The Radical Ions of Dipleiadiene (Dicyclohepta[de,ij]naphthalene) and Its 12b,12c-Homo Derivative. An ESR and ENDOR study

The radical anions and the radical cations of dipleiadiene (dicyclohepta[de,ij]naphthalene; 1 ) and its 12b, 12c-homo derivative 2 were characterized by ESR and ENDOR spectroscopy. Their singly occupied orbitals are related to the degenerate nonbonding MOs of a 16-membered π-perimeter. The π-spin distribution over the perimeter is similar in the radical cations 1 ^.+ and 2 ^.+, and an analogous statement holds for the radical anions 1 ^.? and 2 ^.?. However, deviations of the π-system from planarity lead to a decrease in the absolute values of the negative coupling constants of the perimeter protons in 2 ^.+ and 2 ^.? relative to those in 1 ^.+ and 1 ^.?. The hyperfine data for the perimeter protons in the radical ions correlate with the changes in ¹³C chemical shifts on passing from the neutral compounds to the corresponding diions. It is concluded from the coupling constants of the CH₂ protons in the radical ions of 2 that the cation 2 ^.+ exists in the methano-bridged form ( A ) of the neutral 2 (and, presumably, also of the dication 2 ²⁺), whereas the anion 2 ^.? adopts the bisnorcaradiene form ( B ) of the dianion 2 ^2?.     

The Structure of 2,5-Semiquinones derived from 1,6-Bridged [10] Annulenes

ESR. spectra are reported for the radical anions of the diketones I and II (see below), recently prepared from 1, 6-methano[10]annulene and its 11, 11-difluoro-derivative, respectively [1]. The π-spin populations of I? and II? are shown to be incompatible with the structure A an enedione-norcaradiene. Although the alternative structure B of a [10]annulenequinone is acceptable for both I? and II?, the ESR. data is more satisfactorily rationalized in terms of a structure ‘intermediate’ to A and B. This is particularly true for the radical anion I?, for which the π-spin populations suggest a structural ‘shift’ B → A relative to II?. Structures A and B were postulated [1] for the neutral diketones I and II, respectively.     

The Radical Anions of [2.2]Paracyclophane-1,9-diene and Some of its Derivatives. An Unexpected Conformational Interconversion

The radical anions of [2.2]paracyclophane-1,9-diene ( 2 ) and its 1,10,12,13,15,16-hexadeuterio derivative 2 -D₆, as well as those of 4,5,7,8-tetramethyl[2.2]paracyclophane-1,9-diene ( 3 ) and its 12,13,15,16-tetradeuterio derivative 3 -D₄, have been studied by ESR spectroscopy. The coupling constants for 2 ^?· at 178 K are 0.422 mT for four equivalent olefinic protons and 0.046 and 0.020 mT, each for a set of four equivalent aromatic protons. This hyperfine pattern is consistent with either benzene ring bearing two pairs of equivalent protons and it points to a lowering of the anticipated D_2h symmetry. The ESR spectra of 2 ^?· are strongly temperature dependent, due to modulation of the two coupling constants of 0.046 and 0.020 mT; these have opposite signs and average to 0.013 mT at 273 K. The experimental findings are interpreted in terms of a transition state of D_2h symmetry, 33 kJ/mol above two interconverting equivalent conformations of lower symmetry. Several pieces of evidence suggest that this symmetry is D₂, i.e., the benzene rings in 2 ^?· are twisted in opposite directions about the vertical axis. Temperature dependence of the ESR spectra, resulting from modulation of the hyperfine interactions with the aromatic protons, is also observed for 2 -D₆^?· and 3 ^?·. In the case of 3 ^?·, the olefinic protons are, as expected, only equivalent in pairs, the pertinent coupling constants being 0.560 and 0.325 mT. Upon standing at low temperatures, 2 ^?· and 3 ^?· gradually convert into the radical anions of [2.2]paracyclophane ( 1 ) and its 4,5,7,8-tetramethyl derivative, respectively. At higher temperatures, cleavage of one bridging chain in 2 ^?· also occurs, with the formation of the radical anion of (E)-4,4′-dimethylstilbene ( 7 ). Both reactions of 2 ^?· must involve the transient radical anion of [2.2]paracyclophane-1-ene ( 4 ) as proved by the observation of the spectra of 1 ^?· and 7 ^?· with 4 as the starting material.     

The Radical Anion of 1,2-Diphenylcyclopentene

ESR. and ENDOR. studies are reported for the radical anions of 1,2-diphenylcyclopentene ( 3 ) and its di(pe+deuteriophenyl)-derivative (3-D₁₀). Comparison of the coupling constants of the phenyl protons in 3 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}. with the analogous values for the radical anions of 1,2-diphenyl substituted cyclopropene ( 1 ) and cyclobutene ( 2 ) reveals regular changes in the sequence 1 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, 2 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, 3 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, which are caused by an increasing twist of the phenyl groups about the C(1), C(1′)- and C(2), C(1″)-bonds linking them to the ethylene fragment. Such a twist is shown to be also responsible for the large difference in the coupling constants of the methylene β-protons in 3 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}. (0.659 and 0.293 mT). It is suggested that - in order to minimize the losses caused by this twist in the π-delocalization energy - the 2 p_z-axes at the centres 1 and 2 deviate from a perpendicular orientation to the mean plane of the cyclopentene ring. A deviation by 19° from such an orientation is required to account for the observed β-proton coupling constants in terms of their conventional cos²-dependence on the dihedral angles θ.     

The Radical Ions of Benzo[b]biphenylene,a Test for HMO Models of Biphenylene and its Derivatives

ESR.-spectra are reported for the radical anion and the radical cation of benzo[b]-biphenylene (III). Comparison of the proton coupling constants (a_Hμ) for III · ? and III · ⊕ with π-spin populations (?_μ), calculated by the McLachlan procedure, permits a lower limit of 0.77 to be set for the parameter κ = β′/β where β′ represents a reduced value of the HMO integral for the two essentially single bonds linking the benzene with the naphthalene π-system. The differences in the a_Hμ values for III · ? and III · ⊕ are substantially larger than those generally found for the two corresponding radical ions of alternant, purely benzenoid hydrocarbons, but they closely parallel the analogous differences observed for the radical anion and the radical cation of biphenylene.     

The Radicals and Radical Dianions of Bridged [11]- and [15]Annulenyls as Compared with Those of Benzotropyl and 2,3-Naphthotropyl

The 1,6-methano[11]annulenyl ( 1 ·), 1,6:8, 14-propane-1,3-diylidene[15]annulenyl ( 2 ·), benzotropyl ( 3 ·) and 2,3-naphthotropyl ( 4 ·) radicals have been characterized by their ESR. spectra. The corresponding radical dianions, , , and , have also been studied both by ESR. and ENDOR. spectroscopy. Assignment of the coupling constants a_Hμ to protons in the individual positions μ of these radicals and radical dianions is to a large extent based on investigations of specifically deuteriated derivatives. The radicals 1· , 2· , 3· and 4· exist in temperature-dependent equilibria with ( 1 )₂, ( 2 )₂, ( 3 )₂ and ( 4 )₂, respectively, where ( 1 )₂ to ( 4 )₂ denote mixtures of dimers of 1 · to 4 ·. The dissociation enthalpies, ΔH°, of ( 1 )₂ (102 kJ/mol) and ( 2 )₂ (88 kJ/mol) are considerably smaller than those of ( 3 )₂ and ( 4 )₂ which do not significantly differ from the ΔH° value of bitropyl (139 ± 6 kJ/mol). This finding indicates that the gain in π-electron delocalization energies, Δ(DE)_π, upon dissociation markedly increases on going from bitropyl, ( 3 )₂ and ( 4 )₂ to ( 1 )₂ and ( 2 )₂, and thus points to an additional ‘resonance stabilization’ of 1 · and 2 ·, as compared with 3 · and 4 ·. A more pronounced π-spin localization on the 7-membered ring is observed in 3 ·, 4 ·, and relative to the corresponding species, 1 ·, 2 ·, and . It can be interpreted in terms of simple π-perimeter models without explicitly invoking substantial homoconjugative interactions between the bridged centres in 1 ·, 2 ·, and . However, the shortcomings of these crude models do not allow one to make a clear-cut statement about the contributions of the homotropyl structures to the π-systems of these paramagnetic species. The radical dianions and exhibit considerable hyperfine splittings from one ²³Na or ³⁹K nucleus of the counter-ion, whereas for and such splittings stem from two equivalent alkali metal nuclei. This finding is readily rationalized by different geometries of the bridged annulenyls and their benzo- and naphthotropyl analogues. Hyperfine data are also given for the radical anions of 7 H-benzocycloheptene, ( 3-H )\documentclass{article}\pagestyle{empty}\begin{document}$2^{\ominus \atop \dot{}}$\end{document}, and 6 H-(2,3-naphtho)cycloheptene, ( 4-H )\documentclass{article}\pagestyle{empty}\begin{document}$2^{\ominus \atop \dot{}}$\end{document}, as well as for the radical dianion of 1,6:8,14-bismethano[15]annulenyl, 5 \documentclass{article}\pagestyle{empty}\begin{document}$2^{\ominus \atop \dot{}}$\end{document}.     

Soliton parameters and chaotic sets

In this work we apply a nonperturbative approach to analyze soliton bifurcation in the presence of surface tension, which is a reformulation of standard methods based on the reversibility properties of the system. The hypothesis is nonrestrictive and the results can be extended to a much wider variety of systems. The usual idea of tracking intersections of unstable manifolds with some invariant set is again used, but reversibility plays an important role establishing in a geometrical point of view some kind of symmetry which, in a classical way, is unknown or nonexistent. Using a computer program we determine soliton solutions and also their bifurcations in the space of parameters giving a picture of the chaotic structural distribution to phase and amplitude shift phenomena.     

Global s-solvability, global s-hypoellipticity and Diophantine phenomena

In this paper we consider the problem of global Gevrey solvability for a class of sublaplacians on a toruswith coefficients in the Gevrey class Gs(TN). For this class of operators we show that global Gevrey solvability and global Gevrey hypoellipticity are both equivalent to the condition that the coefficients satisfy a Diophantine condition.     

The role of fuzzy interfaces in the nucleation, growth and agglomeration of aluminum hydroxide in concentrated caustic solutions

Fundamental crystal growth theory relies on classical concepts of monomeric addition at step sites on crystal surfaces. The nucleation and growth of crystalline aluminium hydroxide from concentrated caustic solutions does not follow classical crystal growth mechanistic pathways. Numerous techniques including static and dynamic light scattering, small angle X-ray and neutron scattering, cryovitirification transmission electron microscopy, rheology and atomic force microscopy have been employed in the study of aluminium hydroxide crystallisation from concentrated caustic solutions. The observations from these techniques have been interpreted on the basis polymer crystal growth theory, thermodynamic phase inversions analysis and entropically driven insolubility.

The experimental observations can be interpreted on the basis that aluminium hydroxide nuclei and crystals are surrounded by a diffuse interface which grades in density from the crystalline aluminium hydroxide particle core to the surrounding solution. A mechanism for the nucleation and growth mechanisms of aluminium hydroxide has been proposed: initial solution formation of a loose polymeric network; clustering of this network followed by gradual densification to form amorphous nuclei; further densification of the core of the nuclei to form crystallites and gradual densification but not crystallisation of the still amorphous diffuse interface.

The presence of this diffuse interface enables the slow agglomeration behaviour of aluminium hydroxides particles in concentrated caustic liquors to be explained. In liquors of very high ionic strength (in this case up to 6 M NaOH) particulate agglomeration would be expected to be rapid due to the small double layer thickness as predicted by DLVO theory. During rapid growth the diffuse interface inhibits the sufficiently close approach of the dense part of the particles to the point where attractive inter-particulate van der Waals forces would dominate and agglomeration would take place. As supersaturation is depleted and the growth rate of the diffuse interface decreases but densification is still occurring the particles can approach more closely and agglomeration will occur. Thus it is probable that the observed agglomeration behaviour is supersaturation and growth rate related.