Hydrocarbon links in an octet truss

We use the octet truss of R. Buckminster Fuller to develop a geometric placement method for synthesizing braid representations of knots and links of oligo (phenylene ethynylene)s using the 60° ortho, 120° meta or 180° 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.