*3.4. GSI Experiment Results*

Figure 6 demonstrates a PAA-F1 inhibited RO membrane gypsum scaling (Figure 6c') relative to the un-inhibited one (Figure 6c). Like in a blank experiment, an increase of Ca2<sup>+</sup> content from 15 mmol·dm−<sup>3</sup> (K <sup>=</sup> 1) up to 48 mmol·dm−<sup>3</sup> at K <sup>=</sup> 3 is observed (Figure 6c,c'). This corresponds to the gypsum saturation SI~2. Then [Ca2<sup>+</sup>] decreases due to the gypsum crystals deposition, and at the final moment (K = 5) it corresponds almost to its initial level, Figure 6c'. A variation of calcium concentration with K in retentate for a Blank C and GSI experiments is nearly the same for K ≤ 1.5, e.g., before gypsum starts to form, Figure 6c,c'. When K > 1.5 the crystals of CaSO4·2H2O start to form in the Blank C experiment, while in presence of PAA-F1 this process starts at K>3, and the gypsum formation goes slower relative to the blank run. A significant shift of curve "c' " (GSI experiment) relative to curve "c" (blank experiment) clearly indicates that an effective inhibition takes place. For K = 3 PAA-F1 reveals c.a. 90% inhibition, and for K= 4 − c.a. 60%.

Fluorescent images of retentate (Figure 8) correspond well to the calcium content data, Figure 6c'. Indeed, there are no any crystals in the stock solution (K = 1) and at K = 2 saturation level, Figure 8A,B. At K = 3 gypsum deposition starts. The corresponding image (Figure 8C) indicates the landslide formation of numerous gypsum stick-like crystals with a mean size c.a. 10 to 20 μm. These are much smaller than those found later on the membrane surface after GSI experiment is finished, Figure 7C. Images (Figure 8C) leave no doubt that the major location of gypsum crystals formation is the bulk retentate solution, but not the membrane surface. Most of them have no any traces of antiscalant presence neither on their surface, nor inside of the crystals, Figure 8C–E. Meanwhile, the big bright green spherical solids with diameter ranging from 10 to 50 μm belong to the solid particles of pure [Ca-PAA-F1] complexes, which do not have any gypsum inclusions, Figure 8C. Bearing in mind that there are 360 g of gypsum per 1 g of PAA-F1, their size indicates that almost all antiscalant is concentrated in [Ca-PAA-F1] particles.

Indeed, if it is assumed that [Ca-PAA-F1] species form 100 nm size primary spherical particles, then each green sphere presented in Figure 8C corresponds to an aggregate of 105–107 such particles. Thus most of PAA-F1 and gypsum seem to form solids by itself with no interaction with each other. This observation is very similar to that one found by us previously for HEDP-F/gypsum system [22]. For K = 4 most of gypsum and of [Ca-PAA-F1] complexes are deposited on membrane surface. Therefore much less gypsum crystals remain in the bulk solution, Figure 8D. At K = 5 only a few gypsum crystals remain in the bulk retentate, while the rest are completely deposited on membrane, Figures 7C and 8E.

Notably, the size and shapes of gypsum crystals deposited in presence of PAA-F1 (Figure 7C) are similar to those, observed in a Blank C experiment, Figure 7A. This indicates that there is very little interaction of antiscalant with gypsum if any during its growth stage. Meanwhile, the size of CaSO4·2H2O crystals at the end of GSI experiment (Figure 7C) is at least twice bigger than of those formed in the bulk solution at K = 3 (Figure 8C). Thus, it is likely that, after fast formation in the bulk medium at K=3, the gypsum crystals pass sedimentation and proceed to grow already on membrane surface.

Although, there is no bulk crystal formation detected by fluorescent microscopy for K < 3 (Figure 8A,B), the DLS experiment, run in a parallel way, reveals an intensive formation and aggregation of colloids already at K = 1 and K = 2, Figure 9a,b.

**Figure 8.** Fluorescent images of initial undersaturated gypsum solution droplets (**A**), K = 1, and of retentate at K = 2 (**B**), K = 3 (**C**), K = 4 (**D**), K = 5 (**E**) within the GSI experiment.

**Figure 9.** DLS particle size distribution by intensity in retentate of the GSI experiment for K = 1 (a), K = 2 (b) and K = 3 (c).

These data are unable to distinguish gypsum and [Ca-PAA-F1] particles, but they provide some additional information on what happens in a transparent retentate before visible gypsum crystals appear. However, DLS gives some independent approval of heterogeneous mechanism of gypsum particles in the bulk: it clearly indicates that CaSO4·2H2O and/or [Ca-PAA-F1] aggregates appear in retentate almost immediately after saturation starts. Indeed, according to the classical crystallization theory [23], this is possible only in the case, when gypsum passes bulk heterogeneous nucleation, and exactly the "nanodust" plays the role of the solid phase template.

It should be noted that PAA-F1 is more efficient than HEDP-F in a gypsum scale formation inhibition, reported in [22]. In a similar experiment, run under the same conditions, HEDP-F provides supersaturated gypsum solution stabilization only for 1 < K ≤ 2 [22], while PAA-F1 is effective for 1 < K ≤ 3. This result is in a good agreement with a sequence found earlier in the batch experiments for the non-fluorescent analogues HEDP and PAA: PAA>>HEDP [34].

#### *3.5. Tentative Mechanism of Gypsum Membrane Fouling Inhibition by PAA-F1 in RO Process*

PAA-F1 has definitely proved itself as an effective antiscalant in gypsum brine RO desalination, Figure 6. This was also confirmed earlier by the static experiment tests [36]. However, the visualization of PAA-F1 molecules indicates clearly that there is no definite interaction between antiscalant and gypsum along the brine RO treatment. The same result was obtained earlier for HEDP-F/gypsum RO desalination process [22] as well as for batch static experiments with gypsum [20] and barite [21] in presence of HEDP-F. A tentative mechanism of gypsum inhibition in RO membrane fouling is proposed [22] and our present data for PAA-F1 give a further approval to this hypothesis.

This mechanism involves interaction of foreign solid impurities ("nanodust"), which are always present in RO brines (Table 1), with antiscalant. In the absence of scale inhibitor the gypsum nucleation has a heterogeneous origin with solid foreign particles ("nanodust") serving as nucleation centers in the bulk retentate solution. Antiscalant molecules block these nucleation centers partly or completely, via sorption on their surface before retentate gets supersaturated relative to gypsum. Thus, when gypsum solution gets supersaturated, the potential sorption centers on the surface of "nanodust" particles become much less available for gypsum layers formation. This hampers and retards the process of scale formation.

Indeed, as it was mentioned earlier, there are at least 10<sup>6</sup> molecules of PAA-F1 (with a mean number of 50 monomer units, e.g., 4000 Da) per one nano/microdust particle in the system studied. A simple calculation indicates, that one PAA-F1 molecule is capable to cover 4 nm<sup>2</sup> of a particle surface, being completely stretched, Assuming that all nano/microdust particles have an equal size of 100 nm and an ideally spherical form, there are only 7.9·103 molecules of PAA-F1 needed to cover the whole single particle surface by a monolayer. An option to occupy only some active centers diminishes this number, while globular conformation of polymer molecule increases it. Evidently PAA-F1 is capable

to cover all potential nucleation centers several times. Anyhow a supposition that it blocks a sufficient part of them is a quite realistic one.

On the other hand, although a high excess of PAA-F1 over nano/microdust particles surface area slows down gypsum scale formation, it does not stop this process. Therefore, both CaSO4·2H2O and [Ca-PAA-F1] phases are formed in a parallel way braking each other, as they compete for one and the same set of natural nucleation centers (colloid impurities) present in retentate. Notably, our conclusions derived from antiscalant visualization are perfectly supported by the independent DLS studies [38,39].

At the same time our results conflict somehow with the conclusions of numerous reports on static gypsum crystals formation in supersaturated aqueous solutions [24–33]. All these studies are built on the grounds of homogeneous nucleation scenario, excluding the possibility of "nanodust" presence. Meanwhile, the "nanodust" was surely present in these experiments, that all use Sigma-Aldrich high purity reagents (>98–99%), a double-deionised boiled water, and (in some cases) stock solutions filtration operating 200 nm filter. However, none of these solutions was then examined for the residual solid nanoparticles content. In order to make the situation clear, we have done a blank test, operating model Sigma-Aldrich KCl salt (ACS reagent, 99.0–100.5% CAS 7447-40-7) and a particle counter. Then KCl was dissolved in deionized water (340 particles bigger than 100 nm in 1 mL) to make 0.1 mol·dm−<sup>3</sup> solution. This KCl solution revealed 268000 particles bigger than 100 nm in 1 mL. This solution was filtered with 220 nm filter and a "purified" solution demonstrated still 1540 particles bigger than 100 nm in 1 mL. A homogeneous scenario was unlikely to take place in [24–33] as an energy barrier for crystals nuclei formation is much lower for heterogeneous scenario, than for homogeneous one [23].

It should be noted that in an excellent study by Nicoleau, Van Driessche and Kellermeier [30] on static gypsum crystallization, in the presence of polyacrylate and of some other polymers, run on the other grounds, a conclusion was partly similar and partly alternative to ours. It was indicated that the polymers do not change the nature of the nucleating primary species, but rather modulate their subsequent growth and/or aggregation increasing the viscosity of the solution. However, the authors of this study [30] did not control "nanodust" content and could not monitor the polymer location. On the other hand, we did not control the viscosity. Our data could be a valuable supplement to the studies [24–33].

Our recent results [20–22], and the data of a present study, indicate the importance of natural background particles for scale inhibitors application strategies. As ppb impurities, these are always present in any ultrapure reagent or solvent, specially prepared for microelectronics, to say nothing of technical grade purity reagents and brackish water commonly used in RO technologies. The particular chemical nature of this "nanodust" is a challenge for researchers, as far as it is hardly possible to isolate them completely from a liquid phase. In our opinion, these solid impurities are chemically non-uniform, and their different ingredients have different affinity towards scale material and antiscalants. Their composition may vary between water samples. At present, only a rough and incomplete estimation of its chemical composition and particle size distribution is feasible. However, even the treatment of "nanodust" as a "blackbox" may become very fruitful.

At the same time, the fluorescent antiscalants may become a promising tool in scale formation studies. This method has very high sensitivity and is widely used in analytical applications [35] as well as a powerful traceability approach in medicine [40]. Normally, the method sensitivity corresponds to the ppb level for both solid and liquid samples. For example, the detection limit of Rhodamine is in the range of 0.01 ppb in distilled water (25 mm cuvette) [35], and fluorescence quantum yield of our fluorescent inhibitor is quite close to Rhodamine [35,36]. Thus, localization of fluorescent inhibitor upon crystals/particles of scale is a valid approach. On the other hand, an absence of fluorescence is a clear indication that the fluorescent inhibitor is not present in the solution but either forms self-aggregates or participates in the crystal formation.
