Tilting and Tumbling of Janus Nanoparticles at Sheared Interfaces

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Tilting and Tumbling of Janus Nanoparticles at Sheared Interfaces Hossein Rezvantalab, and Shahab Shojaei-Zadeh ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.6b01521 • Publication Date (Web): 28 Apr 2016 Downloaded from http://pubs.acs.org on May 2, 2016

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Tilting and Tumbling of Janus Nanoparticles at Sheared Interfaces Hossein Rezvantalab1 and Shahab Shojaei-Zadeh1,2,* 1

Department of Mechanical and Aerospace Engineering, Rutgers, The state University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854-8058, United States

2

Institute for Advanced Materials, Devices and Nanotechnology, 607 Taylor Road, Piscataway, New Jersey 08854-8019, United States *Corresponding author, E-mail: [email protected]

ABSTRACT: We investigate the response of a single Janus nanoparticle adsorbed at an oilwater interface to imposed shear flows using molecular dynamics simulations. We consider particles of different geometry including spheres, cylinders, and discs, and tune their degree of amphiphilicity by controlling the affinity of their two sides to the fluid phases. We observe that depending on the shape, amphiphilicity, and the applied shear rate, two modes of rotational dynamics takes place: a smooth tilt or a tumbling motion. We demonstrate that irrespective of this dynamic behavior, a steady-state orientation is eventually achieved as a result of the balance between the shear- and capillary-induced torques, which can be tuned by controlling the surface property and flow parameters. Our findings provide insight on using flow fields to tune particle orientation at an interface and to utilize it to direct their assembly into ordered monolayers. KEYWORDS: Janus nanoparticles, liquid-liquid interface, equilibrium orientation, rotational dynamics, tumbling, shear-induced assembly

The adsorption of nanoparticles at fluid interfaces is becoming a central topic in colloidal science and has attracted significant research efforts over the past decade. A driving force for such

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studies is the range of potential applications of these systems. For instance, stabilization of emulsions by employing nanoparticles is a very attractive tool in food, cosmetics, oil and pharmaceutical industries.1, 2 This method of emulsification offers several advantages over the traditional use of surfactants, including improved stability, reduced toxicity, environmental benignity, and the possibility of introducing additional functionality by e.g. using ferromagnetic particles.3 Recent development in the synthesis of nanoparticles has enabled fabrication of complex geometries with heterogeneous surface properties, thus providing alternative routes for directing their assembly e.g. by tuning specific interactions. Janus particles composed of two chemically or physically distinctive surfaces have been fabricated in a variety of shapes and sizes, and are being used in applications ranging from switchable display panels to biosensors.4-6 The difference in wettability of the two surfaces leads to amphiphilic Janus particles which can strongly adsorb to liquid interfaces7-9 Viscous flows are used as a tool to direct the assembly of homogeneous nanoparticles at liquid interfaces.10 For Janus particles, the equilibrium orientation and consequently inter-particle forces at the interface can be tuned in the presence of shear flows, thus leading to structures that are not thermodynamically achievable at a stationary interface. Although important aspects of the physical behavior of Janus nanoparticles at stationary interfaces have been revealed, little is known about their dynamics and response to shear flows. Earlier studies using molecular dynamics simulations focused on the stability and desorption energy of Janus nanoparticles from a liquid interface,11, 12 contact angle measurements,13 or interfacial diffusion.14 The dynamics of Janus particles with a slip-stick character or those possessing a self-diffusiophoretic nature have been investigated under shear flow in bulk fluid.15, 16 The structure and kinetics of amphiphilic


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particles has been studied in a binary polymer mixture subject to an external shear field,17 revealing that the shear facilitates uniform alignment of one-dimensional Janus nanorods at the phase interface. However, there is currently no knowledge of the configuration of nanoparticles with different size, shape, and amphiphilicity at a liquid interface subject to hydrodynamic flows. Predicting interfacial dynamics of Janus particles at fluid interfaces will provide guidelines for designing colloidal structures with desired orientation, transport, and rheological properties. In this study, we use molecular dynamics simulations to investigate shear-induced response of a single Janus nanoparticle at the interface between two immiscible fluids. We consider spherical, cylindrical, and disc-shaped particles with differing affinity of their two sides to the fluid phases, and evaluate different scenarios for their rotational dynamics subject to a linear symmetric shear flow. We demonstrate the possibility of directing particles to different orientations by controlling their surface chemistry and the applied shear rate, and will discuss the origin of their steady-state behavior by measuring the net torque imposed by the two fluid phases. The outcome of our analysis can have important implications in a number of fields where the interaction of nanoparticles with liquid interfaces is significant including in the development of Pickering systems with enhanced stability, interaction of biological entities (e.g. proteins) or drug carriers with cell membrane, as well as fabrication of 2D ordered structures.

RESULTS AND DISCUSSION The molecular dynamics simulation scheme is explained in Methods Section. In order to validate our calculations, we first evaluated the average fluid properties at a stationary interface in the absence of nanoparticles. The numerical approach for estimating the fluid density and interfacial tension are presented in the Supporting Information. The results indicate excellent agreement


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with earlier molecular simulations using similar fluids. In the following, we focus on particle dynamics at sheared interfaces.

Translational Motion of Janus Particles at a Sheared Interface We investigate the motion of Janus particles at the interface between two fluids with equal density of ρ = 0.8 σ-3, viscosity of η = 2.0 m.σ-1.τ-1, and the interfacial tension calculated as γ = 1.47 ε.σ-2, where σ, τ, ε are the length-scale, time-scale, and energy-scale of the simulations. The translational motion is quantified using the mean-squared displacement of the particle as a function of time

〈∆ 〉 〈 0 〉

(1)

where is the center of mass position of the particle at time t and the angle brackets denote averaging over realizations with different initialization of fluid velocity profile. Figure 1 shows the components of mean-squared displacement along different coordinate axes for the sample case of a spherical particle with the amphiphilicity characterized by β = 60º subject to a shear-

rate of 0.015 . We observe that the particle shows negligible motion in the direction

Figure 1. Mean-Squared Displacement (MSD) for a Janus sphere with a radius of R = 6σ and amphiphilicity characterized by β = 60˚ at a liquid interface subject to a symmetric shear flow with 0.015 .


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normal to the interface (MSDy ≈ 0), thus indicating that the shear flow does not lead to particle detachment. A similar trend was found for all particle geometries within the whole investigated

range of shear rate (0.005 < < 0.05 ). Calculating the average fluid velocity profile shows a symmetric distribution with respect to the interface plane. Comparing the center-of-mass velocity of the particle with that of the surrounding fluid species indicates negligible slip at the solid boundary. As a result, all nanoparticles remain stable and maintain their energetically favorable position at the interface. On the other hand, the components of mean-squared displacement along the interface plane (x,z directions) are very similar, thus indicating negligible bulk motion of the particle upon applying the shear flow. This is in fact expected as MSDy suggests that the particle barely moves away from the plane of interface where the symmetric shear flow induces zero bulk velocity. The motion within the interface plane clearly follows a diffusive trend governed by thermal fluctuations. As a similar trend is observed for all geometries under the investigated range of shear rates, we conclude that the orientational configuration can be independently controlled without moving the particle.

Rotational Dynamics of Janus Particles under Shear Flow In the absence of shear, each particle adsorbs at the interface according to the energetically favorable orientation dictated by preferred wetting condition. For Janus spheres, this corresponds to the upright configuration (θ = 0º in Figure 10) where each side is completely in contact with its favorite fluid phase.18-20 Continuum predictions suggest a similar upright orientation for discshaped particles and cylinders of intermediate aspect ratio studied here.21 Our molecular simulations on Janus nanoparticles at a stationary interface (udrive = 0) also resulted in an


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analogous prediction as the particle was found to preserve the initial orientation of θ = 0º over long simulation times. Upon shearing the interface, the particle may start to deviate from the upright orientation as in Figure 10, due to the clockwise torque imposed by the symmetric shear flow. To evaluate this hypothesis, we placed a Janus sphere with R = 6σ and β = 60º at the interface and increased the

shear rate from 0 to 0.045 . The temporal evolution of the orientation angle subject to

different hydrodynamic flows is depicted in Figure 2 over a period of 0 / 1000. We observe that at a stationary interface, the orientation is θ = 0º as expected based on the preferred wetting condition between apolar/oil and polar/water interfaces. Upon applying the shear flow, the particle starts to rotate out of the original upright configuration and the shear torque can partially expose each region to both fluid phases. There is a relaxation period over which the orientation angle smoothly increases until reaching a steady-state configuration which is maintained over long simulation times. If the shear rate is further increased, the particle undergoes an overshoot in orientation and eventually exhibits an oscillatory variation in θ. Careful observation of the dynamics suggests

Figure 2. Temporal evolution of the orientation angle of a Janus sphere with β = 60º under various interfacial shear rates.


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that the particle experiences a tumbling motion at such high shear rates, but eventually approaches a steady-state configuration after sufficient time ( 3000 ). The tumbling can be

attributed to the significantly large ratio of the shear to capillary torque, which continuously rotates the particle until finding the optimum configuration. This will be discussed in more details in the following section. Similar to spherical particles, we found that the dynamics of Janus discs/cylinders towards the steady-state configuration also follows these two possible regimes: smooth tilt and tumbling. Depending on the geometry and surface chemistry, the dynamics can be different at a particular shear-rate. This is demonstrated in Figure 3 by phase diagrams for particles with three different amphiphilicities and over a wide range of aspect ratio and shear rate. Note that AR < 1 corresponds to discs, while AR > 1 represents cylindrical particles. We observe that the tumbling region shrinks upon increasing β due to enhanced preferred wetting of each side with its favorite fluid, leading to larger resistance against rotation above θ = 90º. Interestingly, the shape of this region is basically similar irrespective of the amphiphilicity, showing a minimum near AR = 1. More isotropic particles have a higher tendency to undergo tumbling as the geometry does not impose a preferred orientation under the flow. Furthermore, the phase diagrams suggest that

Figure 3. Phase diagrams showing the orientational dynamics of cylindrical and disc-shaped particles as a function of the aspect ratio and the applied shear rate at the interface for different amphiphilicities.


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elongated Janus cylinders do not experience tumbling dynamics within the investigated range of shear rates, while homogeneous cylinders with AR > 3 can exhibit such behavior under strong shear. This may suggest the enhanced stability of Janus particles under shear flow compared to their homogeneous counterparts, which can be attributed to the preferred wetting at solid-fluid interfaces resulting in a larger resistive capillary-induced torque. Overall, Figure 3 enables first-hand prediction of the orientational dynamics experienced by discs/cylinders with different aspect ratio and amphiphilicity subject to interfacial shear flows. It suggests the possibility of obtaining various dynamics for different particles subject to imposed shear flows simply by tuning their surface chemistry. The driving mechanism leading to such dynamics and a steady-state orientation for the particle under shear is discussed in the following section.

Driving Mechanism for the Observed Rotational Dynamics of Nanoparticles We observed that depending on the shear rate as well as the shape and amphiphilicity, a particle may experience two types of dynamics at a liquid interface: (1) Smooth tilt: the orientation angle smoothly increases over a relaxation period, after which a steady-state orientation is maintained; (2) Tumbling: the particle tumbles but does not detach from the interface, until it eventually finds a stable configuration. In case of smooth tilting, the magnitude of rotation out of upright orientation would generally depend on the shear-induced torque. For elongated cylinders with AR > 1, the shear-facing area is larger than that of thin discs, such that a larger shear torque would result under similar flow conditions. Also, a smaller capillary torque resists against the rotation due to smaller length of the contact line. Therefore, Janus cylinders tilt more than discs of similar area at a sheared interface. On the other hand, when a Janus cylinder tilts more toward


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a horizontal orientation, the contact length increases as the shear-facing area decreases. As a consequence, the capillary torque increases and the shear-induced torque decreases, inducing a smooth tilt as the net torque approaches zero. The trend is reversed in case of disc-shaped particles (AR < 1), such that the increasing Tshear and decaying Tcap favor further rotation of the particle under shear flow. Consequently, the particle rotates over θ ≈ 90º leading to significant distortion of the interface which can favor a tumbling motion. In order to further clarify the role of capillary torque in controlling the orientation and the interface deformation induced by preferred wetting condition, we examine the radial and circumferential distribution of the fluid atoms around a sample particle. Due to simplicity in computation and visualization, we carry out this analysis on a spherical particle but the physics also holds for other geometries. For a Janus sphere with a size of R = 6σ and amphiphilicity β = 120º, the distribution function g(r,θ) is measured by decomposing the region around the particle into several cells in polar coordinates, counting the number density of each fluid species in each cell, and averaging that over sufficient time and several realizations. Figure 4 shows contour plots of the distribution function g1(r,θ) for the bottom fluid around the particle under three different interfacial shear rates. The steady-state orientation of the sphere under each flow is also demonstrated for visualizing the solid/fluid interfaces. As the shear rate increases and the particle

Figure 4. Contour plots of the distribution function for bottom fluid around a spherical particle with R = 6σ and β = 120º subject to different interfacial shear rates.


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rotates more out of the upright (θ = 0º) configuration, the interface deformation becomes more pronounced. The distortion is such that each solid region remains mostly exposed to its favorable fluid phase as expected based on the continuum prediction.22 Similarly, in case (c) where the particle rotates by ≈ 98º, a thin wetting layer of each fluid phase rotates with its favorable solid surface into the opposite side of the interface and extending up to the location of the Janus boundary. Since the distribution is obtained by averaging over a long period of time, it implies that this wetting layer is formed and maintained around the nanoparticle as is rotates at the interface. Such microscopic layering has also been observed upon translating a Janus particle from one bulk fluid to the other phase.23 Overall, the increasing deformation of the interface upon deviating from the upright orientation confirms the resistive nature of the capillary torque against clockwise rotation induced by the shear flow. Therefore, the steady-state configuration adopted by the particle is expected to be governed by the balance between these two contributions. To evaluate this, we measure the ensemble-average torque acting on the particle in x-y plane by tracking the particle in multiple realizations and building histograms of the net torque as the particle crosses specific orientations. The result is shown in Figure 5(a) over a limited range of orientations for three example cases corresponding to cylindrical particles with AR = 1,2,3 and β

= 60º under a shear rate of 0.015 . The temporal evolution of the orientation for these Janus cylinders is shown in Figure 5(b) showing a smooth tilting before reaching the steady-state configuration. We clearly observe that in all cases, the orientation at which the net torque becomes zero corresponds exactly to the equilibrium orientation θeq achieved after the relaxation stage. This has been verified for other tilting particles including those with AR < 1. Therefore, the equilibrium orientation is justified based on the balance between shear and capillary torques.


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Figure 5. (a) The average net torque acting on cylindrical particles with β = 60º and AR = 1,2,3 under an interfacial shear rate of 0.015 τ-1, (b) the evolution of the orientation angle for these particles.

A similar methodology was followed for particles with tumbling interfacial dynamics. In such cases, as the particle covers a wider range of orientations during its evolution and can go beyond 180º rotation, we use an alternative definition of θ depending on the location of normal vector !"#

in x-y plane in order to distinguish between the clockwise and counter-clockwise rotation. The

ensemble-average torque 〈$% 〉 is shown in Figure 6(a) over the full range of 0º ≤ θ ≤ 360º for a

sample case corresponding to a Janus cylinder with AR = 1 and β = 60º tumbling at the interface under the maximum investigated shear rate of 0.045 τ-1. The result suggests that the net torque becomes negligible at three intermediate orientations. More importantly, the magnitude of the 11 ACS Paragon Plus Environment

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torque and its variation with θ is much smaller than the cases with non-tumbling dynamics shown in Figure 5(a) (~7ε as compared to ~80ε). Having measured 〈$% 〉, we can then calculate the change in Helmholtz free energy & by integrating the average torque as the particle rotates from a reference point (θref = 0º) using ∆& '( & '( &')*+ ,- 1 〈$% 〉-. /'′ -

(2)

234

The resulting free energy profile is shown in Figure 6(b), revealing two energy minima

Figure 6. (a) The average net torque acting on the particle, (b) the free energy, for a Janus cylinder with AR = 1 and amphiphilicity β = 60º undergoing tumbling dynamics at an interface sheared at 0.045 τ-1.


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corresponding to stable/metastable states at θ ≈ 100º, 250º, respectively. Note that both states correspond to zero mean torque thus trapping the particle at these orientations. Interestingly, the stable state (θ ≈ 100º) coincides with the final orientation adopted by the particle after the tumbling motion is suppressed. Therefore, the steady-state configuration for this tumbling particle is also driven by a minimization in free energy. Our simulations predict an analogous trend for particles of other geometries and surface chemistry undergoing tumbling dynamics. Furthermore, we note that the difference in free energy of all orientations is

EF

(3)

in which rij represents the separation distance between atoms i and j, σ is roughly the size of the repulsive core, ε is the depth of the potential well, and rc = 2.5σ denotes the potential cutoff 17 ACS Paragon Plus Environment

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distance. The coefficient A is introduced to control the attraction between solid/fluid atomic species in the system, which in turn defines the surface tension and wetting properties. The attraction coefficient for atoms in the same fluid and with the moving walls are set to Aff = Afw = 1 (with f = f1, f2), while atoms of the two different fluids interact with Af1f2 = 0.5 in order to establish their immiscibility. For the particle-fluid interactions, this parameter can be linked to the contact angle θ at a solid-liquid interface using the established correlation cosθ = −1+2A.28, 29

We consider three particle geometries, namely spheres, cylinders, and discs. The surface area of all particles is fixed at A = 144 σ2 (corresponding to a sphere 6σ in radius), and the aspect ratio of discs/cylinders is varied in the range of AR = L / D = 1/3−3. Here, L is the axis length and D is the cross-sectional diameter as shown in Figure 10.The amphiphilicity is controlled by tuning the affinity of the atoms on each side of the particle with the two fluids. We assume that the two regions possess opposite wettability (i.e., apolar and polar), represented by θa = 90°+β/2 and θp = 90°−β/2, with the parameter β = θa − θp characterizing the degree of amphiphilicity. Such symmetric wetting condition has been extensively used in earlier studies concerning amphiphilic spheres and ellipsoids.21, 22, 30-32 Nevertheless, our methodology is generally applicable to Janus particles comprised of any two polar and apolar regions subject to interfacial shear. We enhance the degree of amphiphilicity by increasing the attraction coefficients between each region and its favorite fluid Af1J1, Af2J2, while symmetrically reducing the adhesion with the opposite fluid Af1J2, Af2J1 (see Figure 9). The symmetric shear flow results in negligible bulk fluid velocity at the interface plane. The shear rate is calculated as 2JE)(K* /LM where LM is the overall length of the domain occupied by the two fluids along y, as shown in Figure 9. We control the shear rate by adjusting the


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Figure 10. Representation of Janus particles of different geometry subject to an interfacial shear flow, showing the orientation angle θ adopted by the sphere and the geometrical parameters for the cylinder/disc.

velocity of bounding walls in a range where the shear velocities are considerable compared to the Brownian motion of nanoparticles, while at the same time not too large to induce non-linear slip between nanoparticle and the fluids.33, 34 The important dimensionless groups characterizing this

problem are the Capillary number NO PJE)(K* /, Reynolds number QR SJE)(K* /P, and Peclet number TR JE)(K* /U , where S, P and represent the fluid density, dynamic

viscosity, and surface tension respectively, and U is the translational diffusivity of the spherical Janus particle.14 The range of parameters investigated in this work correspond to Ca = 0.13−1.3,

Re = 0.5−5, and Pe = 17−170, which are within the range reported for flows at particle-laden interfaces. More details of the simulation procedure are given in the Supporting Information.

Analysis Upon applying the shear, the particle may detach from the interface plane if the shear rate leads to significant slip between particle surface and the surrounding fluid. We evaluate this possibility by tracking the long-term normal transport of the particle in several realizations, revealing the potential instability of the particle subject to imposed shear flow. More amphiphilic particles are expected to be less susceptible to detachment from the interface due to the higher affinity between solid/fluid species. 19 ACS Paragon Plus Environment

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On the other hand, the shear flow may result in rotation of the particle out of the initially upright configuration. We monitor this rotational dynamics by tracking the angle θ between the normals to Janus boundary and the interface plane, respectively denoted by !"#, V# in Figure 10. This

orientation angle can be calculated as ' WXY Z‖[\‖‖]̂ ‖` WXY AMM /aA bM + A MM + A %M [\.]̂

(4)

where AbM , AMM , A%M are the components of the second column of the rotation matrix A# with respect to the initially upright configuration at any particular time step. The magnitude of θ will generally depend on particle size, shape, degree of amphiphilicity, and the applied shear rate. We monitor the rotational dynamics until reaching a steady configuration. It should be noted though that such analysis cannot be fully captured with theoretical methods due to presence of capillary wave effects at the nano-scale as well as complex directional particle-fluid interactions.35

ACKNOWLEDGEMENTS This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors also acknowledge the support from Rutgers School of Engineering Computing Center. We thank J. Koplik and G. Drazer for helpful discussions and suggestions.

ASSOCIATED CONTENT Supporting Information Available: A detailed description of simulation steps and relevant parameters including the imposed shear flow, thermostat for NVT ensemble, integration method, and physical scales; Calculation of fluid properties including the density, surface tension, and 20 ACS Paragon Plus Environment

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interface width, along with validation of the estimated values with available studies. This material is available free of charge via the Internet at http://pubs.acs.org.

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Contour plots of the distribution function g(r,θ) for lower fluid around a spherical Janus particle with R = 6σ and β = 120º subject to three shear rates. 580x183mm (96 x 96 DPI)

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Tilting and Tumbling of Janus Nanoparticles at Sheared Interfaces

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