Negative slope

The concentration of fluoride in drinking water may be determined indirectly by its ability to form a complex with zirconium. In the presence of the dye SPADNS, solutions of zirconium form a reddish colored compound, called a lake, that absorbs at 570 nm. When fluoride is added, the formation of the stable ZrFe complex causes a portion of the lake to dissociate, decreasing the absorbance. A plot of absorbance versus the concentration of fluoride, therefore, has a negative slope. 

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

Fig. 2. PT diagram for a pure substance that expands on melting (not to scale). For a substance that contracts on melting, eg, water, the fusion curve. A, has a negative slope point / is a triple state point c is the gas—Hquid critical state (—) are phase boundaries representing states of two-phase equiUbrium ...

FIG. 22-55 Typical capital-cost schematic for membrane equipment showing trade-off for membrane area and mechanical equipment. Lines shown are from families for parallel hues showing hmiting costs for membrane and for ancillary equipment. Abscissa Relative membrane area installed in a typical membrane process. Minimum capital cost is at 1.0. Ordinate Relative cost. Line with positive slope is total membrane cost. Line with negative slope is total ancillary equipment cost. Curve is total capital cost. Minimum cost is at 1.0. 

Plotting the heat demand against T should produce a straight line with a negative slope coefficient. 

The microphase separation of an amphiphilic polyelectrolyte is clearly reflected in the viscosity behavior of its aqueous solution. As a representative example, Fig. 5 shows the reduced viscosities of ASt-x with different styrene (St) content plotted against the polymer concentration in salt-free aqueous solution [29], The AMPS homopolymer and its copolymers with low St content exhibit negative slopes, which is the typical behavior of polyelectrolytes in the concentration range shown in Fig. 5. With increasing St content, however, the slope systematically decreases and eventually turns to be slightly positive, while reduced viscosity itself markedly decreases. These data indicate that, with increasing St content, the... 

The graphical presentation of the equation shows a straight line with a negative slope for kA. As the death rate constant follows Arrhenius law,1 the death rate constant is temperature dependent. The value of kA is about 0.02 min 1 at 100 °C, the death rate constant increases by 10-fold at 110 °C and 100-fold at 120 °C.2... 

If the rate is measured at several temperatures, in most cases a plot of In k against T (T stands for absolute temperature) is nearly linear with a negative slope, and fits the equation... 

Fig. 1. Methods of Huggins (positive slope), Kraemer (negative slope) (a), Schulz-Blaschke (b), and Martin (c). Data obtained from experimental measures for gelatin B at 37.4°C.

Data Analysis Because of the danger of false conclusions if only one or two parameters were evaluated, it was deemed better to correlate every parameter with all the others, and to assemble the results in a triangular matrix, so that trends would become more apparent. The program CORREL described in Section 5.2 retains the sign of the correlation coefficient (positive or negative slope) and combines this with a confidence level (probability p of obtaining such a correlation by chance alone). 

Negative slopes are flagged an W is to be interpreted in the sense that the slope is negative, and J decreases as I increases positive slopes remain unmarked. 

Rodbard and Chrambach [77,329] developed a computer program that allows the determination of molecular parameters, i.e., free mobility, molecular radii, molecular weight, and charge or valence, from measured electrophoretic mobilities in gels with different monomer concentrations. For a set of mobility versus gel concentration data they used the Ferguson [18,115,154] equation to obtain the retardation constant from the negative slope and the free mobility from the extrapolated intercept. From the retardation constant they determined the molecular radius using... 

Figure 3.10 Illustrative example of linear regression between two artificial variables for six experimental units. For each unit, denoted by a different graphical symbol, a closely packed set of five observations with negative slope is measured. The whole data set, if fitted naively, would show a very significant positive slope.

Eq. (44)). In Eig. 20, we show the result of this approximation for reasonable a = 1 and cOc = 2 a/ Q )D- Even though these curves resemble the experimental data better than in the previous figure, they do not really provide more material support for the theory than the earlier method. This discussion simply demonstrates that the basic estimates are robust enough to survive different levels of treatment. Also, curiously, these curves reflect the experimental tendency that the higher T plateaus seem to have a more negative slope as compared to the low T ones (see Fig. 1), which was less obvious in Fig. 19. 

---