Early Dynamics and Stabilization Mechanisms of Oil-in-Water

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Early dynamics and stabilization mechanisms of oilin-water emulsions containing colloidal particles modified with short amphiphiles: a numerical study. Manuella Cerbelaud, Arnaud Videcoq, Lauriane Alison, Elena Tervoort, and André R. Studart Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03472 • Publication Date (Web): 27 Nov 2017 Downloaded from http://pubs.acs.org on December 2, 2017

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Early dynamics and stabilization mechanisms of oil-in-water emulsions containing colloidal particles modified with short amphiphiles: a numerical study. Manuella Cerbelaud,∗,† Arnaud Videcoq,† Lauriane Alison,‡ Elena Tervoort,‡ and Andr´e R. Studart∗,‡ Univ. Limoges, CNRS, SPCTS, UMR 7315, F-87000 Limoges, France, and Complex Materials, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland E-mail: [email protected]; [email protected]

Abstract Emulsions stabilized by mixtures of particles and amphiphilic molecules are relevant for a wide range of applications, but their dynamics and stabilization mechanisms at the colloidal level are poorly understood. Given the challenges to experimentally probe the early dynamics and mechanisms of droplet stabilization, Brownian dynamics simulations are developed here to study the behavior of oil-in-water emulsions stabilized by colloidal particles modified with short amphiphiles. Simulation parameters are based on an experimental system that consists of emulsions obtained with octane as oil phase and a suspension of alumina colloidal particles modified with short carboxilic acids as ∗

To whom correspondence should be addressed Univ. Limoges, CNRS, SPCTS, UMR 7315, F-87000 Limoges, France ‡ Complex Materials, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland †

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continuous aqueous medium. The numerical results show that attractive forces between the colloidal particles favor the formation of close packed clusters on the droplet surface or of a percolating network of particles throughout the continuous phase, depending on the amphiphile concentration. Simulations also reveal the importance of a strong adsorption of particles at the liquid interface to prevent their depletion from the droplet surface when another droplet approaches. Strongly adsorbed particles remain immobile on the droplet surface, generating an effective steric barrier against droplet coalescence. These findings provide new insights into the early dynamics and the mechanisms of stabilization of emulsions using particles and amphiphilic molecules.

Introduction Emulsions are of great scientific and technological interest due to their widespread use in a variety of applications ranging from foods and pharmaceuticals to paints, inks, cosmetics and industrial processes. 1 In all these applications, it is necessary that the emulsions keep their properties over long periods of time. However, such requirement is often difficult to meet because the thermodynamically unstable nature of droplets makes them diffuse, coalesce and coarsen over time. To obtain stable emulsions, long-chain surfactants, amphiphilic polymers, lipids or proteins are generally added to formulations to modify the liquid-liquid interface and thus slow down coalescence and coarsening processes. Alternatively, Ramsden and Pickering have demonstrated more than one century ago that solid particles can also be used to effectively stabilize emulsions. 2,3 Stabilization of emulsions in this case is achieved by the adsorption of the particles at the liquid-liquid interface, which occurs when they are partially wetted by the two immiscible liquids. The interfacial adsorption of such solid particles markedly increases the stability of emulsions compared to surfactant stabilized systems. 4,5 This stability is attributed to the strong adsorption energy of the colloids at the liquid-liquid interface, which depends on the contact 2


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angle θ of the particles at the interface. If θ is lower than 90◦ stabilization of an oil-in-water emulsion is obtained, whereas a contact angle θ larger than 90◦ , enables the stabilization of a water-in-oil emulsion. 1 A theoretical analysis considering both adsorption energies and capillary forces, suggests that a contact angle between 70 and 86◦ should lead to very stable oil-in-water emulsions. 6 However, this theoretical estimate is obtained assuming equilibrium conditions that are not fulfilled at the early stage of stabilization. In addition to an appropriate contact angle, experimental studies have shown that droplets should be sufficiently covered by colloidal particles to form a steric barrier that prevents thinning of the liquid film that separates approaching droplets. 7–9 Several approaches have been utilized to produce Pickering emulsions either using chemically functionalized particles 10–13 or synergistic interactions between particles and surfactants. 4,14,15 In one example of such experimental systems, Akartuna et al. produced very stable octane-in-water emulsions using alumina particles modified by short amphiphiles such as carboxylic acids containing 5 or less carbons. 4 Experimental results show that the stability of these emulsions depends on the concentration and on the nature of the amphiphile used to modify the alumina particles. Generally, stable emulsions are obtained when the amphiphile concentration lies between two limits. The lower limit is defined by the amount of amphiphiles necessary to generate alumina particles with sufficient hydrophobicity to adsorb at the oil-water interface. The upper limit is given by the concentration of amphiphiles above which the alumina particles become too hydrophobic and aggregate into a highly viscous structure that can no longer be emulsified. The longer the amphiphile is, the lower are these two limit concentrations. Mixtures of particles and amphiphilic molecules within such optimum concentration range have been exploited as a versatile approach to produce Pickering emulsions and foams. 16,17 However, the complexity of the system and the experimental difficulties to probe the multiple interactions that can occur between the involved building blocks, makes it very difficult to understand the early dynamics of the stabilization process. Understanding such early dynamics would help establish the limits of the reported

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experimental systems and could provide insights on the applicability of such stabilization mechanism to emulsification and foaming approaches involving short timescales, such as in microfluidic emulsification and high-energy homogenization. In this paper, we use Brownian dynamics simulations to study the interactions between the various components of complex Pickering emulsions and thus shed light on the early dynamics and mechanisms of the stabilization process involving particles and amphiphiles. The simulation parameters are obtained from the experimental characterizations reported in our earlier work. 4 First, the interaction potential between the emulsion constituents is calculated and the simulation method is described. This is followed by the investigation of the role of the concentration and of the nature of the amphiphile, as well as the particle concentration, on the colloidal behavior of particles around the droplets. Finally, interactions between particle-coated droplets will be discussed, with focus on the role of the strong interfacial adsorption of particles in preventing the coalescence of droplets at an early stabilization stage.

Modeling of the experimental system Experimental system The experimental system used in this study is described in detail in previous work by Akartuna et al . 4 In this paper, we briefly describe such system, highlighting the parameters that are used in the simulations. The experimental system consists of an oil-in-water emulsion prepared through the addition of octane into a suspension of alumina particles modified with short amphiphiles at pH 4.75. In the simulations, droplets of octane are considered as non-deformable spherical droplets with a diameter of 7 µm or 10 µm and a density of 703 kg m−3 . 18 Alumina particles are considered spherical with a diameter of 200 nm and a density of 3980 kg m−3 . To model the interactions that occur in the emulsion, the surface charge of such droplets and particles is 4


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required. Here, we use zeta potential measurements reported in the literature as an approximation of the electrical surface potential arising from surface charges. The evolution of the zeta potential of small oil droplets as a function of pH is extracted from previously reported data. 18 At pH 4.75, the oil droplets are negatively charged and have a zeta potential ζoctane of -32 mV. 18 The zeta potential of the alumina particles is affected by the surface adsorption of carboxilic acids. In this paper, two kinds of carboxilic acids are used: propionic acid (3 carbon atoms) and valeric acid (5 carbon atoms). The zeta potential of alumina particles change according to the nature and the concentration Ca of the amphiphiles, as reported by Studart et al. 19 Importantly, the different hydrophobicities of the two amphiphiles is captured through their distinct effect on the zeta potential of the particles. The more hydrophobic valeric acid molecules are able to compress the electrical double layer around the particles more effectively as compared to the less hydrophobic propionic acid molecules. This results in lower zeta potential values for particles coated with valeric acid in comparison to those containing propionic acid for the same added amphiphile concentration. 19 This feature of the investigated colloid-amphiphile systems enables us to describe the behavior of the complex emulsion without directly invoking poorly-understood hydrophobic interactions. The different values of zeta potential used in this numerical study are summarized in Table 1. Interactions between particles and droplets within the emulsion are also affected by the concentration of ions in the aqueous phase. At pH 4.75, one-half of the carboxylic groups of the amphiphile molecules is deprotonated. As a result, the concentration of ions in the emulsion is approximated by half of the amphiphile concentration : Ci =Ca /2 (see Table 1). Finally, the energy of adsorption of modified particles on the surface of the oil droplets depends on the interfacial tension of the octane-water interface (γwo ). Here, a γwo value of 50.8 mN m−1 was assumed for the octane-water interface. 20

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Table 1: Ionic concentration in the aqueous phase of the emulsion Ci and ζ potential of the modified alumina particles as a function of the nature and of the concentration Ca of the amphiphile. Amphiphile Ø propionic acid propionic acid propionic acid propionic acid propionic acid valeric acid valeric acid valeric acid valeric acid valeric acid

Ca (M) 0 5 × 10−3 1 × 10−2 3 × 10−2 1 × 10−1 2 × 10−1 5 × 10−3 9 × 10−3 1 × 10−2 1 × 10−1 2 × 10−1

Ci (M) 10−3 2.5 × 10−3 5.0 × 10−3 1.5 × 10−2 5.0 × 10−2 1.0 × 10−1 2.5 × 10−3 4.5 × 10−3 5.0 × 10−3 5.0 × 10−2 1.0 × 10−1

ζAl2 O3 (mV) +45 +40 +40 +30 +20 +15 +25 +20 +20 +3 -2

Interaction potentials In this system, three different interactions are taken into account: interactions between two colloids, between one colloid and one oil droplet and between two oil droplets (see Figure 1a). All these interactions are described by a DLVO (Derjaguin, Landau, 21 Verwey and Overbeek 22 ) potential, which is the sum of an attractive potential due to van der Waals forces (here the Hamaker potential VijvdW 23 ) and a potential that describes the electrostatic interactions (here the HHF potential Vijel 24 ): VijDLVO = VijvdW + Vijel

(1)

with

VijvdW

2 rij − (ai + aj )2 2ai aj 2ai aj Aij + + ln 2 =− 6 rij2 − (ai + aj )2 rij2 − (ai − aj )2 rij − (ai − aj )2

6


(2)

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and

Vijel

= πaeff

ψi2

+

ψj2

2ψi ψj ln ψi2 + ψj2

1 + exp(−κhij ) 1 − exp(−κhij )

+ ln (1 − exp(−2κhij ))

(3)

where Aij is the Hamaker constant, is the dielectric constant of the solvent, κ is the inverse Debye length, hij is the surface to surface distance between particles i and j, rij is the center to center distance between particles i and j, ai and aj are the radii of the particles i and j, respectively, and aeff = ai aj /(ai + aj ). ψi and ψj are the surface potentials of particles i and j, respectively, which are approximated here by the zeta potential. The following Hamaker constants for alumina-alumina, octane-octane and octane-alumina interactions in water are √ used: AAA = 4.76 × 10−20 J, 25 AOO = 0.4 × 10−20 J 26 and AAO = AOO AAA = 1.38 × 10−20 J, respectively. κ is given by: s κ=

2e2 z 2 NA Ci kB T

(4)

where e is the elementary charge, z is the valence of ions (here z = 1), Ci is the ionic concentration, NA is the Avogadro’s constant, kB is the Boltzmann constant and T is the temperature (here T = 293 K). In our model, the presence of carboxylic acid on the alumina particles or in the continuous aqueous phase is only taken into account through the changes in zeta potential and ionic concentration caused by the effect of such molecules. As explained earlier, these two properties change indeed as a function of the nature and of the concentration of the acid. No explicit modeling for the carboxylic acid is introduced. Because the DLVO potential becomes infinitely attractive at small interparticle distance, we cut the calculated curves at an arbitrary potential value to avoid divergence in the simulations. For the interactions between two alumina particles or between two oil droplets, the DLVO potential is cut at −14 kB T and a repulsive linear potential is added to prevent unrealistic interpenetration when the particles come into contact. This procedure was chosen 7


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because it has been proven to capture the physics underlying heteroaggregation between colloids. 27,28 As opposed to interparticle and interdroplet interactions, the potential energy governing the interactions between droplets and particles at short separation distances is strongly affected by the possible adsorption of the particle at the oil-water interface. Due to their opposite charges, alumina particles are attracted by the oil droplets until contact is made. To avoid divergence at the contact, the interaction potential between one alumina particle and one oil droplet is also cut at −14 kB T . However, in this case, different scenarios are considered. In a first scenario, the alumina particles are hydrophobic and can thus penetrate the oil droplet, replacing part of the oil-water interface by two new solid-liquid interfaces. The extent of penetration into the droplet depends on the contact angle (θ) of the particle at the oil-water interface. In this study, we will consider an extreme case where θ = 90◦ to describe the scenario where strong interfacial adsorption of the alumina particles is assumed (see Figure 1b). Thus, when oil and alumina are in contact, an adsorption potential defined as follows is added in this case 29 :

Vattach =

πγwo a2A

z2 −1 aA

(5)

where γwo is the octane/water interfacial tension and z is the distance between the center of the alumina particle and the surface of the oil droplet (see Figure 2). In between the DLVO and the adsorption potentials, an attractive linear potential is added to ensure continuity of the curves. The DLVO potential, which diverges at short separation distance is indeed always cut before the contact between the particle and the droplet. The coefficient of the linear potential is then chosen such as coef f = ((Vc − Vadh )/(rc − radh ), with Vc = −14 kB T , rc being the distance at which the DLVO potential is cut, radh = 0.9999(aA + aO ) and Vadh being the value of Vattach at radh . In a second scenario, the alumina particles are considered to be hydrophilic and thus do not

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penetrate the oil droplet, forming a contact angle of θ = 0◦ at the interface (see Figure 1b). The adsorption of the alumina on the oil-water interface is weak in this case. As for the potential between two alumina particles, only a repulsive linear potential is added at the contact to avoid interpenetration between the alumina particles and the oil droplet. This scenario represents an experimental system in which the zeta potential of the particles and the ionic concentrations in the aqueous medium are determined by fully hydrophilic species rather than the amphiphilic molecules considered in the first case.

(a)

(b)

Figure 1: (a) Interactions that occur in the system at an early stage of the emulsion stabilization process: I→ colloid-colloid, II → colloid-oil droplet and III → oil droplet-oil droplet; (b) Summary of the two different adsorption cases considered in the simulations.

While an exact description of the experimental system would have to take into account the variation of the contact angle with the amphiphile content, 30,31 we perform simulations for θ of 0 and 90◦ to understand the colloidal behavior of the emulsions in two extreme scenarios. With this approach, we also neglect the fact that optimum stabilization is expected for a contact angle ranging from 70 to 86◦ . Such a simplification is reasonable because it only mildly affects the adsorption energy, which is in all cases much higher than the other energies used in the simulations. Finally, possible attractive or repulsive interactions arising from unequal charging

32

or the different dielectric properties of the aqueous and oil media are

also ignored. These assumptions imply that our numerical results should be interpreted in a 9


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0 -50000 -100000 -150000

Vattach/kBT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-200000 -250000 -300000 -350000 -400000 0.94 0.95 0.96 0.97 0.98 0.99 rij/(aA+aO)

1

1.01

Figure 2: Adsorption potential Vattach of one alumina particle onto the oil droplet for the case when particles are assumed to replace part of the oil-water interface. The high value of the well-depth effectively prevents the desorption of alumina particles from the liquid interface. qualitative manner, as first order approximations of the behavior of these complex colloidal systems.

Simulation methods The experimental system is simulated by Brownian dynamics according to the method developed by Cerbelaud et al. 27 In this method, the solvent is regarded as a continuum medium and its effect upon the particles is modeled by a combination of frictional and random forces. The particle motion is thus described by the Langevin equation:

mi

X dvi (t) = −ζi vi (t) + Fij {rij (t)} + Γi (t) dt j

(6)

with mi and vi being the mass and the velocity of particle i respectively, and ζi = 6πηai is the friction coefficient, which depends on the particle radius ai and on the solvent viscosity η (here η = 10−3 Pa.s for water). Fij {rij (t)} represents the force between the pairs of particles which derives from the interaction potentials (Fij = −∇Vij ). Γi is the random force obeying

10


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the following statistical properties:

hΓi (t)i = 0 and hΓi (t)Γj (t0 )i = Cδ(t − t0 )δij

(7)

C = 2kB T ζi to satisfy the thermal equilibrium condition, the first δ is the Dirac distribution and the second one δ is the Kronecker symbol. The particles trajectories are obtained by numerically integrating the Langevin equation using the algorithm developed by Mannella and Palleschi. 33 In this study, a time step of δt = 10−8 s is used. This time step is lower than the velocity relaxation time of the oil droplets τv . Considering that τv = mi /ζi , relaxation times of 3.9×10−6 s and 1.9×10−6 s were calculated for droplets of 10 and 7 µm, respectively. This allows for full integration of the Langevin equation. The velocities and positions of oil droplets in each spatial direction evolve as follows: √ vi (t + δt) = vi (t) +

1 2kB T ζi (δt)1/2 Yi + mi mi

! −ζi vi (t) +

X

Fij {rij (t)} δt

(8)

j

ri (t + δt) = ri (t) + vi (t)δt

(9)

where Yi are uncorrelated Gaussian-distributed random numbers with an average of zero and a standard deviation of 1. In equations 8 and 9, the index i stands for both for the particle index and the space direction. By contrast, the time step is larger than the relaxation time of the modified alumina particles (τv = mi /ζi = 8.8 × 10−9 s). Considering that the acceleration can be neglected in the Langevin equation, the Ermak algorithm is therefore used for the alumina particles in each spatial direction: 34 s ri (t + δt) = ri (t) +

1X 2kB T (δt)1/2 Yi + Fij {rij (t)}δt ζi ζi j

(10)

Simulations are performed in a cubic box with periodic boundary conditions. Initially, particles are randomly placed in the box avoiding overlapping. The initial velocity of each oil

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droplet is randomly chosen such as its norm is equal to

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p

(3kB T )/mi .

Simulations snapshots were obtained by VMD, a molecular graphics program originally designed for the interactive visualization and analyses of biological materials, developed by the Theoretical Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign. 35

Results and discussion In the following, we first discuss the colloidal interactions between the different building blocks present in the complex emulsion. Second, simulations are performed with a single oil droplet to understand the assembly of colloidal particles with different amphiphile concentrations at the oil-water interface. Next, we investigate the interactions between two particle-coated droplets for one selected amphiphile concentration to evaluate the role of particle adsorption at the oil-water interface in the stabilization of the emulsion.

Analysis of the interaction potentials The presence of carboxylic acid changes the zeta potential of the particles and the ionic strength of the aqueous medium. This modifies the interactions between the emulsion constituents. The DLVO potentials for the interactions between two modified alumina particles, between one modified alumina particle and one oil droplet and between two oil droplets are plotted in Figures 3, 4 and 5 respectively, for different concentrations of propionic and valeric acid. In all cases, the interactions between the modified alumina particles and the oil droplets are attractive, whereas the interactions between two modified alumina particles depend on the nature and on the concentration of the amphiphile. For both types of amphiphiles, the interactions between the modified alumina are repulsive at low concentrations, but they eventually become attractive when the concentrations are increased. Figure 3 shows also that for the same concentration of amphiphiles, particle interactions are more attrac-

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tive with the valeric acid compared to the propionic acid. Droplet-droplet interactions are strongly repulsive at short distances, but the presence of a secondary well at larger separations suggests that droplets might weakly agglomerate in the emulsion. These distinct interactions directly affect the behavior of the particles and droplets in the early stages of the stabilization process, as discussed below.

60

60

Ca = 5x10-3 M Ca = 1x10-2 M Ca = 3x10-2 M -1 Ca = 1x10-1 M Ca = 2x10 M

(a) 50 40

50 40

30 20 10

30 20 10

0

0

-10

-10

-20 0.95

1

1.05 1.1 rij/(2aA)

1.15


(b)

VDLVO/kBT

VDLVO/kBT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-20 0.95

1.2

1

1.05 1.1 rij/(2aA)

1.15

1.2

Figure 3: DLVO interaction potential V DLVO between two modified alumina particles as a function of the dimensionless center-to-center separation distance for different amphiphile concentrations (Ca ) in case alumina particles are modified with propionic acid (a) and valeric acid (b).

Interactions between particles around a droplet Simulations are first performed with one oil droplet of 10 µm and 5000 modified alumina particles. The volume fraction of alumina particles in the aqueous phase is fixed at 3.3 v% (volume of alumina particles/ (volume of water + volume of alumina particles)). In this simulation, alumina particles are considered hydrophobic and, thus, they can absorb onto the oil droplet with a contact angle of θ= 90◦ . Different concentrations of propionic and valeric acids are considered. For each concentration, the particle-particle and the droplet-particle interactions change according to the 13


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20

10


(b)

15 10

5

VDLVO/kBT

VDLVO/kBT

20


(a)

15

0 -5

5 0 -5

-10

-10

-15

-15

-20

-20 1

1.002

1.004 1.006 rij/(aA+aO)

1.008

1.01

1

1.002

1.004 1.006 rij/(2aA+aO)

1.008

1.01

Figure 4: DLVO interaction potential V DLVO between one modified alumina particle and one oil droplet of 10 µm as a function of the dimensionless center-to-center separation distance for different amphiphile concentrations (Ca ). In (a) alumina particles are modified with propionic acid and in (b) alumina particles are modified with valeric acid.

2500

10


(a) 2000

5

1500

1000

500

0

-5

-10

0 0.998


(b)

VDLVO/kBT

VDLVO/kBT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1

-15 0.995

1.002 1.004 1.006 1.008 1.01 rij/(2aO)

1.005

1.015 1.025 rij/(2aO)

1.035

Figure 5: (a) DLVO interaction potential V DLVO between two oil droplets of 7 µm as a function of the dimensionless center-to-center separation distance for different amphiphile concentrations (Ca ). Graph (b) is a magnification of the secondary minimum of the curves shown in (a).

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Propionic acid

5.10-3M

1.10-2M

3.10-2M

1.10-1M

2.10-1M

9.10-3M

1.10-2M

1.10-1M

2.10-1M

Valeric acid

5.10-3M

Figure 6: Snapshots of Brownian dynamics simulations obtained at t = 3 s. Simulations are performed with one oil droplet (in red) and 5000 alumina particles (in blue) modified with different concentrations of propionic and valeric acid.

3.10-2 M 1.10-1 M

5.10-3 M 1.10-2 M

50 45 40 35 30 25 20 15 10 5 0

2.10-1 M

(a)

0

0.5

1

1.5 2 time (s)

2.5

1.10-2 M 1.10-1 M

5.10-3 M 9.10-3 M

Scov (%)

Scov (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3

50 45 40 35 30 25 20 15 10 5 0

2.10-1 M

(b)

0

0.5

1

1.5 2 time (s)

2.5

3

Figure 7: Fractional area of droplets covered with adsorbed particles as a function of time for different concentrations of amphiphiles : (a) propionic acid and (b) valeric acid. Results are obtained for one oil droplet and 5000 alumina particles. The coverage is defined as the number of adsorbed particles multiplied by the area of their central section divided by the area of the oil droplet.

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calculations shown in the previous section (see Figures 3 and 4). Snapshots of emulsion simulations obtained at t = 3 s for the different concentrations of propionic and valeric acids are displayed in Figure 6. The assembly and arrangement of the alumina particles around the droplet change significantly depending on the concentrations and the nature of the carboxylic acids. However, we observe the same overall trend as the amount of amphiphile is increased. At low amphiphile concentrations, particles form a homogeneous layer on the surface of the droplets and remain well-dispersed due to electrostatic repulsive interactions. Higher amphiphile concentrations reduce the repulsive forces between particles, leading to the formation of close-packed particle arrays on the surface of the droplets. A further increase in the amphiphile content results in extensive agglomeration of the particles in the continuous aqueous phase, eventually reducing the droplet surface coverage.

The qualitative information provided by the simulation snapshots is confirmed by the quantitative analysis of the fractional area of droplets covered with adsorbed particles Scov (Figure 7). The surface coverage is defined as the number of adsorbed particles Nads multiplied by the area of their central section divided by the area of the oil droplet ( Scov = Nads a2A /(4a2O )). At low amphiphile concentrations, large amounts of particles adsorb at the oil-water interface, leading to droplet surface coverages up to 45-50%. A reduction in droplet surface coverage by a factor of 4 to 5 occurs at higher amphiphile concentrations (Figure 7). This is caused by the change in the nature of the interactions between the particles from repulsive to attractive (Figure 3). In agreement with the interaction potential calculations, such a transition is observed at a relatively narrow range of amphiphile concentrations. For propionic acid, a twofold drop in surface coverage happens at Ca values between 1 × 10−2 and 3 × 10−2 M. Due to its stronger screening effect over the zeta potential of the particles, a major reduction in droplet coverage for valeric acid is observed at lower amphiphile concentrations in a very narrow range between 9 × 10−3 and 3 × 10−2 M. In addition to surface coverage, we also analyzed the trajectory of representative particles

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adsorbed on the droplet surface for propionic acid concentrations spanning over the transition range (Figure 8(a)). At the Ca value of 5 × 10−3 M, before the transition, particles are found to be very mobile, despite the high droplet surface coverage. A quantitative analysis of the mean square displacement gives a diffusion coefficient of 7.8 × 10−13 m2 s−1 (Figure 8(b)). This is explained by the highly repulsive interactions and the high energy barrier against agglomeration predicted for this concentration (Figure 3). Conversely, the mobility of the surface-adsorbed particles is much lower at the transition concentration of 3 × 10−2 M. The diffusion coefficent decreases in this case to 4.8 × 10−14 m2 s−1 , which is a factor of ten lower compared to the previous case. In this case, the interaction potential energy curve predicts a weak agglomeration of particles around a secondary well, leading to the formation of close packed clusters in the form of patches on the surface of the droplets. A higher concentration of such clusters would be expected on the surface of the droplets if the simulations would have involved a larger total number of particles. Time-lapse videos of the simulations show that these trajectories are representative of the behavior of the other particles (See Movies S1 and S2 in the Supporting Information).

0.1 0

3.5⋅10-12

Ca = 5x10-3 M Ca = 3x10-2 M

(a)

3.0⋅10 ++ (m2)

-0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

2.5⋅10-12 2.0⋅10-12 -12

1.5⋅10

-12

1.0⋅10

5.0⋅10-13

-0.9 -1 -0.3 -0.2 -0.1

Ca = 5x10-3 M Ca = 3x10-2 M

(b)

-12

-0.1

y (µm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

0

0.1 0.2 0.3 0.4 0.5 0.6

0

x (µm )

0.1

0.2

0.3

0.4

0.5

0.6

t (s)

Figure 8: (a) Trajectories and (b) mean square displacement of representative alumina particles adsorbed on the oil droplets over a time period of 0.5 s. Simulations were performed for alumina particles modified with propionic acid. At an amphiphile concentration Ca = 3 × 10−2 M the alumina particle belongs to a patch as opposed to a fully dispersed state when Ca = 5 × 10−3 M. The mean square displacement is averaged over 20 particles.

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Although the simulations discussed so far were performed with a contact angle of θ = 90◦ it is known from experiments that this angle varies with the amphiphile concentration. 36 To investigate the effect of the contact angle on the assembly of particles around a single oil droplet, we performed additional simulations in which particles modified with propionic acid were assumed to display θ = 0◦ . Our results show that the arrangement of particles at the oil-water interface and throughout the aqueous continuous phase is not significantly affected by the contact angle of the particles (see Figure 9). To understand the surprising observation that the configuration of particles is not influenced by the contact angle, we consider the different possible interaction potential energies between the particles and droplets at increasing modifier concentrations. At high amphiphile concentrations, particles agglomerate extensively throughout the continuous phase and remain trapped in a kinetically arrested network. Instead, at low and intermediate concentrations of amphiphiles, the particles are not completely trapped into strong agglomerates in the continuous phase and thus can interact with the surface of the oil droplets. Because the attractive potential energy between the particles and droplets amounts to more than 14 kB T for all amphiphile concentrations (Figure 4), even particles that do not penetrate into the oil-water interface (θ = 0◦ ) will be very strongly adsorbed on the droplet surface. To estimate the effect of this purely electrostatic attractive interactions, we estimate the dissociation rate (r) of the particle from the droplet surface from transition state theory: 37 r = ω 2 τv /(2π) exp(−E/kB T ), where ω is the angular frequency in the minimum, τv is the velocity relaxation time, E is the interaction potential energy, kB is the Boltzmann constant and T is the absolute temperature. For E = 14 kB T , τv = 8.8 × 10−9 s and ω = 6.5 × 105 rad s−1 , we find a desorption rate at room temperature on the order of 5 × 10−4 s−1 . This effectively means that particles are expected to strongly adsorb on the surface of the droplets even if θ = 0◦ . It is important to note that if the particles and the droplets show repulsive interactions (alike charges), the scenario changes significantly for one in which the contact angle is likely to play a more decisive role. Besides the effect of the amphiphile type and concentration, simulations were also con-

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=0°

1.10-2M

3.10-2M

1.10-1M

=90°

Figure 9: Snapshots of Brownian dynamics simulations obtained at t = 2 s. Simulations are performed with one oil droplet (in red) and 5000 alumina particles (in blue) modified with different concentrations of propionic acid, first considering a contact angle θ = 0◦ and then considering a contact angle θ = 90◦ . ducted to gain insights into the influence of the particle concentration on the dynamics of the particle-particle and particle-droplet interactions. To this end, the system comprising alumina particles modified with Ca = 3 × 10−2 M of propionic acid and that forms compact clusters on the droplet surface, was simulated. Simulations were performed by fixing the concentration of alumina particles in the aqueous phase at 0.3, 0.65, 1.31 and 4.58v%. Figure 10(a) shows the evolution of Scov as a function of time for the different concentrations of alumina, whereas Figure 10(b) depicts the evolution of Scov as a function of particle concentration at different times. Overall, the surface coverage of the oil droplets with particles increases with the colloid volume concentrations in the water phase. Higher particle concentrations lead to faster adsorption. A more detailed analysis of the data shows that the surface coverage of the droplets follows a square-root dependence on time, t, at an early stage (Figure 10(c)). When plotted against t1/2 , the surface coverage data nicely collapse into a single line if a simple scaling factor is used for normalization. Such scaling factor is chosen such that the linear parts of the curves at short time superimpose. This dependence is typical of diffusion-limited processes, indicating that the dynamics of adsorption of particles

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on the droplet surface at early stage is controlled by their diffusion towards the oil-water interface. In such a diffusion-controlled process, particles should readily adsorb at the interface once they reach the droplet surface. This results from the attractive interactions expected between particles and droplets (Figure 4). For longer elapsed time, the dependence of the surface coverage over time no longer follows the square-root relation observed at the early stage. This is likely a consequence of collisions between the initially freely diffusing particles, which ultimately hinders their diffusion and adsorption at the droplet surface. Interestingly, the deviation from the initial square-root dependence occurs at earlier elapsed times when the particle concentration increases. We interpret this result as an evidence that interparticle collisions initiate at earlier times in more concentrated systems, in which the distance between particles is smaller. If the surface coverage is analyzed as a function of the particle concentration (Figure 10(b)), we observe a linear correlation at short elapsed times. This is consistent with the idea that at early stages the droplet surface is totally free for the adsorption of particles that have diffused towards their liquid interface. Conversely, a non-linear dependence between surface coverage and particle concentration is found for longer elapsed times. We interpret this behavior as an effect of the partial saturation of the droplet surface with previously adsorbed particles. This reduces the probability of adsorption of new particles as they approach the interface, deviating from the linear response observed at shorter elapsed times. By considering that an emulsion can be stabilized when colloid particles adsorb quickly on the oil surface before neighbor droplets encounter each other, our simulation results suggest that emulsion stabilization will be promoted by using higher concentrations of colloids in the water phase. This is in line with experimental observations that a minimum particle concentration of 25v% is required to obtain stable emulsions with small droplet sizes using the alumina particles and short amphiphiles investigated here. 17 It is also interesting to note that in spite of the extensive agglomeration in the bulk, a finite surface coverage around 10% is still observed for high amphiphile concentrations. Such interfacially adsorbed

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particles eventually form an interconnected network with the particles agglomerated in the bulk. All these results are obtained considering only a diffusive regime. When mixing occurs, results should qualitatively be the same, however convective forces should transport more easily the colloids on the droplet surface and thus decrease the adsorption time. 38

In addition to the early dynamics of the system, comparison of our simulation data with experimental results previously reported for the same system reveals thus far unaccessible information about the stabilization mechanism of such complex emulsions. Experiments have shown that stabilization happens when the colloidal particles are sufficiently modified to adsorb on the droplet surface, but also to slightly agglomerate at the interface. 4 The amphiphile concentrations required to reach this optimum emulsification conditions are schematically illustrated in the diagram shown in Figure 11. Amphiphile concentrations below this optimum range result in particles that are not hydrophobic enough to enable emulsion stabilization. Particles hydrophobized with amphiphile contents above the optimal interval agglomerate extensively in the bulk, increasing too much the viscosity of the continuous phase and thus preventing emulsification. This optimum window changes towards lower concentrations if the number of carbons in the amphiphile is increased. This can be attributed to the fact that longer amphiphiles screen more strongly the surface charges of the alumina particles. Introducing into the experimental diagram the results of our simulations, we obtain insights into the underlying stabilization mechanisms of the emulsions. We focus the analysis first on the data obtained for propionic acid, which shows a broader optimum window. Remarkably, we find that the experimental conditions at which the emulsions are stabilized, correspond to the simulated scenarios in which particles either cluster on the droplet surface or agglomerate throughout the aqueous phase. This correlation suggests that droplet stabilization can be achieved through two different mechanisms. On the one hand, the formation of close-packed particles adsorbed at the liquid interface leads to the classical mechanism of Pickering stabilization. On the other hand, the formation of an elastic percolating chain

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of particles that immobilize droplets by spanning throughout the continuous phase can also prevent coalescence and coarsening effects, which is known as network stabilization. While these mechanisms have been previously observed in other particle-stabilized systems, 39 our numerical results show the first evidence that they are likely operative also in emulsions that combine particles with short amphiphiles. For amphiphile concentrations below the optimum experimental range, our simulations indicate that particles are adsorbed at the oil-water interface, but remain individualized and very mobile on the droplet surface. This suggests that a mobile array of particles can probably be easily displaced on the droplet surface by thermal fluctuations and thus are not enough to prevent the coalescence of droplets. A similar trend is expected for the emulsions containing valeric acid as short amphiphile. However, in this case, the sharper transitions makes the analogies between experiments and simulation less visible. Yet, the results obtained with valeric acid suggest that the formation of a particle network might in some cases lead to an excessively high viscosity of the continuous phase that ultimately prevents emulsification by mechanical shearing. All these results indicate that the DLVO potential is sufficient to qualitatively understand microstructural mechanisms underlying the stabilization of emulsions using colloidal particles modified with short amphiphiles. Even though these results are obtained for emulsions, they should also be applicable in foams where similar behaviors have already been experimentally observed. 40

Interactions between particle-coated droplets Our simulations of the colloidal behavior of particles around droplets indicate that the stabilization of emulsions is effective when the particles form a protective layer at the oil-water interface or when they immobilize the oil droplets through the formation of a percolating network throughout the continuous phase. These mechanisms are governed by attractive forces between the colloidal particles and their attractive interactions with the oil. Since DLVO interactions alone are sufficient to describe the attractive forces responsible for these mechanisms, one might expect that stable emulsions could in principle also be prepared by 22


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(a)

1.31% 3.3%

0.3% 0.65%

4.58%

0.10 s 0.45 s

(b) 0.02 s 0.06 s

1.50 s 3.00 s

(c)

30

30

25

25

25

20

20

15 10 5

normalized Scov (%)

30

Scov (%)

Scov (%)

15 10 5

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1 1.5 2 time (s)

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3

0.3% 0.65%

1.31% 3.3%

4.58%

20 15 10 5 0

0 0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Concentration of alumina (%)

0

0.1 0.2 0.3 0.4 0.5 0.6 t (s √

1/2

)

Figure 10: (a) Fractional area of droplets covered with adsorbed particles as a function of (a) the time t for different concentrations of alumina particles √ in the aqueous phase, (b) the alumina particle concentrations at different times and (c) t. For (c) data are normalized with a pre-factor different for each concentration. Results are obtained for one oil droplet and alumina particles modified with 3.10−2 M of propionic acid. The concentration of alumina is given in volume percentage (Concentration = volume of alumina/(volume of water + volume of alumina))

Amphiphile concentration (mM)

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Langmuir

100

Stable foams (>3min mixing)

Coagulated suspensions

Particle agglomeration in bulk

Stable foams (

Early Dynamics and Stabilization Mechanisms of Oil-in-Water

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