Polymer–polymer interaction parameters of polystyrene and polybutadiene from studies in solutions of toluene or tetrahydrofuran

Equations used for the determination of polymer–polymer interaction parameters for narrow molecular weight distribution polymers which have undergone phase separation in solutions are discussed. Binodals with tie lines and plait points are presented for ternary systems polystyrene-polybutadiene-toluene and polystyrene-polybutadiene-tetrahydrofuran. Typical interaction parameters determined from the experimental data for the polystyrene-polybutadiene systems are presented.     

Vapour—liquid equilibrium of the systems 1-propanol—2,2,4-trimethylpentane and 2-propanol-n-hexane

The vapour—liquid equilibrium data were measured for the binary systems 2-propanol—n-hexane at 328.21 K and 1-propanol—2,2,4-trimethylpentane at 328.37 K and 348.52 K by using the recirculation still proposed by Berro et al. (1975). The excess volumes for these systems were measured with an Anton Paar densimeter. The reduction of VLE data and analysis of experimental errors were performed. The NRTL temperature-dependence parameters were estimated. The measured VLE data and the activity coefficients were compared with the values predicted by the chemical-reticular group-contribution method (CRG) (Neau and Péneloux, 1979). For both systems satisfactory agreement was found. This proves that the CRG model can be used to predict the vapour—liquid equilibria of alcohol—alkane systems containing branched components.     

Photolytic closure of 4,5-diphenyl-oxazol-2-ones to phenanthro[9,10-d]oxazol-2-ones and an improved synthesis of benzoins

The synthesis of phenathrenes substituted by nitrogen and oxygen atoms in position 9 and 10 by photolysis of 4,5-diphenyl-oxazol-2-ones (cf. Scheme 4) is described. Moreover an improved general procedure for the synthesis of benzoins in aprotic solvent (tetra-t-butylammonium cyanide in DMF/DMSO) is developed.     

Convex optimization and lagrange multipliers

The duality theorem of linear programming is used to prove several results on convex optimization. This is done without using separating hyerplane theorems.This work was supported in part by a grant from Investors in Business Education.     

Isotactic sequence lengths by ozonation of poly(propylene oxide)

Ozonation followed by lithium aluminum hydride reduction cleaved high molecular weight isotactic poly(propylene oxide) to crystalline polyglycols. From the melting point and molecular weight of the latter, the molar freezing point depression produced by end groups is found to be ca. 18°C./mole, as compared to that estimated for poly(ethylene glycols), K_f = 12°C./mole, from earlier data. By assuming syndiotactic placements (or other irregularities) would produce the same molar depression, the melting point of isotactic poly(propylene oxides) produced by various catalysts has been used to estimate the isotactic sequence lengths.     

Electron impact induced fragmentations and rearrangements of some phenyl substituted phosphine oxides

Electron impact induced fragmentations and rearrangements of 1-phenyl-2,2,3-trimethylphosphetane 1-oxide, 1-phenylphospholane 1-oxide and 1-phenylphosphorinane 1-oxide were investigated. A process common to all of these phosphine oxides was electron impact induced formation of new carbon-carbon bonds involving the phenyl rings. Evidence for such rearrangements included observation of hydrocarbon fragment ions containing seven or more carbons.     

Contractive projections with contractive complement in Lp space

Using the concepts of conditional expectation and independence of subalgebras, we characterize those contractive projections, P, on L_p, over a probability measure space, having the property that I − P is contractive. By contractive projection we mean a linear operator, P, on the Lebesgue space, L_p, 1 < p < ∞, ≠2, with P² = P, ∥ = 1.