Structure of binary solution droplets: Continuum theory and Monte Carlo simulation

Abstract

To calculate the formation energy of a binary mixture droplet out of the gas phase in classical ‘heteromolecular’ nucleation theory, one has to take into account that the concentration of the solution near the droplet surface can be different from the composition in the droplet interior (‘surface enrichment’, Gibbs adsorption equation). This problem is solved in a simple picture where the composition varies spatially but where one has a sharp liquid-gas surface. In a material independent continuum theory, the variation of the composition is assumed to give a free energy contribution proportional to the square of the concentration gradient. This treatment of the surface enrichment gives a formation energy contribution smaller (for large droplets) by a factor 1 −1/√3 than previous theories (Doring and Neumann, 1940; Stauffer and Kiang, 1974), which therefore overestimated the surface enrichment for large droplets. This continuum theory is tested by Monte Carlo methods on a particularly symmetric mixture, the magnetic spin 1/2 Ising model. Here up-spins are identified with one type of molecule and down spins with another type. Reasonable agreement with the continuum theory is found, even for parameter ranges where the assumptions of the continuum theory are no longer valid. The results show clearly a strong but smooth variation of the concentration within the droplet. They constitute to our knowledge the first computer simulations of mixture microclusters.