The physical basis for the head-to-tail rule that excludes most fullerene cages from self-assembly.
In the companion article, we proposed that fullerene cages with head-to-tail dihedral angle discrepancies do not self-assemble. Here we show why. If an edge abuts a pentagon at one end and a hexagon at the other, the dihedral angle about the edge increases, producing a dihedral angle discrepancy (DAD) vector. The DADs about all five/six edges of a central pentagonal/hexagonal face are determined by the identities-pentagon or hexagon-of its five/six surrounding faces. Each "Ring"-central face plus specific surrounding faces-may have zero, two, or four edges with DAD. In most Rings, the nonplanarity induced by DADs is shared among surrounding faces. However, in a Ring that has DADs arranged head of one to tail of another, the nonplanarity cannot be shared, so some surrounding faces would be especially nonplanar. Because the head-to-tail exclusion rule is an implicit geometric constraint, the rule may operate either by imposing a kinetic barrier that prevents assembly of certain Rings or by imposing an energy cost that makes those Rings unlikely to last in an equilibrium circumstance. Since Rings with head-to-tail DADs would be unlikely to self-assemble or last, fullerene cages with those Rings would be unlikely to self-assemble.
Schein
Stan
S
Department of Psychology, University of California at Los Angeles, Los Angeles, California, USA. schein@ucla.edu
Sands-Kidner
Michelle
M
Friedrich
Tara
T
D003198:Computer Simulation; D003460:Crystallization / Q000379:methods*; D037741:Fullerenes / Q000737:chemistry*; D046911:Macromolecular Substances / Q000737:chemistry; D008956:Models, Chemical; D008958:Models, Molecular; D008968:Molecular Conformation; D049329:Nanostructures / Q000737:chemistry* / Q000648:ultrastructure*
D037741:Fullerenes; D046911:Macromolecular Substances