Advances in the Understanding of the Transfer of Saccharides Through NF

membranes

Article Advances in the Understanding of the Transfer of Saccharides through NF Membranes in the Presence of Electrolytes by Coupling Quantum Mechanics and Thermodynamic Methods

Johanne Teychené 1,Hélène Roux-de Balmann 2,3 and Sylvain Galier 2,3,*

1 Toulouse Biotechnology Institute (TBI), Université de Toulouse, CNRS INRA, INSA, CEDEX 04, F-31077 Toulouse, France; [email protected] 2 Laboratoire de Génie Chimique, Université de Toulouse, INPT, UPS, CEDEX 09, F-31062 Toulouse, France; [email protected] 3 CNRS, Laboratoire de Génie Chimique, CEDEX 09, F-31062 Toulouse, France * Correspondence: [email protected]

Abstract: Different studies have shown that the presence of electrolytes modifies the nanofiltration performances and that the variation of the neutral solute transfer is mainly governed by the modification of the solute properties. The objective of this work is to strengthen the understanding of the impact of the ion composition and to progress in the long-term objective for the prediction of the nanofiltration performances. The methodology is based on the comparison of the hydration properties obtained by experimental and theoretical approaches with the mass transfer of saccharides. The key role of the saccharide hydration number to understand the impact of the ionic composition on the saccharide transfer is clearly demonstrated. Moreover, it is established that the number Citation: Teychené, J.; Balmann, of saccharide/cation interactions, which increases with the cation coordination number, is a key H.R.-d.; Galier, S. Advances in the parameter to understand the mechanisms governing the impact of the nature of the cation on the Understanding of the Transfer of saccharide mass transfer modification. Finally, correlations are obtained between the saccharide hy- Saccharides through NF Membranes dration number decrease and the variation of the saccharide radius calculated using a hydrodynamic in the Presence of Electrolytes by model for different ionic compositions and operating modes (diffusion and filtration). From these Coupling Quantum Mechanics and results, it could be possible to evaluate the saccharide transfer for a given saccharide/electrolyte Thermodynamic Methods. Membranes system transfer. 2021, 11, 341. https://doi.org/ 10.3390/membranes11050341 Keywords: nanofiltration; mass transfer modelling; saccharide; electrolyte; hydration number;

Academic Editor: Wolfgang Samhaber interactions; ion coordination number

Received: 14 April 2021 Accepted: 3 May 2021 Published: 5 May 2021 1. Introduction Membrane separation techniques, such as nanofiltration (NF), constitute an interesting Publisher’s Note: MDPI stays neutral alternative for developing high-performance processes capable of treating fluids containing with regard to jurisdictional claims in variable proportions of organic and mineral solutes [1,2]. However, NF development is published maps and institutional affil- still hampered, in particular due to the difficulty of predicting its performances when the iations. ionic composition of the fluids to be treated varies or when new, more demanding uses are considered [3–6]. In recent years, various studies have shown that the presence of electrolytes sig- nificantly modifies the performances of NF due to the variation of the neutral solutes Copyright: © 2021 by the authors. transfer [7–13]. For instance, Wang et al. [14] showed that glucose transfer increases in the Licensee MDPI, Basel, Switzerland. presence of NaCl, and that this increase is all the more important as the NaCl concentration This article is an open access article is high. Neutral solute transfer in nanofiltration is essentially governed by steric effects, distributed under the terms and depending on the ratio between the size of the solutes and the size of the membrane pores. conditions of the Creative Commons Thus, to explain the increase in solute transfer in the presence of electrolytes, several as- Attribution (CC BY) license (https:// sumptions have been made [15,16], such as an increase in apparent pore size [11,12,14,17], creativecommons.org/licenses/by/ a different pore size distribution in the membrane [12], an increase in the solution viscos- 4.0/).

Membranes 2021, 11, 341. https://doi.org/10.3390/membranes11050341 https://www.mdpi.com/journal/membranes Membranes 2021, 11, 341 2 of 16

ity [18], a change in the interactions between the solute and the membrane [15] and finally the partial dehydration of the solute [7–11,17,19]. The relation between the solute hydration properties and the dehydration phenomenon has also been proposed to explain the impact of the nature of the ions (valence and size) on their transfer through membranes [20]. For instance, Zhao and al. [21,22] observed a good agreement between the decrease in the ion hydrated radius and the increase in the membrane ion exchange capacity. Moreover, these authors also pointed out that the ions need to eliminate a part of their coordinated water molecule to transfer through the membrane. The ion dehydration sequence has been correlated with ion membrane selectivity and explained by the ion hydration energy which reflects the ion/water interactions [21]. Concerning the impact of the presence of ions on the neutral solute transfer, the solute dehydration has been confirmed within the works of Bouranene and et al. [7,19] and Boy and et al. [9,10]. More precisely, in the case of the investigation of the transfer of saccharides in the presence of electrolytes, it has been pointed out that the impact of the modification of the membrane properties on saccharide transfer is negligible and that the transfer is, therefore, essentially governed by the modification of the solute properties. The assumption of saccharide dehydration has been validated from the good correlations obtained between the variation of the saccharide flux, determined in both diffusion and filtration operating modes for a given electrolyte, and the variation of the saccharide apparent molar volume, which reflects the saccharide hydration state [9,10]. Moreover, it has been demonstrated that these results are physically relevant to the dehydration phenomenon since the solute radius variation in the presence of electrolytes, calculated from the mass transfer modelling, using a hydrodynamic model, was found to correspond to a fraction of a water molecule [10]. These works also clearly demonstrated the impact of the ion valence on the increase in the saccharide transfer (divalent > monovalent). More precisely, it has been shown that the increase in saccharide transfer, due to the impact of the electrolyte on the saccharide properties, is all the more important as the ions in solution are hydrated (divalent ions > monovalent ions). However, concerning the impact of the electrolyte nature, it has not been possible to establish a clear quantitative relationship between the mass transfer modification and the variation of the saccharide apparent molar volume [9]. Then, in order to further understand the impact of the ionic composition on the transfer of a neutral solute, recent investigations using complementary approaches at different scales were carried out to investigate the mechanisms governing the saccharide/electrolyte interactions. First, at the macroscopic scale, a thermodynamic method, based on the determination of the apparent molar volume of saccharides in the presence of electrolytes, was used to characterize the saccharide hydration. The determination of the volumetric properties of saccharides (xylose, glucose and sucrose) in different electrolytes (LiCl, NaCl, KCl, Na2SO4,K2SO4, CaCl2, MgCl2 and MgSO4) confirmed that most of the contributions to saccharide dehydration in the presence of electrolytes is due to the ion valence (divalent ions > monovalent ions). Additionally, it was also observed that the saccharide dehydration + + 2+ 2+ − 2− increases according to the following sequences: Na < K < Mg < Ca and Cl < SO4 , − 2− and that the anions (Cl or SO4 ) have no influence on the cation sequence [23]. Moreover, the saccharide hydration numbers, which reflect the solute hydration state, were also determined for the various electrolytes and the different concentrations investigated from the corresponding partial molar volume of saccharides [24]. More recently, the interactions in saccharide/electrolyte systems were also determined at the microscopic scale using a theoretical method (DFT, theory of density functionality). First, the computation of the ion hydration properties in water confirmed that the presence − 2− of an anion (Cl or SO4 ) does not lead to a change in the first cation hydration layer (Na+,K+, Mg2+ and Ca2+)[25]. Considering this last point, the saccharide/electrolyte interactions have been characterized in saccharide/cation/water systems showing that in such systems, cations and saccharides are both dehydrated [26]. In agreement with the results obtained from the volumetric properties, quantum mechanics calculations Membranes 2021, 11, 341 3 of 16

have shown that the saccharide dehydration increases with the ion valence and that the saccharide dehydration increases according to the following sequences: Na+ < K+ and Mg2+ < Ca2+. Simulation results showed that the number of saccharide/cation interactions increases with the cation coordination number in water (i.e., the number of water molecules directly interacting with the cation), and that this increase is directly linked to an increase in the saccharide dehydration. Finally, ion and saccharide properties, obtained from thermodynamic data as well as simulation works, were compared in order to rationalize the relation between the saccharide hydration number and the hydration properties of ions [24]. It was shown that the saccharide hydration number decreases linearly with the cation coordination number, regardless of the cation valence. Divalent cations have a greater impact than monovalent ones due to the stronger electrostatic interactions with the saccharide hydroxyl groups which induce higher coordination numbers. For a given cation valence, the coordination number increases with the size of the cation. This allows the cation to create stronger interactions with the saccharide and then to dehydrate the saccharide. Thus, the combination of the characterization of the hydration properties of both ions and saccharides at different scales has shown that the knowledge of the hydration properties of ions makes it possible to evaluate the saccharide hydration number. As previously mentioned, mass transfer models, such as the hydrodynamic model, can be considered to investigate the impact of the dehydration phenomenon on the mass transport of neutral solutes in confined space through the determination of the solute radius [10]. However, it is still difficult to integrate the influence of the confined space and, more precisely, the impact of the solution/membrane interactions on the mass transfer of molecules. Interactions at the membrane interface are related to space as well as time scales. Thus, knowledge at the molecular scale of the behaviors of aqueous solutions, containing organic and inorganic species, which interact with the membrane surfaces, in confined spaces, are essential to their understanding. In molecular simulation, given the size of the macromolecular systems to study, most of the models used to simulate systems containing membrane and aqueous solution are on a “coarse grain” scale due to their high computational effort (time and space). For instance, molecular dynamics simulation has recently been used to model the mass transfer through NF/RO membranes [27], showing interesting results in the case of single ions or water, although it is impossible to compute “practical” conditions in terms of pressure, for instance. Moreover, in any case, it is impossible to implement non-covalent interactions in molecular dynamics, which is the key point for the investigation of the dehydration phenomenon. Then, based on these recent results, the aim of this paper is to advance the knowledge of the mechanisms and the estimation of the mass transfer of neutral solutes through nanofiltration membranes as a function of the ionic composition. More precisely, the objective of this work is to strengthen the understanding of the impact of the ion nature, especially for a given valence, since it has not been completely explained to date. The envisaged methodology is based on the comparison of the hydration properties obtained by experimental and theoretical approaches (volumetric properties from a thermodynamic method and quantum mechanics data) with the mass transfer of saccharides through an NF membrane. Thus, correlations between the solute hydration properties obtained at different scales [23–26] and the mass transfer parameters, which characterize the impact of the electrolyte on the saccharide transfer, are investigated to improve the understanding of the impact of the nature (cation, anion, size, valence, etc.) and the concentration of the ions. Special attention is paid to the saccharide hydration number and to the coordination number of ions since it has been shown that these hydration properties are closely linked and relevant to describe and understand saccharide dehydration in the presence of electrolytes. Then, in order to progress in the long-term objective for the prediction of the NF performances, the relation between the variation of the saccharide hydration number in the presence of the electrolyte and the modification of the saccharide radius calculated using a hydrodynamic model is investigated. Membranes 2021, 11, x FOR PEER REVIEW 4 of 16

the presence of the electrolyte and the modification of the saccharide radius calculated using a hydrodynamic model is investigated.

2. Materials and Methods 2.1. Mass Transfer Experiments In order to understand and highlight the impact of the nature of the ion on the modification of saccharide transfer in nanofiltration, additional transfer measurements were Membranes 2021, 11, 341 performed in this work. The experiments were performed in the diffusion operating mode 4 of 16 (concentration gradient driving force) to avoid the impact of ion retention on saccharide mass transfer [9]. The mass transfer study was carried out for glucose (180.16 g mol−1) in electrolytes containing2. Materials Cl− (NaCl, and KCl, Methods MgCl2 and CaCl2) with a purity > 99%, for given glucose and cation2.1. concentrations Mass Transfer (1 Experiments mol.kg−1). The schematic device of the experimental setup is shown in Figure 1. The mass transfer measurements were conducted using the same nan- ofiltrationIn membrane order to (Dow understand Filmtec NF and membrane, highlight polyamide the impact active layer), of the diffusion nature cell of the ion on the andmodification experimental ofprocedure saccharide as described transfer in in Boy nanofiltration, and et al. [9]. additional transfer measurements were performedThe diffusion in thisexperiments work. Thewere experiments carried out with were glucose/water performed and in glucose/electro- the diffusion operating mode lyte(concentration solutions at 25 °C gradient after the membrane driving force) soaking to with avoid the the given impact electrolyte of ion for retention 24 h. on saccharide massFor any transfer set of [experiments,9]. the glucose concentration was measured by HPLC with a Jasco system,The mass using transfer a Shodex study column was (SH carried 1011) and out a Jasco for glucose RI 2031 refractometer. (180.16 g mol The−1 ) in electrolytes mobile phase was a− 0.02 mol.L−1 H2SO4 solution at 0.8 mL.min−1. The injection volume was containing Cl (NaCl, KCl, MgCl2 and CaCl2) with a purity > 99%, for given glucose 20 µL, and the column temperature as 50 °C. −1 andThe cation experiments concentrations were carried (1 out mol.kg at least tw).ice. The For schematic all experiments, device the ofevolution the experimental of setup theis number shown of inmoles Figure of glucose1. The as mass a function transfer of time measurements was linear, confirming were conducted that the glu- using the same cosenanofiltration concentration membranegradient was(Dow constant Filmtec throughout NF membrane, the experiment. polyamide The same active mem- layer), diffusion branecell sample and experimental was used for all procedure the experiments. as described in Boy and et al. [9].

Figure 1. Nanoﬁltration experimental device (solvent = water for saccharide/water systems; solvent Figure 1. Nanofiltration experimental device (solvent = water for saccharide/water systems; solvent= = electrolyte electrolyte for for saccharide/electrolyte saccharide/electrolyte systems). systems).

2.2. MassThe Transfer diffusion Parameters experiments were carried out with glucose/water and glucose/electrolyte ◦ solutionsThe specific at 25protocolC after developed the membrane by Boy et al soaking. [9] was withused to the dissociate given electrolyte and quantify for 24 h. the contributionFor any of set the ofmodification experiments, of the thesolutes glucose or the concentrationmembrane properties was to measured the trans- by HPLC with fer aof Jasco saccharides. system, The using impact a Shodexof electrolytes column on the (SH membrane 1011) and properties a Jasco was RI character- 2031 refractometer. The −1 −1 izedmobile by the phasesaccharide was flux a 0.02 measured mol·L in water,H2SO JS,W4. solutionThe impact at of 0.8 electrolytes mL·min on. the The sac- injection volume charidewas 20propertiesµL, and was the estimated column fr temperatureom the additional as 50saccharide◦C. flux, ∆J, expressed as the difference between the saccharide flux measured in saccharide/electrolyte systems, JS,El, The experiments were carried out at least twice. For all experiments, the evolution of and the one determined in saccharide/water systems: the number of moles of glucose as a function of time was linear, confirming that the glucose concentration gradient was constant throughout the experiment. The same membrane sample was used for all the experiments. 2.2. Mass Transfer Parameters The specific protocol developed by Boy et al. [9] was used to dissociate and quantify the contribution of the modification of the solutes or the membrane properties to the transfer of saccharides. The impact of electrolytes on the membrane properties was characterized by the saccharide flux measured in water, JS,W. The impact of electrolytes on the saccharide properties was estimated from the additional saccharide flux, ∆J, expressed as the difference between the saccharide flux measured in saccharide/electrolyte systems, JS,El, and the one determined in saccharide/water systems:

∆J = JS,El − JS,W. (1)

In diffusion mode, the solute transfer was modelled using a hydrodynamic model [28] in which the solute ﬂux is related to the driving force (concentration gradient) through the characteristic parameters of the systems studied [10]: Membranes 2021, 11, 341 5 of 16

φ × K × D × A J = d ∞ k ∆C, (2) S L 2 −1 where φ is the partitioning coefficient; Kd is the hindrance factor for diffusion; D∞ (m ·s ) is the diffusion coefficient of the solute at infinite dilution; Ak is the membrane porosity; L (m) is the pore length; and ∆C (mol·m−3) is the concentration difference between the feed and eluate compartments, i.e., across the membrane. The partition coefficient, φ, and the hindrance factor for diffusion, Kd, are related to the pore radius, rP, and the solute radius, rS. The equations are given in ref. [10]. Then, the solute radius in the electrolyte, rS,El, can be obtained by assuming that the variation of the saccharide transfer in the presence of electrolytes compared to that in water is due to a decrease in the solute radius (rP is assumed constant and independent of the electrolyte composition). More precisely, the solute radius in the electrolyte was determined from the comparison between the ratio of the experimental and calculated values of the diffusion flux in the electrolyte, JS,El, and in water, JS,W, using a mean square method. Then, the modification of the solute radius in the presence of electrolytes, ∆rS, was calculated according to the following expression:

∆rS = rS,El − rS,W, (3)

where rS,W is the saccharide radius in water. The values of the membrane pore radius considered in this work for xylose, glucose and sucrose are 0.45, 0.50 and 0.54 nm, respectively. They were obtained for the same membrane with saccharide water systems in ﬁltration operating mode (pressure driven driving force) [10,29]. Indeed, it is commonly reported that increasing values are obtained for increasing solute size due to the pore size distribution, since strongly retained solutes are transferred through the larger pores [12,29].

3. Results The objective is to improve the understanding and evaluation of mass transfer in nanoﬁltration in the presence of electrolytes. In order to progress in this objective, the methodology developed in the present work is based on the comparison between quan- tities characterizing the impact of the ionic composition on the saccharide transfer and the hydration properties of solutes. These properties are obtained by different methods characterizing the hydration at macroscopic and microscopic scales.

3.1. Mass Transfer and Saccharide Hydration Number 3.1.1. Inﬂuence of the Cation The results obtained in this work with glucose/water and glucose/electrolyte systems in diffusion mode and in the presence of various electrolytes containing Cl− with different cations, are given in Table1.

Table 1. Impact of the cation nature. Glucose flux in water, JS,W, and in the electrolyte, JS,El; additional glucose flux, ∆J; glucose hydration number, nH (from [24]); fitted glucose radius, rS,El, and its variation in the presence of electrolyte, ∆rS. Cation and glucose molality = 1 mol.kg−1; diffusion mode; T = 25 ◦C. Glucose hydration number and radius in water: nH = 4.72; rS,W = 0.363 nm.

J J ∆J n r ∆r Electrolyte S,W S,El H S,El S (×10−7 mol·m−2·s−1)(×10−7 mol·m−2·s−1)(×10−7 mol·m−2·s−1) (nm) (nm) NaCl 4.7 8.6 3.9 4.36 0.346 0.017 KCl 2.7 11.4 8.7 4.26 0.337 0.026 MgCl2 4.6 16.6 12.0 4.15 0.325 0.038 CaCl2 4.6 25.2 20.6 4.02 0.311 0.052 Membranes 2021, 11, x FOR PEER REVIEW 6 of 16

mol.m−2.s−1, while it ranged between 8.6 and 25.2 × 10−7 mol.m−2.s−1 in glucose/electrolyte systems.

Membranes 2021, 11, 341 Table 1. Impact of the cation nature. Glucose flux in water, JS,W, and in the electrolyte,6 of 16 JS,El; additional glucose flux, ∆J; glucose hydration number, nH (from [24]); fitted glucose radius, rS,El, and its variation in the presence of electrolyte, rS. Cation and glucose molality = 1 mol.kg−1; diffusion mode; T = 25 °C. Glucose hydration number and radius in water: Values obtained in the present study are of the same order of magnitude than those nH = 4.72; rS,W = 0.363 nm. obtained in a previous work [9]. The differences can be explained by the use of different JS,W JS,El J nH rS,El rS Electrolyte membrane samples (derived from the same commercial reference). Such differences have (×10−7 mol.m−2already.s−1) been(×10−7 observed. mol.m−2.s−1) (×10−7 mol.m−2.s−1) (nm) (nm) NaCl 4.7 The saccharide8.6 fluxes in water, J3.9S,W , measured for4.36 the membrane0.346 conditioned0.017 with KCl 2.7 NaCl, MgCl2 and11.4 CaCl 2 were identical.8.7 For the membrane4.26 soaked with0.337 KCl, the0.026 values of MgCl2 4.6 JS,W were lower16.6 than those measured12.0 in the other electrolytes.4.15 0.325 0.038 CaCl2 4.6 Results showed25.2 that the saccharide20.6 flux increased in the4.02 presence of0.311 electrolytes, 0.052JS,El > JS,W (factor of 1.5 to 6). The glucose flux in water ranged between 2.7 and 4.7 × 10−7 mol.m−2.s−1, −7 −2 −1 whileResults it ranged reported between in Table 8.6 and 1 show 25.2 × that10 themol.m additional.s influx glucose/electrolyte of glucose, ∆J, into systems. the elec- trolytesResults followed reported the given in Tablesequence:1 show NaCl that < KCl the < additional MgCl2 < CaCl flux2. of Although glucose, for∆ theJ, into mem- the electrolytes followed the given sequence: NaCl < KCl < MgCl < CaCl . Although for the brane soaked in KCl, JS,W was smaller than JS,W for the membrane2 soaked2 in NaCl, JS,El in themembrane presence soakedof KCl instill KCl, remainedJS,W was larger smaller than than theJ S,Wglucosefor the flux membrane in NaCl. soakedIn spite in of NaCl, the singularityJS,El in the of presence the glucose of KCl flux still in remained water for larger a membrane than the soaked glucose with flux inKCl, NaCl. which In spiteis not of investigatedthe singularity in this of thework, glucose one can flux noti in waterce that for there a membrane was no singularity soaked with of K KCl,+ on the which glucose is not + fluxinvestigated in the presence in this of work, electrolyte. one can Therefore, notice that the there additional was no singularity glucose flux, of K ∆Jon, depends the glucose on J theflux nature in the of presence the electrolyte, of electrolyte. and the Therefore, increase in the saccharide additional flux glucose is greater flux, ∆in ,electrolytes depends on the nature of the electrolyte, and the increase in saccharide flux is greater in electrolytes containing divalent cations than in electrolytes containing monovalent ones. containing divalent cations than in electrolytes containing monovalent ones. As specified in the introduction, the saccharide hydration number at an infinite dilu- As specified in the introduction, the saccharide hydration number at an infinite dilution, nH, is more relevant than the variation of the partial molar volume to reveal the solute tion, nH, is more relevant than the variation of the partial molar volume to reveal the solute hydration degree. The nH glucose values, calculated from thermodynamic data, are re- hydration degree. The nH glucose values, calculated from thermodynamic data, are reported in Table 1 [23]. The comparison of nH values in different electrolyte showed that ported in Table1[ 23]. The comparison of n values in different electrolyte showed that glu- glucose dehydration increased according toH the following sequence: Na+ < K+ < Mg2+ < Ca2+. cose dehydration increased according to the following sequence: Na+ < K+ < Mg2+ < Ca2+. Thus, with regard to the influence of the nature of the cation, a good agreement was ob- Thus, with regard to the influence of the nature of the cation, a good agreement was tained between the two sequences characterizing the increase in saccharide transfer and obtained between the two sequences characterizing the increase in saccharide transfer and its dehydration in the presence of electrolyte. its dehydration in the presence of electrolyte. Then, in order to further understand the impact of the cation on the additional sac- Then, in order to further understand the impact of the cation on the additional saccha- charideride flux, flux, the the glucose glucose hydration hydration numbers numbers and an thed the glucose glucose additional additional flux flux values values measured measured in the presence of electrolytes containing− Cl− (NaCl, KCl, MgCl2 and CaCl2) were in the presence of electrolytes containing Cl (NaCl, KCl, MgCl2 and CaCl2) were compared comparedand represented and represented in Figure2 in. Figure 2.

5.0

H2O

4.5 NaCl KCl MgCl2 CaCl2 4.0 glucose H n

3.5

3.0 0 5 10 15 20 25 ΔJ(x10-7 mol.m-2.s-1)

Figure 2. Impact of the cation nature. Correlation between the glucose hydration number, nH, and the glucose additional ﬂux, ∆J, in the presence of different electrolytes (NaCl, KCl, MgCl2 and CaCl2). Cation and glucose molality = 1 mol.kg−1; diffusion mode; T = 25 ◦C. Glucose hydration number in water: nH = 4.72.

It can be observed that a good relationship was obtained between the decrease in the glucose hydration number and the increase in glucose ﬂux, under diffusion conditions, in the presence of electrolytes containing different cations. It is interesting to note that it was Membranes 2021, 11, 341 7 of 16

not possible to establish this kind of correlation from the variation of the apparent molar, which also revealed the solute hydration state [9].

3.1.2. Influence of the Anion In order to confirm the key role of the saccharide hydration number, the additional saccharide fluxes obtained for various ionic compositions and operating modes (diffusion and filtration) obtained in a previous study were also considered (Boy et al. [9]). The saccharide additional flux values (xylose, glucose and sucrose) obtained in diffusion mode and in the presence of electrolytes containing Na+ with different anions (Cl− and 2− −1 SO4 ) for a given cation molality (1 mol·kg ), as well as the corresponding saccharide hydration number, are given in Table2 and represented in Figure3.

Table 2. Impact of the anion nature. Additional saccharide ﬂux (from [9]), ∆J; saccharide hydration

number, nH (from [24]); ﬁtted saccharide radius, rS,El, and its variation in the presence of electrolyte, −1 ◦ ∆rS. Cation and saccharide molality = 1 mol·kg ; diffusion mode; T = 25 C.

∆J n r ∆r Saccharide Electrolyte H S S (×10−7 mol·m−2·s−1) (nm) (nm) water 0 3.88 0.319 0 Xylose NaCl 3.2 3.57 0.305 0.014 Na2SO4 10.2 3.45 0.289 0.030 water 0 4.72 0.363 0 Glucose NaCl 3.0 4.36 0.333 0.030 Na2SO4 10.5 4.08 0.299 0.064 water 0 7.93 0.449 0 Membranes 2021, 11, x FOR PEER REVIEW 8 of 16 Sucrose NaCl 0.2 7.41 0.429 0.020 Na2SO4 5.7 7.06 0.366 0.083

9.0 H2O 8.0 xylose Na2SO4 glucose 7.0 NaCl sucrose 6.0 saccharide

H H2O n 5.0 NaCl Na2SO4 4.0

3.0 024681012 ΔJ(x10-7 mol.m-2.s-1)

Figure 3. Impact of the anion nature. Correlation between the saccharide hydration number, n , and Figure 3. Impact of the anion nature. Correlation between the saccharide hydration number, nHH, andthe the saccharide saccharide additional additional ﬂux, flux,∆J, inΔJ the, in presencethe presence of different of differ electrolytesent electrolytes (NaCl (NaCl and Na and2SO Na4).2SO Cation4). − ◦ Cationand saccharide and saccharide molality molality = 1 mol = ·1kg mol.kg1; diffusion−1; diffusion mode; mode; T = 25 T =C. 25 °C.

3.1.3. InfluenceFigure3 shows of the thatElectrolyte the greater Concentration increase in saccharide flux with Na 2SO4 than with NaCl is related to higher saccharide dehydration in the presence of Na SO . This confirms The additional saccharide flux values obtained for various electrolyte2 4concentrations thermodynamic results [23], showing that saccharide dehydration increases according to in both diffusion mode (Na2SO4) and filtration mode (NaCl) with the corresponding sac- the following sequence: Cl− < SO 2−. Moreover, as observed with the cations, a good charide hydration number are given4 in Tables 3 and 4 and represented in Figures 4 and 5, relationship was obtained between the saccharide hydration number and the increase respectively.in saccharide flux, under diffusion conditions, in the presence of electrolytes containing differentIn both anions. operating modes (diffusion or filtration), Figures 4 and 5 show a good relationship between the increase in additional saccharide flux and the corresponding saccharide hydration number decrease for increasing electrolyte concentrations.

Table 3. Impact of the electrolyte concentration. Additional saccharide flux (from [9]), ∆J; saccharide hydration number, nH (from [24]); fitted saccharide radius, rS,El, and its variation in the presence of Na2SO4, rS. Saccharide = 1 mol.L−1; diffusion mode; T = 25 °C.

[Na2SO4] ∆J nH rS rS Saccharide (mol.L−1) (×10−7 mol.m−2.s−1) (nm) (nm) 0 0 3.88 0.319 0 0.25 2.4 3.60 0.309 0.010 Xylose 0.5 10.2 3.45 0.289 0.030 1 19.9 3.08 0.273 0.046 0 0 4.72 0.363 0 Glucose 0.25 3.4 4.35 0.333 0.033 0.5 10.5 4.08 0.299 0.064 0 0 7.93 0.449 0 Sucrose 0.25 2 7.50 0.393 0.056 0.5 5.7 7.06 0.366 0.083

Table 4. Impact of the electrolyte concentration. Additional saccharide flux (from [9]), ∆J, determined at a permeate flux of Jv = 0.5 × 10−5 m.s−1; saccharide hydration number, nH (from [24]); fitted saccharide radius, rS,El, and its variation in the presence of NaCl, rS (from [9]). Saccharide = 0.1 mol.L−1; filtration mode; T = 25 °C.

[NaCl] ∆J nH rS rS Saccharide (mol.L−1) (x10−7 mol.m−2.s−1) (nm) (nm) Xylose 0 0 3.88 0.319 0

Membranes 2021, 11, 341 8 of 16

3.1.3. Inﬂuence of the Electrolyte Concentration The additional saccharide flux values obtained for various electrolyte concentrations in both diffusion mode (Na2SO4) and filtration mode (NaCl) with the corresponding saccharide hydration number are given in Tables3 and4 and represented in Figures4 and5 , respectively.

Table 3. Impact of the electrolyte concentration. Additional saccharide ﬂux (from [9]), ∆J; saccharide

hydration number, nH (from [24]); ﬁtted saccharide radius, rS,El, and its variation in the presence of −1 ◦ Na2SO4, ∆rS. Saccharide = 1 mol·L ; diffusion mode; T = 25 C.

[Na SO ] ∆J n r ∆r Saccharide 2 4 H S S (mol·L−1)(×10−7 mol·m−2·s−1) (nm) (nm) 0 0 3.88 0.319 0 0.25 2.4 3.60 0.309 0.010 Xylose 0.5 10.2 3.45 0.289 0.030 1 19.9 3.08 0.273 0.046 0 0 4.72 0.363 0 Glucose 0.25 3.4 4.35 0.333 0.033 0.5 10.5 4.08 0.299 0.064 0 0 7.93 0.449 0 Sucrose 0.25 2 7.50 0.393 0.056 0.5 5.7 7.06 0.366 0.083

Table 4. Impact of the electrolyte concentration. Additional saccharide flux (from [9]), ∆J, determined −5 −1 at a permeate flux of Jv = 0.5 × 10 m·s ; saccharide hydration number, nH (from [24]); fitted saccha- −1 ride radius, rS,El, and its variation in the presence of NaCl, ∆rS (from [9]). Saccharide = 0.1 mol·L ; filtration mode; T = 25 ◦C.

Membranes 2021, 11, x FOR PEER REVIEW [NaCl] ∆J nH rS 9 of 16 ∆rS Saccharide (mol·L−1) (x10−7 mol·m−2·s−1) (nm) (nm) 0 0 3.88 0.319 0 0.25 15 3.80 0.317 0.002 Xylose 0.25 15 3.80 0.317 0.002 0.5 0.532 323.71 3.710.309 0.3090.010 0.010 1 154 543.57 3.570.308 0.3080.011 0.011 0 00 04.72 4.720.363 0.3630 0 0.25 0.256 64.60 4.600.360 0.3600.003 0.003 GlucoseGlucose 0.5 0.530 304.48 4.480.355 0.3550.008 0.008 1 44 4.36 0.352 0.011 1 44 4.36 0.352 0.011

9.0 xylose H2O 8.0 0.25 mol.L-1 glucose -1 0.5 mol.L sucrose 7.0

6.0 saccharide H

n 5.0 H O 2 0.25 mol.L-1 0.5 mol.L-1 4.0 1 mol.L-1 3.0 0 5 10 15 20 25 ΔJ(x10-7 mol.m-2.s-1)

FigureFigure 4. 4.ImpactImpact of the of theelectrolyte electrolyte concentration. concentration. Correlation Correlation between between the saccharide the saccharide hydration hydration num- −1 number,ber, nH ,n andH, and the the saccharide saccharide additional flux, ﬂux, ΔJ∆, inJ, inthe the presence presence of Na of2SO Na4. 2SaccharideSO4. Saccharide = 1 = 1 mol·L ; mol.Ldiffusion−1; diffusion mode; mode; T = 25 T ◦=C. 25 °C.

5.0

H2O 0.25 mol.L-1 0.5 mol.L-1 4.5 1 mol.L-1

4.0 H O 2 0.25 mol.L-1 0.5 mol.L-1 saccharide -1 H 1 mol.L n 3.5 xylose glucose 3.0 0 102030405060 ΔJ(x10-6 mol.m-2.s-1)

Figure 5. Impact of the electrolyte concentration. Correlation between the saccharide hydration number, nH, and the saccharide additional flux, ΔJ, determined at a permeate flux of Jv = 0.5 × 10−5 m.s−1, in the presence of NaCl. Saccharide = 0.1 mol.L−1; filtration mode; T = 25 °C.

To summarize, it was demonstrated that the saccharide hydration number is a key parameter to describe the impact of the presence of electrolytes on the saccharide mass transfer since good correlations were obtained for different ionic compositions (ion nature and concentration) and operating modes (diffusion and filtration).

Membranes 2021, 11, x FOR PEER REVIEW 9 of 16

0.25 15 3.80 0.317 0.002 0.5 32 3.71 0.309 0.010 1 54 3.57 0.308 0.011 0 0 4.72 0.363 0 0.25 6 4.60 0.360 0.003 Glucose 0.5 30 4.48 0.355 0.008 1 44 4.36 0.352 0.011

9.0 xylose H2O 8.0 0.25 mol.L-1 glucose -1 0.5 mol.L sucrose 7.0

6.0 saccharide H

n 5.0 H O 2 0.25 mol.L-1 0.5 mol.L-1 4.0 1 mol.L-1 3.0 0 5 10 15 20 25 ΔJ(x10-7 mol.m-2.s-1)

Figure 4. Impact of the electrolyte concentration. Correlation between the saccharide hydration Membranes 2021, 11, 341 9 of 16 number, nH, and the saccharide additional flux, ΔJ, in the presence of Na2SO4. Saccharide = 1 mol.L−1; diffusion mode; T = 25 °C.

5.0

H2O 0.25 mol.L-1 0.5 mol.L-1 4.5 1 mol.L-1

4.0 H O 2 0.25 mol.L-1 0.5 mol.L-1 saccharide -1 H 1 mol.L n 3.5 xylose glucose 3.0 0 102030405060 ΔJ(x10-6 mol.m-2.s-1)

FigureFigure 5. 5. ImpactImpact of of the the electrolyte electrolyte concentration. concentration. Correlation between thethe saccharidesaccharide hydrationhydration num- −5 −1 × ·−5 number,ber, nH, andnH, and the saccharidethe saccharide additional additional flux, ∆flux,J, determined ΔJ, determined at a permeate at a permeate flux of fluxJv = of 0.5 Jv = 100.5 × m10 s , − ◦ m.sin the−1, in presence the presence of NaCl. of NaCl. Saccharide Saccharide = 0.1 = mol 0.1· Lmol.L1; filtration−1; filtration mode; mode; T = T 25 = 25C. °C.

ToIn summarize, both operating it was modes demonstrated (diffusion or that ﬁltration), the saccharide Figures4 hydrationand5 show number a good relation-is a key parametership between to describe the increase the impact in additional of the saccharidepresence of ﬂux electrolytes and the corresponding on the saccharide saccharide mass transferhydration since number good correlations decrease for were increasing obtained electrolyte for different concentrations. ionic compositions (ion nature and concentration)To summarize, and it wasoperating demonstrated modes (diffusion that the saccharideand filtration). hydration number is a key parameter to describe the impact of the presence of electrolytes on the saccharide mass

transfer since good correlations were obtained for different ionic compositions (ion nature and concentration) and operating modes (diffusion and ﬁltration).

3.2. Mass Transfer and Cation Hydration Properties In our previous work, an original approach combining a quantum mechanics tech-

nique (DFT) and experimental measurements (thermodynamic properties) was developed to explain the relationship between the saccharide hydration and the hydration properties of cations [24]. More precisely, it was found that the saccharide hydration number, nH, decreases linearly with the increase in the cation coordination number, CN, which reflects the ion’s ability to form direct interactions with the saccharide hydroxyl groups. In our previous works, the solute hydration properties (ions and saccharides) in pure water and in mixture were studied via a full geometry optimization using the DFT method [24–26]. First, the ion coordination number, CN, which is defined as the number of water molecules directly bonded to the central ion in its solvation first layer, was determined [25]. Then, the number of interactions between the cation and the oxygen, ninter S/C+, defined as the number of oxygen belonging to the saccharide in direct interaction with the ion, was calculated [26]. Results concerning the ion coordination number and the number of interactions between glucose and different cations are given in Table5[ 25,26]. In saccharide/cation/water systems, results showed that saccharides are all the more dehydrated as the number of saccharide/cation interactions increases, ninter S/C+ [26]. The number of saccharide/cation interactions increases with the ion coordination number in water, CN.

Table 5. Cation coordination number, CN, in pure water and interaction number between the cation ◦ and glucose, ninter S/C+, at 25 C[25].

Na+ K+ Mg2+ Ca2+ Pure water CN 5 6 6 8 Glucose ninter S/C+ 2 2.5 3 3 Membranes 2021, 11, x FOR PEER REVIEW 10 of 16

3.2. Mass Transfer and Cation Hydration Properties In our previous work, an original approach combining a quantum mechanics tech- nique (DFT) and experimental measurements (thermodynamic properties) was developed to explain the relationship between the saccharide hydration and the hydration properties of cations [24]. More precisely, it was found that the saccharide hydration number, nH, decreases linearly with the increase in the cation coordination number, CN, which reflects the ion’s ability to form direct interactions with the saccharide hydroxyl groups. In our previous works, the solute hydration properties (ions and saccharides) in pure water and in mixture were studied via a full geometry optimization using the DFT method [24–26]. First, the ion coordination number, CN, which is defined as the number of water molecules directly bonded to the central ion in its solvation first layer, was determined [25]. Then, the number of interactions between the cation and the oxygen, ninter S/C+, defined as the number of oxygen belonging to the saccharide in direct interaction with the ion, was calculated [26]. Results concerning the ion coordination number and the number of interactions between glucose and different cations are given in Table 5 [25,26]. In saccharide/cation/water systems, results showed that saccharides are all the more dehydrated as the number of saccharide/cation interactions increases, ninter S/C+ [26]. The number of saccharide/cation interactions increases with the ion coordination number in water, CN. For a given cation valence, the saccharide dehydration sequence, as a function of the cation, was found to be identical to that obtained with the thermodynamic method (Na+ < K+ < Mg2+ < Ca2+).

Membranes 2021, 11, 341 In order to strengthen the understanding of the mechanisms governing the impact10 of of 16 the presence of electrolytes on the saccharide transfer, the additional saccharide flux and hydration properties of cations (CN cations) were compared (Figure 6).

Table For5. Cation a given coordination cation valence, number, the CN, saccharide in pure water dehydration and interaction sequence, number between as a function the cat- of ionthe and cation, glucose, was ninter found S/C+, at to 25 be °C identical [25]. to that obtained with the thermodynamic method + + 2+ 2+ (Na < K < Mg < Ca ). Na+ K+ Mg2+ Ca2+ In order to strengthen the understanding of the mechanisms governing the impact of Pure water CN 5 6 6 8 the presence of electrolytes on the saccharide transfer, the additional saccharide ﬂux and hydrationGlucose properties ninter S/C+ of cations (CN2 cations) were 2.5 compared (Figure 3 6). 3

25.0 Ca2+ 20.0 ) -1 .s -2 15.0 Mg2+ mol.m

-7 10.0 K+ J(x10 Δ 5.0 Na+

0.0 0246810 CN cation

Figure 6. Impact of the cation. Evolution of the glucose additional ﬂux, ∆J, measured in the presence Figure 6. Impact of the cation. Evolution of the glucose additional flux, ∆J, measured in the pres- + + of NaCl, KCl, MgCl and CaCl as a function of the cation coordination number, CN, of Na ,K+ , ence of NaCl, KCl, MgCl2 2 and CaCl2 2 as a function of the cation coordination number, CN, of Na , 2+ 2+ −1 ◦ KCa+, Caand2+ and Mg Mg.2+ Cation. Cation and and glucose glucose molality molality = = 1 1 mol mol.kg·kg −1; diffusion mode;mode ; T T = = 2525 °C.C.

ItIt was was observed observed that that the the additional additional glucose glucose flux flux increased increased linearly linearly with with the the cation cation coordinationcoordination number number of of the the electrolyte. electrolyte. Howe However,ver, it it was was not not possible possible to to distinguish distinguish the the impact of the cations of different valences with the same coordination number (K+ and impact of the cations of different valences with the same coordination number (K+ and Mg2+) on the additional glucose flux. Contrarily, as observed in Table5, the number of saccharide/cation interactions allowed us to distinguish K+ and Mg2+. Figure7 shows the evolution of the additional saccharide flux as a function of the number of saccharide/cation interactions. One can observe that the increase in glucose flux is related to the increase in the number of saccharide/cation interactions and thus to the increase in saccharide dehydration. A linear relationship was established between the number of saccharide/cation interactions and the additional glucose flux, except in the presence of Ca2+. Indeed, it was not possible to distinguish the impact of the cations 2+ which had the same number of saccharide/cation interactions (ninter Glucose/Mg = 2+ ninter Glucose/Ca = 3). The variation of the number of saccharide/cation interactions is very sensitive to small variations in saccharide/cation interactions. Thus, one can expect that the number of glucose/cation interactions should be higher in the presence of Ca2+ than in the presence of Mg2+, as previously observed with sucrose [26]. Indeed, Ca2+ is able to create more interactions with glucose than Mg2+, due to its higher coordination number. Thus, as observed in Figure7, a linear relationship can be obtained between the number of glucose/cation interactions and the glucose additional flux, by increasing the 2+ 2+ number of glucose/Ca interactions by one unit (ninter Glucose/Ca = 4). This point merits further investigation. Consequently, it was demonstrated that both the cation coordination number, CN, and the number of saccharide/cation interactions, ninter S/C+, are necessary to understand the mechanisms governing the impact of the nature of the cation on the saccharide mass transfer modification in the presence of electrolytes. Membranes 2021, 11, x FOR PEER REVIEW 11 of 16

Mg2+) on the additional glucose flux. Contrarily, as observed in Table 5, the number of saccharide/cation interactions allowed us to distinguish K+ and Mg2+. Figure 7 shows the evolution of the additional saccharide flux as a function of the number of saccharide/cation interactions. One can observe that the increase in glucose flux is related to the increase in the number of saccharide/cation interactions and thus to the increase in saccharide dehydration. A linear relationship was established between the number of saccharide/cation interactions and the additional glucose flux, except in the presence of Ca2+. Indeed, it was not possible to distinguish the impact of the cations which had the same number of saccharide/cation interactions (ninter Glucose/Mg2+ = ninter Glu- cose/Ca2+ = 3). The variation of the number of saccharide/cation interactions is very sensitive to small variations in saccharide/cation interactions. Thus, one can expect that the number of glucose/cation interactions should be higher in the presence of Ca2+ than in the presence of Mg2+, as previously observed with sucrose [26]. Indeed, Ca2+ is able to create more interactions with glucose than Mg2+, due to its higher coordination number. Thus, as observed in Figure 7, a linear relationship can be obtained between the number of glucose/cation interactions and the glucose additional flux, by increasing the number of glucose/Ca2+ interactions by one unit (ninter Glucose/Ca2+ = 4). This point merits further investigation. Consequently, it was demonstrated that both the cation coordination number, CN, and the number of saccharide/cation interactions, ninter S/C+, are necessary to understand the Membranes 2021, 11, 341 mechanisms governing the impact of the nature of the cation on the saccharide mass trans-11 of 16 fer modification in the presence of electrolytes.

25.0 Ca2+ 20.0 ) -1 .s -2 15.0 Mg2+ mol.m

-7 10.0 K+ J(x10 Δ 5.0 Na+

0.0 012345 ninter S/C+

FigureFigure 7. 7. ImpactImpact of of the the cation. cation. Evolution Evolution of of the the glucose glucose additional additional flux, ﬂux, ∆∆J,J in, in the the presence presence of of NaCl, NaCl, KCl,KCl, MgCl MgCl2 2andand CaCl CaCl2 2asas a afunction function of of the the number number of of glucose/cation glucose/cation interactions, interactions, ninterninter S/C+ S/C+. Cation. Cation andand glucose glucose molality molality = = 1 1mol.kg mol·kg−1−; diffusion1; diffusion mode; mode; T = T 25 = 25°C.◦ C.

3.3.3.3. Hydration Hydration Number Number and and Saccharide Saccharide Radius Radius AsAs mentioned mentioned in in the the introduction, introduction, the the perfor performancesmances of the of thenanofiltration nanofiltration process process de- penddepend on the on thecombination combination of quite of quite complex complex and andimbricated imbricated mechanisms, mechanisms, such suchas the as im- the pactimpact of the of theion ion composition composition on onthe the transfer transfer of ofneutral neutral species species investigated investigated in in this this work. work. As As aa result, result, it it was was barely barely possible possible to to predict predict them them,, and and this this is is a a bottleneck bottleneck for for the the development development ofof this this operation. operation. This This problem problem will will be be solved solved once once the the parameters parameters required required for for the the mass mass transfertransfer modelling, modelling, such such as asmembrane membrane and and solu solutionstions properties, properties, are accessible. are accessible. It is a Itlong- is a long-term objective that requires the elucidation of the phenomena. term objective that requires the elucidation of the phenomena. Then, based on the better understanding of the mechanisms governing the mass Then, based on the better understanding of the mechanisms governing the mass transfer of saccharide in the presence of electrolyte, i.e., the phenomena of saccharide transfer of saccharide in the presence of electrolyte, i.e., the phenomena of saccharide de- dehydration, one can expect to progress in this long-term objective. hydration, one can expect to progress in this long-term objective. Typically, the mass transfer of a neutral solute can be described and predicted using a hydrodynamic model [10,28]. More precisely, the neutral solute transfer is fixed by the membrane properties (pore radius, membrane porosity and pore length), the solute radius and the operating conditions. For instance, the saccharide transfer in the presence of electrolytes was modelled by Boy et al. to evaluate the saccharide radius in the presence of electrolytes, rS,El, and to deduce the variation of the saccharide radius, ∆rS (see Equation (3)), in both diffusion and filtration operating modes [10]. In the present work, the correlation between the saccharide flux variation and the saccharide hydration number for various ionic compositions was clearly demonstrated. Then, in order to progress in the mass transfer prediction, the relation between the saccharide hydration number in the presence of the electrolyte and the variation of the saccharide radius calculated from the modelling of the saccharide flux using the hydrodynamic model, was investigated. The membrane properties and, more precisely, the membrane pore radius, rp, was assumed to be constant since it was shown that the saccharide fluxes measured in water, JS,W, are weakly influenced by the nature of the electrolyte used for the membrane soaking. Usually, the membrane pore radius is obtained in filtration operating mode from the modelling of a neutral solute transfer using the hydrodynamic model. In diffusion mode, the saccharide radius in the presence of electrolyte, rS,El, and the variation of the saccharide radius, ∆rS, were determined according to the procedure developed by Boy et al. [10] and described in Section 2.2. The values obtained with various cations, anions and electrolyte concentrations are given in Tables1–3, respectively. The saccharide radius in the presence of electrolytes, rS,El, and the variation of the saccharide radius, ∆rS, in filtration mode were obtained from [10] and given in Table4. Membranes 2021, 11, x FOR PEER REVIEW 12 of 16

Typically, the mass transfer of a neutral solute can be described and predicted using a hydrodynamic model [10,28]. More precisely, the neutral solute transfer is fixed by the membrane properties (pore radius, membrane porosity and pore length), the solute radius and the operating conditions. For instance, the saccharide transfer in the presence of electrolytes was modelled by Boy et al. to evaluate the saccharide radius in the presence of electrolytes, rS,El, and to deduce the variation of the saccharide radius,rS (see Equation (3)), in both diffusion and filtration operating modes [10]. In the present work, the correlation between the saccharide flux variation and the saccharide hydration number for various ionic compositions was clearly demonstrated. Then, in order to progress in the mass transfer prediction, the relation between the saccharide hydration number in the presence of the electrolyte and the variation of the saccharide radius calculated from the modelling of the saccharide flux using the hydrodynamic model, was investigated. The membrane properties and, more precisely, the membrane pore radius, rp, was assumed to be constant since it was shown that the saccharide fluxes measured in water, JS,W, are weakly influenced by the nature of the electrolyte used for the membrane soaking. Usually, the membrane pore radius is obtained in filtration operating mode from the modelling of a neutral solute transfer using the hydrodynamic model. In diffusion mode, the saccharide radius in the presence of electrolyte, rS,El, and the variation of the saccharide radius, rS, were determined according to the procedure de-

Membranes 2021, 11, 341 veloped by Boy et al. [10] and described in Section 2.2. The values obtained with various12 of 16 cations, anions and electrolyte concentrations are given in Tables 1–3, respectively. The saccharide radius in the presence of electrolytes, rS,El, and the variation of the saccharide radius, rS, in filtration mode were obtained from [10] and given in Table 4. TheThe variations variations of of saccharide saccharide hydration hydration number numberss as as a afunction function of of the the saccharide saccharide radius radius variation,variation, calculated calculated in in diffusion diffusion mode, mode, as as a afunction function of of the the cation cation and and anion anion nature, nature, are are reportedreported in in Figures Figures 88 andand 99,, respectively.

5.0

H2O

4.5 NaCl KCl MgCl2 CaCl2 4.0 glucose H n

3.5

3.0 0 0.01 0.02 0.03 0.04 0.05 0.06 Δ rS (nm)

Figure 8. Impact of the cation. Correlation between the glucose hydration number, n , and the Figure 8. Impact of the cation. Correlation between the glucose hydration number, nH, andH the variation of the glucose radius, ∆r , in the presence of different electrolytes (NaCl, KCl, MgCl and Membranes 2021, 11, x FOR PEER REVIEWvariation of the glucose radius, ΔrS, Sin the presence of different electrolytes (NaCl, KCl, MgCl132 and2of 16 −1 ◦ CaClCaCl2).2 ).Cation Cation and and glucose glucose molality molality = 1 = mol.kg 1 mol−·kg1; diffusion; diffusion mode; mode; T = 25 T °C. = 25 GlucoseC. Glucose hydration hydration numbernumber in in water: water: nHn H= 4.72.= 4.72.

9.0

H2O 8.0 NaCl

Na2SO4 7.0

xylose 6.0

saccharide glucose H

n 5.0 H2O NaCl sucrose Na2SO4 H O 4.0 2 NaCl Na2SO4

3.0 0 0.02 0.04 0.06 0.08 0.1 Δ rS(nm)

Figure 9. Impact of the anion. Correlation between the saccharide hydration number, nH, and the Figure 9. Impact of the anion. Correlation between the saccharide hydration number, nH, and the variation of the saccharide radius, ∆r , in the presence of different electrolytes (NaCl and Na SO ). variation of the saccharide radius, ΔrS,S in the presence of different electrolytes (NaCl and Na2SO2 4).4 −1 ◦ CationCation and and saccharide saccharide molality molality = = 1 1mol.kg mol·kg−1; diffusion; diffusion mode; mode; T = T 25 = 25°C. C.

AsAs expected, expected, it was observedobserved thatthat thethe variation variation of of the the saccharide saccharide radius radius in thein the presence pres- of electrolytes increased, i.e., lower saccharide radius, with the decrease in the saccharide ence of electrolytes increased, i.e., lower saccharide radius, with the decrease in the sac- hydration number. More precisely, it is worth noting that in the condition investigated in charide hydration number. More precisely, it is worth noting that in the condition inves- this work, a linear relation was observed in the presence of electrolytes containing a given tigated in this work, a linear relation was observed in the presence of electrolytes contain- anion (various cations; Figure8) or a given cation (various anions; Figure9). The slight ing a given anion (various cations; Figure 8) or a given cation (various anions; Figure 9). deviation observed for the glucose hydration number in water merits further investigation. The slight deviation observed for the glucose hydration number in water merits further The variations of saccharide hydration numbers as a function of the saccharide radius investigation. variation, calculated in both diffusion and ﬁltration operating modes, as a function of the The variations of saccharide hydration numbers as a function of the saccharide radius electrolyte concentration, are reported in Figures 10 and 11, respectively. variation, calculated in both diffusion and filtration operating modes, as a function of the electrolyte concentration, are reported in Figures 10 and 11, respectively.

9.0

H O 8.0 2 0.25 mol.L-1 0.5 mol.L-1 7.0

xylose 6.0

saccharide glucose H

n 5.0 0.25 mol.L-1 sucrose -1 H2O 0.5 mol.L 4.0 -1 0.25 mol.L 0.5 mol.L-1 1 mol.L-1 3.0 0 0.02 0.04 0.06 0.08 0.1 Δ rS(nm)

Figure 10. Impact of the electrolyte concentration. Correlation between the saccharide hydration number, nH, and the variation of the saccharide radius, ΔrS, in the presence of Na2SO4 (various concentrations indicated in the figure). Saccharide = 1 mol.L−1; diffusion mode; T = 25 °C.

Membranes 2021, 11, x FOR PEER REVIEW 13 of 16

9.0

H2O 8.0 NaCl

Na2SO4 7.0

xylose 6.0

saccharide glucose H

n 5.0 H2O NaCl sucrose Na2SO4 H O 4.0 2 NaCl Na2SO4

3.0 0 0.02 0.04 0.06 0.08 0.1 Δ rS(nm)

Figure 9. Impact of the anion. Correlation between the saccharide hydration number, nH, and the variation of the saccharide radius, ΔrS, in the presence of different electrolytes (NaCl and Na2SO4). Cation and saccharide molality = 1 mol.kg−1; diffusion mode; T = 25 °C.

As expected, it was observed that the variation of the saccharide radius in the presence of electrolytes increased, i.e., lower saccharide radius, with the decrease in the saccharide hydration number. More precisely, it is worth noting that in the condition investigated in this work, a linear relation was observed in the presence of electrolytes containing a given anion (various cations; Figure 8) or a given cation (various anions; Figure 9). The slight deviation observed for the glucose hydration number in water merits further investigation. The variations of saccharide hydration numbers as a function of the saccharide radius Membranes 2021, 11, 341 variation, calculated in both diffusion and filtration operating modes, as a function of13 ofthe 16 electrolyte concentration, are reported in Figures 10 and 11, respectively.

9.0

H O 8.0 2 0.25 mol.L-1 0.5 mol.L-1 7.0

xylose 6.0

saccharide glucose H

n 5.0 0.25 mol.L-1 sucrose -1 H2O 0.5 mol.L 4.0 -1 0.25 mol.L 0.5 mol.L-1 1 mol.L-1 3.0 0 0.02 0.04 0.06 0.08 0.1 Δ rS(nm)

Figure 10. Impact of the electrolyte concentration. Correlation between the saccharide hydration Membranes 2021, 11, x FOR PEER REVIEWFigure 10. Impact of the electrolyte concentration. Correlation between the saccharide hydration14 of 16 number, nH, and the variation of the saccharide radius, ∆rS, in the presence of Na2SO4 (various number, nH, and the variation of the saccharide radius, ΔrS, in the presence of Na2SO4 (various con- −1 ◦ centrationsconcentrations indicated indicated in the in figure). the ﬁgure). Saccharide Saccharide = 1 mol.L = 1 mol−1; diffusion·L ; diffusion mode; mode; T = 25 T °C. = 25 C.

5.0

H2O 0.25 mol.L-1 0.5 mol.L-1 4.5 1 mol.L-1

4.0 H2O 0.25 mol.L-1 0.5 mol.L-1 saccharide H n 3.5 1 mol.L-1 xylose glucose 3.0 0 0.002 0.004 0.006 0.008 0.01 0.012 Δ rS(nm)

Figure 11. Impact of the electrolyte concentration. Correlation between the saccharide hydration Figure 11. Impact of the electrolyte concentration. Correlation between the saccharide hydration number, n , and the variation of the saccharide radius, ∆r , in the presence in the presence of NaCl number, nHH, and the variation of the saccharide radius, ΔrS,S in the presence in the presence of NaCl −1 ◦ (various(various concentrations concentrations indicated indicated in the figure). figure). Saccharide == 0.1 molmol.L·L−1; ;filtration filtration mode; mode; T T = = 25 25 °C.C. In both operating modes (diffusion or filtration), it was shown again that the variation In both operating modes (diffusion or filtration), it was shown again that the varia- of the saccharide radius in the presence of electrolytes of various concentrations increased tion of the saccharide radius in the presence of electrolytes of various concentrations in- linearly with the decrease in the saccharide hydration number. creased linearly with the decrease in the saccharide hydration number. Consequently, the key role of the saccharide hydration number was strengthened, Consequently, the key role of the saccharide hydration number was strengthened, since clear correlations with the saccharide radius in the presence of electrolytes were since clear correlations with the saccharide radius in the presence of electrolytes were ob- obtained for different ionic compositions (ion natures and concentrations) and operating tained for different ionic compositions (ion natures and concentrations) and operating modes (diffusion and filtration). Moreover, linear correlations were obtained for the modes (diffusion and filtration). Moreover, linear correlations were obtained for the con- conditions considered in this work. ditions considered in this work. As previously discussed, the saccharide hydration number in the presence of elec- trolytesAs previously can be determined discussed, from the the saccharide experimental hydr determinationation number in of the thermodynamic presence of electro- proper- lytesties (volumetriccan be determined properties) from [23 the] or experimental evaluated from determination the correlations of thermodynamic with the ion coordination proper- tiesnumber (volumetric (see [24 properties)]). Thus, using [23] the or evaluated previous linear from correlations,the correlations it is with possible the toion evaluate coordina- the tionvariation number of the(seesaccharide [24]). Thus, radius using accordingthe previous to the linear ionic correlations, composition it andis possible to estimate to eval- the uatesaccharide the variation radius of in the the saccharide presence of radius electrolytes. according Finally, to the for ionic a given composition saccharide/electrolyte and to estimate the saccharide radius in the presence of electrolytes. Finally, for a given saccharide/electrolyte system, knowing the saccharide radius in water as well as the membrane pore radius, it could be possible to predict the saccharide transfer using the hydrodynamic model.

4. Conclusions Various studies focusing on the study of the influence of ionic composition on the transfer of neutral solutes across nanofiltration membranes have shown that the increase in the transfer of the neutral solute in the presence of electrolytes is mainly governed by the modification of the neutral solute hydration properties due to solute/electrolyte interactions. Recently, investigations on the mechanisms governing the saccharide/electrolyte interactions using complementary approaches at different scales have shown that the saccharide hydration numbers in the presence of electrolytes are closely linked to the hydration properties of the ions. Thus, the objectives of the present work were to strengthen the understanding of the impact of the ion nature, especially for a given valence, since it has not been completely explained to date, and to progress towards the long-term objective in the prediction of nanofiltration performances. The influence of the nature of the cation on the transfer of glucose in diffusion mode was first investigated. The glucose hydration numbers, calculated from thermodynamic data, and the glucose additional flux values measured through an NF membrane in the

Membranes 2021, 11, 341 14 of 16

system, knowing the saccharide radius in water as well as the membrane pore radius, it could be possible to predict the saccharide transfer using the hydrodynamic model.

4. Conclusions Various studies focusing on the study of the influence of ionic composition on the transfer of neutral solutes across nanofiltration membranes have shown that the increase in the transfer of the neutral solute in the presence of electrolytes is mainly governed by the modification of the neutral solute hydration properties due to solute/electrolyte interactions. Recently, investigations on the mechanisms governing the saccharide/electrolyte interactions using complementary approaches at different scales have shown that the saccharide hydration numbers in the presence of electrolytes are closely linked to the hydration properties of the ions. Thus, the objectives of the present work were to strengthen the understanding of the impact of the ion nature, especially for a given valence, since it has not been completely explained to date, and to progress towards the long-term objective in the prediction of nanofiltration performances. The influence of the nature of the cation on the transfer of glucose in diffusion mode was first investigated. The glucose hydration numbers, calculated from thermodynamic data, and the glucose additional flux values measured through an NF membrane in the − presence of electrolytes containing Cl (NaCl, KCl, MgCl2 and CaCl2), were compared. A good agreement was obtained between the increase in the glucose transfer and its hydration number in the presence of electrolytes according to the following sequence: Na+ < K+ < Mg2+ < Ca2+. This result was confirmed from the additional saccharide flux values obtained for various ionic compositions and operating modes (diffusion and filtration). Consequently, the key role of the saccharide hydration number to understand the impact of the ionic composition on the saccharide transfer through an NF membrane was clearly demonstrated. Second, in order to strengthen the understanding of the mechanisms governing the impact of the presence of electrolytes on the saccharide transfer, the additional saccharide flux and hydration properties of cations were compared. Indeed, on one hand, the relation between the saccharide hydration number and the cation coordination number has been established in previous works, and on the other hand, the correlation between the saccharide hydration number and the saccharide mass transfer was demonstrated in the present work. Thus, it was demonstrated that the number of saccharide/cation interactions, ninter S/C+, which increases with the cation coordination number, is a key parameter to understand the mechanisms governing the impact of the nature of the cation on the saccharide mass transfer modification in the presence of electrolyte. Finally, in order to progress in the long-term objective toward the prediction of NF performances, the relation between the saccharide hydration number in the presence of the electrolyte and the variation of the saccharide radius calculated using the hydrodynamic model was investigated. The key role of the saccharide hydration number was strengthened since clear correlations with the saccharide radius in the presence of electrolyte were obtained for different ionic compositions and operating modes. Thus, based on the knowledge of the saccharide hydration number and the linear correlations established in this work, it could be possible to evaluate the saccharide transfer for a given saccharide/electrolyte system transfer using the hydrodynamic model. This last point merits further investigation.

Author Contributions: Conceptualization, J.T., S.G. and H.R.-d.B.; methodology, J.T., S.G. and H.R.- d.B.; software, J.T. and S.G.; validation, J.T. and S.G.; formal analysis, J.T. and S.G.; investigation, J.T. and S.G.; resources, J.T. and S.G.; data curation, J.T. and S.G.; writing—original draft preparation, J.T. and S.G.; writing—review and editing, J.T., S.G. and H.R.-d.B.; visualization, S.G. and H.R.-d.B.; supervision, S.G. and H.R.-d.B.; project administration, S.G. and H.R.-d.B.; funding acquisition, S.G. and H.R.-d.B. All authors have read and agreed to the published version of the manuscript. Funding: Funding for this work was provided by the French governement for the PhD grant of Johanne Teychené. Membranes 2021, 11, 341 15 of 16

Institutional Review Board Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: The authors wish to acknowledge Laurent Maron for his crucial contribution in molecular modelling and for many helpful discussions. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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