Universality of the Entanglement Plateau Modulus of Comb and Bottlebrush Polymer Melts

• Published in: Macromolecules 2018-12, Vol.51 (23), p.10028-10039
• Main Authors: Liang, Heyi, Morgan, Benjamin J, Xie, Guojun, Martinez, Michael R, Zhulina, Ekaterina B, Matyjaszewski, Krzysztof, Sheiko, Sergei S, Dobrynin, Andrey V
• Format: Article
• Language: English
• ISSN: 0024-9297; 1520-5835
• DOI: 10.1021/acs.macromol.8b01761

A combination of scaling analysis and rheological experiments was used to study correlations between the entanglement plateau modulus and grafting density of graft polymers in a melt. Using the crowding parameter Φ, which describes overlap of side chains belonging to neighboring macromolecules, we identified two classes of graft polymerscombs and bottlebrushesthat demonstrate distinct conformational and rheological behaviors. In comb systems, both the backbones and sparsely grafted side chains are coiled that allow side chains of neighboring macromolecules to overlap (Φ < 1). In bottlebrush systems, steric repulsion between densely grafted side chains causes chain extension and inhibits side chain interpenetration (Φ ≥ 1). The ratio G e,gr/G e,lin ≅ φ3(1 + (Φ/0.7)3) of the plateau modulus of a graft polymer melt, G e,gr, to that of a melt of linear chains, G e,lin, is a universal function of the crowding parameter Φ ≅ φ–1 n sc –1/2 and graft polymer composition φ = n g/(n g + n sc), where n sc and n g are the degrees of polymerization of side chains and a spacer separating two consecutive side chains along the polymer backbone, respectively. This dependence of the plateau modulus is verified for poly­(n-butyl acrylate) combs and other graft polymer systems reported in the literature. In a special case of graft polymers with long entangled side chains, the G e,gr/G e,lin ratio is proportional to φ2.