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Orientation of Janus Particles Under Thermal Fields Orientation of Janus Particles under thermal fields: the role of internal mass anisotropy Orientation of Janus Particles under thermal fields: the role of internal mass anisotropy Juan D. Olarte-Plata1, a) and Fernando Bresme1, b) Department of Chemistry, Imperial College London White City Campus, W12 0BZ, London, UK (Dated: 16 June 2020) Janus particles (JPs) are a special kind of colloids that incorporate two hemispheres with distinct physical properties. These particles feature a complex phase behavior and they can be propelled with light by heating them anisotropically when one of the hemispheres is metallic. It has been shown that JPs can be oriented by a homogeneous thermal field. We show using multiscale simulations and theory that the internal mass gradient of the JPs can enhance and even reverse the relative orientation of the particle with the thermal field. This effect is due to a coupling of the internal anisotropy of the particle with the heat flux. Our results help to rationalize previous experimental observations and open a route to control the behavior of JPs by exploiting the synergy of particle-fluid interactions and particle internal mass composition. I. INTRODUCTION torques, and the orientation of axially symmetric particles in a thermal field9–11. Hence, our hypothesis is that coupling ef- Janus particles (JPs) are colloids made of two ore more fects associated to internal degrees of freedom contribute to components with different properties. The first synthetic the orientation of JPs too, and might contribute significantly Janus particle consisted of amphiphilic glass spheres fea- to determine the preferred orientation of the JPs. We explore turing hydrophilic and hydrophobic hemispheres1. Since this hypothesis in the present Letter using both atomistic and then, a range of particles with different compositions have mesoscopic simulations supported by a theoretical approach been synthesized, including colloids coated with metallic that describes accurately the orientation of JP in terms of their patches2. Metals are of particular interest in thermal appli- internal mass distribution. cations, since the metallic patch can be heated with light, by exploiting the plasmon resonance effect. This idea was re- alized by Jiang et al.3, who measured the temperature dis- II. SIMULATION METHODS tribution and temperature slip around a JP, and demonstrated that the anisotropic temperature distribution leads to the self- We show in Fig. 1a the atomistic simulation setup, consist- propulsion of the colloids. Following these works the inves- ing of two JPs suspended in an atomic fluid. The particles are tigation of JP suspensions have gained much popularity in located in the geometric center of the two subvolumes around the area of active matter, and as models to investigate exotic the middle of the simulation box. The simulation cell is fully phase behavior4 and test non-equilibrium transport theories periodic, and it incorporates two thermostatting regions that employed in the description of biological microswimmers5. define hot and cold boundaries (see coloured regions, red-hot A good understanding of the physical behaviour of JPs un- and blue-cold in Figure 1(a), and see reference9 for a extended der non-equilibrium conditions will contribute to their imple- discussion). In the stationary state the thermostats generate a mentation in practical applications6, by exploiting their am- stationary heat flux and temperature profile. The center of phiphilic and self-propulsion properties. mass of the colloids was tethered to the geometric center of In this work we investigate the behaviour of JPs in a homo- each compartment using a harmonic potential. The solvent geneous thermal field. Recently, it was predicted that JPs ori- is modelled atomistically, setting its density to that of a typ- ent in a thermal field7. Experimental work using polysterene ical liquid, r∗ = (N=V)s 3 = 1:0, where N is the number of beads with one hemisphere coated with gold confirmed the solvent particles, V = Lx × Ly × Lz is the volume of the sim- existence of a preferred orientation, with the gold side point- ulation cell, Lx the box length in direction x, and ss is the ing to the heat source8. This orientation effect was interpreted diameter of the solvent particles. The JPs were modelled in terms of an effective slip velocity associated to a varying as amorphous rigid bodies composed of atoms of diameter thermal gradient around the particle surface. sp = ss. The mass of the solvent, and the atoms in the JP were Due to the anisotropic composition of JPs, the colloids fea- ms = mp = 1:0. Solvent-solvent (ss) and solvent-particle (sp) ture internal mass gradients, with the center of mass of the col- interactions were modelled using the Lennard-Jones potential, loid shifted from its center of geometry. We showed recently, truncated and shifted at rc = 2:5s. The solvent-solvent and using non-equilibrium thermodynamics theory and simula- solvent-particle interaction strength was set to ess=kBT = 1. In tions, that such internal mass gradients lead to thermophoretic all the simulations reported here ∇TT −1R < 1, hence within the the linear response regime. To investigate the mesoscopic length-scales associated to very large colloid to solvent diameter ratios, we performed a)Electronic mail: [email protected] mesoscopic simulations using the Stochastic Rotation Dy- b)Electronic mail: [email protected] namics (SRD) algorithm12, implemented in LAMMPS13,14. Orientation of Janus Particles under thermal fields: the role of internal mass anisotropy 2 Specific details on the treatment of the SRD fluid are pre- III. THERMOPHORETIC TORQUE AND ORIENTATION sented in the SI. The number of SRD particles per cell was OF THE JP set to n = 5, with reduced mass density rhom = 1:0 and mean free path l = 0:1a0, where a0 = 1:0 is the lateral size of the To understand the role of the internal mass anisotropy on SRD cells. The mesoscopic JPs were modelled as core-shell the thermophoretic torque, we simulated JPs with different particles of radius R with mass density equal to that of the mass distributions, g = mA=mB ≥ 1, where ma is the total SRD fluid. The coupling between the SRD fluid and JPs is mass of hemisphere a. We kept the solvent-particle inter- achieved through stochastic collisions with the shell, follow- actions for both hemispheres identical (espA = espB = 1:0). ing the method reported in reference10 to simulate thermal The simulations show that the JPs orient in a thermal field fields. Further details of the SRD-JPs model are given in the (see Figure 3), and the orientation increases with the mass Supplementary Information. anisotropy (g) and particle size (R). We note that the ori- entation of JPs has been interpreted before in terms of the changes in the slip velocity around the nanoparticle, which arise from different hemisphere-fluid interactions7. Our sim- ulations were performed using the same interaction strength for both hemispheres, hence the effect reported here is due (a) to the mass anisotropy. We also performed simulations using our mesoscopic SRD model. This model features a very sim- ilar dependence, with the particle orientation increasing both with g and R, showing hat the mass anisotropy induced torque operates in a wide range of length scales. We find in both cases, atomistic and mesoscopic, that the the JP orients with the heavier side pointing preferentially towards the hot region. (a) 0.2 R=3.0 0 R=4.0 R=5.0 -0.2 > ¡ -0.4 (b) <cos -0.6 -0.8 -1 1 1.5 2 2.5 3 3.5 4 ¢ (b) 0.2 0 -0.2 > ¡ -0.4 <cos -0.6 R=2 R=3 -0.8 R=4 R=5 -1 0 2 4 6 8 10 FIG. 1. (a) Snapshot of the simulation box employed in our work. ¢ Red and blue regions indicate the position of the hot and cold ther- mostats, respectively. The fluid particles are represented as translu- FIG. 2. (a) Average orientation of atomistic JP as a function of the cent grey spheres and the JP with yellow and green spheres. (b) mass ratio, g and particle size, R. All the data were obtained with Sketch of the Janus particle, showing the polar (q) and azimuthal ∇T = 0:08, the average temperature of the colloid centre of mass (f) angles, as well as the definition of the mass dipole D, which T = 2:5 and particle-fluid interaction espA = espB = 1:0. (b) Average appears in the figure fully aligned along the direction (x) of the ther- orientation of the mesoscopic SRD JP as a function of g. The data mal gradient, ∇T. The vector r connects the centre of mass of the correspond to ∇T = 0:12 and average temperature T = 2:5. The solid particle to the surface element, S, highlighted in orange. The inset lines in panels (a) and (b) represent the theoretical predictions from shows the rotation of the JP by an angle b. The orientation vector Eqs. (5) and (6). with respect to the heat flux, Jq, is given by cosb = uc · uJq , with j j uc = (rcmA − rcmB )= rcmA − rcmB , and rcmA and rcmB being the vec- We discuss in the following a theoretical model that ex- tors defining the centre of mass of the hemispheres A and B. plains the dependence of the orientation with the mass Orientation of Janus Particles under thermal fields: the role of internal mass anisotropy 3 anisotropy, g, and the particle size R. It is well known that where b defines the angle that the mass dipole of the JP thermal fields induce thermophoretic forces in colloidal par- makes with the thermal gradient (see Figure 1b). The torque ticles, with the colloids drifting towards hot or cold regions.
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