CT values

In exposures by inhalation of airborne materials, the dose is the concentration multiplied by the time (CT), and is roughly a constant for any given material and specified effect. The CT value can be used to provide a rough approximation of other combinations of concentration and time which would have about the same effect. Although this concept must be used very cautiously and cannot be applied at extreme conditions of either concentration or time, it is most important in setting limits for airborne contaminants and physical agents in respect to environmental exposures. The worker is exposed for various periods of time, day after day, to the... 

Probably the most important development of the past decade was the introduction by Brown and co-workers of a set of substituent constants,ct+, derived from the solvolysis of cumyl chlorides and presumably applicable to reaction series in which a delocalization of a positive charge from the reaction site into the aromatic nucleus is important in the transition state or, in other words, where the importance of resonance structures placing a positive charge on the substituent - -M effect) changes substantially between the initial and transition (or final) states. These ct+-values have found wide application, not only in the particular side-chain reactions for which they were designed, but equally in electrophilic nuclear substitution reactions. Although such a scale was first proposed by Pearson et al. under the label of and by Deno et Brown s systematic work made the scale definitive. 

The total experimental material known to the present authors is summarized in Table I. Unfortunately, few of the data presented come from the most thoroughly studied and best documented reaction series. However, the picture is quite discouraging. Very likely, separate a - and normal ct-values and, possibly further, a separate CT+-value might be applicable for the 2- and 4-aza groupings since resonance structures such as 2-4 may contribute in appropriate systems, although 4 may not be too important, and, consequently. 

CT+-values may not differ too widely from ct-values. Since the charges in 2 and 4 actually reside in the ring, the pyridine system may, in addition, be particularly subject to the variability of cr-values, and consequently a careful analysis of some rather extensive material in the sense of some of the most refined methods might be very profitable... 

Closely related to the basicity of pyridine is its hydrogen-bonding ability two indices of this property have been measured for a very short series of substituted pyridines and are very well correlated by CT-values. ... 

Charton has recently examined substituent effects in the ortho position in benzene derivatives and in the a-position in pyridines, quinolines, and isoquinolines. He concludes that, in benzene derivatives, the effects in the ortho position are proportional to the effects in the para position op). However, he finds that effects of a-sub-stituents on reactions involving the sp lone pair of the nitrogen atoms in pyridine, quinoline, and isoquinoline are approximately proportional to CT -values, or possibly to inductive effects (Taft s a ). He also notes that the effects of substituents on proton-deuterium exchange in the ortho position of substituted benzenes are comparable to the effects of the same substituents in the a-position of the heterocycles. 

Finally, two sets of physical properties have been correlated by the Hammett equation. Sharpe and Walker have shown that changes in dipole moment are approximately linearly correlated with ct-values, and Snyder has recently correlated the free energies of adsorption of a series of substituted pyridines with u-values. All the reaction constants for the series discussed are summarized in Table V. 

Shindo studied the hydrogen-bonding ability of a fairly long series of substituted pyridine 1-oxides with methanol in chloroform solution and found that the OH frequency of the hydrogen-bonded OH group in methanol is well correlated with the <7-values. For four compounds, the intensity of the same band is also well correlated. In a similar study the OH frequencies of phenol vary monotonically with the CT-values, but not in a linear fashion. 

The value of p was set at 1.00 for ionization of XC6H4CO2H in water at 25°C. The parameters a and Cp values were then calculated for each group (for a group X, a is different for the meta and para positions). Once a set of a values was obtained, p values could be obtained for other reactions from the rates of just two X-substituted compounds, if the a values of the X groups were known (in practice, at least four well-spaced values are used to calculate p because of experimental error and because the treatment is not exact). With the p value thus calculated and the known ct values for other groups, rates can be predicted for reactions that have not yet been run. 

The CT values are numbers that sum up the total electrical effects (resonance plus field) of a group X when attached to a benzene ring. The treatment usually fails for the ortho position. The Hammett treatment has been applied to many reactions and to many functional groups and correlates an enormous amount of data quite well. Jaffe s review article lists p values for 204 reactions, many of which have different p values for different conditions. Among them are reactions as disparate as the following ... 

The only groups in Table 9.5 with negative values of CT/ are the alkyl groups methyl and tert-butyl. There has been some controversy on this point. One opinion is that CT/ values decrease in the series methyl, ethyl, isopropyl, /ert-butyl (respectively, — 0.046, —0.057, —0.065, —0.074). Other evidence, however, has led to the belief that all alkyl groups have approximately the same field effect and that the a/ values are invalid as a measure of the intrinsic field effects of alkyl groups. Another attempt to divide ct values into resonance and field contributions is that of Swain and Lupton, who have shown that the large number of sets of ct values (cTm, <3p, a, a+, CT/, csp etc., as well as others we have not mentioned) are not entirely independent and that linear combinations of two sets of new values F (which expresses the field-effect contribution) and R (the resonance contribution) satisfactorily express 43 sets of values. Each set is expressed as... 

The use of Ct values also expands the dynamic range of quantitation because data are collected for every PCR cycle. A linear relationship between Ct and initial DNA amount has been demonstrated over flve orders of magnitude, compared with the one or two orders of magnitude typically observed with an endpoint assay. 

This difference is clearly shown by the p/CTS values plotted in Fig. 4, which are calculated from the extensive data for ester cleavage by /3-CD (Tables A5.2 and A5.3) accumulated by Fujita and coworkers (Matsui et al., 1985 Fujita, 1988). For m-alkyl and halogen substituents there is a good... 

Fig. 8 Plots of half-lives for deglycosylation rates of 8-/>-X-Ph-dG adducts versus Hammett CT+ values in 0.1 N HCl at 37.2°C (a) and 0.05 M citrate buffer (pH = 4.0), /i = 0.31 M NaCl at 48.4°C (b). The X-substituent of the phenyl ring is identified next to its data point.

Acid-base equilibrium constants have been used to calculate the a-values of azoles as substituents on an aromatic ring or on an aliphatic chain. An example of this last case is the determination of ct, values of 1- (acetic acids 740,741, and 721 (Table 11-5) (82KGS264). 

Another attempt to divide a values into resonance and field contributions511 is that of Swain and Lupton, who have shown that the large number of sets of ct values (linear combinations of two sets of new values F (which expresses the field-effect contribution) and R (the resonance contribution) satisfactorily express 43 sets of values.19 Each set is expressed as... 

Electrophilic chlorination of quinoline under neutral conditions occurs in the orientation order 3 > 6 > 8. Hammett ct+ values predict an order for electrophilic substitution of 5 > 8 = 6 > 3. The reactivity order can be affected by substitution of an electron-withdrawing group in the benzene ring, which directs the chlorination to the pyridine ring. Thus, NCS in acetic acid or sulfuryl chloride in o-dichlorobenzene converts 8-nitroquinoline into 3-chloro-8-nitroquinoline in high yield (91M935). 

Calculate CD and CT values from their respective absorbances, but express the results as extinction values, using the following equation ... 

Spectrophotometric measurements of CD and CT values in oils or lipid extracts requires 45 min depending on the number of samples to be analyzed. The classical PV determination requires a bit of ti me for preparation of reagents and standardization of the sodium thiosulfate solution. The analysis itself is not very time consuming ( 30 min), but in all, about 3 to 3.5 hr should be anticipated. The FOX method has an assay time of < 10 min however, with sample preparation and time to construct the calibration curve, 2 to 3 hr should be expected. 

We will first concentrate on the illumination cone. A spherical wavefront is emitted in all directions from a point source (A) and expands with the speed of light. In our chosen coordinate system, which is limited to only two space coordinates and one time coordinate, this phenomenon is represented by a cone with its apex at A, expanding in the direction of the positive time axis. The passing of time is represented by cross sections of the cone by planes parallel to the x-y plane at increasing ct values (Fig. 2). These intersections will, when projected down to the x-y plane, produce circles of increasing radius that in our 3D world represent the expanding spherical wavefront from the point source at A. As time increases, the circles around A expand, while those around B contract. The ellipses caused by the intersection of those circles stay fixed and unchanged as explained later, in Section IV. 

Ability to detect residual for disinfection Good Poor cannot calculate CT value for disinfection credit... 

Computed tomography offers a great potential for nondestructive studies of transport phenomena in foods. For example, accurate quantification of salt concentration in cured pork was made by computed tomography relating the CT values to the chemical analysis of salt (Vestergaard et al., 2004). 

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