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Environmental Processes

Ionic Charge Density-Dependent Donnan Exclusion in Nanofiltration of Monovalent Anions Razi Epsztein, Evyatar Shaulsky, Nadir Dizge, David M. Warsinger, and Menachem Elimelech Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b06400 • Publication Date (Web): 06 Mar 2018 Downloaded from http://pubs.acs.org on March 7, 2018

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Environmental Science & Technology

Ionic Charge Density-Dependent Donnan Exclusion in Nanofiltration of Monovalent Anions

Environmental Science & Technology Revised: February 25, 2018 Razi Epsztein1, Evyatar Shaulsky1, Nadir Dizge1,2, David M. Warsinger1, and Menachem Elimelech1* 1

Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520-8286, USA 2

Department of Environmental Engineering, Mersin University, Mersin 33343, Turkey

* Corresponding author. E-mail: [email protected]; Tel: +1 (203) 432-2789

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ABSTRACT 1

The main objective of this study is to examine how the charge density of four monovalent anions

2

 fluoride (F-), chloride (Cl-), bromide (Br-), and nitrate (NO3-)  influences their Donnan

3

(charge) exclusion by a charged nanofiltration (NF) membrane. We systematically studied the

4

rejection behavior of ternary ion solutions containing sodium cation (Na+) and two of the

5

monovalent anions as a function of pH with a polyamide NF membrane. In the solutions

6

containing F- and Cl- or F- and Br-, F- rejection was higher than Cl- or Br- rejection only when the

7

solution pH was higher than 5.5, suggesting that F- (which has higher charge density) was

8

repelled more strongly by the negatively charged membrane. The order of change in the

9

activation energy for the transport of the four anions through the polyamide membrane as a

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response to the increase of the membrane negative charge was the following: F- > Cl- > NO3- >

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Br-. This order corroborates our main hypothesis that an anion with a smaller ionic radius, and

12

hence a higher charge density, is more affected by the Donnan-exclusion mechanism in NF. We

13

conclude with a proposed mechanism for the role of ionic charge density in the rejection of

14

monovalent anions in NF.

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INTRODUCTION 16

Compared to reverse osmosis (RO) membranes, nanofiltration (NF) membranes are unique in

17

having varying selectivity towards different electrolytes.1–5 Rejection mechanisms in NF include

18

mainly steric (size) and Donnan (charge) exclusion.6,7 Species with much larger hydrated size

19

than the membrane pore size are sterically retained,8 while transport within the pores of species

20

with similar size to the membrane pores may be hindered.9 A membrane with fixed charged

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groups repels ions with the same charge (co-ions) and attracts ions with the opposite charge

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(counter-ions).10,11 These rejection mechanisms result in high selectivity of NF membranes for

23

the passage of monovalent ions,12,13 which is exploited in various applications for removing

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selectively multivalent ions and small organics.1,3,7,14

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Nanofiltration membranes are also capable of removing monovalent ions to different

26

extents.15–18 However, the difference in selectivity for the passage of different monovalent ions is

27

usually small and the mechanism for such difference is relatively poorly understood. The net

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charge of different monovalent ions is the same (i.e. -1 or +1). Also, the minor difference in the

29

hydrated radius of specific monovalent anions19 may sometimes fail to explain differences in

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selectivity for different anions as in the commonly observed case of chloride (Cl-) and nitrate

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(NO3-).20–22 Both anions have a net charge of -1 and similar hydrated radius, but Cl- is rejected

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more favorably than NO3- by NF membranes.

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An alternative explanation for the difference in selectivity for different ions with similar net

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charge and hydrated radius is based on the so-called dehydration phenomenon.17,23–27 According

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to this theory, an ion that approaches the membrane pore can strip and rearrange temporarily the

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water shells surrounding it so it can fit more easily into the pore. The extent to which

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dehydration occurs depends specifically on the hydration energy of the ion: the higher the

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hydration energy, the more difficult for the ion to undergo dehydration.17,24 For monoatomic ions,

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the hydration energy depends on both the ionic size and charge. In general, higher ionic charge

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and smaller ionic size result in higher hydration energy.25,28,29 The dehydration phenomenon,

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which is associated more with size-exclusion mechanism, can partially explain some differences

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in rejection of ions with the same charge and similar hydrated radius, including the case of Cl-

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and NO3-.30



44

Yet, some observations cannot be adequately explained solely by size-exclusion mechanism.

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For example, fluoride (F-) has a smaller ionic radius, larger hydrated size, and higher hydration

46

energy compared to Cl-

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However, reports on F- rejection by NF compared to Cl- are inconsistent and often show a higher

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Cl- rejection than F-.17,18,31–35 Studies have shown a major effect of pH on F- rejection, which was

49

attributed to fluorine speciation and conversion to an uncharged form of hydrogen fluoride (HF)

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at low pH and to the increase in membrane charge at high pH.36,37 Hong et al.30 and Malaisamy et

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al.31 successfully fabricated an NF membrane with increased Cl-/F- selectivity (i.e. more

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favorable passage of Cl- than F-) using layer-by-layer polyelectrolyte modification and attributed

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the mechanism for such selectivity to size exclusion. However, these studies could not explain

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the higher rejection of Cl- than F- with an unmodified NF270 membrane. More recently, a study

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on the rejection of Cl- and NO3- in NF showed that the energy barrier for the transport of the Cl-

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anion became higher than that of NO3- when an uncharged cellulose acetate membrane was

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replaced by a charged polyamide membrane, suggesting that Cl- was more affected than NO3- by

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the membrane charge.30

19,29

, suggesting higher rejection of F- than Cl- by NF membranes.

59

Although more often related to polyelectrolytes and charged interfaces and particles, the term

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charge density may also refer to the charge distribution over the volume of a molecule, atom, or

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ion and is defined as the charge per unit volume of space.38–41 According to this definition, ions

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with smaller ionic radius possess inherently higher charge density than ions with larger ionic

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radius and with the same charge.42 As both hydration energy and hydrated radius depend

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considerably on the ionic charge density,42,43 it is well accepted that the ionic charge density

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plays an important role in size-exclusion mechanism in NF. 17,24,25,27 However, the effect of ionic

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charge density on the Donnan (charge)-exclusion mechanism was not established. Besides

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affecting the size of a hydrated ion complex, ionic charge density-dependent phenomena, such as

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expansion (i.e. hydration) and shrinkage (i.e. dehydration), may significantly influence the

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electrostatic interaction between the ion and the fixed charge on the membrane.

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The objective of this study is to investigate the effect of ionic charge density of monovalent

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anions on Donnan (charge)-exclusion mechanism in NF. We systematically studied the

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mechanisms involved in the rejection of four different monovalent anions with different ionic

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sizefluoride (F-), chloride (Cl-), bromide (Br-), and nitrate (NO3-)by a polyamide NF


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membrane. Our results suggest that a smaller anion with higher ionic charge density is more

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affected by Donnan exclusion than a larger anion with lower ionic charge density. MATERIALS AND METHODS

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Materials and Chemicals. A commercial polyamide NF membrane (NF270, Dow FilmTec)

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was used for the anion rejection tests. Sodium bromide (NaBr), sodium fluoride (NaF), sodium

78

nitrate (NaNO3), and glucose were purchased from Sigma-Aldrich. Sodium chloride (NaCl),

79

sulfuric acid (H2SO4), isopropanol, glycerol, and phenol were purchased from J.T. Baker

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Chemicals. Sodium hydroxide (NaOH) was purchased from Macron Fine Chemicals. Deionized

81

water (MilliPore Academic A-10, resistance 15 MΩ-cm) was used for preparing solutions,

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compaction/equilibration of membranes, and rinsing the NF system.

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NF Membrane Characterization. The commercial polyamide NF270 membrane was

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selected for this study due to its varying selectivity towards different anions and changeable

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number of negatively charged carboxyl groups and positively charged amine groups as a

86

function of pH

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using a bench-scale NF system (described in the next subsection) at different solution pH

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(between 3.5 and 8.5), pressure of 5.5 bar (80 psi), and temperature of 25 °C. The pH was

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adjusted by sodium hydroxide (NaOH) and sulfuric acid (H2SO4). We have used H2SO4 rather

90

than the more commonly used HCl or HNO3 because chloride and nitrate were among the anions

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investigated in this study. Except for the measurement at pH 3.5, the conductivity during the pure

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water permeability tests was kept below 12 µS/cm. At pH 3.5, the conductivity increased to 93

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µS/cm due to the addition of H2SO4. Glucose rejection (feed concentration of 100 mg L-1) was

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measured under the same conditions as in the water permeability tests to ensure that membrane

95

pore size is not affected by solution pH. Feed and permeate glucose concentrations were

96

quantified by the phenol-sulfuric acid method for total carbohydrates46 with spectrophotometer

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(50 Bio UV-visible spectrophotometer, Cary) at a wavelength of 490 nm. The surface zeta

98

potential of the NF270 membrane as a function of solution pH (3-9) was determined from

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streaming potential measurements (EKA Electro Kinetic Analyzer, Anton Paar) as described

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44,45

. Pure water permeability (A, L m-2 h-1 bar-1) of the membrane was measured

elsewhere.47

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Nanofiltration System and Anion Rejection Experiments. A bench-scale system

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operating in cross-flow mode with a flat sheet membrane cell was used for all membrane tests. 5 ACS Paragon Plus Environment


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The total surface area of the membranes tested was 20.02 cm2. Both retentate and permeate were

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recirculated between the feed tank and the membrane cell. Prior to filtration experiments,

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membrane was compacted overnight under pressure of 6.9 bar (100 psi) using deionized water.

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Filtration experiments were performed with an applied inlet pressure between 3.4 and 5.5 bar (50

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and 80 psi) and cross flow velocity of 21.4 cm/s.

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Before use, the NF270 membrane was agitated in 25% isopropanol solution for 30 min using

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a rotating shaker. Then, the membrane was rinsed with deionized water three times (each time

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for 30 min) and kept in deionized water overnight to remove impurities. Except for the

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experiments to determine the activation energy for anion transport through the membrane, water

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temperature was maintained constant at 25 ºC. For the experiments to determine the activation

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energy, temperature was increased gradually from 22 °C or 25 °C to 40 °C and samples were

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taken at four different temperatures. Feed solution pH was monitored and adjusted throughout all

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experiments using sulfuric acid (H2SO4) or sodium hydroxide (NaOH). Feed and permeate were

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collected for anions analysis by ion chromatography (Dionex DX-500 with an AS14A IonPac

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column). All experiments were carried out with deionized water amended with NaF, NaCl, NaBr,

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and NaNO3 (as binary, ternary, or mixed ion solution). We performed all the experiments within

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the operating pH range (2-11) and below the maximum temperature (45 °C) specified by the

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membrane manufacturer.

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Determination of Energy Barrier for Anion Transport in NF. Activation energies for

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anion transport through the NF270 membrane were determined using single sodium salt

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solutions (i.e. NaF, NaCl, NaBr, or NaNO3) at different pH. The solute flux (Jsolute) was first

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calculated at four different temperatures of 22, 28, 34, and 40 ºC or 25, 30, 35, and 40 °C using:

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=

(1)

126

where Jw is the water flux through the membrane (L m-2 h-1) and Cp is the permeate anion

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concentration (mmol L-1). The activation energy, Ea, was then calculated from the linearized

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form of the Arrhenius equation:

129

130

"#(

= exp −

!

) = ln() −

(2)

(


(3)

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where Cin is the feed concentration (mmol L-1), B is the pre-exponential factor, R is the gas

132

constant, and T is the absolute temperature. As the feed concentration (Cin) increased slightly

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after each sampling due to permeate collection (accompanied by a slight recovery increase), the

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solute flux (Jsolute) was normalized to the specific feed concentration for each sampling to

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eliminate the potential effect of the varying feed concentration on the solute flux.

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Modeling of Anion Exclusion Mechanisms. We used the Donnan steric pore model

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with dielectric exclusion (DSPM-DE) to model the experimental conditions and examine

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whether currently considered mechanisms can explain the anion rejection trends we observed.

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The model, its input parameters, and its implementation are described in detail in Roy et al.48

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(using MATLAB vR2015b).The DSPM-DE is a pore-flow model considering the following ion

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rejection mechanisms: Donnan (charge-based) exclusion, steric (size-based) exclusion, and

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dielectric exclusion (due to image charges and the Born solvation energy barrier associated with

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the ion shedding its hydration shell to enter the membrane pore).11,49–51 Here, we account for

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solvation energy effects and neglect the image forces as suggested by Bowen et al.50 Applying

145

the DSPM-DE model involves fitting parameters that characterize the membrane structure (pore

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radius and active layer thickness) as well as electrical properties (effective volume-averaged

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charge density and pore dielectric constant).49,52 We emphasize that the DSPM-DE model

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accounts for all known mechanisms of ion exclusion, unlike its predecessor, the DSPM, which

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does not account for dielectric exclusion.48,50 Several previous studies successfully fitted

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experimental data to the DSPM-DE model.50,53 To fit the model parameters in this study,

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experimental data for a given solution were taken across a range of pH. The rejection at neutral

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membrane charge was used as a reference point to fit the dielectric constant. With the dielectric

153

constant fitted, the membrane charge was then fitted to points of different pH. Input parameters

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for the model are described in Tables S2 and S3.

RESULTS AND DISCUSSION 155

NF Membrane Characteristics. The NF270 is a “loose” thin film composite (TFC) NF

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membrane prepared via the interfacial polymerization of a monomeric polyamine with a

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polyfunctional acyl chloride (trimesoyl chloride) on a polysulfone support. 44,54,55 The interfacial

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polymerization process results in an ultrathin (15-40 nm) piperazine-based semi-aromatic 7 ACS Paragon Plus Environment


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polyamide selective layer.54–56 After the interfacial polymerization reaction, unreacted carboxyl

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and amine groups can be ionized, depending on the pH of the solution in contact with the

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membrane.6 Previous studies have shown that the point of zero charge of the NF270 membrane

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(i.e., the pH at which the number of ionized amine groups is equal to the number of ionized

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carboxyl groups) is between pH 4 and 5.30,57

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During the experiments described in the next subsections, we vary the solution pH to explore

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the effect of membrane charge on anion rejection and transport. The observed stable water

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permeability and glucose rejection (Figure S1) at different solution pH, together with the

167

increase in surface zeta potential at higher pH (Figure S2), indicate that solution pH affects the

168

membrane charge (due to increase in the ionized carboxyl group density),58 but not the

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membrane pore size. We note that the isoelectric point obtained by zeta (electrokinetic) potential

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measurements (pH ~3), correlating to the electric potential at the shear plane of the electric

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double layer,59 is lower than the point of zero charge estimated by ion rejection (pH ~4.5),30

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which is determined by the membrane fixed charged groups (carboxyl and amine).60 The average

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pore size of the NF270 membrane (Table S1) is in the range of the hydrated size of the

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monovalent anions tested in this study (Table 1), implying that the anions undergo partial

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dehydration to enter the membrane pore.17

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TABLE 1

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Anion Rejection in a Mixed Salt Solution. The first set of experiments was carried out

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to obtain a preliminary assessment of the effect of membrane charge on the rejection of F-, Cl-,

179

Br-, and NO3- in a mixed solution using the NF270 membrane at pH 4.5 and 5.5 (Figure 1). Steric

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(size)-exclusion mechanism dominates anion rejection at pH 4.5 where the membrane is nearly

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neutrally charged30 (i.e., near the point of zero charge of the membrane).60 Higher anion rejection

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was observed at pH 5.5 than at pH 4.5 (except for NO3-) due to partial ionization of the carboxyl

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groups on the membrane, accompanied with the addition of Donnan (charge)-exclusion

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mechanism. The increase in rejection for the different anions was not equal, leading to a change

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in the order of rejection (i.e., F- rejection became higher than Br- rejection). This observation

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suggests that each anion was affected to a different extent by the increase in membrane charge.

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However, the results of a mixed anion solution cannot reflect accurately the effect of Donnan

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exclusion on each anion. First, in a mixed anion solution with a relatively high ionic strength (8 8 ACS Paragon Plus Environment

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mM), the effect of Donnan exclusion is reduced due to the screening of membrane charge by the

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Na+ cations, resulting in lower contribution of Donnan exclusion to the overall rejection.6,61

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Second, the counter-ion (Na+) effect and co-ion (anions) competition can also affect the order of

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anion rejection. Specifically, in a mixed salt solution with higher concentration of Na+, more Na+

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cations permeate through the membrane, resulting in higher permeation of the less rejected

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anions (e.g. NO3-) through the membrane to maintain electroneutrality. The permeation of co-

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ions (anions) due to counter-ion (Na+) passage is dictated by both steric and charge effects,

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making the impact of Donnan exclusion on each anion less distinct. Therefore, we further

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investigated the effect of Donnan exclusion on anion rejection in a simpler experimental matrix,

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i.e., ternary ion solution as discussed below.

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FIGURE 1

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Anion Rejection in Ternary Ion Solutions. The following set of experiments was

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designed to explore the rejection behavior of the anions in ternary ion solutions containing

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sodium (Na+) and two of the investigated anions as a function of a broader range of pH, between

203

3.5 and 8.5 (Figure 2). The use of different ternary ion solutions (containing two anions and Na+)

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is advantageous for better understanding of the anion rejection mechanisms.30 Specifically,

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ternary ion solutions allow the comparison of the rejection behavior of two anions under the

206

same conditions, while reducing the aforementioned effects involved in a multiple salt solution

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(i.e. charge screening and counter-ion effect).

208

FIGURE 2

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Figure 2 (a-c) reveals a minimum rejection for Cl-, Br-, and NO3- near pH 4.5, the point of

210

zero charge of the membrane, due to the absence of Donnan (charge)-exclusion mechanism at

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this pH.30 A difference between the rejections of two anions in a ternary ion solution was

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observed near neutral (pH 4.5) and at negative membrane charge (pH > 4.5). Excluding the F-

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anion, the order of anion rejections at pH ≥ 4.5 was the following: Cl- > Br- > NO3-. As all three

214

anions have a similar hydrated radius, this order can be well explained by the order of the

215

hydration energy of the anions (Table 1). Hence, the observed order of rejection is attributed to

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size-exclusion mechanism and dehydration:17 an anion with higher hydration energy (e.g. Cl-)

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holds its hydration shell more strongly and undergo less dehydration compared to an anion with

218

lower hydration energy (e.g. NO3-). At a positive membrane surface charge (pH < 3.5), the 9 ACS Paragon Plus Environment


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rejections of the anions approached a similar value, suggesting that the Na+ cation dictated the

220

rejections at this pH, independently of the anion type. This evidence also suggests that the anion

221

rejection by the relatively “loose” NF270 membrane is dictated by the co-ions (i.e. the ions that

222

possess the same charge as the membrane).62 Therefore, we assume that at negative membrane

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charge (pH > 4.5), where rejection is dictated by the anions, the effects of size and charge

224

exclusion are coupled and cannot be properly distinguished. To support our proposition that the

225

rejection of ions by the NF270 membrane is dictated by the co-ions, we carried out NF ion

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rejection experiments with an “opposite” ternary ion solution containing one anion (Cl-) and two

227

cations (Na+ and NH4+) (Figure S3). Here, a difference in cation rejection was observed at pH ≤

228

4.5 (where the membrane is positively charged) and similar cation rejections were observed at

229

pH > 4.5 (where the membrane is negatively charged).

230

Existing Model Incapable of Predicting Experimental Observations. The order of

231

anion rejection in ternary ion solutions containing F- was pH dependent (Figure 2 d-e). At pH 3.5,

232

F- rejection was always lower than the rejection of the other anions, which we attribute to

233

fluorine (F) speciation and presence of hydrogen fluoride (HF) at pH < 5 (pKa of HF is 3.2).36

234

Hydrogen fluoride is uncharged and therefore has lower rejection than the F- anion by the

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polyamide membrane. In the case of solutions containing F- and Cl- (Figure 2d) or F- and Br-

236

(Figure 2e), the rejection order is swapped when pH is increased from 5.5 to 6.5, i.e. F- rejection

237

becomes higher than Br- and Cl- rejection. We attribute this observation to the higher ionic

238

charge density of F- due to its significantly smaller ionic radius compared to the other anions

239

(Table 1). The higher ionic charge density of F- results in higher Donnan (charge) exclusion in

240

response to the increase in membrane charge compared to the other anions. The effect of the

241

difference in the ionic charge density is reflected also in the case of F- and NO3- (Figure 2f),

242

showing an increased gap between the rejection curves when pH is increased from 5.5 to 6.5. We

243

have shown previously that the hydrated radii are not affected by changes in solution pH,30

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suggesting that the changes in rejection order observed at pH > 5 (where fluorine is completely

245

in the form of F-) are Donnan-exclusion related.

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We note that similar rejection trends in ternary ion solutions were obtained using real anion

247

rejection, i.e., anion rejection based on anion concentration on the membrane surface after

248

accounting for the effect of concentration polarization (Figure S4). Ion concentration at the

249

membrane surface was determined by calculating the mass transfer coefficient at the boundary 10 ACS Paragon Plus Environment

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layer on the membrane according to the film theory.63,64 As the difference in concentration

251

polarization for different anions in a mixed solution depends exclusively on the anion diffusivity

252

and rejection, we attribute the similarity between rejection trends based on experimental (Figure

253

2) and real (Figure S4) rejections to the similar diffusivities of the anions (Table 1).

254

Modeling of NF also supports the influence of ionic charge density on Donnan-exclusion by

255

ruling out other mechanisms. As described earlier, this established model (DSPM-DE) for NF

256

incorporates the impacts of the three understood ion exclusion mechanisms. Notably, the model

257

does not include the new mechanism proposed in the present study, namely that ionic charge

258

density impacts Donnan exclusion. To use the model, membrane parameters of pore size,

259

thickness, dielectric constant, and charge must be fitted to the experimental conditions. The pore

260

size and thickness of the NF270 membrane were thoroughly studied with this model and

261

therefore were taken from the literature.54,65,66 The dielectric constant of the membrane and the

262

membrane charge at different pH were fit to the data shown in Figure 2 (d and e) with two major

263

steps: (i) by fitting the dielectric constant to the data at the point of zero charge of the membrane

264

and (ii) by fitting the membrane charge to the experimental rejection data at each pH using the

265

dielectric constant that was fitted in the first step (as determined by a least-squares difference

266

between modeled and experimental results).

267

The model results (Figure 3) describe the exclusion partitioning factors to elucidate the

268

relative contribution of the three exclusion mechanisms  steric, Donnan, and dielectric  to

269

anion rejection. The exclusion partitioning factors vary from 0 to 1, and have no influence at 1,

270

while very high contribution to rejection as they approach zero. For convenience, the relative

271

contributions of each partitioning factor in Figure 3 are displayed by the natural logarithm of the

272

partitioning factors for each exclusion mechanism. Using the natural logarithm, larger values

273

correlate with a larger influence on anion rejection. For instance, rejection is highest at a pH of

274

7.5, and Donnan exclusion dominates rejection at this pH.

275

FIGURE 3

276

We explored the ability of the model to predict specifically the experimental results observed

277

for the solutions containing F- and Cl- (Figure 2 d) or F- and Br- (Figure 2 e), where the rejection

278

order of the two anions was changed when pH was increased from 5.5 to 6.5. The model (Figure

279

3) predicts higher rejection for Cl- or Br- than F- for all pH values, and therefore is incapable of 11 ACS Paragon Plus Environment


280

predicting the trend observed at pH > 5.5, where F- rejection is higher than that of Cl- and Br-

281

(Figure 2 d-e). According to the model, the contribution of Donnan exclusion to the overall

282

rejection is virtually identical for the three ions, while dielectric exclusion yields the opposite of

283

the experimental trend (at high pH), and steric exclusion is relatively negligible. This set of

284

results implies that the model is missing a Donnan exclusion-related key mechanism that can

285

distinguish between anions with the same net charge.

286

Activation Energy for Transport of Monovalent Anions. Similarly to rejection, the

287

activation energy for anion transport through the membrane is influenced by all possible

288

mechanisms limiting the passage of the solute through the membrane pores. Conceptually, the

289

more mechanisms hindering the anion transport through the pore (e.g. steric hindrance, charge

290

repulsion, and dehydration), the higher its activation energy. However, as activation energy

291

reflects the dependence of anion transport on temperature change and does not always correlate

292

perfectly with rejection, it provides some additional insights regarding the transport mechanism

293

of the anions through the membrane. 17,30,67

294

We evaluated first the activation energy for the transport of sodium chloride (NaCl) through

295

the NF270 membrane at a broad pH range (3.5-9.0) using the linearized form of the Arrhenius

296

equation (eq 3). The Cl- flux through the membrane (Jsolute) was measured at different feed

297

solution temperatures in the range of 25-40 °C. The data was plotted as ln(Jsolute) versus 1/T to

298

obtain the activation energy from the slope of the curve (Figure 4). FIGURE 4

299 300

Provided that membrane charge is the only parameter affected by the change in the solution

301

pH (Figure S1 and S2), Figure 4 shows a good correlation between membrane charge and the

302

activation energy for the passage of Cl- through the NF membrane. The minimum activation

303

energy was obtained at pH 4.5, the point of zero charge of the membrane, where charge-

304

exclusion mechanism is absent. This observation corroborates the use of activation energy as an

305

indicator for the extent to which charge-exclusion mechanism affects the transport of a specific

306

anion through the membrane.

307

In a following set of experiments, we evaluated the change in the activation energy for the

308

passage of F-, Cl-, Br-, and NO3- as a response to the increase in the solution pH from 4.5 to 8.5

309

(Figure 5). The obtained order of change in the activation energy (F- > Cl- > NO3- > Br) inversely 12 ACS Paragon Plus Environment

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310

correlates to the ionic radii of the anions (Table 1), and therefore also to the ionic charge

311

densities of the anions. As increasing the solution pH from 4.5 to 8.5 results in an increase in the

312

ionized carboxyl group density on the membrane, this set of results corroborates our findings in

313

the previous subsection, suggesting that a smaller anion with higher charge density is affected

314

more by Donnan (charge)-exclusion mechanism compared to a larger anion with a smaller

315

charge density. The much higher change in activation energy calculated for F- compared to the

316

other anions cannot be explained by fluorine speciation and the presence of HF at pH 4.5, since

317

at this pH the relative fraction of the F- anion is above 95%.36 FIGURE 5

318 319

The gap between the two lines in Figure 5 represents the change in anion flux as a response to

320

the increase in solution pH from 4.5 to 8.5. As expected, anion flux was lower at pH 8.5 than at

321

pH 4.5 due to the addition of Donnan-exclusion mechanism at pH 8.5. Except for NO3-, the

322

increase in the activation energy as a response to the increase in membrane charge correlated

323

well with the decrease in anion flux. The relatively low decrease in the NO3- anion flux with the

324

increase of pH from 4.5 to 8.5 can be explained by its higher B value (eq. 3) compared to the

325

other anions. This value depends on inherent properties of the anion, regardless of temperature

326

and energy barriers, and is defined as the anion flux at infinite temperature (i.e. the intercept with

327

the vertical axis when 1/T approaches zero). We attribute this behavior of NO3- to its polyatomic

328

non-spherical structure that allows it to fit to more membrane pores compared to the other

329

monoatomic spherical anions investigated.

330

Mechanism for the Role of Ionic Charge Density in Anion Rejection. Our results

331

presented in the previous subsections suggest that a smaller monovalent anion with higher ionic

332

charge density is more affected by the increase in the negative membrane charge compared to a

333

larger monovalent anion with lower ionic charge density. Treating all relevant charged species

334

(i.e. anions, water molecule dipoles, and charged groups on the membrane surface) as point

335

charges, all anions should have exactly the same charge (-1) located in the center of the anionic

336

sphere. Therefore, the magnitude of the electrostatic interactions between the anions and other

337

charged species is distance dependent.43 This approach can explain, for example, the strength of

338

anion hydration (Figure 6a): small anions (e.g. F-) are strongly hydrated (i.e. have higher

339

hydration energy) because their point charge is close to the point charge of opposite sign on the 13 ACS Paragon Plus Environment


340

water molecule, whereas large anions (e.g. Cl-) are weakly hydrated because their point charge is

341

distant from the point charge of opposite sign on the water molecule.25,43 FIGURE 6

342 343

Due to their similar hydrated radius, different monovalent anions in solution can approach the

344

same distance from the center of other charged species (e.g. the ionized carboxyl groups on the

345

membrane surface). Therefore, while hydrated in solution, monovalent anions are expected to be

346

equally affected by the ionized carboxyl groups on the membrane. When entering the membrane

347

pore, however, anions undergo dehydration and reduce their hydrated radius temporarily.17,25,27

348

At this stage, the dehydrated anions can approach closer to the negatively charged carboxyl

349

group in the membrane pore and be affected (i.e. repulsed) to higher extent compared to their

350

hydrated form (Figure 6b). Our experimental results show that smaller anions are more affected

351

by the negatively charged membrane carboxyl groups compared to larger anions. We attribute

352

this observation to the lower ionic radius of smaller anions, allowing them to approach closer to

353

the charged carboxyl groups in the pore after partial dehydration compared to larger anions with

354

higher ionic radius (Figure 6b).

355

In the case of F-, we observed lower F- rejection at low membrane charge (pH ≤ 5.5) and

356

higher F- rejection at high membrane charge (pH > 5.5) compared to Cl- (Figure 2d) and Br-

357

(Figure 2e). Fluoride, with much smaller ionic radius (and hence larger hydrated radius) than Cl-

358

and Br- (Table 1), is likely to have a second (less strongly attached) hydration shell.68,69 Despite

359

its higher hydration energy, F- loses water molecules from its second hydration shell more

360

easily,69 becomes smaller, and experiences lower size exclusion compared to Cl- and Br-.

361

Therefore, at low membrane charge when size-exclusion mechanism dominates anion rejection,

362

Cl- and Br- rejection is higher than F-. At higher membrane charge, when Donnan (charge)-

363

exclusion mechanism becomes more dominant, the higher ionic charge density of the dehydrated

364

F- (due to its smaller size) results in higher F- rejection compared to Cl- and Br- (Figure 6b).

365

Importantly, the fact that smaller anions are more affected by the negative membrane charge than

366

larger anions provides an additional evidence for the phenomenon of temporary dehydration in

367

the membrane pore.


Page 14 of 30

Page 15 of 30


ASSOCIATED CONTENT Reported molecular weight cut-off (MWCO) and average pore size of the NF270 membrane (Table S1); model input parameters for ions (Table S2); model input parameters for the NF270 membrane and water (Table S3); pure water permeability and glucose rejection by a polyamide NF membrane (NF270) as a function of solution pH (Figure S1); zeta potential as a function of feed solution pH for a polyamide NF membrane (NF270) (Figure S2); cation rejection by a polyamide NF membrane (NF270) as a function of solution pH for ternary ion solution containing sodium chloride (NaCl) and ammonium chloride (NH4Cl) (Figure S3); real anion rejection by a polyamide NF membrane (NF270) as a function of solution pH for different ternary ion solution containing sodium (Na+) and two different anions (Figure S4).

ACKNOWLEDGEMENTS This research was made possible by the postdoctoral fellowship (to Razi Epsztein) provided from the United States-Israel Binational Agricultural Research and Development Fund BARD, Fellowship number FI-549-2016. We thank the Scientific and Technological Research Council of Turkey, the Department of Science Fellowships and Grant Programs (1059B191501137) for financially supporting Nadir Dizge. We thank the NSF Nanosystems Engineering Research Center for Nanotechnology-Enabled Water Treatment (Grant EEC-1449500) and the Purdue School of Mechanical Engineering (supporting David Warsinger). We acknowledge Yagnaseni Roy for proving the NF modeling software used in this work, under the guidance of John H. Lienhard V at MIT. This software was developed under the support of King Fahd University of Petroleum and Minerals for financial support through the Center for Clean Water and Clean Energy at MIT and KFUPM under project R13-CW-10'. We also acknowledge Dr. Serge Rosenblum from the Department of Applied Physics at Yale University for valuable discussions. 368



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Table 1. Ionic radius, hydrated radius, and hydration energy of the anions (i.e. fluoride, chloride, nitrate, and bromide) investigated in this study. For consistency, data was collected from the same source for a specific parameter when possible. Anion

Ionic radius a

Hydrated radius a

Hydration energy b

Bulk diffusion

(nm)

(nm)

(kJ mol-1)

coefficient, 25 °C (10-9 m2 s-1)

Fluoride (F-)

0.116

0.352

-465

1.460 c

Chloride (Cl-)

0.164

0.332

-340

2.033 d

Nitrate (NO3-)

0.179

0.340

-300

1.903 d

Bromide (Br-)

0.180

0.330

-315

2.081 d

a

From ref. 19

b

From ref. 70

c

From ref. 17

d

From ref. 71



25 Rejection (%)

20

Chloride Fluoride Bromide Nitrate

15 10 5 0

pH 4.5

pH 5.5

Figure 1. Anion rejection by a polyamide NF membrane (NF270) at pH 4.5 and 5.5 for a mixed salt solution containing sodium chloride (NaCl), sodium fluoride (NaF), sodium bromide (NaBr), and sodium nitrate (NaNO3). Experimental conditions during the NF experiments: feed concentration of 2 mM for each salt (total salt concentration of 8 mM), applied pressure of 5.5 bar (80 psi), initial water flux of 125 L m-2 h-1, cross flow velocity of 21.4 cm/s, and temperature of 25 °C.


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Figure 2. Anion rejection by a polyamide NF membrane (NF270) as a function of solution pH for ternary ion solutions containing sodium (Na+) and two different anions. (A) Chloride (Cl-) and bromide (Br-) (i.e. NaCl plus NaBr). (B) Bromide and nitrate (NO3-) (i.e. NaBr plus NaNO3). (C) Chloride and nitrate (i.e. NaCl plus Na NO3). (D) Fluoride (F-) and chloride (i.e. NaF plus NaCl). (E) Fluoride and bromide (i.e. NaF plus NaBr). (F) Fluoride and nitrate (i.e. NaF plus NaNO3). Experimental conditions during the NF experiments: feed concentration of 1 mM for each salt (total ionic strength of 2 mM), applied pressure of 5.5 bar (80 psi), initial water flux of 125 L m-2 h-1, cross flow velocity of 21.4 cm/s, and temperature of 25 °C.



561

Figure 3. Modeled contribution to rejection of each exclusion mechanisms for the ion combinations of (A) NaCl and NaF (1 mM each) and (B) NaBr and NaF (1 mM each), analyzed at different solution pH (rejection data from Fig. 2). Contributions are represented by the natural log of the absolute value of the partitioning factor for each anion, as calculated by the DSPM-DE (Donnan Steric Pore Model with Dielectric Exclusion).


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Figure 4. (A) Activation energy (Ea) for the transport of Cl- (sodium chloride salt) through a polyamide NF membrane (NF270) as a function of solution pH. (B) Activation energies were determined from the slopes of these plots according to eq 3. Anion flux (Jsolute) expressed in mmol m-2 h-1 was determined from NF filtration experiments with a feed concentration of 4 mM NaCl at 3.45 bar (50 psi) applied pressure and temperatures of 25 °C, 30 °C, 35 °C, and 40 °C. For each sampling, the anion flux was normalized to the current feed concentration (Ci, mmol L-1) to neutralize the effect of varying feed concentration at different measurements due to the minor recovery increase after each sampling. The crossflow velocity for all experiments was fixed at 21.4 cm/s.



Figure 5. Activation energy for the transport of bromide, nitrate, chloride, and fluoride anion through a polyamide NF (NF270) membrane at pH 4.5 and pH 8.5. Activation energies were determined from the slopes of the plots according to eq 3. Anion flux (Jsolute) expressed in mmol m-2 h-1 was determined from NF filtration experiments of separate salt solutions with feed concentration of 1 mM NaBr, NaNO3, NaCl, or NaF at 5.5 bar (80 psi) applied pressure and temperatures of 22 °C, 28 °C, 34 °C, and 40 °C. For each sampling, the anion flux was normalized to the current feed concentration (Ci, mmol L-1) to neutralize the effect of varying feed concentration at different measurements due to the minor recovery increase after each sampling. The crossflow velocity for all experiments was fixed at 21.4 cm/s. Similar fluxes with less than 5% deviation were measured for the different anion solutions under the same pH and temperature.


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Figure 6. Proposed mechanism for the role of ionic charge density in exclusion of monovalent anion by NF membrane: (A) A smaller anion with higher charge density (e.g. fluoride, F-) is surrounded by a stronger hydration shell than a larger anion with lower charge density (e.g. chloride, Cl-). During hydration, anions decrease their charge density. (B) Anions are partially dehydrated to enter the membrane pore. During dehydration, anions increase their charge density. Coordination number (i.e. the number of water molecules in the primary hydration shell) and degree of partial dehydration for F- and Cl- are illustrated schematically based on previous molecular dynamics simulation.69 Fluoride can have a second hydration shell.68,69



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Role of Ionic Charge Density in Donnan Exclusion ... - ACS Publications

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