Species functionally defined

Bn is the cluster function defined previously and the last equation defines the cluster sum 2 (n). For species in the set Nx it is found ... 

The distribution of Cd(II) surface species is shown as a function of SORy in Figure 14b. The mole fraction of Cd(II) surface species is defined as the ratio of the concentration of a Cd(II) surface species relative to the total Cd(II) on the surface, e.g., [SO=-CdOH ]/[Icd(II)adsorbed]. 

Functionally defined species are exemplified by the plant-available species mentioned in Section 1.1 in which the function is plant availability. 

These equations define the formation of all the species in terms of formation constant and other solution components. It is usually better to use the overall constant when solving problems numerically, because every species is defined with a minimum set of unknowns rather than as functions of several other species as would be the case if the stepwise constants were used. 

Development of chemical speciation schemes which can be directly related to measures of bioavailability - This would allow the determination of which active trace element species merit the most intensive research from the standpoint of environmental perturbation. Some studies have attempted to correlate metal fractions determined by a particular technique (operationally defined speciation) with those that are bioavailable (functionally defined speciation) (Larsen and Svensmark, 1991 Buckley, 1994 Deaver and Rodgers, 1996). However, any correlation is only empirical and more research is required to achieve an understanding of the mechanisms involved in bioavailability and to develop rational predictive models. 

Such methods are used in more fundamental studies to elucidate the soil chemistry, to determine the structure and composition of soil components and to improve understanding of the processes in the soil that control the mobilisation and retention of nutrient and toxicant elements in soil as well as to illuminate their transport mechanisms. They are, therefore, more important for the soil physical chemist than the functionally defined procedures that are the main concern of the agronomist. Both methods are of major interest to the environmental scientist particularly in the study of the fate of environmental pollutants. Many of the extractants intended to target particular species are also used in a functional speciation role. 

Extractants for functionally defined species 10.4.1 Plant-available species in agricultural crops... 

Functionally defined species in hea vily polluted soils... 

The Fukui function or frontier function was introduced by Parr and Yang in 1984 [144], They generously gave it a name associated with the pioneer of frontier molecular orbital theory, who emphasized the roles of the HOMO and LUMO in chemical reactions. In a reaction a change in electron number clearly involves removing electrons from or adding electrons to the HOMO or LUMO, respectively, i.e. the frontier orbitals whose importance was emphasized by Fukui.4 The mathematical expression (below) of the function defines it as the sensitivity of the electron density at various points in a species to a change in the number of electrons in the species. If electrons are added or removed, how much is the electron density... 

Here we illustrate the utility of the function defined in the previous section. By "correcting off the counter ion contribution to the mass flux (see the form of equation [3]), neutral species fluxes are highlighted they are the departure of from zero. 

In a second, more realistic thought experiment, we assume to know the molar absorptivity sAiX of species A only, and thus have to fit sB X and k. The equivalent ssq analysis as above leads to a surface in a three-dimensional space when we plot ssq vs. k and sBiX. This is illustrated in Figure 7.4. Again, the task is to find the minimum of the function defining ssq, or in other words, the bottom of the valley (at A s 0.05 s 1... 

Functionally defined No chemical speciation analysis. No species... 

If one takes g n gir) as the pair correlation function defined in Eq. (5.2), the radial distribution function represents the number of particles of 5 in a shell up to rj around A. If r, is then (see Fig. 5.7), one can regard Eq. (5.2) as giving the coordination number of A in the liquid. In the example chosen for simplicity, species A is the same as species B but this of course is only true for radial distributions of monatomics, e.g., sodium. It is found in practice that in a liquid, g B r) settles to unity by the third or fourth atom away from the reference atom A. 

Ci and Cj are the concentrations of atomic species i and j, and bi and bj are the corresponding neutron scattering lengths. gy r) is the pair distribution function, defined such that the probability of finding an atom of species j within the range of distances r to r + dr from an atom of atomic species i is equal to Cj4w gij(r)dr. It is common to define the quantity T(r) as... 

Functionally defined speciation. Functionally defined species are exemplified by the plant-available species or chemical pools in which the function is plant availability. Available forms of trace metal cations are not necessarily associated with one particular chemical species or a specific soil component. Hence, to predict the availability of trace metals, we either have to establish the species involved and develop methods that specifically determine those forms only, or we have to establish an empirical relationship between an accepted diagnostic measure of the metal and plant growth. Both speciation in solution and fractionation of the solid phase to identify the chemical pools can affect plant uptake (phytoavailability) of trace metals and water pollution. 

Each molecular species is defined by the chemical nature of the polar headgroup, the type of linkage to glycerol, and the aliphatic chains at both the sn-l and sn-2 positions. Different molecular species have different metabolic and physical properties. The molecular species composition of membrane phospholipids is associated with membrane fluidity and the function and activity of membrane-bound enzymes (Lynch and Thompson, 1984, Lin etal., 1990). 

The eco-toxicity and mobility of metals in the environment depends strongly on their specific chemical forms or types of binding rather than the total element contents. Consequently these have to be determined in order to assess the toxic effects and geochemical pathways. The determination of specific chemical species or binding forms is difficult and often hardly possible. Therefore, in practice determinations of broader operationally or functionally defined forms or phases can be a reasonable compromise ... 

Extraction procedures for plant uptake studies have existed for many years. These species are defined by their function, e.g. plant-available forms. The species defined in this way, however, are unlikely to be distinct chemical forms but may include a range of chemical entities that share the same function, e.g. are all available to plants. This type of functionality, using selective chemical extractants, has been widely employed in soil and agricultural laboratories to diagnose or predict toxicity deficiencies in crops and in animals eating such crops. Table 5.7 illustrates the diversity of this type of selective extraction. It is noted that the methods, evolved over many years on an empirical basis, are both element-specific and crop-specific. 

The overall (apparent) initial reaction rate can be represented as the product of several functionalities, which include a function dependent on the chemical species concentration defined at the initial condition /i(C,a function dependent on the catalyst concentration fiiCc) or the catalyst weight, and a function dependant on the rate of absorbed photons f (Pa). 

The functionality of the initial reaction rate on the i chemical species concentration defined at the initial condition /i(Ci, ) is illustrated in Figures 1.5 and 1.6. 

RYAN, C.A., PEARCE, G., Systemins A functionally defined family of peptide signal that regulate defensive genes in Solanaceae species, Proc. Natl. Acad. Sci. USA, 2003, 100, 14577-14580. 

It is straightforward to describe multi-species atomic environments using the bispectmm. We modify the atomic density function defined in Eq. 2.18 as... 

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