Molecular Weight Development in Free‐Radical Polymerization with Polyfunctional Chain‐Transfer Agents, 2. Substitution Effects

The analytic expression for the weight‐average molecular weight development proposed in the first part of this series^[1] is extended to account for the substitution effects of the functional groups in a polyfunctional chain‐transfer agent. The obtained functional form of the matrix formula, P_w = W { D _w + ( I + T ) SPE ( I – TSPE )^–1 D _f } is essentially the same as for equal reactivity model, but the NxN square matrixes, S and P in the equal reactivity model is now expanded to NxfN and fNxfN matrixes, respectively, to account for the different reactivities of f functional groups. The number of chain types, N is extrapolated to infinity to obtain the P_w‐value for free‐radical polymerization. Practically, such extrapolation can be conducted with calculated P_w‐values for only three different N‐values. Illustrative calculations show that the obtained results agree with those from the Monte Carlo method. The present approach provides newer insight into the branched structure formation during complex polymerization reactions.     

A q-analog of the sixth Painlevé equation

A q-difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear q-difference equations, in close analogy with the monodromy-preserving deformation of linear differential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed.     

Diastereomer-specific effects of double-stranded peptides conjugated with -L-Tyr-L-Phe- or -L-Tyr-D-Phe- residues on tyrosine phosphorylation and inhibition of src(ts)NRK, A431, MCF-7, and DU145 cell growth

The interaction between growth inhibition and chirality, especially of diastereomers, has an important modifying effect on cancer cell proliferation. Previously, we have reported on the design, synthesis, and chemical properties of a series of novel, double-stranded peptides, (y-AA-x-AA)(2)-(CH(2))(12), with -y-AA-x-AA- and -z-AA-y-AA-x-AA- sequences conjugated to the spacer. Here, we extend those results by showing that (D-, L-) and (L-, D-) diastereomers are more potent inhibitors of tyrosine phosphorylation than (L-, L-). Although the replacement of the L-Phe-L-Phe sequence with L-Tyr-L-Phe produces a less active inhibitor, the double-stranded peptide conjugated with L-Tyr-D-Phe is more active than that conjugated with L-Tyr-L-Phe. In addition, we show that SDS-PAGE gel profiles of tyrosine phosphorylation following treatment with bis(y-Tyr-x-Phe)-N,N-dodecane-1,12-diamine appear very similar to profiles of tyrosine phosphorylation following treatment with an analog of the tyrosine kinase inhibitor, erbstatin. Moreover, the level of autophosphorylation of the epidermal growth factor receptor kinase domain (EGFRKD) treated with bis(L-Tyr-D-Phe)-N,N-dodecane-1,12-diamine was lower than that seen following treatment with bis(L-Phe-D-Phe)-N,N-dodecane-1,12-diamine. These data provide new insights for the control of cancer cell proliferation through drug designs which replace the less active -L-Phe-L-Phe- (and -D-Phe-L-Phe-) with the more active -L-Tyr-L-Phe- (and -L-Tyr-D-Phe-) sequence.     

An organopalladium(II) compound including enolate oxy­gen‐ and sp3‐carbon‐bound 1,3‐di­methyl­barbiturate ligands: (1,2‐di­amino­ethane)­bis(1,3‐di­methyl­barbiturato)­palladium(II) 5.5‐hydrate

In the title compound, [Pd(C₆H₇N₂O₃)₂(C₂H₈N₂)]·5.5H₂O, the Pd atom is coordinated by two 1,3‐di­methyl­barbiturate anions through a deprotonated tetrahedral carbon and the enolate oxy­gen. The Pd—N bond length of 2.078 (2) Åtrans to the C atom is shorter than the Pt—N distance of 2.098 (3) Å in the Pt analog.     

Molecular weight distribution in random branching of polymer chains

Analytical expressions for the average molecular weights of randomly branched polymer molecules with any primary chain distribution are developed. A full molecular weight distribution (MWD) function is also derived for the case where primary chains conform to the most probable distribution. This MWD function can be separated into the fractional MWDs containing k branch points; therefore, very detailed information on the structure of randomly branched polymers can be obtained. The average molecular weights of the polymer fraction containing k branch points are linear functions of the number of branch points k, and the distribution becomes narrower as k increases. The heterogeneity in the distribution of branch points can make the weight-average degree of polymerization larger, although it is impossible to form a gel molecule only via branches (T-shaped junctions) without assistance of crosslinkages (H-shaped junctions).     

Room‐temperature epitaxial growth of high‐quality m ‐plane InGaN films on ZnO substrates

The authors have grown high‐quality m ‐plane In_0.36Ga_0.64N (1 00) films on ZnO (1 00) substrates at room temperature (RT) by pulsed laser deposition (PLD) and have investigated their structural properties. m ‐plane InGaN films grown on ZnO substrates at RT possess atomically flat surfaces with stepped and terraced structures, indicating that the film growth proceeds in a two‐dimensional mode. X‐ray diffraction measurements have revealed that the m ‐plane InGaN films grow without phase separation reactions at RT. The full‐width at half‐maximum values of the 1 00 X‐ray rocking curves of films with X‐ray incident azimuths perpendicular to the c ‐ and a‐axis are 88 arcsec and 78 arcsec, respectively. Reciprocal space‐mapping has revealed that a 50 nm thick m ‐plane In_0.36Ga_0.64N film grows coherently on the ZnO substrate, which can probably explain the low defect density that is observed in the film. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A simulation model for long-chain branching in vinyl acetate polymerization: 1. Batch polymerization

A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double-bond polymerization is proposed. This model is based on the branching density distribution of the primary polymer molecules. The theory of branching density distribution is that each primary polymer molecule experiences a different history of branching and provides information on how each primary polymer molecule is connected with other chains that are formed at different conversions, therefore making possible a detailed analysis on the kinetics of the branched structure formation. This model is solved by applying the Monte Carlo method and a computer-generated simulated algorithm is proposed. The present model is applied to a batch polymerization of vinyl acetate, and various interesting structural changes occurring during polymerization (i.e., molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule) are calculated. The present method gives a direct solution for the Bethe lattice formed under nonequilibrium conditions; therefore, it can be used to examine earlier theories of the branched structure formation. It was found that the method of moments that has been applied successfully to predict various average properties would be considered a good approximation at least for the calculation of not greater than the second-order moment in a batch polymerization. © 1994 John Wiley & Sons, Inc.