Relationship between Graft Density and the Dilute Solution Structure of Bottlebrush Polymers: An Inter-chemistry Comparison and Scaling Analysis

Bottlebrush polymers are an important class of materials which consist of side chains grafted along a linear backbone. There has been a significant effort to understand structure-property relationships of bottlebrush polymers in solution, with experiments and simulations mapping the impact of parameters such as side chain length, backbone length, and concentration. Improvements in the ability to synthetically control the graft density have resulted in greater interest in understanding how the side chain density influences polymer conformation. However, the impact of graft density on bottlebrush polymers with polynorbornene backbones, which are now ubiquitous, remains relatively unexplored. Here, we examine two sets of polynorbornene-based bottlebrush polymers with polystyrene side chains where the graft density varies between 0.4 and 1.0 side chains per norbornene repeat (i.e., 40 to 100% grafted). The solution conformation of these materials in a good solvent, toluene, is probed through small-angle neutron scattering measurements. Fitting these data with a shape-based model allows for the extraction of parameters such as the radius of gyration and the persistence length. Scaling the radius of gyration based on the Flory theory for grafted chains shows that the side chain-side chain interactions have a greater contribution to the polymer conformation compared to the side chain-backbone interactions, in agreement with results from other backbone chemistries. Additionally, there now exist literature studies rich with dilute solution studies of other chemistries, which are used to develop general scaling relationships for both the radius of gyration and the persistence length as a function of the crowding parameter (product of the side chain degree of polymerization and graft density). Several different representations of the crowding parameter are studied to emphasize the importance of the backbone chemistry to the scaling relationships and solution conformation.