Self-Assembly and Viscosity Behavior of Janus Nanoparticles in

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Self-assembly and viscosity behavior of Janus nanoparticles in nanotube flow Yusei Kobayashi, and Noriyoshi Arai Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02694 • Publication Date (Web): 05 Jan 2017 Downloaded from http://pubs.acs.org on January 10, 2017

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Self-assembly and viscosity behavior of Janus nanoparticles in nanotube flow Yusei Kobayashi∗ and Noriyoshi Arai∗ Department of Mechanical Engineering, Kindai University, Osaka, Japan E-mail: [email protected]; [email protected]

Abstract Janus nanoparticles (JNPs) have received considerable attention because of their characteristic physical properties that are due to more than two distinct chemical or physical surfaces. We investigated the rheological properties of a JNP solution in the nanotubes using a computer simulation. Prediction and control of the self-assembly of colloidal nanoparticles is of critical importance in materials chemistry and engineering. Herein, we show computer simulation evidence of a new type of velocity profile and a hallmark shear-thinning behavior by confinning a JNP solution to a nanotube with hydrophobic and hydrophilic wall surface. We derived curves of the shear rate versus the viscosity for two quasi-one-dimensional nanotube systems including diluted and concentrated volume fractions of JNP solutions. For the diluted system, under relatively low shear rates, shear-thinning behavior with a moderately slope or behavior similar to a Newtonian fluid is observed because of the clustering of JNPs. Under relatively high shear rates, the slope of shear thinning changes markedly because the self-assembled structures are rearranged. Moreover, for concentrated systems, when the nanotube wall is hydrophobic, new characteristic velocity profiles that have not been reported ∗

To whom correspondence should be addressed

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before are observed. Our simulation offers a guide to controll the rheological properties of JNP solutions by the chemical patterns on the surfaces of nanochannels, the effect of confinement, and the self-assembled structure.

Introduction The self–assembly of nanoparticles is widely used in industry. For example, the optical transparency of liquid crystal displays is controlled by the regular arrangement of particles, and the viscosity of coating materials is controlled by a self–assembled surfactants. Moreover, self–assembled materials have been developed, such as micelles, 1,2 quantum dots, 3,4 and nanomachines. 5,6 Thus, it is crucial to predict and control the self–assembly of nanoparticles. Designing colloidal particles with anisotropic shapes and chemical interactions is an effective method to control the morphologies of self–assembled nanoparticles. The complex structures or phases that anisotropic particles generate are expected to have special rheological properties. Janus nanoparticles (JNPs) have received considerable attention because of their characteristic physical properties, which are due to two distinct chemical or physical surfaces. We expect them to have new self–assembled structures and rheological properties. In a recent study, anisotropic nanoparticles were synthesized experimentally. Urban et al. 7 developed several routes for the effective fabrication of composite particles with asymmetric morphology and dual functionalities. JNPs with one biodegradable face and a nonbiodegradable face with a surface can be manufactured using their process. Lone et al. 8 reported a method of preparing polymeric Janus particles is effective techniques by droplet microfluidics. Furthermore, Yang et al. 9 developed a new fabrication method to prepare metallic Janus silica particles by embedding nanosized silica particles in a spherical polystyrene substrate in supercritical CO2. According to the literature, the supercritical CO2–aided masking method allowed for the controlled particle particle embedding. In addition, anisotropic nanoparticles have been reported via simulation. Bordin et al. 10 reported the pressure versus temperature 2 ACS Paragon Plus Environment

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phase diagram of a Janus dumbbells system to investigate the effects of the competition between a standard Lennard–Jones potential and a core–softened potential. They found a rich variety of micelles and the lamellar phase in the hydrophobic–hydrophilic Janus dumbbell. DeLaCruz–Araujo et al. 11 demonstrated the self–assembly of JNPs under steady shear flow. Their study found that cluster structures of JNPs form because of steady shear flow, and the mean cluster size decreases at high shear flow. Beltran–Villegas et al. 12 investigated the phase behavior of short–range interacting isotropic particles and single–patch JNPs. According to the literature, a lamellar phase with a different range of stability than that observed in previous studies has been observed. In recent years, JNPs have been investigated, and a variety of self–assembled structures have been found, including bilayers, hexagonal crystals, and Kagome lattices, depending on the surface properties and anisotropy of the JNPs and the temperature. However, predicting and controlling the size, structure, and properties of the JNPs remains challenging. Rheological properties and morphologies not observed in the bulk can be found in confined systems. Many studies of self–assembled structures have been reported for confined systems. Chang 13 showed that, even for simple fluids such as water, a special dynamic behavior is observed by the effect of confinement. Double–walled Ice–NT is found by molecular dynamics simulations of water which confined in a carbon nanotube. They also found that the melting temperature was lower than that of the bulk water because of its quasi–one– dimensional nature. Moreover, in recent years, complex fluids, including JNP solutions confined in nanoscale channels has already been reported. 14–18 However, there has been no study that tried to measure the viscosities and velocity profiles of JNPs solutions confined in nanotubes. In this report, we demonstrate the viscosity behavior and velocity profile of JNPs solutions in nanotubes using the dissipative particle dynamics (DPD) method. In addition, the selfassembly of diblock JNPs under shear flow and nanotube flow is discussed.


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Method Dissipative particle dynamics (DPD) method We used the dissipative particle dynamics (DPD) method 19,20 to investigate the rheological properties of JNPs solutions in nanotubes using in–house code. The DPD method can be used in simulations on millisecond timescales and micrometre length scales. This is because we only have to simulate the motion of coarse–grained particles (composed of a group of atoms or molecules). In this simulation, we treated each JNPs as a rigid body. 21 We calculated equation of translational motion and rotational motion by the method. We can calculate the motion of particle using the Newton equation. The basic equation of the DPD method consists of Newton’s equations of motion. Newton’s equation of motion for a particle i are given as

mi

∑ ∑ ∑ dvi FR FD FC = fi = ij , ij + ij + dt j̸=i j̸=i j̸=i

(1)

Here, m is the mass of a particle, v is the velocity, FC is the conservative force, FR is the pairwise random force, and FD is the dissipative force. Namely, the force fi is a sum of the conservative force, the pairwise random force, and the dissipative force within the DPD method. The conservative force is defined by the following formula:  ( ) |rij |   −aij 1 − nij , |rij | ≤ rc C r c Fij =    0, |rij | > rc .

(2)

Here, aij is a parameter which determines the magnitude of the repulsive force between particles i and j and it is reflective of the property of the material. aij is the only parameter which has the information of the material in the DPD method. rc is the cutoff distance and D rij = rj − ri and nij = rij / |rij |. Next, the random force (FR ij ) and the dissipative force (Fij )


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are defined by the following formula:

FR ij =

and FD ij =

   σω R (|rij |) ζij ∆t−1/2 nij , |rij | ≤ rc   

|rij | > rc

0,

   −γω D (|rij |) (nij · vij ) nij , |rij | ≤ rc   

(3)

(4)

|rij | > rc ,

0,

where σ is the noise parameter, γ is the friction parameter, ζij is a random number based on the Gaussian distribution, and vij = vj −vi . the random force (FR ij ) is equivalent to frictional force. The combination of dissipative and random forces controlled the temperature. 20 The weighting function ω R and ω D are related by the following formula: [ ]2 |rij |   , |rij | ≤ rc [ ]2  1 − r c ω D (r) = ω R (r) =    0, |rij | > rc .

(5)

The noise parameter σ and the friction parameter γ are linked to each other by the “fluctuation– dissipation theorem”, defined by the following equation:

σ 2 = 2γkB T,

(6)

where kB is the Boltzmann constant and T is the temperature.

Simulation model and conditions Figure 1a shows the model diblock JNP used in our simulation. The JNP consists of both hydrophobic and hydrophilic DPD beads on a diamond lattice with a lattice constant of α = 0.47 nm. Each JNP consists of 1,684 DPD beads: 870 are hydrophobic (labelled by the letter O) and another 814 are hydrophilic (labelled by the letter I). The JNP radius, 5 ACS Paragon Plus Environment

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RNP is 1.94 nm. In this simulation, we use reduced units in terms of the cutoff radius rc , the particle mass m, and the energy kB T . To relate results of simulations to a realistic system requires substitution of realistic values of rc , m, and kB T for that system. We set three water molecules are coarse–grained for a single DPD particle, and accordingly, the unit of mass is 54 in atomic units. The particle density ρrc3 is 3. The three DPD particles ˚3 due to the are contained in a cube of rc3 and therefore corresponds to a volume of 270 A ˚3 . Thus, the physical value of the unit of length volume of a water molecule being 30 A rc is (270)1/3 ˚ A= 6.463 ˚ A, which was previously derived by Groot and Rabone to fit the measured diffusion constant of water. 22 The solvent bead (or monomer) is labelled by the letter S. The interaction parameters between any two DPD beads are shown in Table 1, similar to early studies. 16,17 The interaction parameter between two solvent beads is set at the same value (25 kB T /rc ) when the number density of the solvent is 3.0 according to the Groot–Warren theory. 23 The interaction parameters aOS (= 100 kB T /rc > aSS ) and aIS (= 25 kB T /rc = aSS ) represent hydrophobic and hydrophilic interactions, respectively. We considered one radius for the nanotube, RNT /RNP = 3.5, and two distinct types of nanotube walls, namely hydrophobic and hydrophilic. Here, RNT is the radius of the nanotube. The interaction parameters between the nanotube wall and DPD bead are shown in Table 2. The surface density of nanotube wall is about 4.5. We assumed that the nanotube wall is consisted single–walled zigzag carbon nanotube. Note that in our systems, we assume that the colloids are uncharged and systems like a screening electrolyte (e.g., in dilute solution of ionic latex spheres). Hence, long range electrostatic repulsion is not considered. We used 40,416 beads for JNP construction, and the total number of JNPs in the system is 24. Then, 1,802 beads are used for nanotube wall construction, and the remaining beads are solvent. In this simulation, self–assembly structures for the JNP solution in nanotube are prepared using our previous study, which adopted a smoothed wall. 17 The noise parameter σ is 3.0, the friction parameter γ is 4.5, and time step dt is 0.01. The self–assembly structures are distinguished based on the radial distribution function (RDF). The volume fraction of


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JNPs and axial length of nanotube for liquid and amorphous phase are shown in Table 3. However, we set frozen particles (Fig. 1b) as the inner surface of the cylindrical nanotube to satisfy the non-slip boundary conditions. We also confirmed that initial configurations can be maintained for a long period of time. In order to generate a flow, the virtual density gradient method, which Kinjo et al. devised with a new boundary condition, 24 was employed. In this method, the image cells is controlled by elongation and contraction of the boundary condition. As a results, a density (or pressure) gradient occurs in the system. Then, this method enables flow generation by the pressure gradient. The mean shear rate of a laminar pipe flow 25 is given by γ˙ m =

2(1 + 3n) V , 1 + 2n RNT

(7)

where V is the mean velocity of fluid, and n is the power law parameter. Here, we set n = 1/3 for a plug flow. 26 We estimated the volumetric flow rate (see Fig. S1) by applying the method of cylindrical shells to a velocity profile. The curve of the velocity profile is fitted using a seventh degree polynomial function. Then, the volumetric flow rate (Q) obtained by rotating about the y–axis is

∫

RNT

2πr|Uz (r)|dr .

Q=

(8)

0

In a power-law fluid, the viscosity (η) is typically derived by the ratio of shear stress (τ ) to shear rate (γ). ˙ For a power-law fluid, τ = K γ˙ m n , therefore η = K γ˙ m n−1 . The flow consistency index (K) can be extracted by computing the volumetric flow rate (Q). Table 1: Interaction Parameters aij (in kB T /rc units) between Bead Pairs in Eq 2 O I S

O 10 50 100

I 50 100 25


S 100 25 25

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Table 2: Interaction Parameters awall,p (in kB T /rc units) between Bead and Nanotube Wall hydrophobic wall hydrophilic wall

O 15 40

I 40 15

S 40 15

Table 3: Volume fraction of JNPs and axial length of nanotube for liquid and amorphous phase volume fraction [%]

axial length [nm]

19 19

26.7 26.7

33 41

15.1 12.2

liquid phase hydrophilic wall hydrophobic wall amorphous phase hydrophilic wall hydrophobic wall

Results and Discussion We performed simulations for four models which the initial configuration are the liquid phase and amorphous phase (Fig. 1c). We measured the Reynolds numbers for all systems. The Reynolds numbers range from 14 to 320. The results suggest that only laminar flow is observed in this study. We calculated velocity profiles depending on the chemical nature of wall surface and the shear rate as shown in Fig. 2. The shear rate γ˙ ranges from 0.05 to 0.7 in reduced unit. In Figures 3a and b, we show curves of the shear rate (γ) ˙ versus the viscosity (η) for quasi-one-dimensional (Q1D) nanotube systems. We calculated slopes of the viscosity using the function η = aγ˙ b . The ratio of the nanotube radius to the JNP radius (RNT /RNP ) is 3.5. Here, the RNP is 3 in reduced unit. The vertical axis is the viscosity (η), and the horizontal one is the shear rate (γ). ˙ Red circles shows data for hydrophobic nanotube, and blue circles shows data for hydrophilic nanotube. We derived curves of pressure in the axial (z) direction versus reduced simulation time to confirm enough to ensure the relaxation to the pipe flow (Fig. 4). Moreover, in order to identify the reason why the viscosity behavior changes, we calculated the radial distribution function (see Fig. 5). Figure 6 shows the density profiles of the hydrophobic part, the hydrophilic part, and the water of the JNP solution in the radial direction with the state becoming a steady condition. 8 ACS Paragon Plus Environment

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Velocity behavior of Janus nanoparticle solution in nanotube Amorphous phase

In the first series of this simulation, amorphous phases (Figs. 1c3 and c4) are considered. A non–Newtonian fluid in a pipe sometimes exhibits a “plug flow”, which is defined as a flow regime with no longitudinal dispersion. 27 In our simulation, plug flow is obtained only in the hydrophilic nanotube (see Fig.2b). When the nanotube wall is hydrophobic, flow closer to the center region of the nanotube is faster than that far from the center (see Fig. 2a). According to our knowledge, this velocity profile has not been reported before. Here, the solvent particles prefer to be located in the center of the nanotube, and the hydrophobic sides of JNPs prefer to be in contact with the inner wall (see Fig. 6a). The JNPs effectively block a flow near the wall surface (see Fig. 7). As a result, loss flow is generated, then the velocity near the wall surface is quite slow. The fact is also confirmed by the RDF of the hydrophobic nanotube (see Fig. 5a); the solvent particles are distributed within a relatively small radius (RNT < 4.0), and the other particles are distributed within a relatively lager radius (RNT > 4.0) for hydrophobic nanotubes. The velocity near the wall surface is quite slow; therefore, the velocity of solvent particle located in the center region is faster than that of JNPs. In contrast, when the nanotube wall is hydrophilic, the solvent particles prefer to be in contact with the inner wall, as shown in Fig. 6d. Hence, in comparison with the case when the nanotube wall is hydrophobic, the velocity of the solvent particles is comparatively slow. As a result, a plug flow is generated by reducing the difference between the speed of solvent particles and that of the JNPs. Moreover, it suggests that the shape of the velocity profiles is dominated by the positions of the solvent particles.


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Liquid phase

In the second series of this simulation, liquid phases (Figs. 1c1 and c2) are considered. For the liquid phase, the velocity distribution is the same as that of plug flow and does not depend on the chemical nature of the wall surface (see Figs. 2c and d). We were able to observe similar velocity profiles in both nanotubes. The volume fraction of JNPs that self–assembled in the liquid phase is lower than that of JNPs that self-assembled in the amorphous phase. Solvent particles can move freely, and consequently the solvent particles evenly distributed in both nanotubes (see Figs. 6c and d). Thus, no significant difference was observed in velocity behaviors of JNP solutions in the liquid phase. Here, when the nanotube wall is hydrophobic, the flow of closer to the center of the nanotube is insignificantly faster, as shown in Fig. 2c. In common with amorphous phase, the solvent particles prefer to be located in the center of the nanotube, and the hydrophobic sides of JNPs prefer to be in contact with the inner wall (see Fig. 6c) We considered that loss flow is generated, then the velocity near the wall surface is quite slow. As a result, an insignificantly faster flow closer to the center region occurs in the hydrophobic nanotube. As the shear rate increases,the JNPs which contact with the inner wall decreases. In short, effect of block a flow near the wall surface is weak (see Fig. 7). Therefor, the velocity profile of hydrophobic nanotube become that of hydrophilic nanotube.

Viscosity behavior of Janus nanoparticle solution in nanotube Liquid phase

Figure 3a shows viscosity behavior of JNP solution in hydrophobic nanotube (red circle) and hydrophilic nanotube (blue circle) for liquid phase. The viscosity which confined in hydrophobic nanotube is about one and a half times as high as that in hydrophilic nanotube.


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For both nanotubes, a slope of η which consists of two stages is observed. The JNP solutions behaves as newtonian fluid for γ˙ < 0.2 in the first stage. Then, the shear–thinning behavior is seen at γ˙ = 0.2 in the second stage. Leng and Cummings 28 reported the shear dynamics of hydration water confined in nanoslit. When the effect of confinement is strong (the thickness of the nanochannel (D) = 0.92 nm), a shear–thinning behavior is observed. On the other hand, when the effect of confinement is relatively weak (D = 1.65 and 2.44 nm), the solution behaves as a newtonian fluid. In our simulation, the nanotube diameter is 13.57 nm. In fact, in comparison with their study, the effect of confinement is comparatively weak. Hence, the reason why the shear–thinning occurred, we considered that specific of the Janus nature of the colloids influenced the results. Here, for low shear rates (γ˙ < 0.2), the self– assembled structures remain unchanged; clustering of JNPs occurred in the center region of the hydrophilic nanotube. As the shear rate increases (γ˙ < 0.3), the JNP solutions behaves as newtonian fluid because the self-assembled structures remain unchanged in the hydrophilic nanotube. For high shear rates (γ˙ > 0.3), the mean cluster size decreases and shear-thinning behavior occurs. Nikoubashman et al. reported the self–assembly of diblock JNPs under shear flow in a slit–like channel. 18 They showed the relation between the shear rate and single Janus micelles for aggregation numbers. According to the literature, when high shear is applied, a decrease in Janus micelles for aggregation numbers is observed. Furthermore, we compared the self–assembled equilibrium structures under low and high shear rates based on the RDF (see Figs. 5c and d). For both nanotubes, when a low shear rate is applied, two close peaks are observed at 6.0 < RNT < 6.8 (blue line). We found similar peaks in the equilibrium state (no shear) in an early study. 17 The results suggest that the self–assembled structures remain almost unchanged under low shear rates. In contrast, single blunt peak arise under high shear rate. For γ˙ > 0.3, it seems that the cause of the change in the slope of η is the rearrangement of self-assembled structures, which can easily flow.


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Amorphous phase

Figure 3b shows the viscosity behavior of a JNPs solution in a hydrophobic nanotube (red circles) and a hydrophilic nanotube (blue circles) in the amorphous phase. The viscosity of the solution confined in the hydrophobic nanotube is at least two and a half times as high as that in the hydrophilic nanotube. For both nanotubes, the slope of η consists of two stages. First, when the nanotube wall is hydrophobic, shear–thinning behavior is seen at γ˙ < 0.3 with a moderate slope in the first stage. However, the self–assembled structure is not changed much by a relatively low shear rate. One of the reasons that shear–thinning behavior occurs without changing the self–assembled structure is because the flow closer to the center of the nanotube is faster than that far from the center. As the shear rate increases (γ˙ < 0.3), the JNPs which contact with the inner wall decreases. The velocity profile of hydrophobic nanotube become that of hydrophilic nanotube, then volumetric flow rate increases. As a result, shear–thinning behavior occurs. Then, for γ˙ > 0.3, the slope of η changes markedly in the second stage. The RDF (see 5a) also shows that two close peaks and single blunt peak arise at 6.0 < RNT < 6.8 (red and blue line). The self–assembled structures are rearranged by high shear rate. When the nanotube wall is hydrophilic, the JNP solution behaves as a Newtonian fluid for γ˙ < 0.3 in the first stage. Then, shear–thinning behavior becomes significant at γ˙ > 0.3 in second stage. In contrast, we observed a clear difference in viscosity behavior of the solution confined in the hydrophilic nanotube. The reason for this difference can be explained as follows. Solvent particles prefer to be in contact with the inner wall of the nanotube, and the hydrophobic sides of the JNPs prefer to be in contact with other hydrophobic sides. As a result, JNPs located near the wall move from inner wall of the nanotube, and the self–assembled structures are rearranged (see Fig. 5b). We found that the self–assembled structure confined in the hydrophilic nanotube is easier to change by pipe flow than that in the hydrophobic nanotube.


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Conclusions In summary, we investigated the viscosity behavior and velocity profiles of JNP solutions confined in nanotubes using a dissipative particle dynamics simulation. We found that the viscosity behavior depends on the self–assembled phase and the chemical nature of the wall surface. Graphs of the viscosity (η) versus the shear rate (γ), ˙ and velocity profiles for diblock JNP solutions confined in nanotubes with hydrophilic and hydrophobic walls are shown. For the liquid phase, when the nanotube wall is hydrophilic, the viscosity shows almost no change for slower shear rates (γ˙ from 0.08 to 0.2). However, shear–thinning behavior is observed for relatively fast shear rates (γ˙ > 0.3). When the nanotube wall is hydrophobic, shear-thinning behavior is observed with no dependence on shear rate. When the shear rate is comparatively large, the mean aggregation number decrease and shear-thinning behavior occurs. For the amorphous phase, when the nanotube wall is hydrophobic, shear–thinning behavior occurs with changing the self–assembled structure. The radial distribution function shows that two close peaks and a single blunt peak arise (Fig. 5a). The self–assembled structures are rearranged by a high shear rate. When the nanotube wall is hydrophilic, the JNP solutions behave as a Newtonian fluid for γ˙ < 0.3. Shear–thinning behavior is significant at γ˙ > 0.3 Here, JNPs located near the wall move from the inner wall of the nanotube, and the self–assembled structures are rearranged (Fig. 5b). We found that self–assembled structures confined in hydrophilic nanotubes change more easily than those in hydrophobic nanotubes because of pipe flow. Moreover, velocity profiles of JNP solutions in nanotubes were investigated. For the amorphous phase, a plug flow is obtained only in the hydrophilic nanotube (see Fig. 2b). However, when the nanotube wall is hydrophobic, new characteristic velocity profiles that have not been previously reported are observed. The present study found that the plug flow is generated by reducing the difference between the speed of solvent particles and JNPs. It also suggests that the shape of the velocity profiles is dominated by the positions of solvent particles and JNPs. 13 ACS Paragon Plus Environment

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For the liquid phase, the velocity distribution is the same as that of plug flow and does not depend on the chemical nature of the wall surface (see Figs. 2c and d). Solvent particles have greater space for nanotubes, then no significant difference was observed in velocity profile. Controlling and predicting the rheological properties of JNP solutions is still challenging because a variety of factors affects the physical properties. Hence, we feel that our study contributes to the discussion of complex fluids. Herein, we showed computer simulation evidence of the characteristic rheological properties of JNP solutions including viscosity and velocity profiles. Our simulation offers a guide to control rheological properties with chemical patterns on the surface of nanochannels, the effect of confinement, and the self–assembled structure.


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Figure 1: (a) The JNP model is composed of a hydrophobic side (red) and a hydrophilic side (blue). The water model is a single DPD particle (aqua). (b) The left panel is a model of the nanotube and side views of snapshots, showing water molecules and the JNP. The right panel is top views in the axial direction. (c) Snapshots of equilibrium morphologies (initial configurations) of the JNP solution confined to hydrophobic and hydrophilic nanotubes.


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Figure 2: Comparison of velocity profiles (diamonds shape, triangles, squares, circles) of JNP solutions. The upper left panel is the velocity profile of hydrophobic nanotubes and the amorphous phase. The upper right panel is the velocity profile of hydrophilic nanotubes and the amorphous phase. The lower left panel is the velocity profile of hydrophobic nanotubes and the liquid phase. The lower right panel is the velocity profile of hydrophilic nanotubes and the liquid phase.


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Figure 3: The red circles are data for hydrophobic nanotubes, and the blue circles are data for hydrophilic nanotubes. (a) Shear rate γ˙ versus viscosity η (red and blue circles) for the liquid phase. (b) Shear rate γ˙ versus viscosity η (red and blue circles) for the amorphous phase.


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Figure 4: Representative data of temporal pressure change. IA: shear rate (γ˙ = 0.47), for hydrophilic nanotube, the purple line is data in the amorphous phase. IL: shear rate (γ˙ = 0.57), for hydrophilic nanotube, the blue line is data in the liquid phase. BA: shear rate (γ˙ = 0.43), for hydrophobic nanotube, the red line is data in the amorphous phase. BL: shear rate (γ˙ = 0.60), for hydrophobic nanotube, the orange line is data in the liquid phase.


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Figure 5: Amorphous phase: RDF for a JNP solution confined in a hydrophobic nanotube (a). (a) Red line: high shear rate (γ˙ = 0.58, blue line: low shear rate (γ˙ = 0.074). RDF for a JNP solution confined in a hydrophilic nanotube (b). (b) Red line: high shear rate (γ˙ = 0.62), blue line: low shear rate (γ˙ = 0.086). Liquid phase: RDF for a JNP solution confined in a hydrophobic nanotube (c). (c) Red line: high shear rate (γ˙ = 0.64), Blue line: low shear rate (γ˙ = 0.064). RDF for a JNP solution confined in a hydrophilic nanotube (d). (d) Red line: high shear rate (γ˙ = 0.43), blue line: low shear rate (γ˙ = 0.071).


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Figure 6: Amorphous phase: Density profiles of hydrophobic nanotubes in the radial direction (a). Density profiles of hydrophilic nanotubes in the radial direction (b). Liquid phase: Density profiles of hydrophobic nanotubes in the radial direction (c). Density profiles of hydrophilic nanotubes in the radial direction (d).


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Figure 7: Comparison of the self–assembly of JNPs and the differences of velocity profiles.

Acknowledgement The authors are grateful to Mr. K. Nomura (Keio University) for the coding the main simulation program.

Supporting Information Available Sequence of estimation method for volumetric flow rate is showed. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Viscosity

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Shear rate

Table of Contents.


Self-Assembly and Viscosity Behavior of Janus Nanoparticles in

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