Determination of Non-Ionic Surfactants of the Alcohol Polyethoxylate Type by Means of High Temperature Gas Chromatography and Atomic Emission Detection

High temperature gas chromatography (HT-GC) coupled to atomic emission detection (AED) has been applied for the determination of alkyl chain distribution, mole average degree of ethoxylation and weight percent distribution of the corresponding homologues of alcohol ethoxylates without all the actual homologues being available as pure references. Based upon its constant elemental response, the HT-GC-AED system has been evaluated for its applicability to compound independent calibration within the homologous series of the alcohols and alcohol ethoxylates. Discrimination against high molecular weight components by gas chromatography requires conversion to the acetyl or trimethylsilyl derivatives. The latter includes introduction of the hetero atom silicon and thus allows monitoring of the silicon trace. Thus selectivity will be enhanced by excluding detection of compounds which do not react with the derivatization reagent. The method has been validated with the analysis of the technical product Brij 30, consisting of a mixture of alcohol ethoxylates with a vendor-specified mole average degree of ethoxylation of four. The experimental result yields a mole average degree of 4.0 ± 0.1 in the carbon, silicon and oxygen traces.     

On the Laplace Transform of the Lognormal Distribution

Integral transforms of the lognormal distribution are of great importance in statistics and probability, yet closed-form expressions do not exist. A wide variety of methods have been employed to provide approximations, both analytical and numerical. In this paper, we analyse a closed-form approximation \(\widetilde {\mathcal {L}}(\theta )\) of the Laplace transform \(\mathcal {L}(\theta )\) which is obtained via a modified version of Laplace’s method. This approximation, given in terms of the Lambert W(?) function, is tractable enough for applications. We prove that ~(??) is asymptotically equivalent to ?(??) as ?? → ∞. We apply this result to construct a reliable Monte Carlo estimator of ?(??) and prove it to be logarithmically efficient in the rare event sense as ?? → ∞.     

Monitoring of visible light photopolymerization of an epoxy/dimethacrylate hybrid system by Raman and near-infrared spectroscopies

Hybrid systems formulated with epoxy and methacrylate monomers at mass fraction either 50:50 or 75:25 were studied. The individual monomer conversions during photopolymerization with visible light were monitored by Raman and near-infrared spectroscopies. The rate of polymerization and final degree of conversion of the methacrylate groups were raised when the epoxy monomer was present. This is attributed to enhancement of the mobility of the reactive species caused by the presence of the epoxy monomer. Conversely, the earlier vitrification of the system due to the faster polymerizing methacrylate network resulted in reduced conversion of epoxy rings.     

A novel approach for lignin modification and degradation

We report on a novel approach, the integration of the photochemical and electrochemical oxidation, for the modification and degradation of kraft lignin, where the Ta₂O₅–IrO₂ thin film was used as the electrocatalyst and the TiO₂ nanotube arrays were used as the photocatalyst. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) were used to characterize the fabricated catalysts. A UV–Vis spectroscopy was used to monitor the processes of the photochemical and/or electrochemical degradation of lignin. The modified lignin was characterized using Fourier transform infrared (FTIR) and nuclear magnetic resonance (NMR) spectroscopy, while the intermediates produced during the photoelectrochemical process were analyzed by high-performance liquid chromatography (HPLC). Our study has demonstrated that the innovative approach described in this communication provides a promising and energy efficient, environmentally friendly method for lignin modification and degradation.     

Synthesis of silsesquioxanes based in (3-methacryloxypropyl)-trimethoxysilane using methacrylate monomers as reactive solvents

The polycondensation of (3-methacryloxypropyl)-trimethoxysilane in acidic conditions using different methacrylate monomers as reactive solvents resulted in incompletely condensed methacrylate-functionalized silsesquioxanes with a very large fraction of intramolecular cycles. UV-MALDI-TOF-MS analysis demonstrated that the species present after 2 weeks of reaction at 60 °C were: T₆(OH)₂, T₇(OH), T₈(OH)₂, T₉(OH), T₁₀(OH)₂ and T₁₁(OH). Analysis of samples after 30 months of storage at room temperature revealed the presence of T₁₂(OH)₂ and T₁₃(OH) species. The absence of higher molar mass oligomers after prolonged storage periods is attributed to dilution of the reacting medium, which discourages bimolecular reactions that lead to polymer growth. ²⁹Si NMR spectroscopy showed that the conversion in the polycondensation reaction was in the range 0.91-0.96. The methacrylate monomers are not involved in the hydrolysis-condensation reactions with MPTMS and therefore can be polymerized by thermal or photochemical means, thereby cross-linking the preformed nanosized cagelike silsesquioxanes. The formulations containing silsesquioxanes showed a markedly reduced content of extractable monomer after photopolymerization, which makes these resins very attractive for dental filling materials.     

Behavior of a Microwave Cavity Discharge over a Wide Range of Pressures and Flow Rates

Experiments are conducted over a wide range of pressures, flow rates, and power levels to demonstrate the versatility of a microwave cavity discharge. The experimental results are justified using a linear, cold plasma theory that accounts for the electron-neutral particle collisional losses in the plasma. The resonant coupling of E. M. energy to a surface wave and the resulting formation of a long, large volume plasma column is demonstrated. The absorbed power characteristics of the microwave cavity discharge are examined for gas pressures up to 500 torr and flow rates up to 2500 cm3/min in the TE011 and TE*111 mode operation of the plasma cavity system. The experimental results show that the absorbed power variation as a function of pressure of this discharge is uniform. The power absorbed by the flowing plasma is shown to increase directly as a function of the flow rate initially and reach a saturation at high flow rates. By simultaneously optimizing the cavity length, discharge pressure, and the gas flow, it is possible to couple as much as 90% of the incident power to the plasma.     

Rejection rules in theM/G/1 queue

We consider aM/G/1 queue modified such that an arriving customer may be totally or partially rejected depending on a r.v. (the barricade) describing his impatience and on the state of the system. Three main variants of this scheme are studied. The steady-state distribution is expressed in terms of Volterra equations and the relation to storage processes, dams and queues with state-dependent Poisson arrival rate is discussed. For exponential service times, we further find the busy period Laplace transform in the case of a deterministic barricade, whereas for exponential barricade it is shown by a coupling argument that the busy period can be identified with a first passage time in an associated birth-death process.     

Equilibrium properties of the M/G/1 queue

Summary Various aspects of the equilibrium M/G/1 queue at large values are studied subject to a condition on the service time distribution closely related to the tail to decrease exponentially fast. A simple case considered is the supplementary variables (age and residual life of the current service period), the distribution of which conditioned upon queue length n is shown to have a limit as n. Similar results hold when conditioning upon large virtual waiting times. More generally, a number of results are given which describe the input and output streams prior to large values e.g. in the sense of weak convergence of the associated point processes and incremental processes. Typically, the behaviour is shown to be that of a different transient M/G/1 queueing model with a certain stochastically larger service time distribution and a larger arrival intensity. The basis of the asymptotic results is a geometrical approximation for the tail of the equilibrium queue length distribution, pointed out here for the GI/G/1 queue as well.     

Methane mobility in carbon nanotubes

Quasi-elastic neutron scattering has been used to characterize the diffusivity of CH₄ molecules condensed in single-wall carbon nanotubes. It is shown that the two sites of adsorption, previously observed by adsorption volumetry and calorimetry measurements, correspond to a solid-like phase for the more strongly bound site at T<120 K and to a liquid-like component for the more weakly bound site at 70<T<120 K. The diffusion coefficients of the mobile molecules range between 3×10⁻⁷ to 15×10⁻⁷ cm² s⁻¹. The fraction of this viscous liquid diminishes as the temperature is decreased; the adsorbate is fully solidified at 50 K and below.     

Calculation of the Steady State Waiting Time Distribution in GI/PH/c and MAP/PH/c Queues

We consider the waiting time (delay) W in a FCFS c-server queue with arrivals which are either renewal or governed by Neuts' Markovian arrival process, and (possibly heterogeneous) service time distributions of general phase-type F _i , with m _i phases for the ith server. The distribution of W is then again phase-type, with m ₁m _c phases for the general heterogeneous renewal case and phases for the homogeneous case F _i =F, m _i =m. We derive the phase-type representation in a form which is explicit up to the solution of a matrix fixed point problem; the key new ingredient is a careful study of the not-all-busy period where some or all servers are idle. Numerical examples are presented as well.