Substituent effects in mass spectrometry—II. The effect of substituents on the dissociation of para and meta disubstituted benzenes

The effect of substituents on the activation energy for primary dissociation processes in the molecular ions of mono- and para and meta di-substituted benzenes has been examined. Where the daughter ion retains the substituent group, variation of the energy of activation derives from a combination of the effects of substituents on the ionisation potential of the molecular ion and the appearance potential of the daughter ion. An equation relating the energy of activation for the fragmentation of the molecular ion of a mono-substituted benzene to that of related para and meta di-substituted benzenes is presented.     

Fractals in physics: Squig clusters,diffusions, fractal measures,and the unicity of fractal dimensionality

The three topics discussed in this paper are largely independent. Part 1: Fractal squig clusters are introduced, and it is shown that their properties can match to a remarkable extent those of percolation clusters at criticality. Physics on these new geometric shapes should prove tractable. As background, the author's theories of squig intervals and squig trees are reviewed, and restated in more versatile form. Part 2: The notion of latent fractal dimensionality is introduced and motivated by the desire to simplify the algebra of dimensionality. Scaling noises are touched upon. A common formalism is presented for three forms of anomalous diffusion: the ant in the fractal labyrinth, fractional Brownian motion, and Lévy stable motion. The fractal dimensionalities common to diverse shapes generated by diffusion are given, in Table I, as functions of the latent dimensionalities of the support of the motion and of the diffusion itself. Part 3: It is argued that every fractal point set has a unique fractal dimensionality, but it is pointed out that many fractals involve diverse combinations of many fractal point sets. Such is, in particular, the case for fractal measures and for fractal graphs, often called hierarchical lattices. The fractal measures that the author had introduced in the early 1970s are described, including new developments.     

Stericaliy Congested Molecules: 2,2′-[(Biaryldiyl)bis(oxy)]bis[1,3,2-oxazaphospholidines]

The original suggestion that a through-space mechanism was operative in the seven-bond J(P, P) coupling constant of 30.3 Hz observed for 3.3′-bis(1,1-dimethylethyl)-2,2′-[3,3′,5,5′-tetrakis(1,1-dimethylethyl)-1,1′-biphenyl-2,2′-diyl]bis(oxy)}bis[1,3,2-oxazaphospholidine] ( 1a )) was investigated. In the solid-state CP-MAS ³¹PNMR spectrum of 1a , two nonequivalent P -atoms were observed; sufficient resolution could not be obtained to determine whether P, P coupling was present. The preparation and spectral data of the N-methyl analogue 1b and of the acyclic N-isopropyl analogue 6 (Scheme 1) provided evidence that a) the essentially exclusive formation (R*, R*,S*)- 1a in the reaction of the disodium biphenyldiolate 3a with the phosphorochloridite 4a is the result of significant differences in the free energy of activation (ΔG*) for the formation of the various diastereoisomers due to the steric congestion within the molecule and that b) the magnitude of the observed P,P coupling is dependent upon the degree of conformational freedom within the molecule. In the ³¹P-NMR spectrum of the P-sulfide 7 , which was prepared by the reaction of la with sulfur, 2s resonances were observed that strongly suggested that the lone electrons pair on P are involved in the mechanism for the transmission of coupling data. The (4S,5R) -12 and (4R, 5S) -12 of la were prepared in a three-step reaction sequence starting from the corresponding enantiomerically pure norephredine 8 (Scheme 2). Both (4S, 5R)- and (4R, 5S) -12 were obtained as a diastereoisomer mixture that differ by the configuration of the axis of chirality, i.e., (R*R*,R*)- and (R*,S*,R*) -12 were obtained. The major diastereoisomer was obtained upon recrystallization, and the atropisomers were observed to equilibrate in solution by monitoring the H? C(5) resonance in the ¹H-NMR with time (ΔG° = 0.4 kcal/mol; Fig. 2). The process observed corresponds to the restricted rotation about the central single bond of the biphenyl system. The isolation of an atropisomer with only a single ortho substituent on each aryl ring is quite rare. In the ¹³C-NMR spectrum of both (R*,R*,R*)- and (R*,S*,R*) -12 , C(5) is two-bond-coupled to the oxazaphospholidine P-atom (²J(C(5),P((2)) = 8.5 Hz) that is further virtually coupled to the P-atom of the other oxazaphospholidine ring (7J(P(2),P(2′)) = 30 Hz; ⁹J(C(5),P(2′)) = 0 Hz; δ(P(2)) = δ(P(2′)) = 136 ppm. In the ³¹P-NMR spectrum of (R*,R*,S*) -12 , which was prepared from the racemic chloridite (mixture of three diastereoisomers was obtained), a ⁷J(P(2),P(2′) of 36 Hz was observed. These observations provide strong evidence that seven-bond P,P coupling occurs in all three diastereoisomers of 12 . The observed P,P coupling is both independent of the configuration of the chiral axis and the configuration of the asymmetric P-centers. This independence of P,P coupling upon the configuration on P implies also the independence of the observed coupling upon the orientation of the lone-pair of electrons on P provided that the conformations of the diastereoisomers are similar in solution. The X-ray crystal structure of the complex formed from 1a and dichloro(cycloocta-1,5-diene)platinum(II) was obtained and the solid-state structure discussed. The major diastereoisomer of (4S,5R) -12 was used as a chiral ligand in asymmetric hydrosilylation and hydrogenation reactions (Scheme 3).     

Linear and nonlinear optical properties of carbon nanotube-coated single-mode optical fiber gratings

Single-wall carbon nanotube deposition on the cladding of optical fibers has been carried out to fabricate an all-fiber nonlinear device. Two different nanotube deposition techniques were studied. The first consisted of repeatedly immersing the optical fiber into a nanotube supension, increasing the thickness of the coating in each step. The second deposition involved wrapping a thin film of nanotubes around the optical fiber. For both cases, interaction of transmitted light through the fiber core with the external coating was assisted by the cladding mode resonances of a tilted fiber Bragg grating. Ultrafast nonlinear effects of the nanotube-coated fiber were measured by means of a pump-probe pulses experiment.     

Squig sheets and some other squig fractal constructions

Squig intervals are a class of hierarchically constructed fractals introduced by the author. They can be visualized as the final outcome upon a straight interval of a suitable cascade of local perturbative eddies ruled by two processes called decimation and separation. Their theory is summarized and their scope is extended in several new directions, especially by introducing new forms of separation. Squig intervals are generalized in two dimensions, with fractal dimensions ranging from 1.2886 to 1.589. Squig sheets are constructed in three dimensional space with fractal dimensions ranging from 8/3 up. They should prove useful in modeling the fractal surfaces associated with turbulence and related phenomena. Squig intervals are constructed in three dimensions. Nonsymmetric eddies and the resulting squigs are tackled. Squig trees and intervals are drawn on unconventional lattices, either in the plane or in a prescribed fractal surface. Peyriére'sM systems are mentioned: their study includes the proof that the informal renormalization argument (involving a transfer matrix) is exact for squigs.Presented at theThird Conference on Fractals: Fractals in the Physical Sciences, held at the National Bureau of Standards, Gaithersburg, Maryland, on November 20–23, 1983.The reader's attention should be drawn to the fact that the second and later printings of this book include an update chapter and additional references. Though it should not have been necessary, it may be useful also to mention here that most of the material in this book that concerns physics, e.g., polymers and percolation clusters, wasnot found in either of my two earlier Essays on fractals,Les objects fractals: forme, hasard et dimension (Flammarion,     

Equilibrium schemes for scalar conservation laws with stiff sources

We consider a simple model case of stiff source terms in hyperbolic conservation laws, namely, the case of scalar conservation laws with a zeroth order source with low regularity. It is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced CFL condition and refined meshes required because of the lack of accuracy on equilibrium states. The source term should be taken into account in the upwinding and discretized at the nodes of the grid. In order to solve numerically the problem, we introduce a so-called equilibrium schemes with the properties that (i) the maximum principle holds true; (ii) discrete entropy inequalities are satisfied; (iii) steady state solutions of the problem are maintained. One of the difficulties in studying the convergence is that there are no estimates for this problem. We therefore introduce a kinetic interpretation of upwinding taking into account the source terms. Based on the kinetic formulation we give a new convergence proof that only uses property (ii) in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions. The computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that, in comparison with an usual upwind scheme, the corresponding equilibrium version is far more accurate. Furthermore, numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients.

     

Two-dimensional electrons-holes droplets in superlattices

We show that two dimensional electrons-holes droplets can exist in superlattice having a structural defect such as a layer with an additional atomic plane. This is a new and cleaner way to produce and study a plasma in two dimensions.     

Magnetic ordering in TmTe

Neutron diffraction experiments were performed on the divalent thulium compound TmTe. Magnetic structure determination leads to a type II antiferromagnet below the Néel temperature T_N = .43 K. No crystal field excitations were observed.