Tension amplification in molecular brushes in solutions and on substrates

Molecular bottle-brushes are highly branched macromolecules with side chains densely grafted to a long polymer backbone. The brush-like architecture allows focusing of the side-chain tension to the backbone and its amplification from the pico-Newton to nano-Newton range. The backbone tension depends on the overall molecular conformation and the surrounding environment. Here we study the relation between the tension and conformation of the molecular brushes in solutions, melts, and on substrates. In solutions, we find that the backbone tension in dense brushes with side chains attached to every backbone monomer is on the order of f(0)N(3/8) in athermal solvents, f(0)N(1/3) in theta solvents, and f(0) in poor solvents and melts, where N is the degree of polymerization of side chains, f(0) approximately equal k(B)T/b is the maximum tension in side chains, b is the Kuhn length, k(B) is Boltzmann's constant, and T is the absolute temperature. Depending on the side chain length and solvent quality, molecular brushes develop tension on the order of 10-100 pN, which is sufficient to break hydrogen bonds. Significant amplification of tension occurs upon adsorption of brushes onto a substrate. On a strongly attractive substrate, maximum tension in the brush backbone is approximately f(0)N, reaching values on the order of several nano-Newtons, which exceeds the strength of a typical covalent bond. At low grafting density and high spreading parameter, the cross-sectional profile of an adsorbed molecular brush is approximately rectangular with a thickness approximately b (A/S)1/2, where A is the Hamaker constant, and S is the spreading parameter. At a very high spreading parameter (S > A), the brush thickness saturates at monolayer approximately b. At a low spreading parameter, the cross-sectional profile of adsorbed molecular brush has a triangular tent-like shape. In the cross-over between these two opposite cases, covering a wide range of parameter space, the adsorbed molecular brush consists of two layers. Side chains in the lower layer gain surface energy due to the direct interaction with the substrate, while the second layer spreads on the top of the first layer. Scaling theory predicts that this second layer has a triangular cross-section with width R approximately N(3/5) and height h approximately N(2/5). Using self-consistent field theory we calculate the cap profile y(x) = h(1 - x2/R2)2, where x is the transverse distance from the backbone. The predicted cap shape is in excellent agreement with both computer simulation and experiment.