Single-parameter approach

Kosower in 1958 was the first to use solvatochromism as a probe of solvent polarity. The relevant Z-scale is based on the solvatochromic shift of 4-methoxycarbonyl-1-ethylpyridinium iodide (1). Later, Dimroth and Reichardt suggested using betain dyes, whose negative solvatochromism is exceptionally large. In particular, 2,6- 

These compounds can be considered as zwitterions in the ground state. Upon excitation, electron transfer occurs from the oxygen atom to the center of the aromatic system. The dipole moment is thus about 15 D in the ground state whereas it is nearly zero in the excited state. 

The fcT( 30) value for a solvent is simply defined as the transition energy for the longest wavelength absorption band of the dissolved pyridinium-N-phenoxide be-tain dye 2 measured in kcal mol-13. An extensive list of fcT(30) values is available (Reichardt, 1988) they range from 30.9 in w-heptane to 63.1 in water. 

Attention should be paid to the additional hydrogen bonding effect in protic solvents like alcohols. It has indeed been observed that correlations of solvent-dependent properties (especially positions and intensities of absorption and emission bands) with the fcT(30) scale often follow two distinct lines, one for non-protic solvents and one for protic solvents. 

Moreover, in many investigations using probes other than betains, the parameter Et(30) has still been used to characterize the solvent polarity. However, a polarity scale based on a particular class of molecules applies, in principle, only to probe molecules that resemble these molecules. 

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Extensive use of the three-dimensional solubility parameters for predicting adhesion seems not to have been made, although its additional flexibility should make it successful over a wider range of conditions than the single-parameter approach. Some recent studies involving dental adhesion employed the method with success. Asmussen and Uno fl40 successfully correlated the shear bond strength of various dental adhesive resins, characterized in terms of their three-... 

In Section II, devoted to intermolecular processes, it appeared that most of the quantitative analysis of steric effects was made using a single parameter approach. However, analysis has shown that a correct description of the size of a substituent rests on its preferred conformational states, which are related to the interactions with both the planar heteroaromatic ring to which it is bonded and neighboring groups. This was the topic of Section III. 

Though satisfying from a numerical point of view, correlation (35) disregards an essential physical effect associated with the constitutional isomerism in allenes and must be subjected to a criticism which has been given in connection with Equation 8. Any numerical improvement of the preceding correlation (35) using instead of a single-parameter approach a dual-substituent parameter (DSP) approach (2,4) also buries these physical problems. 

As a first try, we may consider a single parameter approach, as used by Heitzmann, in which all the recirculation ratios are the same Rj = R for every i. Figure 6-a shows an... 

The special appeal of this approach is that it allows the heat of mixing to be estimated in terms of a single parameter assigned to each component. This considerably simplifies the characterization of mixing, since m components (with m 6 values) can be combined into m(m - l)/2 binary mixtures, so a considerable data reduction follows from tabulating 6 s instead of AH s. Table 8.2 is a list of CED and 6 values for several common solvents, as well as estimated 6 values for several common polymers. 

This approach is useful when dealing with relatively simple partial differential equation models. Seinfeld and Lapidus (1974) have provided a couple of numerical examples for the estimation of a single parameter by the steepest descent algorithm for systems described by one or two simultaneous PDEs with simple boundary conditions. 

The variance approach may also be used to determine n. From Illustration 11.2 the variance of the response data based on dimensionless time is 30609/(374.4)2, or 0.218. From equation 11.1.76 it is evident that n is 4.59. Thus the results of the two approaches are consistent. However, a comparison of the F(t) curves for n = 4 and n = 5 with the experimental data indicates that these approaches do not provide very good representations of the data. For the reactor network in question it is difficult to model the residence time distribution function in terms of a single parameter. This is one of the potential difficulties inherent in using such simple models of reactor behavior. For more advanced methods of modeling residence time effects, consult the review article by Levenspiel and Bischoff (3) and textbooks written by these authors (2, 4). 

It is important to remember that absolute oral bioavailability is a function of both absorption and first-pass metabolism. Therefore, a linear approach to predicting absolute oral bioavailability based on a single parameter, such as rate or extent of absorption (fraction of dose absorbed or estimated dose absorbed) or the rate of metabolism (microsomal or hepatic intrinsic clearance), may result in an inaccu-... 

The basis for the foam properties is given by interfacial parameters. Although correlations have been shown between a single parameter and foam properties, there is still a lack in a general correlation between interfacial properties and the foam behavior of complex systems in detergency. The simplest approach to correlate interfacial parameters to foam properties is the comparison of the surface activity measured by the surface tension of a surfactant system and foam stability. 

Staikova, M., Wania, F., Donaldson, D. J. Molecular polarizability as a single-parameter predictor of vapour pressures and octanol-air partitioning coefficients of non-polar compounds A priori approach and results. Atmos. Environ. 2004, 38, 213-225. 

Many different approaches have been reported in the last decade toward a better understanding of the medium factors that influence reaction rates. Fundamental studies have been devoted to probe the reaction at a microscopic level in order to obtain information on the nature of several specific solvent-solute interactions on S Ar and to attempt a description of these effects quantitatively. Recent works have shown the wide applicability of a single parameter scale such as the Ex(30) Dimroth and Reichardt37, as well as other multi-parameter equations. 

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