Partition coefficients experimental methods

Table 4-3, with partition coefficient estimation results for 13 aroma compounds partitioned between polyethylene (PE) and ethanol, shows an example of the estimation accuracy one can expect comparing UNIFAC to experimental data and the other partition coefficient estimation methods (Baner, 1999). In order to compare the different estimation methods, average absolute ratios of calculated to experimental values were calculated partitioned substances. When the calculated values are greater than experimental values the calculated value is divided by the experimental value. For calculated values less than the experimental values the inverse ratio is taken. Calculating absolute ratios gives a multiplicative factor indicating the relative differences between values of the experimental and estimated data. A ratio of one means the experimental value is equal to the estimated value. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

A sampling of appHcations of Kamlet-Taft LSERs include the following. (/) The Solvatochromic Parameters for Activity Coefficient Estimation (SPACE) method for infinite dilution activity coefficients where improved predictions over UNIEAC for a database of 1879 critically evaluated experimental data points has been claimed (263). (2) Observation of inverse linear relationship between log 1-octanol—water partition coefficient and Hquid... 

However, as stated above, the partition coefficients measured by the shake-flask method or by potenhometric titration can be influenced by the potenhal difference between the two phases, and are therefore apparent values which depend on the experimental condihons (phase volume ratio, nature and concentrahons of all ions in the solutions). In particular, it has been shown that the difference between the apparent and the standard log Pi depends on the phase volume raho and that this relationship itself depends on the lipophilicity of the ion [80]. In theory, the most relevant case for in vivo extrapolation is when V /V 1 as it corresponds to the phase ratio encountered by a drug as it distributes within the body. The measurement of apparent log Pi values does not allow to differentiate between ion-pairing effect and partihoning of the ions due to the Galvani potential difference, and it has been shown that the apparent lipophilicity of a number of quaternary ion drugs is not due to ion-pair partitioning as inihally thought [80]. 

Although experimental partition coefficients are the values of reference, drug design often necessitates log evaluations before the compound has been synthesized. Consequently, various methods have been developed to predict lipophilicity [188], and they generally apply only to neutral compounds in the water-OCT system. 

The advantage of using the time lag method is that the partition coefficient K can be determined simultaneously. However, the accuracy of this approach may be limited if the membrane swells. With D determined by Eq. (12) and the steady-state permeation rate measured experimentally, K can be calculated by Eq. (10). In the case of a variable D(c ), equations have been derived for the time lag [6,7], However, this requires that the functional dependence of D on Ci be known. Details of this approach have been discussed by Meares [7], The characteristics of systems in which permeation occurs only by diffusion can be summarized as follows ... 

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

The experimental approaches are similar to those for solubility, i.e., employing shake flask or generator-column techniques. Concentrations in both the water and octanol phases may be determined after equilibration. Both phases can then be analyzed by the instrumental methods discussed above and the partition coefficient is calculated from the concentration ratio Q/Cw. This is actually the ratio of solute concentration in octanol saturated with water to that in water saturated with octanol. 

A wide variety of solubilities (in units of g/m3 or the equivalent mg/L) have been reported. Experimental data have the method of determination indicated. In other compilations of data the reported value has merely been quoted from another secondary source. In some cases the value has been calculated. The abbreviations are generally self-explanatory and usually include two entries, the method of equilibration followed by the method of determination. From these values a single value is selected for inclusion in the summary data table. Vapor pressures and octanol-water partition coefficients are selected similarly. 

The physical properties of -hexane (see Table 3-2) that affect its transport and partitioning in the environment are water solubility of 9.5 mg/L log Kow (octanol/water partition coefficient), estimated as 3.29 Henry s law constant, 1.69 atm-m3 mol vapor pressure, 150 mm Hg at 25 °C and log Koc in the range of 2.90 to 3.61. As with many alkanes, experimental methods for the estimation of the Koc parameter are lacking, so that estimates must be made based on theoretical considerations (Montgomery 1991). 

In systems where only dynamic quenching occurs, then steady-state fluorescence intensities can be measured instead of lifetimes/101 103-,07) In experiments where comparisons are being made (i.e., for a comparison of different experimental conditions or types of membrane), it is important that the lifetime of the fluorophore (r0) is not affected by the experimental conditions. Fluorescence intensities can be obtained much more rapidly and without specialized instrumentation. Blatt and Sawyer(101) have employed a relationship essentially the same as Eq. (5.20) in this way. They have pointed out that since the quenching mechanism is collisional, the partition coefficient that is derived is a partition coefficient of the quencher into the immediate environment of the fluorophore and is therefore a local Kp. It is therefore possible to investigate the partition coefficient gradient across the lipid bilayer by using a series of probes, such as the anthroylstearates,(108) located at different depths. In their method, Eq. (5.20) has the form... 

The use of distribution coefficients for the QSAR treatment of ionizable compounds has been extended to consideration of ion-pair partitioning into biolipid phases. Two experimental methods for determining ion-pair partition coefficients are described. One is a single-phase titration in water-saturated octanol, in which case (for acids) log Pj = log P + pKa - pKa. The other is a two-phase titration (octanol/water) from which the ratio (P + 1)/(Pj + 1) can be calculated. An example outcome is that the uncoupling activity of phenols can be represented by an equation in log instead of log D and pKa. 

Among the large number of existing lipophilicity parameters [31], the descriptor frequently estimated by in silica methods is the partition coefficient of a solute between 1-octanol and water, expressed as log Poet [32]. However, lipophilicity determination in different solvent systems, such as alkane/water system, proved its utility in (Q)SAR studies and therefore some predictive methods also emerged in this field. Many publically available databases include numerous experimental values collected through the literature the quality of the experimental data represents the cornerstone of most of the models developed to predict lipophilicity. 

The LFER approach of Abraham was the most powerful method to predict partition coefficients in varied experimental conditions (for example, see [68-72]). In particular, since 1,2-dichloroethane and o-nitrophenyl octyl ether are good experimental substitutes for alkane, in silico tools were developed with LFER equations to predict log Pdce [73] or log Pnpoe [74, 75]. 

It is interesting to note that various QSAR/QSPR models from an array of methods can be very different in both complexity and predictivity. For example, a simple QSPR equation with three parameters can predict logP within one unit of measured values (43) while a complex hybrid mixture discriminant analysis-random forest model with 31 computed descriptors can only predict the volume of distribution of drugs in humans within about twofolds of experimental values (44). The volume of distribution is a more complex property than partition coefficient. The former is a physiological property and has a much higher uncertainty in its experimental measurements while logP is a much simpler physicochemical property and can be measured more accurately. These and other factors can dictate whether a good predictive model can be built. 

The isolation method of solvent extraction has been suggested as a potentially feasible process to concentrate trace organic compounds from finished drinking water (4). One positive attribute of the solvent extraction method is that its performance for any given compound is theoretically predictable from a partition coefficient of a compound between the water sample and an organic solvent. The partition coefficient can be experimentally determined for any solute in any two-phase solvent system (7, 8). Variables of the extraction procedure such as solvent-to-water ratio and the choice of solvents can be adjusted to achieve optimum recovery. 

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