Scaling limit homogeneous models

We first consider the intermolecular modes of liquid CS2. One of the details that two-dimensional Raman spectroscopy has the potential to reveal is the coupling between intermolecular motions on different time scales. We start with the one-dimensional Raman spectrum. The best linear spectra are based on time domain third-order Raman data, and these spectra demonstrate the existence of three dynamic time scales in the intermolecular response. In Fig. 3 we have modeled the one-dimensional time domain spectrum of CS2 for 3 cases (A) a single mode represented by the sum of three Brownian oscillators, (B) three Brownian oscillators, and (C) a distribution of 20 arbitrary Brownian oscillators. Case (A) represents the fully coupled, or isotropic case where the liquid is completely homogeneous on the time scales of the simulation. Case (B) deconvolutes the linear response into the three time scales that are directly evident in the measured response and is in the limit that the motions associated with each of the three timescales are uncoupled. Case (C) is an example where the liquid is represented by a large distribution of uncoupled motions. 

For homogeneous systems, the kinetic parameters k and tq are commonly determined by lab-scale batch experiments in which all reagents are combined at the start of the reaction. Following the concentration of all components (reactants and products) over the course of the reaction then allows for the estimation of the kinetic parameters. Since water has limited solubility in the reaction mixture at the start, conventional kinetic batch experiments could result in erroneous calculation of kj and tq if the limits for homogeneity are crossed. To ensure reaction homogeneity and reliable kinetic measurements, the gradual and continuous addition of water was selected as a suitable method for experimentation (semi-batch mode). The kinetic parameters were then recovered using an appropriate mathematical model with parameter estimation module. 

Biphasic hydroformylation is a typical and complicated gas-liquid-liquid reaction. Although extensive studies on catalysts, ligands, and catalytic product distributions have appeared, the reaction mechanism has not been understood sufficiently and even contradictory concepts of the site of hydroformylation reaction were developed [11, 13, 20]. Studies on the kinetics of hydroformylation of olefins are not only instructive for improvement of the catalytic complexes and ligands but also provide the basic information for design and scale-up of novel commercial reactors. The kinetics of hydroformylation of different olefins, such as ethylene, propylene, 1-hexene, 1-octene, and 1-dodecene, using homogeneous or supported catalysts has been reported in the literature. However, the results on the kinetics of hydroformylation in aqueous biphasic systems are rather limited and up to now no universally accepted intrinsic biphasic kinetic model has been derived, because of the unelucidated reaction mechanism and complicated effects of multiphase mass transfer (see also Section 2.4.1.1.2). 

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