  The co-solvency method is a method for the size controlled preparation of
nanoparticles like polymersomes, where a poor co-solvent is mixed into a
homogeneous copolymer solution to trigger precipitation of the polymer. The
size of the resulting particles is determined by the rate of co-solvent
addition. We use the Cahn-Hilliard equation with a Flory-Huggins free energy
model to describe the precipitation of a polymer under changing solvent quality
by applying a time dependent Flory-Huggins interaction parameter. The analysis
focuses on the characteristic size R of polymer aggregates that form during the
initial spinodal decomposition stage, and especially on how R depends on the
rate s of solvent quality change. Both numerical results and a perturbation
analysis predict a power law dependence $R \sim s^{-1/6}$, which is in
agreement with power laws for the final particle sizes that have been reported
from experiments and molecular dynamics simulations. Hence, our model results
suggest that the nanoparticle size in size-controlled precipitation is
essentially determined during the spinodal decomposition stage.
