Bond Tension in Tethered Macromolecules

The paper presents scaling analysis of mechanical tension generated in densely branched macromolecules tethered to a solid substrate with a short linker. Steric repulsion between branches results in z-fold amplification of tension in the linker, where z is the number of chain-like arms. At large z ~ 100-1000, the generated tension may exceed the strength of covalent bonds and sever the linker. Two types of molecular architectures were considered: polymer stars and polymer "bottlebrushes" tethered to a solid substrate. Depending on the grafting density, one distinguishes the so-called mushroom, loose grafting, and dense grafting regimes. In isolated (mushroom) and loosely tethered bottlebrushes, the linker tension is by a factor of [Formula: see text] smaller than the tension in a tethered star with the same number of arms z. In densely tethered stars, the effect of interchain distance (d) and number of arms (z) on the magnitude of linker tension is given by f ≅ f₀z^3/2(b/d) for stars in a solvent environment and f ≅ f₀z² (b/d)² for dry stars, where b is the Kuhn length and f₀ ≅ k is intrinsic bond tension. These relations are also valid for tethered bottlebrushes with long side chains. However, unlike molecular stars, bottlebrushes demonstrate variation of tension along the backbone f ≅ f₀s z^1/2 / d as a function of distance s from the free end of the backbone. In dense brushes [Formula: see text] with z ≅ 1000, the backbone tension increases from f ≅ f₀ = 1 pN at the free end of the backbone (s ≅ b) to its maximum f ≅ zf₀ ≅ 1 nN at the linker to the substrate (s ≅ zb).