On-line monitoring of enantiomer concentration in chiral simulated moving bed chromatography

Simulated moving bed chromatography is a key technology for the pilot and production scale separation of enantiomers of chiral chemical species. Product quality control is probably the most important issue in this kind of separation at both scales, and for this it is clear that on-line monitoring of absolute enantiomer concentrations plays a major role. In this work, an on-line system consisting of a UV detector and a polarimeter in series is used to monitor the composition of the extract and raffinate streams of a laboratory SMB unit. The model system adopted is the separation of the enantiomers of the Tr?ger's base on microcrystalline cellulose triacetate (CTA) using ethanol as mobile phase. The technique is effective and accurate, thus providing promising perspectives for SMB process control and dynamic optimization.     

Superexponential stability of KAM tori

We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/)], being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.     

Optimizing control of simulated moving beds--linear isotherm

A new optimization based adaptive control strategy for simulated moving beds (SMBs) is proposed. A linearized reduced order model, which accounts for the periodic nature of the SMB process, is used for online optimization and control. The manipulated variables are the four inlet flow rates, the outputs are the raffinate and extract concentrations. Concentration measurements at the raffinate and extract outlets are used as the feedback information. The state estimate from the periodic Kalman filter is used for the prediction of the outlet concentrations over a chosen horizon. Predicted outlet concentrations are the basis for the calculation of the optimal input adjustments, which maximize the productivity and minimize the desorbent consumption subject to constraints on product purities. The realization of this concept is discussed and the implementation on a virtual eight column SMB platform is assessed, in the case of binary linear systems. For a whole series of typical plant disturbances it is shown that the proposed approach is effective in minimizing off-spec products and in achieving optimal SMB operation, also in the case where there are significant model uncertainties.     

Maltodextrin as stabilizer for emulsion polymerization: Adsorption and grafting behavior

Emulsion polymerization of the three-monomer system butyl acrylate–styrene–methacrylic acid was performed in batch using a commercial maltodextrin derived from starch degradation as stabilizer. Stable latexes with narrow particle size distributions were obtained in all examined cases. A method was developed to analyze and quantify the partitioning of the maltodextrin between the continuous phase (supernatant) and the particle phase. Significant differences between the polysaccharides adsorbed onto particles with or without emulsion polymerization reaction were observed. The possible reactions of maltodextrin in presence of a radical initiator were studied in aqueous phase, thus confirming maltodextrin degradation. The formation of copolymers involving the original monomers and the stabilizer according to two different reactive pathways was also confirmed. In terms of adsorbed maltodextrin, two different contributions were observed: maltodextrin physically adsorbed and maltodextrin chemically grafted and/or physically incorporated into the polymer.     

A simple model for the structure of fractal aggregates

Structural properties of small aggregates containing up to 100 particles have been studied through detailed Monte Carlo cluster-cluster aggregation simulations in both diffusion-limited and reaction-limited conditions. First, the radius of gyration, the radius of the smallest sphere encompassing the cluster, and the particle-particle correlation function, g(r), have been computed based on the positions of all the particles in the cluster, and their fractal scaling has been analyzed. Then, an empirical model has been developed to simulate the g(r) function for aggregates of any size and used to determine the corresponding structural properties and scattering structure factors. Finally, in order to illustrate the application of the structural properties thus computed, two experiments on diffusion-limited aggregation have been performed, and the average scattering structure factors have been measured as a function of time using a small-angle light-scattering device. The obtained average scattering structure factors have been simulated using the Smoluchowski population balance equations, using the single aggregate structural properties and scattering structure factor predicted by the developed empirical g(r) model.     

Solvent gradient operation of simulated moving beds. 2. Langmuir isotherms

Simulated Moving Bed separations of enantiomers or fine chemicals are usually carried out in the isocratic mode, i.e. by applying the same operating conditions (temperature, pressure, mobile phase composition, pH) in the whole SMB unit. However, it has been recently recognized that by properly modulating operating conditions in the SMB sections. i.e. Sections 1-4 normally, separation performance in terms of productivity and solvent consumption can be significantly improved. In this work, we study solvent gradient SMB (SG-SMB) operation, where the concentration of a modifier in the main solvent constituting the mobile phase is adjusted along the SMB unit, so as to have weaker retention of the species to be separated in the first two sections, and stronger retention in Sections 3 and 4. Overload chromatographic conditions are considered, where the adsorption behavior is characterized by a nonlinear competitive adsorption isotherm, e.g. a binary Langmuir isotherm. Design criteria to achieve complete separation are developed in the frame of the equilibrium theory of chromatography. The theoretical findings are discussed in view of typical effects of the modifier concentration on retention times and solubility of the species to be separated, and an overall assessment of the SG-SMB technology is attempted.     

Behavior of human serum albumin on strong cation exchange resins: II. Model analysis

Experiments with human serum albumin on a strong cation exchange resin exhibit a peculiar elution pattern: the protein elutes with two peaks in a modifier gradient. This behavior is modeled with a general rate model, where the two elution peaks are modeled with two binding conformations, one of which is at equilibrium conditions, while for the other, the adsorption process is rate limited. Isocratic experiments under nonadsorbing conditions were used to characterize the mass transfer process. The isotherm of both adsorption conformations as well as the kinetic of adsorption and desorption for the second conformation are functions of the modifier concentration. They are evaluated with linear modifier gradient experiments and step experiments with various adsorption times. All experimental features are well reproduced by the proposed modified general rate model.     

Generalized Jacobi Identities and Ball-Box Theorem for Horizontally Regular Vector Fields

Consider a family $\mathcal{H}:= \{X_{j} =: f_{j}\cdot\nabla: j=1,\ldots , m\}$ of C ¹ vector fields in ? ⁿ and let s∈?. We assume that for all p∈{1,…,s} and j ₁,…,j _p ∈{1,…,m} the horizontal derivatives $X_{j_{1}}X_{j_{2}}\cdots X_{j_{p-1}}f_{j_{p}}$ exist and are Lipschitz continuous with respect to the control distance defined by  $\mathcal{H}$ . Then we show that different notions of commutator agree. This involves an accurate analysis of some algebraic identities involving nested commutators which seem to have an independent interest. Our principal applications are a ball-box theorem, the doubling property, and the Poincaré inequality for Hörmander vector fields under an intrinsic “horizontal regularity” assumption on their coefficients.