Hydrothermal Synthesis and X‐Ray Structural Characterization of Manganese,Nickel, and Cadmium Coordination Polymers Containing 2,3‐Pyridinedicarboxylate as Multidentate Ligands

Three divalent transiton‐metal complexes of 2,3‐pyridinedicarboxylate (2,3‐pda²), [Mn(2,3‐pda)‐(H₂O)3]_∞ ( 7 ), [Ni(2,3‐pda)(H₂O)3]_∞ ( 8 ), and [Cd2(2,3‐pda)₂(H₂O)]_∞ ( 9 ) have been hydrothermally synthesized and structurally characterized. X‐ray diffraction analyses reveal that compounds 7 and 8 are zigzag‐ and linear‐type one‐dimension (1D) coordination polymers, respectively, whereas compound 9 is a three‐dimension (3D) coordination polymer. A simple comparison of the coordination geometries with the available neutral analogues {M_x(2,3‐pda)_x(H₂O)_y}_∞ containing one or two divalent transition‐metal atoms and equal ligands in the presence or absence of coordinated water molecules is also presented.     

Extremal k *-Cycle Resonant Hexagonal Chains

Denote by ^* _n the set of all k ^*-cycle resonant hexagonal chains with n hexagons. For any B _n ^* _n , let m(B _n ) and i(B _n ) be the numbers of matchings (=the Hosoya index) and the number of independent sets (=the Merrifield–Simmons index) of B _n , respectively. In this paper, we give a characterization of the k ^*-cycle resonant hexagonal chains, and show that for any B _n ^* _n , m(H _n )m(B _n ) and i(H _n )i(B _n ), where H _n is the helicene chain. Moreover, equalities hold only if B _n =H _n .     

Sensitivity in Supramolecular Architectures of Polyaromatic Salts Containing Two Singly‐Pimerized Bipyridines

Three novel supramolecular arrays of zigzag polyaromatic salts are reported. Both the conformation and disposition of the dications are subjected to various noncovalent interactions. Thus, the presence or absence of the π‐π interacting enclathrated molecules, the efficient packing and the involved hydrogen bonding interactions of anions, as well as the increased hydrophobic property of the dications themselves exert influence.     

Low molecular weight organogelators derived from threefold symmetric tricarbamates

A group of new low molecular weight organogelators based on threefold symmetric tricarbamate were synthesized and characterized. The tricarbamates with long alkyl chains were able to gelate a wide range of polar and nonpolar organic solvents such as acetonitrile and cyclohexane, generally at concentrations lower than 20 g/L. The best organogel formation was obtained using a threefold symmetric tricarbamate in n-dodecane, in which a sufficiently transparent gel was formed at the critical gelation concentration 1 g/L. Intermolecular hydrogen bonding by the tricarbamate in a nonpolar solvent benzene-d₆ was indicated by ¹H NMR spectra. Its maximum UV absorption was 11 nm higher in chloroform than in n-dodecane, and this red shift indicated increased conjugation between the benzene core and the carbamate substituents, which confirmed a change in its conformation from nonpolar to polar solvent. The self-assembling behavior of the tricarbamate in dilute solutions was investigated by TEM. Fiber-like networks were observed in a large range of solution concentrations.     

The absence of physical aging effects on the relaxation of rubbing-induced birefringence in polystyrene

We found, through extensive experimental studies, that the physical aging effects are absent in the relaxation of rubbing-induced birefringence (RIB) in polystyrene (PS), and the relaxation involves very small length scale. A phenomenological model based on individual birefringence elements is proposed for the RIB relaxation. The relaxation times (RTs) of the elements are found to be independent of the thermal or stress history of the samples, either before or after the formation of the birefringence. The RTs are also independent of the molecular weight, rubbing conditions, and film thickness, while the RTs distribution function does depend on the molecular weight and rubbing conditions. The model provides quantitative interpretations that agree very well with all the reported experimental results, and sheds important light on the novel behaviors of the RIB relaxation. The absence of physical aging effects is probably due to the combined effects of small length scale of the RIB relaxation, and the accelerated aging speed in the near surface region in which the RIB concentrates.     

Reactive resonance in a polyatomic reaction

In the course of an extensive investigation aimed at understanding the detailed mechanisms of a prototypical polyatomic reaction, several remarkable observations were uncovered. To interpret these findings, we surmise the existence of a reactive resonance in this polyatomic reaction. The reaction of concern is F+CH4-->HF+CH3, and the abnormal attributes were revealed only near the reaction threshold. The discovery of reactive resonance in a polyatomic reaction is more than just an extension from a typical atom+diatom reaction. As shown here, it holds great promise to disentangle the elusive intramolecular vibrational dynamics of transient collision complex in the critical transition-state region.     

On Some Three-Color Ramsey Numbers

 In this paper we study three-color Ramsey numbers. Let K _i,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G ₁, G ₂ and G ₃, if r(G ₁, G ₂)≥s(G ₃), then r(G ₁, G ₂, G ₃)≥(r(G ₁, G ₂)−1)(χ(G ₃)−1)+s(G ₃), where s(G ₃) is the chromatic surplus of G ₃; (ii) (k+m−2)(n−1)+1≤r(K _1,k , K _1,m , K _n )≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K _k,m , K _k,m , K _n )≤c(n/logn), and r(C _2m , C _2m , K _n )≤c(n/logn) ^m/(m−1) for sufficiently large n. Received: July 25, 2000 Final version received: July 30, 2002 RID="*" ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of education ministry of China, and the foundations of Jiangsu Province Acknowledgments. The authors are grateful to the referee for his valuable comments. AMS 2000 MSC: 05C55