Recent advances in thermodynamic modelling of ionic liquid solutions

doi:10.11949/0438-1157.20191184

Abstract

Abstract:

Ionic liquids (ILs) is a novel and green solvent, and shows prospective applications in ILs related reaction and separation processes. Their thermodynamic properties and fluid phase equilibria data are instrumental for the ILs-related process design. This paper reviewed the recent advances in thermodynamic modelling of ILs solutions in terms of the following aspects, viz. study methods of solution thermodynamics, construction of solution thermodynamic models, the structure and intermolecular forces of ILs, thermodynamic models of ILs solution and their applications in fluid phase equilibria. Special focuse was given to the development of equation of state and excess Gibbs free energy or activity coefficient models, electrolyte and non-electrolyte solution models, as well as their treatment for ILs structure, hydrogen bonding and electrostatic interactions. The merits and demerits of these models were analyzed, and some suggestions were proposed for the study of molecular thermodynamic models of ILs solutions.

Key words: thermodynamics, activity coefficient, equation of state, phase equilibria, electrostatic interaction, hydrogen bond

摘要：

离子液体是近年来发展起来的一种绿色介质，在化工反应和分离过程中具有广泛的应用前景。离子液体的溶液热力学性质和相平衡数据是其相关工艺过程设计的基础。本文从如下几个方面综述了离子液体溶液热力学模型的研究进展，即溶液热力学研究方法、溶液热力学模型的构建、离子液体的结构和分子间作用力、离子液体的溶液热力学模型及其在相平衡计算中的应用。重点分析了适用于离子液体溶液热力学性质计算的状态方程模型和过量Gibbs自由能模型或活度系数模型，离子液体的电解质和非电解质溶液模型，以及这些模型对ILs结构、氢键和静电作用的处理方法。分析了这些模型的优缺点，并对今后离子液体的溶液热力学研究提出了建议。

关键词: 热力学, 活度系数, 状态方程, 相平衡, 静电作用, 氢键

CLC Number:

TQ 013.1

Chunxi LI. Recent advances in thermodynamic modelling of ionic liquid solutions[J]. CIESC Journal, 2020, 71(1): 81-91.

李春喜. 离子液体的溶液热力学模型研究进展[J]. 化工学报, 2020, 71(1): 81-91.

Figures/Tables 2

Table 1 Treatment of ILs’ structure and interaction forces in various thermodynamic models

ILs’ structure and interaction force	Thermodynamic model	Model parameter	Application
neutral molecule^①；SR^②	SRK	3- adjustable parameter for ( $a, b$ ) with vdW-1 mixing rule	VLE correlation for 48 binary ILs aqueous solutions, AARD<1% for most systems ^[61]
neutral molecule；SR	PR	3-adjustable parameter ( $U 12, U 21, l 12$ ) for ( $a, b$ ) with W-S mixing rule	VLE correlation for 28 ILs-containing binary mixture with ARD=3.38% ^[45]
neutral molecule； SR + assoc^③	PR-TS^?	5-molecule parameter $(a 0, c 1, b, E 11, v 11$ ), 2-adju-stable parameter( $k i j, l i j$ ) for vdW-1 mixing rule	H₂S solubility in 12 ILs, AAD=3.4%^[62]
neutral molecule；SR	NRTL, UIQUAC	3-NRTL parameter ( $τ i j, τ j i, α j i)$ , 2-UNIQUAC parameter( $τ i j, τ j i)$	LLE prediction for IL-containing ternary systems with binary parameters ^[63]
neutral molecule；SR	Wilson-NRF	4-adjustable parameter for a binary system, i.e. ( $τ i j, τ j i) w i t h ?? τ i j = a i j + b i j / T$	LLE correlation for 38 binary and 52 ternary systems with RMSD being 8.78 and 4.08 respectively^[34]
neutral molecule (group solution)^④；SR	UNIFAC	group volume, surface area and interaction energy parameter $R k, Q k, a j i, a i j$	correlation of $γ ∞$ and VLE prediction^[38], prediction of VLE, LLE, $γ ∞$ and $H e x$ ^[40,64]
neutral molecule；SR	NRTL-SAC	4- molecule-specific parameters	correlation of $γ ∞$ of organics in ILs, and prediction of the resultant VLE, LLE ^[41]
neutral molecule with homo-segment^⑤;hc^⑥+dis^⑦+ polar^⑧+ assoc	PC-PSAFT	segment parameter ( $m, σ, ε, μ, Q, σ D$ ) and association parameter $(κ A B, ε A B$ ) with one adjustable parameter $k i j$	accurate correlation of CO₂ solubility in ILs^[65]
neutral molecule with homo-segment;LJ^⑨+chain^⑩+polar+assoc	soft-SAFT	segment parameter ( $m, σ, ε, κ A B, ε A B$ ) with one adjustable parameter $ξ$	correlation and prediction of CO₂ solubility in 7 ILs^[66]
molecule with heterosegment^?; hs^?+chain+dis+assoc	SAFT	9 adjustable parameters	accurate correlation of CO₂ solubility in 11 ILs^[67]
neutral molecule with homo-segment; hc+dis	PHSC	chain site parameter( $m, σ, ε$ ) with one adjustable parameter $k i j$ between H₂ and IL	correlation and prediction of H₂solubility in 11 ILs^[68] and CO₂ solubility in 4 ILs^[47]
neutral molecule with homo-segments; SWC^?+dis	SWCF	segment parameter ( $m, σ, ε$ ) with 2—6 adjustable parameter ( $k i j, l i j$ )	VLE correlation for CO₂and alkane in 12 ILs with ARD=5.2%^[69]
neutral molecule with hetero-segments; SWC+dis+assoc	SWCF	segment parameter ( $m, σ, ε, k c a$ ) with 2-adjustable dispersive parameter( $k A S, k B S)$	VLE correlation for 22 IL-containing binary systems with ARD=5.4% ^[70]
neutral molecule with homo-segments; SR	Sanchez-Lacombe EOS	3-molecular parameter( $? , v , r$ ), and 3-adjustable parameter	solubility of 11 refrigerants in 12 ILs with ARD=5.7% ^[46]
neutral molecule (group solution)；SR	GC-EOS	3-4 adjustable NRTL group parameter ( $α i j, α j i, k i j *, k i j'$ )	solubility correlation for 11 gas in ILs with ARD< 10% in most cases^[71]
strong electrolyte^?; DH^?+dis	Pitzer	$Φ M N, Ψ M N X, β 0, β 1, C ?$	solubility correlation for inorganic salts in IL aqueous solution^[72]
strong electrolyte; NRTL-SR^?+ PDH^?	e-NRTL	2-adjustable parameter( $τ m - c a, τ c a - m$ )	correlation of activity coefficients of electrolyte aqueous with satisfactory results^[60,73]
strong electrolyte; LR+MR^?+SR	e-UNIQUAC	6 adjustable MR parameter( $b i j$ , $c i j$ ) and 2 SR parameter ( $a j i, a i j$ )	ionic mean activity coefficients and VLE of electrolyte solutions^[57]
strong electrolyte; LR+ MR+ SR	e-UNIFAC	6 adjustable group parameter( $b i j$ , $c i j$ ) for MR and 2 group parameter ( $a j i, a i j$ ) for SR	ionic mean activity coefficients and VLE of electrolyte solutions^[57]
strong electrolyte; hs+dis+LR	P=P ^hs +P ^dis +P ^elec	2 group dispersive parameter( $σ, ε$ ), without adjustable parameter	density prediction for 29 ILs with ARD=0.63%^[53]
strong electrolyte; SWC+assoc + MSA^?	SWCF-VR-MSA	site parameter ( $r, σ, ε, λ$ )+ association parameter $δ ε c a a s s o c$	correlation and prediction of density, activity coefficients and VLE for ILs aqueous solutions^[54]
strong electrolyte; hc+dis+DH	ePC-SAFT	segment parameter (m, $σ, ε$ ) without adjustable parameter	prediction of derivative properties of ILs and CO₂ solubility in ILs^[55,74]

Table 1 Treatment of ILs’ structure and interaction forces in various thermodynamic models

ILs’ structure and interaction force	Thermodynamic model	Model parameter	Application
neutral molecule^①；SR^②	SRK	3- adjustable parameter for ( $a, b$ ) with vdW-1 mixing rule	VLE correlation for 48 binary ILs aqueous solutions, AARD<1% for most systems ^[61]
neutral molecule；SR	PR	3-adjustable parameter ( $U 12, U 21, l 12$ ) for ( $a, b$ ) with W-S mixing rule	VLE correlation for 28 ILs-containing binary mixture with ARD=3.38% ^[45]
neutral molecule； SR + assoc^③	PR-TS^?	5-molecule parameter $(a 0, c 1, b, E 11, v 11$ ), 2-adju-stable parameter( $k i j, l i j$ ) for vdW-1 mixing rule	H₂S solubility in 12 ILs, AAD=3.4%^[62]
neutral molecule；SR	NRTL, UIQUAC	3-NRTL parameter ( $τ i j, τ j i, α j i)$ , 2-UNIQUAC parameter( $τ i j, τ j i)$	LLE prediction for IL-containing ternary systems with binary parameters ^[63]
neutral molecule；SR	Wilson-NRF	4-adjustable parameter for a binary system, i.e. ( $τ i j, τ j i) w i t h ?? τ i j = a i j + b i j / T$	LLE correlation for 38 binary and 52 ternary systems with RMSD being 8.78 and 4.08 respectively^[34]
neutral molecule (group solution)^④；SR	UNIFAC	group volume, surface area and interaction energy parameter $R k, Q k, a j i, a i j$	correlation of $γ ∞$ and VLE prediction^[38], prediction of VLE, LLE, $γ ∞$ and $H e x$ ^[40,64]
neutral molecule；SR	NRTL-SAC	4- molecule-specific parameters	correlation of $γ ∞$ of organics in ILs, and prediction of the resultant VLE, LLE ^[41]
neutral molecule with homo-segment^⑤;hc^⑥+dis^⑦+ polar^⑧+ assoc	PC-PSAFT	segment parameter ( $m, σ, ε, μ, Q, σ D$ ) and association parameter $(κ A B, ε A B$ ) with one adjustable parameter $k i j$	accurate correlation of CO₂ solubility in ILs^[65]
neutral molecule with homo-segment;LJ^⑨+chain^⑩+polar+assoc	soft-SAFT	segment parameter ( $m, σ, ε, κ A B, ε A B$ ) with one adjustable parameter $ξ$	correlation and prediction of CO₂ solubility in 7 ILs^[66]
molecule with heterosegment^?; hs^?+chain+dis+assoc	SAFT	9 adjustable parameters	accurate correlation of CO₂ solubility in 11 ILs^[67]
neutral molecule with homo-segment; hc+dis	PHSC	chain site parameter( $m, σ, ε$ ) with one adjustable parameter $k i j$ between H₂ and IL	correlation and prediction of H₂solubility in 11 ILs^[68] and CO₂ solubility in 4 ILs^[47]
neutral molecule with homo-segments; SWC^?+dis	SWCF	segment parameter ( $m, σ, ε$ ) with 2—6 adjustable parameter ( $k i j, l i j$ )	VLE correlation for CO₂and alkane in 12 ILs with ARD=5.2%^[69]
neutral molecule with hetero-segments; SWC+dis+assoc	SWCF	segment parameter ( $m, σ, ε, k c a$ ) with 2-adjustable dispersive parameter( $k A S, k B S)$	VLE correlation for 22 IL-containing binary systems with ARD=5.4% ^[70]
neutral molecule with homo-segments; SR	Sanchez-Lacombe EOS	3-molecular parameter( $? , v , r$ ), and 3-adjustable parameter	solubility of 11 refrigerants in 12 ILs with ARD=5.7% ^[46]
neutral molecule (group solution)；SR	GC-EOS	3-4 adjustable NRTL group parameter ( $α i j, α j i, k i j *, k i j'$ )	solubility correlation for 11 gas in ILs with ARD< 10% in most cases^[71]
strong electrolyte^?; DH^?+dis	Pitzer	$Φ M N, Ψ M N X, β 0, β 1, C ?$	solubility correlation for inorganic salts in IL aqueous solution^[72]
strong electrolyte; NRTL-SR^?+ PDH^?	e-NRTL	2-adjustable parameter( $τ m - c a, τ c a - m$ )	correlation of activity coefficients of electrolyte aqueous with satisfactory results^[60,73]
strong electrolyte; LR+MR^?+SR	e-UNIQUAC	6 adjustable MR parameter( $b i j$ , $c i j$ ) and 2 SR parameter ( $a j i, a i j$ )	ionic mean activity coefficients and VLE of electrolyte solutions^[57]
strong electrolyte; LR+ MR+ SR	e-UNIFAC	6 adjustable group parameter( $b i j$ , $c i j$ ) for MR and 2 group parameter ( $a j i, a i j$ ) for SR	ionic mean activity coefficients and VLE of electrolyte solutions^[57]
strong electrolyte; hs+dis+LR	P=P ^hs +P ^dis +P ^elec	2 group dispersive parameter( $σ, ε$ ), without adjustable parameter	density prediction for 29 ILs with ARD=0.63%^[53]
strong electrolyte; SWC+assoc + MSA^?	SWCF-VR-MSA	site parameter ( $r, σ, ε, λ$ )+ association parameter $δ ε c a a s s o c$	correlation and prediction of density, activity coefficients and VLE for ILs aqueous solutions^[54]
strong electrolyte; hc+dis+DH	ePC-SAFT	segment parameter (m, $σ, ε$ ) without adjustable parameter	prediction of derivative properties of ILs and CO₂ solubility in ILs^[55,74]

Table 2 Thermodynamic properties required in calculation of fluid phase equilibria

Fluid phase equilibria	Phase equilibria equation	Note
GLE	$y i φ i G a s = x i φ i L i q$ $y i P φ i G a s T, P = x i γ i P i s φ i s T, P i s = x i H i, I L$ ^[17]	$x i, γ i, φ i L i q, P i s, φ i s$ 分别为 $i$ 组分的液相摩尔分数、活度系数、逸度系数、饱和蒸气压以及 $P i s$ 下的逸度系数。 $y i 、 φ i G a s$ 为 $i$ 组分的气相摩尔分数和逸度系数
LLE	$x i φ i α = x i φ i β$ ^[48] $x i γ i α = x i γ i β$ ^[34]	$x i, γ i, φ i$ 分别为 $i$ 组分的液相摩尔分数、活度系数和逸度系数
VLE	$y i φ i V = x i φ i L$ ^[45] $P y i φ i V = x i γ i P i s e x p ∫ P i s a t P v m, i L d P R T$ ^[17]	$v m, i L$ 为 $i$ 组分的液相摩尔体积，在中低压条件下 $e x p ∫ P i s a t P v m, i L d P R T ≈ 1$ ，其余同上
SLE	$P x 2 L φ 2 L = f 2 S T$ $x 2 γ 2 L = a 2 S T = e x p - ? f S R T m T - 1$ ^[17]	固体溶质2析出时的活度 $a 2 S T$ 或逸度 $f 2 S T$ 为定值，而溶液中溶质2的活度或逸度可由活度系数方程或EOS计算

Table 2 Thermodynamic properties required in calculation of fluid phase equilibria

Fluid phase equilibria	Phase equilibria equation	Note
GLE	$y i φ i G a s = x i φ i L i q$ $y i P φ i G a s T, P = x i γ i P i s φ i s T, P i s = x i H i, I L$ ^[17]	$x i, γ i, φ i L i q, P i s, φ i s$ 分别为 $i$ 组分的液相摩尔分数、活度系数、逸度系数、饱和蒸气压以及 $P i s$ 下的逸度系数。 $y i 、 φ i G a s$ 为 $i$ 组分的气相摩尔分数和逸度系数
LLE	$x i φ i α = x i φ i β$ ^[48] $x i γ i α = x i γ i β$ ^[34]	$x i, γ i, φ i$ 分别为 $i$ 组分的液相摩尔分数、活度系数和逸度系数
VLE	$y i φ i V = x i φ i L$ ^[45] $P y i φ i V = x i γ i P i s e x p ∫ P i s a t P v m, i L d P R T$ ^[17]	$v m, i L$ 为 $i$ 组分的液相摩尔体积，在中低压条件下 $e x p ∫ P i s a t P v m, i L d P R T ≈ 1$ ，其余同上
SLE	$P x 2 L φ 2 L = f 2 S T$ $x 2 γ 2 L = a 2 S T = e x p - ? f S R T m T - 1$ ^[17]	固体溶质2析出时的活度 $a 2 S T$ 或逸度 $f 2 S T$ 为定值，而溶液中溶质2的活度或逸度可由活度系数方程或EOS计算

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