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Massimo Morbidelli

Publications and source records attributed to Massimo Morbidelli.

14 recordsLinked to original sources
PubMed2005

Scattering structure factor of colloidal gels characterized by static light scattering, small-angle light scattering, and small-angle neutron scattering measurements.

The scattering structure factor of a colloidal gel in a q range of 5 orders of magnitude has been determined by combining static light scattering, small-angle light scattering, and neutron scattering measurements. It exhibits simultaneously two types of structure information: a mass fractal scaling within the clusters that constitute the gel and a surface fractal scaling for length scales larger than that of the clusters. Such scattering behavior can be well interpreted by the pair-correlation function proposed in the literature to model an ideal structure constituted of mass fractal objects inside surface fractal objects.

Journal Article↗
PubMed2005

Scaling of the kinetics of slow aggregation and gel formation for a fluorinated polymer colloid.

The aggregation and gelation kinetics in moderately concentrated (0.004 </= phi(0) </= 0.1) colloidal dispersions of fluorinated polymer particles has been studied. The aggregation was adjusted to proceed slowly enough to allow a convenient characterization of the kinetics through static and dynamic light scattering on quenched and diluted samples. A population balance model based on second-order aggregation rates is developed to compute the time evolution of the cluster mass distribution, from which we calculate the values of the average radii and structure factor measured by light scattering, so as to allow a direct comparison between measured and calculated quantities. The model suggests the introduction of a dimensionless time which allows the scaling of all the aggregation data on unique master curves defined by only two parameters: the exponent of the power-law aggregation kernel, lambda, and the aggregate fractal dimension, d(f). The predicted master curves were observed experimentally, which confirms the validity of the aggregation model and allows the unique determination of the kinetic and structural parameters of the aggregation process. The cluster growth behavior, although significantly slower than DLCA, shows power-law kinetics rather than the exponential one typical of RLCA and the cluster structure is characterized by an unexpectedly small fractal dimension, d(f) = 1.7. The occurrence of gelation has been characterized using small amplitude oscillatory shearing to monitor the time evolution of the elastic modulus. It is found that also these curves, together with the gel time value, scale with the stability ratio of primary particles for a given solid volume fraction. We further use the model to calculate the cumulative occupied volume fraction of the growing aggregates and quantify in this way the increasing space filling, which is solid volume fraction dependent. The experimentally determined dimensionless gel times, which are also solid volume fraction dependent, scale then directly with the dimensionless time to reach a certain degree of the space filling in the model. This finding suggests that, like the aggregation kinetics, the gelation kinetics is governed by a second-order rate process.

Journal Article↗
PubMed2004

Kinetics of gel formation in dilute dispersions with strong attractive particle interactions.

We report a combined experimental and modeling study to investigate the kinetics of the transformation of a colloidal dispersion with strong attractive particle interactions into a gel. In the model, a two step mechanism is proposed, where an initial aggregation step is followed by an interconnection step leading to a particle network spanning the entire system volume. Using the Smoluchowski aggregation equation for the first step, we introduce a criterion to determine when the aggregation process is arrested and clusters become caged. In the second step the caged clusters diffuse over short distances and interconnect to form the particle network. The reliability of the gelation times computed by the model has been tested by comparison with a suitable set of experimental data. In addition, we show that the concept of mathematical gelation within the Smoluchowski aggregation equation is not appropriate for the description of the entire gel formation process in this system.

Journal Article↗
PubMed2004

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.

Models, Theoretical↗
PubMed2004

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.

Chromatography↗
PubMed2003

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.

Journal Article↗
PubMed2003

Hydrodynamic radius of fractal clusters.

The Kirkwood-Riseman theory has been used to derive an analytical formula for the evaluation of the hydrodynamic radii of fractal clusters. The proposed relation is based on knowledge of the particle-particle correlation function and can be applied to clusters containing any number of particles larger than 4. The calculated values of the hydrodynamic radius are compared with the results of other theoretical approaches proposed in the literature, as well as several experimental data. Finally, the developed relation has been used in connection with a population balance equation model that computes the clusters' mass distribution to estimate the average hydrodynamic radius for a population of fractal clusters of different sizes. The obtained results have been compared to suitable experimental data for a silica colloidal suspension aggregating under reaction-limited conditions.

Journal Article↗
PubMed2003

PowerFeed operation of simulated moving bed units: changing flow-rates during the switching interval.

A possible way to improve the separation performance of simulated moving bed (SMB) units is to change the internal and external liquid flow-rates during the switching period. This operation mode, referred to as PowerFeed, is examined in this work through a model analysis. Similar to the Varicol process, which allows for the asynchronous movement of the ports, the PowerFeed process exhibits more degrees of freedom than the classical SMB process and therefore allows more room for optimization. Using an optimization technique based on a genetic algorithm, all three processes have been optimized for a few case studies in order to determine their relative potentials. It is found that PowerFeed and Varicol provide substantially equivalent performances, which are however significantly superior to those of the classical SMB process.

Algorithms↗
PubMed2003

Aggregation kinetics of polymer colloids in reaction limited regime: experiments and simulations.

The kinetics of reaction-limited cluster aggregation of fluorinated polymer colloids in a broad range of particle volume fractions has been investigated experimentally by measuring independently the Fuchs stability ratio W and the time evolution of both the average radius of gyration and the average hydrodynamic radius of the aggregates mass distribution. The W value is determined from the aggregation rate at the very initial stage of the aggregation, where the presence of triplets is negligible. The time evolutions of and are then simulated using the cluster mass distribution calculated from the population balance equations with various aggregation kernels proposed in the literature. It is found that, when the measured W value is used, the only kernels that can correctly simulate the experimental results are the product kernel and the one derived by Odriozola et al. (Europhys. Lett. 53 (2001) 797), with some proper tuning of the exponent in the kernel. For the particle volume fraction phi<1%, the obtained value for the exponent is 0.4 and independent of phi, while it tends to decrease for larger phi values, most likely indicating a significant effect of multi-body interactions on the aggregation kinetics.

Journal Article↗
PubMed2003

Multiobjective optimization of simulated moving bed and Varicol processes using a genetic algorithm.

The size of the packing material, the total number of columns and the total feed concentration have significant impacts on the economics of a preparative chromatographic separation, through their effects on column pressure drop, column efficiency and thermodynamics. In this work, the role of these parameters on the performances of a simulated moving bed and a Varicol process is investigated on a chiral separation system from literature, using an equilibrium stage model. A multiple objective optimization technique based on a genetic algorithm is adopted, which allows to maximize simultaneously the purity of the extract and productivity of the unit. In this way, it is possible to optimize and compare the performances of both processes in a wide range of parameter values, so as to assess their relative potential under equally optimized conditions. The optimization results, i.e. the so-called Pareto sets, have been discussed in the frame of equilibrium theory and the roles of these three parameters have been clarified.

Algorithms↗
PubMed2002

Experimental investigation of the behavior of gas phase simulated moving beds.

The preparative, continuous gas chromatographic separation of the enantiomers of the inhalation anaesthetic enflurane has been studied on a chiral stationary phase based on octakis(3-O-butanoyl-2,6-di-O-n-pentyl)-gamma-cyclodextrin, dissolved in polysiloxane SE-54 and coated on Chromosorb particles. This has been carried out in a gas chromatographic simulated moving bed (GC-SMB) unit, equipped with eight columns, yielding a total volume of 1.128 l. With reference to this particular system, the separation performance and the behavior of GC-SMB units have been analyzed in depth. We have varied the internal flow-rates in the four sections of the unit in the range between about 1 and about 5 std l/min, the temperature between 20 and 45 degrees C, the switch time between about 2 and about 14 min, and the feed concentration in the range 0.32-0.90 mol%. Similarities and differences in the behavior of GC-SMBs as compared to conventional liquid phase SMBs have been described, and discussed. Operating conditions leading to more than 99% purity in one or both outlet stream have been identified, together with those achieving optimal throughput. Under such optimal conditions, about 20 g of each enflurane enantiomer with enantiomeric purity larger than 98% have been prepared.

Adsorption↗
PubMed2002

Solvent gradient operation of simulated moving beds. I. Linear isotherms.

The simulated moving bed (SMB) is a multi-column chromatographic separation process, which--with respect to the single-column preparative batch process--allows for a continuous separation with larger productivity and smaller solvent consumption at the same time. The benefits of this process have been shown for several different applications in fine chemistry, particularly for the separation of enantiomers. In general, SMBs are operated under isocratic conditions. However, separation performance can be further improved by applying some sort of gradient mode operation, in order to optimize the operating conditions of each individual section of the unit. This can be achieved by tuning the retention behavior of the solutes to be separated along the unit, namely by enforcing weak adsorption conditions in sections 1 and 2, and strong adsorption conditions in sections 3 and 4. This can be achieved by applying a temperature gradient (high temperature in section 1, and low temperature in section 4), a pressure gradient (e.g. in the supercritical SMB, when pressure is high in section 1, and low in section 4), or a solvent gradient, which is the aim of this work. In the solvent gradient mode the mobile phase consists of a mixture of two or more solvents. To different mobile phase compositions corresponds a different retention behavior of the solutes, i.e. different adsorption isotherms. In this work we study a closed loop SMB unit with solvent mixtures of two different compositions entering the unit at the feed and desorbent inlet ports, respectively. Thereby two different mobile phase compositions are established in sections 1 and 2, and sections 3 and 4, respectively. To optimize this process the equilibrium theory design criteria for non-linear SMBs are extended to describe this operation mode. It is shown how the region of separation is derived and how the optimal operating conditions can be found. Finally the solvent gradient mode is compared with the isocratic mode in terms of productivity and solvent consumption.

Adsorption↗
PubMed2002

Separation of binaphthol enantiomers through achiral chromatography.

Chromatography is a key technique for the analytical, preparative, and production scale separation of enantiomers, particularly in the pharmaceutical and fine chemicals industries. Although it is common belief that this separation can be accomplished only using a chiral stationary phase, it has been recently shown that under certain circumstances a non-racemic mixture of specific chiral compounds can be separated in two fractions which differ in enantiomeric excess (e.e.) also on an achiral stationary phase. In this work we show that in the case of the enantiomers of binaphthol in chloroform achiral chromatography on LiChrospher 100 NH2 furnishes two fractions constituted of the pure enantiomer present in excess and of the racemic mixture, respectively. This is demonstrated by on-line monitoring the concentration of both enantiomers at the outlet of a chromatographic column fed with a non-racemic pulse of the two enantiomers by using a UV detector and a polarimeter in series. Furthermore, we provide experimental evidence of the presence of homo- and hetero-dimers in solution through NMR experiments and develop a consistent physico-chemical model of the solution itself and of the competitive achiral adsorption equilibria. When combined with a standard rate model of the chromatographic column this not only confirms the possibility of achieving 100% e.e. through achiral chromatography, but also allows for a qualitative and quantitative description of all the experimentally observed phenomena. Among these, the effect of the enantiomeric excess and of the overall concentration of the injected pulse on the chromatographic behaviour are worth mentioning.

Adsorption↗