Scaling Laws of Bottle‐Brush Polymers in Dilute Solutions

Abstract

The structural determination and manipulation of bottle-brush polymers, a class of polymers with serially grafted side-chains, is challenging due to the interplay of side-chain and backbone interactions over various length scales. The present work performs a detailed analysis, using molecular dynamics simulation techniques, to unravel these interactions by probing the distinct rod to a flexible real-chain with self-avoiding walk (SAW) type crossover in the backbone static structure factor. This analysis elucidates the deviation from flexible chain behavior, while also providing a quantitative measure of persistence length, P . Significantly, the results identify a trend in P which is consistent with the debated theoretical prediction of ∼ N P s 15/8 , where N s is the number of monomers in each side-chain of the bottle-brush polymer.

Experimental Validation on Average Conformation of a Comblike Polystyrene Library in Dilute Solutions: Universal Scaling Laws and Abnormal SEC Elution Behavior

“…The result supported the prediction of the scaling theory only in the case of longer side chains ( N g = 20 ∼ 40, N b = 800, σ –1 = 10), but not in the case of shorter side chains and spacers . In contrast, the molecular dynamics simulation from Chatterjee et al confirmed the validity of predictions by Fredrickson . In addition to the above approaches, alternative approaches have been used to understand the behavior of bottlebrush polymers, including the self-consistent field theory, renormalization group methods, and the Rosenbluth method …”

“…18 In contrast, the molecular dynamics simulation from Chatterjee et al confirmed the validity of predictions by Fredrickson. 23 In addition to the above approaches, alternative approaches have been used to understand the behavior of bottlebrush polymers, including the self-consistent field theory, 24 renormalization group methods, 25 and the Rosenbluth method. 26 Quasi-Two-Parameter (QTP) Theory.…”

Dilute solution structure of bottlebrush polymers

“…24 Some agreement with molecular dynamics simulations have been observed. 59 Alternative approaches have also been used to understand bottlebrush structure, including perturbative methods, 60 self-consistent field theory, 61 and renormalization group methods. 62,63 Indeed, while most recent work has focused on models for dense melts, [64][65][66][67][68][69][70][71] there remains a need for further insight into dilute-solution bottlebrush structure.…”

“…31 The large volume of experimental and theoretical work remains rife with conflicting ob-servations. 23,24,[30][31][32]35,[49][50][51][52][53][54]59,61,74,75,85 Many of these issues have been discussed at length in a recent review by Binder et al 86 This is in part due to the idealization required to make progress with theory, which is compounded by the reliance on experimental characterization that does not directly image the bottlebrush chains but instead infers structure from model predictions. Furthermore, efforts to include simulation data have often used similarlyidealized molecular models, that rarely invoke the specific chemistry used in a given bottlebrush in favor of universal statements.…”

Dilute Solution Structure of Bottlebrush Polymers

“…This shows some inconsistency with later simulation and theoretical work, 49-55 however Monte Carlo simulations have placed the backbone size exponent to be in the range of 0.6 -0.7. 52,54,[56][57][58] Alternative scaling arguments by Fredrickson,24 who considered the related case of surfactant-associated polymer chains, predicted the effects of progressively increasing the grafting density f as moving through three regimes; a low grafting density where the bottlebrush appears coil-like (f N 59 Alternative approaches have also been used to understand bottlebrush structure, including perturbative methods, 60 self-consistent field theory, 61 and renormalization group methods. 62,63 Indeed, while most recent work has focused on models for dense melts, [64][65][66][67][68][69][70][71] there remains a need for further insight into dilute-solution bottlebrush structure.…”