Effect of Graft Length and Matrix Molecular Weight on String Assembly of Aligned Nanoplates in a Lamellar Diblock Copolymer

Grafted nanoparticle polymer composites have been used to create a highly bespoke class of materials, with spherical nanoparticles serving as the gateway design into this class. Grafted nanoplates (nanoparticles where the radius is longer than the height of the particle) provide opportunities and pathways to control overall system properties through their anisotropic properties. Current research on addressing the challenges associated with assembly is quite limited and unexplored. Using hybrid particle/self-consistent field theory (hSCFT) simulations, we build upon our previous work examining polyethylene glycol (PEG) grafted nanoplates within a nearly symmetric (f ≈ 0.5) lamellar poly(styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymer (BCP) matrix. We examine the interplay between the nanoplate graft length and matrix molecular weight and their effect on the potential of mean force (PMF). Ultimately, we discover that the location and depth of both the energetic well (local minimum) and the energetic barrier (local maxima) of the PMF, as well as the existence of the local maxima, are dependent on the relative width of the nanoplates to the lamellar domain, with the longer grafts experiencing deeper energetic wells and further interplate separation distances. The results are driven by the interfacial tension due to the local domain bulging effects caused by the insertion of the nanoplates into the lamellar system. With experimental separation distances of a PEG-grafted gadolinium trifluoride doped with ytterbium and erbium, GdF3:Yb/Er (20/2 mol %) nanoplates corroborate the correlation found in the simulations between larger matrix domains and a widening of the energetic well. Additionally, the average separation distance follows a trend similar to the hSCFT data. We anticipate these results to help in the development and design of anisotropic nanoparticles within BCPs to create nanocomposites tailored for specific applications and properties.