CDS model

Pyrolyzer CDS Model Pyroprobe 2000 with coil sample probe and quartz boat sample holder Pyrolysis temperature about 650°C for 20 sec Pyrolysis sample size 0.2-0.3 mg GC Hewlett Packard Model 5890... 

Pyrolysis-Gas Chromatography-Mass Spectrometry. In the experiments, about 2 mg of sample was pyrolyzed at 900°C in flowing helium using a Chemical Data System (CDS) Platinum Coil Pyrolysis Probe controlled by a CDS Model 122 Pyroprobe in normal mode. Products were separated on a 12 meter fused capillary column with a cross-linked poly (dimethylsilicone) stationary phase. The GC column was temperature programmed from -50 to 300°C. Individual compounds were identified with a Hewlett Packard (HP) Model 5995C low resolution quadruple GC/MS System. Data acquisition and reduction were performed on the HP 100 E-series computer running revision E RTE-6/VM software. 

As will be shown for the CD model, early mixing models used stochastic jump processes to describe turbulent scalar mixing. However, since the mixing model is supposed to mimic molecular diffusion, which is continuous in space and time, jumping in composition space is inherently unphysical. The flame-sheet example (Norris and Pope 1991 Norris and Pope 1995) provides the best illustration of what can go wrong with non-local mixing models. For this example, a one-step reaction is described in terms of a reaction-progress variable Y and the mixture fraction p, and the reaction rate is localized near the stoichiometric point. In Fig. 6.3, the reaction zone is the box below the flame-sheet lines in the upper left-hand corner. In physical space, the points with p = 0 are initially assumed to be separated from the points with p = 1 by a thin flame sheet centered at... 

The CD model was first proposed by Curl (1963) to describe coalescence and breakage of a dispersed two-fluid system. In each mixing event, two fluid particles with distinct compositions first coalesce and then disperse with identical compositions.75 Written in terms of the two compositions (f>A and [Pg.292]

Several variants of the CD model exist wherein only partial coalescence occurs. The final particle compositions are then only partially mixed, and thus will not be identical. 

The CD model can also be written in terms of a convolution integral with respect to the joint composition PDF. However, its properties are more easily understood in terms of a mechanistic model for a mixing event. 

In other words, the CD model assumes that all scalars have the same micromixing rate. 

Modifications have been made to improve the CD model (Janicka et al. 1979 Pope 1982 Dopazo 1994), but its fundamental properties remain the same. 

The CD model also satisfies the strong independence condition proposed by Pope (1983). 

Mixing models based on the CD model have discrete jumps in the composition vector, and thus cannot be represented by a diffusion process (i.e., in terms of and B ). Instead, they require a generalization of the theory of Markovian random processes that encompasses jump processes136 (Gardiner 1990). The corresponding governing equation... 

Composite HC-CD Model Frequency Dependence of Wideband FIR Absorption X. Conclusions and Perspectives... 

The 802.3 CSMA/CD model defines a bus topology network that uses a 50-ohm coaxial baseband cable and carries transmissions at 10Mbps. This standard groups data bits into frames and uses the Carrier Sense Multiple Access with Collision Detection (CSMA/CD) cable access method to put data on the cable. 

Experimental studies in our laboratory on the aldol condensation were carried out in a lin. CD column using Ambelite IRA-900 anion-exchange resin housed in fiberglass bags. The reboiler duty, which affected the flow rates, was found to play an important role in the selectivity to DAA. A rate-based three-phase CD model was developed, which accurately predicts the yield and selectivity obtained under steady-state and transient conditions. Model predictions and experimental data indicate that the production of DAA is external mass transfer controlled while the production of MO is kinetically controlled. The external mass transfer resistance was caused by the fiberglass bags. Recently,... 

A study of Cd adsorption on goethite was the first application of the CD model for cations [97], Distribution of the positive charge of adsorbed cation between the surface and the 1 plane is explained by attributing this positive charge to the first shell of oxygen atoms around the cation. For a typical CN of 6, no more than three of six oxygen atoms can be simultaneously located on the surface for geometrical reasons. 

The CD concept can be also combined with the Stern or TLM model without introduction of the additional electrostatic plane. This offers a possibility of formulation of problem in terms of the CD model within standard features offered by commercial speciation programs. Recent study of Gd and Ni adsorption on alumina in the framework of TLM model produced significantly better fit for the charge of the specifically adsorbed cations distributed 50-50 between the surface and the / -plane than for inner- or outer-sphere complexation [99]. 

The ionic strength effect on the uptake curves calculated for various / values is significantly different. The uptake slightly decreases on increase of the ionic strength from 0.001 to 0.1 mol dm" for inner sphere complexation (Fig. 5.105), and increases for outer sphere complexation (Fig. 5.106), and with CD model (Fig. 5.107) the ionic... 

The above observations regarding the ionic strength effects (Figs 5.105-5.116) do not represent any general trends, namely, they are only valid for certain set of TLM parameters. Figures 5.112 and 5.117-5.119 show the ionic strength effect on the uptake curves calculated for the same electrostatic position of Pb (CD model,/ 0.5), and the same number (two in the present example) of protons released per one adsorbed Pb, but using different sets of TLM parameters from Table 5.18. The stability constants of the alumina-Pb surface complex are presented in Table 5.22. 

However, the possibilities to adjust the course of model uptake curves by the selection of the simple model of specific adsorption (electrostatic position and the number of protons released per one specifically adsorbed cation or per one molecule of weak acid) are limited. It should be emphasized that the CD model was introduced quite recently, and in most publications summarized in Tables 4.1 and 4.2 only the choice between two electrostatic positions (inner- and outer-sphere) was considered. Thus, the ability to find a simple model properly simulating the actual uptake curves was even more limited than nowadays. But even when the charge distribution concept is taken into account, it often happens that the simple models fail to properly reflect the experimentally observed effects of the pH and ionic strength on the specific adsorption. This problem has been solved by... 

Probably some sets of surface reactions reported in literature (outer sphere complex + inner sphere complex) can be replaced by single reaction formulated in terms of the CD model. A few publications report two sets of surface species along with their stability constants that produced equally good simulation of experimental data. These sets are separated by or in Tables in Chapter 4. 

Such a definition is a crucial assumption in the approach that follows and, somewhat surprisingly, is not commonly exploited in alternative approaches. Consider, for example, the d-d transitions. If the metal ion is taken as the chromophore, it is generally inpossible to get realistic energies and intensities for the normal absorption because of the importance of the metal-ligating atom overlap. Thus it is unlikely to provide a satisfactory basis for a CD model. On the other hand, if the chromo-phore is taken to include both the metal and the ligating atom system, both the d-d and charge transfer regions in the normal absorption spectrum may be exploited to parametrize the chromophore as much as possible. The remainder of the complex (the chelate system) then constitutes another chromophoric system. 

The importance of this to the development of a CD model arises in the following way. Consider the complex to comprise two chromophores, A and B, such that A is achiral, and B is the chiral perturber. The CD at the transitions of A arises through simple coupling of A and B as described by perturbation theory, yielding expressions containing the transition moments and energies of the unperturbed chromophore. The utility of the perturbation theory therefore depends critically on the definition of the unperturbed chromophores. The dominant terms in the perturbation expansion may then be extracted unambiguously. 

Thus the aim of a good CD model is to define the chromophores in such a way that, ideally, (i) a single perturbation term dominates, and (ii) the quantities appearing in this term may be calculated realistically or determined empirically (e.g. from the normal absorption spectrum). 

The art of developing a good CD model thus lies totally in the chromophore definitions, a factor usually swamped by complex perturbation expressions. The importance of this point cannot be overstressed, as the failure of some CD models stems ultimately from an oversimplified chromophore definition, a deficiency that, in most cases, cannot be remedied by any subsequent theoretical refinements (e.g. going to higher order in perturbation theory). 

No attempt will be made in this paper to review the large body of literature on CD models of complexes, and the reader is especially referred to a recent, comprehensive review by Richardson (3). The discussion here will be restricted mainly to the approaches developed recently by this author for the CD of charge transfer (4) and d-d transitions (5),and the specific application to tris(bidentates) and determination of their absolute configuration. 

This rather exhaustive definition of the chromophores should illustrate the importance of a detailed description of the model, because all the assumptions of the CD model to be described have already been made. Any deficiencies in its description of real systems may be traced directly back to the preceding discussion. We now turn to discussing those perturbation terms which lead to the CD of the CT and d-d transitions of such chromophores. 

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