## 3 Results and Discussion
### Electrochemical Characterizations
In any case, due to the similar material of both NPAM+TO\({}_{2}\) samples, EIS analysis for clean membranes is concordant with that previously performed by membrane potential results with respect to pore radii influence. Figure 5: Nyquist plots for (\(\square\)) Sf-NPAM/TiO\({}_{2}\) membrane and (\(\lozenge\)) Ox-NPAM/TiO\({}_{2}\) membrane. (e) Electrolyte solution; (m) membrane; (f) interface; \(\omega\): angular frequency and values increase tendency. The BSA fouling effect on membrane potentials for the Ox-NPAM/TiO\({}_{2}\)(f) sample is shown in Figure 6a where, for comparison, \(\Delta\Phi_{\text{mbr}}\) values for the clean Ox-NPAM/TiO\({}_{2}\) are also indicated. Both membranes show rather similar values at low concentrations (interfacial or Donnan potential contribution) but differ at high concentrations, which is an indication of differences in ion diffusion between both samples that might be caused by pore size reduction due to BSA deposition on pore walls (although surface deposition might also exist). Fitted values of characteristic parameters were \(\text{X}_{\text{ef}}=+0.014\) M, \(\text{D}_{\text{Cl}}-/\text{D}_{\text{Na}}-=5.4\), and \(\text{P}_{\text{Cl}}-=58.2\%\), as these two latter values were much higher than those determined for the clean membrane. Figure 6b shows the comparison between experimental and fitted values depending on variable solution \(\text{C}_{\text{v}}\), as well as the separate contributions of diffusion and Donnan potentials; this second contribution does not differ significantly from that in Figure 3b for clean membrane at high \(\text{C}_{\text{v}}\) values. Figure 6: (**a**) Comparison of membrane potential with solution concentration ratio for Ox-NPAM/TiO\({}_{2}\) (\(\Diamond\)) and Ox-NPAM/TiO\({}_{2}\)(f) (\(\blacklozenge\)) membranes. (**b**) Comparison of experimental and calculated (solid line) values, Donnan (dashed-dot line), and diffusion (dashed line) potential contributions for Ox-NPAM/TiO\({}_{2}\)(f) membrane. However, the protein fouling effect or mechanism exhibited by the Sf-NPAM/TiO\({}_{2}\)(f) membrane seems to be different according to results shown in Figure 7a, where a similar concentration ratio dependence for fouled and clean samples can be observed, but the results obtained for the Sf-NPAM/TiO\({}_{2}\)(f) membrane present an almost constant shift to lower \(\Delta\Phi_{\rm mbr}\) values. This result could indicate the presence of a BSA layer on the membrane surface, rather than pore-wall deposition (which could be related with a \"static\" fouling nature because any hydrostatic pressure is applied to the BSA solution), giving rise to a kind of \"composite\" or two-layer membrane, as can be deduced from results shown in Figure 6b, where \(\Delta\Phi_{\rm mbr}\) values for the fouled sample after subtraction of that determined at C\({}_{\rm v}\) = C\({}_{\rm f}\) = 0.01 M are compared with those determined for the clean Sf-NPAM/TiO\({}_{2}\) membrane, and only small differences exist between them. Figure 7b also shows the data points obtained when \(\Delta\Phi_{\rm mbr}\) values for the clean membrane are subtracted from those corresponding to the fouled sample. In this context, the difficulty of obtaining quantitative information from these results should be pointed out because they do not correspond to similar interfacial situations, and a compact BSA layer on membrane surface may also affect the concentration gradients. Figure 7: (**a**) Comparison of membrane potential with solution concentration ratio for Ox-NPAM/TiO\({}_{2}\) (\(\lozenge\)) and Ox-NPAM/TiO\({}_{2}\)(f) (\(\blacklozenge\)) membranes. (**b**) Comparison of experimental and calculated (solid line) values, Donnan (dashed-dot line), and diffusion (dashed line) potential contributions for Ox-NPAM/TiO\({}_{2}\)(f) membrane. EIS measurements have also been used in the study of porous membrane fouling by comparing impedance plots obtained with clean and fouled samples [56; 57], as shown in Figure 8 for Ox-NPAM/TiO\({}_{2}\) and Ox-NPAM/TiO\({}_{2}\)(f) membranes.