Shell particles, trials, tribulations and triumphs

The concept of pellicular particles was imagined by Horváth and Lipsky fifty years ago. They were initially intended for the analysis of macromolecules. Later, shell particles were prepared. The rational behind this concept was to improve column efficiency by shortening the pathways that analyte molecules must travel and, so doing, to improve their mass transfer kinetics. Several brands of superficially porous particles were developed and became popular in the 1970s. However, the major improvements in the manufacturing of high-quality, fully porous particles, that took place in the same time, particularly by making them finer and more homogeneous, hampered the success of shell particles, which eventually disappeared. Recently, the pressing needs to improve analytical throughputs forced particle manufacturers to find a better compromise between the demands for higher column efficiency that require short diffusion paths of analyte molecules in columns and the need for columns that can be operated with the conventional instruments for liquid chromatography, which operate with moderate column back-pressures. This lead to the apparition of a new generation of columns packed with shell particles, which bring chromatographic columns to a level of efficiency undreamed of a few years ago. This evolution is reviewed, the reason that motivated it, and the consequences of their success are discussed.     

Kinetic investigation of narrow-bore columns packed with prototype sub-2 μm superficially porous particles with various shell thickness

The recent successful breakthrough of sub-3 μm shell particles in HPLC has triggered considerable research efforts toward the design of new brands of core-shell particles. We investigated the mass transfer mechanism of a few analytes in narrow-bore columns packed with prototype 1.7 μm shell particles, made of 1.0, 1.2, and 1.4 μm solid nonporous cores surrounded by porous shells 350, 250, and 150 nm thick, respectively. Three probe solutes, uracil, naphthalene, and insulin, were chosen to assess the kinetic performance of these columns. Inverse size exclusion chromatography, peak parking experiments, and the numerical integration of the experimental peak profiles were carried out in order to measure the external, internal, and total column porosities, the true bulk diffusion coefficients of these analytes, the height equivalent to a theoretical plate, the longitudinal diffusion term, and the trans-particle mass transfer resistance term. The residual eddy diffusion term was measured by difference. The results show the existence of important trans-column velocity biases (7%) possibly due to the presence of particle multiplets in the slurry mixture used during the packing process. Our results illustrates some of the difficulties encountered by scientists preparing and packing shell particles into narrow-bore columns.     

Accurate measurements of peak variances: importance of this accuracy in the determination of the true corrected plate heights of chromatographic columns

The true efficiency of a column is derived from the differences between the variances of the peak profiles of the same compound recorded in the presence and the absence of the chromatographic column. These variances are usually derived using one of three methods: (1) the retention time of the peak apex and its half-height width; (2) the moments of the best fit between the experimental data and a hybrid response function, e.g., an exponentially convoluted Gaussian; or (3) the exact moments of the experimental band profiles. Comparisons of the results of these methods show that the first method is always inaccurate because all the band profiles recorded are strongly tailing. The peak fit method is accurate only for 4.6mm I.D. columns operated with instruments having low extra-column volume but fails for short narrow-bore columns due to the severe tailing of peaks passing through the complex channels of the extra-column volumes and to the inaccuracies in the fit of experimental data to the selected function. Although far better, the moment method may be inaccurate when the zero dead volume union used to measure the extra-column peak variances has a higher permeability than the column, causing the upstream part of the instrument to operate under comparatively low pressures.     

Protonation of the oxygen axial ligand in galactose oxidase model compounds as seen with high resolution X-ray emission experiments and FEFF simulations

X-ray Emission Spectroscopy (XES) crossover peaks were shown to be sensitive to the protonation state of solvent molecules in the Zn protein carbonic anhydrase and its model compounds. Here we extend such studies to galactose oxidase models i.e. Cu(ii) open d-shell systems, illustrating that XES combined with FEFF8 simulations reflect changes in the protonation state of the phenolate ligand for the copper center.     

Quaternionic Brownian Windings

Journal of Theoretical Probability - We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the...     

Bayesian Inference of a Parametric Random Spheroid from its Orthogonal Projections

Methodology and Computing in Applied Probability - The paper focuses on a new method for the inference of a parametric random spheroid from the observations of its 2D orthogonal projections. Such a...     

Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain

Motivated by queueing systems playing a key role in the performance evaluation of telecommunication networks, we analyze in this paper the stationary behavior of a fluid queue, when the instantaneous input rate is driven by a continuous-time Markov chain with finite or infinite state space. In the case of an infinite state space and for particular classes of Markov chains with a countable state space, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop an algorithm to compute the stationary probability distribution function of the buffer level in the fluid queue. This algorithm relies on simple recurrence relations satisfied by key characteristics of an auxiliary queueing system with normalized input rates.      

Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications

We prove smoothing estimates for Schrödinger equations it_∂?+x_∂(a(x)x_∂?)=0 with a(x)∈BV, real and bounded from below. We then bootstrap these estimates to obtain optimal Strichartz and maximal function estimates, all of which turn out to be identical to the constant coefficient case. We also provide counterexamples showing a∈BV to be in a sense a minimal requirement. Finally, we provide an application to sharp well-posedness for a generalized Benjamin-Ono equation.     

Numerical spectral analysis of a grid: Application to strain measurements

We present a nondestructive and noncontact extensometry technique, which has been developed in order to study the behavior of different materials such as polycarbonate, araldite, urethane, etc. A spectral analysis of a crossed grating marked on the surface of a specimen and recorded by a charge coupled device camera is presented. The procedure is based on the use of a bidimensional fast Fourier transform algorithm coupled with an interpolation process. It leads to the accurate determination of frequencies. Numerical simulations have been made to evaluate the strain sensitivity; it depends on both the initial phase and the number of cycles characterizing the grid. Theoretically, the strain sensitivity can reach 10^-5 in best cases, but practically it is notbetter than 10^-4. Several applications on different materials are presented: polyurethane, paper and cloth.     

Detection of 20‐hydroxyecdysone in calf urine by comparative liquid chromatography/high‐resolution mass spectrometry and liquid chromatography/tandem mass spectrometry measurements: application to the control of the potential misuse of ecdysteroids in cattle

Ecdysteroids, which are steroid hormones in invertebrates, but which are also present in plants, could potentially be used as anabolic agents in food‐producing animals. The control of ecdysteroid misuse in cattle relies on the development of an efficient method for their detection in biological matrices at trace levels (µg L⁻¹). In order to propose an analytical procedure dedicated to the identification of excreted 20‐hydroxyecdysone (20E) in urine and faecal samples of breeding animals, a comparative study of the spectrometric behaviour of these compounds was carried out both by LC/(ESI‐)/HRMSⁿ (hybrid linear ion trap – orbital trap) and by LC/(ESI+)/MS/MS (triple quadrupole). This study revealed the formation of a large number of product ions both in positive and negative ion mode, corresponding to losses of water molecules and specific cleavages on the side chain. The sample preparation consisted of sequential purification on two solid‐phase extraction cartridges (SPE octadecylsilyl and SPE silica). The detection limits were around 0.5 µg L⁻¹ in the selected reaction monitoring (SRM) mode and recoveries above 60% were obtained. The method was successfully applied to the analysis of real samples collected from calves treated with 60 mg 20E over 4 days. Analysis of the samples allowed the investigation of the kinetics of elimination of 20E in calf urine and determination of the time‐frame for the control of potential abuse. Copyright © 2008 John Wiley & Sons, Ltd.