P-scales

Figure C-1. Pressure-impulse diagram for lung injury. P scaled overpressure. / scaled impulse. (Bowen et al. 1968).

Measures of potency are log normally distributed. Only p-scale values (i.e., pEC50) should be used for statistical tests. 

Log normal distribution, the distribution of a sample that is normal only when plotted on a logarithmic scale. The most prevalent cases in pharmacology refer to drug potencies (agonist and/or antagonist) that are estimated from semilogarithmic dose-response curves. All parametric statistical tests on these must be performed on their logarithmic counterparts, specifically their expression as a value on the p scale (-log values) see Chapter 1.11.2. 

The susceptibility or mixing coefficients, pj and pj , depend upon the position of the substituent (indicated by the index, /) with respect to the reaction (or detector) center, the nature of the measurement at this center, and the conditions of solvent and temperature. It has been held that the p/scale of polar effects has wide general applicability (4), holding for substituents bonded to an sp or sp carbon atom (5) and, perhaps, to other elements (6). The or scale, however, has been thought to be more narrowly defined (7), holding with precision only for systems of analogous pi electronic frameworks (i.e., having a dependence on reaction type and conditions, as well as on position of substitution). 

PROS REJECT jcls Section 3.6, Fig. 1.29 In a production environment there are often several superimposed processes that yield measurement series like that depicted in the lower panel there is drift that unexpectedly changes slope, there is bias and measurement noise, and there are operators who take corrective action. The model includes the probability of drift occurring and a feed-back loop that permits both positive and negative coefficients. The operators can be ordered to react if a single value exceeds a set limit, or only if 2, 3, or more successive values do so. The program calculates the two-sided (asymmetric) total probability of a value being OOS and depicts this in the upper panel on a log(p) scale. The red horizontal is the upper limit on the total risk as set in cell B20. 

Witkin, A. P., Scale space filtering A new approach to multi-scale description. In Image Understanding (S. Ullman and W. Richard, eds.), pp. 79-95. Ablex, Norwood, NJ, 1983. 

The P scale of solvent polarity is based on a combination of gas-liquid partition coefficients reported by Rohrschneider [43]. 

In case of fast gradient (below 15 min), S could be considered constant for all the investigated molecules and wiU only have a small influence on the retention time of the compounds. Thus, the gradient retention times, of a calibration set of compounds are linearly related to the ( )o values [39]. Moreover, Valko et al. also demonstrated that the faster the gradient was, the better the correlation between t, and < )o [40]. Once the regression model was established for the calibration standards, Eq. 8 allowed the conversion of gradient retention times to CHI values for any compound in the same gradient system. Results are then suitable for interlaboratory comparison and database construction. The CH I scale (between 0 and 100) can be used as an independent measure of lipophilicity or also easily converted to a log P scale. 

HPLC log P techniques, first described by Mirrlees et al. [374] and Unger et al., [375], are probably the most frequently used methods for determining log/1. The directly measured retention parameters are hydrophobicity indices, and need to be converted to a log P scale through the use of standards. The newest variants, breadths of scope, and limitations have been described in the literature [292-298]. A commercial automated HPLC system based on an extension of the approach described by Slater et al. [150] has just introduced by Sirius (www. sirius-analytical. com). 

Figure 11 MCT P-scaling for the amplitudes of the von Schweidler laws fitting the plateau decay in the incoherent intermediate scattering function for a R value smaller than the position of the amorphous halo, q = 3.0, at the amorphous halo, q = 6.9, and at the first minimum, q = 9.5. Also shown with filled squares is the P time scale. All quantities are taken to the inverse power of their predicted temperature dependence such that linear laws intersecting the abscissa at Tc should result. 

Crook, M.A., Johnson, P., Scales, B Eds. (1972). Liquid Scintillation Counting. Heyden Son, London. 

Attempts have also been made to separate non-specific effects of the local electrical field from hydrogen-bonding effects for a small group of ionic liquids through the use of the K scale of dipolarity/polarizability, the a scale of hydrogen bond donor acidity, and the P scale of hydrogen bond basicity (see Table 3.5-1) [13, 16]. 

For reviews, sec Abraham Doherty Kamlet Taft Chem. Br. 1986, 551-554 Kamlet Abboud Taft Prog. Phys. Org. Chem. 1981,13, 485-630. For a comprehensive table and a and p values, see Kamlet Abboud Abraham Taft J. Org. Chem. 1983, 48, 2877. For a criticism of the p scale, see Laurence Nicolet Helbert J. Chem. Soc., Perkin Trans. 2 1986, 1081. See also Nicolet Laurence Lugon J. Chem. Soc., Perkin Trans. 2 1987, 483 Abboud Roussel Gcntric Sraidi Lauransan Guihgncuf Kamlet Taft./. Org. Chem. 1988,53, 1545 Abraham Grcllier Prior Morris Taylor J. Chem. Soc., Perkin Trans. 2 1990, 521. 

The p excess extensities f(KX) are scale factors of the composite system, which may be exhibited in a p x p scale-factor matrix D defined by... 

Ftotal can be expressed in terms of three independent variables p, and r/ and requires the specification of model parameters iVA, /Vn, NH, x. n and r. Calculations by Leibler et at. (1983) showed that for small incompatibility, p scales as N° 6, and RB N0. Under conditions of strong segregation, for the case of symmetric diblocks considered by them, Leibler et at. (1983) found that the cmc depends exponentially on y NA = %NB, for a fixed homopolymer degree of polymerization. 

Matsuo, Nozaki, and Jyo (20) showed that heterogeneity at 100 A scale and under can be detected readily. Thus, microscopy can offer a measure of heterogeneity down to 0.01 p scale which is much smaller than the domain size of most polyblends. Results of microscopy have established convincingly that nearly all polyblends are heterogeneous two-phase systems. How does one describe the results Obviously, heterogeneity as revealed by microscopy is a relative property. If compatibility is used in a qualitative sense, a polyblend with a finer domain size will be more compatible than one with a larger size, provided equilibrium size distribution has been attained in both cases. 

It was later shown by Laurence and coworkers that there are significant systematic differences between P values of solvents obtained with indicators with an oxygen donor atom and those with a nitrogen donor atom (Nicolet and Laurence 1986). These authors recommended the use of a single indicator, preferably 4-nitrophenol relative to 4-nitroanisole or else 4-nitroaniline relative to 4-nitro-N,N-di/rae%>/aniline (rather than 4-nitro-N,N-die// y/aniline used by Kamlet and Taft 1976), to establish a basicity scale. The main point of difference is with respect to solvents that do not have an oxygen donor atom, such as amines, pyridines, and sulfides. In order to save the P scale, Kamlet and Taft proposed a family-dependent covalency parameter, equal to -0.20 for P=0 bases, 0.00 for C=0, S=0, and N=0 bases, 0.20 for -O-bases, 0.60 for pyridines, and 1.00 for amines, for use in linear free energy relationships (Kamlet etal. 1985). 

Many other scales of electron-pair donation abilities have been proposed over the years, which are in general in good correlation with DN e g., the heat of complexation of the solvent molecules with boron trifluoride in dichloromethane (Maria and Gal 1985), and P e.g., SB, the solvatochromism of 5-nitroindoline compared with l-methyl-5-nitroindoline in neat solvents (Catalan el al. 1996) scales. The latter, the SB scale, has the advantage that the N-H acid function of the 5-nitroindoline probe has only a single hydrogen atom, contrary to the nitroanilines used for the P scale, that have two. It was devised quite recently for... 

Another property that characterizes solvents is their softness, in terms of the HSAB concept (Pearson 1963), according to which the interactions of soft solvents are strongest with soft solutes, of hard solvents with hard solutes, but are weaker for hard solvents with soft solutes and vice versa. The applicability of the softness property takes into account that it is superimposed on the more general electron pair donation property discussed above. In fact, it can replace (Marcus 1987) the notion of the family dependence of the P scale, expressed by the , parameter (Kamlet etal. 1985). A few quantitative scales have been... 

For a reliable choice of pairs hydrides, and also for designing hydrides it would be desirable to have universal P-C-T dependence for hydrides. In the literature there is semi-empirical equation for equilibrium P-C-T of dependences [4] where the data are generalized with use of function of free energy RTLn(P/PXI) (where P - scale of pressure for reference composition XT, for example, taken in the middle a plateau of an isotherm of P-C). The given function reduces isotherms for various temperatures on one curve. Thus branches of isotherms of absorption and desorption can agree with a suitable choice of reference pressure PXI. For... 

Physical organic chemists have tended to examine parameters based on shifts in the absorption peaks in the spectra of various dyes or indicator molecules. The a and P scales of Taft and Kamlet, the ET(30) scale of Dimroth and Reichardt, the 7t scale of Taft and co-workers and the Z value of Kosower are all examples of this type of parameter. The definitions and measurement means for these parameters, as well as important references, are shown in Table 5. An alternative definition of the Dimroth-Reichardt parameter is the dimensionless, ETN, which is now preferred by some organic chemists (for a discussion see Ref. 15). The Z value is important in that it led to the scale of Dimroth and Reichardt, which overcomes many of the limitations of the earlier scale. Several workers have shown that relationships exist, with good correlation coefficients, between similar parameters. Thus, DN is linearly related to p, both parameters being designed to measure the donor properties (or Lewis basicity) of solvent molecules. Also, Lr(30) is related to a as well as to AN all three parameters purport to measure the electron acceptor properties (or Lewis acidity) of solvent molecules. It has been found that different solvent types have different coefficients in linear relationships between n and the dipole moment. The Taft and Dimroth-Reichardt parameters, in particular, have been found to correlate with free energies and... 

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