Crystallization of interfacially tethered colloids in an emergent optofluidic potential Alessio Caciagli, 1 Rajesh Singh, 2 Darshana Joshi, 1 R. Adhikari, 2, 3 and Erika Eiser 1, ∗ 1 Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE, UK 2 DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK 3 The Institute of Mathematical Sciences-HBNI, CIT Campus, Chennai 600113, India The interplay between laser light, trapped particles, and fluid flow can produce counterintuitive effects in optical tweezing. Here we uncover an attractive, long-ranged, non-equilibrium force field centered on an optically trapped particle near a water-oil interface, produced by local heating and mediated by global fluid flow. This causes surrounding untrapped colloids, tethered to the interface but allowed to diffusely freely along it, to crystallize around the force center. In this configuration, the non-equilibrium force is the gradient of a potential, of strength proportional to the local heating, which, surprisingly, allows for an effective equilibrium description. Our results open unexplored routes to optofluidic manipulation and assembly of colloidal particles. Since their introduction [1], optical tweezers have rev- olutionised the manipulation of matter at the nano- to micro-meter scale [2–6]. Tweezers have found extensive use in the trapping and assembly of micron-sized col- loidal particles [7–9] and yielded novel forms of colloidal matter that are held together by optical forces [10–16]. While these forces have been thoroughly understood in terms of the transfer of momentum from radiation to particles, much less studied are the effects of heating, due to the transfer of energy from radiation to the sur- rounding fluid medium. Such effects can be unexpect- edly subtle, as for example in the vicinity of fluid-fluid interfaces, where local heating, by altering the interfacial tension, can set both fluids into motion [17, 18]. While trapping and heating are caused by the interaction of light with, respectively, the particles and the medium, it is natural to ask what new effects might arise from the combined interaction of light, particles, and the medium. Two recent experiments touch on this question. In the first, a light-controlled thermoelectric field is generated in the medium, which contains a mixture of surfactant, ions, and micellar depletants, to assemble colloidal par- ticles into a variety of two-dimensional aggregates. In the second [19], the differential heating of trapped Janus particles is used to sustain a thermo-osmotic flow which entrains untrapped particles into clusters. These sug- gest the possibility of harnessing the interaction of laser light with simple solvents (like water or oil) and simple colloids (like polystyrene particles) for manipulation and assembly. In this Letter, we show that the optical trapping of a thermophoretic colloidal particle near a water-oil in- terface sets up a long-ranged, non-equilibrium force field whose effect on untrapped particles, that are tethered to the interface but otherwise free to diffuse along it, is to cause them to crystallise around the force center. The sign, magnitude, and distance-dependence of this force cannot be accounted for by standard colloidal interac- tions or entrainment in surface-tension driven Marangoni flows. Using theory and simulation, we show that the force is mediated by hydrodynamic flow produced by stalled thermophoresis of the optically trapped colloid, whose effect on the fluid, to a very good approximation, is that of a hydrodynamic monopole. For motion parallel to the interface, the force is the gradient of a potential and the particle dynamics admits an effective equilib- rium description. Brownian dynamics simulations in this emergent potential, whose strength is determined by the local heating, is in excellent agreement with experiments. The emergent potential is of much longer range than the optical trapping potential, couples to the size of the par- ticle and not its dielectric properties, and manifests itself in simple solvents such as water or oil. These desirable features open unexplored routes to the optofluidic ma- nipulation and assembly of colloidal particles on multi- ple spatial scales [20]. We now describe our experimental results, theoretical analyses, and numerical simulations. Experimental setup: Our setup is shown schematically in the inner panel of Fig. (1). We prepare oil droplets of radius between 20μm and 30μm and coat them with a surfactant-polymer layer, following [21]. Single-stranded (ss)DNA chains denoted by A, attach to this layer and densely cover it. Polystyrene particles (PS) of radius a =0.53μm, functionalised by complementary A ′ ssDNA strands, are then grafted on to the coated interface. The DNA coating of the particles prevents them from aggre- gating. Compared to colloids straddling the interface, grafting eliminates capillary forces, light-wave reflections and long-ranged electrostatic dipolar interactions from the asymmetry of charge distributions on interfacially wetted colloids [22, 23]. The surfactant-polymer coat- ing sterically stabilises the interface from deforming and maintains the grafted colloids approximately 50 nm away from it. The colloids thus diffuse freely on the interface, which appears almost flat on the particle scale. A grafted colloid is optically trapped by focussing the laser beam above the interface on the water side. A fraction of the colloids remain ungrafted and diffuse freely in the bulk. They serve as tracers, providing information on bulk fluid flow. Further details of the system and the calibration of the trap, using both standard and Bayesian methods, are provided in the SI [24]. arXiv:2003.04284v1 [cond-mat.soft] 9 Mar 2020