Brush Architecture and Network Elasticity: Path to the Design of Mechanically Diverse Elastomers

Abstract

We unveil universal correlations between architectural parameters and nonlinear elastic properties of brush polymer networks. A comprehensive library of poly(n-butyl acrylate), poly(dimethylsiloxane), and polyisobutylene brush networks was synthesized with systematically varied side chain length (∼n sc ), grafting density (∼n g −1 ), and backbone degree of polymerization between cross-links (n x ). This allowed experimental verification of theoretical scaling relationships between mechanical properties (shear modulus and strain-stiffening), architectural parameters [n sc , n g , n x ], and microstructure from in situ small-angle X-ray scattering in both comb and bottlebrush conformational regimes. These results can be used as a foundation for the programmable design of mechanically diverse solvent-free elastic materials. Article pubs.acs.org/Macromolecules

Mechanically Diverse Gels with Equal Solvent Content

“… The network uniformity is validated by the agreement between the experimental and theoretical elongations-at-break, λ max,exp ≅ λ max,theo for different [ n sc , n g , n x ] triplets (Figure S10). …”

“…The n x values are assessed by measuring the shear modulus of dry elastomers (Table S1 and Figures S6−S9). 30 The network uniformity is validated by the agreement between the experimental and theoretical elongations-at-break, λ max,exp ≅ λ max,theo for different [n sc , n g , n x ] triplets (Figure S10). 30 Even though knowing the architectural parameters is vital for understanding molecular mechanisms of gel behavior, the equilibrium swelling ratio, Q eq , can be predicted from the mechanical properties of dry elastomers without specifying [n sc , n g , n x ] values.…”

“…30 The network uniformity is validated by the agreement between the experimental and theoretical elongations-at-break, λ max,exp ≅ λ max,theo for different [n sc , n g , n x ] triplets (Figure S10). 30 Even though knowing the architectural parameters is vital for understanding molecular mechanisms of gel behavior, the equilibrium swelling ratio, Q eq , can be predicted from the mechanical properties of dry elastomers without specifying [n sc , n g , n x ] values. For linear networks, Q eq is given by the Flory−Rehner model as Q eq ∼ G −3/8 , where the elastomer shear modulus G ∼ n x −1 is proportional to its cross-link density.…”

“…A structural interpretation of the observed trend is exposed by plotting Q eq versus φ −1 = 1 + n sc /n g for different n x (Figure 3c) using the known correlations between G, β, and the architectural triplet [n sc , n g , n x ]. 30,32 The theoretical dashed lines indicate two main correlations: (i) Q eq increases with side chain length (∼n sc ) and grafting density (∼n g −1 ) for a given n x , and (ii) likewise, Q eq increases with n x for a given brush structure φ −1 . The experimental data demonstrate good agreement with the predicted trends (symbols in Figure 3c).…”

“…The n x values are assessed by measuring the shear modulus of dry elastomers (Table S1 and Figures S6–S9). The network uniformity is validated by the agreement between the experimental and theoretical elongations-at-break, λ max,exp ≅ λ max,theo for different [ n sc , n g , n x ] triplets (Figure S10). …”