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Dynamics of Pickering emulsions in the presence of an interfacial reaction: a simulation study Shuangliang Zhao, Bicai Zhan, Yao-Feng Hu, Zhaoyu Fan, Marc Pera-Titus, and Honglai Liu Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b03046 • Publication Date (Web): 04 Nov 2016 Downloaded from http://pubs.acs.org on November 17, 2016

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Dynamics of Pickering emulsions in the presence of an interfacial reaction: a simulation study Shuangliang Zhao,a Bicai Zhan,a,b Yaofeng Hu,a Zhaoyu Fan,c Marc Pera-Titus,c,* and Honglai Liua,b,* a

State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China

b

Department of Chemistry, East China University of Science and Technology, Shanghai 200237, China

c

Eco-Efficient Products and Processes Laboratory (E2P2L), UMI 3464 CNRS – Solvay, 3966 Jin Du Road, Xin Zhuang Ind. Zone, 201108 Shanghai, China *

Corresponding authors: [email protected]; [email protected]

Abstract Pickering emulsions combining surface-active and catalytic properties offer a promising platform for conducting interfacial reactions between immiscible reagents. Despite the significant progress in the design of Pickering Interfacial Catalysts for a broad panel of reactions, the dynamics of Pickering emulsions under reaction conditions is still poorly understood. Herein, using benzene hydroxylation with aqueous H2O2 as a model system, we explored the dynamics of benzene/water Pickering emulsions during reaction by dissipative particle dynamics (DPD). Our study points out that the surface wettability of the silica nanoparticles is affected to a higher extent by the degree of polymer grafting rather than by an increase of the chain length of hydrophobic polymer moieties. A remarkable decline of the O/W interfacial tension was observed when increasing the yield of the reaction product (phenol), affecting the emulsion stability. However, phenol did not alter to an important extent the distribution of immiscible reagents around the nanoparticles sitting at the benzene/water interface. A synergistic effect between phenol and silica nanoparticles on the O/W interfacial tension of the biphasic system could be ascertained. Keywords: Pickering emulsion, wettability, DPD simulation, interfacial reaction.

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1. Introduction Biphasic reactions involving two immiscible reagents are ubiquitous in the chemical industry in a diversity of fields such as petrochemical engineering, fine chemistry and organic synthesis. Biphasic reactions usually suffer from resilient mass/heat transfer limitations due to a poor interfacial contact between the reagents even under vigorous stirring. In common practice, co-solvents, surfactants, phase-transfer catalysts,1,2 and even surfactant-combined catalysts are required to promote the interfacial contact and distribute the catalyst between the phases,3-5 affecting unavoidably the economy and eco-efficiency of the process. Amphiphilic nanoparticles can stabilize Pickering emulsions, allowing per se facile separation and recycling after operation.6,7 Appropriate functionalization of their surface with catalytic centers can afford interfacial reactions (i.e. Pickering Interfacial Catalysis, PIC).8,9 In this concept, the particle assembly at the liquid/liquid (L/L) interface increases not only the interfacial contact area between the reagents, but also alleviates external mass transfer limitations. A rich variety of amphiphilic catalysts have been reported in the last years with variable complexity. These systems can be broadly classified in six families: (1) silicas and zeolites functionalized with alkyl chains and incorporating acid centers for alkylation,10 acetalyzation,11 and etherification reactions,12,13 (2) alkyl-functionalized silicas with Pd nanoparticles for hydrogenation reactions,14 (3) Ru/C, Ag/C and carbon-alumina nanohybrids incorporating Fe-Mn for partial oxidation reactions,15-19 (4) polyoxometallates (POMs) incorporating alkyl ammonium chains and POM-paired ionic copolymers for epoxidation reactions;20,21 (5) carbon-silica and carbon-alumina nanocomposites incorporating Pd and alkali moieties for cascade reactions,22-25 and (6) encapsulated and mineralized enzymes for acid-base catalyzed reactions.26,27 Despite the above stated developments, the dynamics of Pickering emulsions under reaction conditions is still poorly understood. Recent simulation studies outline the particle assem-


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bly at the L/L interface for surface-modified nanoparticles in a random and ordered (i.e. Janus) fashion,28-30 polymer-coated spherical nanoparticles,31-34 and combinations of uncharged nanoparticles and nonionic surfactants.35-37 Using molecular dynamics (MD) simulations, Striolo and co-workers found that the decane/water interfacial tension is not much influenced by the presence of nanoparticles.28 In a further study, using dissipative particle dynamics (DPD) simulations, the same authors reported that the steric interactions between nanoparticles adsorbed on coalescing droplets as well as the stability of the film formed between the coalescing droplets are important phenomena that can help stabilizing Pickering emulsions.38 In the case of polymer-grafted nanoparticles, Lo Verso et al.31 studied by MD simulations the interactions between spherical polymer brushes in different solvents and found that for short-chain lengths and moderate grafting degrees, isolated spherical brushes in a poor solvent regime exhibited incomplete coverage by nanoparticles. Finally, using coarse-grained MD simulations of uncharged nanoparticles and non-ionic surfactants at the oil/water interface, Ranatunga et al.35 reported a cooperative effect between nanoparticles and surfactants at low concentrations by lowering the oil/water interfacial tension, while at higher surfactant concentration this synergy can be attenuated. In this paper we explore the effect of the surface properties of silica nanoparticles in stabilizing Pickering emulsions, as well as the dynamics of emulsions in the presence of a reaction product. To this aim, the biphasic hydroxylation of benzene using aqueous H2O2 as an oxidant was considered as a case study.39 Indeed, some of us have shown that TS-1@KCC-1 composites with an internal TS-1 core and an external KCC-1 silica shell grafted with octyl chains could afford a catalytic activity up to 1.1 mol/molTi at 60 oC after 1 h reaction for benzene hydroxylation using aqueous H2O2 (30 wt.%) due to the genesis of stable benzene/water Pickering emulsions. For comparison, the parent TS-1 was unable to stabilize emulsions, showing in this case a catalytic activity of 0.65 mol/molTi at the same reaction conditions.


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2. Simulation details 2.1. Dissipative particle dynamics (DPD) Dissipative particle dynamics (DPD) describes a fluid system by sorting it out in small interacting packages or beads.40-42 In analogy to MD simulation, the particle positions and velocities in DPD are governed by a Newtonian law of motion

 dr  i = v i  dt  dvi mi dt = Fi

(1)

where ri, vi and mi are the position, velocity and mass of the ith bead, respectively, whereas Fi is total force exerted upon the bead. The total force can be regarded as the sum of conservative forces (FijC), dissipative forces (FijD) and random forces (FijR):

Fi = ∑ (FijC + FijD + FijR )

(2)

i≠ j

The conservative force between the ith and the jth beads, FijC, can be written in soft repulsion form as follows

 a (1− r / r )rˆ  ij ij c ij F = 0  C ij

rij < rc

(3)

rij ≥ rc

where rij = |ri-rj| is the distance between the ith and the jth bead, rîj is the unit vector along the direction from the bead position ri to rj, rc is the cutoff radius in the DPD formalism indicating the extent of the interaction range between a pair of beads, and coefficient aij is a parameter expressing the maximum repulsion between the ith and jth beads. Parameter aij can be calculated from the Flory-Huggins binary interaction parameter, i.e. χij,40-42 using the following relation for a scaled number density ρ rc3 equal to 3 as in refs:29,30,38


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aij = (131.5+ 3.27 χ ij )

k BT rc

(4)

where kB is the Boltzmann constant and T is the absolute temperature. Different experimental methods have been reported for the derivation of aij parameters including pair-interaction calculations,43 vapor pressures,44 and solubilities, as well as atomistic dynamic simulations.45 If we assume that the heat of mixing obeys the HildebrandScatchard regular solution theory, parameter χij can be estimated from the Hildebrand solubility parameters δi(T) and δj(T)

χ (T ) = ij

2 Vij   δ T − δ T j  RT  i

( )

( )

(5)

where R is the gas constant, and Vij is the partial molar volume. In DPD, the nearest equivalent of a partial molar volume is the volume associated to a DPD bead (see below). The Hildebrand solubility parameters δi(T) and δj(T) can be found in ref.46 In addition to conservative forces, the other two forces in Eq 2 are the dissipative forces (FijD) and random forces (FijR), which can be expressed as follows

FijD = −ηω D (rij )(rîj ⋅ v ij )rîj

(6)

FijR = σ ω R (rij )ζ ij ∆t −1/2rîj

(7)

In Eq 6 and Eq 7, vij = vi - vj is the relative velocity between the ith and jth beads, η is the friction coefficient, σ is the amplitude of the noise, ζij is a random number between 0 and 1 that is herein for simplicity subjected to a uniform distribution being statistically independent from the pair of beads, ∆t is the time step for solving Eq 1, and ωD(rij) and ωR(rij) are weight functions for dissipative and random forces, respectively. The combination of dissipative and random forces leads to a thermostat that conserves the total momentum of the system. To obey


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the fluctuation-dissipation theorem, the ωD(rij) and ωR(rij) functions should satisfy the following conditions

ω D (rij ) = [ω R (rij )]2

(8)

σ 2 = 2ηk BT

(9)

where

 rij  1− ; rij < rc  rc ω R (rij ) =   0; rij ≥ rc   (10 ) Throughout this work, we used reduced DPD units in the simulations to accelerate the calculations. In particular, we used rc as length unit and kBT as energy unit. The mass of the beads, m, were set equal. In such a situation, the time unit, τ, can be determined as follows

τ = rc m / k BT

(11)

2.2. Models and interaction parameters 2.2.1. Reagents and products The DPD simulation is a mesoscopic approach that relies on the construction of a coarse-grained model of the real system. The system simulated here was composed of a hydrophilic reagent (water), a hydrophobic reagent (benzene), a reaction product (phenol) and a series of functionalized catalytic silica nanoparticles. The coarse-grained models for each component are schematically depicted in Figure 1a. For simplicity, H2O2 was modeled as water. Each “water bead” (W) and “oil bead” (O) for the hydrophilic and hydrophobic reagents, respectively, represented 5 water and 1 benzene or “oil” molecules. The volume of the water


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and oil beads was set in both cases at 150 Å3 corresponding to a water/benzene molar ratio of 5.0 (i.e. benzene was the limiting reactant).46,47 The mass density of the water and oil phases was 0.995 g/cm3 and 0.862 g/cm3, respectively, matching the experimental densities at 298 K.48 The reaction product (phenol) was modeled as a two-bead assembly composed of a hydrophilic head (H) and a hydrophobic ring (R) being connected by a harmonic spring with spring constant ks = 100 and equilibrium distance r0 = 0.7 rc as follows46,49,50

Figure 1. (a) Schematic representation of water beads (W), oil beads (O) and the surfaceactive product (H-R) consisting of a hydrophilic head (H) and a hydrophobic tail (R) connected with a harmonic spring; (b) Simplified representation of core-shell TS-1@KCC catalytic nanoparticles as a silica shell.

Fijbond = −k s (rij − r0 )rîj

(12)

The system density, ρ, being defined as the number of beads in a cube of radius rc (i.e. rc3), was scaled to 3 beads / rc3 with rc = 3 3×150 = 0.77 nm. 2.2.2. Catalytic nanoparticles For the sake of simplicity, the core-shell TS-1@KCC-1 catalyst (φ = 300-500 nm) was simplified to a silica shell (Figure 1b). On the guidance of previous studies, the nanoparticles were modeled as hollow rigid spheres composed of 192 beads that distributed uniformly on the surface.29,30,38,51 To accelerate the calculations, the diameter of the simulated nanoparticles


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was reduced to φ = 4rc = 3.08 nm with a surface number density of 6.5 beads/nm2. To adjust the surface properties of the nanoparticles, the beads were modified with hydrophilic and hydrophobic polymers that were connected to the surface beads, which are hereinafter referred to as PW and PO, respectively. Since the hydrophilic groups in the nanoparticles consist of silanol (Si-OH) groups, the PW polymers were simplified to one hydrophilic bead. In contrast, the PO polymers consisted of a variable number of hydrophobic beads connected with a harmonic spring with the same parameters as in Eq 12. The PW and PO beads were set to have rather uniform distributions on the nanoparticle surface to mimic the random distribution of surface moieties usually found in experimental preparations of nanoparticles. The number of beads in the PO polymers, as well as their surface density, was modified to adjust the hydrophilic-lipophilic balance (HLB) of the nanoparticles. Overall, 5 different families of catalytic nanoparticles were simulated. For the sake of clarity, the label ξ_POm_NP was used for the different nanoparticles, where m and ξ designate the number of beads in the PO polymers (m = 1-5) and their grafting degree or coverage ratio on the nanoparticles (ξ = 0-100%). The different nanoparticles differed from the grafting degree of PO polymers (see example in Figure 2 for ξ_PO1_NP nanoparticles): (a) nanoparticles with only PW beads (ξ = 0%); (b) nanoparticles with 48 PO and 148 PW beads (ξ = 25%); (c) nanoparticles with 96 PO and 96 PW beads (ξ = 50%); (d) nanoparticles with 148 PO and 48 PW beads (ξ = 75%), and (e) nanoparticles with only PO beads (ξ = 100%). The interaction parameters between the particle beads (PW-PO) and the reagent/product beads (W-W, O-O, W-O, W-H, W-R, O-H, O-R) were set as indicated in Table 1. It is worth noting that when grouping five water molecules rather than one into a DPD bead, i.e., the coarse-graining degree of water is 5 instead of 1, the value of aii aii should be 131.5 instead of 25.40 The different cross parameters were expressed as a function of mutual solubility parameters (X, Y, Z) as follows: (X) mutual solubility parameters between W-O reagents, O-PW and


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PO-PW polymer beads; (Y) mutual solubility parameters between H-W product head and hydrophilic reagent, H-PW and PW-PW polymer beads, as well as between R-O product ring and hydrophobic reagent, R-PO and PO-PO polymer beads; and (Z) mutual solubility parameters between H-O product head and hydrophobic reagent and H-PO polymer beads, as well as between R-H product ring and head, R-W product ring and hydrophilic reagent and R-PW polymer beads. These parameters were set at X=15, Y=1 and Z=25 to reproduce the bonding pattern in the benzene/water system and the polymer-modified silica nanoparticles considered in this study.

(a) 0%_PO1_NP

(c) 50%_PO1_NP

(b) 25%_PO1_NP

(d) 75%_PO1_NP

(e) 100%_PO1_NP

Figure 2. Schematic representation of polymer-grafted silica nanoparticles with different surface densities of hydrophobic polymer (PO). The red and cyan beads represent the hydrophilic (PW) and hydrophobic (PO) polymer beads, respectively, whereas the yellow beads represent the core silica beads. From (a) to (e), the grafting degree of PO polymer (ξ) is: 0%, 25%, 50%, 75% and 100%.


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Table 1. Conservative interaction parameters aij in units kBT/rc. The symbols W, O, H-R, PW, PO and B represent the hydrophilic reagent beads, the hydrophobic reagent beads, the head and ring product beads, the hydrophilic polymer beads in the NPs and the hydrophobic polymer beads in the NPs, respectively, whereas the symbols X, Y, and Z indicate the mutual solubility between the different beads. W

O

PW

PO

H

R

B

W

131.5

-

-

-

-

-

-

O

131.5+X

131.5

-

-

-

-

-

PW

131.5

131.5+X

131.5

-

-

-

-

PO

131.5+X

131.5

131.5+X

131.5

-

-

-

H

131.5+Y

131.5+Z

131.5+Y

131.5+Z

131.5

-

-

R

131.5+Z

131.5+Y

131.5+Z

131.5+Y

131.5+Z

131.5

-

B

131.5

131.5

131.5

131.5

131.5

131.5

131.5

2.3. Computational details The DPD simulations were performed using the LAMMPS package. The simulation box size was set at Lx x Ly x Lz ≡ 15 x 15 x 30 rc3, where Li refers to the length of the simulation box along the i direction. Orthorhombic boxes were used, and periodic boundary conditions were applied in all three directions. The z-direction was perpendicular to the W/O interface, which was considered as planar. The reduced number density of the simulation cell was set to 3 and the cell was large enough to estimate the interfacial tension.52 The constants for the dissipative and random forces (Eq 6 and Eq 7) were set at η = 4.5 and σ = 3 to keep the temperature constant at a scaled value of kBT = 1. The simulation runs were established at 2,000,000 steps with a time step of 0.04 τ to ensure steady state equilibrium. Preliminary equilibration experiments reflected that steady state could be achieved after only 5,000 steps.

3. Results and Discussion 3.1. Benzene/water interfacial tensions in the absence of particles


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Before assessing the particle assembly at the L/L interface, we carried out a series of preliminary calculations to estimate the benzene/water interfacial tension using DPD simulations. The interfacial tension of the benzene/water system, γw/o, both in the presence and absence of nanoparticles was computed as the difference between normal and tangential stresses across the interface according to the Irving-Kirkwood equation by integrating the stress difference over x (normal axis to the interface)52

1 γ o w = ∫ [Pxx − (Pyy + Pzz )]dx 2

(13)

where Pxx, Pyy and Pzz are the diagonal components of the pressure tensor (P). The conversion factor kBT / rc2 = 7.0 mN/m at 298.13 K was used for transforming DPD simulation results into interfacial tensions.46 The computed value for the benzene/water interfacial tension was 34.3 mN/m, which compares well with the theoretical value measured from the literature (36.0 mN/m).53 This observation confirms that the DPD methodology used in this study provides a suitable platform for modelling interfacial phenomena in the benzene/water system. 3.2. Interfacial properties in the presence of nanoparticles The nature and stability of Pickering emulsions are strongly conditioned by the nanoparticle wettability, which can be in turn characterized by the interfacial contact angle, θw/o, between the nanoparticles and the W/O interface (Figure 3). Typically, hydrophilic particles with interfacial contact angles θw/o < 90° tend to stabilize O/W emulsions, whereas hydrophobic particles with θw/o > 90° promote W/O emulsions.6,54 The different modified nanoparticles simulated in this study possess different wettability, resulting in a different location in the benzene/water system after equilibration (Figure 4). For each nanoparticle, the interfacial contact angle was computed using the following expression derived geometrically from Figure 3


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Figure 3. Representation of nanoparticle wetting at the W/O interface and definition of the interfacial contact angle.

(a) 0%_PO1_NP

(b) 25%_PO1_NP (c) 50%_PO1_NP (d) 75%_PO1_NP (e) 100%_PO1_NP

Figure 4. Snapshots illustrating the steady-state location of a ξ_PO1_NP nanoparticle as a function of the grafting degree (ξ = 0-100%). The blue and grey beads represent the hydrophilic (W) and hydrophobic (O) reagents, respectively, whereas the red and cyan beads represent the hydrophilic (PW) and hydrophobic (PO) polymers on the nanoparticles, respectively, and the yellow beads represent the silica core. Movies showing the dynamics for the different particles can be found in the SI.

d 

θ w o = 180 − θ o w = arccos  

(14)

 R

where d is the distance between the nanoparticle center and the W/O interface and R is the radius of nanoparticles. The interface is defined when the number density of W beads decreases from 90% to 10%. The interfacial contact angle together with the interfacial tension can be used to calculate desorption energy of the nanoparticles, Ed, which reflects the required energy for removing one nanoparticle from the interface to either the water or oil phases55

( )

Ed = π R 2γ o/w 1± cos θ w o 

2

(15)


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In Eq 15, R is the radius of nanoparticle, and the sign in parentheses is positive for nanoparticle removal into the organic (benzene) phase and negative for removal into the water phase. The stability of a nanoparticle at the W/O interface becomes promoted for θw/o = 90° (i.e. pure amphiphilicity) and at lower product yield. The interfacial tension for the O/W system in the presence of particles, γo/w,P, can be further computed as a function of the desorption energy using the expression

γ o w,P = γ o w −

N p Ed

(16)

A

The term Np/A in Eq 16 refers to the number of nanoparticles per unit surface of interfacial area equaling to 7.50×10-3 particles/nm2 for particles with φ = 3.08 nm. This value can be rescaled to 2.84×10-7 particles/nm2 for theoretical particles with φ = 500 nm and skeletal density of 2.0 g/cm3 by assuming equal contact angles, which compares well with the experimental value measured for TS-1@KCC with the pore mouths of KCC partially grafted with octyl chains (7.22×10-6 particles/nm2 for φ = 500 nm). Table 2 compiles the location and interfacial contact angles for the different catalytic nanoparticles considered in this study. Among the different nanoparticles, 25%_PO1_NP provided the most stable emulsions (O/W in this case), exhibiting a θw/o interfacial contact angle of 77.3o, an interfacial tension of 32.0 mN/m and a desorption energy of 93.6 kJ/mol. Overall, two main trends emerge from the results: (1) keeping the same hydrophobic polymer length, a decrease of the surface density of hydrophobic polymers promotes the location of nanoparticles from the oil to the water phase; and (2) 50%_PO1_NP and 25%_POX_NP (X = 2-4) will remain at the W/O interface, whereas the remaining nanoparticles will stay preferentially in either the water or oil bulk phases (contact angles of 0o and 180o, respectively). Unlike the hydrophobic polymer length, the grafting degree of hydrophobic polymers appears to exert a larger effect on the particle wettability, promoting the adsorption at the W/O interface.


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Table 2. Location of a ξ_POm_NP nanoparticle in the W/O system as a function of the chain length of hydrophobic polymers (m=1-5) and the ratio between hydrophilic and hydrophobic poymers (ξ=0-100%). The values in brackets indicate the θw/o interfacial contact angle. ξ

0%

25%

50%

75%

100%

PO1

W

O/W (77.3)

W/O (133)

O

O

PO2

W

W/O (130)

O

O

O

PO3

W

W/O (131)

O

O

O

PO4

W

W/O (137)

O

O

O

PO5

W

O

O

O

O

3.2.1. Density profiles around a nanoparticle We further computed the density profiles around a nanoparticle. These profiles show the evolution of the local density of the different reagents as a function of the distance to the nanoparticle center, reflecting the spatial distribution of the reagents in the vicinity of the nanoparticle. Figure 5 plots the density profiles of W and O beads around a single ξ_PO1_NP nanoparticle with variable grafting degree of PO1 polymers (ξ = 0-100%). In all cases, an increase of the grafting degree results in a higher densification of O beads (i.e. benzene) around the nanoparticle at the expense of W beads (i.e. water) with the total density of W + O beads keeping almost constant. Several peaks are observed for the different nanoparticles, suggesting the presence of different layers of adsorbed benzene and water surrounding the nanoparticle in the nearby of the O/W interface.


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Figure 5. Density profiles of: (a) the hydrophilic reagent (W), (b) the hydrophobic (O) reagent, and (c) all the reagents (W+O), around a single ξ_PO1_NP nanoparticle (ξ=0-100%) as a function of the grafting degree of hydrophobic polymers.

Figure 6 plots the density profiles of W and O beads around a 25%_POX_NP nanoparticle with variable hydrophobic polymer length (X = 1, 2, 5). An increase of the hydrophobic polymer length enhances the density of O beads around the nanoparticle with the total density of W + O beads keeping almost constant. The shape of the different curves is similar to that described in Figure 5, reflecting the presence of different layers of adsorbed benzene and water surrounding the nanoparticle.


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Figure 6. Density profiles of: (a) the hydrophilic reagent (W), (b) the hydrophobic (O) reagent, and (c) all the reagents (W+O), around a single 25%_POm_NP nanoparticle as a function of the grafting degree of hydrophobic polymers. 3.3. Coexistence of a nanoparticle and the reaction product at the W/O interface 3.3.1. Dynamic evolution process and density profiles Figure 7 displays the emulsification dynamics of the benzene/water system in the presence of the reaction product (phenol, H-R) and a 25%_PO1_NP catalytic nanoparticle, whereas Figure 8 plots the corresponding density profiles at steady state. In all the simulations, the initial system configuration was set to a homogeneous state. The presence of 2% phenol together with the W and O reagents does not exert any remarkable emulsifying effect on the system (Figure 7a, Figure 8a). As a result, the W and O phases show a phase separation just after 60τ with a slight increase of the product segregation at the W/O interface. In contrast, the reaction product appears to affect to an important extent the stability of a 25%_PO1_NP nanopar-


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ticle sitting at the O/W interface, especially at higher yield (Figure 7b-d, Figure 8b-d), depleting it away from the interface to the W phase. These results point out the moderate surfaceactive properties of the reaction product, affecting the HLB properties of the biphasic system near the interface.

(a)

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(c)

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200

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(d)

0

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2400

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Figure 7. Synergy between the catalytic nanoparticles and the reaction product at the W/O interface for different scenarios as a function of the reduced time t/τ: (a) 2% product yield in the absence of nanoparticles; (b) 25%_PO1_NP nanoparticle in the absence of product; (c) 25%_PO1_NP nanoparticle with 2% product yield; and (d) 25%_PO1_NP nanoparticle with 10% product yield. The white beads represent the reaction product (H-R). Color labels as in Figure 4. Movies showing the dynamics for the different particles can be found in the SI. ACS Paragon Plus Environment

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Figure 8. Density profiles for different scenarios: (a) 2% product in the absence of catalytic nanoparticles; (b) 25%_PO1_NP nanoparticle in the absence of product; (c) 25%_PO1_NP nanoparticle with 2% product yield; (d) 25%_PO1_NP nanoparticle with 10% product yield. 3.3.2. Density profiles To further assess the influence of the reaction product on the emulsifying properties of the nanoparticles, we computed the density profiles of the reagents and reaction product around a single 25%_PO1_NP nanoparticle (Figure 9). No qualitative difference can be ascertained for the W and O distributions around the nanoparticle. However, an increase of the product yield (between 5-10%) results in a decline of the distribution of reagents around the nanoparticle reaching an almost constant density profile. Overall, even if the reaction product can affect the emulsion stability, this is not expected to alter the distribution of W and O reagents around the nanoparticle. This result suggests that, during the benzene hydroxylation reaction, the number density of W and O reagents surrounding the nanoparticle might keep stable, whereas the number density of the product might increase. ACS Paragon Plus Environment

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Figure 9. Density profiles of: (a) the hydrophilic reagent (W), (b) the hydrophobic reagent (O), and (c) the reaction product (H-R) around a 25%_PO1_NP nanoparticle as a function of the product yield. 3.3.3. Interfacial properties Figure 10 shows the evolution of the interfacial contact angle for a 25%_PO1_NP nanoparticle sitting at the W/O interface as a function of the product yield. The interfacial contact angle decreases with the product yield from a value of 77.3o in the absence of product to 42.7o for 10% yield. As a result, the distance between the nanoparticle and the W/O exhibits a slight increase with a shift to the W phase, matching the trends obtained on the density profiles plotted in Figure 8. The desorption energy for the nanoparticle removal into the W phase displays


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a decline from 93 kJ/mol in the absence of product to 11 kJ/mol for a 10% product yield (Table 3). The stability of the nanoparticles is still large in the presence of product, which might explain the absence of dramatic change of the nanoparticle location at the W/O interface.

Figure 10. (a) Distance between a 25%_PO1_NP nanoparticle center and the W/O interface as the function of the product yield; (b) Interfacial tension in the presence or absence of a 25%_PO1_NP nanoparticle as a function of the product yield.

Table 3. Interfacial tension, interfacial contact angle and desorption energy of a 25%_PO1_NP nanoparticle at the W/O interface as a function of the product yield. Product yield

0%

2%

5%

8%

10%

γw/o,P (mN/m)

32.0

22.5

14.9

11.4

10.5

θw/o (o)

77.3

74.3

69.5

58.9

42.7

Ed (kJ/mol)

93.6

82.0

65.0

36.0

10.8

Figure 10(b) displays a remarkable effect of the reaction product on the O/W interfacial tension both in the presence and absence of a 25%_PO1_NP nanoparticle, this showing a decrease by 30% compared to the value measured in the absence of product. We can attribute this decrease to both the solubilization of phenol in benzene and water, approaching the HLB properties of both cases, as well as to a partial surface-active effect of phenol at the benzene/water interface. Noticeably, this trend is consistent with that observed experimentally for


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the benzene/water system in the presence of phenol and caprolactam.54 Furthermore, even if the decreasing trend of the W/O interfacial tension with the product yield is still preserved, the presence of a 25%_PO1_NP nanoparticle adsorbed at the W/O interface shows a slightly positive effect on the interfacial tension due to their weak surface-active properties.

4. Conclusions Using benzene hydroxylation with aqueous H2O2 as model reaction system, we have shown along this paper that the dynamics of benzene/water Pickering emulsions during reaction can be conveniently simulated by Dissipative Particle Dynamics by considering the adsorption of a single catalytic silica particle at the O/W interface. Our study points out that the surface wettability of the silica nanoparticles is affected to a higher extent by the degree of polymer grafting rather than by an increase of the chain length of hydrophobic polymer moieties. The density profiles and interfacial tension of the benzene/water system stabilized by a single silica nanoparticle suggests an interfacial role of the reaction product (phenol), affecting the emulsion stability. However, phenol is not expected to alter to an important extent the distribution of immiscible reagents around the nanoparticles at the benzene/water interface. Phenol and silica nanoparticles exhibit a synergistic effect on the benzene/water interfacial tension.

Glossary aij

Maximum repulsion between the ith and jth beads [J.m-1]

d

Distance between the nanoparticle center and the W/O interface [m]

Ed

Desorption energy of nanoparticles from the W/O interface [J.mol-1]

Fi

Total force exerted on the ith bead [N]

FijC

Conservative force between the ith and jth beads [N]

FijD FijR

Dissipative force between the ith and jth beads [N]

kB

Boltzmann constant (1.38x10-23 J.K-1)

kS

Spring constant [N.m-1]

Li

Length of the simulation box along the ith direction [m]

Random force between the ith and jth beads [N]


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mi

Mass of the ith bead [kg]

Np/A

Number of nanoparticles per unit surface of interfacial area [m-2]

P

Pressure tensor [Pa]

rC

Cutoff radius [m]

r0

Equilibrium distance [m]

ri

Position of the ith bead [m]

rij

Distance between the ith and jth beads [m]

rîj

Unit vector along the direction from the bead position ri to rj [m]

R

Constant of perfect gases [8.314 J.mol-1.K-1]; Radius of nanoparticles [m]

T

Temperature [K]

vi

Velocity of the ith bead [m.s-1]

vij

Relative velocity between the ith and jth beads [m.s-1]

Vij

Partial molar volume [m3.mol-1]

m

Number of beads in the hydrophobic polymers [-]

X, Y, Z

Mutual solubility parameters [J.m-1]

Greek symbols χij

Flory-Huggins binary interaction parameter [-]

δ

Hildebrandt solubility parameter [Pa1/2]

φ

Particle size [m]

γo/w

Interfacial tension [N.m-1]

γo/w,P

Interfacial tension in the presence of adsorbed particles [N.m-1]

η

Friction coefficient [J.s.m-2]

θw/o

Interfacial contact angle [o]

ρ

System density [beads.m-3]

σ

Amplitude of the noise [J.m-1.s-1/2]

τ

Time unit [s]

ω (rij)

Weight functions for dissipative forces [-]

ω (rij)

Weight functions for random forces [-]

ξ

Grafting degree of hydrophobic polymers on the silica nanoparticles [-]

ζij

Random number between 0 and 1

D

R

Acronyms DPD

Dissipative Particle Dynamics

H

Hydrophilic head of the product (phenol)

HLB

Hydrophilic-lipophilic balance

KCC

Kaust Catalysis Center

MD

Molecular Dynamics

O

Oil bead (benzene)

PIC

Pickering Interfacial Catalysis

POM

Polyoxometallates

PO

Hydrophobic polymer on the silica nanoparticles (alkyl chains)


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PW

Hydrophilic polymer on the silica nanoparticles (Si-OH groups)

R

Hydrophobic ring of the product (phenol)

TS

Titanosilicate

W

Water bead

Supporting Information A series of movies showing the dynamics of ξ_PO1_NP nanoparticles until steady state for the benzene/water system (files 0%_PO1_NP, 25%_PO1_NP, 50%_PO1_NP, 75%_PO1_NP and 100%_PO1_NP) and dynamics of 25%_PO1_NP nanoparticles for the benzene/water/phenol system in the presence of 2% and 10% phenol (25%_PO1_NP_2%_product and 25%_PO1_ NP_10%_product).

Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 91334203, 91434110), the 111 Project of China (No.B08021) and the Fundamental Research Funds for Central Universities of China. SZ acknowledges the support of Fok Ying Tong Education Foundation (151069). CNRS and Solvay are also acknowledged for funding.

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