Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

Methanofullerene Molecular Scaffolding: Towards C60-substituted poly(triacetylenes) and expanded radialenes,preparation of a C60–C70 hybrid derivative,and a novel macrocyclization reaction

The synthesis of (E)-hex-3-ene-l, 5-diynes and 3-methylidenepenta-1, 4-diynes with pendant methano[60]-fullerene moieties as precursors to C₆₀-substituted poly(triacetylenes) (PTAs, Fig. 1) and expanded radialenes (Fig. 2) is described. The Bingel reaction of diethyl (E)-2, 3-dialkynylbut-2-ene-1, 4-diyl bis(2-bromopropane-dioates) 5 and 6 with two C₆₀ molecules (Scheme 2) afforded the monomeric, silyl-protected PTA precursors 9 and 10 which, however, could not be effectively desilylated (Scheme 4). Also formed during the synthesis of 9 and 10 , as well as during the reaction of C₆₀ with thedesilylated analogue 16 (Scheme 5 ), were the macrocyclic products 11, 12 , and 17 , respectively, resulting from double Bingel addition to one C-sphere. Rigorous analysis revealed that this novel macrocyclization reaction proceeds with complete regio- and diastereoselectivity. The second approach to a suitable PTA monomer attempted N, N′-dicyclohexylcarbodiimide(DCC)-mediated esterification of (E)-2, 3-diethynylbut-2-ene-l, 4-diol ( 18 , Scheme 6) with mono-esterified methanofullerene-dicarboxylic acid 23 ; however, this synthesis yielded only the corresponding decarboxylated methanofullerene-carboxylic ester 27 (Scheme 7). To prevent decarboxylation, a spacer was inserted between the reacting carboxylic-acid moiety and the methane C-atom in carboxymethyl ethyl 1, 2-methano[60]fullerene-61, 61-dicarboxylate ( 28 , Scheme 8), and DCC-mediated esterification with diol 18 afforded PTA monomer 32 in good yield. The formation of a suitable monomeric precursor 38 to C₆₀-substituted expanded radialenes was achieved in 5 steps starting from dihydroxyacetone (Schemes 9 and 10), with the final step consisting of the DCC-mediated esterification of 28 with 2-[1-ethynyl(prop-2-ynylidene)]propane-1, 3-diol ( 33 ). The first mixed C₆₀-C₇₀ fullerene derivative 49 , consisting of two methano[60]fullerenes attached to a methano[70]fullerene, was also prepared and fully characterized (Scheme 13). The C_s-symmetrical hybrid compound was obtained by DCC-mediated esterification of bis[2-(2-hydroxy-ethoxy)ethyl] 1, 2-methano[70]fullerene-71, 71-dicarboxylate ( 46 ) with an excess of the C₆₀-carboxylic acid 28 . The presence of two different fullerenes in the same molecule was reflected by its UV/VIS spectrum, which displayed the characteristic absorption bands of both the C₇₀ and C₆₀ mono-adducts, but at the same time indicated no electronic interaction between the different fullerene moieties. Cyclic voltammetry showed two reversible reduction steps for 49 , and comparison with the corresponding C₇₀ and C₆₀ mono-adducts 46 and 30 indicated that the three fullerenes in the composite fullerene compound behave as independent redox centers.     

Pillar[n]arenes: Chemistry and Their Material Applications

Background Pillar[n]arene(PA[n])contains a symmetrical structures,where para-bridge connection between the units looks like a column-like or pillar shape and polygonal structure from side and top views,respectively.The attached groups to the PA[n]are pointing towards the opposite directions along the columnar axis.     

Photopolymerized monolithic capillary columns for rapid micro high-performance liquid chromatographic separation of proteins

The preparation of monolithic poly(butyl methacrylate-co-ethylene dimethacrylate) capillary columns using photoinitiated in situ polymerization within 200 microm i.d. capillaries and their application for microHPLC separations of proteins have been studied. The low resistance to flow characteristic of monolithic columns, enabled the use of very high flow rates of up to 100 microL/min representing a flow velocity of 87 mm/s. Very good separations of a model protein mixture consisting of ribonuclease A, cytochrome c, myoglobin, and ovalbumin was achieved in less than 40 s using a very simple single step gradient of the mobile phase. Interestingly, no effect of the pore size on the separations of proteins was observed for these monolithic columns within the size range of 0.66-2.2 microm. The monolithic microHPLC columns are found very robust and no changes in the long term separation performance and back pressure were observed.     

Rose Bengal‐Sensitized Photooxidation of the Dipeptides l‐Tryptophyl‐l‐Phenylalanine,l‐Tryptophyl‐l‐Tyrosine and l‐Tryptophyl‐l‐Tryptophan: Kinetics,Mechanism and Photoproducts¶

The Rose Bengal‐sensitized photooxidations of the dipeptides l ‐tryptophyl‐l ‐phenylalanine (Trp‐Phe), l ‐tryptophyl‐l ‐tyrosine (Trp‐Tyr) and l ‐tryptophyl‐l ‐tryptophan (Trp‐Trp) have been studied in pH 7 water solution using static photolysis and time‐resolved methods. Kinetic results indicate that the tryptophan (Trp) moiety interacts with singlet molecular oxygen (O₂(¹Δ_g)) both through chemical reaction and through physical quenching, and that the photooxidations can be compared with those of equimolecular mixtures of the corresponding free amino acids, with minimum, if any, influence of the peptide bond on the chemical reaction. This is not a common behavior in other di‐ and polypeptides of photooxidizable amino acids. The ratio between chemical (k_r) and overall (k_t) rate constants for the interaction O₂(¹Δ_g)‐dipeptide indicates that Trp‐Phe and Trp‐Trp are good candidates to suffer photodynamic action, with k_rlk_t values of 0.72 and 0.60, respectively (0.65 for free Trp). In the case of Trp‐Tyr, a lower k_rlk_t value (0.18) has been found, likely as a result of the high component of physical deactivation of O₂(¹Δ_g) by the tyrosine moiety. The analysis of the photooxidation products shows that the main target for O₂(¹Δ_g) attack is the Trp group and suggests a much lower accumulation of kynurenine‐type products, as compared with free Trp. This is possibly because of the occurrence of another accepted alternative pathway of oxidation that gives rise to 3a‐oxidized hydrogenated pyrrolo[2,3‐b]indoles.     

Synthesis and Characterization of p—[Perfluoro—1—（2—fluorosulfonylethoxy）]ethylated Polystyrene

A new fluorinated polystyrene bearing a p-sulbstiuted perfluoro[1-(2-fluorosulfonylethoxy)]ethyl group was synthesized via one-electron oxidation of polystyrene by perfluoro[2-(2-fluorosulfonylethoxy)]propionyl peroxide at different peroxide to polystyrene molar ratios.The yield of perfluoroalkylation decreases with the increase of the reactant molar ratio.The modified polymer has been characterized by various techniques:the ring pefluoro[1-(2-fluorosulfonylethoxy)]ethylation has been proved by FT-IR and ^19FNMR;the X-ray photoelectron spectra(XPS) show the maximum binding energy of F18,O18,C18(two kinds of carbon atoms,namely C-H and C-F)and S2p,respectively; desulfonylation of the fluorinated polystyrene appearing at 217℃ has been found by its thermogravimetric analysis (TGA).The determinations of contact angle,refractive index and glass transition temperature of the modified polymer have disclosed that when the contact angle increases with the increase of the molar ratio,the refractive index and glass transition temperature decrease.The polydispersity values indicate that the degradation of the polymer chains did not occur during the reaction.     

Achiral Calcium‐Oxalate Crystals with Chiral Morphology from the Leaves of Some Solanacea Plants

The leaves of some plants, particularly among the Solanacea, contain crystals of calcium oxalate with a peculiar chiral pseudo‐tetrahedral morphology, even though the calcium oxalate crystal structure is centrosymmetric, hence achiral. We studied the morphology of these crystals extracted from the leaves of three Solanacea plants: the potato, the hot pepper, and a species of wild Solanum. The crystal morphology was the same in all three species. Based on the examination of more than 100 crystals from each plant, we showed that the crystal morphology is chiral with invariant chirality. We suggest that morphological chirality is induced by macromolecules during nucleation from a specific, genetically encoded crystal plane, and is further established during subsequent controlled crystal growth. This is one of few examples where it is possible to deduce a molecular mechanism for biologically induced breaking of morphological symmetry in organisms. A very high level of recognition is required by the macromolecules to allow them to distinguish between symmetry‐related crystal planes. It is also surprising that this finely controlled mechanism of crystal formation, including the chiral morphology, has been conserved during evolution.     

Electrochemical Immunoassay for Carbohydrate Antigen‐125 Based on Polythionine and Gold Hollow Microspheres Modified Glassy Carbon Electrodes

A new electrochemical immunosensor for the detection of carbohydrate antigen‐125 (CA125), a carcinoma antigen, was developed by immobilization CA125 antibody (anti‐CA125) on gold hollow microspheres and porous polythionine (PTH) modified glassy carbon electrodes (GCE). The gold hollow microspheres provided a biocompatible microenvironment for proteins, and greatly amplified the coverage of anti‐CA125 molecules on the electrode surface. The performance and factors influencing the immunosensor were investigated in detail. The detection is based on the current change before and after the antigen‐antibody interaction. Under optimal conditions, the amperometric changes were proportional to CA125 concentration ranging from 4.5 to 36.5 U/mL with a detection limit of 1.3 U/mL (at 3σ). The CA125 immunosensor exhibited good precision, high sensitivity, acceptable stability, accuracy and reproducibility. The as‐prepared immunosensors were used to analyze CA125 in human serum specimens. Analytical results suggest that the developed immunoassay has a promising alternative approach for detecting CA125 in the clinical diagnosis.     

Solid State Regeneration of Carbonyl Compounds from Oximes and Semicarbazones with Poly [N‐Bromo‐Benzene‐1,3‐Disulfonylamide]

Poly [N‐bromo‐benzene‐1,3‐disulfonylamide] [ PBBS ] is a novel and efficient reagent for the conversion of oximes and semicarbazones under solid state to their corresponding carbonyl compounds in high yields.     

Differing Coordination Modes of (O‐Alkyl)‐p‐Ethoxyphenyldithiophosphonato Ligands in Copper(I), Silver(I) and Gold(I) Triphenylphosphine Complexes

The three (O‐methyl)‐p‐ethoxyphenyldithiophosphonato triphenylphosphine complexes of copper, silver and gold, [(Ph₃P)_nM{S₂P(OMe)C₆H₄OEt‐p}] (M = Cu, n = 2; M = Ag, Au, n = 1) investigated structurally by X‐ray diffraction exhibit remarkable structural differences. The copper compound is a four‐coordinate chelate monomer with Cu–S 2.4417(6) and 2.5048(6) Å; P–Cu–S 104.24(2)–114.01(2)°; Cu–S–P 82.49(3)° and 80.85(2)°. The silver compound is a cyclic dimer with bridging dithiophosphonato ligands and three‐coordinate silver atoms [Ag–S 2.5371(5) and 2.6867(5) Å; P–Ag–S 122.88(2)° and 122.17(2)°; Ag–S–P 89.32(2)° and 103.56(2)°]. The gold compound is monomeric with linear dicoordinate gold [Au–S 2.3218(6) Å; P–Au–S 177.72(2)°, Au–S–P 100.97(3)°].