A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model

LetH=–+V onl ²(), whereV(x),x, are i.i.d.r.v.'s with common probability distributionv. Leth(t)=e ^–itv dv(v) and letk(E) be the integrated density of states. It is proven: (i) Ifh isn-times differentiable withh ^(j)(t)=O((1+|t|)^–) for some >0,j=0, 1, ...,n, thenk(E) is aC ⁿ function. In particular, ifv has compact support andh(t)=O((1+|t|)^–) with >0, thenk(E) isC . This allowsv to be singular continuous. (ii) Ifh(t)=O(e ^–|t|) for some >0 thenk(E) is analytic in a strip about the real axis.The proof uses the supersymmetric replica trick to rewrite the averaged Green's function as a two-point function of a one-dimensional supersymmetric field theory which is studied by the transfer matrix method.Research partially supported by the NSF under grant MC-8301889     

Effects of contact time and polarity level on adhesion between interacting surfaces

We have measured the rate at which adhesion develops between two surfaces that interact by hydrogen bonding. A poly(dimethylsiloxane) elastomer lens with a slightly oxidized surface was pushed against a polystyrene-based copolymer substrate that contained acid groups. The interaction was measured on both forming and breaking the contact using the JKR technique. The toughness of the joint, Gc, increased considerably with increasing acid content in the substrate while the apparent work of adhesion, W, measured while making the contact, decreased with increasing acid content. This decrease in W implies that the acid groups caused repulsion between the surfaces when they were not in contact, but the increase in Gc shows that they formed bonds after contact was made. The rate of increase of Gc with time was found to depend on the acid content in the substrate, but for moderate acid levels, Gc was found to saturate at values that varied approximately linearly with acid content. For 8% acid and 47% acid substrates, the rate of adhesion development over a period of 24 h could be fitted by a model assuming (i) the toughness increased linearly with areal density of bonds between the substrate and the elastomer and (ii) the rate of reaction between the substrate and the elastomer varied as the cube of the density of unreacted acid groups. This cube law may possibly be explained by the kinetics of motion of the elastomer chains on the substrate.     

Carbonyl- and carboxyl-substituted enediynes: synthesis, computations, and thermal reactivity

The influence of electron-withdrawing groups (carbonyl and carboxyl) at the alkyne termini on the reactivity of enediynes was investigated by a combination of experimental and computational techniques. While the general chemical reactivity of such enediynes, especially if non-benzannelated, is increased markedly, the thermal cyclization, giving rise to Bergman cyclization products, is changed little relative to the parent enediyne system. This is evident from kinetic measurements and from density functional theory (DFT, BLYP/6-31G + thermal corrections) computations of the experimental systems which show that the Bergman cyclization barriers slightly (3-4 kcal/mol) increase, in contrast to earlier theoretical predictions. The effect on the endothermicities is large (DeltaDeltaH(r) = 7-12 kcal/mol). Hence, the increased reactivity of the substituted enediynes is entirely due to nucleophiles or radicals present in solution. This was demonstrated by quantitative experiments with diethylamine and tetramethyl piperidyl oxide (TEMPO) which both give fulvenes through 5-exo-dig cyclizations.     

Core–shell morphology as a model for the study of gas permeation in composite systems

Structured latex particles prepared by emulsion polymerization were used as a model to simulate the interphase region between two phases. Multiphase polymer films comprised of high and low permeability polymers of various compositions were used. The model system consisted of a poly(n-butyl methacrylate) (PBMA) matrix and a discontinuous phase with core and shell morphology. The structured particle had a PBMA core and a vinylidene chloride – n-butyl methacrylate (VDC–BMA) copolymer shell. The shell transport characteristics wer altered by changing the (VDC–BMA) copolymer molar ratio. The physical and transport properties for each individual component were measured. Nitrogen was the probe gas. Films used for permeation experiments were prepared by latex casting. The results showed that the morphology of a heterogeneous polymeric system and the transport characteristics of their components had a considerable effect on the magnitude of the transport properties. Experimental data also showed the dependence of the gas global permeability coefficient on the nature of the simulated interphase region, the shell, and the weight percentage of such interphase in the heterogeneous polymeric films. Upon increasing the VDC content in the VDC–BMA copolymer, the gas permeability decreased. The data were fitted to the electrical analogs of conductivity in composite systems. For the matrix filled with structured particles the overall permeability coefficient could best be described when the individual permeabilities were considered as the inverse resistances in parallel.     

Synthesis of pyrrolo[2,1-f][1,2,4]triazine congeners of nucleic acid purines via the N-amination of 2-substituted pyrroles

The synthesis of several new 4-mono- and 2,4-disubstituted pyrrolo[2,1-f][1,2,4]triazines is described. Key 1-aminopyrrole-2-carbonitrile intermediates 3 and 15 were obtained by N-amination of the corresponding pyrrole-2-carboxaldehyde followed by CHO → CN conversion with either hydroxylamine-O-sulfonic acid for 3 or O-mesitylenesulfonylhydroxylamine for 15. Cyclization of 3 or 15 with a variety of amidine reagents or, after conversion of 3 to its corresponding amide, base-catalyzed annulation completed the synthesis of the title products.