Limits of the numerical estimation of the adsorption energy distribution from adsorption isotherm data using the expectation-maximization method

The limits of the use of the expectation-maximization (EM) method for the study of the heterogeneity of adsorbent surfaces were tested by calculating the adsorption energy distribution of systems having known degrees of heterogeneity. Connecting on-line two different columns allows the simulation of a heterogeneous system. The two columns used were endcapped, C(18)-bonded silica used as stationary phases and having different degrees of C(18) chain coverages (0.42 and 2.03 micromol/m(2)). The adsorption constants of phenol measured by frontal analysis (FA) are significantly different on these two columns. On each column, the adsorption behavior was best accounted for by a bi-Langmuir isotherm model, corresponding to a heterogeneous surface with a bimodal energy distribution. The difference between the adsorption energies on the weak adsorption sites of the two columns is 1.5 kJ/mol. The energy difference of their high energy sites is 2.2 kJ/mol. The EM method can readily distinguish between adsorption sites having energies that differ by more than 5 kJ/mol after more than 10 million iterations, but it cannot distinguish between adsorption sites for which this energy difference is less than 2 kJ/mol, even after 100 million iterations. For highly heterogeneous systems, (e.g., those with more than three different types of adsorption sites), the EM program does not converge necessarily towards the actual energy distribution function but toward a simpler one, having fewer adsorption sites that are almost equally spaced in the energy space. This failure of the EM program is related to the fact that, despite the excellent precision of the FA measurements (<1%), any series of adsorption data can be represented by several distinct AEDs. Thus, the degree of heterogeneity of RPLC adsorbents determined with the EM method might often be minimized, resulting in erroneous values of the isotherm parameters.     

Csaba Horváth and preparative liquid chromatography

Few chromatographers have been interested in furthering preparative liquid chromatography. The pioneers, Tswett, Kuhn and Lederer, A.J.P. Martin, Tiselius, isolated fractions but as an intermediate step in the analysis of their samples. The progress in electronics and sensors, and in their miniaturization has lead to the paradoxical situation that the analysts never see the transient pure fractions that their detector quantitates. Yet, over the last 25 years, preparative liquid chromatography has become an important industrial process for the separation, the extraction, and/or the purification of many pharmaceuticals or pharmaceutical intermediates, including pure enantiomers, purified peptides and proteins, compounds that are manufactured at the relatively large industrial scale of a few kilograms to several hundred tons per year. This development that has strongly affected the modem pharmaceutical industry is mainly due to the pioneering work of Csaba Horváth. His work in preparative HPLC was critical at both the practical and the theoretical levels. He was the first scientist in modem times to pay serious attention to the relationships between the curvature of the equilibrium isotherms, the competitive nature of nonlinear isotherms, and the chromatographic band profiles of complex mixtures. The thermodynamics of multi-component phase equilibria and mass transfer kinetics in chromatography attracted his interest and were the focus of ground-breaking contributions. He investigated displacement chromatography, an old method invented by Tiselius that Csaba was first to implement in HPLC. This choice was explained by the essential characteristic of displacement chromatography, in that it delivers fractions that can be far more concentrated than the feed. Remarkably, once the basics of nonlinear chromatography had been mastered in his group, most of the applications that were studied by his coworkers dealt with peptides of various sizes and with proteins. Thus, all the applications of preparative HPLC in the biotechnologies derive directly from Csaba's work. Although displacement did not pan out as a general method, the reasons are related more to practical constraints of the production of pharmaceuticals and to the long period of cheap energy that might be ending now. This report reviews Csaba's work in nonlinear chromatography.     

Separation mechanism of nortriptyline and amytriptyline in RPLC

The single and the competitive equilibrium isotherms of nortriptyline and amytriptyline were acquired by frontal analysis (FA) on the C18- bonded discovery column, using a 28/72 (v/v) mixture of acetonitrile and water buffered with phosphate (20 mM, pH 2.70). The adsorption energy distributions (AED) of each compound were calculated from the raw adsorption data. Both the fitting of the adsorption data using multi-linear regression analysis and the AEDs are consistent with a trimodal isotherm model. The single-component isotherm data fit well to the tri-Langmuir isotherm model. The extension to a competitive two-component tri-Langmuir isotherm model based on the best parameters of the single-component isotherms does not account well for the breakthrough curves nor for the overloaded band profiles measured for mixtures of nortriptyline and amytriptyline. However, it was possible to derive adjusted parameters of a competitive tri-Langmuir model based on the fitting of the adsorption data obtained for these mixtures. A very good agreement was then found between the calculated and the experimental overloaded band profiles of all the mixtures injected.     

Amine capture strategy for peptide bond formation by means of quinolinium thioester salts

A new and unprecedented exploitation of quinolinium thioester salts 2 in peptide bond formation is reported. These synthetic tools were assessed during the preparation of a number of dipeptides 3a-f obtained in good yields with complete stereochemical integrity. A sequential mechanism related to a prior amine capture strategy is well-established. Additionally, a tripeptide 3g was prepared according to a "safety-catch" approach, thus demonstrating the important potential of these new synthetic tools in the design of new safety-catch linkers exploitable in Solid-Phase Peptide Synthesis (SPPS).     

Extrathermodynamic study of surface diffusion in reversed-phase liquid chromatography with silica gels bonded with alkyl ligands of different chain lengths

Surface diffusion on adsorbents made of silica gels bonded to C1, C4, C8, and C18 alkyl ligands was studied in reversed-phase liquid chromatography (RPLC) from the viewpoints of two extrathermodynamic relationships: enthalpy-entropy compensation (EEC) and linear free-energy relationship (LFER). First, the values of the surface diffusion coefficient (D(s)), normalized by the density of the alkyl ligands, were analyzed with the modified Arrhenius equation, following the four approaches proposed in earlier research. This showed that an actual EEC resulting from substantial physicochemical effects occurs for surface diffusion and suggested a mechanistic similarity of molecular migration by surface diffusion, irrespective of the alkyl chain length. Second, a new model based on EEC was derived to explain the LFER between the logarithms of D(s) measured under different RPLC conditions. This showed that the changes of free energy, enthalpy, and entropy of surface diffusion are linearly correlated with the carbon number in the alkyl ligands of the bonded phases and that the contribution of the C18 ligand to the changes of the thermodynamic parameters corresponds to that of the C10 ligand. The new LFER model correlates the slope and intercept of the LFER to the compensation temperatures derived from the EEC analyses and to several parameters characterizing the molecular contributions to the changes in enthalpy and entropy. Finally, the new model was used to estimate D(s) under various RPLC conditions. The values of D(s) that were estimated from only two original experimental D(s) data were in agreement with corresponding experimental D(s) values, with relative errors of approximately 20%, irrespective of some RPLC conditions.     

Tunable single-frequency operation of a diode-pumped vertical external-cavity laser at the cesium D<Subscript>2</Subscript> line

We report on a diode-pumped vertical external-cavity surface-emitting laser emitting around 852 nm for Cesium atomic clocks experiments. We have designed a 7-quantum-well semiconductor structure optimized for low laser threshold. An output power of 330 mW was achieved for 1.1 W of incident pump power. Furthermore, a compact setup was built for low-power single-frequency emission. We obtained an output power of 17 mW in a single longitudinal mode, exhibiting both broad (9 nm) and continuous (14 GHz) tunability around the Cesium D₂ line. The laser frequency has been stabilized on an atomic transition with residual frequency fluctuations ∼300 kHz. Through a beatnote experiment the −3 dB laser linewidth has been measured to <500 kHz over 10 ms.     

Numerical and experimental studies of molten pool formation during an interaction of a pulse laser (Nd:YAG) with a magnesium alloy

A pulse laser (Nd:YAG) interaction with an AZ91 magnesium alloy has been experimentally and numerically studied. A two-dimensional (2D) axisymmetric model of a molten pool created by a laser heat source has been developed. The elaborated model solves the coupled equations of a laminar fluid flow and heat transfer to demonstrate the flow behavior in the pool. This model takes into account the coupled effects of buoyancy and Marangoni forces, the thermophysic variation properties with temperature, and the radiation and convection heat losses. Concerning numerical results, the molten temperature distribution, velocity field and molten shape were discussed. It was noted that the Marangoni flow significantly alters the characteristics of the thawing and solidifying processes, and makes the molten pool wider and shallower. On the other hand, the experimental results showed that the material thermal properties have significant effects on the transport phenomena which takes place in the molten pool, and consequently on the formation as well as the shape of the pool. Finally, a comparison between the numerical and experimental results exhibited a good agreement.     

Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy

We propose a Raman spectroscopy technique which is able to probe the one-particle Green function, the Fermi surface, and the quasiparticles of a gas of strongly interacting ultracold atoms. We give quantitative examples of experimentally accessible spectra. The efficiency of the method is validated by means of simulated images for the case of a usual Fermi liquid as well as for more exotic states: specific signatures of, e.g., a d-wave pseudogap are clearly visible.     

On Two Theorems about Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones). Dedicated to my friend J.-C. Cortet.