Estimation from LFER

In summary, we should realize that, when applying Kioi values determined at high concentrations or derived from LFERs such as Eq. 9-26 (Table 9.2), we may underestimate equilibrium sorption at low concentrations (i.e., below 1% of the compound s solubility) by a factor of 2 or more. Due to competition with other sorbates present in a natural system, the effect of specific adsorption could, however, be significantly attenuated (Chiou et al., 2000). Furthermore, the abundance of specific adsorption sites may be rather low in certain environments. Hence, in cases in which the effect can be expected to be moderate and in which we need only to get an order of magnitude estimate of Kioc, we may decide to neglect the nonlinearity of the isotherm. In other situations, however, such as the PAH case discussed in Illustrative Example 9.3, adsorption to carbonaceous materials or other high-affinity sorbents present in significant abundances has to be taken into account. 

Miermodynamic parameters such as the redox potential are difficult to measure lor discrete surface species at the mineral-water interface. If the surface omplexes are also oxidized by an os mechanism, we may use the LFER in I ijMirc 8 to estimate /. from observed rate constants. The LFER plot translates... 

Large numbers of reactions of interest to chemists only take place in strongly acidic or strongly basic media. Many, if not most, of these reactions involve proton transfer processes, and for a complete description of the reaction the acidities or basicities of the proton transfer sites have to be determined or estimated. These quantities are also of interest in their own right, for the information available from the numbers via linear free energy relationships (LFERs), and for other reasons. 

In the last several years, a set of BBB QSAR models have been developed. One of the top models, developed by Abraham et al. in 2006 [44], reached the predictive limit obtainable from the data set they used. The experimental errors of the logBB measurements were estimated to be 0.3. Their model utilized linear free energy relationship (LFER) as descriptors. For the 328-molecule data set, r2 and RMSE of the MLR model were 0.75 and 0.3 log units, respectively. Interestingly, the RMSE for their test set (n = 164) was even lower (0.25 log units). 

Note that our multiparameter LFER Eq. 5-20 includes two terms that contain a volume term (a quantitative measure of the volume of one mole molecules) as a size parameter ( vdW, size -terms). This Vi value can be the molar volume, Vn of the compound (derived from the molar mass and the density of the compound, see Chapters 3 and 4), or it can be an estimated entity (see Box 5.1). Therefore, we denote this term as Vt and not Vl. We will, however, use the term molar volume even if we refer to estimated Vt values. 

When properly applied, LFERs of these types may be quite useful for estimating Kiow from YiW or QJ (L). Additionally, these relationships can be used to check new Kiovi and/or Cf (L) values for consistency. 

Any attempt to estimate a Kioc value for a compound of interest (with its particular abilities to participate in different intermolecular interactions) should take into account the structural properties of the POM present in the system considered. To this end, the use of multiparameter LFERs such as the one that we have applied for description of organic solvent-water partitioning (Eq. 7-9) would be highly desirable (Poole and Poole, 1999). Unfortunately, the available data do not allow such analyses, largely due to the very diverse solid phase sources from which reported Kioc values have been derived. 

Therefore, for estimates of Kioc s it is more feasible to use compound class-specific LFERs. These include correlations of log Kioc with molecular connectivity indices (or topological indices for an overview see Gawlik et al., 1997), with log Cf (L) (analogous to Eq. 7-11), and with log Kiow. Although molecular connectivity indices or topological indices have the advantage that they can be derived directly from the structure of a chemical, they are more complicated to use and do not really yield much better results than simpler one-parameter LFERs using C (L) or Kmv/ as compound descriptors. 

Apply Eq. 11-12 to estimate the Kiastaf value of an apolar compound with p L = 1 Pa at 15°C by using an apparent vdWsurf value that you can calculate from the slope of the LFER Eq. 2 (slope = 0.135 vdWsurf note that the slope is independent of the units in which the partition constant is expressed) ... 

Owing to the original determination from uv—vis spectral solvatochromic shifts, 7T, B, and QLm are called solvatochromic parameters. General rules for estimation of these variables have been proposed (258). Examples of individual parameter investigations are available (260,261). As previously mentioned, individual LFER—LSER studies are performed on related materials. A common method to link these individual studies to group contribution methods, and thereby expand the applicability, is by expansion of solvatochromic parameters to log—linear relationships, such as... 

From the Hammett equation [Hammett, 1935, 1937], the seminal vork of Hammett gave rise to the a—p culture in the delineation of substituent effects on organic reactions, whose aim was to search for linear free energy relationships (LFER) [Hammett, 1938] steric, electronic, and hydrophobic constants were derived for several substituents and used in an additive model to estimate the biological activity of congeneric series of compounds. 

In fact, several well known models in the literature allow solubilities in water to be estimated reasonably well from a knowledge of log P (and according to the functional groups present). For example, Hansch et al. (1968) has published several linear free energy relationships (LFERs) between molal solubility and log P for various classes of monofunctional molecules. The correlation coefficients for the LFERs (a measure of goodness of fit ) were in the range 0.93-0.99, indicating that solubility estimations, at least for some classes of material, are likely to be relatively accurate. 

Another level involves an analytical procedure which almost matches the users requirements. Perhaps the analyte molecule has a slight structural difference from the stored procedure, requiring a change in the pH of the medium during the analysis. Such slight differences in structure or reaction conditions require that CHESS have the ability to reason. Parameter estimation and calculation can be performed using Linear Free Energy Relationships (LFERs) and other types of additive relationships to predict properties. 

In fact, several well-known models in the literature allow solubilities in water to be estimated reasonably well from knowledge of logP (and according to the functional groups present). For example, Hansch et al. (1968) has published several linear free-energy relationships (LFERs)... 

One can thus use tt values (Table 2.16) to estimate for a compound when an experimental value is not available providing is known for a related compound that differs from the unknown by one or at the most two substituents. For example, if log for anisole (methoxybenzene) is known to be 2.11, one would predict that logiifow for 3-chloroanisole would be 2.11 - - 0.77 = 2.88. This procedure illustrates the concept of linear free energy relations (LFERs) that depends on the fact that the different components of an organic molecule interact both with one another and their environment in a consistent manner and the behavior of the molecule can be defined as the sum of its components. 

Table 6.1 summarizes recommended methods for estimating the dimensionless aerosol particle/air partition coefficient, Kpa, from vapor pressure, Kqa or using pp-LFERs. 

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