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Colloids and Surfaces A: Physicochemical and Engineering Aspects, Volume 432, 2013, Pages 132-138.
Peter Lebedev-Stepanov, Konstantin Vlasov.
Lab of nanoparticles self-organization at Photochemistry Center, Russian Academy of Sciences, Novatorov St., 7a, Moscow, 119421, Russia and
Condensed matter physics department at National Research Nuclear University “MEPhI”, Kashirskoe Shosse St., 31, Moscow, 115409, Russia
Abstract
A method of Brownian dissipative dynamics of charged colloidal nanoparticles in microdroplet of solution deposited on plane substrate is proposed for investigation of self-assembly and self-ordering of colloids during solute evaporation. Method is based on the numerical solution of multi-scale Langevin equation for each particle, the hydrodynamic microflows approach, and droplet evaporation model. The method takes into account the DLVO-forces between the particles, their interaction with the substrate (adhesion, friction, roughness); Stokes’, Brownian, and capillary forces (wetting and depinning, outflow angles, surface tension). The self-assembled pattern morphology dependence on the model parameters is investigated. The nature of coffee ring effect was studied. It is shown that the hexagonal domain ordering of particles ensemble in pattern can be formed onto plane substrate as a result of interparticle repulsion and the capillary compression during evaporation of solvent. Numerical results are in good agreement with experiments on self-assembly in colloidal droplet deposited by inkjet technology.
Additional information
A number of papers devoted to heat and mass transfer of evaporating drops on a flat substrate have been published over the last years, mainly due to the importance of the evaporating drop problem for fundamental and applied sciences. Particularly, it is important to investigate how inkjet print technology could revolutionize manufacturing processes.
The physical and computational model of self-assembly in an evaporating picoliter drop of solution is described as a further development of dissipative particle dynamics methods for systems with a changeable volume. The calculation starts with generating the initial particle distribution in the drop with a uniform volume concentration of particles in the solution. Particle trajectories are then calculated step by step from the initial to the final state. To generate the uniform initial distribution, a repulsive Coulomb-type potential is introduced and the assemblage energy is then optimized by particle positions inside the drop. After the initial particle distribution is achieved, a step by step integration algorithm is run for each particle. The i-th particle acceleration is calculated by the Langevin equation (Fig.1).
The self-assembled pattern morphology dependence on the model parameters is investigated. It is shown that the hexagonal domain ordering of particles ensemble in pattern can be formed onto plane substrate as a result of interparticle repulsion and the capillary compression during evaporation of solvent (Fig.2). If interparticle repulsive barrier is small, the particles coagulate in solution and form the colloidal clusters (agglomerates) adsorbed on the substrate surface after solvent evaporation. Numerical results are in good agreement with experiments on self-assembly in colloidal droplet deposited by inkjet technology (Fig.3).
The application includes inkjet technologies and printable electronics fabrications; medical diagnostics by dry pattern analysis, design of microstructures and materials with new properties, and also in the scientific tutoring. A number of our modeling results (for example, a particle rate reverse near pinned triple line) remained outside this paper and will be published later. We are elaborating the useful software complex to predictive modeling of setup, spreading, evaporation of liquid droplet of inkjet size, as well as self-assembly of solvated nanoparticles or macromolecules from the drop during evaporation.
