Surface States of Microdroplet of Suspension D. Jakubczyk,* M. Kolwas, G. Derkachov, and K. Kolwas Institute of Physics of the Polish Academy of Sciences, Al. Lotniko ´w 32/46, 02-668 Warsaw, Poland ReceiVed: January 27, 2009; ReVised Manuscript ReceiVed: March 30, 2009 Surface thermodynamic states of single evaporating microdroplets of aqueous suspension of nanospheres were studied by analyzing the surface pressure (surface activity) isotherm. Surface pressure evolution was found from the temporal evolution of the droplet radius. The droplet radius was inferred from the azimuthal angular distribution of the irradiance of s-polarized scattered light. Several thermodynamic states of the surface layer formed of nanospheres were identified: surface gas, surface gas-liquid coexistence, two states of surface liquid, and surface solid. The collapse of the surface monolayer was detected. 1. Introduction Properties of suspensions are of importance to science, technology, and everyday life. These properties (mechanical and optical, etc.) are intrinsically connected with the properties of interfaces present in the suspension and on its surface (e.g., ref 1). An evaporating droplet of suspension makes an even more complicated system. In particular, the state of its surface changes dynamically in an intricate way. 2 A drying suspension of nanoparticles can exhibit complex transitory internal structures. This phenomenon has been observed for nanoparticle suspension drying on a substrate. 3,4 The evaporation of dispersing liquid can lead to the formation of a monolayer of nanoparticles 3 and/ or to the formation of surface assemblies of nanoparticles of various morphologies. By analogy to colloids, it should be possible to distinguish thermodynamic states of the surface layer (e.g., ref 5). We report a study of the evaporation of single, free droplets of aqueous suspension of nanospheres. Individual droplets were levitated in the electrodynamic quadrupole trap. 6,7,9 The evapo- ration of dispersing water led primarily to the gathering of inclusions on the droplet surface and second to the increase of their density in the droplet volume. The process can be perceived as an evaporation-driven assembly of nanostructures under the condition of spherical symmetry imposed by the surface tension of the droplet. 2 We followed the evaporation process by analyzing the temporal evolution of the droplet radius. The droplet radius was found from the analysis of the azimuthal angular frequency of the interference pattern of light scattered by the droplet. 10,11 The optical properties of a spherical droplet containing inclusions may depend on the inclusion (inclusion structures) morphology (see, e.g., ref 12). This would manifest in patterns of light scattered by such droplet. Some features of the scattering pattern (rainbow angle 13 and angular frequency 14 ) practically depend on a limited set of droplet parameters only. Azimuthal angular frequency of s-polarized scattered light, for a certain range of angles, carries information about the radius of a droplet, whereas it is practically independent of the droplet refractive index. It gives opportunity to determine droplet radius even when its refractive index is unknown or the droplet composition is nonuniform. This is a well-established technique used for particle sizing, e.g., in sprays (see, e.g., ref 15 and references therein). There are many variants of this sizing technique under different names: laser imaging for droplet sizing (ILIDS), interferometric particle imaging (IPI), Mie scattering imaging (MSI), and interferometric Mie imaging (IMI), etc. By analyzing the evaporation rate of a droplet (within the framework of a model that we adopted), we were able to determine the effective surface pressure evolution (changes of surface tension). As the droplet of suspension looses water and evolves from liquid to dry aggregate of inclusions, its surface undergoes transitions through various surface thermodynamic states. They can be identified by analyzing the surface pressure. We observed several states: from surface gas of inclusions (first stage of droplet drying), through surface gas-liquid coexistence, surface liquid to the surface solid (2D) followed by its collapse. In other words, the effective surface pressure reflects the formation and evolution of the surface nanostructured layer of inclusions. We believe that the evolution of thermodynamic surface states of a droplet is a fundamental phenomenon influencing evapora- tion rate of any droplet of broadly defined suspension. We expect that controlled drying of droplets of suspension could also be of technological value. It opens a possibility for engineering of various surface and volume micro- and nanostructures, which could be employed as photonic crystals or meta-materials. 2. Evaporation Model and Surface Phenomena The process of droplet evaporation is associated with the mass and heat transport through the droplet surface. It is driven by the gradients of vapor density and temperature around the droplet. Therefore it depends on the vapor pressure near the droplet surface p a and far from the droplet p cc , as well as on the temperature of the droplet surface T a and the temperature of the reservoir T cc . The conventional way of tackling the problem, which can be found, e.g., in ref 16, is based on combining equations of diffusion of mass and heat with the gas kinetic equations. In this manner, convenient expressions describing the dynamics of evaporation of a spherical droplet of pure liquid can be obtained: * To whom correspondence should be addressed. E-mail: jakub@ ifpan.edu.pl. J. Phys. Chem. C 2009, 113, 10598–10602 10598 10.1021/jp9007812 CCC: $40.75  2009 American Chemical Society Published on Web 05/19/2009