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Modeling of surface tension for ionic liquids using group method of data handling

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Abstract

The group method of data handling (GMDH) was utilized to estimate the surface tension of 59 ionic liquids. In this regard, an extensive experimental data was selected from literature over the range 268.3 to 532.4 K. The GMDH model can predict the surface tension of ionic liquids by a grand polynomial correlation function of molar density, reduced boiling temperature, reduced temperature and pressure, acentric factor, and critical compressibility factor. The values of the GMDH model showed a very good regression with the experimental data. The average absolute relative deviation (AARD%) of the GMDH model for all ionic liquids was 4.59 % which indicated a good precision in comparison with those obtained from the generalized dimensionless equation, Mousazadeh–Faramarzi equation, and Parachor equation with AARDs% of 10.31, 13.02, and 11.89, respectively.

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Abbreviations

IL:

Ionic liquid

[C2OHmim] [BF4]:

1-(2-Hydroxyethyl)-3-methylimidazolium tetrafluoroborate

[C10C10im] [bti]:

1,3-Decylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C4C4im] [bti]:

1,3-Dibutylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C2C2im] [bti]:

1,3-Diethylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C1C1im] [bti]:

1,3-Dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Dmim] [MSO4]:

1,3-Dimethylimidazolium methylsulfate

[C3C3im] [bti]:

1,3-Dipropylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C7C7im] [bti]:

1,3-Heptylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C6C6im] [bti]:

1,3-Hexylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C9C9im] [bti]:

1,3-Nonylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C8C8im] [bti]:

1,3-Octylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[C5C5im] [bti]:

1,3-Pentylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Bmpyr] [bti]:

1-Butyl-1-methylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide

[Bdmim] [bti]:

1-Butyl-2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Bdmim] [PF6]:

1-Butyl-2,3-dimethylimidazolium hexafluorophosphate

[Bmim] [bti]:

1-Butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Bmim] [Cl]:

1-Butyl-3-methylimidazolium chloride

[Bmim] [dca]:

1-Butyl-3-methylimidazolium dicyanamide

[Bmim] [PF6]:

1-Butyl-3-methylimidazolium hexafluorophosphate

[Bmim] [I]:

1-Butyl-3-methylimidazolium iodide

[Bmim] [MSO4]:

1-Butyl-3-methylimidazolium methylsulfate

[Bmim] [BF4]:

1-Butyl-3-methylimidazolium tetrafluoroborate

[Bmim] [tca]:

1-Butyl-3-methylimidazolium thiocyanate

[Bmim] [TfO]:

1-Butyl-3-methylimidazolium trifluoromethanesulfonate

[Mbpy] [bti]:

1-Butyl-4-methylpyridinium bis[(trifluoromethyl)sulfonyl]imide

[Mbpy] [BF4]:

1-Butyl-4-methylpyridinium tetrafluoroborate

[Emim] [bti]:

1-Ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Emim] [dca]:

1-Ethyl-3-methylimidazolium dicyanamide

[Emim] [ESO4]:

1-Ethyl-3-methylimidazolium ethylsulfate

[Emim] [BF4]:

1-Ethyl-3-methylimidazolium tetrafluoroborate

[Emim] [TfO]:

1-Ethyl-3-methylimidazolium trifluoromethanesulfonate

[N-epy] [bti]:

1-Ethylpyridinium bis[(trifluoromethyl)sulfonyl]imide

[Hpmim] [bti]:

1-Heptyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Hmim] [bti]:

1-Hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Hmim] [Cl]:

1-Hexyl-3-methylimidazolium chloride

[Hmim] [PF6]:

1-Hexyl-3-methylimidazolium hexafluorophosphate

[Hmim] [BF4]:

1-Hexyl-3-methylimidazolium tetrafluoroborate

[Hpy] [bti]:

1-Hexylpyridinium bis[(trifluoromethyl)sulfonyl]imide

[Omim] [bti]:

1-Octyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Omim] [PF6]:

1-Octyl-3-methylimidazolium hexafluorophosphate

[Omim] [BF4]:

1-Octyl-3-methylimidazolium tetrafluoroborate

[Pmim] [bti]:

1-Pentyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Prmim] [bti]:

1-Propyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

[Prmim] [PF6]:

1-Propyl-3-methylimidazolium hexafluorophosphate

[Prmim] [BF4]:

1-Propyl-3-methylimidazolium tetrafluoroborate

[2-HDEA][HCO2]:

2-Hydroxydiethylammonium formate

[Mbupy] [BF4]:

2-Methyl-N-butylpyridinium tetrafluoroborate

[Prmpy] [bti]:

3-Methyl-1-propylpyridinium bis[(trifluoromethyl)sulfonyl]imide

[N1136] [bti]:

Dimethylhexyl(i-propyl)ammonium bis[(trifluoromethyl)sulfonyl]imide

[N1134] [bti]:

Dimethylpropylbutylammonium bis[(trifluoromethyl)sulfonyl]imide

[Mbpyr] [dca]:

n-Methyl-n-butylpyrrolidinium dicyanamide

[P2444] [DEP]:

Tributyl(ethyl)phosphonium diethylphosphate

[N6222] [bti]:

Triethylhexylammonium bis[(trifluoromethyl)sulfonyl]imide

[6,6,6,14-P] [bti]:

Trihexyltetradecylphosphonium bis[(trifluoromethyl)sulfonyl]imide

[6,6,6,14-P] [Cl]:

Trihexyltetradecylphosphonium chloride

[N1114] [bti]:

Trimethylbutylammonium bis[(trifluoromethyl)sulfonyl]imide

[N111,10] [bti]:

Trimethyldecylammonium bis[(trifluoromethyl)sulfonyl]imide

[N1116] [bti]:

Trimethylhexylammonium bis[(trifluoromethyl)sulfonyl]imide

[N8111] [bti]:

Trimethyloctylammonium bis[(trifluoromethyl)sulfonyl]imide

a :

Polynomial coefficient in Eq. (1) and adjustable parameter in Eq. (7)

b :

Adjustable parameter in Eq. (7)

F (0) F (1) :

Functions in Eq. (6)

k :

Boltzmann constant

l :

Number of layers

M :

Number of observations

MW:

Molecular weight (g mol−1)

n :

Number of data points

N :

Intermediate layer

P :

Pressure (bar)

P ch :

Parachor ((mN m−1)1/4 cm3 mol−1)

T :

Temperature (K)

x :

Input parameters in Eq. (1)

y 0 :

Output

Z :

Compressibility factor

γ :

Surface tension (mN m−1)

σ :

Hard-sphere segment diameter (0A)

ε/k :

Well depth parameter (K)

ρ :

Density (g cm−3)

ω :

Acentric factor

b:

Boiling

br:

Reduced boiling

c:

Critical

cal:

Calculated

exp:

Experimental

m:

Melting

r:

Reduced

exp:

Experimental

GMDH:

Group method of data handling

* :

Dimensionless

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Authors and Affiliations

  1. Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Saeid Atashrouz & Gholamreza Pazuki

  2. School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Ershad Amini

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  1. Saeid Atashrouz
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  2. Ershad Amini
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Correspondence to Gholamreza Pazuki.

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Atashrouz, S., Amini, E. & Pazuki, G. Modeling of surface tension for ionic liquids using group method of data handling. Ionics 21, 1595–1603 (2015). https://doi.org/10.1007/s11581-014-1347-1

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