Quantifying Nanoparticle Ordering Induced by Polymer Crystallization

It has recently been established that polymer crystallization can preferentially place nanoparticles (NPs) into the amorphous domains of a lamellar semicrystalline morphology. The phenomenology of this process is clear: when the time for NP diffusion is shorter than the crystal growth time, then the NPs are rejected by the growing crystals and placed in the amorphous domains. However, since there is no quantitative characterization of this ordered NP state, we develop a correlation function analysis for small-angle X-ray scattering data, inspired by classical methods used for enunciating the local morphology of lamellar semicrystalline polymers. We show that when the spherulitic growth rate is slower than NP diffusion, then all the NPs are expelled from the crystals. As we increase the crystallization temperature, T_c, the long period characterizing the periodically repeating crystal-amorphous polymer structure, r_cc, increases. This results in a smaller number of amorphous domains per unit volume-the number of NPs per amorphous domain thus increases. While the scattering contrast between the pure silica and the polymer is constant, these arguments predict that the apparent contrast between the NP-rich and the polymer-rich domains scale linearly with r_cc, as we confirm from our experiments. These facts allow us to posit that the NPs become more efficiently packed in the interlamellar zone with increasing T_c until they form a fully filled monolayer. Above this temperature, NP multilayers form within each of the NP-rich domains. Our analysis approach, therefore, describes NP ordering that is achieved when driven by polymer crystallization.