Dissociation of 2,2′-substituted thioindigo whites,and recombination of their radicals in solution and in polymer matrix

The dissociation of 2,2′-disubstituted thioindigo whites into captodative radicals and the recombination of these radicals have been examined in solution and in polymeric matrix. For the methyl- and ethyl-substituted TIW the quantum yield of dissociation in solution is equal to 4 × 10^?4 and 5 × 10^?4, respectively. Using the iodine scavenging method the quantum yield of formation of free radicals was almost 3 to 4 × 10^?4, i.e. 20–25% radicals recombine in cage. For the isopropyl and aryl TIWs partial dissociation occurs already at room temperature. Their dissociation enthalpies have been evaluated in solution on the basis of the ESR signal surfaces at different temperatures. For the aromatic substituted Δ H_diss amounts to 88–95 kJ mol^?1, while for i-PrTIW ΔH_diss is 150 kJ mol^?1. The behavior of these compounds was studied in three different matrices: polymethyl methacrylate (PMMA), polypropyl methacrylate (PPMA), and polystyrene (PST). In the cases of the aryl substituted derivatives, cage dimensions of the TIW-radical pairs were measured at low temperature, and their apparent dissociation enthalpies above their glass transition temperatures were evaluated using ESR spectrometry; they are equal to 118 ± 3 kJ mol^?1 in PPMA and around 155 kJ in PMMA and PST. The decay kinetics of the radicals after photolysis of the TIWs below T_g were interpreted on the basis of Waite's equations for diffused controlled reactions. The great influence of steric effects in the cases of the 2-orthochlorophenyl and the 2,4-dichlorophenyl TIWs is stressed as well as the importance of the merostabilization of the captodative radicals on these kinetic characteristics. The nature of the polymeric matrix is also underlined; below T_g the diffusion rate constant is only one-third in PST compared to PMMA. The radicals generated from Ph TIW and its para-nitro and p-methoxy derivatives show a strong inhibiting effect toward the polymerization of methyl methacrylate, while the alkyl TIWs behave as free radical initiators.     

Synthesis of poly-α,α-diphenylglycine. II. Cationic polymerization of 4,4-diphenyl-Δ2-1,2,3-triazolin-5-one

4,4-Diphenyl-Δ²-1,2,3-triazolin-5-one (I) was found to undergo a cationic polymerization under the influence of boron trifluoride etherate in an anhydrous solvent. The poly-α,α-diphenylglycine (III) thus formed contained a larger amount of oligomers than the polymer obtained by thermal decomposition as described in the preceding paper. The molecular weight distribution was further shown to depend on the monomer and catalyst concentration and on the nature of the solvent. A mechanistic rationalization is proposed, involving propagating triazolinium ion pairs (VII) which are not interrupted by chain transfer or termination in the absence of water or alcohol. In the presence of water or alcohol, no polymerization occurred, but the normal acid-catalyzed decomposition products (IV and V) were then obtained. 1-Methyl-4,4-diphenyl-Δ²-1,2,3-triazolin-5-one (VIII) was also treated with BF₃ · OEt₂ in a dry solvent at room temperature and furnished 1-methyl-3-phenyl-indolin-2-one (XII) instead of a polyamide. This reaction constitutes a new method for the synthesis of these heterocycles.     

Slow motion for gradient systems with equal depth multiple-well potentials

For scalar reaction-diffusion in one space dimension, it has been known for a long time that fronts move with an exponentially small speed for potentials with several distinct minimizers. The purpose of this paper is to provide a similar result in the case of systems. Our method relies on a careful study of the evolution of localized energy. This approach also has the advantage of relaxing the preparedness assumptions on the initial datum.     

Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities

We study a time-independent nonlinear Schrödinger equation with an attractive inverse square potential and a nonautonomous nonlinearity whose power is the critical Sobolev exponent. The problem shares a strong resemblance with the prescribed scalar curvature problem on the standard sphere. Particular attention is paid to the blow-up possibilities, i.e. the critical points at infinity of the corresponding variational problem. Due to the strong singularity in the potential, some new phenomenon appear. A complete existence result is obtained in dimension 4 using a detailed analysis of the gradient flow lines.

     

Acid-catalyzed polycondensation of bisdiazoalkanes

Dimerization reactions of diphenyldiazomethane have been applied to the polycondensation of six bisdiazobenzyl arylenes, namely 1,4- and 1,3-bis(α-diazobenzyl)-benzenes C₆H₅CN₂? (C₆H₄)? CN₂C₆H₅; 1,4- and 1,3-bis(α-diazo-p-methoxybenzyl)-benzenes, p,p′-MeO? C₆H₄? CN₂? (C₆H₄)? CN₂C₆H₄? OMe; 4,4′-bis(α-diazobenzyl)-diphenylmethane, C₆H₅CN₂? (C₆H₄CH₂C₆H₄)? CN₂C₆H₅; and 4,4′-bis(α-diazobenyl)-diphenyl ether, C₆H₅CN₂? (C₆H₄? O? C₆H₄)CN₂C₆H₅. Depending on the nature of the catalysts, polyene-arylenes (? C(Ar)?C(Ar)? C₆H₄)_n, and polyazine-arylenes, (? C(Ar)?N? N? C(Ar)? C₆H₄? )_n, can be obtained selectively by acid-catalyzed decomposition of these bisdiazoalkanes at room temperature. With perchloric acid and with arylsulfonic acids in strong polar media, polyene-arylenes are formed. On the other hand, boron trifluoride and arylsulfonic acids in solvents of low dielectric constant afford polyazine-arylenes. Less selective is the thermal decomposition at 75°C in toluene solution; it gives a polymer containing about 90% azine and 10% olefinic groups. All these polymers are soluble in common solvents. Their molecular weight vary from 3 200 to 5 000, i.e., X?_n from 12 to 20. The polyene-arylenes are very stable and decompose only around 500°C; the polyazine-arylenes are less stable and decompose around 370°C by losing nitrogen.     

A definition of subjective possibility

Based on the setting of exchangeable bets, this paper proposes a subjectivist view of numerical possibility theory. It relies on the assumption that when an agent constructs a probability measure by assigning prices to lotteries, this probability measure is actually induced by a belief function representing the agent’s actual state of knowledge. We also assume that the probability measure proposed by the agent in the course of the elicitation procedure is constructed via the so-called pignistic transformation (mathematically equivalent to the Shapley value in game theory). We pose and solve the problem of finding the least informative belief function having a given pignistic probability. We prove that it is unique and consonant, thus induced by a possibility distribution. This result exploits a simple informational ordering, in agreement with partial orderings between belief functions, comparing their information content. The obtained possibility distribution is subjective in the same sense as in the subjectivist school in probability theory. However, we claim that it is the least biased representation of the agent’s state of knowledge compatible with the observed betting behaviour.     

Rational Design of Heat‐Set and Specific‐Ion‐Responsive Supramolecular Hydrogels Based on the Hofmeister Effect

Smart supramolecular hydrogels have been prepared from a bolaamphiphilic L ‐valine derivative in aqueous solutions of different salts. The hydrogels respond selectively to different ions and are either reinforced or weakened. In one case, in contrast to conventional systems, the hydrogels are formed upon heating of the system. The use of the hydrogels in the controlled release of an entrapped dye is described as a proof of the potential applications of these systems. The responsive hydrogels were rationally designed by taking into account the noticeable effect of different ions from the Hofmeister series in the solubility of the hydrogelator, which was assessed by using NMR experiments. On the one hand, kosmotropic anions such as sulfate produce a remarkable solubility decrease in the gelator, which is associated with gel reinforcement, as measured by rheological experiments. On the other hand, chaotropic species such as perchlorate weaken the gel. A dramatic effect was observed in the presence of guanidinium chloride, which boosted the solubility of the gelator, in accordance with its chaotropic behaviour reported in protein science. In this case, a direct interaction of the guanidinium species with the carbonyl groups of the hydrogelator is detected by ¹³C NMR spectroscopy. The weakening of this interaction upon a temperature increase allows for the preparation of heat‐set hydrogelating systems.     

Remarks on a Hardy–Sobolev inequality

We compute the optimal constant for a generalized Hardy–Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a nonlinear elliptic equation arising in astrophysics. To cite this article: S. Secchi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).