Molecular Dynamics Simulation of the Motion of Colloidal Nanoparticles in a Solute Concentration Gradient and a Comparison to the Continuum Limit Nima Sharifi-Mood, 1 Joel Koplik, 2, * and Charles Maldarelli 1,† 1 Benjamin Levich Institute and Department of Chemical Engineering, City College of the City University of New York, New York, New York 10031, USA 2 Benjamin Levich Institute and Department of Physics, City College of the City University of New York, New York, New York 10031, USA (Received 22 April 2013; published 28 October 2013) Chemical-mechanical transduction mechanisms which can actuate the movement of colloids through liquids are highly sought after as engines to propel miniaturized micro- and nanobots. One mechanism involves harnessing the long-range van der Waals attractive forces between the colloid and solute molecules dissolved in the liquid around the particle. If a concentration gradient of this solute is applied across the particle, then the imbalance in the van der Waals attraction drives the particle towards the higher concentration of solute. We present a molecular dynamics simulation using Lennard-Jones interactions between molecules of the solvent, solute, and colloid cluster which include short-range repulsive and long-range attractive potentials. The simulations demonstrate that a solute gradient can propel nanosized colloids, and that the velocity decreases with the colloid size. The solute-colloid short-range repulsive interactions are observed to be restricted to a region of specifically adsorbed solutes on the particle surface which are symmetrically adsorbed and do not contribute to the motion. The size of this region provides a cutoff for a continuum level description of the motion, and with this cutoff, continuum calculations are in excellent agreement with the molecular dynamics simulation results, completing a description of the propulsion from the nano- to the microscale. DOI: 10.1103/PhysRevLett.111.184501 PACS numbers: 47.15.G, 47.11.Mn, 82.70.Dd, 83.10.Mj Microbots and nanobots [1] are locomoting objects which are designed to traverse liquids in a programed way along small scale landscapes in highly imaginative applications such as the targeted delivery of drugs to individual cells [2], roving sensors for chemical detection [3], or deployed agents for capturing targeted molecules [4], engines for micropumping [5], shuttles for moving cargo through microfluidic cells [6], and transporters for directly assem- bling supramolecular structures from molecular building parts [7]. While top-down ‘‘phoretic’’ approaches for engi- neering object motors resort to the classical paradigms of applying external fields to the objects to cause their motion, such as, for example, electrophoresis [8], dielectrophoresis [9], magnetophoresis [10], the attendant miniaturizations in the force fields required to move objects through the small scale venues envisioned for these locomotors are challeng- ing. As technological interest progresses and moves towards the design of nanobots, other mechanisms for locomotion that take advantage of forces which, in particular, become effective on the micro- and nanoscale are the logical further choices for a bottom-up approach. This Letter studies theoretically one potential transduc- tion mechanism which derives from unbalanced van der Waals forces which are exerted on the molecules of a colloid engine by low molecular weight solute molecules (less than 1 nm in diameter) distributed asymmetrically around the particle. The van der Waals interaction of a solute molecule in solution near a colloid with all the molecules comprising the colloid is confined to an inter- action zone around the particle with thickness L of the order of 1–10 nm (a few to several molecular diameters). Within this zone, the concentration gradient must exist for the colloid to move. This driving force for colloidal motion is diffusiophoresis [11]. In rectified diffusiophoresis, the concentration gradient is applied externally [12], but the force can be integrated into a self-propulsion design by choosing as a solute a reactant which undergoes a surface reaction on one face of the colloid to generate the required solutal concentration gradient [13,14]. The scope of this Letter is to use molecular dynamics simulations [15] to study the motion of a colloid driven by a solute gradient. Most theoretical studies of this motion use either a continuum framework, in which a solute- colloid intermolecular interaction potential is introduced into the mass and momentum conservation equations within the interaction zone L [16], or a micromechanical perspective, in which the colloid as well as solute are Brownian particles in a continuum solvent [17]. The con- tinuum approach has limitations, as L is of molecular scale and the interaction potential requires an empirically intro- duced cutoff. More importantly, the intermolecular inter- actions within L which drive the motion include both the repulsive and long-range attractive interactions of the solutes immediately adjacent to the colloid, and the long- range attractive interactions of solutes a few molecular diameters away, with each modulated by the interaction PRL 111, 184501 (2013) PHYSICAL REVIEW LETTERS week ending 1 NOVEMBER 2013 0031-9007= 13=111(18)=184501(5) 184501-1 Ó 2013 American Physical Society