Mass-fractal clustering and power-law decay of cluster size in 1-propanol aqueous solution

Mesoscale structure of 1-propanol aqueous solutions with propanol mole fraction xp ranging from 0.1 to 0.33 has been studied by means of small angle neutron scattering (SANS) and large-scale reverse Monte Carlo (RMC) technique. Analysis of the SANS intensities in terms of a fractal model shows that the fractal dimension df of mesoscale structure of the solution is about 1.8–1.9 for water-rich solution and about 1.5 for propanol-rich solution. Percolation analysis on the RMC results reveals that the water molecules and the propanol molecules cluster, respectively, as a mass fractal, the dimension dM of which is about 2.3–2.5 for both clusters for water-rich solution. Furthermore, the distribution of the cluster size is expressed by a simple power law with an exponent τ of about 1.35–1.5 for the propanol clusters and 1.05–1.2 for the water clusters. These results imply that the current solution is characterized by polydisperse mass fractals. In fact, a theoretical relation for polydisperse system of mass fr...