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