Effect of solvent quality on the dispersibility of polymer-grafted spherical nanoparticles in polymer solutions

In this work, lattice-based self consistent field theory is used to study the structural properties of individual polymer-grafted spherical nanopartices and particle-particle interactions in polymer melts and solutions under variable solvent conditions. Our study has focused on the depth of the minimum in the potential of mean force between the two brush-coated nanoparticles, if such a minimum occurs, and we have also addressed the corresponding radial density profiles of free and grafted chains around a single nanoparticle, in an attempt to clarify the extent of correlation between the depth of the minimum, W(min), and the parameter δ characterizing the interpenetration between the profiles of free and grafted chains. Although one cannot establish a simple one-to-one correspondence between W(min) and δ, we do find common trends, in particular, if the solvent conditions for free and grafted chains differ: varying the volume fraction of the free chains, δ typically exhibits a broad minimum, corresponding to a region where the magnitude of W(min) exceeds thermal energy k(B)T, leading to particle aggregation.