Linear viscoelasticity of poly(acrylic acid) complexed with ferric ion

Abstract

Linear viscoelasticity was studied for aqueous solutions of poly(acrylic acid) (PAA) complexed with ferric ion (Fe³⁺). Concentration of PAA was fixed in the semidilute regime, and concentration of Fe³⁺ varied within a wide range. Sol-to-gel transition was observed at low Fe concentration, and syneresis was observed at high Fe concentration. In between, the system was reversible gel with relaxation time governed by the effective breakup of the complexing sites. Analysis of stress relaxation behavior and temperature dependence enabled consistent determination of the association energy of ~ 75 kJ/mol. Syneresis at high Fe³⁺ concentration was associated with a decrease in solvent quality and increase in elastic energy with increasing density of the PAA/Fe³⁺ complexing sites.

Appendix

Figure 10 plots the master curves of G′ and G″ reduced at T_r = 30 °C against ω. The overall trend is the same as that shown in Fig. 5: the plateau modulus increased and the cross-point of G′ and G″ shifted to low ω with the increase of C_Fe.

Fig. 10

Comparison of master curves of representative samples reduced at T_r = 30 °C, where normalized moduli, b_TG′ and b_TG″, are plotted against reduced angular frequency a_Tω

Figure 11 plots the vertical and horizontal shift factors against 1000/T. One trend observed in panel a is that the temperature dependence of b_T, which was explained in Fig. 6 as a decrease of number density of interchain association with increasing T. The T dependence of b_T becomes weaker with increasing C_Fe, which seems to be a surprising result at first glance because the ratio of number density of interchain association at T and T_r should be ~ exp(E_a/R× (1/T – 1/T_r)), which is the same for all samples. However, we should remember that a change of plateau modulus with a number density of interchain aggregation is quite different for different scaling regimes during the gelation. For example, the gel point usually corresponds to 1/(N_blob-1), which corresponds to ~ 1 interchain association per chain when a number of blobs per chain N_blob is much larger than one. Above the gel point, double the number of interchain association from ~ 1 to ~ 2 per chain will lead to a significant increase of plateau modulus up to C_PAART/M. In comparison, further doubling the number of interchain association from 2 to 4 per chain would only increase the plateau from C_PAART/M to 3C_PAART/M. This difference can be seen in Fig. 9 a where C_Fe dependence of G_N is stronger for plots below C_PAART/M (circles) than those in between C_PAART/M and 8C_PAART/M (squares). This difference qualitatively explains the lower temperature dependence of b_T for samples of C_Fe ≥ 20 mM compared with the samples of C_Fe < 20 mM because C_Fe = 20 mM roughly corresponds to the full gelation point (i.e., two interchain associations per chain). The weakening of T dependence of b_T with increasing C_Fe is in accordance with the slightly weakening of a_T dependence with increasing C_Fe. The larger difference of b_T in panel a than a_T in panel b is mainly owing to a different vertical scales for two panels. The overall trend of a_T against 1000/T is quite similar for all samples, which enable us to estimate consistent E_a of 87 ± 2 kJ/mol from the gradient (The highest and lowest gradients give E_a of 89 and 85 kJ/mol, respectively), and accordingly E_a of 71 ± 2 kJ/mol after subtracting the activation energy for motion of the water molecules.

Fig. 11

Panel a plots of the vertical and horizontal shift factors b_T, against 1000/T. Panel b plots of the horizontal shift factor a_T against 1000/T. Two dotted lines in panel b have the highest and lowest gradients, giving E_a of 89 and 85 kJ/mol, respectively