Titration curves sigmoid

Figure 17-5 Sigmoidal titration curves will allow you to determine the titer of an antibody.

In this chapter and several that follow, we deal exclusively with sigmoidal titration curves. We explore linear-segment curves in Section 26A-5. 

The vertical axis in a sigmoidal titration curve is either the p-function of the analyte or reagent or the potential of an analyte- or reagent-sensitive electrode. 

Paramount to the experimental setup is the purpose of the calorimetric titration that is, whether the association constant and stoichiometry along with the standard enthalpy are to be determined or only the latter is the final goal. Such decision dictates the selection of the dimensionless c-value (7), which should lie within a span from 5 to 500 in order to render the titration curve sigmoidal. In this case, the step height between the asymptotic values at 0 and CX3 with respect to the molar ratio axis is read from a nonlinear least-square fit of the experimental data points and represents the standard enthalpy A 77°. The position of the inflection point in the sigmoidal titration curve defines the association stoichiometry, whereas the slope of the curve at this point translates as the association constant, which can be converted into the free energy AG° (1). 

The titration curve in Figure 9.1 is not unique to an acid-base titration. Any titration curve that follows the change in concentration of a species in the titration reaction (plotted logarithmically) as a function of the volume of titrant has the same general sigmoidal shape. Several additional examples are shown in Figure 9.2. 

Various pH sensors have been built with a fluorescent pH indicator (fluorescein, eosin Y, pyranine, 4-methylumbelliferone, SNARF, carboxy-SNAFL) immobilized at the tip of an optical fiber. The response of a pH sensor corresponds to the titration curve of the indicator, which has a sigmoidal shape with an inflection point for pH = pK , but it should be emphasized that the effective pKa value can be strongly influenced by the physical and chemical properties of the matrix in which the indicator is entrapped (or of the surface on which it is immobilized) without forgetting the dependence on temperature and ionic strength. In solution, the dynamic range is restricted to approximately two pH units, whereas it can be significantly extended (up to four units) when the indicator is immobilized in a microhetero-geneous microenvironment (e.g. a sol-gel matrix). 

The pH is an important factor that can influence the ionization of the surface silica groups. As a result, C is directly dependent on the pH. Therefore, the relationship of /teof as a function of pH is governed by the behavior of the dissociation of the silanol groups. Different capillary materials result in different profiles of the electroosmotic mobility as a function of the pH (due to differences in Q. Typically a sigmoid curve behavior resembling the titration curve of the surface active groups is observed. ... 

The combination of Equations 15.7 and 15.8 represents the net retention factor as a function of pH and results in a sigmoid curve with the same form as an acid-base titration curve. 

Logarithmic titration curve — A sigmoidal shaped titration curve in which the -> cell voltage or a -> p-function of the titrand or - titrant is plotted as a func-... 

A second approach is to calculate the change in potential-per-unit change in volume in reagent (AE/AV). By inspection, the endpoint can be located from the inflection point of the titration curve. This is the point that corresponds to the maximum rate of change of cell emf per unit volume of titrant added (usually 0.05 or 0.1 mL). The first-derivative method is based on the sigmoid shaped curve. 

The end point can be taken as the inflection point of the titration curve. With a sigmoid-shaped titration curve, the inflection point is the steepest part of the titration curve where the pH change with volume is a maximum. This can be estimated visually from the plot or by using calculus to find the first and. second derivatives of the titration curve. The first derivative, ApH/AK gives the slope of the titration curve. It goes from nearly zero far before the end point to a maximum at the end point back to zero far beyond the end point. We can differentiate a second time to locate the maximum of the first derivative, since the slope of the first derivative... 

The FV data acquired are analyzed as sketched in the examples above. The pull-off force values for each f-d curve are estimated and a histogram of forces for each pH and treatment condition is calculated. In Fig. 4.11 some normalized force titration curves (average pull-off force as a reference of value at pH 4 versus pH) on flame treated LDPE are shown. These titration curves display a typical sigmoidal shape, while the untreated polymer exhibited by contrast an almost constant pull-off force over the entire pH range. 

A is the surface area, and t is time. A sigmoidal curve, reminiscent of a titration curve, was obtained when the initial rate of monolayer contraction, Rif was plotted as a function of pH (23). The apparent pKa, estimated from the midpoint of the sigmoidal curve, depended on the chain length and the degree of unsaturation of the fatty acid. The apparent pKa always exceeded the pKa for soluble carboxylic acids. 

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