Inmaculada Suárez

The Role of the Hydroxyl Groups on the Silica Surface When Supporting Metallocene/MAO Catalysts

The behaviour of mesoporous silica as a support for anchored catalytic species depends on its physical and chemical surface properties, particularly those related with the hydroxyl groups. #An earlier version of this paper was presented at ECOREP II, 2nd European Conference on Reaction Engineering of Polyolefins, Lyon, France, July 1–4, 2002. In this report, the number and nature of hydroxyl groups of a commercial silica sample calcined at different temperatures have been determined by titration with triethylaluminium and IR, respectively. The preparation of supported metallocene catalyst has been studied by different ways. The calcination temperature affects deeply the ability of the support to anchor the different species involved in this catalytic system. The polymerization reactions carried out using silica and MAO/silica supports show how the chemistry of the silica surface plays a determinant role in the immobilization of this catalytic system.

Monte Carlo method to explain the probabilistic interpretation of atomic quantum mechanics

Quantum mechanics description of physical and chemical systems is included in books of Physics, General Chemistry or Physical Chemistry including mathematical, graphical, and conceptual descriptions. Mathematical calculations are complex and are covered only in advanced courses. Main problem in the first degree courses is the understanding of the probabilistic interpretation of quantum mechanics. The Monte Carlo method is based on probabilistic concepts and its application to quantum calculations can be carried out quite straightforward. In this work, a simple Monte Carlo method was used to obtain a sequence of random electron coordinates according to the probability given by the wave function. Electron is seen as a shot whose appearance is only accepted and plotted when probability is high enough. Hydrogen atom was studied as it is a familiar system for most students and its description can be easily related to previous knowledge of atomic orbitals. The objective of the present work is to supply all the crucial points that students need to create their own program to plot atomic orbitals according to the above ideas. All the numerical details are indicated in order to get the proposed programming project as a simple task. Student should be able to generate random electron coordinates, to compute wave functions and probabilities, and to obtain plots according to the right probabilistic interpretation of quantum mechanics. In order to show the quantitative obtained plots some results were shown. Typical s, p, and d orbitals were obtained and compared to the usual angular and radial representation.

Broadening of polymer chromatographic signals: Analysis, quantification and correction through effective diffusion coefficients

Average molecular weights and polydispersity indexes are some of the most important parameters considered in the polymer characterization. Usually, gel permeation chromatography (GPC) and multi angle light scattering (MALS) are used for this determination, but GPC values are overestimated due to the dispersion introduced by the column separation. Several procedures were proposed to correct such effect usually involving more complex calibration processes. In this work, a new method of calculation has been considered including diffusion effects. An equation for the concentration profile due to diffusion effects along the GPC column was considered to be a Fickian function and polystyrene narrow standards were used to determine effective diffusion coefficients. The molecular weight distribution function of mono and poly disperse polymers was interpreted as a sum of several Fickian functions representing a sample formed by only few kind of polymer chains with specific molecular weight and diffusion coefficient. Proposed model accurately fit the concentration profile along the whole elution time range as checked by the computed standard deviation. Molecular weights obtained by this new method are similar to those obtained by MALS or traditional GPC while polydispersity index values are intermediate between those obtained by the traditional GPC combined to Universal Calibration method and the MALS method. Values for Pearson and Lin coefficients shows improvement in the correlation of polydispersity index values determined by GPC and MALS methods when diffusion coefficients and new methods are used.

Euler algorithm to solve reaction kinetic equations: Mathematical formulation, programing, and applications

Integration of rate laws to obtain the several concentrations in terms of time is well described in books of General Chemistry, Physical Chemistry, or Chemical Engineering including mathematical and graphical descriptions. When several reactions have to be considered simultaneously, the mathematical solution of involved differential equations became difficult for students and is a good task from the mathematical point of view. Qualitative interpretation has interest from the chemical and engineering point of view and it is usually related with the change of concentrations along reactions which in turns modifies the rate of the several processes involved. In this work, no differential equations are solved analytically and no functions are obtained in order to reduce the mathematical complexity for students but a numerical solution is obtained by using the differential method and the computation of changes in concentration. A general formulation of the involved equations is presented including the effect of reactant concentration in the rate laws and an arbitrary number of simultaneous reactions. Details for numerical solution of involved equations are indicated and the task for students is to create their own program to solve the rate laws. Student should be able to input a set of compounds and reactions, to compute the evolution of concentrations of the several species with time and to plot such concentrations. Some applications with increasing complexity were computed and analyzed. In order to show the quantitative obtained results, comparison with analytical functions was carried out for simple systems.

Influence of the feeding control on the final properties of ethylene/propylene copolymers obtained in laboratory semi-batch reactor

AbstractThe slurry polymerization reactors on the industrial scale operate in continuous mode at low monomer conversion per pass to minimize mass and heat transfer limitations. Nevertheless, for the screening of catalytic systems, the laboratory tests are carried out using batch or semi-batch reactors. In this work, ethylene/propylene copolymers were synthesized in a semi-continuous reactor under similar conditions, where the only difference involves the modification of the feed ratio during the reaction. The key point of the control system is a micro-gas chromatograph (MGC), which analyzes the molar ratio ethylene (C2) to propylene (C3) in the gas phase during the reaction, and the composition in the liquid phase was calculated using the Soave-Redlich-Kwong equation of state. The effect of the ethylene/propylene copolymer microstructure has been studied using different techniques that allow us to conclude that the method of synthesis influences the comonomer distribution and the final copolymer properties.