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Modeling Bi-solute Adsorption of Aromatic Compounds based on Adsorbed Solution Theories (ASTs) Huichun Zhang, and Shubo Wang Environ. Sci. Technol., Just Accepted Manuscript • Publication Date (Web): 24 Apr 2017 Downloaded from http://pubs.acs.org on April 24, 2017

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Environmental Science & Technology

Modeling Bi‐solute Adsorption of Aromatic Compounds based on Adsorbed Solution Theories (ASTs)

1 2 3

4

Huichun Zhang* and Shubo Wang

5 6

*Department of Civil and Environmental Engineering, Temple University, Philadelphia, PA 19122 Phone: 215‐204‐4807, e‐mail: [email protected]

7

8

ABSTRACT

9

A large number of organic contaminants are commonly found in industrial and municipal wastewaters.

10

For proper unit design to remove contaminant mixtures by adsorption, multi‐component adsorption

11

equilibrium models are necessary. The present work examined the applicability of Ideal Adsorbed Solution

12

Theory (IAST), a prevailing thermodynamic model, and its derivatives, i.e., Segregated IAST (SIAST) and Real

13

Adsorbed Solution Theory (RAST), to bi‐solute adsorption of organic compounds onto a hyper‐crosslinked

14

polystyrene resin, MN200. Both IAST and SIAST were found to be less accurate in fitting the experimental

15

bisolute adsorption isotherms than RAST. RAST incorporated with an empirical four‐parameter equation

16

developed in this work can fit the adsorbed phase activity coefficients, , better than RAST combined with

17

Wilson equation or Nonrandom two‐liquid (NRTL) model. Moreover, two poly‐parameter linear free energy

18

relationships were developed for the adsorption of a number of solutes at low concentrations in the presence

19

of a major contaminant (4‐methylphenol or nitrobenzene). Results show that these relationships have a great

20

potential in predicting of solutes when the adsorbed amounts are dominated by a major contaminant. To the

21

best of our knowledge, this is the first study predicting for bi‐solute adsorption based on molecular

22

descriptors. Overall, our findings have proved a major step forward to accurately modeling multi‐solute

23

adsorption equilibrium.

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Single Solute

Same spreading pressure of adsorbed phase

Bi-Solute

IAST: RAST: Adsorbed phase activity coefficient

25

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70% 60%

IAST

50%

RAST-FPM

40%

10% errors

30% 20% 10% 0% 0.0

0.5

1.0

Adsorbed phase mole fraction


26 27

Relative errors of predicted adsorbed amount


TOC Art INTRODUCTION

28

The occurrence of a large number of organic contaminants (OCs) in our water systems and in the

29

environment is among important environmental challenges facing the world.1‐4 Examples include priority

30

contaminants such as pesticides, dyestuffs, petrochemicals, and chemical intermediates, and emerging

31

contaminants such as pharmaceutical and personal care products. Their broad range of applications and

32

inefficient removal from waste streams have led to their ubiquitous presence in drinking water, wastewater,

33

and many environments, including surface water, groundwater, soils, and sediments.1, 2, 4, 5 The persistence of

34

OCs in the environment likely poses serious problems to ecosystems and human health. 6‐9 Adsorption is one of the most frequently used methods for removing OCs from contaminated water.10‐

35 36

13

37

among the most important limits for proper design and operation of a treatment system. For instance, a

38

common design for adsorption is fixed‐bed adsorbers, for which equilibrium adsorption data is essential for

39

adsorbent selection, prediction of breakthrough curves, and estimation of the maximum service life of the

40

adsorber.14, 15 Poor prediction of multicomponent equilibrium can cause a large error in dynamics prediction.16

During the application of a given adsorbent, adsorption equilibrium data over a broad range of conditions are

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Also, adsorption kinetics are dependent on adsorption equilibrium such that kinetic models can only be applied

42

if equilibrium data are available.14

43

Raw water or wastewater typically contains mixtures of OCs while the presence of a single‐solute is

44

likely the exception rather than the rule. For instance, mixtures of aromatic compounds such as BTEX (benzene,

45

toluene, ethylbenzene, and xylene) are frequently detected in groundwater due to their release during

46

production, transportation, and storage.17‐19 Drinking water and municipal wastewater are undoubtedly

47

mixtures of a number of OCs.5, 20 Competition in multi‐solute systems typically decreases adsorption capacity as

48

compared to that of single‐solute systems. Therefore, proper design of an efficient adsorber requires reliable

49

adsorption equilibrium data of the multi‐solute mixture, i.e., the adsorbed amount of each adsorbate and the

50

composition of the solution phase at equilibrium (adsorption isotherms). However, it is not feasible to

51

experimentally obtain all equilibrium data for the vast number of OC mixtures of different compositions under

52

changing operating conditions. Predictive models that can be used to accurately estimate equilibrium data for

53

multi‐solute adsorption based on the available single solute adsorption isotherms will be extremely valuable.

54

Many widely used multicomponent adsorption models are based on empirical fitting to Langmuir,

55

Freundlich or Toth equation.21 For example, Zhang et al. and Valderrama et al. studied the binary adsorption of

56

phenol/aniline onto resin MN200 and granular activated carbon (GAC) using the extended Langmuir and

57

Freundlich equation. 22, 23 In comparison, Ideal Adsorbed Solution Theory (IAST) that is thermodynamically

58

consistent and relies solely on single‐component isotherms has been shown to be more widely applicable,24‐28

59

and is considered the standard method to predict multicomponent adsorption.14 IAST has gained a large

60

success in modeling gas‐phase adsorption of mixed volatile organic compounds. 27‐29 It also has some success in

61

modeling multi‐component adsorption from water.15, 25, 26, 30‐38 However, the two ideal assumptions of IAST (i.e.

62

ideal adsorbed mixtures in which all solutes have activity coefficients of unity and homogenous adsorption

63

sites) have proven to often deviate from real adsorption behavior. 18 3 ACS Paragon Plus Environment


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Since early 1980’s, chemical engineers have begun to incorporate nonideality into IAST by developing

65

different versions of ASTs such as RAST (Real Adsorbed Solution Theory).39 ASTs have been successfully used to

66

model adsorption of a number of multi‐component mixtures from the gas phase,39‐43 and have recently been

67

extended to adsorption from the solution phase, but only with limited success for a small number of OCs under

68

selected conditions.44‐46 Compared to IAST that has been widely accepted by environmental engineers,15, 26

69

surprisingly, other ASTs are largely unknown to the environmental community.47, 48 Even among chemical

70

engineers, the focus has been on multicomponent adsorption from the gas phase.39‐43 More importantly, the

71

existing models are mostly fitting models with predictive ability confined to a few well‐defined solution

72

conditions,49‐53 it remains challenging to have a reliable prediction of multisolute adsorption equilibrium for a

73

diverse range of OC mixtures. 21 Therefore, it is imperative to establish AST‐based predictive models that will

74

allow accurate estimation of multi‐solute adsorption equilibrium of various OCs by common adsorbents.

75

To examine the validity of ASTs and apply them to aqueous phase adsorption with necessary

76

modification, binary adsorption experiments of a number of aromatic OCs by polymeric resin were conducted.

77

The reason that resin was selected as a representative sorbent is that polymeric resins have been reported to

78

effectively remove a large variety of organic contaminants during water and wastewater treatment. 54‐61

79

Specifically, our objectives were to: (1) experimentally obtain binary adsorption isotherms of 8 aromatic

80

compounds under varying solute ratios onto polymeric resin MN200 as a model adsorbent; (2) apply IAST,

81

RAST, segregated IAST (SIAST) and multi‐solute dual‐site Langmuir (MSDSL) model to predict adsorption

82

equilibria of the bi‐solute systems. RAST was incorporated with adsorbed phase activity coefficients to

83

eliminate the deviation of IAST. SIAST and MSDSL assume heterogeneous adsorption sites and were studied for

84

comparison; (3) calculate of each solute in all the studied mixtures and model them with classical equilibrium

85

models for liquid mixtures, including Wilson, Nonrandom two‐liquid (NRTL), and a four‐parameter model (FPM)

86

developed in this work. This was to test if thermodynamic activity coefficient equations can be used to fit 4 ACS Paragon Plus Environment

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experimental and whether a better simulation and prediction of multicomponent adsorption equilibrium can

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be achieved through RAST; and (4) develop predictive tools for of all solutes based on poly‐parameter linear

89

free energy relationships (pp‐LFERs) by correlating at infinite dilution with solute molecular descriptors.

90

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EXPERIMENTAL

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Materials and Chemicals Macronet MN200, a hyper‐crosslinked nonionic polymeric resin was obtained from

93

Purolite® (U.S.). Before batch adsorption experiments, the resin was subjected to NaOH/DI‐water/HCl wash,

94

followed by extraction with methanol in a Soxhlet apparatus to remove residual impurities. All selected solutes

95

including nitrobenzene (NB), aniline, 4‐nitroaniline (4‐NA), 4‐chloroaniline (4‐CA), phenol, 4‐chlorophenol (4‐

96

CP), 4‐methylphenol (4‐MP), and 4‐nitrophenol (4‐NP) have high purity (99+%). They were purchased from

97

Fisher Scientific and prepared in DI water without further purification. Physical‐chemical properties of the

98

selected aromatic compounds are shown in Table S1 in the Supporting Information (SI). These 8 compounds

99

were chosen to represent different intermolecular interactions, especially H‐bonding and π‐π electron‐donor‐

100

acceptor (EDA) interactions as reflected by their different aqueous solubility, n‐hexadecane‐water partition

101

coefficient (KHW) and pKa. Because steric effects were not the focus of this work, many of these compounds

102

contain para‐substituents.

103

Batch Adsorption Experiments The adsorption experiments were performed in amber glass bottles equipped

104

with Teflon‐lined screw caps at 23±0.5 . The pH value was adjusted to 4.0±0.5 for 4‐NP and was about neutral

105

for all other compounds. The bottles with different solute‐sorbent combinations were then transferred to a

106

shaker equipped with a thermostat under 175 rpm for 48 hrs. Initial and equilibrium concentrations were

107

determined by HPLC with methanol and distilled water (methanol and pH=3.0 phosphoric acid for 4‐NP) as the

108

mobile phase. For binary‐solute adsorption, at least 90 seconds of difference in the retention times of each pair

109

of solutes were obtained by changing the ratio of methanol and distilled water (or pH=3.0 phosphoric acid). 5 ACS Paragon Plus Environment


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Design of Binary Adsorption Experiments All sets of bi‐solute adsorption data were collected from batch

111

adsorption experiments. Initial concentrations of both components, solution volume, and dosage of MN200

112

resin were designed to fulfill the following rules:

113

1. Targeted equilibrium concentrations of component P, denoted as the primary solute, changed

114

approximately from 0.005 mM to 40 mM, or about 40% of the aqueous solubility.

115

2. Targeted equilibrium concentrations of component C, denoted as the competitor, were set at a

116

constant value.

117

3. The adsorbed amounts of the primary solute and the competitor were predicted by IAST (details

118

below) using the expected equilibrium concentrations of components P and C. By changing the

119

expected equilibrium concentration , we were able to change the expected adsorbed amounts

120

and thus, let the adsorbed phase mole fractions change from 0.1 to 0.9.

121

4. Reactor total volume was either 20 mL or 50 mL based on the concentration of the primary

122

solute.

123

5. Initial concentrations of the primary solute and the competitor

124

adsorption mass balance (

125

obtain a constant initial concentration of the competitor.

,

,

were calculated from batch

) while the dosage of the adsorbent was adjusted to

126

The studied conditions covered a wide range of concentrations and concentration ratios of aromatic

127

compounds to represent common conditions encountered in water and wastewater treatment. The reason

128

that the competitors were maintained at high concentrations is that a small amount of competitors will likely

129

have little impact on the adsorption of a co‐existing contaminant in which case IAST may already have a

130

reasonable fit.

131

MODELING APPROACHES


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Ideal Adsorbed Solution Theory (IAST) The key assumptions in IAST for aqueous phase adsorption are: (1) all

133

the adsorption sites are homogeneous and accessible to all solutes; (2) when there are multiple solutes with

134

moderate adsorption capacity, all the components in the mixture behave as ideal adsorbed solutes; (3) the

135

molar area of mixing is identical in the mixture vs. single‐solute adsorption; and (4) all solutes are ideal dilute

136

solutes and obey Henry’s law. Based on these assumptions, there are five essential equations:26

(1)

∑

∑

(2)

(3)

(4)

(5)

137

where is the equilibrium concentration of solute i in liquid phase,

is the single‐solute liquid phase

138

concentration in equilibrium with the adsorbed phase concentration

at the same temperature and

139

spreading pressure as those of the multi‐solute adsorption, is the adsorbed phase mole fraction of solute i,

140

is the total adsorbed phase concentration, and is the spreading pressure (surface tension, surface

141

potential, or grand potential in other literatures). The superscript 0 in eqs. 1, 4, 5, and equations to follow refers

142

to the single solute adsorption standard state. Since the total adsorption area A in eq. (5) is not available, the

143

reduced spreading pressure is used in the calculation, which has the same unit as adsorption capacity.62

144

Detailed mathematic solution to binary IAST modeling is in Text S1.

145

Real Adsorbed Solution Theory (RAST) When the adsorbed phase mixture is not ideal and IAST prediction

146

deviates from experimental adsorption equilibrium, a correction of IAST is needed. Costa et al. 39 first extended

147

IAST to Real Adsorbed Solution Theory (RAST) by fitting Gibbs excess free energy models such as Wilson 7 ACS Paragon Plus Environment


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equation and UNIQUAC to experimental adsorbed phase activity coefficients ( ) of binary component

149

adsorption, which modeled ternary component adsorption with a good accuracy. One favorable feature of

150

Wilson and UNIQUAC models is that only binary parameters are required to predict multi component

151

equilibrium, however, both models only considered the composition dependency of . Other models that

152

were fitted to include NRTL,41 Flory Huggins equation 63 and a two‐parameter Margules equation.64

153

In RAST, eqs 2‐3 and 5 remain the same but eqs. 1 and 4 have been modified to:

∑

∑

z ∙

(6)

,

(7)

154

Adsorbed phase activity coefficients ( ) are incorporated when the adsorbed mixtures are not ideal which

155

violates eq. 1 (analogous to Raoult’s Law). of less than 1 means that the experimental adsorbed

156

concentrations are greater than the corresponding values predicted by IAST and vice versa. The partial

157

derivatives in eq. 7 illustrate that is a function of spreading pressure. This dependency can be neglected if

158

the ideal solution assumptions are fulfilled, or if the molar area of mixing is zero. Details of calculation of

159

based on experimental data (

To obtain better fitting of

160 161

) are in Text S2. , we propose to use an empirical four‐parameter model (FPM) based on

the two‐parameter Margules equation, 64 as shown below:

ln

(8)

ln

(9)

are adjustable parameters. In FPM, each ln is allowed to have different infinite

162

where

163

values when approaches zero, that is, each solute has its own . In addition, each solute has its own

164

adjustable exponent to achieve better fitting. Details of modeling with Wilson, NRTL, and FPM equations

165

are shown in Text S3.

,

, and


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166

Segregated Adsorption Models. In dealing with nonideality of adsorbed phase mixtures, another approach is

167

to assume heterogeneous adsorption sites, or energetic heterogeneity. 29, 65 The dual‐site Langmuir model

168

(DSL) assumes that adsorbates form ideal adsorbed solution on two independent sites.66‐68 When all solutes

169

have the same maximum adsorption capacity on each site, the DSL model is identical to applying IAST at each

170

site. In a multi‐component dual‐site Langmuir (MSDSL) model, binary/ternary components were allowed to

171

have different maximum adsorption capacities on each site. Thus, MSDSL is not thermodynamically consistent

172

and is not identical to IAST anymore.66 Swisher et al. attempted to keep thermodynamic consistency by using

173

the original IAST on both sites while still allowing differences in adsorption saturation, which is termed

174

segregated IAST (SIAST).68 To our best knowledge, none of these models, MSDSL, and SIAST, have been used for

175

multi‐solute adsorption in the aqueous phase. In the present work, MSDSL and SIAST were applied to make

176

comparison with IAST. Details of modeling based on MSDSL and SIAST are shown in Texts S4 and S5.

177

Effects of Single Solute Adsorption Isotherm Models

178

IAST is not limited to any specific single component isotherm equation. Table S2 shows the most

179

frequently used isotherm equations in IAST to simplify the model calculation: Langmuir, 34, 44 Freundlich, 33, 34

180

Toth, 41 and Dubinin‐Astakhov (D‐A) model.69 Selection of a proper single‐solute isotherm model is important

181

because the best IAST model prediction of adsorption of binary mixtures can only be achieved when the “best‐

182

fit” single‐isotherms are applied. 25, 34 Single solute adsorption data from previous work in our research group is

183

plotted in Figure S1.57 In this study, we developed the quadratic Freundlich equation (eq. 10) to implement

184

algorithm of ASTs because it gave smaller errors (Table S3).70 Dual‐site Langmuir equation was applied in SIAST

185

and MSDSL, to be consistent with common practices. 67, 68

186

ln

187

∙ ln

∙ ln

ln

m, n, K are fitting parameters

(10)



188

Poly‐parameter Linear Free Energy Relationship (pp‐LFER)

189 190

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Abraham’s pp‐LFER has been widely used to study partitioning and sorption which has a general form for any specific partition (

):

(11)

191

where

192

phases of interests, e.g., solvent or a sorbed phase onto a sorbent such as NOM and AC. For instance,

193

be the logarithm of a solute partitioning coefficient between water and the adsorbed phase on an adsorbent.

194

The terms E, S, A, B, and V stand for solute descriptors developed by Abraham’s group.71 The excess molar

195

refraction (E) is used to capture nonspecific interactions associated with induced dipoles due to London

196

dispersive forces and Debye forces;71 the McGowan’s characteristic volume (V) is intended to involve cavitation

197

energy and some additional induced dipole‐induced dipole forces;72 S, the polarity/polarizability parameter, is

198

to account for permanent dipole involved interactions which partly overlap with E for induced dipole forces;

199

and A and B represent the overall H‐bonding donating and accepting ability, respectively.73 The counterparts of

200

these solute descriptors, e, s, a, b, v, and c are coefficients determined by multiple linear regression analysis.

201

They demonstrate the difference between the solution phase and, for example, the adsorbed phase, in their

202

ability to participate in each interaction. It is worth noting that these coefficients can be dependent on the

203

adsorbed amount when adsorption isotherm is nonlinear.74 Multiple linear correlations were carried out in

204

Minitab®. The best regression models were determined by the lowest Mallow’s Cp value while keeping the p‐

205

value of each parameter less than 0.1 to ensure each involved term statistically significant.

206

Error Analysis The correlation of the calculated values,

207 208

is a physical chemical property of a solute related to Gibbs free energy of transfer between two

activity coefficients with the experimental values,

can

, based on fitting equations of adsorption isotherms or , was evaluated using a normalized error (NE, eq. 12). All 10

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209

adjustable parameters in fitting equations for adsorption isotherms and activity coefficients were determined

210

by the least‐square error method (LSE, eq. 13). ∑

∑

100%

100%

211

212

RESULTS AND DISCUSSION

213

Modeling Bi‐Solute Adsorption with IAST, SIAST, and MSDSL

214

(12)

(13)

Binary adsorption data of 4‐MP (primary solute) and aniline (competitor) are shown in Figure 1 and

215

Table S4. For both solutes, it is shown that the adsorbed amounts in bi‐solutes were less than in single solutes,

216

due to the competitive effect of the other solute, while the binary adsorption isotherms approached those of

217

the single solutes as their fractions approach unit. More competition arose with decreasing adsorbed phase

218

mole fraction, as suggested by the increasing deviation of the binary adsorption data from the single solute

219

isotherms. Figure 1 also shows that when the mole fraction of the adsorbed phase decreases, left to right for

220

aniline and the opposite direction for 4‐MP, the adsorbed amounts predicted by all three models, i.e. IAST,

221

SIAST, MSDSL, increasingly deviate from the experimental data and become more underestimated. IAST tends

222

to give better prediction of the more strongly adsorbed component, i.e. 4‐MP, while SIAST and MSDSL perform

223

better for the weakly adsorbed component, i.e. aniline. None of the three models can perfectly fit binary

224

adsorption equilibrium for both solutes at all mole fractions.

225

For binary pairs of 4‐MP/phenol, 4‐MP/4‐CP, and 4‐NP/4‐CP, ideal behavior in the adsorbed phase is

226

expected due to similarity in their molecular structures, so that IAST performs much better than SIAST and

227

MSDSL, as reflected by NE within 10% (Table 1). Although for a few pairs with NB involved, SIAST is only slightly 11 ACS Paragon Plus Environment


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228

worse than IAST in general and even better in NB/4‐CP system, the general trend is that the modeling of SIAST

229

and MSDSL is worse than that of IAST. This is mainly because SIAST and MSDSL are both based on Langmuir

230

types of isotherms. For aqueous phase adsorption onto microporous MN200, the adsorption mechanism is

231

more likely pore‐filling or multi‐layer adsorption as oppose to single‐layer adsorption (assumption of Langmuir

232

equation). Langmuir equation is thus not suitable for modeling adsorption isotherms in this study. Another

233

reason for the less accuracy of SIAST and MSDSL is that the adsorption energy distribution of adsorption sites

234

on MN200 is likely continuous. Segregated two‐site models cannot precisely describe the heterogeneity of the

235

solid surface.

Adsorbed amount mmol/g

10

0.9860 0.9632 0.8847 0.720

0.014 0.0368 0.1153 0.280 0.419

1

0.144 0.091

0.909 0.623

0.582 0.377 0.228

0.7724 0.857

0.1

0.001 0.001

Aniline bi-solute Aniline single-solute Aniline IAST Aniline SIAST Aniline MSDPL

4-MP bi-solute 4-MP single-solute 4-MP IAST 4-MP SIAST 4-MP MSDSL

0.01

236 237 238 239 240 241 242 243

zi of the competitor

zi of the primary solute

0.01

0.1

1

10

0.001

0.01

0.1

Ce of primary solute, mmol/L

1

10

Figure 1. Bi‐solute adsorption isotherms of 4‐MP (primary solute) and aniline (competitor). Symbols are experimental data and lines are model fits. Data points from left to right correspond to an increasing amount of 4‐MP. The equilibrium concentration of aniline decreased from 2.91 to 2.62 mmol/L, which is up to about 10% due to competition of 4‐MP. The adsorbed phase mole fraction of each solute is included for every other points, the range of which for the primary solute is about 0.014~0.923 from left to right (red arrow). Thus, the mole fraction of the competitor ranges correspondingly from 0.077 to 0.986 in the opposite direction (blue arrow). Single solute adsorption data of each solute is also plotted as dotted lines for comparison.

244

In general, IAST always gives better prediction for the adsorption equilibrium of the strongly adsorbed

245

component, that is, smaller errors for 4‐MP than aniline, 4‐NP than 4‐MP, 4‐NA than aniline, and 4‐CA than

246

aniline etc., as reflected in Table 1. 12 ACS Paragon Plus Environment

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247 248 No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 249 250

Table 1. Summary of prediction results of IAST, SIAST and DSL; fitting results of the isotherms of primary solutes in binary mixtures and of qe based on RAST‐ ; and fitting results of by NRTL model, Wilson equation, and FPM NE of (%) NE of adsorbed amount (%) Adsorption Condition Primary solute

Competitor (Cini)

4‐MP 4‐MP 4‐MP 4‐MP 4‐MP 4‐MP 4‐MP Phenol Aniline Aniline NB NB NB NB NB 4‐NP 4‐CP

Phenol (1mM) Aniline (1mM) 4‐NP (1mM) NB (1mM) 4‐CA (1mM) 4‐CP (1mM) 4‐NA (0.5mM) Aniline (1mM) 4‐NA (1mM) 4‐CA (0.5mM) Aniline (1.75mM) 4‐NA (1mM) 4‐NP (0.5mM) 4‐CA (0.5mM) 4‐CP (0.5mM) 4‐CP (1mM) 4‐CA (0.5mM)

No. of batch 16 17 16 18 9 20 14 18 16 12 12 14 14 14 14 16 14

IAST P a 5 18 13 12 30 7 5 18 28 26 13 6 24 24 23 4 14

SIAST

C a 8 33 8 10 23 6 7 34 5 5 21 4 28 19 25 8 17

P 12 22 23 18 41 21 9 21 38 33 15 6 23 38 20 9 13

C 82 12 37 18 10 20 33 33 16 7 24 9 25 15 4 15 12

DSL P 34 42 39 27 51 10 43 15 41 26 20 18 26 40 13 42 39

C 95 17 68 15 13 13 43 42 6 6 17 16 16 17 23 45 25

Fitting results of , ‐ 8 3 6 9 ‐ ‐ 4 10 5 5 ‐ 3 7 3 ‐ 4

fitting of qe by RAST‐ P C ‐ ‐ 5 5 3 3 4 4 3 3 ‐ ‐ ‐ ‐ 2 2 8 8 4 4 4 6 ‐ ‐ 2 2 5 5 2 2 ‐ ‐ 4 4

NRTL

Wilson

FPM

‐

‐

12

13

9

9

5

5

5

11

‐ ‐ 5

‐ ‐ 7

‐ 4 3 5 5 ‐ ‐ 5

10

13

11

12

12

4

10

10

2

‐ 9 4 4 ‐

‐ 9 5 4 ‐

‐ 7 4 2 ‐

5

7

3

Note: a. P = primary solute, C = competitor; b. Binary adsorptions, No. 1, 6, 7, 12, and 16, are approximately ideal adsorbed mixtures since IAST predicts the adsorbed amounts with NEs of less than 10% for both solutes. Thus, adsorbed phase activity coefficients were not calculated and RAST was not applied.



251

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Comparison of RAST Incorporated with Wilson, NRTL, and FPM Models To correct for the deviation of IAST from experimental data,

252

was calculated for each

253

component based on the method in the Modeling Approaches and Text S2. If the values were calculated

254

based on the experimental data without fitting equations of activity coefficients, the results are denoted as

255

RAST‐

. Table 1 shows the errors in fitting

256

,

, i.e., the adsorbed amount of the primary solute in

257

binary mixtures, as a function of equilibrium concentration with the quadratic Freundlich equation. It can be

258

seen that the quadratic Freundlich equation is able to describe well the adsorption isotherms of the primary

259

solutes. Also shown in Table 1 and Figure S2, including

260

of IAST modeling with NE of less than 8%. The good performance of RAST‐

261

reasons. First,

262

and thus Eq. 4 can be directly used in RAST instead of Eq. 7. Second, even if is dependent on spreading

263

pressure, the last term in Eq. 7 is not significant for the adsorption on MN200.

264

in RAST can successfully eliminate the deviation can be explained by two

can be treated as independent on spreading pressure for solute‐adsorbate equilibrium

The activity coefficients calculated above were then fitted into three models, Wilson equation, NRTL,

265

and the empirical four‐parameter model (FPM) (Table 1 and Figure S3). Generally, Wilson and NRTL have

266

very similar fitting results while FPM fits the experimental activity coefficients better. Before we conclude

267

that FPM is better than Wilson and NRTL models, we should also test the ability of RAST combined with

268

Wilson, NRTL, or FPM to fit adsorption equilibrium at different adsorption conditions. For this purpose, for

269

each set of bi‐solutes in Table 1, one additional set of bi‐solute adsorption equilibrium, switching the primary

270

solute with the competitor, referred to as the test set hereafter, was examined experimentally. The data was

271

then compared with the predictions by RAST‐NRTL, RAST‐Wilson, and RAST‐FPM using the parameters


Page 15 of 27


272

determined above. Note that at the same of a solute, the modeling set and the corresponding test set have

273

different total adsorption loadings and spreading pressures.

274

Predictions of the test sets by RAST with NRTL, Wilson and FPM are plotted in Figure S4, whose NEs

275

are shown in Table 2. As reflected by the smaller NEs, RAST‐FPM performs better than RAST‐Wilson and

276

RAST‐NRTL in most cases. RAST‐FPM can reduce NEs to less than 10% when aniline was not involved. This

277

suggests that (1) when

278

treating as independent on will not result in significant errors; and (3) in terms of prediction, binary

279

adsorption systems with a constant initial concentration of the competitor, the method developed in this

280

work, are better than those with constant ratios of initial concentrations where varying concentration ratios

281

of bi‐solutes were employed 33, 75.

282

values are well fitted, RAST can accurately predict adsorbed amounts; (2)

Table 2. Prediction of the test sets by RAST with NRTL model, Wilson equation, and FPM Adsorption Condition

NE of predicted (%) NRTL Wilson

FPM

Corresponding No. in Table 1

Primary solute (P)

Competitor (C)

No. of Data Points

P

C

P

C

P

C

2 3 4 8 9 10 11 13 14 15

Aniline 4-NP NB Aniline 4-NA 4-CA Aniline 4-NP 4-CA 4-CP

4-MP 4-MP 4-MP Phenol Aniline Aniline NB NB NB NB

20 20 11 16 12 18 12 16 14 14

17 16 5 9 12 12 21 5 11 9

3 7 6 9 4 12 9 8 11 4

19 15 5 8 9 12 21 5 12 9

4 7 6 7 8 12 9 7 11 5

16 10 5 10 5 5 17 5 6 6

7 11 6 11 9 6 6 5 5 6

283

284

However, when aniline was involved in the adsorbed mixture, the predicted adsorbed amounts of

285

aniline deviate significantly from the experimental data in the low concentration region (Figure S4), even

286

though activity coefficients were well fitted. Considering that the major difference between the modeling set

287

and the test set is spreading pressure, we believe it is the spreading pressure dependency of that caused 15 ACS Paragon Plus Environment


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288

the less accurate prediction of RAST. This is most likely due to the heterogeneity of the adsorption sites that

289

are involved in the adsorption of aniline onto MN200. As discussed by Nguyen et al.76 and Pan et al.,57 the

290

adsorbed aniline onto microporous sorbents resembles its pure liquid state at room temperature, therefore,

291

it can access some occlusions inside the adsorbents that are not accessible to other solutes that are solids at

292

room temperature (see their melting points in Table S1). As of the binary‐solute adsorption system

293

changes, the predicted adsorbed amount will change accordingly, but part of the real adsorbed amount for

294

aniline is not affected by competition. The result is that becomes dependent on for aniline. NB is also a

295

liquid at room temperature, although with a higher melting point than aniline. The observation that its test

296

sets were well predicted by RAST suggests that its is less dependent on . Future research is thus needed

297

to elucidate the likely mechanism(s).

298

Competitive Effects based on Single‐Solute Adsorption. In Figure 2, the reduced spreading pressures

299

calculated from eq. 5 are plotted for all 8 compounds vs

300

strongly adsorbed components. For a pair of two components, the strongly adsorbed component tends to be

301

more stable in the adsorbed phase and the other one tends to be more stable in the aqueous phase. 77

302

Comparing Figures S1 and 2, we can find that the sequence of these compounds in the adsorbed amount is

303

the same as that in at the same equilibrium concentration:

304

. The ones with higher values are the more

NB > 4‐CA > 4‐NA > 4‐CP > 4‐NP > 4‐MP > Aniline > Phenol

305

It is intuitive to think that more strongly adsorbed components are more competitive than weakly adsorbed

306

components. In a bi‐solute adsorption system, the adsorbed amount of one solute will be reduced due to the

307

presence of another solute. If we consider the condition of infinite dilution solution, i.e.,

308

the infinite dilution value

309

the competitive effect of different solutes on a primary solute by comparing the adsorbed amounts of the

310

primary solute based on IAST. An example is given in Figure 2 using 4‐MP as the primary solute, 4‐NA or

, or

→

approaches

(more details in Text S6)78, we can directly address


Page 17 of 27


Aniline as the competitor. We let the competitors have the same concentration of 2 mM (the vertical blue

312

solid line in Figure 2). Since the curves in Figure 2 are plotted as vs.

313

and 4‐MP/4‐NA can be found at the intersections of the vertical blue solid line with the curves of aniline and

314

4‐NA, respectively, assuming that the infinite dilute 4‐MP does not contribute to of the mixtures.

Reduced spreading pressure, Ψ, mol/kg

311

10

NB 4-CA 4-NA 4-CP 4-NP 4-MP Aniline Phenol

316 317 318

4-NA

4-MP

4-CP 4-NP

Aniline Phenol

0.1 1 Equilibrium concentration Ce, mmol/L

10

Figure 2. Calculated reduced spreading pressures of the eight aromatic compounds as single solutes as a function of equilibrium concentration To calculate the adsorbed amount of the primary solute 4‐MP,

319 320

NB

4-CA

1

0.1 0.01 315

, of the mixtures of 4‐MP/aniline

, based on IAST (derivation of

eq. 14 is in Text S6):

321


(14)


Page 18 of 27

322

we will need

323

lines at the respective value of aniline and 4‐NA, and the corresponding

324

intersections of the horizontal lines with the curve of 4‐MP. According to eq. 14, a larger value of

325

in a smaller

326

not considered since it is much smaller than that in

327

4‐MP more than aniline does. If the same method is applied to all solutes, the sequence of these solutes in

328

their competitive effects is the same as the one shown above if IAST is valid. However, the sequence may be

329

affected by nonideal behavior of the primary solute in the presence of a competitor and be altered by

330

discussed extensively below.

331

Adsorbate‐Adsorbate Interactions and pp‐LFERs

values of 4‐MP at the same spreading pressure. To obtain this value, we can draw horizontal values of 4‐MP are at the results

value, suggesting a stronger competitive effect, as observed for 4‐NA (difference in

is

). Therefore, 4‐NA can reduce the adsorbed amount of

, as

332

Since the prediction of IAST for a solute increasingly deviates from the experimental data as its mole

333

fraction approaches zero, we extrapolated the nonideality to infinite dilution to more conveniently discuss

334

nonideality of the adsorbed mixtures.

335

the fitting parameters obtained in “Comparison of RAST Incorporated with Wilson, NRTL and FPM” (letting

336

be zero) (Table 3).

337

The smaller the

was calculated from the NRTL, Wilson, and FPM models based on

, the more nonideal the solute is in the mixture. Table 3 shows that the

values

338

are smaller than unity for all solutes. This was noted as negative deviation from Rauolt’s law and reported

339

frequently in the literature for both gas phase and multi‐solute adsorption.44, 66, 75, 79 For solutes within the

340

same chemical family, they tend to behave ideally in the adsorbed phase, for example, 4‐MP/phenol, 4‐

341

MP/4‐CP, and 4‐NP/4‐CP, though they have very different single‐solute adsorption isotherms. For

342

phenol/aniline (No. 8), although they have very similar single‐solute isotherms, their adsorbed phase mixture

343

is nonideal. There are also several strongly nonideal mixtures such as 4‐MP/4‐CA and 4‐CP/4‐CA. These

344

compounds are in solid states at room temperature, so there are possibly additional adsorption sites 18 ACS Paragon Plus Environment

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345

accessible to aniline but are not accessible to them. Therefore, it strongly suggests that nonideality should

346

not be interpreted solely based on difference in either single‐solute isotherms or heterogeneity of the

347

sorbent, but rather be attributed to possible intermolecular interactions among the adsorbed molecules.80

348 349

Table 3. Infinite dilution activity coefficients calculated from NRTL model, Wilson equation, and FPM by letting be zero for each solute. No. corresponds to those in Table 1.

Solutes

350

No.

P

C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

4‐MP 4‐MP 4‐MP 4‐MP 4‐MP 4‐MP 4‐MP Phenol Aniline Aniline NB NB NB NB NB 4‐NP 4‐CP

Phenol Aniline 4‐NP NB 4‐CA 4‐CP 4‐NA Aniline 4‐NA 4‐CA Aniline 4‐NA 4‐NP 4‐CA 4‐CP 4‐CP 4‐CA

NRTL P C ‐ ‐ 0.64 0.27 0.56 0.8 0.67 0.64 0.49 0.4 ‐ ‐ 0.66 0.65 0.71 0.29 0.20 0.68 0.63 0.69 0.61 0.6 ‐ ‐ 0.40 0.44 0.56 0.38 0.54 0.37 ‐ ‐ 0.70 0.22

Wilson P C ‐ ‐ 0.60 0.31 0.57 0.73 0.67 0.64 0.52 0.62 ‐ ‐ 0.76 0.65 0.62 0.35 0.28 0.59 0.63 0.69 0.62 0.59 ‐ ‐ 0.39 0.42 0.61 0.53 0.54 0.37 ‐ ‐ 0.62 0.35

FPM P ‐ 0.69 0.62 0.68 0.52 ‐ 0.82 0.66 0.26 0.63 0.65 ‐ 0.44 0.59 0.55 ‐ 0.66

Based on the established FPM with results shown in Table 3,

C ‐ 0.32 0.86 0.64 0.44 ‐ 0.65 0.31 0.72 0.9 0.56 ‐ 0.43 0.51 0.39 ‐ 0.25

of either aniline or 4‐MP, both π‐

351

electron sufficient solutes as the primary solute mixing with the competitor NB, a π‐electron deficient solute,

352

was calculated to be 0.56 or 0.68 (Table S5), indicating non‐ideal mixtures. To demonstrate whether π‐ π EDA

353

is the interaction force causing the nonideality of the adsorbed mixtures, 4‐NP and 4‐NA, two π ‐electron

354

deficient solutes, were separately mixed with the same competitor NB. 4‐NA and NB tend to form an ideal

355

mixture in the adsorbed phase (

356

in Table 3), as reflected by a

357

NA and 4‐NP should be similar in terms of their ability to undergo π‐ π EDA with NB. The observed different 19

0.9) while nonideality is encountered in the 4‐NP/NB mixture (No. 13

of 0.43. Given the comparable E and S values for 4‐NA and 4‐NP (Table S5), 4‐

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358

Page 20 of 27

values are thus most likely associated with the strong H‐bond donating ability of 4‐NP (large A value of

359

0.82 in Table S5). 4‐NA is less likely to be involved in H‐bonding (small A value of 0.42) with NB and thus

360

behaves ideally in the adsorbed phase. In this work, we propose, for the first time, to study infinite adsorbed phase activity coefficients by

361 362

pp‐LFERs. From eq. 11, we can derive (details in Text S7):

ln

(15)

363

By keeping the same competitor while changing primary solutes, we can obtain a set of

364

primary solutes. For the purpose of quantitatively predicting nonideality of adsorbed mixtures, pp‐LFER was

365

applied to correlate

366

Two binary‐solute series were chosen: varying infinite dilution primary solutes with either 4‐MP or NB as the

367

fixed competitor. By conducting multiple linear regression, the best obtained regressions based on the lowest

368

Mallow’s Cp values are:

ln , 0.22 0.43

values for the

with the molecular properties of the solutes, i.e. the solute descriptors in Table S5.

4.17

1.22 0.741,

0.92 8,

3.32 1.10 0.85 ln , 4.01 1.89 2.45 0.84

0.47 0.12

0.70

0.32

2.67

1.65

0.38 0.812,

0.97 8,

0.28 0.09

3.00

1.25

(16)

(17)

369

Because of the small number of solutes involved, the application of pp‐LFER in this work should be viewed as

370

an empirical rather than theoretical approach. Therefore, no further interpretation of the regression

371

coefficients was given to the above equations. Involving a much larger number of compounds in developing

372

pp‐LFERs is warranted for a better understanding of the interaction forces contributing to the nonideality of

373

adsorbed mixtures. The calculated

374 375

values based on eq. 16 and eq. 17 are plotted in Figure 3a vs. experimental

.

The good regression results suggest that pp‐LFER is a promising method to predict adsorbed phase activity 20 ACS Paragon Plus Environment

Page 21 of 27


376

coefficients, although the linear relationships were developed involving only 8 compounds and are not robust

377

enough yet. To the best of our knowledge, this is the first time that adsorbed phase activity coefficients can

378

be predicted based molecular descriptors. 70%

Predicted γ∞

0.8 0.6 0.4

NB as fixed competitor

0.2

4-MP as fixed competitor 0 0

0.5

Experimental γ∞

379

1

Relative errors of predicted adsorbed amount of aniline

a)

1

b)

IAST RAST-FPM RAST-Wilson 10% errors

60% 50% 40% 30% 20% 10% 0% 0.0

0.5

1.0


380 381 382 383

Figure 3. a): Compare calculated based on pp‐LFERs with obtained experimentally. The dashed lines represent 10% error in prediction which will result in about 9~11% error in the predicted adsorbed amount according to Eq. 66 in SI. b): Prediction errors of the adsorbed amounts of aniline in the presence of 4‐MP (test set) using extrapolated from .

384 385

386

parameters in the activity coefficient models. For Wilson equation (eqs. 44 and 45 in SI), it was assumed that

The

387 388

values of the primary solutes, once obtained from the pp‐LFERs, can be used to calculate the

of the competitor is the same as

of the primary solute so the two fitting parameters,

and

, can

be calculated from eqs. 18 and 19 which were derived from eqs. 44 and 45 by letting either or be zero. ln

1

ln

(18)

ln

1

ln

(19)

389

By incorporating the values of

390

solute adsorption capacities.

and

into Wilson equation, RAST‐Wilson can be applied to estimate bi‐



For FPM (eqs. 8‐9), we proposed to set and

391

ln

at 2 as in the original Margules equations while

392

letting

393

ideal behavior for the competitor since is close to 0 in eq. 9). By changing the values, non‐infinite

394

activity coefficients at different mole fractions were then calculated and incorporated in RAST by

395

implementing the iteration process shown in Scheme S2. As shown in Figure 3b, errors for the predicted

396

adsorbed amounts of aniline in the presence of 4‐MP, based on either RAST‐Wilson or RAST‐FPM, were

397

generally less than 10% for all mole fractions of aniline. Much larger errors, particularly at lower mole

398

fractions, are observed when only IAST was applied for the prediction purposes.

399

ENVIRONMENTAL SIGNIFICANCE

be

Page 22 of 27

for the primary solute ( =1 in eq 8), and

be zero for the competitor (assuming

400

In this work, we have successfully combined FPM, proposed in the present work, with RAST to

401

accurately model bisolute adsorption by a polymeric resin. pp‐LFER was demonstrated to have a great

402

potential in predicting

403

with a few assumptions. Overall, our results have moved a major step forward in accurately simulating and

404

predicting bi‐solute adsorption based on single‐solute adsorption isotherms, which may be encouraging to

405

environmental researchers working on multi‐solute adsorption modeling so that more attention will be given

406

to ASTs.

407

, which can be extrapolated to non‐infinite conditions by Wilson equation and FPM

Since accurate equilibrium adsorption data is desirable in predicting breakthrough curves, estimating

408

the maximum service life of the adsorber, and developing models for adsorption kinetics and dynamics for

409

fixed‐bed column adsorption,81 the effort of this work will be important for the application of column

410

adsorption models and resin techniques in water and wastewater treatment. The bi‐solute adsorption

411

experiments in this work have covered a wide range of concentrations and concentration ratios of simple

412

aromatic compounds. They were successfully simulated while test sets were accurately predicted. The 22 ACS Paragon Plus Environment

Page 23 of 27


413

infinite dilution condition defined in this work, which has one predominating solute with a high

414

concentration, is very common in real wastewater streams, for example, from a coking plant.82 On the basis

415

of the modeling approach established in this work, future work will be able to examine multi‐solute mixtures

416

containing one major competitor by treating n‐component systems as n independent bi‐solute systems, each

417

containing the competitor and a primary solute at lower concentrations. This approach would have a great

418

potential in studying the competitive effects of the predominant NOM in water systems if we treat the NOM

419

as the major competitor.

420

421

Supporting Information. Additional figures, tables, and texts. This material is available free of charge via the

422

http://pubs.acs.org.

423

424

AUTHOR INFORMATION

425

Corresponding Author

426

*[email protected]

427

Notes

428

The authors declare no competing financial interest.

429

430

Acknowledgment

431

This material is based upon work partially supported by the US Geological Survey through

432

Pennsylvania Water Resources Research Center and PA Sea Grant.

433

References cited

434 435

1.

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