*3.2. Blank B Experiment Results*

This experiment is intended to estimate possible PAA-F1 participation in its side reaction with excess of Ca2<sup>+</sup> ions via formation of soluble CanPAA-F1 complexes. Indeed, Figure 3B demonstrates some changes relative to Figure 3A. It exhibits that calcium ions do interact with PAA-F1 forming colloid solutions. This manifests in some decrease of fluorescence intensity relative to the Blank A experiment already at K = 1, and in arrival of a light scattering band, indicating formation of CanPAA-F1 colloids with a mean size of c.a. 400 nm, Figure 4.

**Figure 3.** Variation of PAA-F1content monitored by fluorescence intensity within a Blank A (**A**) and Blank B (**B**) experiment: Total content in retentate + membrane (a), its content on membrane, expressed in units of PAA-F1 concentration in retentate (b), in retentate (c), and in permeate (d).

**Figure 4.** DLS particle size distribution by intensity in retentate in a Blank B experiment for K = 1.

Indeed, the individual CanPAA-F1 aggregates are then detected on the membrane surface as bright green spheres with a size ranging from 10 to 20 μm, Figure 5.

**Figure 5.** Fluorescent image of membrane surface deposit after Blank B experiment. Scale marker corresponds to 200 μm.

Notably, an excess of calcium ions relative to antiscalant, forces PAA-F1 to concentrate preferably in [Ca-PAA-F1] moieties, located both in a liquid phase and on a membrane surface. Meanwhile PAA-F1 "free" concentration remains at the level of 2 to 7 mg·dm<sup>−</sup>3, which is still capable to provide scale inhibition in the bulk aqueous phase.
