Processes with light impurities

The interphase mass-transfer rates for the components A, B, and I in the condenser are governed by rate expressions of the form  

In practical applications, for economic and operational reasons, the flow rate of the purge stream is very small compared with the throughput of the process. Hence, we can assume that the ratio of the purge flow rate to the feed flow rate under steady-state conditions is very small, i.e., Ps/FotS = e 1. We will also consider that the mole fraction of the impurity in the feed (and, consequently, the rate at which the impurity enters the system) is very small, or yio = /3ie, where fa is an 0(1) quantity. 

Owing to its high volatility, the impurity does not separate readily in the separation unit. Equivalently the mass transfer rate for component I is very small  

Note that, from steady-state considerations, in order to remove an appreciable amount of impurity from the recycle loop via the purge stream (whose flow rate is small), the mole fraction of the impurity in the vapor phase in the condenser, 2/i, has to be 0(1). This implies that O(e) moles of impurity enter and leave the system through the feed and purge streams. Note also that our assumption concerning the mass-transfer properties of the component I implies that a negligible amount of impurity leaves the recycle loop through condensation, exiting the process with the liquid stream from the bottom of the condenser. 

Using the assumptions above, the dynamic model of the system takes the form 

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In what follows, we begin by introducing two examples of process systems with recycle and purge. First, we analyze the case of a reactor with gas effluent connected via a gas recycle stream to a condenser, and a purge stream used to remove the light impurity present in the feed. In the second case, the products of a liquid-phase reactor are separated by a distillation column. The bottoms of the column are recycled to the reactor, and the trace heavy impurity present in the feed stream is removed via a liquid purge stream. We show that, in both cases, the dynamics of the system is modeled by a system of stiff ODEs that can, potentially, exhibit a two-time-scale behavior. 

According to this equation, the lifetime of excited carriers decreases with increasing majority carrier density and consequently with doping. A similar result is obtained if the recombination process occurs via impurity centers (Shockley-Read equation [20]), which will not be shown here. The recombination rate also influences the stationary density of electrons and holes produced by light excitation. One obtains from Eqs. (6) and (7) ... 

The theory of "impurity" or defect absorption Intensities in semiconductors has been studied by Rashba ( 1). By use of the Fredholm method, he finds that if the absorption transition occurs at k=0 and if the discrete level associated with the impurity approaches the conduction band, the intensity of the absorption line increases. The explanation offered for this intensity behavior is that the optical excitation is not localized in the impurity but encompasses a number of neighboring lattice points of the host crystal. Hence, in the absorption process, light is absorbed by the entire region of the crystal consisting of the impurity and its surroundings. 

Gas-phase reactions may lead to gaseous by-products and impurities. Similarly, a gaseous reactant may contain light impurities that will pass through the reaction system or produce other impurities. As result, processes with gas recycles need the placement of one or several purges to prevent the accumulation of some gaseous components. The above observation may be extended to heavy components, for which exit points (bleeds) must be provided. 

Photoluminescence Spectroscopy Photoluminescence (PL) is a type of luminescence in which the spontaneous emission of light takes place from a material under optical excitation. The technique requires very little sample manipulation or environmental control. Because the sample is excited optically, electrical contacts and junctions are not required and high-resistivity materials pose no practical difficulty. In addition, time-resolved PL can be very fast, making it useful for characterizing the most rapid processes in a material. The fundamental limitation of PL analysis is its reliance on radiative events. Materials with poor radiative efficiency such as low-quality indirect band gap semi-conductors are difficult to study via ordinary PL. Similarly, identification of impurity and defect states depends on their optical activity. Although PL is a very sensitive probe of radiative levels, one must rely on secondary evidence to study states that couple weakly with light. 

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