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This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 4005–4012 4005
Cite this: Phys. Chem. Chem. Phys., 2011, 13, 4005–4012
Kinetic stability of water-dispersed oil droplets encapsulated
in a polyelectrolyte multilayer shell
Anton V. Sadovoy,aMaxim V. Kiryukhin,
aGleb B. Sukhorukov
aband
Maria N. Antipina*a
Received 9th September 2010, Accepted 10th December 2010
DOI: 10.1039/c0cp01762k
The original theoretical model of polyelectrolyte adsorption onto water-dispersed colloid particles
is extended to the system of polydisperse droplets of sunflower oil. Polycation (poly(allylamine
hydrochloride)) and polyanion (poly(sodium 4-styrenesulfonate)) are taken in the theoretically
projected concentrations to perform Layer-by-Layer assembly of a multilayer shell on the surface
of oil droplets preliminary stabilized with a protein emulsifier (bovine serum albumin).
The velocity of gravitational separation in suspension of encapsulated oil droplets is theoretically
predicted and experimentally measured depending on the coating shell’s thickness, aiming to
clarify the mechanism to control over the separation process. Combining the theory and
experimental data, the mass density of a polyelectrolyte multilayer shell assembled in a
Layer-by-Layer fashion is obtained. Polyelectrolyte multilayer coated oil droplets are
characterized by means of z-potential, and particle size measurements, and visualized
by scanning electron microscopy.
Introduction
In the last few decades microencapsulation of a variety of
(bio)active or functional species was demonstrated for a wide
range of practical applications, mainly in drug delivery and
food industry.1–5 Several methods of capsule fabrication, such
as in situ polymerization,6 coacervation,7 precipitation,8,9
Pickering emulsions2,10,11 were developed to house solid colloid
particles, oils, and water-soluble molecules. Alternate Layer-
by-Layer (LbL) adsorption12–14 of oppositely charged poly-
electrolytes was shown to be particularly beneficial for producing
nanoengineered containers with controlled thickness and
permeability,1,13,15,16 responsive to external stimuli,17,18 and
possessing protective properties.19
Recently LbL assembly of a polyelectrolyte multilayer (PM)
shell has been performed on liquid cores, e.g. water-dispersed oil
droplets.20–25 PM coated oil droplets have better stability towards
flocculation and coalescence, as compared to those stabilized
solely with an emulsifier, therefore, they are promising candidates
for applications in food stuff and cosmetic products.26–29
PM encapsulation of oil droplets comprises two consequent
steps: formation of a charged colloid core followed by deposition
of the multilayer shell. Cores are formed by emulsification of
oil in the presence of an ionic surfactant. The surfactant provides
stability of oil droplets and surface charging. The approaches
for shell assembly can be classified as the ‘saturation’25,30 and
‘excess’20,31 depending on the concentration of polyelectrolytes
applied to deposit a coating layer.
The ‘saturation’ approach is based on utilizing each poly-
electrolyte in such concentrations that no free polyelectrolyte
molecules remain in the water phase after adsorption comple-
tion. However, calculation of the polyelectrolyte saturation
concentration becomes a difficult task upon dialing with
polydisperse colloids.
The ‘excess’ approach is based on taking a polyelectrolyte in
concentration well exceeding the ‘saturation’ one to ensure
complete covering of oil droplets by adsorbing macromolecules.
In this case, a certain amount of non-adsorbed polyelectrolyte
remains in the water phase and has to be washed out by any of
the commonly used methods.20,21
Whatever approach is chosen for shell assembly, extensive
flocculation can occur in the system due to wrongly judged
concentration of the adsorbing polyelectrolyte. McClements
has constructed a theoretical model predicting a range of
polyelectrolyte concentrations needed for stability of mono-
disperse colloids over the LbL fashioned shell assembly process.30
In this paper, we first, modify this theoretical model for
polydisperse colloids. The ranges of polyelectrolyte concentra-
tion ensuring the flocculation-free encapsulation are calculated
taking into account the particle size distribution measured
for emulsified droplets of sunflower oil. Second, we give the
a Institute of Materials Research and Engineering, A*STAR,3 Research Link, Singapore, 117602, Singapore.E-mail: [email protected]; Fax: +65 67741042;Tel: +65 68748111
b School of Engineering and Materials Science, Queen Mary,University of London, Mile End Road, London, E1 4NS, UK.E-mail: [email protected]
PCCP Dynamic Article Links
www.rsc.org/pccp PAPER
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4006 Phys. Chem. Chem. Phys., 2011, 13, 4005–4012 This journal is c the Owner Societies 2011
experimental evidence on formation of the PM shell
over water-dispersed droplets of sunflower oil at theoretically
predicted concentrations of the polycation (poly(allylamine
hydrochloride)) and polyanion (poly(sodium 4-styrenesulfonate)),
removing the non-adsorbed macromolecules by a filtration
method. Third, we experimentally investigate the influence
of coating shell’s thickness on the gravitational separation
velocity in suspensions of PM coated oil droplets. In parallel,
the mathematical model based on the Stokes’ law is constructed
to describe the gravitational separation of core/shell particles’
suspension depending on the shell’s thickness. Fourth, we
discuss the other possible aspects of shell’s influence on the
velocity of gravitational separation.
Experimental section
Materials
Poly(sodium 4-styrenesulfonate) (PSS, Mw E 70 000), poly-
(allylamine hydrochloride) (PAH, Mw E 15 000), bovine
serum albumin (BSA), sunflower oil (96%), and tetrahydrofuran
(THF) were purchased from Sigma-Aldrich. All chemicals
were used as-received without further purification. Milli-Q
deionized (DI) water with specific electric conductivity of
18.2 MO cm�1 was used to prepare all aqueous solutions.
Layer-by-Layer coating of oil droplets
Purely unsalted solutions of the polyelectrolytes and BSA were
used for shell assembly. BSA was utilized as a stabilizing agent
at the oil/water interface. Sunflower oil cores were obtained
by adding 1 ml of oil into 9 ml of BSA solution (4 mg ml�1,
pHE 7) and shaking the mixture in a 50 ml centrifuge tube for
10 s. The dispersion was then treated for 2 min by an Ultra
Turrax disperser (IKA, Germany) at 24 000 rpm, and allowed
to relax for 15 min for complete BSA adsorption.
Uncoupled BSA was thoroughly removed via washing
with DI water using a modified stirred 50 ml filtration cell
(Millipore Corp., USA). The commercially available design of
the filtration cell caused particles adhesion onto the surface of
the membrane filter. We modified the stirring system replacing the
build-in stirrer assembly with a polygon or triangular magnetic
stir bar, 25 � 8 mm (Sigma-Aldrich). For washing, 10 ml of
the sample was placed into the filtration cell, filled up with
40 ml of DI water, and then 40 ml of the aqueous phase were
filtered out through a 0.22 mm hydrophilic surfactant free
MF-Milliporet membrane applying compressed air at 20 psi.
z-potential of the dispersed oil droplets was B�20 mV.
Thus, the suspension containing 10% v/v of BSA-stabilized
sunflower oil droplets was obtained.
In the next step, the PM shell was assembled around the
droplets via alternate LbL adsorption of oppositely charged
polyelectrolytes. 10 ml of oil/BSA droplets’ suspension
was slowly dropwise added to 20 ml of PAH water solution
(2 mg ml�1, pH E 5) upon its continuous shaking in a 50 ml
centrifuge tube and then stirred for 10 min. Total concentra-
tion of PAH in the water phase was 1.38 mg ml�1. PAH
adsorption was verified by switching the sign of z-potentialfrom negative to positive (z D +35 mV). Due to high
polydispersity of the droplets, it is not trivial to use the
z-potential value to quantify the amount of absorbed macro-
molecules. However, switching of the sign of z-potential givesan evidence of successful adsorption of a next polyelectrolyte
layer. As the pH in PAH solution added to oil/BSA droplets
was very close to the isoelectric point of BSA (4.7), van der
Waals interactions between PAH and BSA could also play an
important role in PAH adsorption. The uncoupled poly-
electrolyte was thoroughly removed via 2 consecutive washing
steps similar to that described above. Thus, oil/BSA micro-
droplets were coated with a polycation layer. In agreement
with the principles of electrostatic interactions, a polyanion
has to be applied to form a next coating layer. For this
purpose, water solution of PSS (2 mg ml�1, pH E 5) was
added to the suspension of oil/BSA/PAH microdroplets. The
deposition of the polyanion layer was performed in the same
manner as it has been previously described for the polycation.
The deposition was proved by switching the sign of z-potentialfrom positive to negative (z D �35 mV). The described
routine was repeated alternating PAH with PSS to obtain
the desired number of layers in the shell. In this fashion, 2, 4, 6,
and 8 alternating PAH/PSS layers were assembled over micro-
droplets of sunflower oil. It is important to note that the
filtration method used in this work allows us to maintain
approximately constant volume fraction of core/shell particles
(10% v/v) in the suspension over the LbL shell assembly. In
contrast, the ‘saturation’ approach would require sample’s
dilution upon application of each polyelectrolyte layer.
f-potential and particle size distribution
z-potential and size distribution of coated oil droplets were
measured by a ZetaPlus system (Brookhaven Instrument
Corporation, USA). The instrument determines z-potentialby measuring the velocity and direction of particles’ movement
in the applied electrical field based on Doppler-shift measure-
ments. Particle size distribution is analyzed using a light
scattering method.
The samples (10% v/v) were 10 times diluted with DI
water, and then 1.5 ml was placed in a 3 ml plastic cell
(10 � 10 � 30 mm). All measurements were performed at
pH E 5 without adding salts at an equilibrium temperature
of 20 1C.
Creaming velocity
The gravitational separation of suspensions was measured in
terms of creaming velocity, which is a function of upper
creamy layer thickness (cream height).32 The experiments were
carried out by placing 3 ml of each sample into individual
transparent cells of the same type as for particle size distribu-
tion and z-potential studies. The cells were kept at room
temperature (24 1C) over the desired period of time, and then
the cream height was measured by means of a ruler.
Tiny layers of bottom sediment appeared in the cells with
time. However, the resolution of the standard ruler is insufficient
to measure their thickness with enough accuracy.
Scanning electron microscopy
Oil droplets coated with the PM shell were visualized by a
JEOL SEM JSM5600 scanning electron microscope (SEM)
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operating at an acceleration voltage of 15 kV. For sample
preparation, 1 ml of water-dispersed coated oil droplets was
first mixed with 5 ml of THF and then a small droplet of the
obtained mixture was placed on a silica wafer and left until
complete solvent evaporation. (The use of organic solvents
other than THF, such as acetone or toluene, affected the shell
integrity.) The sample’s surface was coated with gold before
taking the SEM images.
Results and discussion
Polydispersity of sunflower oil microdroplets
The original model predicts polyelectrolyte concentration
required for flocculation-free assembly of the multilayer shell
on monodisperse cores,30 oil droplets obtained by a Ultra
Turrax disperser are always polydisperse, though. In order
to introduce polydispersity to the model, it is essential to
determine size distribution of oil droplets.
Fig. 1 (circles) shows the measured particle size (radius)
distribution in the suspension of sunflower oil/BSA droplets
after filtering out all non-adsorbed protein. It can be seen that
the droplets’ radius varies in the range from 0.2 mm to 2.3 mmhaving a maximum at 0.85 mm. The non-symmetric distribution
can be fitted by the log-normal function (Fig. 1, solid line),
given by
PðrÞ ¼ P0 þS
ðrwffiffiffiffiffiffi2ppÞexp �ðln r=rmÞ
2
2w2
!ð1Þ
where P0 is the initial probability, r is the radius of the oil
droplet, rm is the mean radius, w is the standard deviation,
and S is the area under the log-normal curve. The best appro-
priate fit yields to the following parameters of this distribution:
P0 = 0.061, rm= 1.156 mm, w=0.555, S=1 (Fig. 1, solid line).
The particle size distribution in a non-homogenized oil-in-water
emulsion can usually be fitted with a Gauss curve.33 The skewed
shape of the size distribution curve obtained in our case was
probably due to the filtration process, which resulted in some
fraction of oil droplets getting stuck in the 0.22 mm filter pores
filtering out the smaller droplets.
Stability of polydisperse colloids over Layer-by-Layer coating
with oppositely charged polyelectrolytes
In this paragraph, we theoretically predict the range of poly-
electrolyte concentrations required to ensure the flocculation-
free formation of the PM shell over polydisperse colloids by
the example of sunflower oil/BSA droplets (Fig. 1).
Let’s consider polydisperse oil droplets stabilized by an
emulsifier as solid spheres with the log-normal size distribution
displayed above (eqn (1), and Fig. 1), at the moment when a
positively charged polyelectrolyte just has been introduced
into the continuous phase. It is known that charged poly-
electrolyte molecules have mostly elongated conformation in
pure water.35 In order to simplify the simulations, we assume
that the surface of oil droplets is covered by spheres with
diameter cross-section equal to the effective molecular area
Sef of polyelectrolyte molecules in bulk water.
Originally, critical polyelectrolyte concentrations, such as
saturation, depletion, and adsorption, were determined in order
to describe the stability of monodisperse oil droplets towards
flocculation upon the polyelectrolyte adsorption process.30 In
this paper, we review each concentration introducing the
droplets’ polydispersity (Fig. 1).
Saturation concentration. At saturation concentration of
the oppositely charged polyelectrolyte (CSat) all droplets are
completely coated with a polyelectrolyte layer and no free
polyelectrolyte remains in the continuous phase. The lack of
polyelectrolyte will result in uneven coating and non-uniform
charging of the particles surface, thus, leading to bridging
flocculation due to electrostatic attraction between oppositely
charged regions of different droplets.
In our model, the polyelectrolyte saturation concentration
when the ith droplet with the radius ri is totally covered with a
polyelectrolyte monolayer is given by
CSat;i ¼3jGSat
rið1� jÞ ð2Þ
where j is the volume fraction of the oil droplets and Gsat is
the surface density of the adsorbed layer. Assuming that the
ith droplet is being covered by a monolayer of polymer
molecules having the effective molecular square Sef, the density
of this monolayer appears as GSat = M/NASef, where M is the
polyelectrolyte molar mass and NA is the Avogadro’s number,
eqn (2) transfers into
CSat;i ¼3jM
riNASef: ð3Þ
Thus, the averaged saturation concentration for a polydisperse
system is defined as follows:
hCir ¼
Pi
CSat;iðriÞPðriÞPi
PðriÞð4Þ
where P is the function of log-normal distribution with the
parameters determined earlier.
Adsorption concentration. Ideally, complete uniform adsorp-
tion of the polyelectrolyte onto the colloid–water interface
results in inversion of particles’ charge, so that strongly
Fig. 1 Particle size distribution of sunflower oil droplets dispersed
in water and preliminary stabilized with BSA. Experimental data
(symbol) were fitted by the log-normal curve (solid line) with determined
parameters: P0 = 0.061, rm = 1.156 mm, w = 0.555, S = 1.
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charged particles become stable to flocculation. However, the
polyelectrolyte saturation concentration does not ensure the
stability of dispersed colloid particles towards flocculation,
because the processes of polyelectrolyte adsorption and
particles’ collision both are time-dependent.30 So that, if the
time of polyelectrolyte adsorption (tAds) exceeds the time of
particles collision (tCol), then particles’ flocculation will occur
due to non-uniform coating.30 Similar to the original model,
we derive the adsorption concentration CAds, below which the
system of charged colloid particles becomes unstable, taking
into account the impact of tAds/tCol ratio. The characteristic
adsorption time required for the surface to be 90% saturated
with the polyelectrolyte is given by tAds = 10GSat2/(CPE
2DPE),
where CPE is the concentration of the polyelectrolyte in
the continuous phase, DPE is the translation diffusion
coefficient, which is given by DPE = kBT/(6pZref), and Z is
the viscosity of the continuous phase. Brownian motion of oil
droplets in the system promotes the droplets’ collisions. The
average time between collisions is tCol = 4/3pri3/(Kj). K is the
coagulation constant which can be given as K = 8prD, where
D= kBT/(6pZr). In the case of polydisperse particles, K can be
defined as
Kðri; rjÞ ¼8pPi
Pj
ðriþrjÞ2
ðDðriÞþDðrjÞÞ2
PðiÞPðjÞPi
Pj
PðiÞPðjÞ ð5Þ
Considering (5) and the original expression for CAds,30
CAds;i;j ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi45G2
SatrefZjKi;j
r3i kT
s: ð6Þ
Averaging over the polydisperse sample using eqn (1) leads to
hCir ¼
Pk
CAds;m;i;jðrk;i;jÞPðrkÞPi
PðrkÞ: ð7Þ
Depletion concentration. The polyelectrolyte concentration
above CSat ensures complete coating of all colloids in the
system and a fraction of non-adsorbed macromolecules in the
aqueous phase. However, if the concentration of the free
polyelectrolyte exceeds a certain amount called depletion
concentration (CDep), the osmotic pressure becomes sufficient
to overcome electrostatic repulsion of likely charged oil droplets.
Thus, particles collision and flocculation occurs. The depletion
concentration can be introduced as follows:30
CDep;i ¼M
NA
�1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 8u oDep
kBT
� �1
2pr2efðriþ23ref Þ
r4u
0BB@
1CCA; ð8Þ
where
oDep
kBT¼ � 2pCfreeNA
M1þ 2NACfreeu
M
� �r2ef ri þ
2
3ref
� �ð8:1Þ
reveals the strength of depletion attraction between two
contacting spherical particles dispersed in the continues phase
containing the free polyelectrolyte, and
u ¼ 4
3pr3ef ð8:2Þ
is the effective molar volume of the polyelectrolyte in the
continuous phase, and Cfree = (C � CSat)/(1 � j) is the con-
centration of the free polyelectrolyte. Averaging over the
polydisperse system using eqn (1) gives
hCir ¼
Pi
CDep;iðriÞPðriÞPi
PðriÞ: ð9Þ
To simulate these critical polyelectrolyte concentrations, the
following values of parameters were taken: M = 70000
(molar mass of PSS), and those derived from the log-normal
fitting curve (Fig. 1): P0 = 0.061, rm = 1.156 mm, w = 0.555,
and S = 1. ref was estimated using the dimensions of hydrated
PSS molecule. If the ionic strength is low, PSS macromolecule
has elongated conformation with length L = (M/Mm)bU�2/7,
where Mm—molar mass of the monomer unit, b—monomer
size, U—number of monomers between effective charges.35 In
the case of PSS, m = 206, b = 0.26 nm and U = lb/b = 2.7
(where lb = 0.7 nm is the Bjerrum length at 298 K),34 so
L = 66.6 nm. The hydrodynamic diameter of such rods was
estimated to be 1.39 nm.36 In the estimation, polyelectro-
lyte molecule occupies the effective area Sef E 93 nm2.
For the convenience of calculations, we consider that the
surface of the oil droplet is covered by spheres having the
diameter cross-sections equal to Sef, and the effective radius
ref E 5 nm.
Fig. 2 Map of stability for flocculation-free adsorption of the
polyanion (PSS, Mw E 70 000) on oppositely charged polydisperse
microparticles. CSat, CDep, and CAds correspond to saturation,
depletion, and adsorption concentration, respectively. The critical
polyelectrolyte concentrations were simulated taking into account
the log-normal particle sizes distribution (P0 = 0.061, rm = 1.156 mm,
w = 0.555, S = 1). The hatched area corresponds to the range of
concentrations required to avoid particles flocculation.
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The predicted map of system stability is shown in Fig. 2.
The saturation, adsorption and depletion polyelectrolyte
concentrations in the continuous phase with dispersed
oppositely charged polydisperse colloids are plotted versus
the volume fraction of dispersed particles. As discussed above,
the polyelectrolyte concentration range in which particles are
stable towards flocculation is limited by values of CSat, CDep,
andCAds (shown as the hatched area in Fig. 2). Thus, at j=0.1,
which corresponds to the 10% v/v sunflower oil suspension
used in this work, the concentration of PSS should fall into
the 0.30 mg ml�1–2.60 mg ml�1 range in order to ensure
flocculation-free coating of oil droplets. Furthermore, the
simulation shows that flocculation-free coating is not possible,
if the volume fraction of oil droplets with the size distribu-
tion as shown in Fig. 1 exceeds 0.32. Estimated with the
same model, the critical concentrations of PAH (Mw = 15000,
L = 30 nm, ref E 3 nm) are CSat = 0.38 mg ml�1,
CAds = 0.14 mg ml�1, CDep = 2.15 mg ml�1. Thus, the
particles will not flocculate if the concentration of introduced
PAH is selected between 0.38 mg ml�1 and 2.15 mg ml�1. In
our experiments, the actual concentration of each poly-
electrolyte upon multilayer assembly was 1.38 mg ml�1,
which falls into the theoretically modeled range. In practice,
the system was always stable towards flocculation upon
deposition of PAH layers. PSS adsorption sometimes caused
droplets to flocculate, which could be overcome by brief
sonification of the sample in a water bath. The surfactant
properties of PSS appear to be a possible reason for droplets
flocculation causing the decrease of bulk polyelectrolyte
concentration below its critical value.
The polyelectrolytes PAH and PSS were used in the theo-
retically predicted concentrations to assemble a multilayer
shell over BSA-stabilized droplets of sunflower oil according
to the protocol described above. Fig. 3 represents a SEM
image of sunflower oil droplets coated with 8 alternately
adsorbed polyelectrolyte layers. The relatively rough surface
of the particles gives a clear evidence of PM shell assembly. It
is worth to note that the integrity of the coating shell was
almost unaffected over SEM sample preparation and opera-
tion in vacuum. Indeed, the amount of ruptured capsules was
insufficient in the series of images captured from physically
different samples.
Gravitational separation of suspension of PM coated oil droplets
Suspensions of colloid particles separate with time because
of the difference in mass density of dispersed particles and
the continuous phase. By definition, creaming is the upward
movement of colloids, whereas sedimentation is their down-
ward movement.
Oil droplets, as a rule, move upward in water because of
lower mass density, but can be forced to move downward
by introducing a weight agent. For instance, admixing
of a brominated agent (r E 1330 kg m�3) to vegetable oil
(r E 900 kg m�3) changed the speed of droplets’ movement
from +0.02 cm h�1 to �0.1 cm h�1.22 Similar to that, the PM
shell can increase the mean mass density of the oil droplet and
slow down the gravitational separation of suspension. In this
paper, we explore the impact of the PM shell to the creaming
separation velocity by comparing the results of theoretical
modeling and experimental data.
The settling velocity of oil droplet’s motion across the
continuous liquid phase can be calculated by means of the
Stokes’ law:
vStokes0 ¼ �2gr2drðrf � rdrÞ
9Zl; ð10Þ
where g is the gravitational acceleration, rf is the mass density
of the continuous liquid phase, rdr is the mass density of the oil
droplet, rdr is the droplet’s radius, and Zl is the shear viscosity.In the case of oil-in-water emulsion, rdr o rf, thus, the settlingvelocity of the oil droplet is vertically upwards. Eqn (10) was
derived for spherical objects with uniform mass density but
has to be modified to describe a core/shell droplet, which
consists of the PM shell with the mass density rshell > rf andthe oil core with the mass density rcore o rf. If the core/shell
Fig. 3 SEM image of BSA-stabilized sunflower oil microdroplets
additionally coated with 8 alternate PAH/PSS layers.
Fig. 4 Force diagram for core/shell particle moving vertically
upwards with settling velocity v in the continuous fluid. Arrows are
vectors indicating directions of forces. Fg is the gravitational force,
Fd is the frictional force acting opposite to the direction of particle’s
movement, FA is the buoyant force acting vertically upwards, rp is
the overall radius of the core/shell particle, rcore is the radius of
the oil core.
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particle possesses vertical motion in viscous fluid (Fig. 4), the
forces applied can be determined as follows:
Fg ¼ mg ¼ 4
3pr3corercoregþ
4
3pðr3p � r3coreÞrshellg
¼ 4
3pr3coreg rcore þ rshell
r3p
r3core� 1
!" #;
ð11Þ
FA = 43pr3prfg, (12)
Fd = 6pZlrpv (13)
where Fg is the gravitational force, Fd is the frictional force
acting opposite to the direction of particle motion, FA is the
buoyant force acting vertically upwards, rp is the overall radius
of the core/shell particle, rcore is the radius of the oil core.
When the frictional force combined with the buoyant force
exactly balances the gravitational force (Fd + FA + Fg = 0)
the settling velocity
v ¼ �2gr2p
9Zl½rcorA3 þ rshellð1� A3Þ � rf � ð14Þ
is reached. A in eqn (14) is the index of core/shell particle
geometry determined as the ratio between the shell’s thickness
and the overall particle’s radius: A = 1 � d/rp, where d is the
mean thickness of the multilayer shell. The sign in (14)
indicates the direction of particle movement, where ‘�’ and‘+’ correspond to the particles moving vertically upwards and
downwards, respectively.
The shell thickness was determined in accordance to the
data reported in ref. 21, 37 and 38, considering the mean
thickness of one polyelectrolyte layer to be 2 nm in the case of
multilayer assembly in salt-free polyelectrolyte solution. The
thickness of a BSA layer was taken as 10 nm.21 Thus, the
overall thickness of the multilayer shell d varies approximately
from 14 nm to 26 nm for 2–8 PAH/PSS layers, respectively. It
can be clearly seen that for core/shell particles of the same
overall radius, the size parameter A decreases with the increase
of the total number of layers in the shell. If the thickness of the
coating shell is negligible compared to the overall particle
radius (D - 0, A - 1), the settling velocity in (14) tends to
nStokes’ determined by (10).
Eqn (14) represents the Stokes’ lawmodified to describemotion
of the isolated oil droplet coated with the polyelectrolyte shell.
Applicability of (14) is limited to the highly diluted suspensions,
where the volume fraction of droplets does not exceed 0.01.21
At the higher particles’ concentrations, motion velocity
decreases due to additional droplet–droplet collisions. To
take this effect into account, the following specification was
introduced:32
V ¼ n 1� jjc
� �kjc
ð15Þ
where n is defined from (14), jc is the volume fraction of
core/shell particles in the state of close-packing, and k is the
non-dimensional parameter, whose value depends on the
droplet’s type. The value of k = 8 was taken for quantitative
calculations accordingly reported elsewhere.32 The simulations
done by Shi et al.39 give jc = 0.591 for the spherical particles
having the same size distribution as shown in Fig. 1. Mass
densities of the continuous phase (water) and sunflower oil
were taken as rf = 1000 kg m�3 and rcore = 910 kg m�3,
respectively, and the shear viscosity was Zl = 1 mPa s. The
unknown value of the shell’s mass density (rshell) and the size
parameter A were varied. The simulated curves displaying the
settling velocity versus the size parameter A for selected values
of shell mass density are shown in Fig. 5. If rshell is close to rf,the velocity curve is a hyperbola (Fig. 5, curves 1 and 2). Its
value has a positive sign in the whole range of size parameter’s
values (AE 0.85–1), that means droplets in the corresponding
suspension are moving vertically upwards at any core’s
size and shell’s thickness. The settling velocity of oil droplets
coated with the denser shells (Fig. 5, curves 3 and 4) can be of
positive or negative sign depending on the value of size
parameter A.
Table 1 displays the radius of the oil core coated with
8 polyelectrolyte layers, when the settling velocity of corres-
ponding particles turns to zero value, or in other words, when
the particles are floating in fluid without possessing vertical
motion. It can be seen that the core/shell particles having
radius o 250 nm or o350 nm will move downward if the
shell’s mass density is 1200 kg m�3 and 1300 kg m�3, accordingly.
In our experiments, a tiny layer of sediment was observed after
long-term incubation of (PSS/PAH)4 microcapsules. The frac-
tion of deposited core/shell particles was about 10% of the
overall amount of particles in the sample. Thus, taking into
account the particle size distribution (Fig. 1), the mass density
of the PSS/PAH shell should not exceed rshell E 1200 kg m�3.
The coating shell’s impact to the creaming velocity was
experimentally investigated by means of the time dependent
Fig. 5 Settling velocity versus size parameter (A) at selected values of
mass density of the coating shell: 1000 kg m�3 (1), 1100 kg m�3 (2),
1200 kg m�3 (3), 1300 kg m�3 (4).
Table 1 The core’s radius of core/shell particles not possessingvertical motion. (The calculations are done for the shell comprising8 polyelectrolyte layers.)
rshell/kg m�3 Av=0 rcore/nm (n = 8)
1010 — —1100 — —1200 0.88 2501300 0.92 350
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This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 4005–4012 4011
measurements of cream height. The time plots obtained from
the suspensions of 2, 4, 6 and 8 polyelectrolyte layers coated
oil/BSA droplets are shown in Fig. 6. The cream layer’s height
is presented as a percentage with respect to the total height of
suspension in the cell. Cream height increases linearly with
time (Fig. 6). The experimental data collected from the
suspensions of 2 or 4 layers coated microdroplets can be least
square fitted with a single curve (Fig. 6, curve 1), indicating no
substantial difference in the separation process for these
samples. Analogously, just one line fits the data points measured
from the suspensions of microdroplets having 6 or 8 poly-
electrolyte layers in the shell (Fig. 6, curve 2). However, the
slope of curve 2 is remarkably (more than 2 times) higher than
that of curve 1 (see the corresponding linear regressions in Fig. 6).
Thus, there is a threshold increase of creaming velocity with
the number of layers in the shell. The mean values of creaming
velocity derived from curve 1 and curve 2 areB5.6 nm s�1 and
B2.0 nm s�1 respectively. For comparison, the creaming
velocity in uncoated monodisperse emulsion of n-hexadecane
(r = 773 kg m�3, and droplets’ mean radius of rm = 0.86 mm)
was B140 nm s�1 for the volume fraction 0.1.21 The reported
value is approximately 25 times higher than that observed
in our experiment revealing the impact of the coating shell
and particles’ polydispersity to the speed of gravitational
separation.
It is worth to mention the other means of coating shell’s
contribution to the speed of gravitational separation, which
was not considered in the model. The polyelectrolyte film at
the oil/water interface alters the properties of phase boundary
and in consequence influences the hydrodynamic slipping. For
instance, liquid particles are known to move faster than solids
with the same parameters because of reduced friction force
increasing their fluidity.37 In our case, oil droplets are coated
with the PM shell of higher mass density, which may reduce
the slip effect and slow down the velocity of vertical motion
compared to uncoated oil droplets. Moreover, due to its
mechanical nature, the hydrodynamic slipping may depend
on the surface morphology. Thus, the experimentally observed
non-monotonous dependence of the creaming index (see Fig. 6)
can be to some extent a result of inhomogeneous adsorption of
polymer molecules on the particle’s surface typical of the LbL
process.34,40
Conclusion
In this study, we theoretically predicted the range of poly-
electrolyte concentrations for flocculation-free Layer-by-
Layer coating of microparticles dispersed in the continuous
phase, taking into account their size distribution. In the
particular case of 10% v/v water-dispersed droplets of sunflower
oil, the system will be stable when the polyelectrolytes poly-
(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride)
are added in the concentration range of 0.28 mg ml�1–
2.59 mg ml�1 and 0.38 mg ml�1–2.15 mg ml�1, respectively.
Successful assembly of the PAH/PSS shell was demonstrated
using the polyelectrolytes in concentration within the predicted
ranges.
The dependence of the gravitational separation process
on the thickness of the polyelectrolyte multilayer shell has
been theoretically modeled and experimentally measured.
Comparing the theory and experimental data, the poly-
electrolyte shell’s mass density is determined to be close to
but not exceed 1200 kg m�3.
The proposed theoretical model and experimental observations
demonstrate the possibility to control the gravitational separa-
tion process of suspensions where each oil droplet is encapsulated
in the polyelectrolyte multilayer shell by varying the shell’s
thickness and mass density. As the number of materials to
be used for multilayer shell assembly may be limited, the
optimization of the shell’s thickness seems to be the simpler
way to control the kinetic stability of suspensions. The results
of this study on controlling the kinetic stability have an impact
for the development of formulations based on oil-in-water
emulsions.
Appendix A
Nomenclature
A index of the core/shell particle geometry
b monomer size
CAds adsorption polyelectrolyte concentration
CDep polyelectrolyte depletion concentration
CSat polyelectrolyte saturation concentration
CPE concentration of the polyelectrolyte in the
continuous phase
Cfree concentration of the free polyelectrolyte
D translation diffusion coefficient
FA buoyant force
Fd frictional force
Fg gravitational force
g gravitational acceleration
K coagulation constant
k non-dimensional parameter
M molar mass
Mm molar mass of the monomer unit
NA Avogadro’s number
ni particle number
P log-normal distribution function
Fig. 6 Measured data (symbol) and linear fit (solid line) displaying
the height of cream upper column versus the observation time. Total
number of polyelectrolyte layers in the coating shell: 2 (’), 4 (J),
6 (m), 8 (,).
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4012 Phys. Chem. Chem. Phys., 2011, 13, 4005–4012 This journal is c the Owner Societies 2011
P0 initial probability
rcore radius of the oil core
rdr radius of the oil droplet
ref effective molecular radius
ri radius of the ith droplet
rp overall radius of the core/shell particle
rm mean radius of the oil droplets
Sef effective molecular square
Si surface area of the ith droplet
U number of monomers between effective charges
V motion velocity of the core/shell particle
Vi volume of the ith droplet
w standard deviation
Gsat surface density of the adsorbed layer
z zeta potential
Z viscosity of the continuous phase
Zl shear viscosity
nStokes’ Stokes’ settling velocity of the oil droplet
rcore mass density of the oil core
rdr mass density of the oil droplet
rf mass density of the continuous liquid phase
rshell mass density of the polyelectrolyte multilayer shell
tAds time of polyelectrolyte adsorption
tCol time of particles collision
u effective molar volume of the polyelectrolyte in
the continuous phase
j volume fraction of the oil droplets
jc volume fraction of the core/shell particles
Acknowledgements
We are grateful to the Institute of Materials Research and
Engineering of A*STAR (Agency for Science, Technology and
Research), Singapore, for providing financial support.
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