Nanocomposite silica surfactant microcapsules by evaporation induced self assembly: tuning the...

9
Nanocomposite silica surfactant microcapsules by evaporation induced self assembly: tuning the morphological buckling by modifying viscosity and surface charge D. Sen, * a J. Bahadur, a S. Mazumder, a G. Verma, b P. A. Hassan, b S. Bhattacharya, c K. Vijai d and P. Doshi d Received 14th October 2011, Accepted 14th November 2011 DOI: 10.1039/c1sm06964k Nanocomposite microcapsules of silica and surfactants have been synthesized using evaporation induced self-assembly through spray drying. It was established using electron microscopy and small- angle neutron/X-ray scattering experiments that the viscosity of the virgin dispersion and surface charge of colloidal components play a significant role in the buckling of spray droplets during drying. Hollow spherical grains are realized at relatively low viscosity and higher surface charge while mushroom like grains manifest at higher viscosity and lower surface charge. In the intermediate conditions, deformed doughnut shaped microcapsules are obtained. Scattering experiments establish the presence of the organization of micelle like aggregates of surfactants in the dried grains and also corroborate with the observations from electron microscopy. A plausible mechanism regarding the chronological pathways of morphological transformation is illustrated. Computer simulation, based on buckling of an elastic shell using a surface evolver, has been attempted in order to corroborate the experimental results. Introduction In recent years, porous and hollow microcapsules have attracted continuous interest 1–8 in science and technology. This is because of the fact that such hollow capsules are potential candidates for various applications such as, drug delivery, catalysis, photonic crystals, chromatography, protection of biologically active agents, pigments, coatings, waste removal, dye-sensitized solar cells etc. Several strategies, such as, hetero phase polymerization, self-assembly, layer-by-layer assembly, spray drying etc. have been adopted to synthesize 9,10 hollow capsules comprising of polymeric or ceramic materials. In this regard, spray drying has been proven to be an efficient, fast and one step process to realize micrometric and sub- micrometric capsules/grains. 11–20 However, controlling the morphology of such capsules for respective applications remains an important issue. It has been established 14–18,21–23 that depending on several physico-chemical parameters of the drying process, buckling of spray droplets may occur because of total force balance across the air–water interface, which in turn leads to morphological transformation of the droplets during the course of drying. Interesting non-spherical morphologies such as, doughnut, deformed-doughnut with multi invagination zones, mushroom etc., have been observed. It is worthy to mention at this juncture that in everyday life, sudden alteration in object morphology due to buckling is ubiquitous in a macroscopic length scale. This phenomenon is of practical importance too in various architectural design such as, tough pressurized vessels, fluid transporting pipes, bridges etc. Although, the phenomenon of buckling in macroscopic bodies is understood from the behavior of bifurcation in the solution to the equations of static equilibrium, the same phenomenon in a micrometric drying droplet still remains a complex issue. This is primarily because of the interplay between various forces originating from hydrodynamics, inter-particle interaction, capillary forces, visco-elastic transformation etc., and is yet to be understood in detail. In the recent past, 21,23 it has been observed that a drying sessile colloidal droplet, in millimetre length scale, may get transformed from most symmetric spherical geometry to less symmetric buckled geometry. More recently, in micrometre length scale, a sphere to deformed doughnut like morphological trans- formation during evaporation induced self assembly (EISA) of nanoparticles by spray drying has been observed 15,17,18 for free falling colloidal spray droplets. It has been pointed out 16 that interparticle interaction plays an important role in controlling the morphological transformation during EISA of mixed colloids comprising hard silica particles and E. Coli as soft colloids. Recently, it has been demonstrated 16 a Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai, 400085, India. E-mail: [email protected] b Chemistry Division, Bhabha Atomic Research Centre, Mumbai, 400085, India c Technical Physics Division, Bhabha Atomic Research Centre, Mumbai, 400085, India d National Chemical Laboratory, Pune, 411008, India This journal is ª The Royal Society of Chemistry 2012 Soft Matter , 2012, 8, 1955–1963 | 1955 Dynamic Article Links C < Soft Matter Cite this: Soft Matter , 2012, 8, 1955 www.rsc.org/softmatter PAPER Downloaded by Bhabha Atomic Research Centre on 15 February 2012 Published on 23 December 2011 on http://pubs.rsc.org | doi:10.1039/C1SM06964K View Online / Journal Homepage / Table of Contents for this issue

Transcript of Nanocomposite silica surfactant microcapsules by evaporation induced self assembly: tuning the...

Dynamic Article LinksC<Soft Matter

Cite this: Soft Matter, 2012, 8, 1955

www.rsc.org/softmatter PAPER

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online / Journal Homepage / Table of Contents for this issue

Nanocomposite silica surfactant microcapsules by evaporation induced selfassembly: tuning the morphological buckling by modifying viscosity andsurface charge

D. Sen,*a J. Bahadur,a S. Mazumder,a G. Verma,b P. A. Hassan,b S. Bhattacharya,c K. Vijaid and P. Doshid

Received 14th October 2011, Accepted 14th November 2011

DOI: 10.1039/c1sm06964k

Nanocomposite microcapsules of silica and surfactants have been synthesized using evaporation

induced self-assembly through spray drying. It was established using electron microscopy and small-

angle neutron/X-ray scattering experiments that the viscosity of the virgin dispersion and surface

charge of colloidal components play a significant role in the buckling of spray droplets during drying.

Hollow spherical grains are realized at relatively low viscosity and higher surface charge while

mushroom like grains manifest at higher viscosity and lower surface charge. In the intermediate

conditions, deformed doughnut shaped microcapsules are obtained. Scattering experiments establish

the presence of the organization of micelle like aggregates of surfactants in the dried grains and also

corroborate with the observations from electron microscopy. A plausible mechanism regarding the

chronological pathways of morphological transformation is illustrated. Computer simulation, based on

buckling of an elastic shell using a surface evolver, has been attempted in order to corroborate the

experimental results.

Introduction

In recent years, porous and hollow microcapsules have attracted

continuous interest1–8 in science and technology. This is because

of the fact that such hollow capsules are potential candidates for

various applications such as, drug delivery, catalysis, photonic

crystals, chromatography, protection of biologically active

agents, pigments, coatings, waste removal, dye-sensitized solar

cells etc. Several strategies, such as, hetero phase polymerization,

self-assembly, layer-by-layer assembly, spray drying etc. have

been adopted to synthesize9,10 hollow capsules comprising of

polymeric or ceramic materials.

In this regard, spray drying has been proven to be an efficient,

fast and one step process to realize micrometric and sub-

micrometric capsules/grains.11–20 However, controlling the

morphology of such capsules for respective applications remains

an important issue. It has been established14–18,21–23 that

depending on several physico-chemical parameters of the drying

process, buckling of spray droplets may occur because of total

force balance across the air–water interface, which in turn leads

to morphological transformation of the droplets during the

aSolid State Physics Division, Bhabha Atomic Research Centre, Mumbai,400085, India. E-mail: [email protected] Division, Bhabha Atomic Research Centre, Mumbai, 400085,IndiacTechnical Physics Division, Bhabha Atomic Research Centre, Mumbai,400085, IndiadNational Chemical Laboratory, Pune, 411008, India

This journal is ª The Royal Society of Chemistry 2012

course of drying. Interesting non-spherical morphologies such

as, doughnut, deformed-doughnut with multi invagination

zones, mushroom etc., have been observed. It is worthy to

mention at this juncture that in everyday life, sudden alteration

in object morphology due to buckling is ubiquitous in

a macroscopic length scale. This phenomenon is of practical

importance too in various architectural design such as, tough

pressurized vessels, fluid transporting pipes, bridges etc.

Although, the phenomenon of buckling in macroscopic bodies

is understood from the behavior of bifurcation in the solution to

the equations of static equilibrium, the same phenomenon in

a micrometric drying droplet still remains a complex issue. This

is primarily because of the interplay between various forces

originating from hydrodynamics, inter-particle interaction,

capillary forces, visco-elastic transformation etc., and is yet to

be understood in detail.

In the recent past,21,23 it has been observed that a drying sessile

colloidal droplet, in millimetre length scale, may get transformed

from most symmetric spherical geometry to less symmetric

buckled geometry. More recently, in micrometre length scale,

a sphere to deformed doughnut like morphological trans-

formation during evaporation induced self assembly (EISA) of

nanoparticles by spray drying has been observed15,17,18 for free

falling colloidal spray droplets.

It has been pointed out16 that interparticle interaction plays an

important role in controlling the morphological transformation

during EISA of mixed colloids comprising hard silica particles

and E. Coli as soft colloids. Recently, it has been demonstrated16

Soft Matter, 2012, 8, 1955–1963 | 1955

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

that morphological transformation of mixed colloidal suspen-

sion droplets during EISA can be arrested through an effective

coverage of the bigger and softer colloidal components by the

smaller and harder components by suitable tuning of surface

charge. Without the consideration of the effect of surface charge,

the above observation could not be explained solely on the basis

of existing buckling hypothesis.21 Such intriguing results

prompted us to investigate the role of surface charge of colloids

and viscosity of the formulation during EISA of mixed colloids

comprising of both hard and soft colloids. Surfactants, in

aqueous solutions, have the ability to modify the surface charge

of inorganic materials via adsorption and at the same time these

molecules self assemble to form soft colloidal structures such as

micelles, worm-like micelles, vesicles etc. Here, we used micelles,

formed by anionic surfactant SDS, as the soft matrix. The size of

these micelles is smaller than the harder component, i.e. silica

particles. Microstructural transitions in micellar solutions can be

achieved via surface charge modulation, which in turn affects the

macroscopic properties of the fluid, such as viscosity. In the

recent past, it was observed that24 hydrotropic electrolyte, in low

concentration, significantly modifies the surface charge of

anionic micelles and also imparts substantial changes in the

rheological behavior of the fluid. Further, it has been shown25

that such addition of hydrotropic electrolyte, even at low

concentrations, to anionic micelles promotes a transition from

spherical to worm-like micelles through strong binding of

hydrophobic cation to anionic micelles.

The present investigation is a step to improvise the under-

standing on how inter-particle interaction/surface charge and

viscosity of the medium affect the morphological transformation

during drying of spray colloidal droplets.

It is worth mentioning that combined use of an imaging

technique like electron microscopy and neutron or X-ray scat-

tering techniques provide complementary information about the

microstructural features26–30 over a wide length scale. On one

hand, scanning electron microscopy (SEM) provides direct

visualization of the morphology and on the other hand,

scattering techniques such as small-angle neutron/X-ray scat-

tering (SANS/SAXS) allows a quantitative measure of statisti-

cally averaged information of structure over a length scale

10–10 000 �A.

Experimental section

Silica dispersion (40%) was obtained from VISA Chemicals,

Mumbai, India. Sodium dodecyl sulfate (SDS) was obtained

from Sisco Research Labs, Mumbai, India. Hydrotropic elec-

trolyte aniline hydrochloride (AHC) was obtained from Fluka.

Deionized water from a Millipore-MilliQ system (resistivity

�18M U cm) was used in all cases to prepare aqueous disper-

sions. Initially a silica dispersion of 2 wt % was prepared for

spray drying using a LU 228 (LABULTIMA, India) spray dryer.

Mixed dispersions of 2 wt% silica, 2 wt% SDS for varying

concentration of AHC (0, 10, 20, 30 and 50 mM) were prepared

for spray drying. Spray dried grains were also washed carefully

with methanol or calcined in order to expel the organic moieties

from the grains.

SEMmicrographs of the assembled grains were obtained using

a VEGA, TeScan instrument. Rheological properties of the

1956 | Soft Matter, 2012, 8, 1955–1963

dispersions have been measured by a rheometer (Anton Parr

Physica MCR 101) using a double gap concentric cylinder

geometry (DG 26.7) with a Peltier temperature control. The

shear rate was varied from 0.1 to 200 s�1. pH value of the

dispersions prior to spray drying was also measured. The pH

values for the silica dispersion and mixed silica-SDS dispersion

were 9.7 and 9.4, respectively. With addition of AHC, the value

of pH decreases. The pH values for the dispersions with 10, 20, 30

and 40 mM AHC concentration were 7.8, 5.7, 5.2 and 4.5,

respectively.

To obtain small-angle neutron scattering (SANS) data of the

spray dried specimens over a wide scattering-vector (q) range, an

essential requirement to probe microstructure of such hierar-

chically structured grains, scattering experiments were per-

formed at JCNS, FRM-II, Garching, Germany, using two

different instruments namely, KWS-131 and KWS-332 after per-

forming some initial experiments at two SANS facilities33–35 at

the Dhruva reactor, Mumbai, India. Scattering data over a wide

range of wave vector transfer (0.0002–0.2 �A�1) were obtained

from combined facilities KWS-1 and KWS-3. We have also

performed SAXS measurements using a laboratory based SAXS

instrument.

Results and discussion

Hollow nano-composite capsules, comprising inorganic silica

and organic surfactant (SDS) have been synthesized by spray

drying technique. The size and the shape of the organicmatrix has

beenmodulated by the addition of hydrotropic additive, AHC. In

this section, we will discuss the issues related to the effects of

viscosity and surface charge on the buckling behavior. Before

proceeding further, let us describe the spray drying process in

brief. In this process, colloidal spray droplets are generated from

a dilute colloidal dispersion. These droplets are passed through

a hot chamber where the solvent gets evaporated. The nano-

particles come closer, get jammed and form self-assembled grains

because of the attractive capillary forces. Various physico-

chemical conditions during drying decide the buckling phenom-

enon vis-�a-vis the final morphology of the grains. We will discuss

this issue in detail in the later part of this section.

SEMmicrographs of the typical morphology of the assembled

capsules are shown in Fig. 1.

It is worthy to mention here that neither the individual

nanoparticles nor the micelles are visible directly from the SEM

micrographs due to constraints of the microscope resolution.

However, it will be shown later how small-angle scattering can

provide information about the constituent nanoparticles and

their correlation in such assembled grains/capsules. It is evident

from the SEM micrographs (Fig. 1a, 1b) that the assembled

microcapsules, as obtained from spray drying of silica dispersion

alone, are smooth doughnuts with a prominent central hole.

However, just the sole addition of SDS micelles in the disper-

sions, prior to spray drying, results in a sudden change and nearly

spherical microcapsules are realized. Further, from Fig. 1d it is

observed that after removal of SDS, these microcapsules become

hollow with a relatively thin shell. Interestingly, significant

deformation in the grain morphology starts when AHC is added

to the silica-SDS dispersion. At 50 mM AHC concentration, the

spherical droplets during drying get deformed significantly and

This journal is ª The Royal Society of Chemistry 2012

Fig. 1 SEM micrographs of the assembled silica-SDS grains. (a,b)

Doughnut like capsules prepared from only silica colloids. (c) Spherical

capsules synthesized with silica colloids and SDS in absence of AHC. (d)

Same as (c) but after removal of organic moieties. (e) Deformed

doughnut like capsules synthesized with silica, SDS and 20 mMAHC. (f)

Same as (e) but after removal of organic moieties. (g) Mushroom like

grains synthesized with silica, SDS and 50 mMAHC. (h) Same as (g) but

after removal of organic moieties.

Fig. 2 Rheological response of the dispersions prior to drying is shown.

It is evident that the viscosity increases with addition of AHC. The

increase in viscosity is quite significant for the addition of 50 mM AHC.

The inset shows the variation of the z potential with AHC concentration.

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

eventually form a mushroom-like structure (Fig. 1g, 1h) of the

assembled grains. Here, it should be mentioned that although the

amount of AHC has been limited to 50 mM, the addition of this

hydrotropic additive affects the physico-chemical properties of

the dispersion significantly in two ways. It reduces the effective z

potential (inset of Fig. 2) and also modifies the viscosity (Fig. 2)

of the dispersion basically due to changes24,25 in micelle structure

and arrangement. In the absence of AHC, the z potential remains

highly negative (�50 mV). However, with the addition of AHC,

the magnitude of the surface potential decreases in a continuous

fashion suggesting co-adsorption of AHC with SDS. Although

the viscosity change is marginal at low concentrations, say up to

20 mM of AHC, a significant increase in viscosity is observed

(Fig. 2) at 50 mM AHC.

It has been conjectured36 in recent past that the deformation

during the spray drying process may occur due to various factors

This journal is ª The Royal Society of Chemistry 2012

such as, thermo-dynamical instabilities, hydro-dynamical insta-

bilities or particle–particle interactions inside the drying droplet.

Kinetics of the drying process drives a suspension far from

equilibrium, leading to dramatic changes in morphology as

solvent evaporates. The rate of drying is a key feature in this

regard. The quantitative measure of the strength of drying is

represented by the Peclet number (Pe). This is defined as the

ratio of mixing time smix (¼R2/D) and drying time sdry (i.e., Pe ¼R2/Dsdry, where R is the radius of the droplets, D is the diffusion

coefficient of the colloidal particles in the droplet and sdry is thedrying time. If Pe � 1, the drying process is regarded as slow and

the droplets shrink12 in an isotropic fashion throughout the

drying process leading to completely jammed spherical grains.

However, for Pe [ 1, the drying is fast enough and there is

a possibility of the formation of hollow grains during drying,

depending on the other physical parameters. In the present

experiment, the drying time is �0.5 s as calculated from the

geometry of drying chamber and the aspiration rate. It should be

mentioned that at present the exact initial droplet size distribu-

tion could not be measured due to technical limitations.

However, the conservation of mass and the typical average

radius (�2 mm) of the obtained grains (Fig. 1) indicates a typical

average radius of initial droplet to be �8 mm. Diffusion coeffi-

cient (D) may be calculated from the Stokes–Einstein relation, D

¼ KBT/6phr, where KB is Boltzmann constant, h is the viscosity

and r represents the average radius of the colloids. ForT¼ 40 �C,r ¼ 7.5 nm and h ¼ 1 mPa s, D works out to be 3.05 � 10�11 m2

s�1. So, Pe becomes �4, which is more than unity. Thus,

formation of a hollow shell during self assembly is possible in

such a case and is also indicated by the hollow micro-capsules in

Fig. 1. Although in the intermediate stage of drying, the droplets

remain viscous in nature, they become elastic during the course

of drying by formation of a dense shell at the air–water interface.

The thickness and the nature of the shell are important param-

eters and determine the required stress to drive the deformation.

Initially, such a shell is produced and gets thicker as droplet

shrinks. At this stage, the main mechanism of water transfer is

governed by the pressure gradient resulting from the capillary

forces. However, at a certain instant, the capillary forces, driving

Soft Matter, 2012, 8, 1955–1963 | 1957

Fig. 3 SANS data (from facilities at Dhruva reactor, India) for the

assembled silica-SDS microcapsules are depicted. Data from double

crystal based MSANS and pinhole collimation SANS are merged to

access a wide q range.

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

the deformation, of the shell overcome the electrostatic forces

stabilizing the colloidal particles. Then the shell becomes elastic

and undergoes a sol–gel type transition and buckles. Once

buckling occurs, it becomes energetically favourable to force

plastic deformation of the shell through the tip of the invagina-

tion. This gives rise to doughnut like particles with a central hole.

It has been pointed out earlier that the buckling of such hollow

elastic20,21 shell during drying results in formation of doughnut

grains as shown in Fig. 1a, 1b.

However, it has also been observed that the addition of just 2wt

% SDS arrests the buckling and produces the microcapsules with

nearly spherical shape. At the same time, it is revealed from the

SEM investigations that these spherical grains are hollow in

nature. This implies that the addition of SDS in silica dispersion

somehow hinders or retards the buckling process. It is to be

mentioned that SDS in water forms nearly-globular micelles at

concentration of 1.4% (i.e., 50mM) inwater. In the absence of any

hydrotropic electrolyte, these micelles are spherical in nature.

With the addition of hydrotropic electrolyte, like AHC, PTHC

etc., themicelles become elongated24,25 and rod/worm likemicelles

are manifested. Typical sizes of the spherical SDSmicelles remain

in the range 3–4 nm, which is smaller than the size18 of the silica

particles (�10–15 nm) used in the present experiment. As the

micelles are significantly smaller than the silica particles, the

micelles could diffuse faster towards the core away from the air

water interface than the silica particles. This results in formation

of microcapsules with silica rich outer shell and micelle rich inner

shell. Thus, the Peclet number corresponding to the micelles

remains smaller than that of the silica particles. The reduction in

effective Peclet number, vis-�a-vis formation of relatively thick

shell (silica mostly at outer shell and micelles at inner shell)

hinders/slows down the buckling deformation resulting spherical

grains, which otherwise become doughnut-shaped after buckling

when only silica particles are present. Here, it should be

mentioned that after assembly during drying, the dry micelles get

locked and this assembly of micelles should not be confused with

conventional micelles in solutions. Upon removal of the trapped

surfactant aggregates, this gives rise to hollow microcapsules (as

evident from the SEM micrograph in Fig. 1(c)).

With addition of AHC, the rheological properties of the

dispersion get altered and deformation of the grains creeps in.

Further, the internal structure and correlation also get modified.

It has already been mentioned earlier that very recently an arrest

of morphological transformation of mixed colloidal suspension

droplets during EISA has been shown through effective coverage

of larger and softer colloidal components by smaller and harder

components by proper tuning of the surface charges. However,

the opposite scenario i.e., the morphological transformation in

the case where the smaller particles are softer compared to the

bigger one is yet to be investigated. In the present investigation, we

try to improvise such understanding i.e., how inter-particle

interaction/surface charge and viscosity affect the morphological

transformation during spray drying.Here, it should bementioned

that a larger Peclet number implies more buckling and vis-�a-vis

smaller shell thickness. Increase in viscosity is associated with an

enhancement in the Peclet number that leads to a relatively thin

elastic shell at the time of buckling. Later on, we will show in the

simulation how a small relative thickness (i.e., the ratio of shell

thickness to radius) leads to more deformed microcapsules.

1958 | Soft Matter, 2012, 8, 1955–1963

The modifications in the structure and the correlation were

apprehended through the scattering experiments. Scattering data

from facilities33–35 at Dhruva reactor are presented in Fig. 3. The

combined scattering data from KWS-1 and KWS-3 are shown in

Fig. 4. Although the basic features in the scattering profiles were

almost similar, combined data from KWS-1 and KWS-3 were

used for further analysis purpose because of better statistics and

resolution. It is evident from Fig. 4 that, the SANS profiles

primarily contain three distinct zones: Zone-I, Zone-II and

Zones-III. Zone-I bears the signature of the scattering contri-

bution from overall morphology of the assembled grains (i.e., the

largest length scale). Zone-II is primarily due to scattering by

correlated silica particles (i.e., the intermediate length scale) in

the grains. Zone-III reflects the scattering contribution from the

micellar arrangement (smallest length scale) in the assembled

grains. The functionality of Zone-I gets significantly modified

beyond the addition of 20 mM AHC.

As the functionality of the Zone-I is primarily determined by

the scattering from overall grain, it is discernible that the

morphology of the microcapsules change drastically at higher

AHC concentration. This suggests that addition of AHC not

only alters the microstructure of micelles at small length scales

but also affects the overall morphology. Interestingly, a prom-

inent peak in Zone-III appears due to the inter micellar inter-

ference when SDS is added along-with silica. The peak height

gets modified with an increase in AHC concentration, particu-

larly with addition of 50 mM of AHC. These modifications are

also supported by the SAXS data (Fig. 5). In addition, SAXS

data also show the appearance of a second peak at highest AHC

concentration, which arises from the ordered arrangement of

micelles. A reduction in height of the first peak, at highest AHC

concentration, was observed from both SAXS and SANS data.

It is worthy to mention that due to the presence of density

fluctuations in multi length-scale, complexity in analysis of scat-

tering data is quite evident. However, when the length scales in the

hierarchical density fluctuations are widely separated, an analysis

method has been proposed13,37 earlier. Based on this model, the

shape of the scattering profile has been analyzed using an additive

hierarchical model for the spray dried grains. In brief, the

This journal is ª The Royal Society of Chemistry 2012

Fig. 4 SANS data (KWS-1 and KWS-3) for the assembled silica-SDS

microcapsules are depicted. Presence of three structural length scales is

evident from the three distinct zones in the data. Inset shows the zoomed

view of the zone-III which reflects the correlation between the jammed

micelles.

Fig. 5 SAXS pattern from the assembled microcapsules. Peak at around

q� 0.15�A�1 is observed when SDS is present. A double peak manifests at

highest AHC concentration (50 mM).

Fig. 6 Fit of the model with scattering data for the zones-I and II (Left

panel in double logarithmic scale and in right panel in Porod represen-

tation). The profiles are shifted vertically for clarity.

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

scattering intensity from such hierarchical grains may be approx-

imated13,16,18,37 by additive contributions of scattering components

from three different length scales and can be represented as:

I(q) ¼ Igrain(q) + ISilica(q)+Imicelle(q) + B (1)

Igrain, ISilica and Imicelle are the respective intensities from overall

grain, jammed silica particles and micelles.

IgrainðqÞ ¼ CgrainDr2grainVgrain

ðN

0

Pgrainðq; rÞDgrainðrÞV2grainðrÞdr

ðN

0

V2grainðrÞDgrainðrÞdr

(2)

and

IsilicaðqÞ ¼ CsilicaDr2silica

ðU

0

Psilicaðq; rÞDsilicaðrÞV2silicaðrÞSðq; rÞdr

ðU

0

VsilicaðrÞDsilicaðrÞdr(3)

This journal is ª The Royal Society of Chemistry 2012

Cgrain, CSilica are scale factors for scattering contribution from

overall grains and silica nanoparticles, respectively and are

determined by the product of respective volume fraction. P(x)

represents form factor and D(x) represents the size distribution.

S(q,r) represents the correlation term between the silica nano-

particles. The expression for scattering contribution due to

micellar arrangement is similar to that of Isilica(q) except the size

distribution, size and correlation between the micelles. The term

Igrain dominates in the Zone-I, where the scattering signal is

predominantly from the overall grains. The second term origi-

nates from the structure and the correlation of the silica nano-

particles in the grains. The third term is due the structural

correlation between the micelles. It is interesting to note that in

this case the length scale of the grains and the silica nanoparticles

are widely separated and thus the data in the range extending

between Zones-I and II can be analyzed in the light of the above

model taking into consideration of the first two terms of the eqn

(1). To avoid complexity, analysis of the data in Zone-III has

been dealt separately. The fit of the model to the SANS data is

shown in the Fig. 6. It is evident that the model explains the

scattering data reasonably well. The estimated size distributions

(assuming a standard lognormal distribution of the grain size) of

the grains are plotted in the Fig. 7. The important parameters

from data analysis are tabulated in Table 1. It is seen from the

table that the estimated size distribution of silica is slightly

modified with the addition of SDS. This is probably due to the

formation of layer of micelles on silica surface. Further, it is

interesting to note that the grain size distribution gets signifi-

cantly modified with the addition of AHC. The distribution

becomes more polydisperse (Fig. 7) at higher AHC concentra-

tion. This happens because a shape polydispersity, in addition to

the size polydispersity, also comes into picture because of the

formation of deformed grains at higher AHC concentration.

The peak like feature in zone-III (at higher q region) of the

scattering profiles has been modeled separately in terms of

structural correlation between the micelles. A hard sphere type

interaction has been considered between the micelles. It has been

mentioned earlier that a significant modification occurs in the

peak shape for addition of 50 mM AHC. A second peak at q �0.2 nm�1 appears and the height of the main peak at q � 0.15

nm�1 decreases. This indicates that the morphology of the jam-

med micelles in the assembled grains gets modified significantly

at high AHC concentration. The average miceller size was found

Soft Matter, 2012, 8, 1955–1963 | 1959

Fig. 7 Grain size distribution as obtained from SANS analysis.

Fig. 8 Fit of the model to the peak like feature in the scattering data in

Zone-III.

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

to be �4.6 nm and the local volume fraction of the micelles was

found to be �0.6. For the sample with 50 mM AHC, the ratio of

the position of the first peak to that of the second peak is found

to be nearly 1.34. It is to be noted that for a hexagonal

arrangement, the above ratio should have been 1.73 while that

for a lamellar arrangement should have been 2.0. It is worthy to

mention that earlier studies indicated38 that the morphological

transformation from cylindrical micelles to bi-layers does not

take place abruptly but through a sequence of intermediate

structures involving hexagonal and lamellar phases. Such inter-

mediate cubic phases are also indicated39 in the literature.

Interestingly, for the cubic phase the ratio of the inter planer

spacing (d) value for (100) reflection to that of (110) reflection

corresponds to �1.4, which matches reasonably well with the

ratio that has been observed experimentally in the present case.

The fit of the model to the data in Zone-III is depicted in Fig. 8.

It should be noted that the long micelles, formed in an aqueous

suspension at 50 mM AHC, are randomly oriented. However,

upon drying the micelles get aligned and form a cubically packed

system.

When looking carefully, it is interesting to observe from

Fig. 1g,1h that the mushroom like grains also contain local zones

(as seen from the different contrast in the SEM image of a grain

in Fig. 1g,1h) which are micelle rich (or due to templated pores in

the calcined grains). Such distinct local zones are not observed

for the cases with lower AHC content. This implies that at high

enough AHC concentration, the micelles form some larger

assemblies among themselves and increase the effective Peclet

number. Further, the viscosity of the initial suspension has also

Table 1 Parameters estimated from SANS data analysis. Rsilica and ssilica aredistribution of the silica nanoparticles. Rg and sgrain are the median and prepresents nth moment of the grain size distribution. fsilica represents the volu

Specimen Rsilica (nm) ssilica fsilica Csilica/Cgrain (10�10)

SiO2 7.5 0.36 0.66 1.1SiO2 + SDS + 0 AHC 7.5 0.42 0.52 1.5SiO2 + SDS + 10 AHC 7.5 0.42 0.50 1.6SiO2 + SDS + 20 AHC 7.5 0.42 0.50 0.5SiO2 + SDS + 30 AHC 7.5 0.42 0.50 0.1SiO2 + SDS + 50 AHC 7.5 0.42 0.50 0.1

1960 | Soft Matter, 2012, 8, 1955–1963

been high enough and this results in an increase in the value of

the Peclet number. It is interesting to note that an increase in

viscosity by 10 times (Fig. 2) will also increase the Peclet number

by 10 fold. The increase in effective Peclet number enhances the

buckling probability and finally results in mushroom like grains.

It is quite evident from the SEM micrographs of the spherical

grains, as formed when solely SDS has been added to silica

dispersion, that they are hollow but there is no clear signature of

templated pore on the surface of the grains in this case when the

micelles are removed either by thorough washing with methanol

or by calcination. However, it should be recalled that the mass

fraction of SDS in the dispersion prior to the drying has been

significant (�2% and identical to that of the silica mass fraction)

enough with respect to mass fraction of silica. This suggests that

the SDS (i.e., the softer but smaller size component of the

dispersion) remains mostly at the inner surface of the shell of

microcapsules while the silica (i.e., harder and larger size

component) forms the outer surface of the shell. After calcina-

tions (or by washing the grains with methanol) the SDS burns

out (or leaves the grain) and hollow grains are realized (Fig. 1c,

1d). The situation is illustrated schematically in the Fig. 9. It is to

be mentioned that the peak like feature in the SANS/SAXS data

vanishes completely after removal of the micelles either by

rigorous washing of the grains with methanol or by calcinations.

It is interesting to note that the microcapsules were buckled

doughnut shaped for the case of only silica and the buckling gets

arrested when SDS is mixed with silica. This can be explained as

follows. In the case of drying droplets with only silica, the

difference between the shear modulus at the shell and at the inner

part (where density of the silica particle is much less than that at

the median and the polydispersity index, respectively for lognormal sizeolydispersity index, respectively for the grain size distribution. <Rg

n>me fraction of the silica nanoparticles in the assembled grains

Rg (nm) sgrain <Rg> (nm) <Rg2> (nm2) <Rg

3>/<Rg2> (nm)

88.7 0.38 95.3 1.05 � 104 127.398.1 0.41 106.7 1.35 � 104 149.370.0 0.50 79.3 8.08 � 103 130.870.0 0.51 79.7 8.24 � 103 134.143.5 0.69 55.2 4.90 � 103 143.039.5 0.75 52.32 4.81 � 103 161.2

This journal is ª The Royal Society of Chemistry 2012

Fig. 9 Schematic diagram showing the two different situations with no

AHC and with large amount of AHC. At large AHC concentration, the

ordering of cylindrical micelles during self-assembly occurs through an

intermediate cubic phase between hexagonal and lamellar.

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

shell) of the grains is relatively larger than the situation where

SDS micelles reside at the core of the grain and silica at the air–

water interface. Relatively less difference in the shear modulus

between the shell and core retards the buckling phenomenon in

the latter case. In addition, the slight enhancement in repulsive

zeta potential (z ¼ �50 mV for silica + SDS and z ¼ �44 mV for

only silica) slows down the buckling process to some extent.

Further, the doughnut shape in case of only silica was signifi-

cantly smoother than in the case of increased AHC concentra-

tion. This is because of the appearance of heterogeneity of the

shear modulus at the shell surface. At larger concentrations of

AHC, i.e., when the surface charge is reduced, the micelles

deviate from spherical shape and tend to be arranged as elon-

gated cylinders which effectively reduce their diffusion coeffi-

cient. Because of lesser rate of diffusion, some fraction of the

micelles resides at the shell. This leads to heterogeneity in shear

modulus at the shell. Micelle rich zones, being softer than silica,

will be more prone to forming invagination zones on the surface

and thus deformed doughnuts with multi invagination zones are

formed. Further, according to Darcy’s law, larger viscosity

values at high AHC concentration will increase the pressure

gradient (DPf h) across the shell, which leads to easier defor-

mation. At this juncture, it may be worthy to mention that such

a kind of surface wrinkling, as also often seen in nature in

dehydrated peas, dried raisins etc., may be a nuisance to be

avoided in many engineering applications on one hand but on the

other hand is a useful way of achieving unusual physical prop-

erties in the micrometric scale based on larger surface areas.

The buckling instabilities as observed in the present case have

been interpreted and have been attempted to explain using the

thin elastic shell theory.21,22 Mathematically, the total energy of

thin elastic shell can be written as follows:

F ¼ð�

1

2kðC1 þ C2 � C0Þ2 þ 1

23ij Kijkl3kl

�dA (4)

The first term in the expression stands for the bending energy.

Here k is the bending modulus, C1 and C2 are two principal

curvatures of the surface and C0 is the spontaneous curvature.

This journal is ª The Royal Society of Chemistry 2012

The second term stands for the stretching energy along a plane

and Kijkl and the 3 stands for the elasticity and strain tensors. The

deformation of a homogenous thin elastic shell of thickness h is

essentially governed by the interplay of stretching and bending

components of total energy. The ratio of these two components is

represented by a non-dimensional number called the F€oppl–von

Karman number as shown below:

g ¼ AR2

k(5)

Here A is two-dimensional (2D) Young’s modulus given by

Yh, with Y the (3D) Young’s modulus, R is the shell radius and k

is the 2D bending modulus given by Yh3/[12(1�n2)].

The same number (g) is also related to the shell thickness/

radius ratio (h/R) and the Poisson ratio (n) as

g ¼ 12ð1� v2Þðh=RÞ2 (6)

This relationship shows that in thin shell theory, relative shell

thickness (h/R) and Poisson ratio (i.e., the ratio of transverse

strain to the axial strain for a body under applied load) are the

two parameters which control the shape of the elastic shell.

The elastic shell configurations, which minimize the energy

functional given by eqn (4), were found using freely available

software, Surface Evolver.40 The following procedure, which is

based on earlier works by Jie et al.41 and Quilliet et al.,42 is used to

simulate the deformation and buckling of thin elastic shells. A

regular cubic polyhedron is assumed as the initial shape. This

cube is evolved into a sphere by minimizing the surface area while

keeping its volume fixed at Vo. The surface tension is later

removed and the surface area of the shell is made fixed. The

required named methods are then applied on the thin elastic shell

and the completely evolved sphere is taken as the un-strained

shape. The volume of this shell is gradually reduced in steps of

either of 0.0024Vo or 0.0048Vo. The shape is evolved to an energy

minimum state after each volume step using gradient descent and

the conjugate gradient methods. The simulations are stopped at

the point when the surfaces started to inter penetrate, which

varied from 0.5Vo to 0.15Vo based on the value of relative shell

thickness. In order to establish the accuracy and correctness of

this approach, several simulations were carried out to success-

fully reproduce the buckled shapes presented by Quilliet et al.42

Simulations were carried out for varying values of g keeping the

value of n fixed at 1/3. Fig. 10, 11 and 12 show the evolution of

the buckled shape for relative shell thickness of 0.231, 0.054 and

0.023, respectively. As shown earlier, for the experimental situ-

ation of only silica dispersion, the viscosity of the initial disper-

sion has been much smaller than that in the case after addition of

AHC. It indicates that the Peclet number remains relatively less

in the case of only silica dispersion compared to that of the

situation when AHC is added to the colloid. It is expected that

for only the silica case, a relatively thick shell is formed prior to

the onset of buckling instability during drying. Fig. 10 shows the

evolution of the buckled shape for a shell with h/R ¼ 0.23 and

Poisson ratio of 1/3. It is worthy to mention that the value of

Poisson ratio in case of drying network of silica nanoparticle

suspension has been shown43 to be close to 1/3. Further, similar

values of the Poisson ratio have also been used21,42 in studying

buckling of shells. It is clear from eqn (6) as well simulation

Soft Matter, 2012, 8, 1955–1963 | 1961

Fig. 10 Simulated microstructure from thin shell model from surface

evolver for g ¼ 200.

Fig. 11 Simulated microstructure from thin shell model from surface

evolver for g ¼ 3600.

Fig. 12 Simulated microstructure from thin shell model from surface

evolver for g ¼ 20 000.

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

results that the shape of the thin elastic shell is a strong function

of relative shell thickness and Poisson ratio plays a relatively

minor role. It is clear from this figure that an initially spherical

shell buckles through the formation of axis-symmetric depres-

sions in the center and finally resulting in a doughnut like shape.

For the experimental situation of silica, SDS with 20 mM AHC,

1962 | Soft Matter, 2012, 8, 1955–1963

the reduced z potential makes the shell more amenable to

buckling21 and hence it is expected that the buckling transition

occurs at smaller values of h/R. Fig. 11 shows buckled shapes of

a shell with h/R¼ 0.054 and Poisson ratio of 0.33. It is clear from

the sequence of shapes that initially multiple depressions are

formed, which eventually give way to a deformed doughnut

shape with a large depression in the center and smaller depression

on the rim, similar to the shapes presented in Fig. 1e, 1f. In

Fig. 12, evolution of buckled shapes for a shell with h/R ¼ 0.021

are shown. This set of shapes represents the buckling transition

of silica dispersion with 50 mM AHC, for which experimentally

obtained shapes are shown in Fig. 1g, 1h. As discussed earlier, in

this scenario, buckling instability sets in relatively early in the

drying process due to increased Peclet number as well as reduced

z potential. These effects are captured in the simulation by setting

the value of h/R to be very small at 0.021. It is clear from the

figure, that the wrinkled shape with multiple depressions are

formed early in the evolution. These wrinkles both grow and

overlap with the reduction in the volume, resulting in highly

deformed shapes.

Results from the simulation suggest that the relative thickness

of the shell is an important factor in determining typical shapes

of such grains. When the relative thickness (h/R) is large, i.e., for

the situation with smaller g, the smooth doughnuts are obtained.

However, an increase in g value results in formation of deformed

doughnut like capsules. Further, increase in g results in signifi-

cantly distorted shape. These results qualitatively support the

hypothesis which was presented earlier to explain the experi-

mentally obtained shapes as shown in Fig. 1.

Conclusions

In summary, hollow silica microcapsules were synthesized using

evaporation induced self assembly of silica colloids and SDS

micelles with variation in hydrotropic AHC. Ordering of

surfactant in the assembled microcapsules is demonstrated from

neutron and X-ray scattering experiments. A chronological

pathway of morphological transition during drying to hollow

spherical shell, deformed doughnut and mushroom like

morphology of the microcapsules could be obtained by system-

atic tuning of viscosity of the virgin suspension and surface

charge on the constituent colloidal particles. Such hollow

microcapsules with controlled porosity may find applications in

drug delivery, filtration and catalytic applications. Simulation

using thin elastic shell theory in surface evolver supports the

buckling nature of the microcapsules. Further, the present work

opens up an effective experimental as well as a theoretical route

in comprehensive understanding of micrometric droplet buckling

during EISA.

Acknowledgements

Authors thank DrHenrich Frielinghaus and DrG€unter Goerigk,

JCNS, Germany, for their help in SANS experiments at KWS-1

and KWS-3, respectively. DS would like to thank Dr Antoine

Thill and Dr Olivier Spalla, LIONS, SCM, DRECAM, CEA

Saclay, France for many fruitful discussions on spray drying

during his visit at CEA Saclay, France. DS and JB thankfully

acknowledge financial support (DST(5)/AKR/P087/10-11/673)

This journal is ª The Royal Society of Chemistry 2012

Dow

nloa

ded

by B

habh

a A

tom

ic R

esea

rch

Cen

tre

on 1

5 Fe

brua

ry 2

012

Publ

ishe

d on

23

Dec

embe

r 20

11 o

n ht

tp://

pubs

.rsc

.org

| do

i:10.

1039

/C1S

M06

964K

View Online

received from Department of Science and Technology, India

through S. N. Bose National Centre for Basic Science, Kolkata,

India for neutron scattering work at JCNS, Germany. Authors

thank Dr Guruswamy Kumaraswamy, NCL, Pune, India for the

SAXS measurements. PD and KV would like to thank Prof. K.

Brakes for providing the software Surface Evolver and Prof. C.

Quilliet for helping in setting the simulations.

References

1 F. Caruso, R. A. Caruso and H. Mohwald, Science, 1998, 28, 1111–1114.

2 P. Jiang, J. F. Bertone and V. L. Colvin, Science, 2001, 291, 453–457.3 W. Gu, L. Zhang, H. Chen and J. Shi, J. Am. Chem. Soc., 2005, 127,8916–8917.

4 Y. Wang, L. Cai and Y. Xia, Adv. Mater., 2005, 17, 473–477.5 Y. Wang and Y. Xia, Nano Lett., 2004, 4, 2047–2050.6 X. Xu and S. A. Asher, J. Am. Chem. Soc., 2004, 126, 7940–7945.7 K. Yong Joo, L. Mi Hyeon, K. Hark Jin, L. Gooil, C. Young Sik,P. Nam-Gyu, K. Kyungkon and L. Wan In, Adv. Mater., 2009, 21,3668–3673.

8 Wenguang Leng, Min Chen, Shuxue Zhou and Limin Wu, Langmuir,2010, 26(17), 14271–14275.

9 E. Donath, G. B. Sukhorukov, F. Caruso, S. A. Davis andH. M€ohwald, Angew. Chem., Int. Ed., 1998, 37, 2201–2205.

10 M. Sch€onhoff, Curr. Opin. Colloid Interface Sci., 2003, 8, 86–95.11 Ferry Iskandar, Mikrajuddin and Kikuo Okuyama,Nano Lett., 2002,

2(4), 389–392.12 D. Sen, O. Spalla, O. Tach�e, P. Haltebourg and A. Thill, Langmuir,

2007, 23, 4296–4302.13 D. Sen, O. Spalla, L. Belloni, T. Charpentier and A. Thill, Langmuir,

2006, 22, 3798–3806.14 S. Lyonnard, J. R. Bartlett, E. Sizgek, K. S. Finnie, T. Zemb and

J. L. Woolfrey, Langmuir, 2002, 18, 10386–10397.15 J. Bahadur, D. Sen, S. Mazumder, S. Bhattacharya, H. Frielinghaus

and G. Goerigk, Langmuir, 2011, 27, 8404–8414.16 D. Sen, J. S. Melo, J. Bahadur, S. Mazumder, S. Bhattacharya,

S. F. D’Souza, H. Frielinghaus, G. Goerigk and R. Loidl, SoftMatter, 2011, 7, 5423.

17 D. Sen, S. Mazumder, J. S. Melo, A. Khan, S. Bhattyacharya andS. F. D’Souza, Langmuir, 2009, 25(12), 6690–6695.

18 D. Sen, J. S. Melo, J. Bahadur, S. Mazumder, S. Bhattacharya,G. Ghosh, D. Dutta and S. F. D’Souza, Eur. Phys. J. E, 2010, 31,393–402.

This journal is ª The Royal Society of Chemistry 2012

19 D. Sen, A. Khan, J. Bahadur, S. Mazumder and B. K. Sapra, J.Colloid Interface Sci., 2010, 347, 25–30.

20 J. Bahadur, D. Sen, S. Mazumder, B. Paul, A. Khan and G. Ghosh, J.Colloid Interface Sci., 2010, 351, 357.

21 N. Tsapis, E. R. Dufresne, S. S. Sinha, C. S. Riera, J. W. Hutchinson,L. Mahadevan and D. A. Weitz, Phys. Rev. Lett., 2005, 94, 018302.

22 L. Pauchard and Y. Couder, Europhys. Lett., 2004, 66(5), 667–673.23 O. D. Velev, A. M. Lenhoff and E. W. Kaler, Science, 2000, 287,

2240–2243.24 Gunjan Garg, P. A. Hassan, V. K. Aswal and S. K. Kulshreshtha, J.

Phys. Chem. B, 2005, 109, 1340.25 P. A. Hassan, Srinivasa R. Raghavan and Eric W. Kaler, Langmuir,

2002, 18, 2543–2548.26 P. Lindner, T. Zemb,Neutrons, X-Rays and Light: ScatteringMethods

Applied to Soft Condensed Matter Elsevier: Amsterdam, 2002.27 O. Glatter and O. Kratky, Small Angle X-ray Scattering, Academic

Press, London 1982.28 D. Sen, S. Mazumder and J. Bahadur, Phys. Rev. B, 2009, 79, 134207.29 S. Mazumder, D. Sen, A. K. Patra, S. A. Khadilker, R. M. Cursetji,

R. Loidl, M. Baron and H. Rauch, Phys. Rev. Lett., 2004, 93, 255704.30 S. Mazumder, D. Sen, I. S. Batra, R. Tewari, G. K. Dey, S. Banerjee,

A. Sequeira, H. Amentisch and S. Bernstorff, Phys. Rev. B, 1999, 60,822.

31 H. Frielinghaus, et al., JCNS Experimental Report, 2007/2008, http://www.jcns.info/src/report/sr2008_KWS1_new_PB3.pdf.

32 G. Goerigk and Z. Varga, J. Appl. Crystallogr., 2011, 44, 337.33 S. Mazumder, D. Sen, T. Saravanan and P. R. Vijayaraghavan, J.

Neutron Res., 2001, 9, 39.34 S. Mazumder, D. Sen, T. Saravanan and P. R. Vijayaraghavan,

Current Science, 2001, 81, 257.35 V. K. Aswal and P. S. Goyal, Curr. Sci., 2001, 79, 947.36 F. Iskandar, L. Gradon and Kikuo Okuyama, J. Colloid Interface

Sci., 2003, 265, 296–303.37 A. Thill and O. Spalla, J. Colloid Interface Sci., 2005, 291, 477–488.38 M. C. Holmes, M. S. Leaver in Bicontinuous liquid crystals; M. L.

Lynch, P. T. Spicer, ed.; Surfactant Science Series, Volume 127,CRC Press: Boca Raton, FL, 2005; pp 15–39.

39 V. Luzzati, In Biological Membrane, D. Chapman, ed.; AcademicPress: London and New York, p71, 1968.

40 K. Brakke, Exp. Math., 1992, 1, 141.41 Yan Jie, Liu Quanhui, Liu Jixing and Ou-Yang Zhong-Can, Phys.

Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1998,58, 4730–4736.

42 C. Quilliet, C. Zoldesi, C. Riera, A. van Blaaderen and A. Imhof, Eur.Phys. J. E, 2008, 27, 13–20.

43 G. W. Scherer, J. Non-Cryst. Solids, 1997, 215, 155–168.

Soft Matter, 2012, 8, 1955–1963 | 1963