Methods Equivalent to Titration

A few methods may produce PZCs equivalent to those obtained by potentiometric titration (with or without correction for acid or base associated with solid particles). There are a limited number of such methods, although some of them have been re-invented several times, and given different names. Only a few of these names are used in the tables in Chapter 3. The methods that produce results 

The terms batch equilibration [653], pH drift method [654], addition method [552], solid addition method [655], powder addition method (cited in [656] after [654]), potentiometric titration [234] ( sic —in the present book, the term potentiometric titration is reserved for a different method, described in Section 2.5), and salt addition [573] ( sic —in the present book, the term salt addition is reserved for a different method, described later in this section) refer to the same method, which is now described. A series of solutions of different pHs is prepared and their pHs are recorded. Then, the powder is added and the final pH is recorded. The addition of a solid induces a shift in the pH in the direction of the PZC. The pH at which the addition of powder does not induce a pH shift is taken to be the PZC. Alternatively, the PZC is determined as the plateau in the pHfln, (pH . .j) curve. The method assumes that the powder is absolutely pure (free of acid, base, or any other surface-active substance), which is seldom the case. Even with very pure powders, the above method is not recommended for materials that have a PZC at a nearly neutral pH. Namely, the method requires accurate values of the initial pH, which is the pH of an unbuffered solution. The display of a pH meter in unbuffered solutions in the nearly neutral pH range is very unstable, and the readings are not particularly reliable. The problem with pH measurements of solutions is less significant at strongly acidic or strongly basic pHs (see Section 1.10.3). The above method (under different names) became quite popular, and the results are referred to as pH in the Method columns in the tables in Chapter 3. The experimental conditions in the above method (solid-to-liquid ratio, time of equilibration, and nature and concentration of electrolyte) can vary, but little attention has been paid to the possible effects of the experimental conditions on the apparent PZC. The plateau in the pH, , (pH, ,, ) curve for apatite shifted by 2 pH units as the solid-to-liquid ratio increased from 1 500 to 1 100 [653]. Thus, the apparent PZC is a function of the solid-to-liquid ratio. 

The potentiometric mass titration method [657,658] produces results equivalent to those of the drift method described above. The same amount of base is added to three dispersions with different solid-to-liquid ratios and a constant ionic strength. The dispersions are titrated with acid, and the pH is recorded as a function of the amount of acid added. The intersection point of the obtained curves is taken as the PZC. In other words, the PZC is identified with the pH at which solid addition does not induce a change in pH. The drift method and mass titration are based on the same principle, the difference being that in potentiometric mass titration, the reagents are added in a different order. Potentiometric mass titration is affected by the acid or base associated with the powder in the same way as in the drift method and mass titration. The advantage of potentiometric mass titration over the drift method is that in the former the pH is measured only in buffered systems. 

The salt titration method [666] is a modification of the salt addition method. A portion of salt is added to a dispersion, and the ApH is recorded. When ApH 0, base is added to shift the pH to an even higher value. When ApH 0, acid is added to shift the pH to an even lower value. Once a constant pH has been established, a new portion of salt is added, and ApH is recorded again. The series of salt additions followed by acid or base additions is continued until ApH = 0. The advantage of the salt titration method as compared with the classical salt addition method is that only one portion of dispersion is used. Thus, PZC determination requires a smaller amount of solid and only one reaction vessel. Moreover, a series of measurements (e.g., at different temperatures or at different concentrations of a nonaqueous co-solvent) can be carried out with the same portion of solid, and effects due to a difference in surface properties between different portions of solid are avoided. The number of consecutive salt additions in the salt titration method is limited, because the sensitivity of ApH to an addition of the same amount of salt decreases as the initial salt concentration increases. 

A potentiometric titration curve often has an inflection point at the PZC (Section 2.6.3). This property has been proposed as a method to determine the PZC [673]. The inflection point method gained some popularity after a publication by Zalac and Kallay [670]. Also, the differential potentiometric titration described in [674] is equivalent to the inflection point method. This method is not recommended by the present author as a standalone method to determine the PZC, but a few results obtained by the inflection point method, usually in combination with other methods, are reported in the tables in Chapter 3 (as Inflection in the Methods columns). In [675], the potentiometric titration curve of one sample had two inflections, and the inflection at the lower pH was assumed to be the PZC. The potentiometric titration curves of other samples had one inflection each. Reference [676] reports an inflection point in the titration curve of niobia at pH 8, which is far from the pHg reported in the literature. A few examples of charging curves without an inflection point or with multiple inflection points are discussed in Section 2.6.3. 

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