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The Origin of Ion-Pairing and Redissociation of Ionic Liquid Bong-Seop Lee, and Shiang-Tai Lin J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 23 May 2017 Downloaded from http://pubs.acs.org on May 27, 2017

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The Journal of Physical Chemistry

The Origin of Ion-Pairing and Redissociation of Ionic Liquid Bong-Seop Lee‡† and Shiang-Tai Lin*,† ‡

Department of Fire and Disaster Prevention Engineering, Kyungnam University,

Changwon-si, Gyeongsangnam-do, 51767, Republic of Korea †

Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan

10617, Taiwan

Corresponding Author * To whom correspondence should be addressed. E-mail: [email protected]

ABSTRACT: We address the possible occurrence of a minimum extent of dissociation (α) of ionic liquid (IL) in IL-solvent mixtures. This phenomenon, known as the redissociation of IL, is responsible for many interesting composition-dependent properties in such mixtures. A thermodynamic model is developed to provide semi-quantitative prediction on the change of α with solvent concentration. It is found that the occurrence of minimum α coincides with the occurrence of a maximum in the mean activity coefficient of dissociated ions, indicating better solvation of free, dissociated ions both with decreasing and increasing solvent concentration. The favorable solvation of free ions 1

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is found to change from long-range ion-solvent dielectric polarization to ion-ion-pair dielectric polarization with decreasing solvent concentration. Therefore, the composition dependence of the IL solution dielectric constants, determined from that of the ion-pair and the solvent, is found to be the most important factor for the presence of redissociation in IL solutions.

2


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1. Introduction Ionic liquids (ILs) are a class of chemicals made of ions. They possess many unique properties (e.g., nonflammability, negligible vapor pressure, broad liquid state temperature ranges, high thermal and chemical stability and high ionic conductivity, etc1) that are useful for a variety of applications.2-8 The ionic association/dissociation of ILs, quantified by the degree of dissociation α, and its change with addition of a nondissociable solvent is known to have an important influence on many properties of ILs including liquid structure, vaporization enthalpy, viscosity, solubility, and aggregate formation.9 One interesting feature observed in many IL solutions is the re-dissociation phenomena.10-11 In the dilute solution limit, ILs tends to fully dissociate. As the concentration of IL increases, some of the IL starts to associate and form ion-pairs. In such a case, the degree of dissociation of IL continues to decrease with the increasing concentration of the IL. However, it is found that, in some cases (e.g., water and acetonitrile as the solvent), the extent of ion-pairing of IL rises to a maximum (or having minimum value of α) at some intermediate concentration but then decreases monotonically as the concentration of IL approaches saturation.12-14 This breakup of ionpairs depending on solute concentration is referred to as re-dissociation. Many unusual composition dependence of properties of ILs are attributed to the re-dissociation phenomena (e.g., the occurrence of a minimum conductivity in some IL solutions,15-17 and the non-monotonic change of viscosity of ILs with composition13). The re-dissociation of ionic fluids has been studied using various theoretical methods. Ebeling and Grigo18-19 observed the minimum of conductance for 2:2 3



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electrolytes as combining the mean spherical approximation (MSA) theory with the mass action law (i.e., treating the formation of ion-pairs from ions as a chemical reaction)18-19 based on Bjerrum theory. However, they assumed that ion-pairs form thermodynamically ideal mixtures with activity coefficient γCA=1. Fuoss and Kraus17 proposed the presence of triple ions (C+A-C+ or A-C+A-) for appearance of a minimum in conductance; however Grigo20 pointed out that it does not seem to be necessary to take into account an appearance of higher associates such as triple ions in order to interpret the minimum of conductance. On the other hand, the dipole-ion (DI) and dipole-dipole (DD) interactions have long been suspected to favorably contribute to re-dissociation at high ion densities.11, 21

Fisher and Levin22-23 first considered to include DI interactions into Debye-Hückel

(DH) theory. Sukhotin24 predicted the breakup of ion-pairs at higher salt concentrations due to increased Debye shielding by free ions.25 Cavell and Knight21 supported Sukhotin’s work by experiment, and argued that the increase of the dielectric constant due to the ion-pairs leads to a conductance minimum. Weingärtner et al.25 investigated the various contributions (DI, DD and ion-ion (II)) on minimum degree of dissociation by comparing Debye-Hückel-Ebeling theory which define ion-pairing, Fisher-Levin22 theory which accounts for DI interactions, and Weiss-Schröer theory, which includes DD interactions. They found that the minimum of α disappears at higher temperatures in all theories except Weiss-Schröer theory and the loci of density-dependent degree of dissociation minima are found. More recently, Sharygin et al.26 carried out the theoretical modeling of re-dissociation for NaCl and KCl aqueous solution at high temperature (670 K) and pressure (28 MPa) by using equation of state combined with mean spherical approximation and an extended Debye-Hückel limiting law. 4


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In this work, we analyze the occurrence of IL re-dissociation based on a recently developed thermodynamic model for describing the dissociation of IL when mixed with a non-dissociable solvent.27 This model has been shown to provide accurate predictions for a variety of phase behaviors of ILs, including vapor-liquid and liquid-liquid equilibrium, and fluid properties, such as osmotic coefficient and infinite dilution activity coefficient, covering the full range of mixture compositions. Furthermore, the concentration dependence of the extent of dissociation of IL predicted from this model is in good agreement with the experiment. Therefore, this new model provides a new perspective to analyze and understand the fundamental interactions resulting in the re-dissociation behavior of IL solutions. Based on this model we discover that re-dissociation occurs when the mean activity coefficient of the dissociated ions reaches maximum. In other words, the dissociated ions are favorably solvated (as indicated by the lowered values of the mean activity coefficient) by other species in the solution. Both the nondissociated ion-pairs and the solvent play an important role in stabilizing the dissociated ions. In the dilute region, the dissociated ions are solvated mostly by the solvent; whereas it is the ion-pair that stabilizes the free ions in the high concentration limit.

2. Thermodynamic Background In this thermodynamic model, an IL salt is considered to be present either as dissociated ions (C+ and A-) or non-dissociated ion-pairs (C+A-), as indicated by the reaction below

+ ↔

(1)

The equilibrium constant Ka depends only on temperature, and can be expressed in terms of mole fractions (xi) and activity coefficient (γi)28 5



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= =

±

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=

(2)

where ai is activity of species i, the product of mole fraction xi and activity coefficient γi, and Kx and Kγ indicate the ratio of mole faction and activity coefficient, respectively. The reference state of non-dissociated IL is chosen to be the pure liquid of ion-pairs. For the cation and anion, the reference state is chosen to be the infinite dilution of these ions in the pure liquid of ion-pairs. In other words, the last term in eq. 2 (Kγ =

±

) becomes unity

for a completely undissociated IL. The degree of dissociation α of IL is defined as

α = =

=

(3)

where ni is the number of moles of species i, n0i is the number of moles of species i when α=0 (without dissociation). Note that with this definition, the Kx can be expressed as

= =

(4)

where xs is the mole fraction of the solvent. In the limit of pure IL (xs=0), the association constant Ka becomes27 =

(5)

±

where α0 is the degree of dissociation of pure IL. The equilibrium constant Ka can be determined using the experimental degree of dissociation of IL in the pure liquid state (α0). The activity coefficient of a charged species in a solvent has contributions from long-range coulomb interactions and short-range molecular surface interactions.27, 29-30 In this model, the long-range term is modelled by the Pitzer Debye-Hückel (PDH) model31 and a short-range term, modelled by the COSMO-SAC model32, i.e., ln = ln ∗"#$ + ln %&'(&')%

(6) 6


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Details of the PDH and COSMO-SAC models can be found in reference 27 and are briefly summarized in the Supporting Information. It is noteworthy that this model (eq. 6) has been shown to provide accurate prediction of thermodynamic properties and phase behaviors (e.g., vapor-liquid, liquid-liquid equilibria, infinite dilution activity coefficient, osmotic coefficients) for a large variety of IL solutions.27 We thus believe that this model can be used to study the origin of the re-dissociation phenomena in some IL systems.

3. Results and Discussions Figure 1 illustrates the predicted degree of dissociation α of [C2MIM][EtSO4] in water at 298.15 K over the whole composition range. The value of α is about 0.4 for pure [C2MIM][EtSO4]. As water is introduced, the degree of dissociation remains roughly constant at high IL concentrations and starts to decrease (indicating association) after the initial solvent fraction (xowater) becomes greater than about 0.3. The degree of dissociation of [C2MIM][EtSO4] reaches a minimum value of 0.2728 when xos≈0.806. The IL starts to dissociate (i.e. re-dissociate) and becomes fully dissociated (α=1) in the limit of infinite dilution (xos=1). The predicted results are in good qualitative agreement with experiment,33 where a minimum of α is found near xos≈0.841. The increasing uncertainty in experimental values at low IL concentrations is a result of strong dependency on the product of viscosity and conductivity, evidenced by a large deviation at this concentration range.33 Table 1 summarizes the predicted solvent composition at minimum α for 20 IL/solvent combinations. The predicted results are in semi-qualitative to quantitative agreement with the available experiment data. The success of the model may be 7



surprising as only formation of ion-pairs is explicitly considered, while recent experiment show that higher aggregates may form.34 It is noteworthy that the COSMO-SAC model used in this work does not exclude the formation of higher aggregates (trimer, tetramers, etc.) in the system. However, we believe that most of these aggregates are dynamic, meaning they are constantly formed and dissociated. The use of a chemical equilibrium for the ion-pair is to emphasize the much longer life-time of ion-pairs. The success of this approach implies that there are long-lived ion-pairs in the system.

1.0

α (exp) Exp. α(298.15 K) xx_water water xx_C andxAx_A C and xx_CA CA α

0.8

0.6

0.8

0.6

0.4

0.4

0.2

0.2

0.0

The degree of dissociation α

1.0 mole fraction of each components xi

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0.0 0.0

0.2

0.4

xowater

0.6

0.8

1.0

Figure 1. The variation in mole fraction of each species (cation (dashed line), anion (dashed line), ion-pair (dotted-dash line), and the solvent (dotted line)) and degree of dissociation (α (solid line)) of [C2MIM][EtSO4] with the composition of the solvent (water) at 298.15 K. The solvent concentration in the x-axis is calculated by considering the IL being undissociated. The experimental data (open squares) are obtained from literature.33

8


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Table 1. The solvent composition ( *0+,-./ ) of minimum degree of dissociation predicted at 298.15 K from the full thermodynamic model (Eqn. 7) and the simplified model (Eqn. 8) IL/solvent combination [C2MIM][EtSO4]/water [C2MIM][OTf]/water [C2MIM][F3Ac]/water [C2MIM][Ac]/water [C2MIM][HSO3]/water [C4MIM][Cl]/water [C4MIM][BF4]/water [C4MIM][PF6]/water [C2MIM][EtSO4]/DMSO [C4MIM][Cl]/AN [C4MIM][PF6]/AN [C2MIM][EtSO4]/methanol [C2MIM][EtSO4]/propanol [C2MIM][EtSO4]/butanol [C2MIM][EtSO4]/DCM [C4MIM][BF4]/DCM [C4TA][Pic]/1-chloroheptane [C4TA][Pic]/1-tridecanol [C2MIM][EtSO4]/hexane a

Temp. [K]

Exp.

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 348 416.15 298.15

0.7133 0.9933 no33 -a 0.99812 0.99812 0.834, 36 > 0.99637 > 0.99338 0.99915 0.99915 -

Eqn. 7

Eqn. 8

0.85 0.84 0.90 0.90 no no 0.91 0.90 0.92 0.91 0.89 0.89 0.92 0.92 0.93 0.93 0.81 0.80 0.78 0.78 0.90 0.89 no no no no no no 0.9994 no 0.999 no 0.9998 0.9998 0.9998 0.9998 0.999994 0.999994

εsolvent35

εIL30

78.43 78.43 78.43 78.43 78.43 78.43 78.43 78.43 46.83 35.69 35.69 32.61 20.52 17.33 8.82 8.82 3.8 4.3 1.88

18.05 16.87 18.72 22.72 19.73 22.30 18.62 15.86 18.05 22.30 15.86 18.05 18.05 18.05 18.05 18.62 11.14 11.14 18.05

The dash lines indicate no experimental data available. To explore the origin of the occurrence of a minimum value in α, we first express

the degree of dissociation in terms of the initial solvent concentration, xos, and the dissociation constants (see Supporting Information for derivation) 1=

5

2 3 4 5 7 6

(7)

5 8 56

Since the value of xos (mole fraction of solvent when all IL molecules are not dissociated) is usually less than unity and Ka is constant under isothermal condition, eq. 7 can be

9



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simplified such that α is found to be approximately proportional to the square root of ratio of Kγ and 1-xos, 1≈

:;

(8)

2

This equation implies that the dissociation phenomena is a competition between solvent concentration (which favors dissociation: xos ↑, α ↑) and the molecular interactions reflected in the activity coefficients (Kγ). The validity of this simplified equation is examined in Figure 2, where the ratio :< /: 1 − @AB (dotted line) is compared to α determined from eq. 7 (solid line). As can be seen, the simplified equation gives a very similar concentration dependence of α over the whole concentration range (Fig. 2a). The 1/: 1 − @AB term (blue dotted-dash line) always gives an increasing degree of dissociation with increasing solvent concentration, as can be understood from the Le Chatelier's principle. The occurrence of a minimum in α is a result of the decreasing value in Kγ with xos (red dashed line). The re-dissociation would not be present (no local minimum in α vs. xos) if the decreasing of Kγ with concentration is not strong enough (Fig. 2b). Note that the difference between the full and simplified equations is quite noticeable in this case (higher degree of dissociation). Nonetheless, the simplified equation provides good qualitative behavior of the composition dependence of α.

10


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1.0 full eqn. eqn. (Eqn. 7) full simplified eqn. simplified eqn. (Eqn. 8) SQRT(Kr) K : SQRT(1/xoCA) 2 1/ 1 − @0

12

(a) 0.8

D

0.6

8 0.4 4

0.2

0


(Kγ )0.5 and (1/xoCA)0.5

16

0.0 0.0

0.2

0.4

0.6

0.8

1.0

xowater 1.E+04

1.0 full eqn. (Eqn. 7) simplified eqn. (Eqn. 8) :K

1.E+03

(b) 0.8

21/ 1 − @0D

0.6

1.E+02 0.4 1.E+01

0.2

1.E+00


(Kγ )0.5 and (1/xoCA)0.5

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


0.0 0.0

0.2

0.4

0.6

0.8

1.0

xowater

Figure 2. Comparison of predicted degree of dissociation (α) from the thermodynamic model (Eqn. 7, solid line) and the simplified equation (Eqn. 8, dotted line) for (a) [C2MIM][EtSO4] and (b) [C2MIM][F3Ac] in aqueous systems. Also shown are the contributions from : term (dashed line) and 1/: 1 − @AB term (dotted-dash line) in the simplified equation.

11



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Figure 3 illustrates the concentration dependence of Kγ arising from different types of interactions: the PDH term (long-range coulomb interactions), the residual term (the short-range attractive interactions), and the combinatorial term (the short-range repulsive interactions). = "#$

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