Synthetic and Structural Studies of 1,8‐Chalcogen Naphthalene Derivatives

Four novel 1,8‐disubstituted naphthalene derivatives 4 – 7 that contain chalcogen atoms occupying the peri positions have been prepared and fully characterised by using X‐ray crystallography, multinuclear NMR spectroscopy, IR spectroscopy and MS. Molecular distortion due to noncovalent substituent interactions was studied as a function of the bulk of the interacting chalcogen atoms and the size and nature of the alkyl group attached to them. X‐ray data for 4 – 7 was compared to the series of known 1,8‐bis(phenylchalcogeno)naphthalenes 1 – 3 , which were themselves prepared from novel synthetic routes. A general increase in the E???E′ distance was observed for molecules containing bulkier atoms at the peri positions. The decreased S???S distance from phenyl‐ 1 and ethyl‐ 4 analogues is ascribed to a weaker chalcogen lone pair–lone pair repulsion acting in the ethyl analogue due to the presence of two equatorial S(naphthyl) ring conformations. Two novel peri‐substituted naphthalene sulfoxides of 1 , Nap(O?SPh)(SPh) 8 and Nap(O?SPh)₂ 9 , which contain different valence states of sulfur, were prepared and fully characterised by using X‐ray crystallography and multinuclear NMR spectroscopy, IR spectroscopy and MS. Molecular structures were analysed by using naphthalene ring torsions, peri‐atom displacement, splay angle magnitude, S???S interactions, aromatic ring orientations and quasi‐linear O?S???S arrangements. The axial S(naphthyl) rings in 8 and 9 are unfavourable for S???S contacts due to stronger chalcogen lone pair–lone pair repulsion. Although quasi‐linear O?S???S alignments suggest attractive interaction is conceivable, analysis of the B3LYP wavefunctions affords no evidence for direct bonding interactions between the S atoms.     

SPRITE MRI of bubbly flow in a horizontal pipe

Bubble flow is characterised by numerous phase interfaces and turbulence, leading to fast magnetic resonance signal decay and artefacts in spin-warp imaging. In this paper, the SPRITE MRI pulse sequence, with its potential for very short encoding times, is demonstrated as an ideal technique for studying such dynamic systems. It has been used to acquire liquid velocity and relative intensity maps of two-phase gas–liquid dispersed bubble flow in a horizontal pipe at a liquid Reynolds number of 14,500. The fluids were air and water and a turbulence grid was used to generate a dispersed bubble flow pattern. The SPRITE technique shows promise for future research in gas–liquid flow.     

Scope and limitations of the base-catalyzed phospha-peterson P=C bond-forming reaction

Phosphaalkenes (MesP=CRR': R = R' = Ph (1a); R = R' = 4-FC6H4 (1b); R = Ph, R' = 4-FC6H4 (1c); R = R' = 4-OMeC6H4 (1d); R = Ph, R' = 4-OMeC6H4 (1e); R = Ph, R' = 2-pyridyl (1f)) are prepared from the reaction of MesP(SiMe3)2 and O=CRR' in the presence of a trace of KOH or NaOH. The base-catalyzed phospha-Peterson reaction is quantitated by NMR spectroscopy, and isolated yields of phosphaalkene between 40 and 70% are obtained after vacuum distillation and/or recrystallization. The asymmetrically substituted phosphaalkenes (1c, 1e, 1f) form as 1:1 mixtures of E and Z isomers; however, X-ray crystallography reveals that the E isomers crystallize preferentially. Interestingly, E-1e and E-1f readily isomerize in solution in the dark, although the rate of isomerization is much faster when samples are exposed to light. X-ray crystal structures of 1b, E-1e, and E-1f reveal that the P=C bond lengths (average of 1.70 A) are in the long end of the range typically found in phosphaalkenes (1.61-1.71 A). Attempts to prepare isolable P-adamantyl phosphaalkenes following this route were unsuccessful. Although AdP=CPh2 (2a) is detected by 31P NMR spectroscopy, attempts to isolate this species afforded the 1,2-diphosphetane (AdPCPh2)2 (3a), which was characterized by X-ray crystallography.     

The Mixturegram: A Visualization Tool for Assessing the Number of Components in Finite Mixture Models

Certain practical and theoretical challenges surround the estimation of finite mixture models. One such challenge is how to determine the number of components when this is not assumed a priori. Available methods in the literature are primarily numerical and lack any substantial visualization component. Traditional numerical methods include the calculation of information criteria and bootstrapping approaches; however, such methods have known technical issues regarding the necessary regularity conditions for testing the number of components. The ability to visualize an appropriate number of components for a finite mixture model could serve to supplement the results from traditional methods or provide visual evidence when results from such methods are inconclusive. Our research fills this gap through development of a visualization tool, which we call a mixturegram. This tool is easy to implement and provides a quick way for researchers to assess the number of components for their hypothesized mixture model. Mixtures of univariate or multivariate data can be assessed. We validate our visualization assessments by comparing with results from information criteria and an ad hoc selection criterion based on calculations used for the mixturegram. We also construct the mixturegram for two datasets.     

Temperature-dependence of radical-trapping activity of phenoxazine,phenothiazine and their aza-analogues clarifies the way forward for new antioxidant design

The prediction and/or rationalization of diarylamine radical-trapping antioxidant (RTA) activity at the elevated temperatures where they are most useful presents a significant challenge, precluding the development of new technology. Whilst structure–activity relationships at ambient temperatures are well established, their predictive capacity at elevated temperatures is poor due to competing reactions. A striking example involves phenoxazine, which is a superior RTA relative to its sulfur analog phenothiazine at ambient temperature (e.g. k = 3.9 × 10⁷vs. 7.6 × 10⁶ M⁻¹ s⁻¹ at 37 °C, respectively), but is demonstrably inferior at elevated temperatures. Despite being inherently less oxidizable in electrochemical experiments and high-accuracy computations, phenoxazine is more rapidly consumed than phenothiazine in autoxidations at 160 °C – a result which we attribute to a lower reorganization energy barrier to oxidation. Given these observations, we surmised that incorporation of an electronegative N-atom into the phenoxazine ring system would decrease the driving force for oxidation and ‘rescue’ its activity. Indeed, this was found to be the case for nitrogen incorporation at any position, regardless of the impact on the inherent RTA activity. Analogous experiments were carried out on phenothiazines into which nitrogen atoms were incorporated, revealing little benefit at 160 °C. These results suggest that for highly reactive diarylamines (i.e. those with k > 10⁶ M⁻¹ s⁻¹), further enhancements in reactivity do not materially improve their ability to inhibit hydrocarbon autoxidation at elevated temperatures. Instead, their stability to one-electron oxidation determines their efficacy.

Studies of potent diarylamine antioxidants illustrate how their high-temperature activity can be limited by direct reaction with O₂, and how driving force and barrier to oxidation can be modulated for future antioxidant development.     

Tolerance intervals for autoregressive models,with an application to hospital waiting lists

Long waiting lists are a symbol of inefficiencies of hospital services. The dynamics of waiting lists are complex, especially when trying to understand how the lists grow due to the demand of a particular treatment relative to a hospital's capacity. Understanding the uncertainty of forecasting growth/decline of waiting lists could help hospital managers with capacity planning. We address this uncertainty through the use of statistical tolerance intervals, which are intervals that contain a specified proportion of the sampled population at a given confidence level. Tolerance intervals are available for numerous settings, however, the approaches for autoregressive models are far more limited. This article fills that gap and establishes tolerance intervals for general AR(p) models, which may also have a mean or trend component present. A rigorous development of tolerance intervals in this setting is presented. Extensive simulation studies identify that good coverage properties are achieved when the AR process is stationary and the parameters of the AR model are well within the stationarity constraints. Otherwise, a bootstrap‐based correction can be applied to improve the coverage probabilities. Finally, the method is applied to the monthly number of patients on hospital waiting lists in England.     

A note on competitive supply chains with generalised supply costs

This note generalises models from two influential papers in the theory of supply chain outsourcing under competition: 9 and 1. The first paper studies the impact of competitive intensity on the outsourcing decision from the supplier’s point of view for linear supply cost; the second paper examines the impact of supply economies of scale from the retailer’s point of view when selling perfectly substitutable products. By considering competitive intensity and supply economies of scale simultaneously, we find that equilibrium channel structures are primarily determined by the competitive intensity, which is true even under supply diseconomies of scale; the key message in the second paper of scale economies driving retailer’s outsourcing supply decision is highly dependent on the assumption of perfect substitutes. Our finding has no qualitative difference when either the suppliers or the retailers are modeled as the channel leader and make the outsourcing decisions.     

Synthesis and Characterization of Cytocompatible Sulfonated Polyanilines

We report here that by good design, polyaniline (PANI) can be cytocompatible and formed into usable scaffolds for bio‐medical applications. By adjusting the ratio of two monomers, aniline (AN) and metanilic acid (MA), a series of copolymers with different sulfonation degrees have been synthesized. Four‐probe conductivity measurements showed that as the sulfonation degree increased, the conductivity decreased. XPS analysis was used to determine the sulfur/nitrogen ratio. In vitro cell culture study was conducted with human osteosarcoma (HOS) cells. Microscopic observation did not show abnormal cellular behavior when sulfonated polyaniline (SPAN) was put in direct contact with HOS cells. Cells growing on the non‐transparent dark green SPAN films were observed with fluorescence by laser scanning cytometry (LSC). In proliferation studies more than 70% of cells were found viable on SPAN compared to 88% for poly(L ‐lactic acid) with the number of cells growing on glass as a control, indicating generally good biocompatibility. We expect these polymers would have great potential in biological applications of conducting polymers as we determine that a variety of physical and chemical properties can be controlled through synthesis.