Figure 1
Influence of aggregates on the titration of UCB with NaOH. Four models of changes in pH expected during titration of 25 ml of 7 mM UCB with 10.6 mM NaOH, compared with the experimental titration curve of MPEG-S-BR [9]. pH values, calculated according Equations 5 and 6 in the Appendix, are plotted against F, the ratio of the equivalents of added NaOH to the equivalents of MPEG-S-BR. Full neutralization corresponds to F = 1 (light dashed line) and the titration mid-point is at F = 0.5 (heavy dashed line). The models apply our previously estimated constants for UCB [10] of pK1 = 8.1, pK2 = 8.4, and KD = 2.6 × 105 M-1, the formation constant of (B=)2, the dimer of the UCB dianion. The models considered below ignore the even higher multimers of B= and higher mixed aggregates of HB- and B= that would be expected in the real system [9, 47]. See Appendix for details. A. Curve A (open squares) assumes there is no self-association of any UCB species. Curve B (black diamonds) assumes the only aggregate is the dianion dimer, (B=)2. Curve C (gray triangles) assumes dimers and pentamers, the added pentamer species, (B=)5, having a formation constant K5, given by log K5 = 22.66 for the equilibrium 5 B= ↔ (B=)5. B. Curve D (gray squares) incorporates (B=)2, and three octamers, (H+)3(B=)8, (H+)4(B=)8, and (H+)5(B=)8, which are mixed adducts of HB- and B= with formation constants given by log K = 40, 39 and 38, respectively. Curve E (black dots), the experimental potentiometric titration curve of MPEG-S-BR from Figure 2a of Boiadjiev et al. [9] (see text), is approximated by Curve D, but not by Curve A. The pH at the titration mid-point for each curve (A, 8.26; B, 7.62; C, 6.99; D, 6.54) decreases as the size of the UCB aggregates increases, and is lowest for MPEG-S-BR (E, 6.42).