Hydrocarbon links in an octet truss. (English) Zbl 1147.92046
Summary: We use the octet truss of R. B. Fuller [U.S. Patent 2986241 (1961)] to develop a geometric placement method for synthesizing braid representations of knots and links of oligo (phenylene ethynylene)s using the \(60^\circ \) ortho, \(120^\circ \) meta or \(180^\circ \) para phenyl ring substitution angles and respecting the van der Waals repulsion constraints. We show that any knot or link can be realized by a phenylene ethynylene oligomer modeled on the octet truss. Use of this lattice is motivated by the structural constraints of these phenylene ethynylene units. Where in bio-organic chemistry, questions often involve identifying existing knots, for example in DNA strands, organic synthesis is concerned with assembling molecular structures that can be verified to exist in a desired knot topology. This physical realization of a knot as a construction of common organic molecular subunits then facilitates further study of the properties of knotted molecules in general.
MSC:
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 92C40 | Biochemistry, molecular biology |
Keywords:
knot; link; braid; octahedron; tetrahedron; equiangular; octet truss; phenylene ethynylene; equilateralReferences:
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