# Diving into the transfer of small organic solutes in RO of seawater

Fatima Zohra Charik, Saad Alami Younssi, Murielle Rabiller-Baudry

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Fatima Zohra Charik, Saad Alami Younssi, Murielle Rabiller-Baudry. Diving into the transfer of small organic solutes in RO of seawater. Separation and Purification Technology, 2025, 378, Part 1, pp.134260. 10.1016/j.seppur.2025.134260. hal-05246515

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# Diving into the transfer of small organic solutes in RO of seawater

Fatima Zohra CHARIK<sup>1,2</sup>, Saad ALAMI YOUNSSI<sup>2</sup>, Murielle RABILLER-BAUDRY<sup>1*</sup>

## Highlights

* Rejection of organics (265-916 g mol⁻<fnref n="1" />) was studied in RO in presence of synthetic seawater

* At 40 bar all solutes were transmitted through the SW30 membrane

* log K<sub>ow</sub> and Hansen Solubility Parameters partially explained rejections

* Affinity membrane-solvent and membrane-solute partially explained rejection.

* Rejection modeling taking into account membrane-solute-water affinity was successful.

## Abstract

The elimination of small organic pollutants is emerging as a new and growing challenge for reverse osmosis desalination. Charged organic solutes (three azo dyes, a vitamin, an antibiotic) were selected on the basis of their chemical nature and various properties (MW= 265-916 g.mol⁻<fnref n="1" />, charges, hydrophobicity...). The RO membrane (SW30, Filmtec) was used to filter simple, binary and ternary mixtures of organic substances over a range of 30 to 40 bar, either in 30 g L⁻<fnref n="1" /> NaCl or in synthetic seawater (Atlantic Ocean). The applied pressure of 40 bar was specially chosen to obtain a high, but not full rejection of all of these solutes, in order to prevent convection from overpowering all the other forces responsible for the transfers. Accordingly, it has become possible to highlight the variations induced by changes in physico-chemical interactions. To address the latter, a relationship between rejection and solute hydrophobicity assessed from the descriptor logK<sub>ow</sub> has been proposed, but has provided only limited understanding. Secondly, relationships between rejection and the Hansen solubility parameters (HSPs) of solutes were established. They highlight the balanced role of polar, H-bonding and dispersive properties on the rejection. Finally, by the mean of Ra distance calculated from HSPs, the article provides an overview of solute affinity competition for the membrane or solvent (water) in managing the rejection of organic compounds and proposes a model validated for all experimental conditions within an average accuracy of 15%.

**Keywords:** Reverse osmosis; membrane; organic pollutants; hydrophobicity; Hansen Solubility Parameters; transfer mechanism; modelling.

<footnote n="1"><sup>1</sup> Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226, F-35000, Rennes, France</footnote>

<footnote n="2"><sup>2</sup> Laboratory of Materials, Membranes and Environment, Faculty of Sciences and Technologies of Mohammed VI of Casablanca, Morocco</footnote>

<footnote>*Corresponding author: murielle.rabiller-baudry@univ-rennes.fr</footnote>
# 1. Introduction

Because of its energy efficiency and its capacity to highly remove salts, seawater desalination achieved by Reverse Osmosis (RO) has become a reference process to produce fresh water, especially for countries having coastal regions [1-3]. However, the quality of the incoming seawater is crucial to ensure that of the produced fresh water. Depending on countries and their regulations, more or less organic pollutants are susceptible to be discharged and their presence was reported in marine environments at concentrations of µg L⁻¹ order of magnitude [4]. Accordingly, an emerging question concerns the fate of these pollutants not removed by the pretreatments prior to RO: are there fully removed by the RO membrane process? Several papers reported that RO membranes are not an absolute barrier against certain organic solutes, contrary to what was believed for a long time. Small solutes were evidenced to pass through RO membranes, such as ethanol (MW= 92 g.mol⁻¹), pesticides, endocrine disrupter, azo-dye and vitamin of MW up to 300 g.mol⁻¹ and even more such as lactose (MW= 352 g.mol⁻¹) [5-17].

What is the path taken by these solutes in the membrane? A dense RO polyamide membrane should have no pores but only free volumes in between polymer chains. The size distribution of the equivalent diameter of these free volumes was estimated by molecular dynamic simulations [18]. Besides a 0.5 nm size in average, which is a little bit larger than the water molecule size (0.3 nm), the larger cavities were estimated close to 0.8 nm size which could be close to the size of molecule of 300 g.mol⁻¹ (see below). With such structure, either local defects inside the membrane [19], or dynamic deformation of the membrane backbone when passing organics have to be imagined to explain the passage of organics of larger sizes. For instance, the existence of additional voids inside protuberances of the active layer was reported in [20]. Accordingly, beside the solution-diffusion model (SD, [21]) classically used, the inclusion of convection in the transfer mechanism as proposed in the solution-diffusion with imperfections model [22] or more recently in the solution-friction model [23] is in a good agreement with these new understanding of the membrane structure. Note that, the Spiegler-Kedem (SK, [24]) model based on the irreversible thermodynamics is another possibility as the membrane is considered as a black box, as in the previous mentioned models.

What are the properties of solutes that could cause more or less reversible distortion of the membrane's flexible polymer matrix, when solutes are transferred under pressure? Besides these hydrodynamic explanations, several investigations provided evidence that physico-chemical interactions between the solute and the membrane have an impact on the solute rejection. These results have also to be related to the solute adsorption at the membrane wall before the transfer into the membrane. For instance, it was suggested that hydrophobic interactions, can serve as valuable parameters for determining the rejection of uncharged and non-polar solutes in RO [6,7] while other suggested similar approaches for polar and hydrophilic solutes [25]. To date, it is clear that there are still gaps in the understanding of the impact of physico-chemical properties of organic solutes and membranes on the rejection by RO membranes.

The aim of this work was to dive into the RO transfer mechanism of organic solutes dissolved in seawater or 30 g.L⁻¹ NaCl, by a systematic investigation of the contribution of the physico-chemical interactions in the membrane-solute system. A set of model solutes was selected with respect to their molecular weight ranging from 265 to 916 g.mol⁻¹, their structure and hydrophobicity (logK<sub>ow</sub>). Out of them were vitamin, antibiotic and dyes. Experimental results evidenced that all of them were slightly transmitted through the RO selected membrane (SW30, Filmtec) in the 30-40 bar pressure range. The discussion of rejections was first achieved by the
mean of the solute hydrophobicity using logKow as single descriptor. Second, the rejections were discussed by the mean of the calculated Hansen Solubility Parameters (HSPs) able to provide subtler description of the solutes but also of the membrane-solute and solute-water interactions.

## 2. Hildebrand and Hansen solubility parameters (HSPs) to describe membrane-solute-water interactions

According to the best of our knowledge, Ra distances calculated from HSPs were never used in the analysis of RO membrane performances and it is an originality of this work to discuss organics' rejection using these parameters.

### 2.1. Generality

The global solubility parameter of a liquid (δ) was first introduced in 1936 by Hildebrand and Scott [26], and is expressed as follows:

$$ \delta_{\square} = (E_{\text{coh}}/V_{\text{m}})^{0.5} \quad (\text{Eq. 1}) $$

With:

δ: Hildebrand solubility parameter (MPa$^{0.5}$)

Vm: molar volume of the liquid (L.mol$^{-1}$) that can be calculated according to the Fedors' method that is a contribution group method [29].

Ecoh: cohesive energy inside the liquid (J.mol$^{-1}$)

Charles Hansen [27] completed the theory of Hildebrand in 1966, by proposing to decompose δglobal into three contributions, namely: (i) the dispersion solubility parameter δd, (ii) the polar solubility parameter δp and (iii) the hydrogen bonding solubility parameter δh:

$$ \delta_{\square} = \sqrt{\delta_{d}^{2} + \delta_{p}^{2} + \delta_{h}^{2}} \quad (\text{Eq.2}) $$

The 3 HSP parameters (δd, δp, δh, Eq. 3-5) can be calculated using, for instance, the contribution method of van Krevelen [28]. It requires to previously have the molar volume of the component Vm that can be calculated from Fedors' method. Then each chemical group contribution (Fdi, Fpi and Ehi) can be calculated from values given in the database of Van Krevelen.

$$ \delta_d = \frac{\sum F_{di}}{V_m} \quad (\text{Eq.3}) $$

$$ \delta_p = \frac{\sqrt{\sum F_{pi}^2}}{V_m} \quad (\text{Eq.4}) $$

$$ \delta_h = \sqrt{\frac{E_{hi}}{V_m}} \quad (\text{Eq.5}) $$
An easy way to appreciate the mutual affinity between two compounds hereafter denoted 1 & 2 is to calculate their Ra1-2 distance. The lower Ra1-2 is, the higher is the mutual affinity between 1 & 2.

$$Ra_{1-2} = (4(\delta_{d,1} - \delta_{d,2})^2 + (\delta_{p,1} - \delta_{p,2})^2 + (\delta_{h,1} - \delta_{h,2})^2)^{0.5} \quad (Eq.6)$$

With:

Ra1-2 in MPa0.5

δx,i the respective δx HSP parameters with x=d, p, h of the i compound, in MPa0.5

## 2.2. Application to the selected membrane and solutes

Five model organic molecules (Figure 1, Table 1) were selected, all being charged at the natural pH of seawater (pH= 8.2). Some of them was considered as “twins” with respect to their close size but had opposite charges: Thiamin/Tropaeolin O, Brilliant Blue G/Tylosin. The SW30 membrane is known to be a fully aromatic polyamide membrane. The solutes exhibited sometimes a diameter larger than the estimated diameter of the free volumes in dense polyamide membrane (see above).

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Chemical structure of selected organic solutes and fully aromatic polyamide membrane.</figcaption></figure>

The hydrophobic property of a solute was assessed by its octanol-water partition coefficient logKow (= log(Ci, octanol / Ci, water)). The more hydrophobic the solute is, the higher logKow is. The calculated values of HSPs (Eq. 3-5) and the mutual affinities (Ra membrane-solute, Ra solute-solvent, Eq.6) are reported in Table 2 (see also Supplementary S2). On the one hand, the membrane-solute affinity was higher than the solute-solvent affinity, except for Tylosin for which the two were well balanced. On the other hand, the affinity between solutes and water was roughly similar, while there were significant differences in membrane-solute affinity. This underlined the interest of the set of the selected solutes to study the impact of the membrane-solute affinity on the rejection.
<table><caption>**Table 1.** Physico-chemical characteristics of solutes.</caption><thead><tr><th>Solute</th><th>Molecular weight (g mol<sup>-1</sup>)</th><th>Net Charge*** at pH=8.2</th><th>logK<sub>ow</sub></th><th>Molar volume (Fedors)** (cm<sup>3</sup>.mol<sup>-1</sup>)</th><th>r (Fedors) (nm)**</th></tr></thead><tbody><tr><td>Tropaeolin O (azo-dye, TO)</td><td>293</td><td>-2</td><td>1.53 [29]</td><td>149.4</td><td>0.57</td></tr><tr><td>Acid Red 1 (azo-dye, AR1)</td><td>463</td><td>-1</td><td>4.96 [30]</td><td>274.2</td><td>0.69</td></tr><tr><td>Brilliant Blue G (azo-dye, BBG)</td><td>831</td><td>-1</td><td>-2.55 [31]</td><td>545.6</td><td>0.88</td></tr><tr><td>Thiamin (vitamin B1, TH)</td><td>265</td><td>+1</td><td>1.19 [30]</td><td>172.8</td><td>0.60</td></tr><tr><td>Tylosin (antibiotic, TY)</td><td>916</td><td>+0.5</td><td>0.87*</td><td>254.6</td><td>0.75</td></tr></tbody></table>

<table><caption>**Table 2.** Hildebrand (δ<sub>global</sub>), Hansen Solubility Parameters (HSPs, δ<sub>d</sub>, δ<sub>p</sub>, δ<sub>h</sub>) of solutes and membrane, and Ra mutual affinity between membrane and solute & solute and solvent calculated according to Eq.2-Eq.6 and data given in Table 1.</caption><thead><tr><th>solutes</th><th>δ<sub>d</sub> (MPa<sup>0.5</sup>)</th><th>δ<sub>p</sub> (MPa<sup>0.5</sup>)</th><th>δ<sub>h</sub> (MPa<sup>0.5</sup>)</th><th>δ<sub>global</sub> (MPa<sup>0.5</sup>)<sup>2</sup></th><th>Ra membrane-solute</th><th>Ra solute-solvent(water)</th></tr></thead><tbody><tr><td>Troapeolin O</td><td>26.1</td><td>10.1</td><td>19.9</td><td>34.3</td><td>20.2</td><td>31.3</td></tr><tr><td>Acid Red 1</td><td>19.0</td><td>5.2</td><td>11.9</td><td>23.1</td><td>8.1</td><td>33.1</td></tr><tr><td>Brilliant Blue G</td><td>21.0</td><td>6.5</td><td>7.0</td><td>23.1</td><td>8.8</td><td>38.3</td></tr><tr><td>Thiamin</td><td>21.8</td><td>8.5</td><td>15.8</td><td>28.3</td><td>11.5</td><td>30.4</td></tr><tr><td>Tylosin</td><td>51.6</td><td>15.3</td><td>32.0</td><td>62.7</td><td>71.5</td><td>72.9</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Solvent & Membrane</td></tr><tr><td>Water</td><td>15.5</td><td>16.0</td><td>42.4</td><td>47.9</td><td>-</td><td>-</td></tr><tr><td>Fully aromatic Polyamide (PA)</td><td>18.0</td><td>11.9</td><td>7.9</td><td>22.9</td><td>-</td><td>-</td></tr></tbody></table>

# 3. Materials and Methods

## 3.1. Waters and solutes

Deionized (DI) water (18 MΩ resistivity, 1µm filtered) was used to prepare all solutions. The origin and quality of the different solutes are given in **Table 3**.

Synthetic seawater was reconstituted by dissolving a commercial sea salts' mixture called "Instant Ocean" which has a close composition to the one of the Atlantic Ocean, (density=1.023) [33]. For the sake of the comparison 30 g.L<sup>-1</sup> NaCl was prepared in DI water at pH 8.2 adjusted by NaOH addition.

<footnote>*: logP instead of logK<sub>ow</sub> Calculated using Chem 3D software.</footnote>

<footnote>*: calculated using Chem 3D software.</footnote>

<footnote>**: Calculated using the group contribution method of Fedors [32]</footnote>

<footnote>***: calculated using pKa definition and Henderson Hasselbalch equation</footnote>
The five organic solutes of **Figure 1** were filtered at a concentration of 0.5 mmol.L⁻¹ with or without added salts (see result section). This concentration could appear as high with respect to traces found in marine environments, but was selected aiming at evidencing as much as possible the transfer mechanisms through the membrane. These concentrations were too low to induce intermolecular interactions within the solution, but were intended to better highlight the impact of membrane-solute interactions on solutes' rejection. Certainly, rejections would be higher at lower concentrations, but the trends observed would remain qualitatively valid.

Moreover, while RO literature is relatively abundant for dilute organic pollutants, there is a lack of data on more concentrated media. Nevertheless, this issue is important and may become increasingly relevant in scenarios involving accumulation due to continuous discharge into marine environments. Indeed, current practice is to build catchments further and further away from polluted coasts, at high cost. Knowledge of RO performances in more concentrated environments should be part of the decision-making process when it comes to positioning offshore catchments.

The concentration of retentate and permeate was determined from UV measurements performed with a JASCO-V360 spectrophotometer. Accordingly, the accuracy on the rejection was better than 3%.

<table><caption>**Table 3.** Origin and quality of solutes.</caption><thead><tr><td>Solute</td><td>Providers</td></tr></thead><tbody><tr><td>NaCl</td><td>analytical grade corresponding to 99.74% purity<br>Fisher Scientific</td></tr><tr><td>NaOH</td><td>Analytical grade<br>Fisher Scientific</td></tr><tr><td>Synthetic sea water</td><td>Instant Ocean salt mixture<br>reconstituted at 36 g.L⁻¹ dry matter<br>natural pH = 8.2<br>Aquarium Systems (France)</td></tr><tr><td>Tropaeolin O - (azo-dye)</td><td>Monovalent sodium salt<br>Sigma</td></tr><tr><td>Acid Red 1 - (azo-dye)</td><td>Divalent sodium salt<br>Sigma</td></tr><tr><td>Brilliant Blue G - (azo-dye)</td><td>Monovalent sodium salt<br>Sigma</td></tr><tr><td>Thiamin - (vitamin B1)</td><td>Hydrochloride form<br>Acros Organics</td></tr><tr><td>Tylosin - (antibiotic)</td><td>Tartrate form<br>Sigma</td></tr></tbody></table>

## 3.2. Membrane and filtration conditions

The selected RO membrane was a SW30 (Dow-Filmtec, **Table 4**), which is known to be a fully aromatic polyamide membrane [34].
<table><caption>**Table 4.** Characteristics of SW30 membrane according to its provider.</caption><thead><tr><td>Membrane</td><td>Material</td><td>Permeance*<br>(L h<sup>-1</sup> m<sup>2</sup> bar<sup>-1</sup>)</td><td>NaCl rejection<br>(%)</td><td>pH range stability</td><td>Maximum pressure (bar)</td><td>Zeta potential at pH=8.2</td></tr></thead><tbody><tr><td>SW30</td><td>Polyamide/Polysulfone</td><td>2.1 ± 0.1</td><td>99.4<br>at 32 g L<sup>-1</sup><br>at 55 bar</td><td>2-11</td><td>69</td><td>-12 [10]</td></tr></tbody></table>

Flat membranes of 140 cm² filtering area, as well as retentate and permeate spacers, were sampled in a spiral membrane (2540 module type, 2.5 m² filtering area). Each flat membrane was inserted between two spacers (retentate/feed and permeate ones) in a plate and frame SEPA cell (GE Osmonics, USA). Aiming at minimizing the concentration polarization as much as possible, 10 L of feed were filtered at 25°C in batch mode (volume reduction ratio, VRR=1) at a high feed flow rate $Q_{feed} = 1075 \pm 25$ L.h⁻¹ corresponding to a cross-flow velocity, estimated in free channel of 1.25 mm thickness, close to 2.5 m.s⁻¹). The applied pressure varied in the 10-40 bar.

The accuracy on the volumic permeate flux (Jp) was better than 3%. As a general trend the DI water flux was recovered after filtration of solutions. However, the membrane was cleaned at room temperature by a formulated alkaline detergent (Ultrasil 10® Ecolab France, at 0.1 g.L⁻¹ and pH=11) in order to remove organic solutes adsorbed during RO filtration. The colored effluents proved this adsorption in the case of dyes even if fluxes were not able to evidence the phenomenon. Nevertheless, the cleaning was achieved until cleaning effluents remained uncolored suggesting the full desorption from one experiment to the other.

## 4. Results

Firstly, it should be pointed out that the pressure applied in this study (maximum 40 bar) was not the optimum pressure suggested by the membrane supplier (55 bar, **Table 4**) to ensure maximum rejection of seawater salts. However, having a lower permeate flux allowed us to better focus on the different forces impacting the transfer, namely convection, diffusion and physico-chemical interactions. It was systematically checked that the rejection of the overall salt (conductivity) was not altered by the presence of the organic solutes added at the selected low concentration. In addition, the modelling of the experimental salt rejection using the Solution Diffusion model was in good agreement with the expected rejections at a higher flux, highlighting that the RO membrane was not damaged (**Figure S1-1** of **Supplementary 1**). In the following, the focus has therefore been solely on the RO of organic solutes.

The results are divided into three main sections aimed at highlighting the behaviour of solutes dissolved alone in NaCl or synthetic seawater, then in a mixture of 2 or 3 organic compounds once again in the presence of salts.

### 4.1. Filtration of solutes alone in solution at pH= 8.2 with and without salts

The applied pressure depended on the osmotic pressure generated by the filtered solution (in the 10-40 bar range for single solutes and in the 30-40 range in presence of salts). However, the target permeate fluxes were in a short range of variation from 0.3 10⁻⁵ to 2 10⁻⁵ m s⁻¹ allowing direct comparison of the mechanisms at close convection. Regardless of the filtered

<footnote>*: Our measurements at 25°C in good agreement with provider data.</footnote>
solution, neither significant irreversible fouling nor concentration polarisation due to the dyes was evidenced from the flux measurements, in good agreement with the very low concentration of solutes. In presence of salts, the flux decrease compared to the one in DI water was attributed to the osmotic pressure effect.

For a given negatively charged dye, the trend of rejection with the flux seemed not significantly affected by the presence of salts (Figure 2 a,b,c). The 3 dyes (TO, AR1, BBG) depicted transmissions in the 0.06-0.01 range.

As we were surprised by the transmission of BBG with respect to its high MW (831 g.mol⁻¹) a complementary simple experiment was achieved, consisting in the deposition of a BBG solution droplet on the support side of the membrane without any applied pressure (Figure 3a). After few seconds the typical colour of BBG was evidenced on the active layer side (Figure 3b) evidencing the ability of BBG to diffuse through the membrane without any possible doubt. For a given positively charged solute, the trend of rejection with the flux seemed only slightly affected by the presence of salts (Figure 2 d,e). The two solutes (TH, TY) evidenced typical transmissions in the 0.06-0.18 range, greater than those observed with dyes of equivalent MW.

<figure><img src="image_3.png" /><figcaption>**Figure 2:** Rejection of 0.5 mmol.L⁻¹ dyes in various environments vs permeate flux</figcaption></figure>

(a) Tropaeolin O, (b) Brilliant Blue G, (c) Acid Red 1, (d) Thiamin, (e) Tylosin-- (pH= 8.2, 25 °C, 10-40 bar, membrane SW30).

Caption: ■ : solute, ♦ : solute + NaCl ● : solute + seawater.
<figure><img src="image_4.png" /><figcaption>**Figure 3:** Picture of the two sides of a membrane coupon after deposition of a droplet of BBG solution (500 mmol.L⁻¹) on (a) the support layer and (b) the active layer side after diffusion of this droplet through the membrane.</figcaption></figure>

To delve, we calculated the C<sub>feed</sub>/C<sub>p</sub> enrichment factor provides a direct measure of solute passage through the membrane. This metric is particularly useful when rejections are high and close, as it can highlight subtle differences in membrane performance that rejection alone might not sufficiently reveal.

For the two monovalent anions (BBG, AR1) C<sub>feed</sub>/C<sub>p</sub> was significantly decreased in presence of salts (**Figure 4 d,f**). The impact of the presence of salts was less for the divalent anion (TO) whose retention was more likely to vary with the ionic strength

For the two cations (TH, TY), being more or less monovalent, the C<sub>feed</sub>/C<sub>p</sub> enrichment factor (**Figure 4 b,f**) was not significantly modified suggesting that electrostatic interactions were not the main responsible of the transmissions.

The increase in ionic strength leads to the screening of the electrostatic interactions (attractive as well as repulsive) between the (positively, negatively) charged solutes and the active membrane. As a result, hydrophobic interactions become more influential in governing rejection behavior. Given that the solutes differ in their hydrophobicity and polarity, this could be the origin of their different response to salt addition.

## 4.2. Filtration of binary mixture of dyes in various environments at pH= 8.2

The filtration of the TO + BBG mixture was investigated at 0.5 mmol.L⁻¹ concentration of each dye, with and without salts (NaCl and synthetic seawater).

In NaCl and synthetic seawater, TO rejection increased in presence of BBG compared to the filtration of TO alone in solution (**Figure 5a**), when alone TO rejection was similar with and without salt, see above). The behavior of the BBG was apparently more complex, as the variation in rejection was different in the presence of NaCl or synthetic seawater (**Figure 5b, Figure 5c**).

Nevertheless, for each dye, roughly the C<sub>feed</sub>/C<sub>p</sub> enrichment ratio was the same in presence of NaCl and synthetic seawater (**Figure 5d**) either for TO or BBG compared to single solute system in the same environment (**Figure 4 b,f**).

## 4.3. Filtration of dyes ternary mixture in various environments at pH= 8.2

The filtration of the TO + BBG + AR1 mixture was investigated at 0.5 mmol.L⁻¹ concentration of each dye, with and without salts (NaCl and synthetic seawater).
MW ≈ 280 g.mol⁻¹

<figure><img src="image_5.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(b)</figcaption></figure>

MW ≈ 460 g.mol⁻¹

<figure><img src="image_7.png" /><figcaption>(c)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(d)</figcaption></figure>

MW ≈ 870 g.mol⁻¹

<figure><img src="image_9.png" /><figcaption>(e)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(f)</figcaption></figure>

**Figure 4:** Rejection and enrichment factor $C_{feed}/C_{p}$ of 0.5 mmol.L⁻¹ dyes alone in solution in various environments at pH=8.2, 40 bar, 25 °C.
<figure><img src="image_11.png" /><figcaption>**Figure 5:** RO of dye binary mixture in various environments (pH=8.2, 25°C, 10-40 bar, 0.5 mmol.L⁻¹ of each dye) – (a) Tropaeolin O- (b) Brilliant Blue G, (c) rejection at 40 bar, (d) C<sub>feed</sub>/C<sub>p</sub> enrichment factor at 40 bar.</figcaption></figure>

Caption: ■: single dye, ♦: 2 dyes in mixture + NaCl ●: 2 dyes in mixture + seawater.

Note that when alone TO rejection was similar with and without salt
<figure><img src="image_12.png" /><figcaption>**Figure 6:** RO of ternary dye mixture (TO + BBG + AR1) in various environments (pH=8.2, 25°C, 10-40 bar, 0.5 mmol L⁻¹ of each dye) – (a) Tropaeolin O- (b) Brilliant Blue G, (c) Acid Red 1, (d) rejection at 40 bar, (e) C<sub>feed</sub>/C<sub>p</sub> enrichment factor at 40 bar.</figcaption></figure>

Caption: ■: single dye, ♦: 3 dyes in mixture + NaCl ●: 3 dyes in mixture + seawater.

In the ternary dye mixture, the rejection of TO and AR1 were increased compared to single dye solution (Figure 6a, 6c).

At 40 bar, the C<sub>feed</sub>/C<sub>p</sub> enrichment ratio was significantly increased for both TO and AR1 compared to single dye solutions (Figure 6e, Figure 4 b,d). Moreover, C<sub>feed</sub>/C<sub>p</sub> of TO in the ternary dye mixture was close to the ones reached in the binary mixture (Figure 6e, Figure 5d).

The behaviour of BBG was more complex and different in seawater and NaCl (Figure 9b) as it was already the case in presence of TO only. Moreover, C<sub>feed</sub>/C<sub>p</sub> enrichment ratio for BBG was very different in presence of TO+AR1 than with TO alone (Figure 6e, Figure 5d).
**5. Discussion**

This section focuses on the discussion of solutes' rejection based on their physico-chemical properties first and second on their interactions with the polyamide membrane as calculated by the mean of HSPs.

**5.1. Solute hydrophilicity is one parameter mastering the rejection by the polyamide membrane**

At the seawater natural pH= 8.2, the virgin SW30 membrane was negatively charged (Table 4), while TO was mainly a divalent anion, whereas AR1 and BBG were monovalent anions (Table 1). Nevertheless, adsorption of the anionic dye was highlighted on the membrane by the color of the effluent during cleaning. As a result, the charge on the active membrane can only remain negative, and besides size exclusion, electrostatic repulsion can be expected between the soluble dyes and the membrane. The ionic strength was 2 mmol.L⁻¹ as a maximum for the single dye solutions while the ionic strength increased up to 500-600 mmol.L⁻¹ in presence of NaCl and synthetic seawater, respectively. The absence of significant impact of salt addition on dye rejection (Figure 2 a,b,c) supported the idea that electrostatic interactions played little part in rejection. BBG appeared to be the most affected by the increase in ionic strength. BBG was also the largest and most hydrophilic dye (log K<sub>ow</sub> was the lowest, Table 1), suggesting that the hydrophilic/hydrophobic balance of the solute had an impact on rejection.

At the seawater natural pH= 8.2, Thiamin was a monovalent cation associated to a monovalent chloride counter anion, while Tylosin was 50/50 monovalent cation/uncharged solute and was associated to a tartrate divalent counter anion (Table 1). Given that the anionic dyes adsorbed onto the negatively charged membrane, it is highly likely that the positively charged TH and TY would also tend to adsorb onto the negatively charged pristine membrane, although the impact on flux was not evidenced due to the low concentration of TH and TY. At this stage, three hypotheses could be proposed: (1) the active membrane remained negatively charged because adsorption was unable to compensate for all the charges on the virgin membrane, (2) charge compensation was complete and the active membrane was neutral, or (3) the active membrane became positively charged. In cases 1 and 3, electrostatic interactions could have an impact on the rejection of charged solutes, which would then have to be modulated by ionic strength. However, no TY or little TH impact of salt addition was evidenced (Figure 2 d,e), which once again confirms the idea that electrostatic interactions may have played only a limited role in the rejection.

For further understanding, “twin” solutes which has close sizes and opposite charges were compared, namely TO and TH on the one hand, and BBG and TY on the other. At 40 bar, TO was more retained than TH (Figure 4a), while BBG was more retained than TY (Figure 4c). Since electrostatic interactions could only play a limited role in rejection (see above), in presence of NaCl and synthetic seawater the difference in rejection must lie elsewhere. Note that TO is slightly less hydrophilic than TH, while BBG is more hydrophilic than TY, as indicated by their log K<sub>ow</sub> (Table 1). These remarks seem to confirm that the hydrophilicity of the solute favored transmission through the polyamide membrane.

The solutes' rejection was plotted versus logK<sub>ow</sub> (Figure 7) evidencing a poorly linear general trend regardless of the presence of salts. Whatever the selected data (with and without salts) BBG remained out of this trend.
<figure><img src="image_13.png" /><figcaption>**Figure 7:** Rejection of solute versus log K<sub>ow</sub>. (a) solute alone without any salts, (b) ternary dye mixture in seawater (pH=8.2, 25 °C, at 0.9 10<sup>-5</sup> ≤ Jp ≤ 2.3 10<sup>-5</sup> m.s<sup>-1</sup>). Framed zoom: solutes alone in solution without any salt. Caption: 1: solute alone; 2: dye binary mixture; 3: dye ternary mixture</figcaption></figure>

## 5.2. Analysis of rejection with Hansen Solubility Parameters

Following the same approach as for logK<sub>ow</sub>, we continued the analysis of rejections based on the physico-chemical characteristics of solutes, but this time described first by their HSPs. Next, to investigate further, we discussed rejections by using water-solute and membrane-solute affinity as described from Ra<sub>1-2</sub>.

### 5.2.1. Rejection vs solute properties (HSPs)

The rejections of solutes were plotted versus the three HSP parameters (δ<sub>p</sub>, δ<sub>h</sub> and δ<sub>d</sub>) regardless of the salt content and if the solute was alone or in mixture (**Figure 8**). Systematically, a linear trend was found for solutes filtered alone, except Thiamine. Roughly this trend was followed whatever the presence of salts and other solutes. These results underlined that none of the interaction type (polar, H-bonding, dispersive) can be neglected to explain the rejections. As with logK<sub>ow</sub>, this also implied the need to take greater account of interactions, rather than just the physico-chemical properties of solutes.
<figure><img src="image_14.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(b)</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Figure 8:** Variation of solutes' rejection filtered in single solution (0.5 mmol L⁻¹) as a function of (a) δp, (b) δh and (c) 2δd. Framed zooms: solutes alone in solution without any salt.</figcaption></figure>

### 5.2.2. Rejection vs affinity

**Figure 9** depicts the attempt of correlation of the rejections with the membrane-solute affinity ($Ra_{membrane-solute}$) and the solute-water affinity ($Ra_{solute-water}$). General trends were evidenced suggesting curves with maximum. Finally, a mathematical relationship (simulation) was established linking the rejections to the solute-membrane and solute-water affinities assessed by their calculated HSP distances ($Ra$) as shown in **Figure 9c** accounting for all acquired data. The drawn simulation was of good quality as the slope was close to 1 and $R^2$= 0.993 with an average error of 15% between the experimental and simulated rejections. The coefficients in the equation suggest a balanced impact of the two affinities.

## 6. Conclusion

This work focused on the rejection behavior of a set of organic solutes by a SW30 RO membrane, whether in the presence or absence of ionic strength either due to 30 g L⁻¹ NaCl or to synthetic seawater.

The selected organics covered the 265-916 g mol⁻¹ molecular weight range, and had sizes close to the estimated cavity size of a dense polyamide membrane or a little bit larger. However, all these organic solutes passed through the membrane at 40 bar, a pressure specially chosen to study rejection in order to understand the role of physico-chemical interactions. Interestingly, the transmission of one solute could be, more or less, modulated by the presence of other organic compounds.
In order to better understand the impact of physico-chemistry on rejections, these were initially discussed solely in terms of solute characteristics (logK<sub>ow</sub>, HSPs). Considering the solute hydrophobicity, logK<sub>ow</sub> was evidenced to provide only partial, but valuable, explanations of the rejection. The correlation between each of Hansen's solubility parameters and rejection suggested that all possible types of interaction with the solute were involved in rejection (polar, H-bonding and dispersive).

In a second step, the rejection analysis was extended to interactions in the membrane-solute-solvent (water) system. This was made possible by using Ra<sub>1-2</sub> calculated from HSPs to quantify membrane-solute and solute-water interactions. Accordingly, rejections were successfully modelled by combining the two affinities (Ra<sub>membrane-solute</sub> & Ra<sub>solute-water</sub>)—The comparison between the experimental values and the values following the trend modelled from Ras did not exceed 15%, taking into account all the experimental rejections that had been acquired. These results highlighted membrane-solute and solute-solvent affinity competition in the management of organic compound rejection in RO.

The findings of this study contribute to a deeper understanding of the transfer mechanisms of organic solutes through RO membranes, and highlight the decisive role of the hydrophilic/hydrophobic balance of the solutes vs. that of the membrane. This suggests that the findings could be extended to uncharged solutes such as certain uncharged pesticides, for instance. In order to generalize the results, it will also be necessary to study the impact of the presence of other solutes on the retention of a single one. In particular, the dynamics of competitive adsorption on the membrane should be at the heart of these developments.

A better understanding of the transfer mechanisms is necessary in order to gain better control on the rejection during the process, which is essential for enhancing the safety and effectiveness of real-world desalination operations.

However, it also remains clear that membrane ageing will modify its physico-chemical characteristics, and that the presence of biofilm and other fouling species will have an impact on rejection. Further studies are required to take these phenomena into account requesting the ability to better model the aged and fouled membranes.
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 9:** Correlation and modelling of rejections with all collected data (pH=8.2, 25 °C, 0.9 $10^{-5} \le J_p \le 2.3 \cdot 10^{-5}$). (a) $Ra_{membrane-solute}$, (b) $Ra_{solute-water}$, (c) simulated rejection established according to $Ra_{membrane-solute}$ and $Ra_{solute-water}$.</figcaption></figure>
## Acknowledgements

Fatima Zohra Charik acknowledges Eiffel & Campus France for the PhD grant n°EIFFEL-DOCTORAT 2020/n°P757215H, and Toubkal N° TBK/23/171 - CAMPUS N° 48532NL. This work was supported by MESRSI (Ministère de l'Enseignement Supérieur et de la Recherche Scientifique et de l'Innovation) and CNRST (Centre National pour la Recherche Scientifique et Technique-Morocco) (Project: PPR/2015/72).

## Authorship contributions

M. Rabiller-Baudry and S. Alami Younssi were responsible for the conception and supervision of the Toubkal project. The data were acquired by Fatima Zohra Charik and data were analysed and interpreted by FZC and MRB. All the authors approved the final manuscript.

## List of abbreviations

<table><tr><td>HSP</td><td>Hansen solubility parameter</td></tr><tr><td>δ<sub>d</sub></td><td>Dispersion solubility parameter</td></tr><tr><td>δ<sub>global</sub></td><td>Global solubility parameter</td></tr><tr><td>δ<sub>h</sub></td><td>Hydrogen bonding solubility parameter</td></tr><tr><td>δ<sub>p</sub></td><td>Polar solubility parameter</td></tr><tr><td>E<sub>coh</sub></td><td>Cohesive energy density</td></tr><tr><td>J<sub>p</sub></td><td>Permeate flux</td></tr><tr><td>R</td><td>Rejection</td></tr><tr><td>Ra</td><td>Distance in the 3D-HSP diagram</td></tr><tr><td>V<sub>m</sub></td><td>Molar volume</td></tr><tr><td>R<sub>exp</sub></td><td>Experimental rejection</td></tr></table>

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Supplementary information
to

**Diving into the transfer of small organic solutes in RO of seawater**

Fatima Zohra CHARIK <sup>1,2</sup>, Saad ALAMI YOUNSSI <sup>2</sup>, Murielle RABILLER-BAUDRY <sup>1*</sup>

**Supplementary 1 : NaCl rejection by the SW30 membrane**

<figure><img src="image_20.png" /><figcaption>**Figure S1-1:** Rejection of 30 g.L⁻<fnref n="1" /> NaCl by SW30 (pH= 8.2, 25 °C, TMP range: 30-45 bar) and modelling by the solution-diffusion model (SD) in good accordance with provider performances.</figcaption></figure>

<footnote n="1">¹ Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226,
F-35000, Rennes, France</footnote>

<footnote n="2">² Laboratory of Materials, Membranes and Environment, Faculty of Sciences and Technologies of Mohammed VI of Casablanca, Morocco</footnote>

<footnote>*Corresponding author: murielle.rabiller-baudry@univ-rennes.fr</footnote>
Supplementary 2: Hildebrand and Hansen solubility parameters (HSPs) to
describe membrane-solute-water interactions

<figure><img src="image_21.png" /><figcaption>**Fig. S2-1:** 3D-HSP diagram evidencing Ra distance between the polyamide membrane and the solutes.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. S2-2:** 3D-HSP diagram evidencing Ra distance between the solutes and the solvent (water).</figcaption></figure>