A phase diagram to predict the self-assembly of nanoparticle coatings deposited from evaporating colloidal suspensions
Dr. Daniel Attinger
Columbia University, Dpt. of Mechanical Engineering, USA
February 18th, 2010
The ability to precisely coat solid substrates with nanoparticles is important for technologies such as printing, microelectronics manufacturing and biosensing. Evaporating drops containing nanoparticles is a simple way to deposit nanoparticle coatings: the result is however typically inhomogeneous, as exemplified by the coffee ring  deposit, with most particles accumulated at the periphery of the initial drop. In this talk, we investigate the self-assembly of Titania nanoparticles dispersed in aqueous drops evaporating on a glass substrate. The ambient temperature and pH are varied experimentally to control the evaporation rate and the electrostatic interactions between nanoparticles and the solid substrate. The assembly of nanoparticle deposits is investigated experimentally with video microscopy, atomic force microscopy and laser profilometry. On the theoretical side, we have developed a finite-element numerical modeling  that solves the transient fluid dynamics, heat and mass transport equations in a Lagrangian framework. The particle concentration is monitored via a continuum advection-diffusion equation, with consideration of electrostatic and van der Waals interactions. The wetting line motion and the interaction of the free surface of the drop with the growing deposit of nanoparticles are also accounted for. Our experiments show that the pH of the solution controls the dried deposit pattern, from a ring to a uniform layer: this is due to the competition between electrostatic interactions and advective particle transport. Based on this finding and prior work , we propose a phase diagram explaining the structure of nanoparticle deposits by the competition between three flow patterns: a radial flow driven by evaporation at the wetting line, a Marangoni recirculating flow driven by surface tension gradients, and the electrostatic attraction of particles towards the substrate. This phase diagram predicts three common types of deposits, such as a peripheral ring, a central bump, and a uniform coating. Simulations and experiments are found in very good agreement. An outlook is also given on possible strategies to engineer the deposition of nanoparticles coatings.
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 Bhardwaj, R., X. Fang, and D. Attinger, Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study. New Journal of Physics, 2009. 11: p. 075020.