(a) Torsion: A simple five-atom carbyne system with an imposed curvature (κ = 0.016 to 0.395 Å-1, inset κ = 0.2 Å-1) is subject to incremental twist while tracking the potential energy. The cyclical energy change due to a 180° twist increases with initial curvature as shown, defining the energy barrier (indicated by arrows) to untwist a carbyne

chain in the looped configuration. (b) Adhesion: Three short six-atom carbyne chains (to reflect a three-loop adhesion case) were brought into close proximity over time to determine the interchain adhesion energy barrier, defined as the depth of the potential energy well (indicated by arrows). For torsion, involving a complete rotation of the carbyne chain about itself, the associated energy barrier would Volasertib in vivo be a function of the initial curvature. A simple five-atom chain was constructed GSK621 in vivo with a set of 14 initial curvatures ranging from 0.016 to 0.395 Å-1 and subjected to incremental twist while tracking the potential energy (representative plots are given in Figure 5a). During the simulation, one terminal atom is fixed, along with the second-to-the-last atom at the opposite end, while the adjacent terminal atom is then rotated about an axis of rotation and constant curvature maintained. The maximum energy barrier was calculated to be approximately

10 kcal mol-1, exhibited at large curvatures (>0.1 Å-1). A recent study quantified the torsional stiffness of carbyne, albeit using ab initio methods, a straight chain configuration, and the rotation of end-groups [56]. The reported energy barrier due to torsion ranged from approximately 0.2 to 0.6 eV, or 5 to 14 kcal mol-1. While the simulation approach and boundary conditions were different, the energy barrier determined here (approximately 10 kcal mol-1) is in the same order

of magnitude and in a relatively good agreement. For adhesion, three carbyne chains were brought into contact and incrementally separated to determine the interchain adhesion energy (Figure 5b) of approximately 0.5 kcal mol-1 Depsipeptide in vitro atom-1. For the worst case scenario (the longest chain of 180 carbons resulting in three adhered 60 carbon rings plus the highest recorded torsional barrier), we calculate a maximum energy barrier of approximately 40 kcal mol-1 – smaller than all but the BAY 11-7082 chemical structure minimum (n = 54) required energy increase indicated by the unfolding structures (also note that n = 54 unfolds with nominal kinetic energy required, at approximately T ≈ 10 K, representing the smallest possible stable three-loop structure). This indicates an additional contribution that must be overcome to induce unfolding, and we hence turn to the analysis of curvature.