Enhancement factor definition

In the literature there is often some confusion over the precise definition of the enhancement factor as measured experimentally and indeed there are several complications, and frequently assumptions, inherent in the estimation of enhancement factors. This is discussed in depth in a very useful article by Le Ru et al. [37]. 

In the region of extremely rapid reaction the utilization factor approach, which refers the observed rate to the maximum possible chemical rate, has the drawback of requiring accurate values of the rate coefficient, k. An alternate way is to refer to the physical liquid phase mass transfer rate, which is increased by the chemical reaction. This then leads to the definition of an enhancement factor, Fa ... 

Equation 14.20 for the enhancement factor is equally valid for the present system, but the definition of the Hatta number is replaced by Equation 14.40 ... 

This is our operational definition of the effective enhancement factor that is given by the ratio of Eq. (9) to Eq. (8). 

Enhancement factor =da/dilp p/[dcr/(KIdwba - see definition of parameters and com- ... 

Applying the boundary conditions, and the definition of the enhancement factor... 

This definition is analogous to the effectiveness factor, where mass transfer was inhibiting. In this case, mass transfer is being enhanced in the presence of chemical reaction, and the enhancement factor is always greater than 1. 

In an effort to quantitate the increase in GCMS analysis speed, one author has suggested the descriptors fast, very fast, and ulfrafast (154). These are based on the definition of the new term, speed enhancement factor (SEF), which is defined as the product of column length reduction and the increase in carrier-gas Unear velocity for the chromatographic separation. Using this description, SEFs of 5-30, 30-400, and 400-4000 correspond to fast, very fast, and ultrafast. 

This is a more general definition of the enhancement factor E than the one given in eq. (5.41). The function E (9, ) is represented graphically in figure 5A.3. Note diat E defined in this manner, can be greater or smaller than 1. 

Therefore any attempt to model the spatial occurrence and fate of chemicals in the environment will require an appropriate choice of all the factors discussed above, which have a definite influence on the behavior of the chemicals considered. Figure 2 summarizes some of the most relevant. It is worth mentioning that the availability of spatial data sets has been greatly enhanced by the current progress achieved on remote sensing technologies [57, 58]. 

In other studies, mast cells have been shown to be abundant in the marrow of osteoporotic patients, and heparin, which is contained within the secretory granules of connective tissue (peritoneal)-type mast cells, has been shown to enhance bone resorption and to inhibit bone-cell replication and collagen synthesis in vitro [130]. Moreover, heparin is known to bind growth factors such as fibroblast growth factor and may therefore be important in limiting their availability [134], Taken together, these various studies suggest a possible involvement of mast cells in the homeostasis of bone, but much more work is needed before any definitive conclusions can be drawn. 

Information is currently available which allows more definite conclusions than have previously been possible. Rate enhancements have been obtained in several simple chemical reactions that are of similar magnitude to those observed in analogous enzyme-catalysed reactions, and the goal of analysing the individual factors that can give such large rate accelerations is now perhaps within reach. The recent work will be stressed in this review. 

The same models as for intermolccular processes are applied for intramolecular diastereoface differentiating double-bond additions. However, there are some advantages in the intramolecular version. Firstly, the entropy factor lowers the barrier of activation and allows reactions to proceed at lower temperatures, which increases the selectivity. Secondly, the cyclic transition states introduce the elements of ring strain and transannular interactions, which lead to enhanced differences between two diastereomorphous geometries. Both of these factors cooperate to increase the selectivity of the intramolecular reaction. For example, halolactonization, by definition, is an intramolecular process. 

---