Group ib organometallic chemistry : XXXIV. Thermal behaviour and chemical reactivity of tetranuclear Me2N-substituted diarypropenylcopper-copper anion (Vi2Cu4X2) and mixed diarylpropenyl/organocopper (Vi2Cu4R2) compounds

Thermal decomposition of configurationally pure 1,2-diarylpropenylcopper compounds Z-Vi₂CU₄Br₂ and Z-Vi₂Cu₄R₂ [Vi  (2-Me₂NC₆H₄)CC(Me)-(C₆H₄Me-4), R  2-Me₂NC₆H₄ or 4-MeC₆H₄CC] predominantly results in the formation of ViH. In contrast, only dimers (ViVi) were formed on thermolysis of (Z-ViCu₂OTf)_η which is a further illustration of the influence of the counter anion on the reactivity of organocopper cluster compounds. However, in both cases partial inversion of configuration, giving mixtures of isomers, was observed. The thermolysis of (Z-ViCu₂OTf)_η is discussed in terms of OTf-enhanced intraaggregate electron-transfer processes. The formation of incipient vinyl cations which are η²-coordinated to the copper cluster can explain the observed isomerization.Also in the hydrolysis reaction of Z-Vi₂Cu₄Br₂ mixtures of isomeric ViH compounds were obtained, the E/Z ratio being dependent on the type of reagent used. Mixtures of isomeric ViX compounds (X  Br, Cl, I) were formed in the reaction of Z-Vi₂Cu₄Br₂ with I₂ and CuCl₂. An explanation for the occurrence of isomerization is presented.Dimers (ViVi) were almost absent in the product mixture resulting from the reaction of Z-Vi₂Cu₄Br₂ with CuCl₂. In contrast, ViVi is obtained in about 50% yield from the reaction of ViLi with CuCl₂ which is in accord with earlier observations for the reaction of aryllithium compounds with cupric halides.Highly selective E-ViBr formation was observed in the reaction of E-ViLi with AgBr. This reaction probably proceeds via a thermally unstable Z-ViAg₂Br intermediate.     

Activity testing and surface characterization of pretreated fused-silica capillaries for gas chromatography A new modification of existing intermediate column tests

A new modification of existing intermediate capillary column tests for uncoated columns is presented. A short (1 m), thick film (2 μm) precolumn is coupled to the column to be tested. The use of a short precolumn results in a rapid test. This makes it attractive in terms of time to inject the test compounds separately, thus excluding mutual influences, in diluted solutions spiked with n-alkanes as references. Moreover, the short precolumn gives sharp Gaussian injection profiles on the second column. A simple versatile coupling device has been developed, which permits easy control and adjustment of pressures and carrier flows, monitoring of the effluents of the precolumn and introduction of sharp input bands on the second column. The monitor detector accurately shows the shape and time of introduction of the compounds on the second column. This permits the evaluation of peak distortion, peak shift and yield on the second column. Test compounds were selected on the basis of their physico-chemical properties (vapour pressure, acid-base properties, dipole moments, hydrogen bonding, complexation with metals, etc.). A number of differently pretreated capillaries were tested with these compounds under various external conditions. Accurate quantification and qualification of the activity of the capillary present difficulties. The test is a case of nearly ideal non-linear chromatography. When peaks of different sizes are superimposed, the tails lie on a common envelope. The k′ of the end of the tail is fixed, irrespective of the amount injected, and forms an important parameter in the evaluation. Reconstruction of the chromatogram with a k′ scale instead of a time scale eliminates the influence of carrier velocity and column length. The method is a sensitive tool for intermediate column testing and shows promises for surface characterization.     

Continuum formulation of the Scheutjens-Fleer lattice statistical theory for homopolymer adsorption from solution

Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n(1,e) and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction phi; both n(1,e) and phi enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z < or = 2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z = 2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z < or = 2l, continuum for distances z > 2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.     

An experimental study of chromatographic dynamics in open and packed non-cylindrical conduits

A systematic investigation of the influence of the perimeter shape of open and particle packed fused silica capillaries on chromatographic properties such as resistance to flow and dispersion of solutes propelled through these channels has been conducted. Verifications of these uncommon experiments with existing theoretical treatments are presented and the insights transferred to a novel polymer chip design with integrated facilities for complex separations. A comparison of the chromatographic performance of a real life proteomics sample on this chip with a capillary column of "similar" dimensions is presented.     

Structural aspects of antibody-antigen interaction revealed through small random peptide libraries

Summary Two small random peptide libraries, one composed of 4550 dodecapeptides and one of 8000 tripeptides, were synthesized in newly developed credit-card format miniPEPSCAN cards (miniPEPSCAN libraries). Each peptide was synthesized in a discrete well (455 peptides/card). The two miniPEPSCAN libraries were screened with three different monoclonal antibodies (Mabs). Two other random peptide libraries, expressed on the wall of bacteria (recombinant libraries) and composed of 10⁷ hexa- and octapeptides, were screened with the same three Mabs. The aim of this study was to compare the amino acid sequence of peptides selected from small and large pools of random peptides and, in this way, investigate the potential of small random peptide libraries. The screening of the two miniPEPSCAN libraries resulted in the identification of a surprisingly large number of antibody-binding peptides, while the screening of the large recombinant libraries, using the same Mabs, resulted in the identification of only a small number of peptides. The large number of peptides derived from the small random peptide libraries allowed the determination of consensus sequences. These consensus sequences could be related to small linear and nonlinear parts of the respective epitopes. The small number of peptides derived from the large random peptide libraries could only be related to linear epitopes that were previously mapped using small libraries of overlapping peptides covering the antigenic protein. Thus, with respect to the cost and speed of identifying peptides that resemble linear and nonlinear parts of epitopes, small diversity libraries based on synthetic peptides appear to be superior to large diversity libraries based on expression systems.Abbreviations ABTS 2,2-azino-di-3-ethylbenzthiazoline sulfonate - EGF epidermal growth factor - Mab monoclonal antibody - OD_ccd optical density obtained using CCD camera - RAMPO rabbit-antimouse peroxidase - SDS sodium dodecylsulfate - TGEV transmissible gastroenteritis virus     

Conjugate points in

An example of a geodesic in with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnold.

     

A finiteness theorem for maximal independent sets

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG K ₁) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| 2 ^k–1 +k – 2 for anyG inS(k) andk 2; consequently,S(k) is finite for anyk. Supported in part by the National Science Council under grant NSC 83-0208-M009-050