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Developing a new correlation for the aliphatic and aromatic hydrocarbon diffusion coefficients at infinite dilution in ionic liquids
Journal Pre-proof Developing a new correlation for the aliphatic and aromatic hydrocarbon diffusion coefficients at infinite dilution in ionic liquids Noemí Delgado-Mellado, Miguel Ayuso, Julián García, Francisco Rodríguez PII:
S0167-7322(19)33164-2
DOI:
https://doi.org/10.1016/j.molliq.2019.111857
Reference:
MOLLIQ 111857
To appear in:
Journal of Molecular Liquids
Received Date: 4 June 2019 Revised Date:
2 September 2019
Accepted Date: 28 September 2019
Please cite this article as: Noemí. Delgado-Mellado, M. Ayuso, Juliá. García, F. Rodríguez, Developing a new correlation for the aliphatic and aromatic hydrocarbon diffusion coefficients at infinite dilution in ionic liquids, Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/j.molliq.2019.111857. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Developing a new correlation for the aliphatic and aromatic hydrocarbon
2
diffusion coefficients at infinite dilution in ionic liquids.
3
Noemí Delgado-Mellado, Miguel Ayuso, Julián García*, and Francisco Rodríguez.
4
Department of Chemical Engineering, Complutense University of Madrid, E–28040 Madrid,
5
Spain.
6 7 8
Abstract
9 10
In this work the Taylor dispersion technique has been used to measure the diffusion
11
coefficients of n-heptane and toluene at infinite dilution in four ionic liquids, namely 1-ethyl-
12
3-methylimidazolium
13
tricyanomethanide
14
([bmim][TCM]), and 1-butyl-4-methylpyridinium tricyanomethanide ([4bmpy][TCM]), at the
15
range temperatures from (298.2 to 333.2) K. The hydrocarbon diffusion is faster at higher
16
temperatures because of the lower ionic liquid viscosity, and toluene diffuses faster than n-
17
heptane due to its smaller molecular volume. In addition, it is seen that the values of the n-
18
heptane diffusion coefficients decrease with an increase in the molecular weight and molar
19
volume of the ionic liquid. The same is observed for the diffusion coefficients of toluene in
20
the most viscous ionic liquids ([bmim][TCM], [4bmpy][TCM] and [4empy][Tf2N]), but,
21
conversely, they increase for the least viscous ionic liquids ([emim][SCN], [emim][DCA],
22
and [emim][TCM]). This behavior suggests that the strength of the toluene-ionic liquid
23
chemical interactions have a significant effect on diffusion. A new empirical correlation has
24
been proposed as a variation of the Wilke-Chang equation. Two additional variables have
25
been introduced in this correlation; the molar fraction of the maximum hydrocarbon
26
solubility, to take into account the toluene-ionic liquid interactions, as well as the molar
27
volume of the ionic liquid, because of the huge difference between them and the solute. This
28
new correlation satisfactorily fits the experimental data with an average deviation of 9.6%.
thiocyanate ([emim][TCM]),
([emim][SCN]),
1-ethyl-3-methylimidazolium
1-butyl-3-methylimidazolium
tricyanomethanide
29 30
Keywords. Diffusion coefficient; ionic liquids; Taylor dispersion; empirical correlation.
31 32 *
Corresponding author. Tel.: +34 91 394 51 19; Fax: +34 91 394 42 43. E–mail address: [email protected] (Julián García).
1
33
1 Introduction
34 35
The use of the ionic liquids as alternative solvents for several applications has been
36
widely studied for the last two decades. These substances are non-conventional salts which
37
melt at temperatures lower than 100 ºC and present many advantages, such as high stability
38
(chemical, thermal, and electrochemical), non-volatility and negligible vapor pressure, and the
39
possibility of tailoring these properties by selecting the anion and the cation [1,2]. Among all
40
the ionic liquid applications, those with a major interest in the industry are the aromatic
41
separation processes because of the ability of the ionic liquids to preferentially solubilize
42
these hydrocarbons in their mixtures with aliphatics [3,4]. Due to this, a large number of
43
publications focused on this separation has appeared since then, meanwhile, the information
44
related to the molecular diffusion of the hydrocarbons through the ionic liquids is still
45
unavailable. Nowadays, most of the diffusion studies are focused on mutual diffusion
46
coefficients or on ionic liquid diffusion in water or on gas solutes in ionic liquids [5-10], but,
47
to the best of our knowledge, no research has been developed in the field of hydrocarbon
48
diffusion in ionic liquids except for our last published work [11].
49
The determination of the diffusion coefficients has special importance in the
50
prediction of the rate-limiting factor for the chemical processes [12]. In the last decades, many
51
different methods for the measurement of the diffusion coefficients have been used and
52
published in the literature, such as diaphragm cells or porous media [13,14], optical methods
53
[15-17], the total internal reflection fluorescence (TIRF) [18], and the Taylor dispersion
54
technique [19-21]. The latter is widely used because of its high accuracy on the experimental
55
data determination and its easiness to handle [22-25], and it is the selected method in the
56
present work.
57
The diffusion coefficients at infinite dilution of n-heptane and toluene, representing
58
the aromatic and aliphatic content of the pyrolysis and reformer gasolines, the main source of
59
aromatic hydrocarbons in the petrochemical industry [26], in four ionic liquids, namely 1-
60
ethyl-3-methylimidazolium
61
tricyanomethanide
62
([bmim][TCM]), and 1-butyl-4-methylpyridinium tricyanomethanide ([4bmpy][TCM]), have
63
been determined by the Taylor dispersion method for the temperatures ranging from (298.2 to
64
333.2) K. The experimental data have allowed to study the influence of the ionic liquid and
65
hydrocarbon properties, such as viscosity, molecular weight, molar volume, and maximum
66
hydrocarbon solubility, on the diffusion coefficients in order to develop an empirical
thiocyanate
([emim][TCM]),
([emim][SCN]),
1-ethyl-3-methylimidazolium
1-butyl-3-methylimidazolium
tricyanomethanide
2
67
correlation, as a variation of the Wilke-Chang equation, to properly predict the hydrocarbon
68
diffusion through the ionic liquid media. The proposed equation has been compared to the
69
Wilke-Chang correlation, showing an average deviation of ±9.6% the former and ±14.4% the
70
latter.
71 72
2 Experimental
73 74
2.1 Chemicals
75 76
The ionic liquids, namely 1-ethyl-3-methylimidazolium thiocyanate ([emim][SCN]),
77
1-ethyl-3-methylimidazolium
tricyanomethanide
([emim][TCM]),
1-butyl-3-
78
methylimidazolium tricyanomethanide ([bmim][TCM]), and 1-butyl-4-methylpyridinium
79
tricyanomethanide ([4bmpy][TCM]), were supplied by Iolitec GmbH with a mass purity
80
higher than 0.98. Toluene and n-heptane hydrocarbons were supplied by Sigma-Aldrich with
81
a mass purity higher than 0.99. Table 1 shows the compound chemical specifications. All the
82
chemicals were used as received without further purification and the ionic liquids were stored
83
in a desiccator and handled in a glove box under dry nitrogen in order to avoid their hydration
84
since they are hygroscopic substances.
85 86
2.2 Experimental equipment and diffusion coefficient measurement
87 88
The Taylor dispersion technique has been used to measure the hydrocarbon diffusion
89
coefficients at infinite dilution in four ionic liquids. The experimental equipment used to that
90
end is described in our previous work [11]. The ionic liquid is continuously delivered at a
91
constant flow rate of 50 µL/min through a PEEK capillary tubing (10 m length and 0.375·10-3
92
m inner radius) with a Hamilton 1025TLL syringe coupled to a KDS Legato 200 metering
93
pump. The diffusion coefficients were obtained from the concentration gradient signal
94
registered by a Refractive Index Detector Agilent 1260 Infinity II after injecting with a six-
95
port injection valve Agilent G1328 20 µL of the (hydrocarbon + ionic liquid) solution with a
96
solute concentration of (0.020-0.100) ± 0.006 mol·dm-3 in excess into the pure ionic liquid.
97
The sample and reference cells were thermostated at 313.2 K, a higher temperature than the
98
room temperature to reduce the noise in the detector signal. A thermostatic Peltier-cooled
99
incubator Memmert IPP110 with an accuracy of ±0.1 K was used to maintain the temperature
100
range between (298.2 and 333.2 ± 0.1) K. The (hydrocarbon + ionic liquid) solutions were 3
101
gravimetrically prepared in a Mettler Toledo XS 205 balance with a precision of ±1·10−5 g
102
and homogenized in a Labnet Vortex Mixer VX-200.
103 104
Eq. 1 allows the determination of the diffusion coefficients from the changes in the detector signal, y(t): 1/ 2 12· D12 ·(t − t R )2 tR y (t ) = y ∞ + y1·t + y max · ·exp − a 2 ·t t
105
(1)
106
being y∞ the detector baseline, y1·t the expression for the small drifts in the baseline, ymax the
107
peak height relative to the baseline, t the time and tR the retention time in s, a the diffusion
108
tube inner radius in m, and D12 the diffusion coefficient at infinite dilution of the solute (1) in
109
the solvent (2) in m2·s-1. Eq. 1 can be used when the changes in the detector signal are
110
proportional to the solute concentration at the capillary tube outlet [23,27,28].
111 112
Table 1 Compound chemical specifications. Chemical Name
Source
Mass Fraction Purity
Water content in ppm
Halide content in ppm
Analysis Method
n-Heptane
Sigma-Aldrich
>0.995
-
-
GCe
Toluene
Sigma-Aldrich
>0.998
-
-
GCe
[emim][SCN]a
Iolitec GmbH
>0.98
416
<2000
NMRf, ICg, KFh
[emim][TCM]b
Iolitec GmbH
>0.98
976
<500
NMRf, ICg, KFh
[bmim][TCM]c
Iolitec GmbH
>0.98
129
<500
NMRf, ICg, KFh
[4bmpy][TCM]d
Iolitec GmbH
>0.98
129
<500
NMRf, ICg, KFh
113 114 115 116 117 118 119 120 121 122
a
123
3 Results and discussion
[emim][SCN] = 1-ethyl-3-methylimidazolium thiocyanate. [emim][TCM] = 1-ethyl-3-methylimidazolium tricyanomethanide. c [bmim][TCM] = 1-butyl-3-methylimidazolium tricyanomethanide. d [4bmpy][TCM] = 1-butyl-4-methylpyridinium tricyanomethanide. e Gas Chromatography. f Nuclear Magnetic Resonance. g Ion Chromatography. h Karl-Fischer titration. b
124 125
3.1 Diffusion coefficients at infinite dilution
126 127
The hydrocarbon diffusion coefficients at infinite dilution in ionic liquids, D12, were
128
determined for the eight binary systems {n-heptane / toluene + [emim][SCN] / [emim][TCM]
129
/ [bmim][TCM] or [4bmpy][TCM]} at (298.2 – 333.2) K. All the data, collected in Table 2
130
and represented in Fig. 1, are the average of three replicate measurements. As expected,
131
higher temperature enhances the mobility of the solute through the ionic liquid as the
4
132
viscosity of the latter is being decreased. Toluene molecules diffuse faster than n-heptane
133
ones because of the smaller molecular volume, 119 and 146.6 cm3·mol-1, respectively [29]. A
134
great difference between toluene and n-heptane D12 values is observed for the [emim][TCM]
135
ionic liquid. While n-heptane diffusion coefficients are in the same order than those of the rest
136
of the studied ionic liquids, toluene diffusion coefficients present values at least twice higher
137
than in [emim][SCN], [bmim][TCM], and [4bmpy][TCM]. Besides the influence of the ionic
138
liquid viscosity (23.79 mPa·s for [emim][SCN], 15.02 mPa·s for [emim][TCM], 28.30 mPa·s
139
for [bmim][TCM], and 36.70 mPa·s for [4bmpy][TCM] at 298.2 K [30-32]), which clearly
140
benefits the hydrocarbon mobility through [emim][TCM] over the other three ionic liquids, it
141
seems to be another important contribution related to the hydrocarbon-ionic liquid affinity.
142
The maximum toluene solubility in these ionic liquids follows the order: [4bmpy][TCM]
143
(xtol = 0.7417) > [emim][TCM] (xtol = 0.6545) > [bmim][TCM] (xtol = 0.6381) > [emim][SCN]
144
(xtol = 0.2056) [32-34]. By comparing [emim][SCN] and [emim][TCM] ionic liquids, it is
145
seen that the chemical interaction between the solute and solvent, which increases the
146
solubility, has an effect on the solute diffusion as well; both toluene diffusion and toluene
147
solubility in [emim][TCM] are higher than in [emim][SCN]. But the influence of the solute-
148
ionic liquid chemical interactions seems to be present only at lower viscosity values; for more
149
viscous ionic liquids the effect of the similar or higher toluene solubility, e.g. in
150
[bmim][TCM] and [4bmpy][TCM], is counteracted by the high influence of their viscosity.
151 152 153 154
Table 2 Experimental results and standard deviations (∆D12) of diffusion coefficients of nheptane and toluene at infinite dilution in [emim][SCN], [emim][TCM], [bmim][TCM], and [4bmpy][TCM], measured at different temperatures. Ionic liquid [emim][SCN]
[emim][TCM]
[bmim][TCM]
[4bmpy][TCM]
(D12 ± ∆D12)·109 / m2·s-1
Solute 298.2 K
303.2 K
313.2 K
323.2 K
333.2 K
n-Heptane
0.216 ± 0.007
0.264 ± 0.013
0.318 ± 0.019
0.331 ± 0.017
0.394 ± 0.016
Toluene
0.240 ± 0.015
0.290 ± 0.022
0.349 ± 0.027
0.408 ± 0.024
0.459 ± 0.015
n-Heptane
0.205 ± 0.007
0.221 ± 0.009
0.249 ± 0.017
0.332 ± 0.013
0.397 ± 0.016
Toluene
0.516 ± 0.035
0.603 ± 0.028
0.795 ± 0.041
0.839 ± 0.045
0.949 ± 0.061
n-Heptane
0.149 ± 0.006
0.175 ± 0.006
0.245 ± 0.013
0.276 ± 0.010
0.327 ± 0.016
Toluene
0.211 ± 0.008
0.245 ± 0.010
0.340 ± 0.016
0.395 ± 0.013
0.463 ± 0.015
n-Heptane
0.112 ± 0.005
0.133 ± 0.007
0.188 ± 0.012
0.230 ± 0.011
0.272 ± 0.014
Toluene
0.165 ± 0.007
0.191 ± 0.008
0.254 ± 0.012
0.320 ± 0.013
0.395 ± 0.015
155 156 157 158 5
159 160 161
162 163 164 165 166 6
167 168 169
170 171 172 173 174 175
Fig. 1 Diffusion coefficient at infinite dilution of n-heptane (grey symbols) and toluene (black symbols) as function of temperature in: a) [emim][SCN]; b) [emim][TCM]; c) [bmim][TCM]; d) [4bmpy][TCM].
7
176
Different authors have previously studied the relationship between the diffusion
177
coefficients and the viscosity of the solvent (the Stokes-Einstein relation) and determined that
178
there is an inverse dependence [35-38] as:
179
D12 ∝ η2−1 T
180
where η2 is the viscosity of the solvent. When the system is formed by a small solute in a
181
viscous solvent, as the ionic liquid systems studied in this paper, the diffusion coefficient do
182
not vary with the (-1) power of viscosity but with a lower value and around (-2/3) when the
183
solvent viscosity presents the values between 5 and 5000 mPa·s [39]. In Table 3 the power of
184
the viscosity values for the studied ionic liquid systems are collected. It can be seen that the
185
values for the power of the viscosity are close to the (-2/3) value determined by Hiss et al. and
186
that the standard deviation for different solutes in a given ionic liquid is lower than 6.5 %.
(2)
187
The power of viscosity value is dependent of the properties of both solvent and solute,
188
and the deviation from the common systems, widely studied so far, is even more pronounced
189
for the ionic liquids as solvents and small solutes. Therefore, it seems important to deeply
190
study the effect of their properties, apart from the interactions between the ionic liquid and the
191
solute on the diffusion coefficients for these systems.
192 193 194
Table 3 Power of viscosity values for the relation between the diffusion coefficients and the viscosity of the ionic liquids for the Stokes-Einstein relation. Ionic liquid [emim][SCN]
[emim][TCM] [bmim][TCM]
[4bmpy][TCM]
Solute
Power of viscosity
n-Heptane
-0.47
Toluene
-0.55
n-Heptane
-0.62
Toluene
-0.53
n-Heptane
-0.61
Toluene
-0.61
n-Heptane
-0.64
Toluene
-0.62
195 196
3.2 Influence of the physicochemical properties on the hydrocarbon diffusion coefficients
197 198
The influence of some properties of the ionic liquid, such as viscosity, molecular
199
weight, and molar volume, have been studied to search for a satisfactory empirical correlation
200
applicable to hydrocarbon diffusion through ionic liquids. The ratio D12/T for each {n-heptane
201
/ toluene (1) + [emim][SCN] / [emim][DCA] / [emim][TCM] / [bmim][TCM] / 8
202
[4bmpy][TCM] or [4empy][Tf2N] (2)} system is represented against the previous properties
203
in Figs. 2-4. In this Figs., experimental data for [emim][DCA] and [4empy][Tf2N] ionic
204
liquids have been taken from our previous work [11].
205
In Fig. 2 it is seen that the ionic liquid viscosity has a similar effect on n-heptane and
206
toluene diffusion coefficients; the higher the ionic liquid viscosity, the slower the diffusion. A
207
remarkable behavior can be observed for toluene diffusion through [emim][DCA] and
208
[emim][TCM], in which the value of the diffusion coefficients is much higher than in the rest
209
of ionic liquids and the increase of viscosity leads to a more pronounced decrease in the
210
diffusion coefficients. The decrease in the diffusion coefficients is also observed in Fig. 3 and
211
4 for n-heptane but not for toluene. On one hand and related to the n-heptane diffusion, an
212
increase in the molecular weight of the ionic liquid, Fig. 3, and in the molar volume of the
213
ionic liquid, Fig. 4, makes the n-heptane diffusion difficult; as the molecules of the solvent
214
become larger, the diffusion of the solute molecules is slower due to steric hindrance. But on
215
the other hand, toluene diffusion coefficients show two different trends regarding the ionic
216
liquid viscosity. Comparing the diffusion coefficients in [emim]-based ionic liquids, it is seen
217
that an increase in the number of cyano groups attached to the anion leads to higher diffusion
218
coefficients, and an increase in the molecular weight and molecular volume of the ionic liquid
219
does not negatively affect the toluene diffusion. It is important to highlight that the viscosities
220
of the [emim][TCM] and [emim][DCA] (the latter 15.1 mPa·s at 298.2 K [40]) are the lowest
221
of the studied ionic liquids, and it seems that the toluene-ion interaction strength plays an
222
important role in both of them. But the higher the ionic liquid viscosity, the lower the effect of
223
the toluene-ion interaction strength on the diffusion coefficients, as can be inferred by
224
comparing the toluene diffusion coefficient values in [4bmpy][TCM] and [4empy][Tf2N]
225
(which have the highest toluene solubility and the highest viscosity as well) with those in
226
[emim][DCA] and [emim][TCM] (both of them with lower values of maximum toluene
227
solubility but also with a lower viscosity). Based on that, it can be reasonably thought that a
228
parameter related to the solute-ionic liquid interaction strength should be included in the
229
empirical correlation to properly predict the hydrocarbon diffusion coefficients through the
230
ionic liquid media. One main reason that the properties of the ionic liquids are different from
231
the common solvents is their nanoscale ordering; ionic liquids are composed of ions, and this
232
leads to experience interionic interactions and long-lived associations which are not present in
233
the common solvents [41].
234 235 9
236 237 238 239 240 241 242 243 244
245 246 247 248 249 250
Fig. 2 Effect of the ionic liquid viscosity on the diffusion coefficients at infinite dilution of nheptane (a) and toluene (b) at different temperatures. Viscosity values from literature [3032,40].
Fig. 3 Effect of the molecular weight of the ionic liquid on the diffusion coefficients at infinite dilution of n-heptane (a) and toluene (b) at different temperatures.
10
251 252 253 254 255 256 257
Fig. 4 Effect of the molar volume of the ionic liquid on the diffusion coefficients at infinite dilution of n-heptane (a) and toluene (b) at different temperatures.
3.3 Empirical correlation for ionic liquids
258 259
A new empirical correlation to predict the hydrocarbon diffusion through the ionic
260
liquids is proposed as a variation of the Wilke-Chang equation [42] and is based on the
261
hydrocarbon diffusion data and the previous study of the influence of different properties on
262
these coefficients. The goodness of this new correlation has been compared to the Wilke-
263
Chang correlation, the most used one to predict diffusion coefficients: W
= 7.4·10
−8
(φ · M 2 ) ·
0.5
·T
264
D
265
where DW12 is the diffusion coefficient at infinite dilution of the solute (1) in the solvent (2) in
266
cm2·s-1, φ is the association parameter, M2 the solvent molecular weight in g·mol-1, T the
267
temperature in K, η2 the solvent viscosity in cP, and V1 the solute molar volume in cm3·mol-1.
268
The association parameter in the Wilke-Chang correlation has not been widely studied for
269
ionic liquids so it has been determined for all the {hydrocarbon + ionic liquid} systems in the
270
present work. Table 4 shows the values for this association parameter and the predictions of
271
the Wilke-Chang correlation are represented in Fig. 5 and collected in Table S1 of the
272
Supplementary Material. As previously reported [11], the Wilke-Chang correlation does not
273
properly predict the hydrocarbon diffusion in ionic liquids, showing an average deviation of
274
14.4% and a tendency to underestimate the diffusion coefficients at low temperature and
12
η 2 ·V
0.6 1
(3)
11
275
overestimate them at high temperature. Therefore, the association parameter seems to be a
276
nonconstant value influenced by the temperature in ionic liquids. This behavior has not only
277
been observed in these systems but in other ones with ionic liquids as solvents and a great
278
difference between the size of the solute and the solvent molecules [43].
279
The new proposed empirical correlation is an attempt to adapt the Wilke-Chang
280
equation to the studied systems; in which the temperature has an influence on the association
281
parameter and there is a remarkable size difference between the hydrocarbon and the ionic
282
liquid molecules. Besides this, and based on the faster toluene diffusion through
283
[emim][TCM], it seems necessary to introduce in the correlation the maximum hydrocarbon
284
solubility in order to take into consideration the solute-solvent interaction strength. So, the
285
proposed correlation should assume the form:
286
D emp12 M 2α · x1β V1δ = K (T )· γ · ε T η2 V2
287
being Demp12 the diffusion coefficient at infinite dilution of the solute (1) in the solvent (2) in
288
cm2·s-1, K(T) the constant dependent on the temperature, M2 the molecular weight of the ionic
289
liquid in g·mol-1, η2 the ionic liquid viscosity in cP, x1 the molar fraction of the maximum
290
hydrocarbon solubility in each ionic liquid, V1 the hydrocarbon molar volume in cm3·mol-1,
291
V2 the molar volume of the ionic liquid in cm3·mol-1, and α, β, γ, δ, and ε the exponents of the
292
empirical correlation. The temperature dependent constant of Eq. 4 has dimensions; therefore
293
it is necessary to use the set of units previously defined. This equation was tested with a total
294
of 120 data points at infinite dilution and the algorithm was run by means of the Solver tool of
295
Microsoft Excel spreadsheet software. The constants were established giving the following
296
correlation:
297
D emp12 = (a1 + a2 ·T )·
298
in which a1 and a2 present a different value for each ionic liquid, as shown in Table 4.
x10.08 V10.32 · ·T η20.74 ·M 20.59 V20.20
(4)
(5)
299
The proposed correlation is represented in Fig. 5 (predicted values are shown in Table
300
S1 of the Supplementary Material), along with the experimental data and the predicted
301
diffusion coefficients from the Wilke-Chang correlation (Eq. 3). Eq. 5 predicts the diffusion
302
coefficients within ±9.6% limits for these systems, in which solutes with small molecular
303
volume diffuse through high viscous solvents with large molecular volume and have a
304
remarkable solute-solvent chemical interaction. Moreover, Fig. 6 shows that 95% of the data
305
points fall within the ±30% accuracy lines, while the corresponding percentage for the Wilke12
306
Chang correlation is ±60%. It is interesting to highlight that the effect of the molecular weight
307
of the solvent in Eq. 5 is contrary to that in Eq. 3; this is due to the higher molecular weight of
308
the ionic liquids, compared to the common solvents studied to fit the Wilke-Chang
309
correlation, and evidences the importance of the size of the solvent molecules as an additional
310
variable. Finally, the power of the viscosity is lower than 1 because of the high viscosity of
311
the ionic liquids, compared to common organic solvents.
312
Even so, more {hydrocarbon + ionic liquid} mixtures have to be studied to develop a
313
good correlation which properly predicts the diffusion coefficients in these particular systems.
314 315 316
Table 4 Calculated association parameter, φcalc, for the Wilke-Chang equation, and parameters for the empirical correlation (Eq. 5), a1 and a2. Empirical correlation
Wilke-Chang correlation Ionic liquid
317
φcalc
a1
a2
[emim][SCN]
9.50
-7.64·10-9
3.63·10-6
[emim][DCA]
9.22
a
-2.61·10-9
2.20·10-6
[emim][TCM]
3.18
-6.30·10
-9
3.31·10-6
[bmim][TCM]
5.40
-5.12·10-9
2.83·10-6
[4bmpy][TCM]
4.59
-4.65·10-9
2.61·10-6
[4empy][Tf2N] From reference [11].
1.98a
2.94·10-10
1.25·10-6
a
318
319 320 13
321 322 323 324 325 326
327 328 14
329 330 331 332 333 334
335 336 15
337 338 339 340 341 342 343 344
Fig. 5 Diffusion coefficients of n-heptane (in grey) and toluene (in black) at infinite dilution in: a) [emim][SCN]; b) [emim][DCA] (experimental data from reference [11]); c) [emim][TCM]; d) [bmim][TCM]; e) [4bmpy][TCM], and f) [4empy][Tf2N] (experimental data from reference [11]). Dashed lines represent Wilke-Chang correlation (Eq. 3) and solid lines the proposed empirical correlation (Eq. 5).
345 346 347
Fig. 6 Comparison of experimental diffusion coefficients with coefficients predicted by Eq. 5. 16
348
4 Conclusions
349 350
In this work the diffusion coefficients at infinite dilution of n-heptane and toluene in
351
four ionic liquids, namely [emim][SCN], [emim][TCM], [bmim][TCM], and [4bmpy][TCM],
352
have been measured by means of the Taylor dispersion method at the temperatures of (298.2 –
353
333.2) K. The experimental data, along with the previous results for [emim][DCA] and
354
[4empy][Tf2N] as solvent media, have allowed a more detailed study of the different solvent
355
and solute properties which have an influence on the diffusion coefficients. It has been
356
observed that the n-heptane diffusion coefficient values decrease with an increase in the
357
molecular weight and molar volume of the ionic liquid, but toluene coefficient diffusion
358
values do not follow the same trend. Two opposite behaviors can be distinguished depending
359
on how viscous the ionic liquids are; the most viscous ionic liquids, [bmpy][TCM],
360
[4bmpy][TCM] and [4empy][Tf2N], present the same n-heptane trend meanwhile for the least
361
viscous ionic liquids, [emim][SCN], [emim][DCA], and [emim][TCM], the diffusion
362
coefficient values increase with an increase in the molecular weight and molar volume of the
363
ionic liquid. This different behavior has been attributed to the effect that the toluene-ion
364
strength interaction has on the diffusion coefficients. Therefore, it has been proposed the
365
introduction of the molar fraction of the maximum hydrocarbon solubility in the new
366
empirical correlation, proposed as a variation of the Wilke-Chang equation, to take into
367
account these important interactions. Besides this variable, it has been also introduced the
368
molar volume of the ionic liquid molecules because of the great difference between them and
369
the solute molar volume. The predicted values obtained by the proposed empirical correlation
370
for ionic liquids as the solvent media have been compared to those calculated with the Wilke-
371
Chang correlation, and the former has shown a better fit with an average deviation of 9.6%,
372
compared to the deviation of 14.4% for the latter.
373 374
Nomenclature
375
a
Diffusion capillary tube radius, (m)
376
a1
Parameter in eq. 5, (K-1)
377
a2
Parameter in eq. 5, (-)
378
D12
Diffusion coefficient at infinite dilution of the solute (1) in the solvent (2), (m2·s-1)
379
M2
Molecular weight of the solvent, (g·mol-1)
380
tR
Retention time, (s) 17
381
T
Temperature, (K)
382
V1
Molar volume, (cm3·mol-1)
383
y(t)
Detector signal, (RIU)
384
y1·t
Drift in the detector baseline, (RIU)
385
y∞
Detector baseline, (RIU·s-1)
386
ymax
Peak height relative to baseline, (RIU)
387 388
Greek symbols
389
α
Exponent of the equation 4, (-)
390
β
Exponent of the equation 4, (-)
391
γ
Exponent of the equation 4, (-)
392
δ
Exponent of the equation 4, (-)
393
ε
Exponent of the equation 4, (-)
394
η2
Dynamic viscosity of the solvent, (Pa·s)
395
φ
Association parameter for the solvent in the Wilke-Chang correlation, (-)
396 397 398
Acknowledgments
399
The authors are grateful to Ministerio de Economía y Competitividad (MINECO) of Spain
400
and Comunidad Autónoma de Madrid for the financial support of Projects CTQ2017–85340–
401
R and S2013/MAE-2800, respectively. N.D.M. thanks MINECO for her FPI grant (Reference
402
BES–2015–072855).
403 404
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21
Highlights Developing a new correlation for the aliphatic and aromatic hydrocarbon diffusion coefficients at infinite dilution in ionic liquids. Noemí Delgado-Mellado, Miguel Ayuso, Julián García*, and Francisco Rodríguez. Department of Chemical Engineering, Complutense University of Madrid, E–28040 Madrid, Spain. •
Diffusion coefficients at infinite dilution of n-heptane and toluene are reported.
•
Selected
solvents
are
[emim][SCN],
[emim][TCM],
[bmim][TCM],
and
[4bmpy][TCM]. •
The Taylor dispersion method is the selected technique.
•
The effect of the physicochemical properties on the coefficients is studied.
•
An empirical correlation based on the Wilke-Chan equation is proposed.
*
Corresponding author. Tel.: +34 91 394 51 19; Fax: +34 91 394 42 43. E–mail address: [email protected] (Julián García).
1
S0167-7322(19)33164-2
DOI:
https://doi.org/10.1016/j.molliq.2019.111857
Reference:
MOLLIQ 111857
To appear in:
Journal of Molecular Liquids
Received Date: 4 June 2019 Revised Date:
2 September 2019
Accepted Date: 28 September 2019
Please cite this article as: Noemí. Delgado-Mellado, M. Ayuso, Juliá. García, F. Rodríguez, Developing a new correlation for the aliphatic and aromatic hydrocarbon diffusion coefficients at infinite dilution in ionic liquids, Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/j.molliq.2019.111857. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Developing a new correlation for the aliphatic and aromatic hydrocarbon
2
diffusion coefficients at infinite dilution in ionic liquids.
3
Noemí Delgado-Mellado, Miguel Ayuso, Julián García*, and Francisco Rodríguez.
4
Department of Chemical Engineering, Complutense University of Madrid, E–28040 Madrid,
5
Spain.
6 7 8
Abstract
9 10
In this work the Taylor dispersion technique has been used to measure the diffusion
11
coefficients of n-heptane and toluene at infinite dilution in four ionic liquids, namely 1-ethyl-
12
3-methylimidazolium
13
tricyanomethanide
14
([bmim][TCM]), and 1-butyl-4-methylpyridinium tricyanomethanide ([4bmpy][TCM]), at the
15
range temperatures from (298.2 to 333.2) K. The hydrocarbon diffusion is faster at higher
16
temperatures because of the lower ionic liquid viscosity, and toluene diffuses faster than n-
17
heptane due to its smaller molecular volume. In addition, it is seen that the values of the n-
18
heptane diffusion coefficients decrease with an increase in the molecular weight and molar
19
volume of the ionic liquid. The same is observed for the diffusion coefficients of toluene in
20
the most viscous ionic liquids ([bmim][TCM], [4bmpy][TCM] and [4empy][Tf2N]), but,
21
conversely, they increase for the least viscous ionic liquids ([emim][SCN], [emim][DCA],
22
and [emim][TCM]). This behavior suggests that the strength of the toluene-ionic liquid
23
chemical interactions have a significant effect on diffusion. A new empirical correlation has
24
been proposed as a variation of the Wilke-Chang equation. Two additional variables have
25
been introduced in this correlation; the molar fraction of the maximum hydrocarbon
26
solubility, to take into account the toluene-ionic liquid interactions, as well as the molar
27
volume of the ionic liquid, because of the huge difference between them and the solute. This
28
new correlation satisfactorily fits the experimental data with an average deviation of 9.6%.
thiocyanate ([emim][TCM]),
([emim][SCN]),
1-ethyl-3-methylimidazolium
1-butyl-3-methylimidazolium
tricyanomethanide
29 30
Keywords. Diffusion coefficient; ionic liquids; Taylor dispersion; empirical correlation.
31 32 *
Corresponding author. Tel.: +34 91 394 51 19; Fax: +34 91 394 42 43. E–mail address: [email protected] (Julián García).
1
33
1 Introduction
34 35
The use of the ionic liquids as alternative solvents for several applications has been
36
widely studied for the last two decades. These substances are non-conventional salts which
37
melt at temperatures lower than 100 ºC and present many advantages, such as high stability
38
(chemical, thermal, and electrochemical), non-volatility and negligible vapor pressure, and the
39
possibility of tailoring these properties by selecting the anion and the cation [1,2]. Among all
40
the ionic liquid applications, those with a major interest in the industry are the aromatic
41
separation processes because of the ability of the ionic liquids to preferentially solubilize
42
these hydrocarbons in their mixtures with aliphatics [3,4]. Due to this, a large number of
43
publications focused on this separation has appeared since then, meanwhile, the information
44
related to the molecular diffusion of the hydrocarbons through the ionic liquids is still
45
unavailable. Nowadays, most of the diffusion studies are focused on mutual diffusion
46
coefficients or on ionic liquid diffusion in water or on gas solutes in ionic liquids [5-10], but,
47
to the best of our knowledge, no research has been developed in the field of hydrocarbon
48
diffusion in ionic liquids except for our last published work [11].
49
The determination of the diffusion coefficients has special importance in the
50
prediction of the rate-limiting factor for the chemical processes [12]. In the last decades, many
51
different methods for the measurement of the diffusion coefficients have been used and
52
published in the literature, such as diaphragm cells or porous media [13,14], optical methods
53
[15-17], the total internal reflection fluorescence (TIRF) [18], and the Taylor dispersion
54
technique [19-21]. The latter is widely used because of its high accuracy on the experimental
55
data determination and its easiness to handle [22-25], and it is the selected method in the
56
present work.
57
The diffusion coefficients at infinite dilution of n-heptane and toluene, representing
58
the aromatic and aliphatic content of the pyrolysis and reformer gasolines, the main source of
59
aromatic hydrocarbons in the petrochemical industry [26], in four ionic liquids, namely 1-
60
ethyl-3-methylimidazolium
61
tricyanomethanide
62
([bmim][TCM]), and 1-butyl-4-methylpyridinium tricyanomethanide ([4bmpy][TCM]), have
63
been determined by the Taylor dispersion method for the temperatures ranging from (298.2 to
64
333.2) K. The experimental data have allowed to study the influence of the ionic liquid and
65
hydrocarbon properties, such as viscosity, molecular weight, molar volume, and maximum
66
hydrocarbon solubility, on the diffusion coefficients in order to develop an empirical
thiocyanate
([emim][TCM]),
([emim][SCN]),
1-ethyl-3-methylimidazolium
1-butyl-3-methylimidazolium
tricyanomethanide
2
67
correlation, as a variation of the Wilke-Chang equation, to properly predict the hydrocarbon
68
diffusion through the ionic liquid media. The proposed equation has been compared to the
69
Wilke-Chang correlation, showing an average deviation of ±9.6% the former and ±14.4% the
70
latter.
71 72
2 Experimental
73 74
2.1 Chemicals
75 76
The ionic liquids, namely 1-ethyl-3-methylimidazolium thiocyanate ([emim][SCN]),
77
1-ethyl-3-methylimidazolium
tricyanomethanide
([emim][TCM]),
1-butyl-3-
78
methylimidazolium tricyanomethanide ([bmim][TCM]), and 1-butyl-4-methylpyridinium
79
tricyanomethanide ([4bmpy][TCM]), were supplied by Iolitec GmbH with a mass purity
80
higher than 0.98. Toluene and n-heptane hydrocarbons were supplied by Sigma-Aldrich with
81
a mass purity higher than 0.99. Table 1 shows the compound chemical specifications. All the
82
chemicals were used as received without further purification and the ionic liquids were stored
83
in a desiccator and handled in a glove box under dry nitrogen in order to avoid their hydration
84
since they are hygroscopic substances.
85 86
2.2 Experimental equipment and diffusion coefficient measurement
87 88
The Taylor dispersion technique has been used to measure the hydrocarbon diffusion
89
coefficients at infinite dilution in four ionic liquids. The experimental equipment used to that
90
end is described in our previous work [11]. The ionic liquid is continuously delivered at a
91
constant flow rate of 50 µL/min through a PEEK capillary tubing (10 m length and 0.375·10-3
92
m inner radius) with a Hamilton 1025TLL syringe coupled to a KDS Legato 200 metering
93
pump. The diffusion coefficients were obtained from the concentration gradient signal
94
registered by a Refractive Index Detector Agilent 1260 Infinity II after injecting with a six-
95
port injection valve Agilent G1328 20 µL of the (hydrocarbon + ionic liquid) solution with a
96
solute concentration of (0.020-0.100) ± 0.006 mol·dm-3 in excess into the pure ionic liquid.
97
The sample and reference cells were thermostated at 313.2 K, a higher temperature than the
98
room temperature to reduce the noise in the detector signal. A thermostatic Peltier-cooled
99
incubator Memmert IPP110 with an accuracy of ±0.1 K was used to maintain the temperature
100
range between (298.2 and 333.2 ± 0.1) K. The (hydrocarbon + ionic liquid) solutions were 3
101
gravimetrically prepared in a Mettler Toledo XS 205 balance with a precision of ±1·10−5 g
102
and homogenized in a Labnet Vortex Mixer VX-200.
103 104
Eq. 1 allows the determination of the diffusion coefficients from the changes in the detector signal, y(t): 1/ 2 12· D12 ·(t − t R )2 tR y (t ) = y ∞ + y1·t + y max · ·exp − a 2 ·t t
105
(1)
106
being y∞ the detector baseline, y1·t the expression for the small drifts in the baseline, ymax the
107
peak height relative to the baseline, t the time and tR the retention time in s, a the diffusion
108
tube inner radius in m, and D12 the diffusion coefficient at infinite dilution of the solute (1) in
109
the solvent (2) in m2·s-1. Eq. 1 can be used when the changes in the detector signal are
110
proportional to the solute concentration at the capillary tube outlet [23,27,28].
111 112
Table 1 Compound chemical specifications. Chemical Name
Source
Mass Fraction Purity
Water content in ppm
Halide content in ppm
Analysis Method
n-Heptane
Sigma-Aldrich
>0.995
-
-
GCe
Toluene
Sigma-Aldrich
>0.998
-
-
GCe
[emim][SCN]a
Iolitec GmbH
>0.98
416
<2000
NMRf, ICg, KFh
[emim][TCM]b
Iolitec GmbH
>0.98
976
<500
NMRf, ICg, KFh
[bmim][TCM]c
Iolitec GmbH
>0.98
129
<500
NMRf, ICg, KFh
[4bmpy][TCM]d
Iolitec GmbH
>0.98
129
<500
NMRf, ICg, KFh
113 114 115 116 117 118 119 120 121 122
a
123
3 Results and discussion
[emim][SCN] = 1-ethyl-3-methylimidazolium thiocyanate. [emim][TCM] = 1-ethyl-3-methylimidazolium tricyanomethanide. c [bmim][TCM] = 1-butyl-3-methylimidazolium tricyanomethanide. d [4bmpy][TCM] = 1-butyl-4-methylpyridinium tricyanomethanide. e Gas Chromatography. f Nuclear Magnetic Resonance. g Ion Chromatography. h Karl-Fischer titration. b
124 125
3.1 Diffusion coefficients at infinite dilution
126 127
The hydrocarbon diffusion coefficients at infinite dilution in ionic liquids, D12, were
128
determined for the eight binary systems {n-heptane / toluene + [emim][SCN] / [emim][TCM]
129
/ [bmim][TCM] or [4bmpy][TCM]} at (298.2 – 333.2) K. All the data, collected in Table 2
130
and represented in Fig. 1, are the average of three replicate measurements. As expected,
131
higher temperature enhances the mobility of the solute through the ionic liquid as the
4
132
viscosity of the latter is being decreased. Toluene molecules diffuse faster than n-heptane
133
ones because of the smaller molecular volume, 119 and 146.6 cm3·mol-1, respectively [29]. A
134
great difference between toluene and n-heptane D12 values is observed for the [emim][TCM]
135
ionic liquid. While n-heptane diffusion coefficients are in the same order than those of the rest
136
of the studied ionic liquids, toluene diffusion coefficients present values at least twice higher
137
than in [emim][SCN], [bmim][TCM], and [4bmpy][TCM]. Besides the influence of the ionic
138
liquid viscosity (23.79 mPa·s for [emim][SCN], 15.02 mPa·s for [emim][TCM], 28.30 mPa·s
139
for [bmim][TCM], and 36.70 mPa·s for [4bmpy][TCM] at 298.2 K [30-32]), which clearly
140
benefits the hydrocarbon mobility through [emim][TCM] over the other three ionic liquids, it
141
seems to be another important contribution related to the hydrocarbon-ionic liquid affinity.
142
The maximum toluene solubility in these ionic liquids follows the order: [4bmpy][TCM]
143
(xtol = 0.7417) > [emim][TCM] (xtol = 0.6545) > [bmim][TCM] (xtol = 0.6381) > [emim][SCN]
144
(xtol = 0.2056) [32-34]. By comparing [emim][SCN] and [emim][TCM] ionic liquids, it is
145
seen that the chemical interaction between the solute and solvent, which increases the
146
solubility, has an effect on the solute diffusion as well; both toluene diffusion and toluene
147
solubility in [emim][TCM] are higher than in [emim][SCN]. But the influence of the solute-
148
ionic liquid chemical interactions seems to be present only at lower viscosity values; for more
149
viscous ionic liquids the effect of the similar or higher toluene solubility, e.g. in
150
[bmim][TCM] and [4bmpy][TCM], is counteracted by the high influence of their viscosity.
151 152 153 154
Table 2 Experimental results and standard deviations (∆D12) of diffusion coefficients of nheptane and toluene at infinite dilution in [emim][SCN], [emim][TCM], [bmim][TCM], and [4bmpy][TCM], measured at different temperatures. Ionic liquid [emim][SCN]
[emim][TCM]
[bmim][TCM]
[4bmpy][TCM]
(D12 ± ∆D12)·109 / m2·s-1
Solute 298.2 K
303.2 K
313.2 K
323.2 K
333.2 K
n-Heptane
0.216 ± 0.007
0.264 ± 0.013
0.318 ± 0.019
0.331 ± 0.017
0.394 ± 0.016
Toluene
0.240 ± 0.015
0.290 ± 0.022
0.349 ± 0.027
0.408 ± 0.024
0.459 ± 0.015
n-Heptane
0.205 ± 0.007
0.221 ± 0.009
0.249 ± 0.017
0.332 ± 0.013
0.397 ± 0.016
Toluene
0.516 ± 0.035
0.603 ± 0.028
0.795 ± 0.041
0.839 ± 0.045
0.949 ± 0.061
n-Heptane
0.149 ± 0.006
0.175 ± 0.006
0.245 ± 0.013
0.276 ± 0.010
0.327 ± 0.016
Toluene
0.211 ± 0.008
0.245 ± 0.010
0.340 ± 0.016
0.395 ± 0.013
0.463 ± 0.015
n-Heptane
0.112 ± 0.005
0.133 ± 0.007
0.188 ± 0.012
0.230 ± 0.011
0.272 ± 0.014
Toluene
0.165 ± 0.007
0.191 ± 0.008
0.254 ± 0.012
0.320 ± 0.013
0.395 ± 0.015
155 156 157 158 5
159 160 161
162 163 164 165 166 6
167 168 169
170 171 172 173 174 175
Fig. 1 Diffusion coefficient at infinite dilution of n-heptane (grey symbols) and toluene (black symbols) as function of temperature in: a) [emim][SCN]; b) [emim][TCM]; c) [bmim][TCM]; d) [4bmpy][TCM].
7
176
Different authors have previously studied the relationship between the diffusion
177
coefficients and the viscosity of the solvent (the Stokes-Einstein relation) and determined that
178
there is an inverse dependence [35-38] as:
179
D12 ∝ η2−1 T
180
where η2 is the viscosity of the solvent. When the system is formed by a small solute in a
181
viscous solvent, as the ionic liquid systems studied in this paper, the diffusion coefficient do
182
not vary with the (-1) power of viscosity but with a lower value and around (-2/3) when the
183
solvent viscosity presents the values between 5 and 5000 mPa·s [39]. In Table 3 the power of
184
the viscosity values for the studied ionic liquid systems are collected. It can be seen that the
185
values for the power of the viscosity are close to the (-2/3) value determined by Hiss et al. and
186
that the standard deviation for different solutes in a given ionic liquid is lower than 6.5 %.
(2)
187
The power of viscosity value is dependent of the properties of both solvent and solute,
188
and the deviation from the common systems, widely studied so far, is even more pronounced
189
for the ionic liquids as solvents and small solutes. Therefore, it seems important to deeply
190
study the effect of their properties, apart from the interactions between the ionic liquid and the
191
solute on the diffusion coefficients for these systems.
192 193 194
Table 3 Power of viscosity values for the relation between the diffusion coefficients and the viscosity of the ionic liquids for the Stokes-Einstein relation. Ionic liquid [emim][SCN]
[emim][TCM] [bmim][TCM]
[4bmpy][TCM]
Solute
Power of viscosity
n-Heptane
-0.47
Toluene
-0.55
n-Heptane
-0.62
Toluene
-0.53
n-Heptane
-0.61
Toluene
-0.61
n-Heptane
-0.64
Toluene
-0.62
195 196
3.2 Influence of the physicochemical properties on the hydrocarbon diffusion coefficients
197 198
The influence of some properties of the ionic liquid, such as viscosity, molecular
199
weight, and molar volume, have been studied to search for a satisfactory empirical correlation
200
applicable to hydrocarbon diffusion through ionic liquids. The ratio D12/T for each {n-heptane
201
/ toluene (1) + [emim][SCN] / [emim][DCA] / [emim][TCM] / [bmim][TCM] / 8
202
[4bmpy][TCM] or [4empy][Tf2N] (2)} system is represented against the previous properties
203
in Figs. 2-4. In this Figs., experimental data for [emim][DCA] and [4empy][Tf2N] ionic
204
liquids have been taken from our previous work [11].
205
In Fig. 2 it is seen that the ionic liquid viscosity has a similar effect on n-heptane and
206
toluene diffusion coefficients; the higher the ionic liquid viscosity, the slower the diffusion. A
207
remarkable behavior can be observed for toluene diffusion through [emim][DCA] and
208
[emim][TCM], in which the value of the diffusion coefficients is much higher than in the rest
209
of ionic liquids and the increase of viscosity leads to a more pronounced decrease in the
210
diffusion coefficients. The decrease in the diffusion coefficients is also observed in Fig. 3 and
211
4 for n-heptane but not for toluene. On one hand and related to the n-heptane diffusion, an
212
increase in the molecular weight of the ionic liquid, Fig. 3, and in the molar volume of the
213
ionic liquid, Fig. 4, makes the n-heptane diffusion difficult; as the molecules of the solvent
214
become larger, the diffusion of the solute molecules is slower due to steric hindrance. But on
215
the other hand, toluene diffusion coefficients show two different trends regarding the ionic
216
liquid viscosity. Comparing the diffusion coefficients in [emim]-based ionic liquids, it is seen
217
that an increase in the number of cyano groups attached to the anion leads to higher diffusion
218
coefficients, and an increase in the molecular weight and molecular volume of the ionic liquid
219
does not negatively affect the toluene diffusion. It is important to highlight that the viscosities
220
of the [emim][TCM] and [emim][DCA] (the latter 15.1 mPa·s at 298.2 K [40]) are the lowest
221
of the studied ionic liquids, and it seems that the toluene-ion interaction strength plays an
222
important role in both of them. But the higher the ionic liquid viscosity, the lower the effect of
223
the toluene-ion interaction strength on the diffusion coefficients, as can be inferred by
224
comparing the toluene diffusion coefficient values in [4bmpy][TCM] and [4empy][Tf2N]
225
(which have the highest toluene solubility and the highest viscosity as well) with those in
226
[emim][DCA] and [emim][TCM] (both of them with lower values of maximum toluene
227
solubility but also with a lower viscosity). Based on that, it can be reasonably thought that a
228
parameter related to the solute-ionic liquid interaction strength should be included in the
229
empirical correlation to properly predict the hydrocarbon diffusion coefficients through the
230
ionic liquid media. One main reason that the properties of the ionic liquids are different from
231
the common solvents is their nanoscale ordering; ionic liquids are composed of ions, and this
232
leads to experience interionic interactions and long-lived associations which are not present in
233
the common solvents [41].
234 235 9
236 237 238 239 240 241 242 243 244
245 246 247 248 249 250
Fig. 2 Effect of the ionic liquid viscosity on the diffusion coefficients at infinite dilution of nheptane (a) and toluene (b) at different temperatures. Viscosity values from literature [3032,40].
Fig. 3 Effect of the molecular weight of the ionic liquid on the diffusion coefficients at infinite dilution of n-heptane (a) and toluene (b) at different temperatures.
10
251 252 253 254 255 256 257
Fig. 4 Effect of the molar volume of the ionic liquid on the diffusion coefficients at infinite dilution of n-heptane (a) and toluene (b) at different temperatures.
3.3 Empirical correlation for ionic liquids
258 259
A new empirical correlation to predict the hydrocarbon diffusion through the ionic
260
liquids is proposed as a variation of the Wilke-Chang equation [42] and is based on the
261
hydrocarbon diffusion data and the previous study of the influence of different properties on
262
these coefficients. The goodness of this new correlation has been compared to the Wilke-
263
Chang correlation, the most used one to predict diffusion coefficients: W
= 7.4·10
−8
(φ · M 2 ) ·
0.5
·T
264
D
265
where DW12 is the diffusion coefficient at infinite dilution of the solute (1) in the solvent (2) in
266
cm2·s-1, φ is the association parameter, M2 the solvent molecular weight in g·mol-1, T the
267
temperature in K, η2 the solvent viscosity in cP, and V1 the solute molar volume in cm3·mol-1.
268
The association parameter in the Wilke-Chang correlation has not been widely studied for
269
ionic liquids so it has been determined for all the {hydrocarbon + ionic liquid} systems in the
270
present work. Table 4 shows the values for this association parameter and the predictions of
271
the Wilke-Chang correlation are represented in Fig. 5 and collected in Table S1 of the
272
Supplementary Material. As previously reported [11], the Wilke-Chang correlation does not
273
properly predict the hydrocarbon diffusion in ionic liquids, showing an average deviation of
274
14.4% and a tendency to underestimate the diffusion coefficients at low temperature and
12
η 2 ·V
0.6 1
(3)
11
275
overestimate them at high temperature. Therefore, the association parameter seems to be a
276
nonconstant value influenced by the temperature in ionic liquids. This behavior has not only
277
been observed in these systems but in other ones with ionic liquids as solvents and a great
278
difference between the size of the solute and the solvent molecules [43].
279
The new proposed empirical correlation is an attempt to adapt the Wilke-Chang
280
equation to the studied systems; in which the temperature has an influence on the association
281
parameter and there is a remarkable size difference between the hydrocarbon and the ionic
282
liquid molecules. Besides this, and based on the faster toluene diffusion through
283
[emim][TCM], it seems necessary to introduce in the correlation the maximum hydrocarbon
284
solubility in order to take into consideration the solute-solvent interaction strength. So, the
285
proposed correlation should assume the form:
286
D emp12 M 2α · x1β V1δ = K (T )· γ · ε T η2 V2
287
being Demp12 the diffusion coefficient at infinite dilution of the solute (1) in the solvent (2) in
288
cm2·s-1, K(T) the constant dependent on the temperature, M2 the molecular weight of the ionic
289
liquid in g·mol-1, η2 the ionic liquid viscosity in cP, x1 the molar fraction of the maximum
290
hydrocarbon solubility in each ionic liquid, V1 the hydrocarbon molar volume in cm3·mol-1,
291
V2 the molar volume of the ionic liquid in cm3·mol-1, and α, β, γ, δ, and ε the exponents of the
292
empirical correlation. The temperature dependent constant of Eq. 4 has dimensions; therefore
293
it is necessary to use the set of units previously defined. This equation was tested with a total
294
of 120 data points at infinite dilution and the algorithm was run by means of the Solver tool of
295
Microsoft Excel spreadsheet software. The constants were established giving the following
296
correlation:
297
D emp12 = (a1 + a2 ·T )·
298
in which a1 and a2 present a different value for each ionic liquid, as shown in Table 4.
x10.08 V10.32 · ·T η20.74 ·M 20.59 V20.20
(4)
(5)
299
The proposed correlation is represented in Fig. 5 (predicted values are shown in Table
300
S1 of the Supplementary Material), along with the experimental data and the predicted
301
diffusion coefficients from the Wilke-Chang correlation (Eq. 3). Eq. 5 predicts the diffusion
302
coefficients within ±9.6% limits for these systems, in which solutes with small molecular
303
volume diffuse through high viscous solvents with large molecular volume and have a
304
remarkable solute-solvent chemical interaction. Moreover, Fig. 6 shows that 95% of the data
305
points fall within the ±30% accuracy lines, while the corresponding percentage for the Wilke12
306
Chang correlation is ±60%. It is interesting to highlight that the effect of the molecular weight
307
of the solvent in Eq. 5 is contrary to that in Eq. 3; this is due to the higher molecular weight of
308
the ionic liquids, compared to the common solvents studied to fit the Wilke-Chang
309
correlation, and evidences the importance of the size of the solvent molecules as an additional
310
variable. Finally, the power of the viscosity is lower than 1 because of the high viscosity of
311
the ionic liquids, compared to common organic solvents.
312
Even so, more {hydrocarbon + ionic liquid} mixtures have to be studied to develop a
313
good correlation which properly predicts the diffusion coefficients in these particular systems.
314 315 316
Table 4 Calculated association parameter, φcalc, for the Wilke-Chang equation, and parameters for the empirical correlation (Eq. 5), a1 and a2. Empirical correlation
Wilke-Chang correlation Ionic liquid
317
φcalc
a1
a2
[emim][SCN]
9.50
-7.64·10-9
3.63·10-6
[emim][DCA]
9.22
a
-2.61·10-9
2.20·10-6
[emim][TCM]
3.18
-6.30·10
-9
3.31·10-6
[bmim][TCM]
5.40
-5.12·10-9
2.83·10-6
[4bmpy][TCM]
4.59
-4.65·10-9
2.61·10-6
[4empy][Tf2N] From reference [11].
1.98a
2.94·10-10
1.25·10-6
a
318
319 320 13
321 322 323 324 325 326
327 328 14
329 330 331 332 333 334
335 336 15
337 338 339 340 341 342 343 344
Fig. 5 Diffusion coefficients of n-heptane (in grey) and toluene (in black) at infinite dilution in: a) [emim][SCN]; b) [emim][DCA] (experimental data from reference [11]); c) [emim][TCM]; d) [bmim][TCM]; e) [4bmpy][TCM], and f) [4empy][Tf2N] (experimental data from reference [11]). Dashed lines represent Wilke-Chang correlation (Eq. 3) and solid lines the proposed empirical correlation (Eq. 5).
345 346 347
Fig. 6 Comparison of experimental diffusion coefficients with coefficients predicted by Eq. 5. 16
348
4 Conclusions
349 350
In this work the diffusion coefficients at infinite dilution of n-heptane and toluene in
351
four ionic liquids, namely [emim][SCN], [emim][TCM], [bmim][TCM], and [4bmpy][TCM],
352
have been measured by means of the Taylor dispersion method at the temperatures of (298.2 –
353
333.2) K. The experimental data, along with the previous results for [emim][DCA] and
354
[4empy][Tf2N] as solvent media, have allowed a more detailed study of the different solvent
355
and solute properties which have an influence on the diffusion coefficients. It has been
356
observed that the n-heptane diffusion coefficient values decrease with an increase in the
357
molecular weight and molar volume of the ionic liquid, but toluene coefficient diffusion
358
values do not follow the same trend. Two opposite behaviors can be distinguished depending
359
on how viscous the ionic liquids are; the most viscous ionic liquids, [bmpy][TCM],
360
[4bmpy][TCM] and [4empy][Tf2N], present the same n-heptane trend meanwhile for the least
361
viscous ionic liquids, [emim][SCN], [emim][DCA], and [emim][TCM], the diffusion
362
coefficient values increase with an increase in the molecular weight and molar volume of the
363
ionic liquid. This different behavior has been attributed to the effect that the toluene-ion
364
strength interaction has on the diffusion coefficients. Therefore, it has been proposed the
365
introduction of the molar fraction of the maximum hydrocarbon solubility in the new
366
empirical correlation, proposed as a variation of the Wilke-Chang equation, to take into
367
account these important interactions. Besides this variable, it has been also introduced the
368
molar volume of the ionic liquid molecules because of the great difference between them and
369
the solute molar volume. The predicted values obtained by the proposed empirical correlation
370
for ionic liquids as the solvent media have been compared to those calculated with the Wilke-
371
Chang correlation, and the former has shown a better fit with an average deviation of 9.6%,
372
compared to the deviation of 14.4% for the latter.
373 374
Nomenclature
375
a
Diffusion capillary tube radius, (m)
376
a1
Parameter in eq. 5, (K-1)
377
a2
Parameter in eq. 5, (-)
378
D12
Diffusion coefficient at infinite dilution of the solute (1) in the solvent (2), (m2·s-1)
379
M2
Molecular weight of the solvent, (g·mol-1)
380
tR
Retention time, (s) 17
381
T
Temperature, (K)
382
V1
Molar volume, (cm3·mol-1)
383
y(t)
Detector signal, (RIU)
384
y1·t
Drift in the detector baseline, (RIU)
385
y∞
Detector baseline, (RIU·s-1)
386
ymax
Peak height relative to baseline, (RIU)
387 388
Greek symbols
389
α
Exponent of the equation 4, (-)
390
β
Exponent of the equation 4, (-)
391
γ
Exponent of the equation 4, (-)
392
δ
Exponent of the equation 4, (-)
393
ε
Exponent of the equation 4, (-)
394
η2
Dynamic viscosity of the solvent, (Pa·s)
395
φ
Association parameter for the solvent in the Wilke-Chang correlation, (-)
396 397 398
Acknowledgments
399
The authors are grateful to Ministerio de Economía y Competitividad (MINECO) of Spain
400
and Comunidad Autónoma de Madrid for the financial support of Projects CTQ2017–85340–
401
R and S2013/MAE-2800, respectively. N.D.M. thanks MINECO for her FPI grant (Reference
402
BES–2015–072855).
403 404
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Highlights Developing a new correlation for the aliphatic and aromatic hydrocarbon diffusion coefficients at infinite dilution in ionic liquids. Noemí Delgado-Mellado, Miguel Ayuso, Julián García*, and Francisco Rodríguez. Department of Chemical Engineering, Complutense University of Madrid, E–28040 Madrid, Spain. •
Diffusion coefficients at infinite dilution of n-heptane and toluene are reported.
•
Selected
solvents
are
[emim][SCN],
[emim][TCM],
[bmim][TCM],
and
[4bmpy][TCM]. •
The Taylor dispersion method is the selected technique.
•
The effect of the physicochemical properties on the coefficients is studied.
•
An empirical correlation based on the Wilke-Chan equation is proposed.
*
Corresponding author. Tel.: +34 91 394 51 19; Fax: +34 91 394 42 43. E–mail address: [email protected] (Julián García).
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