Multi-Item Scheduling by Benders' Decomposition

Scheduling the production of several items requires the determination of production quantities in different periods in the presence of resource constraints. Several approximate and heuristic algorithms have been proposed to solve this problem. However, no method for finding an optimal solution has as yet been developed. It is shown that the problem may be solved advantageously using Benders' decomposition. The subproblem in Benders' decomposition is shown to be a transportation problem, and some strategies for solving the master problem are indicated. The paper concludes with a sample problem demonstrating the application of the method.     

Platinum carbonyl derived catalysts on inorganic and organic supports: a comparative study

Fumed silica, silica gel, silica-alumina and cross-linked (5.5%) polystyrene have been functionalized with quaternary ammonium groups and the Chini cluster [Pt₁₂(CO)₂₄]²⁻ has been anchored onto these functionalized materials by ion pairing. A catalyst has also been prepared by the adsorption of Na₂[Pt₁₂(CO)₂₄] on unfunctionalized fumed silica. The catalytic activities of the resultant materials, and that of commercially purchased 5% platinum on alumina have been studied for the hydrogenation of a variety of unsaturated compounds. The substrates studied are: α-acetamidocinnamic acid, cyclohexanone, acetophenone, methyl pyruvate, ethyl acetoacetate, nitrobenzene and benzonitrile. Compared to the polystyrene supported catalyst, the inorganic oxide supported catalysts have higher surface areas and for most of the substrates have notably higher activities. The functionalized fumed silica-based catalyst gives higher conversions than functionalized silica gel and silica-alumina-based catalysts. In the hydrogenation of acetophenone and ethyl acetoacetate, the functionalized fumed silica-based catalyst show superior activity compared to the commercial platinum catalyst, and the catalyst made by conventional adsorption method. In benzonitrile hydrogenation with all the cluster-derived catalysts a hydrazine derivative is selectively formed, but when the commercial platinum catalyst is used benzyl amine is the main product.     

Interparticle interactions in agglomerates of alpha-Fe2O3 nanoparticles: influence of grinding

We have chemically prepared a sample of antiferromagnetic alpha-Fe2O3 nanoparticles by a gel-sol technique. M?ssbauer spectra of the as-prepared sample showed that superparamagnetic relaxation was suppressed due to strong magnetic interparticle interactions even at room temperature. However, subsequent grinding of the sample by hand in a mortar for some minutes resulted in fast superparamagnetic relaxation of some of the particles. The effect was even more dramatic if the alpha-Fe2O3 powder was ground for a longer time or together with nonmagnetic eta-Al2O3 nanoparticles. Similar effects were found after low-energy ball milling. Thus it is found that the agglomeration of the nanoparticles during preparation under wet conditions results in strong magnetic interparticle interaction, but a relatively gentle mechanical treatment is sufficient to break up the agglomerates, resulting in much weaker interactions. We show that these effects can also be seen when a soil sample containing magnetic nanoparticles is ground.     

Nickel nitrosyl complexes with the diphenylphosphinoethane ligand

Summary Four-coordinate nickel nitrosyl complexes of the general formula Ni(NO)X(Dppe) (Dppe=Ph₂PCH₂CH₂PPh₂) have been prepared byin situ formation of Ni(NO₂)X(Dppe), (X= Cl, Br, I or SCN) followed by reduction with triphenylphosphine, or carbon monoxide, and/or DMF. Oxygenation of the nitrosyl complexes gives the corresponding nitro products and as indicated by u.v.-vis spectroscopy involves formation of an intermediate. The oxygenation rate increases markedly in the presence of light or of a catalytic amount of benzoyl peroxide and a tentative explanation is offered for these observations. Ionic adducts are formed in reactions between the nitrosyl complexes and donor molecules.Paper presented in part at the XXth ICCC Conference.     

Translucent nanolatexes through emulsion polymerisation of ethyl acrylate

Turbid emulsion systems of ethylacrylate/sodium dodecyl sulphate/water with monomer to surfactant (M/S) ratios 10 and 40 were transformed into stable transparent/translucent nanolatexes through emulsion polymerisation using potassium persulphate as an initiator. The latex particle size was observed to be similar to that obtained by true microemulsion polymerisation where M/S ratio is one. The kinetic plots exhibited two intervals upto M/S ratios 10. AIBN initiated systems showed separation of two phases for the M/S ratio ?10. M/S ratios were varied from 1 to 54 for the comparative study of polymerisation in emulsion and microemulsion media. Gel effect dominance was observed around 40-60% conversion for the microemulsion polymerisation of ethylacrylate. Only one chain per particle was observed for microemulsion system with M/S ratio 1 and three to four chains per particle were observed for the systems with M/S ratios 10 and 40. Unlike M/S=1 system, higher dependency of polymerisation rate on initiator concentration was observed for the systems with M/S=10 and 40. A possible mechanism for such a transformation has been proposed.     

A water soluble nanostructured platinum (0) metal catalyst from platinum carbonyl molecular clusters: Synthesis, characterization and application in the selective hydrogenations of olefins, ketones and aldehydes

High nuclearity platinum carbonyl cluster anions (Chini's clusters) have been used as precursors to prepare a platinum nanocatalyst. The ionic polyelectrolyte poly(diallyldimethylammonium chloride) has been used as the support material for anchoring [Pt₃₀(CO)₆₀]²⁻ via ion-pairing and subsequent stabilization of the nanoparticles. The polymer-supported material has been studied by spectroscopy (NIR, ¹³C NMR, and IR) and TEM before and after its use as a water soluble hydrogenation catalyst. The nanocatalyst is found to be effective for the chemoselective hydrogenation of olefinic, aldehydic and ketonic double bonds. For most of the substrates isolation of the product and reuse of the catalyst are extremely easy due to the automatic phase separation of the products from the catalyst. The spectral features of the fresh catalyst show retention of the carbonyl ligands and molecular identity of the parent cluster, but after use the carbonyl ligands appear to be lost. TEM of the supported material before and after use as a catalyst shows the presence of platinum nanoparticles with majority (≥70%) of the particles in the range of 2–6 nm. Smaller particles are dominant in the used catalyst and this observation is rationalized on the basis of the known reactivity of Chini's clusters with dihydrogen.     

On [Fe4S4]2+ -(mu2-SR)-M II bridge formation in the synthesis of an A-cluster analogue of carbon monoxide dehydrogenase/acetylcoenzyme A synthase

The construction of a synthetic analogue of the A-cluster of carbon monoxide dehydrogenase/acetylcoenzyme synthase, the site of acetylcoenzyme A formation, requires as a final step the formation of an unsupported [Fe(4)S(4)]-(mu(2)-SR)-Ni(II) bridge to a preformed cluster. Our previous results (Rao, P. V.; Bhaduri, S.; Jiang, J.; Holm, R. H. Inorg. Chem. 2004, 43, 5833) and the work of others have addressed synthesis of dinuclear complexes relevant to the A-cluster. This investigation concentrates on reactions pertinent to bridge formation by examining systems containing dinuclear and mononuclear Ni(II) complexes and the 3:1 site-differentiated clusters [Fe(4)S(4)(LS(3))L'](2-) (L' = TfO(-) (14), SEt (15)). The system 14/[{Ni(L(O)-S(2)N(2))}M(SCH(2)CH(2)PPh(2))](+) results in cleavage of the dinuclear complex and formation of [{Ni(L(O)-S(2)N(2))}Fe(4)S(4)(LS(3))]- (18), in which the Ni(II) complex binds at the unique cluster site with formation of a Ni(mu(2)-SR)(2)Fe bridge rhomb. Cluster 18 and the related species [{Ni(phma)}Fe(4)S(4)(LS(3))](3)- (19) are obtainable by direct reaction of the corresponding cis-planar Ni(II)-S(2)N(2) complexes with 14. The mononuclear complexes [M(pdmt)(SEt)]- (M = Ni(II), Pd(II)) with 14 in acetonitrile or Me(2)SO solution react by thiolate transfer to give 15 and [M(2)(pdmt)(2)]. However, in dichloromethane the Ni(II) reaction product is interpreted as [{Ni(pdmt)(mu(2)-SEt)}Fe(4)S(4)(LS(3))](2-) (20). Reaction of Et(3)NH(+) and 15 affords the double cubane [{Fe(4)S(4)(LS(3))}(2)(mu(2)-SEt)](3-) (21). Cluster 18 contains two mutually supportive Fe-(mu(2)-SR)-Ni(II) bridges, 19 exhibits one strong and one weaker bridge, 20 has one unsupported bridge (inferred from the (1)H NMR spectrum), and 21 has one unsupported Fe-(mu(2)-SR)-Fe bridge. Bridges in 18, 19, and 21 were established by X-ray structures. This work demonstrates that a bridge of the type found in the enzyme A-clusters is achievable by synthesis and implies that more stable, unsupported single thiolate bridges may require reinforcement by an additional covalent linkage between the Fe(4)S(4) and nickel-containing components. (LS(3) = 1,3,5-tris((4,6-dimethyl-3-mercaptophenyl)thio)-2,4,6-tris(p-tolylthio)benzene(3-); L(O)-S(2)N(2) = N,N'-diethyl-3,7-diazanonane-1,9-dithiolate(2-); pdmt = pyridine-2,6-methanedithiolate(2-); phma = N,N'-1,2-phenylenebis(2-acetylthio)acetamidate(4-); TfO = triflate.).