Asymmetric Framework (AF) for Modeling Liquid

Asymmetric Framework (AF) for Modeling Liquid-Liquid Equilibrium Involving Ionic Liquids Luke D. Simoni, Joan F. Brennecke and Mark A. Stadtherr Department of Chemical and Biomolecular Engineering University of Notre Dame 2007 AIChE Annual Meeting Salt Lake City, Utah November 4-9, 2007

Outline I. II. III. IV. V. A. B.

Introduction and motivation Background Problem formulation Activity coefficient models used Results Ternary phase equilibrium diagrams Octanol-water partition coefficients (Kow’s)

VI. Conclusions

Introduction and Motivation • Electrolytes ionize to varying degrees in different equilibrium liquid phases – Varying mixed-solvent dielectric constants, ε – Varying electrolyte concentrations

• As first approximation of this behavior assume – ILs completely ionize if ε > εc AND xIL < xcut – ILs are paired if ε < εc – Let εc = 60 AND xcut = 0.1

• Predict multicomponent LLE from binary data • Model separations and extractions with IL solvents – BuOH & EtOH from fermentation broths

• Estimate bioaccumulation – Kow = CILoctanol/CILwater

IL and Alcohol Nomenclature • Cations in this work: R'''

N+

N

R''

General: This work:

[R’R’’R’’’im] [bmim], [hmim], [omim] & [hmmim]

m = methyl b = butyl

h = hexyl o = octyl

R'

• Anions in this work: PF6= (CF3SO2)2N- =

[PF6] [Tf2N]

• Alcohols in this work: Ethanol = EtOH Octanol

Symmetric Predictions for Ternary LLE

Using Only Binary Data EtOH • Can predict multicomponent LLE 0.0 1.0 E 0.1 using same g model Type 1 0.9 0.2 (e.g. NRTL) for all phases 0.8 0.3 0.7 • Model fit to binary data 0.4 0.6 0.5 0.5 • Use reliable algorithm to 0.6 0.4 guarantee stable 0.7 0.3 0.8 equilibrium is found 0.2 0.9 0.1 • Qualitatively predicts 1.0 Type 1 and 2 ternary Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 [hmim][Tf2N] diagrams Experimental Tie Lines NRTL Tie Lines • Can we improve [hmim][Tf2N] = predictions by using 1-hexyl-3-methylimidazolium different models for each bis(trifluoromethylsulfonyl)imide phase?

Problem Formulation Asymmetric Framework System: IL(1)/Alcohol(2)/Water(3) α-phase organic/IL-rich

εα < 60

β-phase aqueous

1 +

-

εβ > 60 -

+

2 3


IL

xILβ < 0.1

2

3

z + z− e 2

g ≡− RT 8πε 0 ε IL k B T σ IL reference (1): Pure dissociated liquid salt at T and P Solvent reference (2 & 3): Pure liquid solvent at T and P

Problem Formulation Asymmetric Framework Alcohol 0.0 1.0 0.1 0.9 Organic/IL-rich Complete 0.2 Phase (α) Dissociation 0.8 0.3 Molecular IL
Electrolyte Model 0.7
Molecular Model 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 > C 1.0 0.0 IL Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Aqueous Phase (β)

ε

ε

∑ i∈ILs

xiβ < 0.1

Problem Formulation Asymmetric Framework • Gibbs energy forms in each phase
g αM g αE α α α gi = ∑ xi ln xi + + ∑ xi RT i∈{E,S} RT i∈E RT E gβM g ν i y±β,i ν i y±β,i β =∑ ln + ∑ yiβ ln yiβ + RT i∈E ν ± ,i RT ν ± ,i i∈S

Molecular phase

Electrolytic phase

• First-order optimality conditions 2   − z z e ν + − β β α α νγ y = γ ( ± ± ) 1 x1 + exp  8π k T ε ε σ  , B 0 2   γ 2β y2β = γ 2α x2α System: IL(1)/Solvent(2)

For Parameter Estimation

Problem Formulation Asymmetric Framework

gº1 RT

x1cut = 0.1

System: IL(1)/Solvent(2)

Problem Formulation Asymmetric Framework

gº1 RT

x1cut = 0.1

System: IL(1)/Solvent(2)

Molecular Model Domain

Problem Formulation Asymmetric Framework

gº1 RT

x1cut = 0.1

Electrolyte Model Domain

System: IL(1)/Solvent(2)

Problem Formulation Stability Analysis

System: IL(1)/Solvent(2) gº1 RT

Case 1 z1 > x1cut x1cut = 0.1

1. Feed composition (z) in molecular domain

Problem Formulation Stability Analysis

System: IL(1)/Solvent(2) gº1 RT

Case 2 z1 < x1cut x1cut = 0.1

2. Feed composition (z) in electrolyte domain

Problem Formulation Stability Analysis

System: IL(1)/Solvent(2)

Case 2 z1 < x1cut

Case 1 z1 > x1cut

x1cut = 0.1

1. Feed composition (z) in molecular domain 2. Feed composition (z) in electrolyte domain

Problem Formulation Stability Analysis T β g g D I = (ν − 1) x1 + 1 − α RT RT

≥0 z

Case 1 Stable Single Phase System: IL(1)/Solvent(2) Dα > 0 DI > 0 x1cut = 0.1

z1

Problem Formulation Stability Analysis gβT

α

D II =

g − (ν − 1) z1 + 1 RT RT

≥0 z

Case 2 Stable l Single Phase z1

Dβ > 0

System: IL(1)/Solvent(2)

DII > 0

x1cut = 0.1

Problem Formulation Stability Analysis T β g g D I = (ν − 1) x1 + 1 − α RT RT

≥0 z

T α g g β D II = − (ν − 1) z1 + 1 RT RT

Cases 1 & 2 Stable Biphasic (DII & Dα) > 0 x1α

x1β

(DI & Dβ) > 0 x1cut = 0.1

≥0 z

Problem Formulation Stability Analysis T β g g D I = (ν − 1) x1 + 1 − α RT RT

≥0 z

T α g g β D II = − (ν − 1) z1 + 1 RT RT

Cases 1 & 2 Stable Biphasic (DII & Dα) > 0

x1β

(DI & Dβ) > 0 x1cut = 0.1

x1α

≥0 z

gE Models Used NRTL (NonRandom Two-Liquid)

IL

•Assumes molecular IL •Describes nonideality via local composition (LC) (Renon & Prausnitz, 1968)

UNIQUAC (UNIversal QUAsi-Chemical theory) •Assumes molecular IL •Describes residual and combinatorial contributions •Requires physical r & q parameters for size and shape (Abrams & Prausnitz, 1975)

eNRTL (electrolyte-NRTL)

IL
+

&

-

•Assumes –completely dissociated IL –Dielectric continuum = mixture of non-IL components

•Describes LC and electrostatic (Pitzer-Debye-Hückel, PDH) contributions •Requires mixed solvent properties (averaged) (Chen et al., 1982)

Results Predicted from Binary Data

1. Ternary phase equilibrium diagrams: 1. Type 1
[hmim][Tf2N]/EtOH/Water 2. Type 2a
[bmim][PF6]/EtOH/Water

2. Octanol-water partition coefficient, Kow predictions

Type 1 [hmim][Tf2N]/Ethanol/Water at 298 K EtOH 0.0 Binary: Ethanol/Water 1.0 NRTL: Kurihara et al. (1993) 0.1 Kato & Gmehling (2005) 0.9 UNIQUAC: DECHEMA VLE 0.2 0.8 0.3 0.7 Binary: IL/Water 0.4 Physical ri and qi data 0.6 Chapeaux et al. (2007) 0.5 Kato & Gmehling (2005) 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [hmim][Tf2N]

Binary: IL/Ethanol

Type 1 experimental

(Chapeaux et al., in preparation)

[hmim][Tf2N] = 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Type 1 [hmim][Tf2N]/Ethanol/Water at 298 K Experimental Tie Lines NRTL

EtOH Type 1 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [hmim][Tf2N]

Type 1 [hmim][Tf2N]/Ethanol/Water at 298 K Experimental Tie Lines UNIQUAC

EtOH Type 1 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [hmim][Tf2N]

Type 1 [hmim][Tf2N]/Ethanol/Water at 298 K Experimental Tie Lines eNRTL

EtOH Type 1 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [hmim][Tf2N]

Type 1 [hmim][Tf2N]/Ethanol/Water at 298 K Experimental Tie Lines AF: UNIQUAC/eNRTL

EtOH Type 1 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [hmim][Tf2N]

Type 1 [hmim][Tf2N]/Ethanol/Water at 298 K Experimental Tie Lines AF: NRTL/eNRTL

EtOH Type 1 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [hmim][Tf2N]

Type 2a [bmim][PF6]/Ethanol/Water Binary: IL/Ethanol

[bmim][PF6]

Binary: Ethanol/Water NRTL: Kurihara et al. (1993) UNIQUAC: DECHEMA VLE

Najdanovic-Visak et al. (2003)

Binary: IL/Water

Physical ri and qi data

Anthony et al. (2004) Najdanovic-Visak et al. (2002)

Banerjee et al. (2005)

Ethanol

Water Type 2a experimental

(Najdanovic-Visak et al., 2003)

[bmim][PF6] = 1-butyl-3-methylimidazolium hexafluorophosphate

Type 2a [bmim][PF6]/Ethanol/Water at 298 K [bmim][PF6] 0.0

Experimental binodal NRTL eNRTL

0.1 0.2 0.3

0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 2 predictions

1.0 0.9 0.8 0.7

0.6 0.5 0.4 0.3 0.2 0.1 0.0

Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 EtOH

Type 2a [bmim][PF6]/Ethanol/Water at 298 K [bmim][PF6] 0.0

Experimental binodal eNRTL AF: UNIQUAC/eNRTL

0.1 0.2 0.3 0.4

0.5 0.6 0.7 0.8 0.9 1.0

Type 2 prediction

1.0 0.9 0.8

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 EtOH

Type 2a [bmim][PF6]/Ethanol/Water at 298 K [bmim][PF6] 0.0

Experimental binodal AF: NRTL/eNRTL

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.8 0.9 1.0

Type 2a prediction

1.0 0.9 0.8

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 EtOH

Octanol-Water Partition Coefficients (Kow’s) Asymm Framework Ionic Liquid

NRTL

UNIQUAC

eNRTL

eNRTL

*Experimental

NRTL

UNIQUAC

[bmim][Tf2N]

0.029

0.23

0.19

0.057

0.33

0.11-0.62

[hmim][Tf2N]

13.9

11.6

2.32

1.84

0.96

1.42-1.66

[omim][Tf2N]

45.0

55.7

3.80

14.7

3.12

6.3-11.1

[hmmim][Tf2N]

0.83

1.55

0.80

1.55

1.54

1.35-1.79

K ow

CILo = w CIL

*(Ropel et al., 2005)

Conclusions • Developed AF that combines… – Molecular model: paired ions – Electrolyte model: completely dissociated ions

• Framework requires – Water as a component – Physical criteria for which model to use (ε and xIL) – Assumption: binary parameters are same for both electrolyte and molecular models • Less accurate UNIQUAC/eNRTL predictions

• AF provides quantitative improvement of IL/alcohol/water – Accurate tie lines (Type 1 & Kow)

• AF provides qualitative improvement of IL/alcohol/water – Multiple phase envelopes (Type 2a)

Acknowledgements • • • •

Dr. Youdong Lin Alexandre Chapeaux Department of Energy (DOE) National Oceanic and Atmospheric Administration (NOAA)

Additional Examples 1. More ternary phase equilibrium diagrams: 1. Type 2
[hmim][Tf2N]/BuOH/Water 2. Type 3b
[bmim][Tf2N]/BuOH/Water

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Butanol

Binary: Butanol/Water

Binary: IL/Butanol

0.0 DECHEMA Binary LLE 1.0 Łatchwa et al. (2006) 0.1 0.9 0.2 0.8 Physical ri and qi data 0.3 Binary: IL/Water 0.7 Kato & Gmehling (2005) 0.4 Chapeaux et al. (2007) 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [hmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 2 experimental

(Chapeaux et al., in preparation)

[hmim][Tf2N] = 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Butanol

Binary: Butanol/Water

Binary: IL/Butanol

0.0 DECHEMA Binary LLE 1.0 Łatchwa et al. (2006) 0.1 0.9 0.2 0.8 Physical ri and qi data 0.3 Binary: IL/Water 0.7 Kato & Gmehling (2005) 0.4 Chapeaux et al. (2007) 0.6 0.5 0.5 0.6 0.4 Compare these 0.7 0.3 Tie lines 0.8 0.2 0.9 0.1 1.0 0.0 [hmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 2 experimental

(Chapeaux et al., in preparation)

[hmim][Tf2N] = 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Experimental tie lines NRTL tie lines

Butanol Type 2 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [hmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Experimental tie lines UNIQUAC tie lines

Butanol Type 2 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [hmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Experimental tie lines eNRTL tie lines

Butanol Type 2 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [hmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Experimental tie lines AF: NRTL/eNRTL tie lines

Butanol Type 2 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [hmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Experimental tie lines AF: UNIQUAC/eNRTL tie lines

Butanol Type 2 prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [hmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 3b [bmim][Tf2N]/Butanol/Water at 288 K Butanol

Binary: IL/Butanol Najdanovic-Visak et al. (2005)

Binary: IL/Water Crosthwaite et al. (2004)

Binary: Butanol/Water DECHEMA LLE data

Physical ri and qi data Kato & Gmehling (2005)

Water Type 3b experimental

[bmim] [Tf2N]

(Najdanovic-Visak et al., 2005)

Type 3b [bmim][Tf2N]/Butanol/Water at 288 K Butanol

1-phase

0.0

NRTL

1.0

0.1

0.9

0.2

Experimental binodal

0.8

0.3 0.4

Type 3 prediction

0.7

2-phases

0.5

0.6 0.5

0.6

2-phases

0.7

3-phases 1-phase

0.8 0.9 1.0

Water

0.4

2-phases

0.3 0.2 0.1 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [bmim][Tf2N]

Type 3b [bmim][Tf2N]/Butanol/Water at 288 K Butanol 0.0

eNRTL

0.1

1.0 0.9

0.2

Experimental binodal

0.8

0.3

0.7

0.4

Type 3a prediction

0.5

0.6

1-phase

0.6

0.3

0.8

1-phase

1.0

0.5 0.4

0.7

0.9

2-phases

2-phases

0.2 0.1 0.0

Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [bmim][Tf2N]

Type 3b [bmim][Tf2N]/Butanol/Water at 288 K Butanol eNRTL AF: UNIQUAC/eNRTL Experimental binodal

Type 3a prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [bmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Type 3b [bmim][Tf2N]/Butanol/Water at 288 K Butanol eNRTL AF: NRTL/eNRTL Experimental binodal

Type 3a prediction

0.0 1.0 0.1 0.9 0.2 0.8 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 [bmim][Tf2N] Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Problem Formulation Asymmetric Framework – Asymmetric Framework applied when •

Dielectric Constant

ε α < 60 < ε β   M i yi π ε = ∑  i∈S  ∑ M i ′ yi′  i′∈S •

  ε   i    

Electrolyte concentration

∑ i∈ILs

xια > 0.1 >

∑ i∈ILs

xιβ

(Chen & Song, 2005)

Computational Method Phase Equilibrium • Alternate between phase stability and flash calculations – Stability: Globally minimize vertical distance between Gibbs energy surface and hyper-plane with reliable algorithm. – Split: Locally minimize total Gibbs free energy of system with quasi-Newton algorithm. Use stationary points from stability global minimization as initial guesses α β

G =G +G

Problem Formulation Stability Analysis T β g g D I = (ν − 1) x1 + 1 − α RT RT

≥0 z

Problem Formulation Stability Analysis T β g g − α D I = (ν − 1) x1 + 1 RT RT

LLE

≥0 z

Type 1 [hmim][Tf2N]/Ethanol/Water at 298 K Experimental Tie Lines Composite Prediction

EtOH Type 1 prediction

0.0 1.0 0.1 Composite Prediction: 0.9 0.2 AF: NRTL/eNRTL 0.8 Symm: UNIQUAC 0.3 0.7 0.4 0.6 0.5 0.5 0.6 0.4 0.7 0.3 0.8 0.2 0.9 0.1 1.0 0.0 Water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [hmim][Tf2N]

Type 2 [hmim][Tf2N]/Butanol/Water at 298 K Model(s)

RMSD (dilute in BuOH)

NRTL

3.5e-5

UNIQUAC

1.2e-4

eNRTL

6.0e-5

NRTL/eNRTL

3.6e-5

UNIQUAC/eNRTL

3.4e-5 2

3

RMSD = ∑ ∑ xi − x j

experiment,j 2 i

j=0i=0

j = phases & i = components

Octanol-Water Partition Coefficients (Kow’s) Ionic Liquid

UNIQUAC

eNRTL

Asymmetric

*Experimental

NRTL eNRTL

UNIQUAC eNRTL

[bmim][Tf2N]

0.23

0.28

0.057

0.33

0.11-0.62

[hmim][Tf2N]

11.8

3.90

1.84

0.96

1.42-1.66

[omim][Tf2N]

55.5

5.88

14.7

3.12

6.3-11.1

[hmmim][Tf2N]

1.62

1.24

1.55

1.54

1.35-1.79

[bmim][BF4]

-

-

-

-

0.0030 ± 0.0002

[hmim][BF4]

-

0.099

-

[omim][BF4]

-

0.47

-

K ow

CILo = w CIL

*(Ropel et al., 2005)