Solvent regression analysis

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

In a recent study of twenty disperse and solvent dyes, data for water solubility, octanol/ water partition coefficient, entropy of fusion and melting point were subjected to regression analysis. Complicating factors such as impurities, polymorphism, tautomerism, polarisation and hydrogen bonding precluded the development of reliable predictions of solubility and partition coefficient. Anthraquinone dyes exhibited much lower entropy of fusion than many of the azo dyes [64,65]. 

A typical time profile of the excited PMMA-Phe fluorescence intensity decay is shown in Figure 2. The MEK permeation commences at 24 sec. The SPR increases during the plasticization period until it becomes constant, the onset of the steady state. It is characterized by a linear relationship between the amount of solvent absorbed and time. It was determined from a linear regression analysis that the PMMA-Phe fluorescence intensity starts to deviate from linearity at 197 sec. This indicates a decrease in the SPR and/or the unquenched PMMA-Phe. The decrease in SPR is unexpected at this film thickness since the SPR in thicker PMMA-Phe films show no anomaly at 1 /tm. A more plausible explanation is the reduction in available PMMA-Phe, which is expected when the front end of the SCP reaches the substrate. 

For NO2 the recommended values of am and ap (benzoic acid scale) in the IUPAC document79 are 0.73 and 0.78, respectively, compared with the traditional values of 0.71 and 0.78, respectively (Section III.B). When these values are used for correlations of processes taking place in other than highly aqueous media, the possibility of specific solvent effects should be borne in mind. The fact that the 0 values of NO2 are very much at the upper end of the scale for commonly used substituents means that they exert a strong influence in regression analysis and there is danger of their biassing a correlation unduly. 

Ihrig and Smith extended their study by running a regression analysis including reaction field terms, dispersion terms and various combinations of the solvent refractive index and dielectric constant. The best least squares fit between VF F and solvent parameters was found with a linear function of the reaction field term and the dispersion term. The reaction field term was found to be approximately three times as important as the dispersion term and the coefficients of the terms were opposite in sign. 

Viscometry measurements were made in benzene at 30 °C and in TFE at 50 °C with uncalibrated Cannon-Ubbelohde dilution viscometers which gave solvent times greater than 100 seconds. The viscometers used had centistoke ranges denoted by viscometer sizes of 50 and 75 for benzene and TFE, respectively. Stock solutions were made up on gram solute/100 gram solution basis and converted to gram/deciliter via the solvent density at the temperature of measurement. The solvent densities used were d ene = 0.8686 (11a) and dlra = 1.3429 obtained from pycno-metric measurements (12). The density—temperature relationship for TFE obtained from regression analysis of the experimental pycnometric data is... 

The extensions of the Hildebrand and Hansen approaches are both empirical. Afterthe solubility behavior has been evaluated in a series of solvent systems, regression analysis can be used to estimate the empirical coefLcients, including th fferm of the extended Hansen approach, and then the solubility can be estimated in a solvent system which has not been included in the experimental portion of the study. The problem with acknowledging the predictive power of these equations is that the solubility in many solvents must be determined before being able to predict the solubility in the solvent of choice. It is probably easier to simply perform the solubility study in the solvent of choice and eliminate the prediction equation altogether. On the other hand, in a study of binary solvent systems consisting of water and a cosolvent appropriate to parenteral products, the solubility maximum in that series can be readily estimated by the mathematical expression Lnally achieved. 

Method validation is important to ensure that the analytical method is in statistical control. A method may be validated by the so-called method evaluation function (MEF) (Christensen et al., 1993), which is obtained by linear regression analysis of the measured concentrations versus the true concentrations. A true concentration in a solution can be obtained by use of a high purity standard obtained from another manufacturer or batch than the one used for calibration. Both the high purity standard and the solvent are weighed using a traceable calibrated balance. If certified reference material is available this is preferred. The method evaluation includes the most important characteristics of the method as the following elements (see Figure 2.7) ... 

The interaction energy of the solute with the solvent is not expressed as the geometric mean of cpx and cp2, as shown in Equation (3.13), but as the polynomial power series of the solubility parameter of the solvent. The coefficients of the polynomial equation are determined experimentally by regression analysis. Figure 3.2 shows that the regressed (calculated) solubilities of caffeine in a mixture of water and dioxane are in good agreement with the experimental values. 

Erom an operational standpoint, the LFER, LSER, QSAR, and QSPR approaches can be quite similar, with distinctions based on their applications. QSAR is usually applied to biological properties, especially those important to pharmacology and toxicology. QSPR usually dwells on physicochemical properties in general. LSER focuses on solute-solvent systems. For organizational purposes, we like to view LSER and some applications of QSAR and QSPR (along with related methods) as subsets of LFER. Each approach typically uses some form of regression analysis (statistics) to help find a mathematical relationship between a property and a set of descriptors. 

The subtraetion of the polarization (y-Y) and polarizability p P) eontribu-tions from the total solvent effeet allows an estimation of the eontribution from speeifie solute-solvent interactions. This correction of j(30) values was made using least-squares regression analysis by correlating the data for suitably selected non-specifically and specifically interacting solvents. values derived in this way from j(30) values are presented in references [6, 115] they range from zero (gas phase, saturated hydrocarbons) to about 22 kcal/mol for water. By definition, e = 1 in Eq. (7-50) for the reference process, i.e. the n n transition of the pyridinium A-phenolate betaine dye (44). The reason for assuming that x(30), and thus , largely relates to Lewis acidity in protic solvents has already been mentioned . 

Multiple regression analysis of Ig ki of the strongly solvent-dependent solvolysis/ dehydrohalogenation of 2-chloro-2-methylpropane (t-BuCl) for n = 21 solvents using the KAT equation (7-54) leads to Eq. (7-55b), with r = 0.997, and s = 0.242 [288] ... 

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