Theoretical studies of growth mechanism of small fullerene cage C24 (D6d)+

The ring‐collapse mechanism of C₂₄ (D_6d) has been analyzed using semiempirical AM1 and B3LYP/cc‐pVDZ methods. Based on the ring‐stacking/circumscribing model, two precursors are selected. Transition states and intermediates are located and energetics are computed. Before the stacking begins, the precursor and belt reach a suitable relative orientation accompanied by the release of a large amount of energy. It is observed that the reactions between the precursors and the belts are essentially endoergic in nature, whereas the reactions between the stable intermediates and the final belts are exoergic. The deformation energies (DE) and the bond lengths R of the precursors have been computed. The DE values suggest that there is a chance of the cleavage of the bicyclic precursors as the growth process proceeds toward the cage formation. In contrast, the monocyclic precursor is found to have lower deformation energies than the bicyclic precursor. Analysis of average bond length at different cages shows that a large window is formed and the system appears to follow a cascade‐type bond formation. Comparisons are made to our previous results on C₂₈ growth. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Synthesis and characterization of photosensitive polyimides from methylthiomethyl-substituted 4,4′-diaminodiphenylmethanes and 3,3′,4,4′-benzophenonetetracarboxylic dianhydride

A series of novel polyimides are synthesized by the reaction of 3,3′,4,4′-benzophenonete-tracarboxylic dianhydride (BTDA) with four methylthiomethyl-substituted aromatic diamines: 3-methylthiomethyl-4,4′-diaminodiphenylmethane ( I ), 3,3′-dimethylthiomethyl-4,4′-diaminodiphenylmethane ( II ), 3,3′,5-trimethylthiomethyl-4,4′-diaminodiphenylmethane ( III ), and 3,3′,5,5′-tetramethylthiomethyl-4,4′-diaminodiphenylmethane ( IV ) in refluxing m-cresol. The polyimide of diamine I and BTDA carrying only one pendant methylthiomethyl group in a repeating unit is readily soluble in m-cresol, chloroform, and polar aprotic solvents. Increasing the number of the pendant group results in higher solubility. These fully imidized polyimides are also intrinsically photosensitive. The fraction of photoreactive benzophenone sites that relates to the rate and degree of completion of photocrosslinking reaction increases systematically with the increase of the pendant group content. As the average number of the pendant group in a repeating unit reaches 3, 63% of benzophenone sites are found to be photoreactive. These methylthiomethyl-substituted polyimides possess moderate tensile strength which falls in the range of 67–81 MPa. As a result of the increase of methylthiomethyl content, this type of polyimide reveals higher glass transition temperature but lower thermal stability due to the considerable dimension of the pendant group and the ready cleavage nature of the C? S bond. © 1993 John Wiley & Sons, Inc.     

The crossing number of posets

The purpose of this paper is to investigate some properties of the crossing number (P) of a posetP. We first study the crossing numbers of the product and the lexicographical sum of posets. The results are similar to the dimensions of these posets. Then we consider the problem of what happens to the crossing number when a point is taken away from a poset. We show that ifP is a poset such that P and (P–)1, then 1/2 (P)(P–)(P). We don't know yet how to improve the lower bound. We also determine the crossing numbers of some subposets of the Boolean latticeB _n which consist of some specified ranks. Finally we show that _n is crossing critical where _n is the subposet ofB _n which is restricted to rank 1, rankn–1 and middle rank(s). Some open problems are raised at the end of this paper.