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Anion exchange on cationic surfactant micelles, and a speciation model for estimating anion removal on micelles during ultrafiltration of water Ming Chen, and Chad T. Jafvert Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01270 • Publication Date (Web): 08 Jun 2017 Downloaded from http://pubs.acs.org on June 16, 2017

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Anion exchange on cationic surfactant micelles, and a speciation model for estimating anion removal on micelles during ultrafiltration of water Ming Chen†, Chad T. Jafvert*,†,‡ †

Lyles School of Civil Engineering, and ‡Division of Environmental and Ecological Engineering,

Purdue University, West Lafayette, IN 47907, United States KEYWORDS: Surfactant, micelle, ion exchange, selectivity coefficient; nutrient removal

ABSTRACT: Surfactant micelles combined with ultrafiltration can partially, or sometimes nearly completely, separate various ionic and nonionic pollutants from water. To this end, the selectivity of aqueous micelles composed of either cetyltrimethylammonium (CTA+) bromide or cetylpyridinium (CP+) chloride towards many environmentally relevant anions (IO3-, F-, Cl-, HCO3-, NO2-, Br-, NO3-, H2PO4-, HPO42-, SO42-, and CrO42-) was investigated.

Selectivity

coefficients of CTA+ micelles (with respect to Br-) and CP+ micelle (with respect to Cl-) for these anions were evaluated using a simple thermodynamic ion exchange model. The sequence of anion affinity for the CTA+ micelles and for the CP+ micelles were the same, with decreasing affinity occurring in the order of: CrO42- > SO42- > HPO42- > NO3- > Br- > NO2- > Cl- > HCO3> H2PO4- ≈ F-. From the associated component mass balance and ion exchange (i.e., mass action) equations, an overall speciation model was developed to predict the distribution of all anions between the aqueous and micellar pseudo-phase for complex ionic mixtures. Experimental results of both artificial and real surface waters were in good agreement to model 1

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predictions. Further, the results indicated that micelles combined with ultrafiltration may be a potential technology for nutrient and other pollutant removal from natural or effluent waters.

1. INTRODUCTION Ultrafiltration (UF) of aqueous surfactant micellar solutions can partially to nearly completely separate various ionic and nonionic pollutants from water or wastewater. As a result, the overall process of “micellar enhanced ultrafiltration” has been viewed as a promising separation technology for decades.1-7 When the concentration of the specific ionic surfactant far exceeds the critical micellar concentration (CMC), there will be a large concentration of charges micelles in solution, composed of surfactant monomers.

These aggregates of tens to hundreds of

monomers are basically nano-scale ion exchangers, with the specific aggregation number a function of the specific surfactant and solution ionic composition. The rejection of micelles by UF membranes leads to the removal of ions associated with the surface of the micelles of opposite charge. Nonionic organic molecules solubilized in the core of the micelles also are removed.1, 6 Removal of cationic metal ions7-10 and nonionic organic pollutants4, 11 with surfactant micelles in ultrafiltration processes has been studied widely. Yet, only a few studies12, 13 have reported on the removal of anionic species using cationic surfactant micelles, despite the fact that many nutrient species are anionic, and currently are removed from water to acceptable levels primarily through advanced treatment processes. For example, nitrate and phosphorous removal from wastewater or polluted water is achieved generally through biological treatment processes, however the efficiency of these treatment methods are generally quite sensitive to temperature and the composition of the water. 2


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Studies that have examined removal or recovery of anions with cationic micelles across UF membranes have focused mainly on single species ion removal or two species competitive removal, emphasizing differences in recovery as a function of surfactant species, or differences in recovery as a function of operating conditions.13-15 There is an absence in the literature on the removal of specific anionic species from complex ionic mixtures, such as natural waters or wastewaters, with competition from naturally occurring divalent ions of special concern. In this study, binary selectivity coefficients for a number of common anions on two types of cationic micelles were determined experimentally based on a simple ion exchange model generally employed for ionic resins or membranes, and the resulting coefficients were used to model micellar ion exchange within complex ionic mixtures. Cetyltrimethylammonium bromide (CTAB) and cetylpyridinium chloride (CPC), two widely used and commercially available cationic surfactants with different hydrophilic head groups (i.e., quaternary ammonium versus pyridine) were used to form the micelles, and binary ion exchange on CTAB and CPC micelles between Br- or Cl-, respectively, and other anions was experimentally measured. Combining all selectivity coefficients into one equilibrium mass balance model for each surfactant, the model was then used to predict anion distribution in waters containing all anions (across UF membranes) to which CTAB or CPC micelles were added. The application for nutrient (i.e., nitrate and phosphate) separation and recovery from waters is discussed. 2. THEORY Simple models that describe ion exchange on resins and ionic membranes have been reported widely,16-19 with the basic theory concerning ion exchange first developed by Helmholtz in 1879.20 Helmholtz envisioned all counter ions as being lined parallel to the charged surface at a distance approximately equal to the ionic diameter, and with the potential decreasing linearly to 3


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zero within a short distance from the surface. Based on Helmholtz’s early work on charged surfaces, Fan et al.21 and Miller22 considered the micelle surface to have discrete exchange sites and defined the exchange of Na+ with Ca2+ on anionic micelles through the following equilibrium equation, where β is the ion exchange equilibrium constant, =

∙ [ ]

(1)

∙ [ ]

and where XCa and XNa are the fractions of Ca2+ and Na+ (in units of equivalence) in the micellar phase (per equivalent of surfactant), respectively; where the subscript f denotes free aqueous solution ion molar concentrations; and n (= 2) is the substitution ratio of Ca2+ to Na+ on the micellar surface. With this equation, complete charge neutralization of the micelle is assumed (XCa + XNa = 1). Equation 1 basically describes a simple double layer model of localized adsorption. Alternatively, a triple layer model23, 24 may be used in which many counter-ions again reside within the plane immediately adjacent to the surface (i.e., the Stern layer), with the additional counter-ions necessary to fully neutralize the surface charge residing a distance away from this plane (i.e., the diffuse layer). The concentration of ions within the diffuse layer can be calculated with the Poisson-Boltzmann equation if a reasonable estimate can be made on the amount of surface charge that is neutralized by Stern layer counter-ions.

Unless inner-sphere ion

association occurs at the surface plane, it is difficult to distinguish the amount of surface charge that has been neutralized by Stern layer versus diffuse layer ions. This distinction of closely associated ions was addressed in work performed by Lissi, et. al.25 and Abuin and Lissi26 who assumed the distinction between bound and unbound ions could be detected by fluorescence quenching of micellar solubilized PAH molecules by ions in the Stern layer, as determined through Stern-Volmer analysis. In using ultrafiltration (UF) or dialysis membranes to separate 4


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dissolved phase aqueous ions from those associated with the micelles, a charge balance is maintained across the membrane. So whereas some ions within the diffuse layer are sheered during mixing processes (resulting in what is known as a zeta potential on charged colloidal particles, like micelles), a reasonable hypothesis is that the mole ratio of these sheered ions insignificantly affects the overall mass balance of ions association with the micelles. Indeed, near the shear plane, it may be the case that the ratio of ionic species within the diffuse layer is approximately the same as the ratio of these same ions within the bulk aqueous phase. If this assumption is valid, then association of ions to micelles as measured across UF or dialysis membranes should follow the simple ion exchange model defined by eq 1. To test this hypothesis in this study, the concentrations of all ions in UF permeate were considered to be (non-micellar) aqueous phase ions, whereas all ions associated with the micellar pseudo-phase were calculated by mass balance assuming complete charge neutralization of the micelles.

2.1 Ion Exchange Model for Binary Systems The initial anion contained in the surfactant salt (Br- or Cl-) exchange with an anion added to the aqueous phase as represented by eq 2,

+ ↔ +

(2)

where A and B represent the different anions; α and β refer to the valences of the anions A and B, respectively; and the subscripts mic and aq refer to micellar phase and aqueous phase, respectively. At equilibrium, the ion exchange equilibrium constant is defined as follows, =

&

{!"# }% {'&# }" ()* &

{!"# }()* {'&# }" %

=

& +" % -()* & +, +" ()* -%

+,

∗

&

[!"# ]% ['&# ]" ()* &

[!"# ]()* ['&# ]" %

5


(3)

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where {i}aq and {i}mic refer to the activities of the anions in the aqueous phase and micellar phase in molar units, respectively; γ is the activity coefficient; [i]aq refers to the molar concentrations of the anions expressed in mole/L in the aqueous phase; and [i]mic refers to the mole fraction of anions expressed in mole/mole surfactant in the micellar phase. Note that eq 3 is different than eq 1 due to the difference in use of molar concentration rather than equivalence to define the surface concentration, yet is more commonly used to describe ion exchange processes. Mole fractions in the micellar phase are calculated from eq 4, [ ] = ([ ]010 − 3 ] 45/7

(4)

where, M is the total number of exchange sites on the micelles (mole); V is the volume of the solution (L); and [i]tot is the initial total concentration of anions (mole/L). If the aqueous concentration of ions is sufficiently dilute (typical of freshwaters), and the micellar phase is considered as an ideal phase (i.e., activity coefficients = 1), the equilibrium coefficient can be expressed as a selectivity coefficient, Ksel, leading to the simple ion exchange model (eq 5). 89 =

&

[!"# ]% ['&# ]" ()*

(5)

&

[!"# ]()* ['&# ]" %

Values of Ksel were calculated from the slope of eq 6 in this study, with eq 6 obtained simply by rearranging eq 5, ['&# ]" ()* & [!"# ]()*

= 89

['&# ]" %

(6)

&

[!"# ]%

In order to compare the selectivity of CTAB and CPC micelles for the different anions, the Ksel values for CTAB micelles for other ions (i.e., target ions) relative to Cl- (eq 7) were calculated "#

from the values of Ksel for the target ions relative to Br- (89 ': # ) (eq 8) and the selectivity #

9 constant for exchange of Br- with Cl- (89 ': # ) (eq 9) on CTAB micelles, "#

"#

#

9 89 9 # = 89 ': # /(89 ': # )

(7) 6


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"#

"# ] [': # ]" % [ ()*

89 ': # = [': # ]" #

9 89 ': # =

()* [

"# ]

(8)

%

[': # ]% [9# ]()*

(9)

[': # ]()* [9# ]%

where, X refers to the target anion and α is its valence.

2.2 Distribution of Anions in Different Phases In the binary systems, there is only one other anion in the water besides the anion initially associated with the surfactant salt. For the bulk aqueous phase, total normality is represented by eq 10. < = [ ] + [ ]

(10)

where C is the total normality of the solution (eq/L); =! = [ ] /
' = ?@

(17)

- FBCDE @-

2.2.2 Monovalent and Divalent Anion Distribution For solutions containing target divalent anions that exchange with the monovalent anions initially associated with the surfactant salt, α = 1 and β = 2. Equation 15 can be rearranged to yield, (?@- ) A-

89 = @

- (?A- )

∗
' = 1 − ((1 + (?@

-)

LB

@-

CDE )I.K − 1)/((?@

-)

)

(19)

3. EXPERIMENTAL SECTION 3.1 Materials Cetyltrimethylammonium bromide (CTAB, 99.9% from Sigma-Aldrich), with a CMC of 0.92 mM15, and cetylpyridinium chloride monohydrate (CPC, 96-101% from Acros Organics), with a 8


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CMC is 1.08 mM,11 were used in this study. Generally, to form sufficient spherical micelles, the surfactant concentration should be much larger than the CMC; however, when the surfactant concentration far exceeds the CMC, the shape of the micelles generally changes to wormlike aggregates.27 Therefore, 3 to 10 mM of CTAB or CPC were used to form spherical micelles in this study. Target anions included IO3-, F-, Cl-, HCO3-, NO2-, NO3-, H2PO4-, HPO42-, SO42-, and CrO42-, which were prepared from their respective potassium salts, and solutions dominated by either H2PO4- or HPO42- were prepared by adjusting the solution pH to 4.5 and 10, respectively. Deionized water was used in all experiments. 3.2 Ultrafiltration A 350 mL dead-end ultrafiltration cell (Amicon, USA) and a cellulose membrane (Amicon, USA) were used to separate the micelles and associated anions from aqueous dissolved ions. The cellulose membrane had an effective surface area of 45 cm2 with molecular weight cut-off (MWCO) of 5000 Da, and all membranes used in this study were pre-saturated with solutions containing the surfactant monomers and target anions used in each experiment. Experiments were performed at room temperature at an applied pressure of 60 psi. The flux of deionized water through the membrane under these conditions was 0.84 m3/(m2 · d). The solutions containing micelles and target anions were stirred for 0.5 to 1 hours before filtration. A 20 mL subsample of each solution before filtration and the first 10% volume of permeate (20 mL) were collected to determine the concentrations of target anions. From these measured concentrations, and concentrations in the micellar phase were calculated from eq 4. 3.3 Anion Analysis The analysis of IO3-, F-, Cl-, NO2-, Br-, NO3-, PO43-, and SO42- ions was performed by ion chromatography (IC, Dionex with a CD20 conductivity detector and AS40 automated sampler). 9


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The mobile phase contained 1 mM NaHCO3 and 2 mM Na2CO3 with a flow rate of 1 mL/min and column pressure of 600 psi. Experimental concentrations of HCO3- were determined by titration, and the concentrations of CrO42- were determined by UV-Vis spectroscopy (Thermo Scientific Evolution 220) at a wavelength of 372 nm. 3.4 Simulated Water and Surface Water Samples Simulated water samples and actual surface water samples were used to test the overall model. The simulated water samples were prepared with potassium salts of each corresponding anion. The concentration of bicarbonate in the water was 5 mM (pH = 7.7), and the concentrations of F-, Cl-, NO2-, NO3-, PO43-, and SO42- were set to 1 mM each. The concentration of the surfactant (CTAB or CPC) ranged from 5 to 10 mM. Surface water samples were collected from the Wabash River at Lafayette, IN, the White River at Indianapolis, IN, the Central Canal in Indianapolis, IN, and Lake Michigan at St Joseph, MI. In addition to these natural waters, phosphate-augmented White River water was used to verify the model. The ionic composition of these water samples is provided in Table 1.

Table 1. Ionic composition of water samples (in mM units, except for pH)

pH [HCO3-] [NO3-] [SO42-] [Cl-] [PO43-]

Wabash River 7.97 4.23 0.50 0.62 0.90 0.0024

White River 7.69 4.74 0.15 0.73 2.54 0.0036

Central Canal 7.76 5.63 0.26 1.22 8.99 0.0026

Lake Michigan 7.02 2.08 0.17 0.28 0.54 0.0045

10


P-Enriched White River 7.80 4.74 0.15 0.73 2.54 0.05 (1.5 mg/L as P)

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An ultrafiltration cell (350 mL) equipped with a 5000 Da cellulose membrane was used to separate non-micellar anions from the bulk water samples. The rejection fraction, R, is defined by eq 20, M =1−

[]%

(20)

[]NON

where, [X]aq and [X]tot represent the anion concentrations in the permeate (i.e., aqueous phase) and the bulk sample (aqueous + micellar), respectively. Hence, a value of R = 0.4 indicates that 40% of the ion in solution is associated with the micellar phase, and that the concentration in the permeate is 60% of the total concentration.

4. RESULTS AND DISCUSSION 4.1 Selectivity Coefficients In all binary system experiments, the total concentration of the target anion was 1 mM, and surfactant concentration ranged from 3 to 10 mM. From the experimental data, each selectivity coefficient (Ksel) was evaluated from the slope of eq 6. Figures 1 and 2 show the experimental data and regression equations (eq 6) for all monovalent and divalent anions towards Br- and Clin CTA+ and CP+ micellar solutions, respectively. The magnitude of each slope for monovalent anion reflects the affinity of the target anion with respect to Br- or Cl- for the surface of the micelles; a slope greater than 1 indicates the target anion has a greater affinity for the micelles compared to the initial anion (Br- or Cl-). The data for NO3- and SO42- exchanging with Br- in CTA+ solutions can be taken as examples, where the regression equations are Y = 1.27·X and Y = 0.0152·X , respectively. Therefore, the selectivity coefficients for NO3- and SO42- with respect to Br- for CTA+ micelles are 1.27 (unitless) and 0.0152 mole/L, respectively.

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0.6

Br¯ H₂PO₄¯ HCO₃¯ NO₂¯

0.5

IO₃¯ F¯ Cl¯ NO₃¯

[X-]mic/[Br-]mic

0.4 0.3 0.2 0.1

a. CTAB

0 0

0.2

0.5

0.4 0.6 0.8 [X ]aq/[Br ]aq

Cl¯ H₂PO₄¯ NO₂¯ NO₃¯

0.4

1

1.2

F¯ HCO₃¯ Br¯

[X-]mic/[Cl-]mic

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.3

0.2

0.1 b. CPC 0 0

0.1

0.2 0.3 0.4 [X-]aq/[Cl-]aq

0.5

0.6

Figure 1. Ratios of target ions to Br- or Cl- in the micellar phase regressed against the same ratio in the dissolved aqueous phase, in CTAB and CPC solutions, respectively

12


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1 a. CTAB

0.9 0.8

SO₄²¯ HPO₄²¯

[X2-]mic/[Br-]mic2

0.7 0.6 0.5

3

0.4 2

0.3 0.2

1

0.1

0

CrO₄²¯

0 20 40 60 80

0 0

50

100 150 [X2-]aq/[Br-]aq2

200

20 30 2[X ]aq/[Cl ]aq2

50

3

b. CPC 2.5

[X2-]mic/[Cl-]mic2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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SO₄²¯

2

HPO₄²¯

1.5 1

0.5 0

0

10

40

Figure 2. Ratios of target divalent ions to Br- or Cl- in the micellar phase (squared), regressed against the same ratio in the dissolved aqueous phase, in CTAB and CPC solutions, respectively

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The measured values of Ksel for the different anions for CTA+ and CP+ micelles, where Br- and Cl- are the competing anions, respectively, are shown in Table 2.

Table 2. Selectivity coefficients of anions for CTAB and CPC towards common anions Hydrated Ksel for CTA+ Anions radius with respect (nm) to BrIO30.21 28 28 F 0.136 0.352 0.22 H2PO40.22 HCO30.15629 0.33 28 28 0.181 0.332 0.47 Cl NO20.19229 0.67 Br0.19528 0.33028 1.00 NO30.19617 1.27 2- ‡ HPO4 0.0057 SO42- ‡ 0.0152 2- ‡ 0.0434 CrO4 † Calculated from eqs 7-9, Radius (nm)

‡

R2 0.96 0.87 0.97 0.98 0.99 0.98 0.99 0.96 0.96 0.97

Ksel for CTA+ with respect to Cl- (†) 0.45 0.47 0.47 0.70 1.00 1.43 2.13 2.70 0.0258 0.0688 0.1964

Ksel for CP+ with respect to R2 Cl0.31 0.96 0.32 0.96 0.60 0.99 1.00 1.27 0.99 2.57 0.99 2.73 1.00 0.0303 0.97 0.0706 0.99 crystalline precipitate

For divalent ions, the unit of Ksel are mole/L

The values of Ksel in Table 2 indicate that NO2-, Br-, NO3-, HPO42-, SO42- and CrO42- have greater affinity to the micellar phase than Cl-.

Although CTA+ has a quaternary ammonium

functional group and CP+ has a pyridine functional group, the relative affinities of all the anions for the two surfactants follows the same sequence of CrO42- > SO42- > HPO42- > NO3- >Br- > NO2- > Cl- > HCO3- > F- ≈ H2PO4-. Additionally, by calculating Ksel for CTA+ with respect to Cl-, the selectivity coefficients for each anion on both types of micelles can be compared directly. The data indicate very similar values for both types of micelles, somewhat contrary to the research of Buckingham et. al.30 and Kellaway and Warr31, who reported that the selectivity coefficient depended on the nature of the surfactant head group. Further, this order is the same 14


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as the order of decreasing retention times for these ions measured by ion chromatography. Note that while Ksel for ions of different charge cannot be compared directly, it is obvious that the divalent ions have much greater affinities for the micellar surface. As with other partitioning processes, the selectivity coefficient is directly related to the Gibb’s free energy change for the reaction, ∆G 0, ∆W X

STU = L.YIYZ[

(21)

For outer-sphere ionic complexation, based on Pauley’s model32 and Marcus’s model,17, 33 the free energy change is a function of the ionic radius. For all the monovalent anions, Figure 3 shows the correlation between Ksel and ionic radius. Ions with larger ionic radii have larger values for Ksel for micelles composed of either surfactant. The smaller ions tend to be hydrated with more water molecules, evident from the nearly identical hydrated radii of F-, Cl-, and Brreported in Table 2, decreasing the electrostatic attractive force for the micellar surface. The ion affinity for the surfactant micelles generally follows the same order as that for ion exchange resins and ion exchange membranes reported in the literature, however the magnitudes of Ksel can differ significantly. For example, Ksel for NO2- and NO3- were measured at 0.73 and 1.56 for an EHDA surfactant foam (with respect to Br-),34 similar to this study. On an anion exchange resin, Ksel (with respect to Cl-) for HCO3-, NO3-, and SO42- were measured at 0.13, 2.8, and 141 (g/L), respectively18, with only Ksel for NO3- close to the value measured in this study (2.70 for CTAB, and 2.73 for CPC). From measurements made on a polymer inclusion membrane, Ksel for HCO3-, NO2-, Br-, and NO3- were calculated at 0.33, 1.67, 4.67, and 15.67, respectively (relative to Cl-).17 Again, while the magnitude of these values is different, the order in affinity is the same. Collectively, these data indicate that while the order in affinity is clearly

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a function of the ionic radius, the magnitudes of the selectivity coefficients also depend on the characteristics of specific ion exchange material. 0.8 0.6

CTAB Br-

CPC

0.4 0.2 log Ksel

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

NO3-

Cl-

0

HCO3-

NO2-

-0.2 -0.4

F-

-0.6 -0.8 0.12

0.14

0.16 0.18 0.2 Ionic radius (nm)

0.22

Figure 3. Correlation between Ksel and ionic radius (r), for CTA+ micelles, STU 89 = 11.041^ − 1.87 (R2 = 0.89) and for CP+ micelles, STU 89 = 14.121^ − 2.45 (R2 = 0.91).

4.2 Comparison between the Simple Ion Exchange Model and the Triple Layer Model In a triple layer model, the surfactant ions are the first layer, closely associated counter-ions within the Stern layer which composes the second layer, and the remaining counter-ions necessary to fully neutralize the charge of the surfactant ions are contained in the diffuse layer.23-25 For non-inner sphere complexation to the surface of the micelles, ions near the surface of micelles (Stern layer) exchange with ions that are a distance away from the surface and in the diffuse layer. The equilibrium constant for this exchange for two monovalent species can be expressed as, 16


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I =

[!# ]c) ['# ]d

(22)

[!# ]d ['# ]c)

where, K0 is the equilibrium constant, and can be viewed as the ratio of activity coefficient corrections for outer-sphere association; [i]dif refers to the ion concentration in the diffuse layer, and [i]b refers to the ion concentrations in the Stern layer (i.e., bound phase). According to the Boltzmann equation, the concentration of monovalent ions in the diffuse layer at the Stern layer plane can be calculated from the concentration of ions in bulk solution, and from the potential at the Stern layer – diffuse layer boundary, as follows, [ ]ef = [ ] g=h

ij

(23)

ij

(24)

Z[

[ ]ef = [ ] g=h Z[

where, F is Faraday’s constant; ψ refers to the electrical potential at the Stern layer - diffuse layer boundary; R is the gas constant, and T is the absolute temperature. Therefore, K0 can be expressed as, I =

[!# ]c) ['# ]d

[!# ]d ['# ]c)

=

lm

# ['# ]d [! ]% @k no

[!# ]d ['# ]% @k

['# ] [!# ]%

d lm = [!# ] [' # ] d

no

(25)

%

The difference between Ksel and K0 now can be understood by comparing equations 5 and 25. The “fraction ionization” of the micelles (β) can be defined as the different between the micellar surfactant charge and the charge of the closely associated ions. The “fraction bound” (α) can be defined as the fraction of micellar surface charge neutralized by closely associated ions (1 - β). Hence, for the simple ion exchange model, β = 0 and α = 1.

In this study, the micellar

concentrations of all ions (Stern layer + diffuse layer) were calculated by mass balance (eq 4) based on membrane rejection. Hence for monovalent species, Ksel can be express also as eq 26, [!# ]% (['# ]NON ['# ]% )

89 = ['# ]

%

([!# ]

NON

[!# ]

% )

[!# ]% (['# ]d F['# ]c) )

= ['# ]

%

([!# ]

d

F[!# ]

c) )

[!# ]% (['# ]d F- [p])

= ['#]

%

([!# ]d F, [p])

17


(26)

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 35

where, [M] refers to the concentration of surfactant in the micellar phase, and βA and βB refer to the fraction ionization of ions A and B in the micellar phase. If β = 0 (i.e., all micellar surfactant charge is neutralized with closely associated {Stern layer} counter-ions), Ksel = K0. On the other hand, if β = 1, then Ksel = 1, with the underlying assumption of this result being that at any distance from the micelle surface, the activity coefficient of all monovalent ions is the same. Overall therefore, Ksel depends on β and is between K0 and 1. This notion is supported by Warr’s35 analysis, based on a site-binding ion-exchange model. It should be noted that β is variable and depends on the surfactant type, the associating ions, and the ionic strength. There is no significant difference in the calculated fraction bound for Cl- on CP+ and CTA+ micelles.23 Based on the relationship between conductivity and concentration, for aqueous solutions of pure CTAB, β = 0.31 and for pure CPC, β = 0.45, indicating Br- associates more closely.

In our experiments in which selectivity coefficients were measured, because the

concentration of surfactant (as micelles) was much higher than the target anion, a constant value of β = 0.45 was assumed in order to calculate K0 for NO3- association on CPC micelles, with the results shown in Figure 4. Under the experimental conditions, K0 (= 4.55) was slightly larger than Ksel (= 2.73). However, it is known that the fraction bound (1 - β) increases with ionic strength,24 and therefore Ksel will be higher and close to K0 at higher ionic concentrations. Indeed, Figure 5 shows the relationship between Ksel and ionic strength for NO3- in aqueous solutions of CPC, indicating Ksel equals K0 at higher ionic strengths. Similar trends (not shown) for selectivity coefficients of I- and Br- were obtained as a function of increasing ionic strength.35

18


Page 19 of 35

0.6 y = 4.5477x

0.5

[NO3-]mic/[Cl-]mic

0.4 0.3 y = 2.7302x

0.2

K₀ 0.1 Ksel 0 0.03

0.05

0.07 0.09 [NO3-]aq/[Cl-]aq

0.11

Figure 4. K0 and Ksel for NO3- in CPC solution

4 3.297 3.509 3.250

3.5 3.137

3 Ksel

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

2.727

2.5

2

1.5 -2.75

-2.25

-1.75 log I (M)

-1.25

-0.75

Figure 5. Ksel for NO3- in CPC solution with different ionic strength The relationship between Ksel of the simple ion exchange model and K0 of the triple layer model can be explained further through the following equations, 19


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

[!# ]%

['# ]%

= I

[!# ]d

(27)

['# ]d

89 = I ([!#]

[!# ]d

d

F[!# ]

Page 20 of 35

c) )

(['# ]d F['# ]c) ) ['# ]d

= I

,

-

= 1 − = >! ! + >' '

(28) (29)

where, αA and αB are for ions A and B, and again depend on the surfactant species and ionic strength. The term α is the fraction bound in the mixed-ion system, and yA and yB again refer to the equivalent fractions of anions A and B in the micellar phase, consistent with equations 13 and 14. When the target anion has a higher affinity for the micelles than the initial ion in the surfactant salt, the value of α will be greater than that of the initial ion, and therefore K0 will be larger than Ksel, consistent with the calculated values for NO3- / Cl- on CPC micelles. However, because α is larger, Ksel will be close to K0, and because the value of α differs with ionic strength and is not simple to model (i.e., calculate) mathematically from ionic composition, or easy to determine for complex mixtures by UF methods, the triple layer model in actual practice is difficult to use in practice. In addition, the triple layer model becomes even more complex when considering exchange between mono- and divalent ions, making application to natural waters even more difficult, without any perceived gain in accuracy.

4.3 Anion Distribution in Binary Systems 4.3.1 Monovalent Anion Distribution To generate Figures 1 and 2, the concentration of each surfactant was varied from 3 to 10 mM while holding the added ion concentrations constant at 1 mM. To further evaluate the simple ion exchange model and the associated values of Ksel reported in Table 2 under a larger range of 20


Page 21 of 35

experimental conditions, the surfactant concentration again was varied from 3 to 10 mM, and the target ion concentrations were varied from 0.5 to 5 mM. These additional data are plotted as “ion exchange isotherms” on Figure 6, along with the predicted isotherms using the previously calculated values of Ksel reported in Table 2. The data above the y = x dashed line are for target anions that have greater affinities for the micelles than the initial anion (Br- or Cl-), and the data below the dashed line are for the anions that have less affinity for the micelles.

Of the

monovalent anions examined, only NO3- has a greater affinity for CTA+ micelles than Br-, and both

Br-

and

NO3-

have

greater

affinity

to

the

0.8 IO₃¯ F¯ H₂PO₄¯ HCO₃¯ Cl¯ NO₂¯ NO₃¯

0.7 0.6 0.5 y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

0.4 0.3 0.2 0.1

a. CTAB

0.0 0.0

0.2

0.4 x

0.6

0.8

21


CP+

micelles

than

Cl-.

Langmuir

0.8 F¯

y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 35

0.7

H₂PO₄¯

0.6

HCO₃¯

0.5

Br¯ NO₃¯

0.4 0.3 0.2

b. CPC

0.1 0.0 0.0

0.2

0.4 x

0.6

0.8

Figure 6. Anions distribution between aqueous phase and micellar phase, where x is the mole fraction of each target anion in aqueous phase, and y is the mole fraction of the target anion in the micellar phase. Note that for CTAB and CPC, exchange is with Br- and Cl-, respectively.

4.3.2 Divalent Anion Distribution, Exchange with a Monovalent Anion Figure 7 (a and b) shows the ion exchange isotherms of SO42-/Br- and HPO42-/Br- at different total concentrations of the target anion in CTAB solutions. Figure 7 (c and d) shows similar ion exchange isotherms for SO42-/Cl- and HPO42-/Cl- in CPC solutions. Equation 19 indicates that equilibrium distribution can be viewed as a function of both Ksel and the solution normality, C, when both monovalent and divalent anions are present in solution. When the solution normality is low, a higher fraction of each target anion is associated with the micelle phase, whereas at higher concentrations, the micelles will become nearly saturated with the target anions.

22


Page 23 of 35

0.7 a. SO42- /Br-

0.6 0.5 0.4 y

0.5 mM

0.3 1 mM 0.2

1.5 mM

0.1 0.0 0.0

0.1

0.2 x

0.3

0.4

0.6 b. HPO42- /Br-

0.5 0.4 y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

0.3 0.5 mM 0.2 1 mM 0.1 0.0 0.0

0.1

0.2

x

0.3

0.4

0.5

23


Langmuir

0.9 c. SO42- / Cl-

0.8 0.7 0.6 y

0.5 1 mM

0.4

2 mM

0.3 0.2 0.1 0 0

0.1

0.2

0.3 x

0.4

0.5

0.6

0.7 d. HPO42- / Cl-

0.6 0.5 0.4 y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 mM

0.3

2 mM 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

x

Figure 7. Distribution of target divalent anions at different target anion concentrations, where x is the equivalent fraction of target divalent anions in the aqueous phase and y is the equivalent fraction of target divalent anions in the micellar phase

24


Page 24 of 35

Page 25 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

4.4 Predicted Anion Rejection From the set of selectivity coefficients determined in the binary systems (Table 2), a model was developed that accounted for multi-anion distribution between the aqueous and micellar phase, accounting for all necessary mass balances and acid-base speciation reactions, to predict the removal efficiencies of all major anions from typical natural waters, as a function of ionic composition, including {H+}. The model equations are shown in Table 3, with all ion specific equations and calculation methods reported in the Supporting Information, (SI). Assumptions inherent in the model are that Ksel is constant and activity coefficients are constant and captured within the value of Ksel. Also, because the CMC of CTAB and CPC are quite low and decrease with increasing ionic strength, the value of the CMC in the equations can be assumed to be negligible for our experimental conditions.

Table 3. Equations for calculating anion distribution between water and micelles‡

[z{HY ]010 9

[ ]010 9 = [qr^stuvtwv]010 9 + [ ]x0 9 7 [ ]010 9 = [ ] + [ ] ∗ 5 7 [ ]010 9 = [ ] + [ ] ∗ 5 7 L L L [y ]010 9 = [y ] + [y ] ∗ 5 7 7 L = [|L z{H ] + [|z{H ] + [|L z{H ] ∗ + [|z{HL ] ∗ 5 5 7 = [qr^stuvtwv]010 9 − SO42- > HPO42- > NO3- > Br- > NO2- > Cl> HCO3- > H2PO4- ≈ F-, which is the same order in affinity that these anions have for anion exchange resins and ion exchange membrane. Yet, the magnitude of the selectivity coefficients differs due to the different characteristics of the ion exchange materials. A more complete model that accounts for mass balances and ion exchange of multiple anionic species was developed to predict anion distribution between cationic micelles and free aqueous species in natural freshwater. The data on anion removal across UF membranes was well predicted by the model 30


Page 31 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

and indicates that significant removal on nutrient species from natural waters will occur across ultrafiltration membranes when cationic micelles are present in solution.

ASSOCIATED CONTENT Supporting information The Supporting Information is available free of charge on the ACS Publications website at DOI: (to be added upon publication). This information includes: All equations used to calculate anion distribution between the water and micellar phases for CPC and CTAB micelles (Table S1 and Table S2); and information on the calculation process (Table S3).

AUTHOR INFORMATION Corresponding Author *Email: [email protected]

ACKNOWLEDGEMENT We acknowledge and thank the support from the China Scholarship Council (CSC) through a Ph.D. fellowship awarded to Ming Chen to study at Purdue University.

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Anion Exchange on Cationic Surfactant Micelles ... - ACS Publications

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