*2.1. Reagents, Membrane Material and Model Solutions*

Antiscalant PAA-F1 (Figure 1) was synthesized by our group as described elsewhere [36] along with its scale inhibition efficiency against gypsum scaling and its fluorescent properties. It has the mean molecular mass 4000 Da with c.a. 1% mass of 1,8-naphthalimide moiety. This corresponds randomly to c.a. 0.2 fluorescent fragments per one molecule of polyacrylate.

For model scaling solutions, the reagent grade CaCl2·2H2O and Na2SO4 were used in crystalline form and were separately dissolved in distilled water (conductivity 2 μS/cm) to prepare stock solutions of 0.04 mol·dm<sup>−</sup>3. After complete dissolution, stock solutions represented transparent colorless liquids, and were deliberately exposed no filtration for a better imitation of saline or brackish water. For gypsum (CaSO4·2H2O) scaling experiments, each stock solution was combined with distilled water to achieve a total volume of 5 L and a final concentration of 0.015 mol·dm−<sup>3</sup> [Ca2+] and 0.015 mol·dm−<sup>3</sup> [SO4 <sup>2</sup>−]. The solvent (distilled water) and all stock solutions were analyzed separately for foreign particles content, Table 1. A particle counter SLS-1100 (Particle Measuring Systems Inc.) reveals a presence of background solid suspended particles ("microdust") in both stock brines, as well as in the distilled water used for the brine preparation, Table 1.


**Table 1.** Initial stock solutions characterization by particle counter.

\* The data deviations found for three replicate measurements constituted ±20%.

The values of gypsum solubility in water at 25 ◦C provided by different research groups, varies from 0.018 to 0.025 mol·dm−<sup>3</sup> and depend drastically on the background NaCl content [37]. Therefore, the stock calcium and sulfate solutions have been prepared (Table 1) in such concentrations, that being mixed in 1:1 volume ratio they would give 0.015 mol·dm−<sup>3</sup> gypsum solution, that is a bit below the saturation level. However, the retentate was expected to exceed the saturation level already at saturation coefficient (concentration factor) K = 1.5 and to reach steadily supersaturation S~4 (K = 5) at the end of the experiment (in absence of scaling). Notably, these supersaturation assessments are very approximate ones as NaCl content in retentate is changed in experiment run from 0.03 to c.a. 0.15 mol·dm<sup>−</sup>3, increasing gypsum solubility.

Here and further saturation coefficient K and saturation ratio S are denoted as:


Thus for S < 1 the solution is undersaturated, while for S > 1 it is supersaturated.

Notably, an antiscalant, where necessary, was added always initially to the sulfate test solution in amounts that provided its final concentration 7 mg·dm−<sup>3</sup> (corresponds to c.a. 1.7·10−<sup>6</sup> mol·dm−<sup>3</sup> PAA-F1 concentration bearing in mind that the mean molecular mass is 4000 Da) in gypsum scaling experiment, and equilibrated there no less than 30 min.

It is well-known that the heterogeneous nucleation, in the presence of such solid impurities, as clay minerals or other foreign particles, is characterized by a lower free energy barrier than the homogeneous one [23]. Bearing in mind the particle counter data, Table 1, a bulk homogeneous formation of solid gypsum phase is unlikely in our case, while the bulk heterogeneous nucleation is the most likely route. It should be noted that deionization of distilled water leads to a significant reduction of suspended particles concentration. However, this operation fails to remove even "microdust" completely, to say nothing of "nanodust". The latter is likely to be present in any aqueous samples in much higher amounts than "microdust", although the "nanodust" (1 nm < particle sizes < 100 nm) is beyond the detection limit of commercial particle counters. This becomes clear by extrapolating

the cumulative number of foreign particles in 1 mL (Table 1) to the 1≤ nm ≤ 100 range. Thus, all the background solid suspended particles are referred to as "nanodust".

A rough estimation indicates that if the number of undetectable by the particle counter "nanodust" particles with a size D < 100 nm is equal to the detected "microdust" ones, than the total heterogeneous impurities concentration constitutes c.a. 3,000,000 units in 1 mL, or 3·109 in 1 L. At the same time PAA-F1 concentration corresponds to 3.5·10<sup>15</sup> molecules per liter. Thus, there are at least 10<sup>6</sup> molecules of PAA-F1 per one nano/microdust particle in the system.

A detailed analysis of the background solid suspended particles nature in all chemicals used (H2O; CaCl2·2H2O; Na2SO4; PAA-F1) represents a special complicated task, and is hardly possible. It is outside of the frames of the present study. However, some preliminary analyses carried out in [22] indicate that a tentative nature of solid impurities in distilled water might be assigned to Al/Fe hydroxo/oxides and to either SiO2 or to some silicate solid impurities. At the same time, it should be noted that all the background solid suspended particles, listed in Table 1, correspond to the ppb level, e.g., to the reagent grade purity solutions.

Studies were carried out using commercial spiral wound BLN-type low pressure reverse osmosis membrane produced by CSM Co. (Seoul, South Korea). The membranes are found to have their own non uniform fluorescence. This makes it difficult to observe PAA-F1 location on membrane surface, as the coresponding images are not very clear.
