Brush Gels: Where Theory, Simulations, and Experiments Meet

• Published in: Macromolecules Vol. 55; no. 17; pp. 7922 - 7931
• Main Authors: Jacobs, Michael, Vashahi, Foad, Maw, Mitchell, Sheiko, Sergei S., Dobrynin, Andrey V.
• Format: Journal Article
• Language: English
• Published: American Chemical Society 13-09-2022
• ISSN: 0024-9297; 1520-5835
• DOI: 10.1021/acs.macromol.2c01149

Polymer networks with brush-like (comb or bottlebrush) strands can have mechanical properties similar to biological tissues and can swell to larger volumes than their linear chain counterparts. We use a combination of the Flory–Rehner approach, scaling analysis, molecular dynamics simulations, and experimental data for poly­(n-butyl acrylate) (PBA) networks swollen in toluene to elucidate the effect of brush strand architecture on the equilibrium swelling ratio, Q eq , the modulus of the swollen gel, G gel (Q eq ), and its relationship with the nonlinear modulus of the dry network, G(Q eq ). Analysis of simulation data and experimental results for PBA gels demonstrates that the gel shear modulus monotonically decreases with increasing equilibrium swelling ratio as G gel (Q eq ) ∝ Q eq –3, which is consistent with a θ-solvent-like swelling behavior. There is a significant effect of the degree of polymerization n sc and grafting density 1/n g of the side chains on the gel modulus that manifests as mechanically diverse gels with the same solvent content. This unique behavior is explained by the architecture-controlled stiffening of the brush strands due to the swelling of the side chains in the gel state. In the framework of a scaling model, the effective Kuhn length of the swollen strands, b K,s , can be expressed in terms of the Kuhn length in the dry state, b K , and the ratio of shear modulus calculated in the framework of the Flory–Rehner approach, G gel FR(Q eq ) = G(Q eq )/Q eq 1/3, to the gel modulus G gel (Q eq ) such that b K,s ≈ b K G gel FR(Q eq )/G gel (Q eq ). The Kuhn length obtained from this analysis highlights different mechanisms of swollen brush rigidity.