum foamability.10 The primary

particles are quasi-spherical of approximately 20 nm diameter,

but aggregate into clusters over 200 nm in size.20

Particle dispersions. We prepared aqueous dispersions of

particles at 1 wt.% concentration by a stepwise procedure using

doubly distilled and deionized Milli-Q water (pH z 5.8), silicaparticles and a small amount of ethanol (

the dispersion was negligible. Using the same apparatus, we also

performed oscillating bubble experiments in order to obtain the

dilational elastic modulus E ¼ dg/dlnA. We imposed sinusoidalvariations of the bubble volume DV¼ 0.5–1 mL and we measuredthe corresponding changes of surface tension by image analysis.

The frequency of the oscillation was swept from 0.1 to 1 Hz.

Ellipsometry and Brewster angle microscopy (BAM). We used

an imaging ellipsometer (Nanofilm, Germany) working with

green laser light (l ¼ 532 nm) in order to gain information onparticle organization in the interfacial region. The aqueous

dispersions were placed in a large dish (diameter¼ 8 cm, depth¼3 cm) and the laser beam was directed at the surface in the center

of the cell where the meniscus effect is negligible. A multiple

angle of incidence (MAI), fixed compensator (¼ �45�) and 4-zone averaging nulling scheme was adopted.24 The ellipsometric

parameters (J,D), which are related to the ratio r of the complex

reflection coefficients by r ¼ rp/rs ¼ tanJ exp(iD), deviatesignificantly from the values of the bare water surface since the

larger refractive index of silica particles (nSi ¼ 1.475) providesa good optical contrast.25 The ellipsometric parameters J and D

were measured around the Brewster angle, scanning the incident

angle by steps of 0.1�. From the fits of the latter quantities, the

refractive index profile along the interfacial region could be

resolved and information on layer thickness and particle

concentration at the water surface could be extracted.

Brewster angle microscopy was also implemented in the same

setup. By this method, we could gain information on the texture

and organization of particles in the interfacial plane, which

served to complement our ellipsometric data with visual infor-

mation. To check the accuracy of our measurement protocols, we

always compared our data with the bare air–water interface.

Individual films. We observed qualitatively the behaviour of

freely suspended horizontal films formed from the same disper-

sions using a home-built apparatus in which we placed 5 mL

drops between two metal barriers of 2 cm width. One barrier was

moved horizontally by a micrometric screw; hence a film could be

formed between the barriers and videos of light reflected from the

film were recorded by means of a camera placed below the film.

The system was closed to the atmosphere and saturated in

vapour, to minimize evaporation effects.

All measurements in this article were conducted at room

temperature, being 20 � 2 �C.

3. Results and discussion

We performed a range of interfacial studies at the air–water

interface of particle dispersions of different concentrations. In the

first part, we combine measurements of the dilational elasticity E

and of the dynamic surface tension g(t) and correlate these results

to foam stability. In the second part, we describe the adsorption

and organization mechanisms of the particles at the water surface.

Fig. 2 Dynamic air–water surface tension measured in the rising bubble

experiments for different silica nanoparticle concentrations: 0.1 (,), 0.3

(B), 0.5 (O), 1 (P) wt.%.

3.1 Purely elastic stabilization against foam coarsening

Non-chemically modified silica particles have commonly

a hydrophilic character; hence the surface tension of their

dispersions is generally independent of the particle concentration

This journal is ª The Royal Society of Chemistry 2009

as no significant particle adsorption to the interface takes place.26

Even if adsorption of particles takes place, no significant change

of g is reported when particle interactions are of purely steric

nature.27 This is different to the kind of particles investigated

here, which adsorb to the interface due to their partial hydro-

phobicity and whose interactions are governed by repulsive

electrostatic forces (see also light scattering results, Section 2.1)

and additionally by attractive capillary forces. We expect the

latter to be generated by surface chemical inhomogeneities or by

the irregular shape of the particle aggregates on whose surfaces

the wetting angle condition must be fulfilled locally, leading to

a curvature of the liquid surface around the particle and hence to

particle interactions.18

Here we have measured changes of the air–water surface

tension g with time t (‘‘dynamic surface tension’’) for a range

of particle concentrations. Some representative examples are

displayed in Fig. 2. We note that the measurement is started

(t ¼ t0 ¼ 0) as soon as the droplet/bubble is formed in themeasurement device (refer to Section 2.2), which takes about 1 s.

It is evident from the variation of the observed surface tension

values at t0 that during this period a significant, concentration-

dependent amount of particles is already adsorbed at the gas–

liquid interface. This is probably due to the additional energy

input resulting from the droplet/bubble generation.

At concentrations lower than 0.1 wt.%, no appreciable

changes of g were observed during a time of up to 104 s. Between

0.1 and 1 wt.%, however, we measured a slow relaxation of the

surface tension with an overall decrease of approximately

5 mN m�1. At the highest concentration studied (1 wt.%), the

surface tension value decreases to around 50 mN m�1, which is

close to the predicted value given by Binks and Clint.28 Thus, the

adsorption of particles can be detected by the change of g with

time, where slow kinetics is usually observed. In fact, as we shall

illustrate in Section 3.2, nanoparticle adsorption is not only

diffusion-controlled but also displays kinetics with an energy

barrier arising from steric and/or electrostatic interactions, as

was demonstrated by Kutuzov et al. for nanoparticles with a size

Fig. 4 (a) Dilational elastic modulus E as a function of particle

concentration c. (b) Variation of E with the surface tension g measured at

t ¼ 104 s (reported in Fig. 2) for four different particle concentrations(given). The solid line shows E ¼ g/2.

for infinite waiting times. The systematic deviation between

surface tensions measured with pendant drops and rising bubbles

(Fig. 3) may be due to two effects. Firstly, particle depletion may

come into play due to the finite amount of particles available in

the small pendant drop (between 5 and 10 mL). Secondly, grav-

itational effects may lead to a more efficient transport of particles

to the interface in the case of the rising bubble. Nonetheless,

measurements obtained by both methods confirm a significant

decrease of g between 0.1 and 1 wt.%.

In order to evaluate the surface elastic properties of the particle-

laden interfaces, we carried out oscillating droplet and bubble

experiments. To obtain quantitative information we preferred the

oscillating bubble over the pendant drop configuration, because

in the latter, after adsorption times of 104 s, the shape of the drop

tended to become non-Laplacian with a corrugated surface. This

phenomenon was seldom observed in the rising bubble configu-

ration. A similar phenomenon was reported for irreversibly

adsorbed mixed polyelectrolyte-surfactant layers, where the

surface can be deformed by thickness gradients that can relax

towards uniformity, at extremely long times.30

The dilational elastic modulus E¼ dg/dlnA was measured (aftert z 104 s) with oscillating bubble experiments performed at thefrequency n ¼ 1 Hz, as a function of the particle concentration c.The results are presented in Fig. 4(a). The absolute value of E

increases markedly with increasing particle concentration c,

reaching a value of approximately 40 mN m�1 at c ¼ 0.7 wt.%. Atlower frequencies, we observed non-elastic phenomena in the form

of non-smooth profiles of surface tension and surface area with

time. It seemed that at low frequencies particles had enough time to

re-arrange during the slow sinusoidal change of the bubble area.30

Combining the results from Fig. 3 and Fig. 4(a), we show in

Fig. 4(b) the dilational elastic modulus E as a function of the

surface tension g in the range of particle concentrations c of

interest. For comparison, Fig. 4(b) also displays the line E ¼ g/2corresponding to the Gibbs stability criterion. From this, it

follows that only dispersions with particle concentrations above

0.5 wt.% can generate foams with significantly reduced coars-

ening. This result is in perfect agreement with the foam stability

investigations reported by Cervantes-Martinez et al.8 for the

same particle dispersions and now allows us to predict when

foams will be stable or not against coarsening. Indeed, the

original work by Cervantes-Martinez et al.8 was based on esti-

mations of the particle concentration at bubble surfaces and

Fig. 3 Surface tension values g obtained at t z 104 s as a function ofsilica nanoparticle concentration c measured using the pendant drop (-)

and the rising bubble (B) technique.

2218 | Soft Matter, 2009, 5, 2215–2222

comparison with independent measurements made with spread

layers.

Moreover, the oscillating bubble experiments indicate the exis-

tence of an adsorption barrier: the surface tension values obtained

for a static bubble after long waiting times can be reached much

more rapidly by oscillating the bubble and hence by providing an

additional energy input facilitating particle adsorption (see Fig. 5).

Such effects are known from similar systems. For example, anionic

latex particles do not adsorb spontaneously at the air–water inter-

face because the interface itself appears anionic and hence repul-

sive.31 Similarly, the silica particles under investigation, being

decorated on the surface by SiO�groups, are also anionic (see also

Section 2.1). Thus, an energy barrier resulting from electrostatic

interactions between the particles and the air–water surface, and

between the particles at the surface and in bulk, may hinder

adsorption to the interface. Additionally, steric interaction between

Fig. 5 In dynamic surface tension measurements in the rising bubble

configuration, the surface tension g decreases more rapidly when the

bubble is oscillated (here n ¼ 0.1 Hz and c ¼ 0.1 wt.%).

This journal is ª The Royal Society of Chemistry 2009

particles at the surface and in bulk tend to slow the adsorption at

high surface concentrations.29

3.2 Organization of nanoparticles at the air–water interface

In this part we discuss and provide experimental evidence of the

adsorption mechanism and of the arrangement of partially

hydrophobic fumed silica particles at the air–water interface of

particle dispersions. We performed ellipsometric measurements

in order to gain information on the kinetics of the adsorption, the

layer thickness and the surface concentration G of particles.

We investigate the influence of the method of preparation of the

dispersions on the organization of particles at the interface. At

the outset, for comparison with previous findings,13,15 we compare

the case of adsorbed particle layers with those of spread layers.

3.2.1 Spread layers. We performed ellipsometric scans of high

accuracy around the Brewster angle (¼ arctan(nwater/nair)¼ 53.12�)on a spread layer of particles. We obtained such a monolayer by

spreading a known amount of particles dispersed in isopropyl

alcohol of c¼ 0.1 wt.% onto a pure water surface of fixed area. Westudied two spread layers with a surface concentration of G¼ 20 mgm�2 and G¼ 40 mg m�2 which served as reference concentrations tobe compared with the adsorbed particle layers.

From the angular dependence of D and J,24 as displayed in

Fig. 6, we can simultaneously extract information on the thick-

ness d and on the refractive index nl of the particle layer (see inset

in Fig. 6).32 From data fitting we obtain d ¼ 162 � 5 nm and nl ¼1.3403 � 0.0005 for G ¼ 20 mg m�2. For twice this surfaceconcentration (G ¼ 40 mg m�2), we find a similar layer thickness

Fig. 6 Results of ellipsometric scans performed around the Brewster

angle on a spread layer of silica nanoparticles at the air–water surface

with surface concentrations G ¼ 20 mg m�2 (,) and G ¼ 40 mg m�2 (B).The solid lines represent the fits. Inset: sketch of the stratified layer model.

This journal is ª The Royal Society of Chemistry 2009

(d ¼ 175 � 1 nm), whilst the refractive index increases tonl ¼ 1.354 � 0.0002. From the latter data we could evaluate thesurface concentration ‘seen’ by ellipsometry using the relation

Gelli ¼ (nl � nwater)/(vn/vc)$d, where vn/vc is the differentialrefractive index increment. Calculating for the two reference

surface concentrations, Gelli changed from 17.6 mg m�2 to 56.9

mg m�2. Those values are in a reasonable agreement with the

actual surface concentrations of 20 and 40 mg m�2. Thus, for

spread layers, in the range of concentration studied, it seems that

the particle aggregates remain trapped at the water surface. It is

worth noting that for nwater ¼ 1.333 < nl < nSi ¼ 1.475, nosatisfying fit can be obtained assuming the presence of non-

aggregated particles of 20 nm diameter. In fact, if d ¼ 20 nm,around the Brewster angle, D would change from 180� to 360�

instead of from 180� to 0�.

3.2.2 Adsorbed layers. We performed the same ellipsometric

scans on the surface of aqueous particle dispersions of concen-

trations between 0.1 and 0.7 wt.%. The dispersions were prepared

and sonicated one day before use. We cleaned the surface of the

dispersions (and of water) several times by means of a pump

before performing the first ellipsometric scan. Then we waited at

least 1 h to allow the interface to equilibrate before performing

further measurements.

Fig. 7 shows J and D as a function of the incident angle 4

for the bare air–water interface and for a particle dispersion at

Fig. 7 Ellipsometric scans performed around the Brewster angle at the

bare air–water interface (x) compared to those conducted at the surface of

an aqueous silica dispersion with a particle concentration of c ¼ 0.1 wt.%after adsorption for one day (,). > corresponds to measurements

obtained with the same dispersion after 10 min of strong sonication. The

dotted line is the simulated step-like profile of the air–water surface and

the solid line is a film model fit giving a layer thickness of d¼ 149 nm witha refractive index nl ¼ 1.348.

Soft Matter, 2009, 5, 2215–2222 | 2219

Fig. 8 Brewster angle microscopy images of the air–water surface for

silica nanoparticle concentrations c of (a) 0.1 wt.% and (b) 0.7 wt.% taken

after one day of aging and 10 min of sonication. The bright areas contain

significantly more particles. At low concentrations (a), one observes

isolated structures which slowly and freely move within a homogeneous

layer of particles. At sufficiently high particle concentrations (b),

a network-like structure of particles appears. The scale bar is 20 mm.

c ¼ 0.1 wt.% after 1 day. Both surfaces give nearly identicalsignals. The same holds for measurements in the whole concen-

tration range between 0.1 and 0.7 wt.%. Even after 1 day, ellip-

sometric scans did not show any change of the interfacial profile,

thus implying that no significant amount of particles had been

adsorbed at the interface. Using Brewster angle microscopy, we

observed islands of particles floating at the water surface, but

their area fraction was not high enough to contribute to the

ellipsometric signal.

These results are in apparent contradiction with those

obtained using spread particle monolayers. The main difference

between the two cases is that in the latter all particles are placed

directly at the surface where they remain due to large desorption

energies. In the case of aqueous dispersions, however, the

particles need to overcome two obstacles: firstly, they need to

overcome energy barriers present at the interface, as discussed at

the end of Section 3.1. Secondly, they need to diffuse against

gravity from the bulk to the surface (silica particles are signifi-

cantly heavier than water with a density of r ¼ 2.2 g cm�3). Thelatter effect may also explain why we see spontaneous particle

adsorption in the case of bubbles or drops (Section 3.1), where

particle sedimentation helps adsorption due to the different

geometry of the air–water interface. To see this, let us evaluate

the relationship between particle diffusion and sedimentation for

our system. The mean square displacement for a diffusing

particle is given by ¼ 6Dt, with ¼ 2.5 � 1012 m2s�1, as evaluated by dynamic light scattering (Section 2.1. and ref.

22). The displacement of a particle due to gravity can be written

as L¼ vt, where the Stokes velocity is given by v¼mg/(6phRh)¼3.4 � 10�8 m s�1 (mg is the gravitational force and Rh ¼ 85 � 10nm, the hydrodynamic radius (Section 2.1)). The two different

lengths are equal ( ¼ L2) for t ¼ 1.2 � 104 s, meaningthat gravitational effects become important at these time scales,

which corresponds well to what we see in Fig. 3.

To test this hypothesis, we strongly sonicated (10 min, Section

3.2.3) the dispersions after one day (at which no significant

particle adsorption had taken place). Performing ellipsometric

scans immediately after sonication reveals significant changes of

the interfacial profile, i.e. significant particle adsorption, which

can be seen thanks to the changes of J and D displayed in Fig. 7

(>) for the case of a dispersion concentration c ¼ 0.1 wt.%.From fitting this profile we obtain a layer thickness of d ¼ 149 �2 nm with a refractive index of nl ¼ 1.3477 � 0.0007.

3.2.3 Particle networks at air–water surfaces. Comparing

Fig. 6 and 7, we noticed that the profile of the interface generated

by sonication-induced adsorption for c ¼ 0.1 wt.% (d ¼ 149 � 2nm, nl¼ 1.3477� 0.0007) differs significantly from the one of thespread layer for G ¼ 40 mg m�2 (d ¼ 175 � 1 nm, nl ¼ 1.3539 �0.0002). This difference is even more evident from Brewster angle

microscopy images. Whilst spread monolayers tend to be very

homogeneous and show compact packing at a surface concen-

tration of G ¼ 60 mg m�2,13,15 we find very inhomogeneousparticle distributions at the interface for adsorbed layers.

Examples of typical Brewster angle microscopy images for

dispersion concentrations of c ¼ 0.1 and 0.7 wt.% are displayedin Fig. 8, clearly indicating pronounced interfacial textures after

sonication for adsorbed monolayers. At low concentrations

(Fig. 8(a)), sonication leads to the formation of some solid

2220 | Soft Matter, 2009, 5, 2215–2222

structures which slowly and freely move within a homogeneous

layer of particles. This observation may also explain the scattered

ellipsometric data obtained after sonication (Fig. 7). At suffi-

ciently high particle concentrations (Fig. 8(b)), a completely

different scenario is observed: a network-like structure of parti-

cles appears. We did not observe changes of these textures within

24 h by Brewster angle microscopy.

Between the two concentrations depicted in Fig. 8, i.e. 0.1

and 0.7 wt.%, foams dramatically change their stability (Section

3.1 and Fig. 4(b)).8,10 Thus, the observation of the different

kinds of structures shown in Fig. 8 could confirm the suggestion

made by Kostakis et al.,33 who related foam stabilization to the

formation of weak gel networks of particles between gas–liquid

interfaces separating the bubbles. At this stage, however, it is

not clear to us what is the origin of the attractive forces between

particles enabling the formation of the observed networks. They

could be capillary-mediated interactions induced by the

complex aggregate geometry.18 Additionally, SiOH groups on

adjacent particles can interact to form siloxane bonds (Si–O–Si)

which allow particles to aggregate. Being partially hydrophobic,

This journal is ª The Royal Society of Chemistry 2009

Fig. 9 Images of a freely suspended, horizontal film drawn from silica nanoparticle dispersions with (a) low c ¼ 0.05 wt.% and (b) high c ¼ 0.5 wt.%particle concentration. Time between images is 30 s. The scale bar is 1 mm.

their charge is reduced compared with the equivalent fully

hydrophilic silica.

3.2.4 Particle networks in thin films. The formation of

network-like particle structures, as described in the previous

section, can also be observed in freely suspended individual thin

films (Section 2.2). Fig. 9 shows the development of two exam-

ples of films drawn from dispersions of two different concen-

trations (Fig. 9(a): c ¼ 0.05 wt.% and Fig. 9(b): c ¼ 0.5 wt.%). Ineach picture, the grey top and bottom parts correspond to the

metal barriers. In the central part, a meniscus (black coloured)

surrounds the thin film region (see sketch in Fig. 9(a)). Colours

and light intensity result from light interference at the two gas–

liquid interfaces and therefore provide information on film

thickness and thickness changes. At low concentrations

(Fig. 9(a)), fairly homogenous thin films are formed whose

thickness fluctuates in time accompanied by rapid colour

changes, and decreases overall with time to cause film rupture

after a few minutes.

At sufficiently high particle concentrations (Fig. 9(b)), the

scenario is quite different: as observed in the previous Section

(Fig. 8(b)), the particles form network-like structures and lead to

the formation of very thick films which are significantly more

stable with lifetimes of up to 1 h.

4. Conclusions

We have presented investigations into the static and dynamic

properties of air–water interfaces of aqueous dispersions of

partially hydrophobic silica nanoparticles (34% SiOH coverage).

Our measurements strongly support the argument that the

stability of particle-stabilised, aqueous foams can be predicted by

the Gibbs elasticity criterion E > g/2, which relates the surface

tension g and the dilational elastic modulus E of the particle

covered interfaces. Both g and E depend on the bulk particle

concentration of the dispersion, making this therefore a key

parameter for the control of foam stability. Our predictions are

in perfect agreement with the results of Cervantes-Martinez

et al., which were based on estimations of the particle concen-

tration at the surface of bubbles.

This journal is ª The Royal Society of Chemistry 2009

We find that particle adsorption is inhibited by a pronounced

energy barrier29 which can be overcome using strong sonication

of the particle dispersions. The precise nature of this adsorption

barrier is not yet clear to us, but it might explain why the

generation of stable particle foams requires high energy tech-

niques, such as turbulent mixing.

Finally, we show that at sufficiently high particle concentra-

tions and after sufficient energy input, particles form network-

like structures at the surface of aqueous dispersions and in thick

horizontal free-standing films. Similar structures were seen

recently in electron microscopy experiments.34 The formation of

such structures requires the presence of attractive particle inter-

actions in the interface, whereas we find repulsive particle

interactions in the bulk from our light scattering data (B2 > 0).

The nature of these interfacial attractive interactions is still

unclear.18

Acknowledgements

The authors would like to thank Pawel Pieranski for discussions

and for kindly sharing his freely suspended film equipment. We

thank Liliane L�eger for lending us her ellipsometer, Eric Ras-

paud for providing the light scattering equipment and Wacker-

Chemie (Burghausen) for providing the silica particles. A. Stocco

was financed by SOCON (European contract RTN 2004-

512331).

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