Interestingly, similar characteristic features are also found in polyelectrolyte solutions and the nature of their origin has triggered an ongoing theoretical discussion, including the origin and meaning of the so-called “polyelectrolyte peak” observed in scattering measurements ( 28). A recent simulation study confirmed the finding, λ of 2/5, in the limit of long backbones ( 17). More recently, it was demonstrated by Chremos and Douglas ( 16) through simulations that the interbackbone spacing scales primarily with the sidechain length N ∼ S C as ξ ∼ N ∼ S C λ, where the exponent λ ranges from 1/3 to 2/5 as backbone length is increased. Early experimental studies suggested that the interbackbone distance scales linearly with the degree of polymerization of the sidechains ( 26, 27), although follow-up simulations considering bottlebrush polymers with longer sidechains proposed a scaling of 1/2 ( 14). This correlation length is typically probed by small-angle neutron and X-ray scattering (SANS and SAXS, respectively) studies, where ξ is defined by the primary peak of intermediate scattering, ξ ∼ q peak −1. One can envision the packing of backbone chains (by rendering the sidechains invisible) similar to polymers in solutions, where the backbone chains interpenetrate to form a meshlike structure characterized by a correlation length, ξ. There have been attempts to define what features differentiate a bottlebrush polymer from a comb polymer ( 15, 24, 25), but how these definitions translate to physical systems of varying backbone chemistry is not yet clear. Even within these studies, there has been minimal attention given to the potential effects of varying brush-backbone chemistry, despite the dramatic differences between the two most common brush backbones (polynorbornene and polyacrylate), both in terms of intrinsic (ungrafted) rigidity and potential grafting density. However, the majority of the brush polymer literature focuses on solution properties and conformations, with interest in bulk properties only gaining traction in the last 5 years ( 14– 23). The discovery of this aspect of bottlebrush polymers has catalyzed the development of an entire field centered on investigating ultrasoft, entanglement-free elastomers for soft robotics and biological tissue mimics ( 3, 11– 13). Previous studies have established that bottlebrush polymers exhibit a lower propensity to entangle, a property derived from the relatively large size of the sidechains in comparison to the overall molecular dimensions ( 7– 10). Polymers with long, densely grafted sidechains, commonly known as bottlebrush polymers, have attracted significant interest in a variety of fields due to their unique properties ( 1– 6). ξ also scales with sidechain length to a power in the range of 0.35–0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers. The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. We find that the correlation length scales with the backbone concentration, ξ ∼ c B B − 0.47, in striking accord with the scaling of ξ with polymer concentration c P in semidilute polyelectrolyte solutions ( ξ ∼ c P − 1 / 2 ). Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position q * = 2 π / ξ by neutron scattering and in simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations.
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