Osmotic properties of aqueous solutions of NaCl and KCl [11, 40].
Abstract
Despite the tremendous progress made toward the realization of wider application for forward osmosis (FO) technologies, lack of suitable draw solutes that provide high water flux, low reverse solute flux, and facile recovery has hindered commercial development. An extensive variety of osmotic agents have been investigated during the past decade, and while simple inorganic salts remain the most widely used, organic-coated magnetic nanoparticles (MNPs) offer exploitable properties that hold great promise. In addition to size-mitigated reverse flux and low-cost recovery via magnetic separation, devitalized MNPs provide enhanced osmotic performance when compared to that of the ungrafted coating material at similar concentration levels, a consequence of greater nonideal solution behavior. This nonideality has been assessed using a simple, semiempirical model and is largely attributable to the increased solvent-accessible surface area and enhanced hydration. When attached to MNPs, polymers appear to behave osmotically as much smaller molecules, providing higher osmotic pressures and improved FO performance.
Keywords
- forward osmosis
- nonideality
- draw solute
- magnetic nanoparticles
- counterion binding
1. Introduction
Forward osmosis (FO) exploits the natural osmotic pressure gradient between two fluids separated by a semi-permeable membrane to induce the net transport of solvent from a solution of lower osmotic pressure to that of higher osmotic pressure. The FO process appears to provide a low-energy, low-cost alternative to more conventional membrane-based separation methods and offers a myriad of potential applications in industries as diverse as desalination, oil and gas, and food processing [1, 2]. Despite advances made in FO during the past decade, several challenges must still be overcome before more widespread relevance of the technology can be realized [3]. Recently, Shaffer et al. [4] provided a thermodynamic argument showing that FO-reverse osmosis (RO) desalination schemes cannot provide energy savings when compared to standalone RO. Although FO technology has been applied to a variety of water treatment strategies, draw solute inadequacies restrict its wider application [5, 6]. Mitigation of these inadequacies requires identification of draw solutions that achieve high osmotic pressure while minimizing reverse solute flux and also providing ease of recovery; the need for osmotic agents that allow for facile, inexpensive recovery remains paramount [7].
During the past decade, researchers have primarily focused their efforts in two areas, FO membrane production and draw solute identification. While considerable progress has been made toward the development of inexpensive and more robust membranes [8, 9], few commercially viable osmotic agents have been identified [10]. Desirable properties of the ideal osmotic agent are that it be nontoxic, inexpensive, stable, and highly water-soluble. In addition, the agent should have limited reverse draw solute flux, reduce internal concentration polarization (ICP), and be easily recoverable. Some osmotic agents and recovery schemes investigated to date include using inorganic salts with recovery by RO [11]; using poly(sodium acrylate) with recovery by ultrafiltration (UF) [12]; using thermoresponsive chitosan derivatives with recovery by aggregation at elevated temperature [13]; using ammonia-carbon dioxide with recovery by thermal separation [14]; using poly(N-isopropylacrylamide-co-acrylic acid) with recovery by heating and centrifugation [15]; using surfactants with recovery by UF [16]; and, using polyelectrolyte-based hydrogels with recovery by elevated temperature and pressure [17]. A critical review of what the authors term non-responsive and responsive draw solutes was recently provided by Cai and Hu [7].
Because they meet several of the aforementioned criteria, low reverse draw flux and easy recovery in particular, functionalized magnetic nanoparticles (MNPs) have garnered much attention as potential osmotic agents [18]. These MNPs typically incorporate a superparamagnetic core of Fe3O4, with a magnetization value of 75.0 emu g−1 [19], onto which organic content is coated. Among the grafting agents that have been affixed to MNPs and investigated in FO processes are 2-pyrrolidine, triethylene glycol, and poly(acrylic acid) [20]; dextran [21]; poly(ethylene glycol) diacid [22]; poly(sodium acrylate) [23, 24, 25]; poly(sodium styrene-4-sulfonate) and poly(N–isopropylacrylamide) [26]; citrate [27]; hyperbranched polyglycerol [28]; and, citric acid and oxalic acid [19]. A primary advantage of using MNPs is their ease of recyclability through magnetic separation, although particle aggregation has been shown to diminish FO water flux values after multiple regeneration cycles [10]. Another benefit of derivatized MNPs is that they have been shown to provide higher osmotic pressures when compared to solutions of the organic grafting agents alone [20], an enhancement attributable to increased solution nonideality.
A solution behaves ideally when: (1) solute/solute, solvent/solvent, and solvent/solute interactions are identical and (2) all solute and solvent molecules occupy the same volume. Real solutions deviate from ideality due to an energetic nonequivalence in one or more of these interactions and/or volume occupancies are not identical. In aqueous solution, water molecules exhibit particularly strong hydrogen bonding with various organic functional groups, carboxylate moieties in particular [29]. Factors such as hydration, ion-pairing, and dimerization can be significant contributors to thermodynamic nonideality [30] and can dramatically impact the osmotic performance of FO draw solutions.
A variety of models have been developed to explain the interesting osmotic behavior of concentrated solutions of proteins and other biological molecules [31, 32, 33, 34]. The nonideal solution behavior of large biological molecules can lead to extreme changes in osmotic pressure. As an example, at a fixed protein concentration, the osmotic pressures of bovine serum albumin (BSA) solutions display greater than fivefold changes in the range 3 < pH < 8 [32]. Such nonideality is generally attributable to variations in solvent-accessible surface area and polymeric segmental motion [35]. Models that adequately describe nonideal behavior in BSA and other polymer solutions provide a basis for explaining the unique osmotic properties of MNPs used in FO.
2. Osmotic theory
In order to function effectively as a draw agent in FO, the osmotic pressure of the draw solution must far exceed that of the feed solution. In terms of desalination, the draw must have an osmotic pressure significantly in excess of 7.7 atm in the case of a brackish feed, and in excess of 27 atm in the case of a seawater feed [4]. Because of their abilities to achieve high osmotic pressures while maintaining low solution viscosities, simple inorganic salts remain the most widely used draw agents. In addition, small ions tend to have greater diffusivity values thus moderating the effect of concentrative ICP. The strong affinity of small inorganic ions for water is revealed in their highly exothermic enthalpies of hydration [36]. This strong affiliation serves to significantly lower the chemical potential of water in draw solutions. Strong solvent/solute interactions provide high solution osmotic pressures while paradoxically making the regeneration of draw solute more difficult. Resolving this paradox has spurn interest in the development of easily removable draw agents that allow for regeneration through exploitation of solute size, thermal sensitivity, or magnetic properties. Of course, to be effective in FO processes these solutes must still provide appreciable osmotic pressure. Interestingly, structural features of various macromolecular species and molecular aggregates that allow for easy removal from aqueous solution can also serve to enhance osmotic pressure through nonideal solvent/solute interactions.
2.1. Osmotic pressure and FO water flux
The effects of osmotic pressure, solution viscosity, and molecular/ionic diffusivity on water flux (
where
2.2. Thermodynamic basis of osmotic pressure
Consider an FO process using a polymer solution as the osmotic agent. If a polymer solution is separated from pure water by a semipermeable membrane the movement of water through the barrier is explained in terms of the chemical potential of the water,
where
As Eq. (2) implies, it is reasonable to differentiate
The definitions of Gibbs free energy and chemical potential are given by Eqs. (4) and (5), respectively,
where
Eq. (6) reveals that under conditions of constant temperature and solution composition, the derivative of Gibbs free energy with respect to pressure is given by Eq. (7).
By differentiating Eq. (5) with respect to pressure, while holding other variables constant, Eq. (8) is obtained.
Similarly, by differentiating Eq. (7) with respect to amount of water Eq. (9) is obtained, in which
Because of the symmetry of second derivatives, meaning the order of differentiation is inconsequential, the partial molar volume of water is also given by Eq. (10).
Next, differentiation of an analogous form of Eq. (2) with respect to
Because
If there is no net flow of water in an apparatus like that depicted in Figure 1,
Substituting Eqs. (10) and (12) into Eq. (13) and then integrating provides Eq. (14).
Assuming the solution is incompressible (meaning that partial molar volume is independent of pressure) allows for simple integration providing Eq. (15).
For dilute solutions (
which upon substitution into Eq. (15) provides the familiar van’t Hoff equation, Eq. (18).
Deviations of solution osmotic pressure data from Eq. (18) are generally attributable to nonideal solvent-solute and solute-solute interactions. One way of expressing the extent to which a solution deviates from ideality is through the osmotic coefficient,
The osmotic coefficient is analogous to the activity coefficient and can be defined in terms of other concentration units. It is often used in conjunction with
Alternatively, and in particularly for polymer solutions, solution osmotic pressure is often expressed as a power series expansion in
where
An empirical, semi-empirical, or theoretical methodology can then be used to relate
In terms of solute molality (
where
2.3. Osmotic pressure of aqueous solutions of inorganic salts
Wilson and Stewart [38] have provided a good discussion of how solution osmotic pressure is affected by the hydration of simple ionic compounds. The short range interactions between electron pairs in water molecules and cations lead to
Compound | Molarity |
|
|
|
|
|
---|---|---|---|---|---|---|
NaCl | 0.869 | 3.9 | 1.84 | 0.968 | 44 | 3.38 × 10−6 |
KCl | 0.943 | 1.7 | 1.85 | 0.968 | 44 | 3.74 × 10−6 |
In terms of osmotic pressure and corresponding FO performance there are diminishing returns on using ever-higher concentrations of ionic compounds, especially when increased solution viscosity is also considered. While hydration numbers tend to increase with increasing cation charge density, they decrease with increasing concentration, owing in part to increased ion-pairing, effectively reducing
2.4. Osmotic properties of aqueous solutions of large organic molecules
In their studies of BSA, Kanal et al. [32] observed that osmotic pressure decreases as solution pH increases from 3 to approximately 4.6 and then increases with pH. Increases in osmotic pressure on either side of the minimum are attributed to increased electrostatic repulsive interactions. At pH values below the isoelectric point (pIBSA = 5.4), the protein adopts a net positive charge along its surface. At pH values above pIBSA, it is net negative. Electrostatic repulsion leads to a less compact protein conformation, greater segmental motion, more effective hydration, and higher osmotic pressures. Near the isoelectric point, the net-neutral protein strands adopt a more compact configuration, are less hydrated, and even tend to aggregate due to reduced intermolecular repulsion. The osmotic nonideality of BSA solutions is generally attributable to two sources: (1) large solvent/solute interactions that effectively increase polymer hydration (
The hydration of PEG of molecular weight 2000 Da (PEG2000), both unattached and attached to distearoyl phosphoethanolamine liposomes ((DSEP)-PEG2000), was investigated by Tirosh et al. [43]. Using differential scanning calorimetry, PEG2000 was found to bind 136 ± 4 water molecules, while (DSEP)-PEG2000 binds 210 ± 6 water molecules. In terms of hydration number per monomeric unit (approximately 46 units in 2000 Da PEG), these binding values correspond to hydration numbers of 3.0 and 4.6 for PEG2000 and (DSEP)-PEG2000, respectively. The increase in water molecule binding is attributed to conformational changes, a coil configuration in PEG2000 and a brush configuration in (DSEP)-PEG2000. When grafted to the liposome surface, the close proximity of the polymeric strands causes them to repel each other and to adopt a more extended, easily hydrated, form. Such behavior has been exploited in the development of draw agents that incorporate superparamagnetic magnetite (Fe3O4) onto which polymers were grafted [19, 20, 21, 22, 23, 24, 25, 26, 27, 28].
3. MNPs as FO draw agents
A summary of some recent applications of derivatized MNPs as draw agents in FO processes is provided in Table 2, which includes approximate concentrations of the repeating (monomeric) units used as capping agents on the MNPs. Other researchers have demonstrated that the osmotic properties of aqueous polymer solutions are perhaps best interpreted in terms of monomer concentration [31, 45].
Coating agent | Size (nm) | [Monomer] (M) |
|
|
Ref. |
---|---|---|---|---|---|
2-Pyrrolidine TREG PAA1800 |
28 24 21 |
0.15 0.20 1.0 |
4.6 5.8 7.6 |
17 23 36 |
[20] |
Dextran | 10 | 11 | 8.9 | N/A | [21] |
PEG250-(COOH)2 PEG600-(COOH)2 PEG4000-(COOH)2 |
11.7 13.5 17.5 |
0.37 0.88 5.9 |
N/A 9.1 N/A |
73 66 55 |
[22] |
PAA1800 | 5 | 1.5 | 11.2 | 70 | [46] |
PAA1800 PNaAA1800 PCaAA1800 |
20 20 20 |
N/A N/A N/A |
N/A 2.1 1.8 |
18 32 27 |
[23] |
PNaSS-PNIPAM | 5 9 |
2.3 2.5 |
14.9 9.9 |
55.0 40.8 |
[26] |
Citrate | 3–8 | 0.015 | 16 | N/A | [27] |
HPG | 20.9 | 2.1 | 6.7 | 15 | [28] |
PNaAA2100 | 9 | 0.0083 | 5.3 | 11.4 | [24] |
Citric acid Oxalic acid |
40 35 |
0.52 0.84 |
12.7 10.3 |
64 47 |
[19] |
PNaAA | 160 | 12.4 | N/A | 19.5 | [25] |
Si-COOH Si-PEG530 |
12.7 13.6 |
0.046 0.43 |
1.7 2.0 |
6.3 7.6 |
[47] |
3.1. Osmotic behavior of draw agents alone vs. grafted onto MNPs
Some investigators have studied the FO properties of osmotic agents that are both alone in aqueous solution and grafted onto MNPs [20, 24]. Ling et al. [20] compared 2-pyrrolidine, TREG, and PAA as draw solutes. When grafted onto MNPs, 2-pyrrolidine exhibited a near sixfold increase in osmolality when compared to the ungrafted solute. TREG and PAA exhibited approximately threefold and thirtyfold increases in osmolalities, respectively, at similar concentrations when grafted onto MNPs. Dey and Izake [24] found that 3.5 wt.% PNaAA provided a FO-water flux value of 1.72 LMH while only 0.078 wt.% PNaAA grafted onto MNPs provided a flux value of 5.32 LMH. These results indicate that anchoring polymers onto nanoparticles serves to significantly improve their osmotic performance.
The tremendous enhancement to osmotic pressure and water flux values associated with polymeric solutes anchored to MNPs can be attributed to improved hydration of the polymeric strands. The dense packing of polymer chains around MNPs leads to a more extended, brush-like, conformation due to excluded volume interactions [48, 49]. In addition, Ling et al. [20] ascribe a reduced interaction between PAA-MNPs and the FO-membrane surface as also contributing to the improved performance; carboxyl groups interacting with ester moieties on the membrane surface are not interacting with water and thereby reducing its chemical potential.
3.2. A semiempirical model
While
where
where
Figure 2 depicts the application of Eq. (25) to data for TREG [20, 31, 52] both alone in solution and grafted to MNPs. The ungrafted TREG molecules display little deviation from ideality, with a relatively small
The application of Eq. (25) to data for which 2-[methoxy-(polyethyleneoxy)6–9propyl] trimethoxysilane (MW: 459–591 g mol−1) was used as the grafting agent [47] is provided in Figure 3. When compared to TREG data, the greater number of monomers per polymeric strand results in a smaller
In Figure 4, data for MNPs coated with PAA [20] and HPG [28] are depicted. These results again demonstrate the significant nonideal solution behavior of derivatized MNPs. The large
3.3. Counterion binding
Another significant contributing factor to the osmotic potential of draw solutions incorporating polyelectrolytes is counterion binding. Oosawa was among the first to introduce the concept of counterion condensation around a polyion [53]. His model considers a fraction of counterions that is
Using this model, bound counterions would not contribute to osmotic pressure while unbound ions would. Polymeric structural features that influence the magnitude of
3.4. Particle size
Data also indicate that MNP particle size influences their osmotic performance because smaller particles have a larger surface area per volume, thus allowing for more effective grafting-agent coverage and increased nonideality. Ling et al. [20] demonstrated the inverse relationship between nanoparticle size and osmolality using PAA-MNPs. However, Kim et al. [56] found that particles smaller than 11 nm were difficult to separate from solution even with the application of a strong magnetic field, while the removal of particles larger than about 20 nm from the magnetic separator column was problematic. Additionally, the larger the mass percentage of coating material on a Fe3O4 core, the lower the saturated magnetization value on a per gram of particle basis. More coating material likely imparts greater osmotic pressure, but it reduces the efficacy of separation. Another significant challenge associated with MNP draw agents is particle aggregation following magnetic separation.
Ge et al. [22] observed a flux decline to approximately 80% of its original value after 9 recycles; this flux decline was accompanied by a particle size increase to 141% of the original value. That study used MNPs with an initial diameter <20 nm. Mino et al. [25] used much larger particles, with diameters of approximately 160 nm, and observed no aggregation even after 10 recycles, though the larger particles achieved only modest osmotic pressures. Park et al. [47] demonstrated that Si-PEG530-MNPs (diameterinitial = 13.6 nm) showed no significant aggregation or FO performance decline after 8 recycles, while Si-COOH-MNPs displayed considerable aggregation after only 5 recycles. Aggregation of the Si-COOH-MNPs was attributed to strong hydrogen bonding between carboxylate groups on adjacent particles when brought into close proximity during magnetic separation and subsequent drying. The oxalic acid- and citric acid-coated MNPs studied by Ge et al. [19] showed no significant particle agglomeration during regeneration, likely the result of strong electrostatic repulsion between particles. Zhao et al. [26] also observed only a slight decline in water flux (<10%) following recycles of their negatively charged PNaSS-PNIPAM-coated particles. In addition, Na et al. [27] demonstrated that small MNPs (3–8 nm) penetrate pores within the FO-membrane support layer (10–40 nm) and become lodged leading to a decline in flux values with time.
4. Summary
While it is now generally accepted that FO processes do not offer an overall energy cost savings when compared to RO for seawater desalination, the prospects of niche applications for FO where RO is unsuitable are numerous. A major challenge for the wider use of FO technology is the development of draw agents that provide high water flux, low reverse solute flux, and facile recovery. Organic-coated superparamagnetic nanoparticles provide properties that address these requirements. The FO performance of MNPs is a function of coating material, particle size, and concentration; with mitigation of particle aggregation during recovery being an essential consideration. The osmotic performance of organic compounds improves significantly when grafted onto MNPs, likely resulting from increased solvent-accessible surface area and enhanced hydration. Application of a simple semiempirical model provides assessments of the nonideality associated with MNPs through calculation of a solvent/solute interaction parameter (
Acknowledgments
Support for this work was provided by the Qatar Foundation and was made possible in part by a grant from the Qatar National Research Fund under its Undergraduate Research Experience Program award no. UREP13-018-1-001. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the Qatar National Research Fund.
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