The branching graphs of polyhexes: Some elementary theorems,conjectures and open questions

This paper presents a few novel results, and collects together what is known and conjectured about the branching graph of a polyhex.     

Benzenoid Molecules with Uniform Distribution of π-Electrons within Rings

In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some other benzenoid systems.     

Interaction between Ti-gel and silver, copper, as well as nickel compounds under ultrasound irradiation

Ag-TiO₂, Cu-TiO₂ and Ni-TiO₂ were prepared by sonication. The interactions of Ti-gel with silver, copper and nickel ions under ultrasound irradiation are very different, although these ions can be dispersed very well in titania. The results of EDXA and XRD analysis indicate that Ti-gel does not react with AgCl and crystallizes unaffectedly to form rutile. M(OH)₂ (M = Cu and Ni), on the other hand, favors polycondensation with Ti-gel and affects the crystallization of Ti-gel. CuO favors stabilization of the anatase phase. Ni²⁺ ions tend to incorporate more easily into titania than Cu²⁺ ions do when the samples are calcined. TEM, and BET were also used to characterize the samples.     

Extremal hexagonal chains

Some extremal properties of the linear chainL _h ofh hexagons are pointed out. In the class of all hexagonal chains withh hexagons,L _h has minimumK,Z andx ₁ values, as well as maximum W and values;K = number of perfect matchings,Z = number of independent edge sets (Hosoya index),x ₁ = largest graph eigenvalue,W = Wiener index, = number of independent vertex sets (Merrifield-Simmons index). The extremality ofL _h with respect toZ, andx ₁ is demonstrated here for the first time.Dedicated to Frank Harary, teacher, inspirer and friend, pioneer, champion and proprietor of graph theory, on the occasion of his 70th birthday.     

Role of Cell Surface Lipopolysaccharides in Escherichia coli K12 adhesion and transport

The influence of bacterial surface lipopolysaccharides (LPS) on cell transport and adhesion has been examined by use of three mutants of Escherichia coli K12 with well-characterized LPS of different lengths and molecular composition. Two experimental techniques, a packed-bed column and a radial stagnation point flow system, were employed to investigate bacterial adhesion kinetics onto quartz surfaces over a wide range of solution ionic strengths. Although the two systems capture distinct deposition (adhesion) mechanisms because of their different hydrodynamics, similar deposition kinetics trends were observed for each bacterial strain. Bacterial deposition rates were directly related to the electrostatic double layer interaction between the bacteria and quartz surfaces, in qualitative agreement with classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. However, DLVO theory does not fully explain the deposition behavior for the bacterial strain with the lengthy, uncharged O-antigen portion of the LPS. Neither the length nor the charge characteristics of the LPS molecule directly correlated to deposition kinetics, suggesting a complex combination of cell surface charge heterogeneity and LPS composition controls the bacterial adhesive characteristics. It is further suggested that bacterial deposition behavior is determined by the combined influence of DLVO interactions, LPS-associated chemical interactions, and the hydrodynamics of the deposition system.     

Stereo- and regioselectivity in asymmetric synthesis of α-amino substituted benzocyclic compounds

The enantiomerically pure chiral benzocyclic amines 6–8 were obtained by asymmetric transamination of the corresponding prochiral ketones 9a–c. The method involves: (a) formation of chiral imines 10a–c from the prochiral ketones 9a–c and the inexpensive chiral auxiliary (R)- or (S)-phenylethylamine (PEA); (b) asymmetrically induced reduction of these imines to the diastereomeric amines 11a–c and 12a–c; (c) catalytic hydrogenation to remove the benzylic fragment of the chiral PEA auxiliary. The stereoselectivity of the imine reduction, as well as the regioselectivity of the catalytic hydrogenation, are strongly dependent on the size of the saturated ring condensed with the benzene ring. This approach was used to develop a convenient, high yielding, and stereoselective route to several practically important optically active α-amino substituted benzocyclic compounds.     

Structural requirements in chiral diphosphine-rhodium complexes. VIII. Asymmetric hydrogenation of N-acetyldehydroamino acids with rhodium(I) complexes containing chiral carbocyclic analogues of DIOP.

Z--acetamidocinnamic acid was hydrogenated with neutral diphosphine-rhodium(I) complexes containing trans-1,2-bis(diphenylphosphinomethyl) cycloalkanes to give N-acetylphenylalanine: 86 % e.e.-(R) [(1R,2R)-cyclobutane]; 63 % e.e.-(R) [(1R,2R)-cyclopentane]; 35 % e.e.-(S) [(1S,2S)-cyclohexane]; and 82 % e.e.-(R) [(2R,3R)-DIOP]. Similarly, -acetamidoacrylic acid was hydrogenated to give N-acetylalanine: 72 % e.e.-(R) [(1R,2R)-cyclobutane]; 72 % e.e.-(R) [(1R,2R)-cyclopentane]; 40 % e.e.-(S) [(1S,2S)-cyclohexane]; and 73 % e.e.-(R) [(2R,3R)-DIOP].     

Graph theory and molecular orbitals. The loop rule

Graph theory is applied to the study of the dependence of total π-electron energy, π-electron charge distribution and free valency indices of conjugated hydrocarbons on molecular topology. It is shown that the number of loops in the molecular graph determines these quantities.     

Effect of solution chemistry on the surface charge of polymeric reverse osmosis and nanofiltration membranes

A streaming potential analyzer has been used to investigate the effect of solution chemistry on the surface charge of four commercial reverse osmosis and nanofiltration membranes. Zeta potentials of these membranes were analyzed for aqueous solutions of various chemical compositions over a pH range of 2 to 9. In the presence of an indifferent electrolyte (NaCl), the isoelectric points of these membranes range from 3.0 to 5.2. The curves of zeta potential versus solution pH for all membranes display a shape characteristic of amphoteric surfaces with acidic and basic functional groups. Results with salts containing divalent ions (CaCl₂, Na₂SO₄, and MgSO₄) indicate that divalent cations more readily adsorb to the membrane surface than divalent anions, especially in the higher pH range. Three sources of humic acid, Suwannee River humic acid, peat humic acid, and Aldrich humic acid, were used to investigate the effect of dissolved natural organic matter on membrane surface charge. Other solution chemistries involved in this investigation include an anionic surfactant (sodium dodecyl sulfate) and a cationic surfactant (dodecyltrimethylammonium bromide). Results show that humic substances and surfactants readily adsorb to the membrane surface and markedly influence the membrane surface charge.     

Benzenoid Molecules with Uniform Distribution of π-Electrons within Rings

Summary. In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some other benzenoid systems.