Janus Dimers at LiquidâLiquid Interfaces - The Journal of Physical

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B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

Janus Dimers at Liquid-Liquid Interfaces Ma#gorzata Borówko, Edyta S#yk, Stefan Soko#owski, and Tomasz Staszewski J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b02467 • Publication Date (Web): 17 Apr 2019 Downloaded from http://pubs.acs.org on April 20, 2019

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The Journal of Physical Chemistry

Janus Dimers at Liquid-Liquid Interfaces M. Bor´owko, E. Slyk, S. Sokolowski, and T. Staszewski∗ Department for the Modelling of Physico-Chemical Processes, Maria Curie-Sklodowska University, 20-031 Lublin, Poland E-mail: [email protected]

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Abstract We study the impact of selected parameters on the behavior of Janus-like dimers at a liquid-liquid interface. The equilibrium orientation and the adsorption depth of a single Janus dimer are calculated using a simple phenomenological method. We have also performed molecular dynamics simulations for different numbers of Janus dimers trapped at the interface between two partially miscible Lennard-Jones fluids. The particles with different wettabilities of both parts of Janus dimers are considered. Depending on the assumed energy parameters we observe various structures: orientationally ordered monolayers, fractal-like aggregates, compact clusters and the ordered multilayers containing alternately arranged layers built of Janus particles and molecules of the fluids.

Introduction Janus particles (JPs) have been extensively studied due to their promising applications in nanotechnology. 1–5 In recent years there is an increasing interests in the design of JPs with various shapes and chemical properties and several reviews on the synthesis of JPs have been published. 6,7 One of the most important application of JPs is the stabilization of multiphasic mixtures such as emulsions and bubbles. 8 The knowledge of the physicochemical aspects regarding the behavior of JPs at fluid-fluid interfaces is of great importance in understanding the emulsion stability. Numerous studies have shown that Janus particles attach to the fluid-fluid interfaces more efficiently than their homogeneous analogues. 10–12 Janus particles with wettability anisotropy can stabilize the Pickering emulsions during longer period of time and under more stressing conditions than homogeneous particles. 8,9 They can exhibit high interfacial activity regard2 ACS Paragon Plus Environment

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less of the degree of amphiphilicity, due to spatial separation of different wettability regions For these reasons, Janus particles can be treated as a new class of surfactants. 12,13 The most of theoretical and experimental works have been focused on adsorption of spherical JPs at fluid-fluid interfaces. 10–12,14–18 The adsorption energy of Janus spheres has been expressed as a function of the contact angles of both parts of the particle surface using Young equation. 10,11 The attachment energy of Janus particles to an interface depends on the ratio of surface area of both patches and on the particle amphiphilicity. Binks and Fletcher 11 have shown that the surface activity of a Janus sphere may be increased 3-fold with respect to a homogeneous particle of the same size. Recently, there is growing interests in the investigation of non-spherical particles, 19–30 such as disks, 26,29 cylinders, 24,25 ellipsoids 20,22,27,28 and dumbbells 19–22,30 at interfaces. These studies have shown that the shape of the particles has strong influence on their configuration and interactions at fluid-fluid interfaces. Two types of non-spherical JPs have been considered, the particle whose Janus boundaries were perpendicular 19–22,30 or parallel 25,26,29 to their longer axes. Park and Lee 19 studied theoretically the behavior of Janus ellipsoids and Janus dumbbells at the water-oil interface. They considered the behavior of a single JP under so-called “supplementary wetting condidion”. 19,21 The orientation of a single JP at this interface is the result of competition between two driving forces: (i) the minimization of the unfavorable water-oil interactions, which is obtained when the JP occupies as much interfacial area as possible, and (ii) the minimization of JP-fluid interface energy which corresponds to a situation when the polar part is immersed in water, while the apolar one is surrounded by oil molecules. The equilibrium orientation was calculated on the basis of a minimum condition of the adsorption energy as a function of orientation angle with respect to the water-oil interface. They found that the JPs adopt the upright orientation if the



particle amphiphilicity is large or if the particle aspect ratio is close to 1. Otherwise, the JPs have a tilted orientation at equilibrium. Moreover, the attachment energy of Janus dumbbells as a function of contact angle, θP , has only one minimum, so these particles always prefer to be in a single orientation. However, Janus ellipsoids can be kinetically trapped in a metastable, state due to a secondary minimum in the energy. Luu et al. 27 used dissipative particle dynamics simulations to study ellipsoidal JP at the decane-water interface. Their results suggest that prolate and oblate nanoparticles are more effective than spherical ones in reducing the interfacial tension. These conclusions are consistent with experimental data obtained by Ruhland et al. 25 The impact of the shape of JPs on their orientation at the fluid-fluid interface has been studied by Gao et al. 29 The considered JPs were characterized by two regions with different wettability divided along their longer axes. Their molecular dynamics simulations have shown that Janus spheres and Janus rods prefer one orientation at the interface. In the equilibrium orientation each side of the JP is completely in contact with its favorite liquid. On the contrary, Janus disks can adopt two orientations: one orientation corresponds to the equilibrium state and the other is kinetically trapped in a metastable state. Gao et al. 29 also showed that changes in the shape of JPs strongly influence the interfacial tension. Another important phenomenon associated with the adsorption of JPs is their selfassembly. 1,2,17,24,25,27,28,31–34 Park et al. 17 have found that JPs spontaneously form fractal-like aggregates at an oil-water interfaces. The aggregation of JPs leads to the formation of various supracolloidal objects. 31,32,34 In this paper we focus on the behavior of Janus dimers at liquid-liquid interfaces. The dimers are built of two tangentially jointed spheres. Our theoretical considerations are based on the phenomenological approach and on the computer simulations. In the first part we


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modify the approach proposed by Park and Lee 19 and discuss in details how the location and orientation of Janus dimers depend on the interfacial tension acting at particular parts of Janus dimers and of two liquid species. In particular, we propose analytical expressions for the equilibrium orientation, the adsorption depth and the attachment energy of a single Janus dimer at the liquid-liquid interface. The phenomenological description neglects completely a microscopic structure of the system. The second problem considered by us is connected with the application of computer simulations, specifically Molecular Dynamics, to evaluate microscopic structure of the interface with Janus dimers. We study how the structure of interface depends on the interactions of Janus dimers with the liquids and on their density. We also compare the phenomenological predictions for single Janus particles with the results of simulations. The paper is organized as follows. In the next section we discuss theoretical aspects of adsorption of Janus dimers at the liquid-liquid interface and describe our simulations. The obtained results are described in Results and Discussion Section and the last Section concludes our findings.

Theory Phenomenological approach We present here the theoretical discussion of the behavior of a Janus-like dimer near a flat interface between two liquids. The dimer consists of spheres P and A. These spheres (segments) have the same diameters (σJ = 2R). The dimer corresponds to a dumbbell with a maximal particle aspect ratio. 19 We assume that the sphere P prefers to be immersed in the more polar liquid, while the sphere A prefers the less polar liquid (see Fig. 1a). In the



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a)

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Figure 1: (a) Geometry of Janus dimers at a planar fluid-fluid interface (W-O). (b) Threephase contact angles of polar (θP ) and apolar (θA ) spherical particles at the interface (W-O). following, W denote the more polar fluid and O the less polar one. The surface wettability of both segments is represented by the three-phase contact angles, θP , θA (Fig. 1b). The segments P (A) display contact angle in the range < 0, 90◦ > (< 90◦ , 180◦ >). In this section we consider the particles that satisfy the condition, θA + θP ≤ 180◦ . Let us consider a dimer adsorbed at the depth, h , with the orientation characterized by the angle, θ (Fig. 1b). The orientation angle (θ) is the angle between the long-axis of a Janus dimer and the interface. The adsorption depth (h) corresponds to the position of the center mass of the dimer relative to the interface (the vertical displacement 20 ). We neglect the radius of curvature of the interface relative to the particle radius, the line tension and the buoyancy effects. Then, the attachment energy of the Janus particle from the liquid phase l (l = W, O) to a flat liquid-liquid interface is given by

∆EIl = EI − El


(1)

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where EI and El represent the surface free energy of the system if the particle is adsorbed at the interface and if the particle is completely submerged in the liquid ”l” , respectively. Using the surface tensions we can write (1)

El = SA γAl + SP γP l + SOW γOW ,

(2) (2)

EI = SAO γAO + SAW γAW + SP O γP O + SP W γP W + SOW γOW

(3) (1)

where γij is the interfacial tension between phases i and j (for i, j = O, W, A, P ), while SOW (2)

and SOW are the surface area of the interface in the absence and in the presence of the Janus dimer, respectively. The surface area of the k-th segment of adsorbed particle exposed to the fluid equals

Sk = SkO + SkW

(4)

for k = A, P . ¿From equations (1)-(4) we obtain

∆EIW = SAO (γAO − γAW ) + SP O (γP O − γP W ) − SI γOW ,

(5)

∆EIO = SAW (γAW − γAO ) + SP W (γP W − γP O ) − SI γOW ,

(6)

and

where SI is the area of the interface occupied by the particle when it touches the interface. ¿From Young equation we have

γOW cos θk = γkO − γkP


(7)


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for k = A, P . Combining equations (5)-(7) we can express the attachment energy as

∆EIl = γOW (SAl cos θA + SP l cos θP − SI )

(8)

for l = O, W . In the case of the considered Janus dimers we can express the areas SAl , SP l (l = A, P ) and SI as functions of the parameters R, θA , θP , θ and h (see Fig. 1b). This leads to the following expression for the attachment energy ∆EIW ∆EIW = 2πγOW R2 (cos θA + cos θP + (cos θA − cos θP ) sin θ + sin2 θ − 1) − Rh(cos θA + cos θP ) + h2 (9) The equilibrium adsorption depth and the equilibrium orientation of Janus particle can be determined by minimizing ∆EIW or ∆EIO . From the conditions ∂∆EIW /∂θ = 0 and ∂∆EIW /∂h = 0 we obtain h0 = 0.5R(cos θA + cos θP )

(10)

sin θ0 = cos θr = 0.5(cos θP − cos θA ),

(11)

where θr is the rotation angle describing how the particle axis is oriented relative to the line perpendicular to the interface. 19 There is only one minimum in the attachment energy. This proves that the Janus dimer does not trap into metastable states at the interface. In the considered case (θA ≥ 90◦ ≥ θP ) if θA + θP = 180◦ the segments of the Janus dimer have the opposite (symmetric)wettability, θA = 90◦ + β and θP = 90◦ − β, where β = 0.5(θA − θP ). This means that cos θA = − cos θP . Under such “supplementary wetting conditions” 19 the center of mass of the Janus dimer always is located at the OW-interface (h0 = 0) and the equilibrium orientation angle is θ0 = β = 90◦ − θP (because sin θ0 = 8 ACS Paragon Plus Environment

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cos θP = sin β). In other words, such particles are pinned at the interface and adopt tilted orientation for an arbitrary value of β but β = 0. Park and Lee 19,20 have studied the Janus dumbbells with opposite wettability and different aspect ratios. They determined the areas SAl , SP l (l = A, P ), SI for different orientations of the particle using the numerical method. Then, for each particle orientation the attachment energy was calculated from Eq. (5). The equilibrium orientation was estimated from the function ∆EIW (θ) . Our results are consistent with those obtained by Park and Lee 19,20 for Janus dimers. However, they have not reported the values of θ0 for Janus dimers . The amphiphilicity of Janus dimers can be tuned through variation of the contact angles of the segments, ∆θAP = θA − θP . Under assumed conditions the strongest amphiphilicity is for θA = 180◦ and θP = 0◦ . The case θA = θP = 90◦ corresponds to zero amphiphilicity (homogeneous dimers). In Figure 2 the equilibrium orientation angle θ0 and the equilibrium adsorption depth h0 (in the inset) are plotted as functions of the contact angle θP , for selected values of the contact angle θA . We see here that for a fixed value of the contact angle θA , an increase of the contact angle θP (a decrease of ∆θAP ) causes a decrease the adsorption depth, h0 , and the orientation angle, θ0 . However, for a given value of the angle θP a decrease of ∆θAP (associated with an increase of the angle θA ) leads to a decrease of the orientation angle but to an increase of the equilibrium adsorption depth h0 . Maximal values of the adsorption depth are observed for θA = 90◦ . As predicted for θA + θP = 180◦ , the Janus particles are located at the interface (h0 = 0). These conclusions are in agreement with the experimental data reported by Innes-Gold et al. 35 Let us analyze the behavior of Janus dimers for selected values of the contact angles θA and θP . In the case of the strongest amphiphilicity (θA = 180◦ , θP = 0◦ ) the dimer adsorbs



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Figure 2: The equilibrium orientation angle of a single Janus dimer as a function of the contact angle θP plotted for: a particle with asymmetric wettability and the fixed contact angle θA : 90◦ , 115◦ , 135◦ and a particle with supplementary wettability (dotted line). In the inset the adsorption height as a function of the contact angle θP is plotted for: a particle with asymmetric wettability and θA : 90◦ , 115◦ , 135◦ .


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at the phase boundary (h0 = 0) and adopts the upright orientation (θ0 = 90◦ ). The polar segment P is completely wetted by the fluid W , and the segment A is completely wetted by the fluid O. When θA = θP = 90◦ the homogeneous dimer is oriented parallel to the interface and h0 = 0. For θP = 0◦ and θA = 90◦ , the dimer is more immersed in the fluid W than in the fluid O (h0 = 0.5R) and tilted to the interface (θ0 = 30◦ ). In general, the Janus dimer built of segments with opposite wettability is always attached to the phase boundary and prefer a tilted orientation. We can calculate the equilibrium attachment energy ∆EIW from Eqs. (9) (10) and (11). ∗ Then, the normalized equilibrium attachment energy, defined as as ∆EIW = ∆EIW /(2πR2 γOW ),

can be expressed as

∗ ∆EIW = cos θA + cos θP − 0.5(cos2 θA + cos2 θP ) − 1.

(12)

If θA + θP = 180◦ the normalized attachment energy becomes simpler ∗ ∆EIW = −1(1 + sin2 β).

(13)

Figure 3 presents the normalized equilibrium attachment energy as a function of the con∗ tact angle, θP . If the segments exhibit opposite wettability ∆EIW increases with increasing

contact angle θP (decreasing amphiphilicity ∆θAP ). However, if θA + θP < 180◦ the normalized equilibrium attachment energy has lower values for greater contact angles θA (for fixed θP ) and θP (for fixed θA ). The attachment energy attains the minimal value for the dimer that exhibits the strongest amphiphilicity (the most profitable situation), and the maximal value for θA = 90◦ and θP = 0◦ . The attachment energy of Janus dimers determines their ability to stabilize emulsions.



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∗ Figure 3: The normalized equilibrium attachment energy, ∆EIW = ∆EIW /(2πR2 γOW ), as a function of the contact angle θP for θA : 90◦ , 115◦ , 135◦ . Dotted line line corresponds to the symmetric wettability.

The above analysis shows how the amphiphilicity of a single Janus dimer affects its adsorption depth and orientation.

Molecular simulations We now consider a microscopic model of the system that contains two immiscible fluids (W ,O) and Janus-like dimers. Molecules of both fluids are spherical and have the same diameters, σW = σO ≡ σ. A single Janus particle is modeled as two tangentially jointed spheres A and P , the sizes of which are assumed to be identical, σA = σP ≡ σJ , and σJ = 3σ. The segment connectivity is assured by imposing the harmonic segment-segment potential

u(b) = k(r − σJ )2 ,

where r is the distance between segments. 12 ACS Paragon Plus Environment

(14)

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All the spherical beads (except for directly bonded beads) interact via shifted-force Lennard-Jones potential 36

(ij)

u

   4εij [(σij /r)12 − (σij /r)6 ] + ∆u(ij) (r), =   0,

(ij)

r < rcut ,

(15)

otherwise,

where (ij)

(ij)

∆u(ij) (r) = −(r − rcut )∂u(ij) (rcut )/∂r,

(16)

(ij)

In the above rcut denotes the cutoff distance, σij = 0.5(σi + σj ) (i, j = W, O, A, P )and εij is the parameter characterizing interaction strengths between spherical species i and j. We assume that the interactions between molecules of the liquids W and O (W W , OO and W O), as well as the AO and P W interactions are attractive. In these cases the cutoff (ij)

(ij

distance rcut = 2.5σij . However, if the rcut = σij , the interactions are purely repulsive. The interactions between the following pairs of species are assumed to be purely repulsive: (i, j) = (A, A), (P, P ), (A, P ), (A, W ) and (P, 0). In all simulations we set εOO = εW W = ε for self-interactions between liquids and εOW = 0.5ε for the cross-interactions. Previous determinations have indicated that the phase diagrams of the binary mixture defined above exhibits the demixing transition. 29,37 In the case of repulsive interactions we assume that εP P = εAA = εAw = εP O = ε. However, the parameters of attractive AO and P W interactions (εAO and εP W ) that determine amphiphilicity of dimers were varied. The energy constant of the binding potential is assumed to be large, k = 1000ε/σ 2 . The parameters σJ , εAA and εP P define the equilibrium properties of the model in question. For simplicity, we also assume that all fluid molecules have the same mass, m. The mass of each dimer segment is set arbitrary to 3m. We use the following units: σ as the size scale, ε as the energy scale and m as the mass 13 ACS Paragon Plus Environment


scale. Thus, the time unit is τ = σ

p

(ε/m). The reduced temperature is defined as usual,

T ∗ = kB T /ε. Molecular Dynamics simulations with the help of the LAMMPS package 38,39 have been performed in a rectangular simulation box with dimensions Lx = Ly and Lz along the x, y and z axes, respectively. The box was elongated in the z-direction and was closed at z = −Lz /2 and z = Lz /2 by hard walls. Standard periodic boundary conditions in the x and y directions were introduced. First, the simulation of the fluid (W, 0) mixture was performed. Equal numbers of molecules of the fluids W and O species have been placed in the lower (z < 0) and in the upper (z > 0) parts of the box. At the equilibrium the demixing into O-rich and W -rich phases has been observed. The liquid-liquid interface was parallel to the XY -plane and its center was at z = 0. Next, the requested number of Janus particles per unit surface area Lx × Ly has been randomly inserted at the liquid-liquid interface. Temperature has been controlled by Nose-Hoover thermostat. The time step was ∆t = 0.005τ . We have carried out long simulations (equilibration lasted at least 108 time steps) and monitored the snapshots. The system was considered to being in equilibrium when the total energy of the system reaches a constant level, at which it fluctuates around a mean value. Then the production runs for at least 107 time steps have been performed. During the production runs, data were collected after every 1000 time steps and used for evaluation of local densities ρi (z) of all spherical beads, i = O, W, A, P . Moreover, we also evaluated the profile of centers of mass of Janus dimers, ρJ (z). The density profiles of liquid species, ρO (z) and ρW (z) possessed well pronounced plateaus around z = ±Lz /4. The local densities at the plateaus satisfied very well the symmetry conditions ρW (z = −Lz /4) = ρO (z = Lz /4) and ρO (z = −Lz /4) = ρW (z = Lz /4), as expected. The values of the local densities of both species corresponding to these plateaus


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were taken as bulk partial densities of two coexisting liquid phases. Obviously, the total bulk density, ρb , being the sum of the partial bulk densities of both fluid components, was the same for two coexisting phases. We abbreviate by φ the mole fraction of the W (O) component in the W -rich (O-rich) phase. Due to entirely repulsive interactions AW and P 0 the dimers accumulate at the interface and do not enter neither the O-rich nor the W -rich bulk phases. The surface density of Janus dimers satisfies the equation Z ΓJ =

Z ρJ (z)dz =

ρi (z)dz,

(17)

where i = A, P . All our simulations have been carried out at the temperature T ∗ = 1. We have assumed the energy parameters similar to those used in the ref. 29 Our model with these parameters can mimic different water-organic solvent (e.g., decane-water) interfaces and a wide class of amphiphilic dimers. 13

Results of Discussion In this section we focus on the discussion of the results of our computer simulations. We have investigated Janus dimers with symmetric (εOA = εP W ) and asymmetric (εAO 6= εP W ) amphiphilicity. We kept all the energy parameters but εP W and εAO fixed, and changed the latter parameters. The strong PW interactions cause that the segments P remain mainly in the fluid W . Thus the contact angle θP is smaller. However, for strong AO-interactions the contact angle θA is greater. Note that an increase of the energy εP W is associated with a decrease of the contact angle θP , and inversely, when the energy εAO increases, the contact angle θA also increases. We have carried out two series of simulations: (i) for single-particle systems, and (ii) for many-particle systems. We have calculated the average z-coordinate 15 ACS Paragon Plus Environment


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Figure 4: The average z-coordinate of the center-of-mass (a) and the average orientation angle of the Janus dimer (b) estimated by single-particle simulations for different values of the energy parameter εP W for particles with: symmetric wettability (circles) (εP W = εAO ) and asymmetric wettability for εAO = 0.4 (diamonds) and 1.2 (squares). The lines drawn through the points serve as a guide to the eye. of the mass-centers of dimers (za ) and their average orientation angle θ0 . The adsorption depth, defined in the previous section, is given by h = |za |. In the studied systems the mole fraction of the W (O) component in the W -rich (O-rich) phase is φ = 0.95. We begin with the discussion of the behavior of a single Janus dimer at the interface. Figure 4 presents the average coordinate za (part a) and the average orientation angle (part b) as functions of εP W for symmetric and asymmetric wettability of dimers. In the case of supplementary (symmetric) wettability, the Janus particle always is located at the phase boundary za = h0 = 0 , while for asymmetric amphiphilicity, the coordinate za decreases (h0 increases) as the εP W increases for εAO = 0.4. Indeed, the dimers are located deeper in the fluid W for stronger P W -interactions. Inversely, for εAO = 1.2 the dimers are sucked into the


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Figure 5: Examples of the equilibrium configurations of a single Janus particle for the symmetric wettability: (a) εP W = εAO = 1.6 and εP W = εAO = 0.4 (b), and the asymmetric wettability (c) εP W = 1.2, εAO = 0.4. The side views of the systems. For clarity, molecules of fluids are represented by small spheres (size ratio is not kept) Green and yellow spheres represent the liquids W and O, respectively, while points, blue and red spheres represent the P and A segments of Janus dimers, respectively. fluid O. However, the average orientation angle always increases as the energy parameter εP W increases (i.e., as θP decreases). Thus, the results of simulations are qualitatively consistent with the theoretical prediction. In Figure 5 we show the examples of the dimer’s orientations for selected parameters of the energies εP W and εAO . For a better visualization of orientations of Janus dimers at the interface, molecules of the liquids are represented by very small spheres (“points”) in the snapshots. In these figures the size ratio σJ /σ is not achieved. In the case of many-particle systems we have performed simulations for two values of the surface density of added Janus dimers ΓJ = 0.037 and ΓJ = 0.102. In the considered cases Janus dimers are very strongly adsorbed at the interface. The Janus dimers are practically absent in the bulk liquid phases. We start with the discussion of the systems that form monolayers at the interface ( ΓJ = 0.037 ). First, we analyze the structure of the systems in which, under the assumed conditions, the Janus particles do not assemble. Figure 6 demonstrates examples of equilibrium con-



Figure 6: The representative snapshot for Janus dimers with symmetric wettability, εP W = εAO = 1.2 and ΓJ = 0.037. Blue and red spheres represent the P and A parts of Janus dimers, respectively, and the green points represent the fluid W , yellow points represent the fluid O. figurations of Janus dimers with symmetrical amphiphilicity. The dimers are adsorbed at the interface and they are randomly distributed at the phase boundary. To quantify the interface structure we have calculated the density profiles of all species. Figure 7 shows the density profiles of fluids (part a) and the density profiles of particular segments of Janus dimers (parts b and c). One can see here that the density profiles of the beads A and P are symmetrical relative to the phase boundary between the fluids for Janus dimers with symmetric amphiphilicity (part b), the centers of Janus molecules are located at the interface. If εP W increases, the distance between the maxima corresponding to the segments P and A increases too. This means that the orientation angle also increases (see Fig. 1a). On the contrary, if εP W 6= εAO the density profiles are considerably shifted towards one of the fluids (part c). The monolayers formed by particles with symmetric and asymmetric wettabilities are compared in Figure 8. We show here examples of configurations obtained for εAO = 1.2 and εP W = 1.2 (part a) and εP W = 0.8 (part b). Dashed black line corresponds to the center


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Figure 7: Reduced density profiles of the system components obtained from simulations. In part (a) the density profiles of the fluid W (dashed-dashed-dotted line) and the fluid O (dashed-dotted line) are shown. In part (b) the density profiles of the segments P (dashed lines) and A (solid lines) are plotted for particles with symmetric wettability and εP W = 0.5, 1.2. In part (c) the density profiles of the segment of particles with the asymmetric wettability are shown for εAO = 1.2 and εP W = 0.5, 0.8. The surface density of Janus particles is ΓJ = 0.037. of the interface (z = 0). In the case of symmetric wettability the dimers are positioned at the interface center. However, dimers with the assumed asymmetric wettability are slightly sucked into the fluid O because εAO > εP W . The particles are almost isolated, so they adopt orientations very similar to those observed for single particle systems. For the discussed systems the average orientation angles are: θ0 = 68.1 (part a) and θ0 = 66.6 (part b). The corresponding orientations of a single Janus dimer are: θ0 = 68.9 and θ0 = 65.0, respectively (see Fig. 4). The impact of the surface density of Janus dimers depends on the assumed energy parameters. We can model the behavior of Janus particles changing their interactions with the fluids.



Figure 8: Vertical sections of snapshots for: (a) symmetric wettability (εP W = 1.2) and asymmetric wettability εP W = 0.8 and εAO = 1.2. The surface density of Janus particles is ΓJ = 0.037. Blue and red spheres represent the P and A parts of Janus dimers, respectively, and green points represent the fluid W , yellow points represent the fluid O. Note that we neglect attractive interactions between Janus particles. Below we describe the structures formed by Janus dimers with symmetric wettability. For selected energy parameters the Janus dimers adsorbed at liquid-liquid interface assemble into warm-like clusters. A example of such a structure is shown in Figure 9. In this case interactions of Janus particles with both liquids are weak, εP W = εAO = 0.4. The interactions between molecules of the liquids are stronger (εW W = εOO = 1). The molecules W and O avoid the unfavorable contacts with the appropriate segments of Janus particles. As a consequence, solubility of Janus dimers in the liquids decreases and they form aggregates. Similar clusters were observed experimentally by Park et al. 17 As the interactions of Janus dimers with the liquids weaken (εP W = εP W = 0.3), the particles agglutinate into a large and compact aggregate that resembles a droplet trapped at the interface (see Fig.10). We observe here a


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Figure 9: The representative snapshot for Janus dimers for εP W = εAO = 0.4 (view form above). The surface density of Janus particles is ΓJ = 0.037. Blue and red spheres represent the P and A segments of Janus dimers, respectively, and the green points represent the fluid W , the yellow points represent the fluid O.

Figure 10: The example of configurations (side view) for εP W = εAO = 0.3. The surface density of Janus particles is ΓJ = 0.037. Blue and red spheres represent P and A parts of Janus dimers, respectively, and green points represent the fluid W , yellow points represent the fluid O.



microphase separation at the liquid-liquid interface. The interface structure becomes very complex if the surface density of Janus dimers is considerably higher (ΓJ = 0.102) In this case we have found mixed multilayers at the liquidliquid interface. In Figure 11 the density profiles of the fluids and of segments of Janus dimers are plotted. We see here that Janus dimers form three layers. The sharp liquid-liquid phase boundary is destroyed. Molecules of the liquids are sucked between the layers of Janus dimers. Obviously, the liquid W wets the beads P , while the beads A are surrounded by the molecules O. As a consequence, two layers of the fluids W and O appear inside the interface. The exemplary configuration of this system is shown in Figure 12. The observed structure resembles ”a triple sandwich”. Note that the central layer of Janus dimers has the opposite orientation than the outer layers. The density functional theory for nanoparticles also predicts the formation of multilayer structures. 40 A comparison of Figures 6 and 12 well illustrates the influence of the density of Janus particles on the structure of the interface. Our simulations show that a picture of fluid-fluid interface in the presence of Janus particles can be much richer than that predicted by simple, phenomenological theories.

Conclusions We have presented the study on the orientation and assembly of Janus-like dimers at fluidfluid interface. We have found the equilibrium orientation and the adsorption depth of Janus dimers using Young equation. We have shown that only one minimum in interfacial energy exists for a single Janus dimer. Our theoretical predictions were confirmed by computer simulations. We have analyzed the equilibrium attachment energy for different contact angles of polar and apolar parts of particles. We have carried out molecular dynamics simulations of Janus dimers at the interface between partially miscible Lennard-Jones liquids.


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Figure 11: The reduced density profiles of the liquids and particular segments of Janus dimers obtained from simulations for εP W = εAO = 1.2 and ΓJ = 0.102. Lines: dasheddashed-dotted - W , dashed-dotted - O, dashed - P , solid A.

Figure 12: Vertical section of the snapshot for εP W = εAO = 1.2 and ΓJ = 0.102. Blue and red spheres represent the P and A parts of Janus dimers, respectively, and green points represent the fluid W , while yellow points represent the fluid O.



The amphiphilicity of Janus particles are controlled by the energies of interactions of the liquids with polar and apolar parts of the Janus dimers. We have considered two types of particles: with the supplementary (symmetric) wettability and “asymmetric” wettability of both parts of Janus dimers. We have found that at low densities and depending on the assumed energy parameters: orientationally ordered monolayers, warm-like aggregates or large, compact clusters. As follows from the analysis of the density profiles of all species for a low surface density of Janus dimers the interface layer is narrow. The adsorbed particles form an almost flat layer. When density of Janus dimers is sufficiently high, mixed multilayers are observed. At the interface Janus dimers and molecules of the liquids form alternately arranged layers. The mechanism of adsorption is explained in terms of a specific competition between interactions of particles with the liquids. The combined shape and wettability properties of Janus dimers have significant impact on their surface activity and the properties of the liquid-liquid interface. The study provides a guidance to constructing systems with a needed structure of the interface. The ability to manipulate the rheology of the interface may open new opportunities for practical applications.

Acknowledgement Authors acknowledge support from National Science Centre, Poland, Grant No. 2015/17/B/ST4/03615.


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