Alkanes knotted

Census of Chiral and Achiral Prime Knots and Alkanes"... 

Nevertheless, thermodynamic reversibility may prove a disadvantage in particular systems. A classic example is provided by the synthesis of individual rotax-anes ( bead on a thread compounds), discussed in detail in Chapter 4. After threading of the macrocyclic bead on to an open-chain component by self-assembly, it has been found desirable to block the reverse (unthreading) pathway by subsequent covalent attachment of branched alkane groups to each end of the thread so that any tendency for separation of the components is blocked. That is, the final covalent step is equivalent to tying a knot in each end of the thread to stop the bead from slipping off. 

The same authors later studied the evolution of the radicals formed after rupture of a single knotted alkane molecule using first-principles molecular dynamics calculation [284]. In knotted chains, recombination of the radicals is totally bypassed in favor of ultrafast (about several hundred femtoseconds) phenomena such as diradicals which generate cyclic alkanes, and disproportionation to form carbon-carbon double bonds. Saitta and Klein suggested that the trefoil knot imposes topological constraints to the velocity distribution of the recoiling radicals at rupture, leading to deviations from the canonical recombination reaction. 

So far we have only reviewed the mechanochemistry of isolated knotting polymers. In real systems, the environment should be taken into consideration. Saitta and Klein studied the rupture processes of a bulk-like PE knot [285]. In the first model, a knotted alkane is surrounded by six linear alkanes (unknotted). For the sake of comparison, a linear alkane is also surrounded by six linear alkanes in the second model. Their results show that the bonds at the entrance and the exit of the trefoil knot are more distorted than elsewhere. Quantitatively, the knot weakens the chain to which it is tied by a factor of about 15%. Indeed, the estimated force to break a knotted alkane is 3.5 nN (the value depends on the timescale), 0.5 nN smaller than that of an unknotted alkane of the same length. 

Saitta AM, Klein ML (1999) Polyethylene under tensile load strain energy storage and breaking of linear and knotted alkanes probed by first-principles molecular dynamics calculations. J Chem Phys 111 9434-9440... 

Saitta AM, Klein ML (1999) Evolution of fragments formed at the rupture of a knotted alkane molecule. J Am Chem Soc 121 11827-11830... 

Adams, C. C. 2004. The Knot Book, Providence, RI American Mathematical Society. Alexiadis, O., Daoulas, K. C., and Mavrantzas, V.G. 2008. An efficient Monte Carlo algorithm for the fast equilibration and atomistic simulation of alkane-thiol self-assembled monolayers on a au(lll) substrate. The J. Phys. Chem. B, 112(4) 1198-1211. 

Fig. 4 Strain distribution in a knotted alkane chain. As the chain is stretched, bonds at edge of the knot are strained more and ultimately rupture. Reprinted by permission from Macmillan Publishers Ltd A. M. Saitta, P. D. Soper, E. Wasserman and M. L. Klein, Nature, 1999, 399, 46-48.

Fig. 5 Schematic diagram of a knotted chain surrounded by unknotted alkane chains as a model system for examining rupture processes in the bulk. The black terminal carbon atoms are fixed and the arrows indicate the direction in which the molecules are deformed. Reprinted with permission from A. M. Saitta and M. L. Klein, J. Chem. Phys., 1999, 111, 9434-9440. Copyright 1999, American Institute of Physics.

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