Theoretical formulation of the distribution function of critical nuclei under precipitation polymerization conditions

Precipitation Polymerization (Pre-Poly) can be considered a nucleation and growth process in which complex and high molecular weight branched polymers are involved. From an experimental point of view, it is well-known that under Pre-Poly conditions the phase transition (nucleation) occurs in the first minutes of polymerization, and then a long growth stage is observed in which the critical nuclei simultaneously grow until reaching a highly monodisperse distribution of microspheres (characteristic mechanism of binodal decomposition). The high rate at which nucleation and growth processes usually take place when radical polymerization (extremely high polymerization rate) under Pre-Poly conditions is used, makes it very difficult to study experimentally some aspects of these processes, such as the size and concentration of critical nuclei, among others. Based on the thermodynamic principles of Pre-Poly, this analytical paper covers for the first time, to the best of our knowledge, the theoretical formulation of the distribution function of critical nuclei under Pre-Poly conditions. In addition, a simple empirical method to calculate the concentration of critical nuclei was also developed using only three global, physical experimental parameters, and good agreement was found between empirical and theoretical calculations.