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Speeds of sound and isentropic compressibilities of (2-ethoxyethanol + ethylene glycol, diethylene glycol, triethylene glycol, and tetraethylene glycol) binary mixtures at 298.15 K
Journal of Molecular Liquids 149 (2009) 81–85
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Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m o l l i q
Speeds of sound and isentropic compressibilities of (2-ethoxyethanol + ethylene glycol, diethylene glycol, triethylene glycol, and tetraethylene glycol) binary mixtures at 298.15 K Cezary M. Kinart a,⁎, Piotr Miecznik b, Magdalena Klimczak a a b
Department of Physical Chemistry of Liquids, University of Łódź, 90-236 Łódź, Pomorska 163, Poland Institute of Acoustics, Adam Mickiewicz University, 61 Poznań, Umultowska 85, Poland
a r t i c l e
i n f o
Article history: Received 21 July 2009 Received in revised form 16 August 2009 Accepted 18 August 2009 Available online 23 August 2009 Keywords: 2-Ethoxyethanol Ethylene glycol Diethylene glycol Triethylene glycol Tetraethylene glycol Speed of sound Isentropic compressibility
a b s t r a c t The speed of sound (u) has been obtained at a frequency of 8.3 MHz in {CH3CH2OCH2CH2OH + HOCH2CH2 (OCH2CH2)nOH}for n = 0, 1, 2, and 3 over the whole composition range of studied binary liquid mixtures, at T = 298.15 K. The speed of sound values were combined with those of our previous results for densities and viscosities to obtain isentropic compressibility (κs), free volume (Vf), and intermolecular free length (Lf). From all these data excess isentropic compressibility (κ Es ), excess free volume (V Ef ) and excess intermolecular free length (LEf ) as well as the deviations of the speed of sound (Δu) were obtained. The results are interpreted in terms of molecular interactions occurring in the solutions. © 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
We have previously reported the density [1] and viscosity [2] of {2-ethoxyethanol (EE) + ethylene glycol (EG), 2-ethoxyethanol + diethylene glycol (DEG), 2-ethoxyethanol + triethylene glycol (TEG), and 2-ethoxyethanol + tetraethylene glycol (TETRAEG)} binary mixtures at 298.15 K. In a continuing effort to collect other physicochemical and thermodynamic quantities for studied mixtures we present in this paper measured values of the speeds of sound at T = 298.15 K, and atmospheric pressure. In order to throw more light on interaction of 2-ethoxyethanol with ethylene glycol and its oligomers, we have undertaken a detailed study of excesses isentropic compressibility (κ Es ), free volume (V Ef ), and intermolecular free length (LEf ) as well as the deviation of the speeds of sound (Δu). These structural parameters are very sensitive to interactions between solute and solvent. The studied solvents have found a wide variety of applications in the petroleum, cosmetics, textile, pharmaceutical, and the other industries [3–5]. Therefore, the study of intermolecular interactions in 2-ethoxyethanol + ethylene glycol mixtures would be interesting owing to their industrial applications.
2.1. Materials The pure components were supplied by Sigma-Aldrich and Fluka. The chemicals, viz., 2-ethoxyethanol, ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol, used in the study were purified by using the methods described in the literature [1,2,6]. The mass fraction purities as determined by gas chromatography are: 2-butoxyethanol > 0.998, ethylene glycol > 0.994, diethylene glycol > 0.996, triethylene glycol > 0.996, and tetraethylene glycol > 0.998. The mixtures were prepared using a Sartorius balance. Conversion to molar quantities was based on the relative atomic mass table of 1985, issued by IUPAC in 1986. The maximum estimated error in the mole fractions is ±1 · 10− 4. Liquids were stored in dry-box over phosphorus pentoxide and degassed by ultrasound just before the experiment. Experimental speeds of sound for the pure solvents, at T = 298.15 K, are compared with values available in the literature and listed in Table 1.
2.2. Measurements
⁎ Corresponding author. E-mail address: [email protected] (C.M. Kinart). 0167-7322/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2009.08.006
The speed of sound was measured by resonance method using the ResoScan™ System (Germany) apparatus. The speed of sound is determined from series of resonance frequencies of the resonator calls
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C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
Table 1 Observed and literature values of speed of sound of pure liquid components, at T = 298.15 K. u m:s − 1
Solvent
This work 2-Ethoxyethanol
1302.012
Ethylene glycol
1654.344
Lit. 1302.5 1300.4 1301.7 1656.9
[7] [8] [9] [10]
1654.89 [11] 1659 [12] 1577 [12] Diethylene glycol
1579.003 1579.34 [10] 1610 [12]
Triethylene glycol
1608.725
Tetraethylene glycol
1597.865
1611.31 [10] –
and also from waviness due to multiple reflections in the signal transmitted through the path length cell [13]. The operating frequency of the transducers was 8.3 MHz. The relative error of the measured speed of sound was lower than 1 ∙ 10− 5 over the entire range of concentration. The temperature of the samples was controlled to within ±0.005 K by Peltier thermostat and it was measured to accuracy of ±0.01 K. 3. Results and discussion The experimental speeds of sound (u) obtained from the measurements of the pure solvents and for the binary mixtures, at T = 298.15 K, are summarized in Table 2. The variations of speeds of sound as a function of volume fraction of EE (φ1) were fitted to a polynomial of type [14,15]: uðφ1 Þ =
4 X
j
α j · φ1 ;
ð1Þ
j=0
by the method of least-squares with each point weighted equally. The values of coefficients αj and standard deviations σ(u) are summarized in Table 3. The deviations in speed of sound (Δu) from a linear dependence on the average volume fraction (φi) have been calculated from the relationship [16]: Δu = u −
2 X
ui · φi ;
ð2Þ
i=1
where u1, u2, and u are the speeds of sound of the EE, ethylene glycols and the mixtures, and φi is the volume fraction of component i. The values of Δu calculated by using Eq. (2) are listed in Table 2. Isentropic compressibility coefficients, κs, are calculated from the relation [16]: 2 −1 κ s = ρ·u :
ð3Þ
The densities ρ required to calculate isentropic compressibilities were taken from our previous paper [1]. The excesses of isentropic compressibility (κ Es ) were calculated from the relation [16,17]: E
ideal
κs = κs − κs
¼κ s −
2 X i=1
0
κ s;i · φi
ð4Þ
Table 2 Ultrasonic speed (u), isentropic compressibility (κs), deviation of the speed of sound (Δu), and excesses isentropic compressibility (κ Es ) for 2-ethoxyethanol + ethylene glycols mixtures, at 298.15 K. x1
φ1
u m: s − 1
Δu m: s − 1
κ s :1012 Pa − 1
κ Es :1012 Pa − 1
EE + EG 0.0000 0.1000 0.2996 0.4005 0.4515 0.5003 0.5502 0.5998 0.6998 0.8005 0.8995 1.0000
0.0000 0.1639 0.4367 0.5513 0.6041 0.6516 0.6973 0.7399 0.8182 0.8875 0.9472 1.0000
1654.344 1594.589 1495.558 1454.525 1435.783 1419.060 1403.136 1388.367 1361.612 1338.412 1318.936 1302.012
0.000 − 2.008 − 4.923 − 5.578 − 5.717 − 5.704 − 5.527 − 5.287 − 4.454 − 3.237 − 1.679 0.000
329.18 362.68 428.77 461.36 477.58 492.90 508.37 523.56 553.55 582.82 610.49 637.61
0.00 − 15.95 − 31.10 − 32.69 − 32.32 − 31.35 − 29.84 − 27.81 − 22.46 − 15.74 − 8.29 0.00
EE + DEG 0.0000 0.0998 0.2300 0.3004 0.4007 0.4492 0.4998 0.5485 0.5996 0.7003 0.8009 0.9001 1.0000
0.0000 0.1017 0.2340 0.3051 0.4063 0.4550 0.5056 0.5544 0.6053 0.7054 0.8048 0.9024 1.0000
1579.003 1548.358 1509.185 1488.212 1459.047 1445.239 1431.958 1417.399 1403.399 1376.430 1350.467 1325.658 1302.012
0.000 − 2.475 − 5.002 − 6.281 − 7.415 − 7.733 − 7.998 − 8.040 − 7.941 − 7.184 − 5.614 − 3.388 0.000
360.35 379.95 408.22 427.00 451.91 465.16 478.94 492.51 507.53 538.04 570.40 604.45 637.58
0.00 − 10.77 − 24.83 − 28.52 − 28.94 − 26.93 − 23.74 − 19.58 − 15.55 − 8.78 − 3.28 − 2.03 0.00
EE + TEG 0.0000 0.1021 0.2031 0.2999 0.3996 0.4502 0.5000 0.5476 0.5998 0.6993 0.7997 0.8980 1.0000
0.0000 0.0756 0.1799 0.2390 0.3275 0.3720 0.4198 0.4675 0.5190 0.6262 0.7414 0.8647 1.0000
1608.725 1584.083 1551.017 1531.784 1503.106 1488.420 1472.815 1457.595 1441.278 1408.622 1374.931 1339.683 1302.012
0.000 − 1.454 − 2.530 − 3.637 − 5.170 − 6.208 − 7.152 − 7.742 − 8.263 − 8.039 − 6.397 − 3.827 0.000
345.10 360.32 377.36 395.81 417.47 429.60 442.38 455.45 470.71 503.42 541.34 584.71 637.61
0.00 − 6.89 − 15.36 − 19.20 − 23.43 − 24.31 − 25.51 − 26.36 − 26.21 − 24.85 − 20.63 − 13.32 0.00
EE + TETRAEG 0.0000 0.1003 0.2038 0.3007 0.4009 0.4515 0.5005 0.5499 0.5982 0.6991 0.7986 0.9003 1.0000
0.0000 0.0593 0.1441 0.1940 0.2711 0.3112 0.3553 0.4003 0.4502 0.5589 0.6837 0.8276 1.0000
1597.865 1579.059 1552.536 1536.313 1511.765 1498.765 1485.024 1470.725 1455.149 1422.739 1386.558 1345.869 1302.012
0.000 − 1.262 − 2.697 − 4.157 − 5.894 − 7.031 − 7.724 − 8.710 − 9.523 − 9.774 − 9.032 − 7.148 0.000
349.65 361.49 375.48 390.60 408.90 419.35 430.36 442.54 455.66 487.46 526.16 575.67 637.61
0.00 − 5.23 − 11.66 − 14.91 − 18.82 − 19.91 − 21.60 − 22.38 − 23.63 − 23.13 − 20.37 − 12.29 0.00
where κ 0s,i is the isentropic compressibility of the pure component i, and φi is the volume fraction of component i. The values of κs and κ Es calculated by using Eq. (3) and Eq. (4) are listed in Table 2. The free volume (Vf) of a binary mixture is calculated from the relation [16]: Vf = ½M · u·K ·η
3=2
ð5Þ
where M, and η are the molar mass and viscosity of the mixture, respectively and K is a dimensionless constant having value of
C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
The corresponding excesses of free volume (V Ef ) were calculated from the relation [16,18]:
Table 3 Coefficients αi and standard deviation σ(u) of Eq. (1) for {EE (1) + EG (2), EE (1) + DEG (2), EE (1) + TEG (2), and EE (1) + TETRAEG (2)} binary mixtures, at T 298.15 K. α0 · 10− 2 EE + EG 16.5435
α1 · 10− 2
α2 · 10− 2
α3 · 10− 2
α4 · 10− 2
83
oðuÞ m:s − 1
E
Vf = Vf −
2 X
ð6Þ
Vf;i · xi
i=1
− 3.6480
0.0015
0.0140
0.1092
0.02
EE + DEG 15.7903
− 3.0488
0.2787
− 0.1293
0.1292
0.29
EE + TEG 16.0841
− 3.0804
− 0.8747
1.5038
− 0.6121
0.30
where Vf,i is the free volume of the pure component i, Vf is the free volume of the mixture, and xi is the mole fraction of component i. The excesses of intermolecular free length (LEf ) were calculated from the relation [16,18]: E
EE + TETRAEG 15.9789 − 3.1301
− 0.3829
− 07924
− 0.2391
Lf = Lf − 0.30
2 X
ð7Þ
xi · Lf;i
i=1
where: 9
4.28 ∙ 10 , independent of temperature and the nature of the liquid system. The viscosities η required to calculate free volumes were taken from our previous paper [2].
Lf = K = u · ρ
1=2
K = ð93:875 + 0:375 · T Þ · 10
−8
K — is a temperature dependence constant [19].
Table 4 Coefficients ai and standard deviation σ(Δu, κEs , VEf and LEf ) of Eq. (8) and (9) for {EE (1) + EG (2), EE (1) + DEG (2), EE (1) + TEG (2), and EE (1) + TETRAEG (2)} binary mixtures, at T 298.15 K. EE + EG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
oðΔuÞ m:s − 1
a0
a1
a2
a3
a4
− 21.7141 a0 ∙ 106
− 10.2088 a1 ∙ 106
− 1.1292 a2 ∙ 106
0.4358 a3 ∙ 106
2.4604 a4 ∙ 106
− 130.1225 a0 ∙ 104
− 18.2946 a1 ∙ 104
− 0.2557 a2 ∙ 104
2.6321 a3 ∙ 104
0.6341 a4 ∙ 104
− 11.4315 a0
− 3.8833 a1
3.5531 a2
4.0813 a3
− 1.6697 a4
oðLEf Þ
0.0396
− 0.0033
0.0016
0.0018
− 0.0032
0.00002
0.018
σ ðκ Es Þ:1012 Pa − 1
0.018
σ ðVfE Þ:104 m3
0.013 o
A
EE + DEG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
oðΔuÞ m:s − 1
a0
a1
a2
a3
a4
− 31.9292 a0 ∙ 106
− 6.2310 a1 ∙ 106
1.6780 a2 ∙ 106
− 1.3028 a3 ∙ 106
− 4.1600 a4 ∙ 106
− 96.0436 a0 ∙ 104
138.1173 a1 ∙ 104
48.9436 a2 ∙ 104
− 122.3757 a3 ∙ 104
− 11.5377 a4 ∙ 104
− 23.7458 a0
− 20.4372 a1
− 8.9395 a2
18.1591 a3
24.834 a4
oðLEf Þ
− 0.0226
0.0005
− 0.0003
0.0007
− 0.0029
0.00005
oðΔuÞ m:s − 1
0.041
σ ðκ Es Þ:1012 Pa − 1
0.026
σ ðVfE Þ:104 m3
0.041 o
A
EE + TEG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
a0
a1
a2
a3
a4
− 32.4541 a0 ∙ 106
− 16.1257 a1 ∙ 106
32.7804 a2 ∙ 106
10.9846 a3 ∙ 106
− 36.0957 a4 ∙ 106
− 105.0206 a0 ∙ 104
0.2730 a1 ∙ 104
− 9.3558 a2 ∙ 104
− 14.3947 a3 ∙ 104
7.1925 a4 ∙ 104
− 23.7458 a0
− 20.4372 a1
− 8.9395 a2
18.1591 a3
24.8340 a4
oðLEf Þ
− 0.0699
− 0.0137
− 0.0049
− 0.0086
0.0027
0.00008
0.065
σ ðκ Es Þ:1012 Pa − 1
0.161
σ ðVfE Þ:104 m3
0.041 o
A
EE + TETRAEG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
a0
a1
a2
a3
a4
oðΔuÞ m: s − 1
− 39.0940 a0 ∙ 106
− 9.1268 a1 ∙ 106
20.0072 a2 ∙ 106
− 24.2450 a3 ∙ 106
− 37.1468 a4 ∙ 106
σ ðκ Es Þ:1012
− 94.3034 a0 ∙ 104
− 2.5318 a1 ∙ 104
− 1.0405 a2 ∙ 104
21.4051 a3 ∙ 104
22.6243 a4 ∙ 104
− 32.3884 a0
− 28.6779 a1
− 4.6806 a2
20.4537 a3
15.6538 a4
oðLEf Þ
− 0.0974
− 0.0335
− 0.0100
− 0.0052
− 0.0019
0.00010
0.14
Pa − 1
0.23
σ ðVfE Þ:104 m3
0.10 o
A
84
C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
Fig. 1. Plot of the deviation of the speed of sound (Δu) against volume fraction EE (j1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
Fig. 3. Plot of the excess free volume (V Ef ) against mole fraction EE (x1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
The standard deviation values were obtained from:
κ Es ,
V Ef ,
LEf
j
E where F = Δu and κ s
For each mixture, the values Δu, and were smoothed to a Redlich–Kister polynomial regression of the type: F = φ1 · ð1 − φ1 Þ
4 X
aj · ð2φ1 −1Þ
ð8Þ
j=0
G = x1 · ð1 − x1 Þ
4 X
j
aj · ð2x1 −1Þ
E E where G = Vf and Lf :
ð9Þ
j=0
The parameters aj in Eqs. (8) and (9) were evaluated by the leastsquares method. The values of these parameters with standard deviation σ(Δu, κ Es , V Ef , and LEf ), are summarized in Table 4. The plots of these functions are presented in Figs. 1–4.
2P
6 σ =4
Xexptl −Xcalcd N −p
2 31 = 2 7 5
;
ð10Þ
where: N is the number of experimental points, p is the number of parameters, Xexptl and Xcalcd are the experimental and calculated properties, respectively. The values of κEs are negative over the entire composition range for all studied mixtures (see Fig. 2). These values become less negative as the chain length of the glycol molecules (the number of oxyethylene groups OCH2CH2 in the glycol) increases in the following order: E
E
E
κ min ðEE + TETRAEGÞ < κ min ðEE + TEGÞ < κ min ðEE + DEGÞ <
E κ min ðEE
+ EGÞ
The values Δu are showing a similar trend as observed in κ Es (are always negative) but these values become more negative as the chain length of the glycol molecules increases as shown in Fig. 1.
Fig. 2. Plot of the excess isentropic compressibility (κEs ) against volume fraction EE (φ1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
Fig. 4. Plot of the excess intermolecular free length (LEf ) against mole fraction EE (x1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
The literature review shows, that the deviations of analyzed function provide experimental evidence for the formation of intermolecular complexes, and provide a valuable aid for determining their stoichiometry and relative stability [16–18]. In general, negative κ Es and Δu values indicate the presence of strong intermolecular bonding between the components in the binary mixtures [7–12,16–21]. Ethoxyethanols and the oligomers of ethylene glycol are a very interesting class of solvents, due to the presence of the oxy and hydroxyl groups in the same molecule, which allow self-association via intra- and intermolecular hydrogen bonds. The formation of intramolecular hydrogen bonds in ethoxyethanols is more favourable when the molecules of these solvents are in the gauche conformations. For these molecules 5-, 6-, 7- and 8-membered rings, of quite different properties, are formed [22–29]. In our opinion, in the case of the present binary mixtures at least four different effects can be identified which contribute to Δu and κ Es values: (1) the breaking of homogeneous liquid order on mixing; (2) favorable interactions between polar groups (OH and O) of unlike molecules; (3) unfavorable hydrophobic interactions between OH groups of ethylene glycols and CH2 groups of alkyl chains of EE molecules and (4) geometrical fitting of one component into the other due to differences in the molar volumes and free volume between unlike molecules. This last effect should be significant and of great importance for (EE + TETRAEG) binary mixtures. The presented behaviors of κ Es and Δu are consistent with that of excess molar volume (V E) for {2-ethoxyethanol (EE) + ethylene glycol (EG), 2-ethoxyethanol + diethylene glycol (DEG), 2-ethoxyethanol + triethylene glycol (TEG), and 2-ethoxyethanol + tetraethylene glycol (TETRAEG)} binary mixtures [1]. The values of V E are negative over the entire composition range for all studied mixtures and decrease from EG to TETRAEG. The EE + TETRAEG mixture corresponds to the densest and most packed mixed solvent. Taking into account the literature information concerning the basicity (SB) and acidity (SA) of pure EE and ethylene glycols it seems necessary to assume that the OH group of glycol is the proton donor and the oxygen atom of ether from the molecule of EE is its acceptor [30–33]. Fig. 3 shows that the excess free volume (V Ef ) in the studied binary mixtures becomes more negative when κ Es and Δu decrease. The plot of this function indicates that the excess free volume created in the mixture is not available for the compression. This means that interstitial accommodation plays an important role by influencing the κ Es and Δu of the liquid mixtures containing EE with ethylene glycols. It also indicates that the molecular size and shape of the components are equally important factors in these mixtures. The course of changes LEf also confirms these conclusions (see Fig. 4), because LEf is generally more negative when the structure has high rigidity and it corresponds to the densest and most packed mixed solvent.
85
4. Conclusions In this paper, the speeds of sound were measured at T = 298.15 K over the entire range of composition for binary mixtures of 2ethoxyethanol with ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol. Various calculated excess properties and deviations (κEs , VEf , LEf and Δu) support that there may be intermolecular hydrogen bonding between the components of studied binary solvents and that the interstitial accommodation also plays an important role in these mixtures.
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Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m o l l i q
Speeds of sound and isentropic compressibilities of (2-ethoxyethanol + ethylene glycol, diethylene glycol, triethylene glycol, and tetraethylene glycol) binary mixtures at 298.15 K Cezary M. Kinart a,⁎, Piotr Miecznik b, Magdalena Klimczak a a b
Department of Physical Chemistry of Liquids, University of Łódź, 90-236 Łódź, Pomorska 163, Poland Institute of Acoustics, Adam Mickiewicz University, 61 Poznań, Umultowska 85, Poland
a r t i c l e
i n f o
Article history: Received 21 July 2009 Received in revised form 16 August 2009 Accepted 18 August 2009 Available online 23 August 2009 Keywords: 2-Ethoxyethanol Ethylene glycol Diethylene glycol Triethylene glycol Tetraethylene glycol Speed of sound Isentropic compressibility
a b s t r a c t The speed of sound (u) has been obtained at a frequency of 8.3 MHz in {CH3CH2OCH2CH2OH + HOCH2CH2 (OCH2CH2)nOH}for n = 0, 1, 2, and 3 over the whole composition range of studied binary liquid mixtures, at T = 298.15 K. The speed of sound values were combined with those of our previous results for densities and viscosities to obtain isentropic compressibility (κs), free volume (Vf), and intermolecular free length (Lf). From all these data excess isentropic compressibility (κ Es ), excess free volume (V Ef ) and excess intermolecular free length (LEf ) as well as the deviations of the speed of sound (Δu) were obtained. The results are interpreted in terms of molecular interactions occurring in the solutions. © 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
We have previously reported the density [1] and viscosity [2] of {2-ethoxyethanol (EE) + ethylene glycol (EG), 2-ethoxyethanol + diethylene glycol (DEG), 2-ethoxyethanol + triethylene glycol (TEG), and 2-ethoxyethanol + tetraethylene glycol (TETRAEG)} binary mixtures at 298.15 K. In a continuing effort to collect other physicochemical and thermodynamic quantities for studied mixtures we present in this paper measured values of the speeds of sound at T = 298.15 K, and atmospheric pressure. In order to throw more light on interaction of 2-ethoxyethanol with ethylene glycol and its oligomers, we have undertaken a detailed study of excesses isentropic compressibility (κ Es ), free volume (V Ef ), and intermolecular free length (LEf ) as well as the deviation of the speeds of sound (Δu). These structural parameters are very sensitive to interactions between solute and solvent. The studied solvents have found a wide variety of applications in the petroleum, cosmetics, textile, pharmaceutical, and the other industries [3–5]. Therefore, the study of intermolecular interactions in 2-ethoxyethanol + ethylene glycol mixtures would be interesting owing to their industrial applications.
2.1. Materials The pure components were supplied by Sigma-Aldrich and Fluka. The chemicals, viz., 2-ethoxyethanol, ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol, used in the study were purified by using the methods described in the literature [1,2,6]. The mass fraction purities as determined by gas chromatography are: 2-butoxyethanol > 0.998, ethylene glycol > 0.994, diethylene glycol > 0.996, triethylene glycol > 0.996, and tetraethylene glycol > 0.998. The mixtures were prepared using a Sartorius balance. Conversion to molar quantities was based on the relative atomic mass table of 1985, issued by IUPAC in 1986. The maximum estimated error in the mole fractions is ±1 · 10− 4. Liquids were stored in dry-box over phosphorus pentoxide and degassed by ultrasound just before the experiment. Experimental speeds of sound for the pure solvents, at T = 298.15 K, are compared with values available in the literature and listed in Table 1.
2.2. Measurements
⁎ Corresponding author. E-mail address: [email protected] (C.M. Kinart). 0167-7322/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2009.08.006
The speed of sound was measured by resonance method using the ResoScan™ System (Germany) apparatus. The speed of sound is determined from series of resonance frequencies of the resonator calls
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C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
Table 1 Observed and literature values of speed of sound of pure liquid components, at T = 298.15 K. u m:s − 1
Solvent
This work 2-Ethoxyethanol
1302.012
Ethylene glycol
1654.344
Lit. 1302.5 1300.4 1301.7 1656.9
[7] [8] [9] [10]
1654.89 [11] 1659 [12] 1577 [12] Diethylene glycol
1579.003 1579.34 [10] 1610 [12]
Triethylene glycol
1608.725
Tetraethylene glycol
1597.865
1611.31 [10] –
and also from waviness due to multiple reflections in the signal transmitted through the path length cell [13]. The operating frequency of the transducers was 8.3 MHz. The relative error of the measured speed of sound was lower than 1 ∙ 10− 5 over the entire range of concentration. The temperature of the samples was controlled to within ±0.005 K by Peltier thermostat and it was measured to accuracy of ±0.01 K. 3. Results and discussion The experimental speeds of sound (u) obtained from the measurements of the pure solvents and for the binary mixtures, at T = 298.15 K, are summarized in Table 2. The variations of speeds of sound as a function of volume fraction of EE (φ1) were fitted to a polynomial of type [14,15]: uðφ1 Þ =
4 X
j
α j · φ1 ;
ð1Þ
j=0
by the method of least-squares with each point weighted equally. The values of coefficients αj and standard deviations σ(u) are summarized in Table 3. The deviations in speed of sound (Δu) from a linear dependence on the average volume fraction (φi) have been calculated from the relationship [16]: Δu = u −
2 X
ui · φi ;
ð2Þ
i=1
where u1, u2, and u are the speeds of sound of the EE, ethylene glycols and the mixtures, and φi is the volume fraction of component i. The values of Δu calculated by using Eq. (2) are listed in Table 2. Isentropic compressibility coefficients, κs, are calculated from the relation [16]: 2 −1 κ s = ρ·u :
ð3Þ
The densities ρ required to calculate isentropic compressibilities were taken from our previous paper [1]. The excesses of isentropic compressibility (κ Es ) were calculated from the relation [16,17]: E
ideal
κs = κs − κs
¼κ s −
2 X i=1
0
κ s;i · φi
ð4Þ
Table 2 Ultrasonic speed (u), isentropic compressibility (κs), deviation of the speed of sound (Δu), and excesses isentropic compressibility (κ Es ) for 2-ethoxyethanol + ethylene glycols mixtures, at 298.15 K. x1
φ1
u m: s − 1
Δu m: s − 1
κ s :1012 Pa − 1
κ Es :1012 Pa − 1
EE + EG 0.0000 0.1000 0.2996 0.4005 0.4515 0.5003 0.5502 0.5998 0.6998 0.8005 0.8995 1.0000
0.0000 0.1639 0.4367 0.5513 0.6041 0.6516 0.6973 0.7399 0.8182 0.8875 0.9472 1.0000
1654.344 1594.589 1495.558 1454.525 1435.783 1419.060 1403.136 1388.367 1361.612 1338.412 1318.936 1302.012
0.000 − 2.008 − 4.923 − 5.578 − 5.717 − 5.704 − 5.527 − 5.287 − 4.454 − 3.237 − 1.679 0.000
329.18 362.68 428.77 461.36 477.58 492.90 508.37 523.56 553.55 582.82 610.49 637.61
0.00 − 15.95 − 31.10 − 32.69 − 32.32 − 31.35 − 29.84 − 27.81 − 22.46 − 15.74 − 8.29 0.00
EE + DEG 0.0000 0.0998 0.2300 0.3004 0.4007 0.4492 0.4998 0.5485 0.5996 0.7003 0.8009 0.9001 1.0000
0.0000 0.1017 0.2340 0.3051 0.4063 0.4550 0.5056 0.5544 0.6053 0.7054 0.8048 0.9024 1.0000
1579.003 1548.358 1509.185 1488.212 1459.047 1445.239 1431.958 1417.399 1403.399 1376.430 1350.467 1325.658 1302.012
0.000 − 2.475 − 5.002 − 6.281 − 7.415 − 7.733 − 7.998 − 8.040 − 7.941 − 7.184 − 5.614 − 3.388 0.000
360.35 379.95 408.22 427.00 451.91 465.16 478.94 492.51 507.53 538.04 570.40 604.45 637.58
0.00 − 10.77 − 24.83 − 28.52 − 28.94 − 26.93 − 23.74 − 19.58 − 15.55 − 8.78 − 3.28 − 2.03 0.00
EE + TEG 0.0000 0.1021 0.2031 0.2999 0.3996 0.4502 0.5000 0.5476 0.5998 0.6993 0.7997 0.8980 1.0000
0.0000 0.0756 0.1799 0.2390 0.3275 0.3720 0.4198 0.4675 0.5190 0.6262 0.7414 0.8647 1.0000
1608.725 1584.083 1551.017 1531.784 1503.106 1488.420 1472.815 1457.595 1441.278 1408.622 1374.931 1339.683 1302.012
0.000 − 1.454 − 2.530 − 3.637 − 5.170 − 6.208 − 7.152 − 7.742 − 8.263 − 8.039 − 6.397 − 3.827 0.000
345.10 360.32 377.36 395.81 417.47 429.60 442.38 455.45 470.71 503.42 541.34 584.71 637.61
0.00 − 6.89 − 15.36 − 19.20 − 23.43 − 24.31 − 25.51 − 26.36 − 26.21 − 24.85 − 20.63 − 13.32 0.00
EE + TETRAEG 0.0000 0.1003 0.2038 0.3007 0.4009 0.4515 0.5005 0.5499 0.5982 0.6991 0.7986 0.9003 1.0000
0.0000 0.0593 0.1441 0.1940 0.2711 0.3112 0.3553 0.4003 0.4502 0.5589 0.6837 0.8276 1.0000
1597.865 1579.059 1552.536 1536.313 1511.765 1498.765 1485.024 1470.725 1455.149 1422.739 1386.558 1345.869 1302.012
0.000 − 1.262 − 2.697 − 4.157 − 5.894 − 7.031 − 7.724 − 8.710 − 9.523 − 9.774 − 9.032 − 7.148 0.000
349.65 361.49 375.48 390.60 408.90 419.35 430.36 442.54 455.66 487.46 526.16 575.67 637.61
0.00 − 5.23 − 11.66 − 14.91 − 18.82 − 19.91 − 21.60 − 22.38 − 23.63 − 23.13 − 20.37 − 12.29 0.00
where κ 0s,i is the isentropic compressibility of the pure component i, and φi is the volume fraction of component i. The values of κs and κ Es calculated by using Eq. (3) and Eq. (4) are listed in Table 2. The free volume (Vf) of a binary mixture is calculated from the relation [16]: Vf = ½M · u·K ·η
3=2
ð5Þ
where M, and η are the molar mass and viscosity of the mixture, respectively and K is a dimensionless constant having value of
C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
The corresponding excesses of free volume (V Ef ) were calculated from the relation [16,18]:
Table 3 Coefficients αi and standard deviation σ(u) of Eq. (1) for {EE (1) + EG (2), EE (1) + DEG (2), EE (1) + TEG (2), and EE (1) + TETRAEG (2)} binary mixtures, at T 298.15 K. α0 · 10− 2 EE + EG 16.5435
α1 · 10− 2
α2 · 10− 2
α3 · 10− 2
α4 · 10− 2
83
oðuÞ m:s − 1
E
Vf = Vf −
2 X
ð6Þ
Vf;i · xi
i=1
− 3.6480
0.0015
0.0140
0.1092
0.02
EE + DEG 15.7903
− 3.0488
0.2787
− 0.1293
0.1292
0.29
EE + TEG 16.0841
− 3.0804
− 0.8747
1.5038
− 0.6121
0.30
where Vf,i is the free volume of the pure component i, Vf is the free volume of the mixture, and xi is the mole fraction of component i. The excesses of intermolecular free length (LEf ) were calculated from the relation [16,18]: E
EE + TETRAEG 15.9789 − 3.1301
− 0.3829
− 07924
− 0.2391
Lf = Lf − 0.30
2 X
ð7Þ
xi · Lf;i
i=1
where: 9
4.28 ∙ 10 , independent of temperature and the nature of the liquid system. The viscosities η required to calculate free volumes were taken from our previous paper [2].
Lf = K = u · ρ
1=2
K = ð93:875 + 0:375 · T Þ · 10
−8
K — is a temperature dependence constant [19].
Table 4 Coefficients ai and standard deviation σ(Δu, κEs , VEf and LEf ) of Eq. (8) and (9) for {EE (1) + EG (2), EE (1) + DEG (2), EE (1) + TEG (2), and EE (1) + TETRAEG (2)} binary mixtures, at T 298.15 K. EE + EG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
oðΔuÞ m:s − 1
a0
a1
a2
a3
a4
− 21.7141 a0 ∙ 106
− 10.2088 a1 ∙ 106
− 1.1292 a2 ∙ 106
0.4358 a3 ∙ 106
2.4604 a4 ∙ 106
− 130.1225 a0 ∙ 104
− 18.2946 a1 ∙ 104
− 0.2557 a2 ∙ 104
2.6321 a3 ∙ 104
0.6341 a4 ∙ 104
− 11.4315 a0
− 3.8833 a1
3.5531 a2
4.0813 a3
− 1.6697 a4
oðLEf Þ
0.0396
− 0.0033
0.0016
0.0018
− 0.0032
0.00002
0.018
σ ðκ Es Þ:1012 Pa − 1
0.018
σ ðVfE Þ:104 m3
0.013 o
A
EE + DEG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
oðΔuÞ m:s − 1
a0
a1
a2
a3
a4
− 31.9292 a0 ∙ 106
− 6.2310 a1 ∙ 106
1.6780 a2 ∙ 106
− 1.3028 a3 ∙ 106
− 4.1600 a4 ∙ 106
− 96.0436 a0 ∙ 104
138.1173 a1 ∙ 104
48.9436 a2 ∙ 104
− 122.3757 a3 ∙ 104
− 11.5377 a4 ∙ 104
− 23.7458 a0
− 20.4372 a1
− 8.9395 a2
18.1591 a3
24.834 a4
oðLEf Þ
− 0.0226
0.0005
− 0.0003
0.0007
− 0.0029
0.00005
oðΔuÞ m:s − 1
0.041
σ ðκ Es Þ:1012 Pa − 1
0.026
σ ðVfE Þ:104 m3
0.041 o
A
EE + TEG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
a0
a1
a2
a3
a4
− 32.4541 a0 ∙ 106
− 16.1257 a1 ∙ 106
32.7804 a2 ∙ 106
10.9846 a3 ∙ 106
− 36.0957 a4 ∙ 106
− 105.0206 a0 ∙ 104
0.2730 a1 ∙ 104
− 9.3558 a2 ∙ 104
− 14.3947 a3 ∙ 104
7.1925 a4 ∙ 104
− 23.7458 a0
− 20.4372 a1
− 8.9395 a2
18.1591 a3
24.8340 a4
oðLEf Þ
− 0.0699
− 0.0137
− 0.0049
− 0.0086
0.0027
0.00008
0.065
σ ðκ Es Þ:1012 Pa − 1
0.161
σ ðVfE Þ:104 m3
0.041 o
A
EE + TETRAEG Δu m: s − 1 κ Es Pa − 1 VfE m3 LEf o
A
a0
a1
a2
a3
a4
oðΔuÞ m: s − 1
− 39.0940 a0 ∙ 106
− 9.1268 a1 ∙ 106
20.0072 a2 ∙ 106
− 24.2450 a3 ∙ 106
− 37.1468 a4 ∙ 106
σ ðκ Es Þ:1012
− 94.3034 a0 ∙ 104
− 2.5318 a1 ∙ 104
− 1.0405 a2 ∙ 104
21.4051 a3 ∙ 104
22.6243 a4 ∙ 104
− 32.3884 a0
− 28.6779 a1
− 4.6806 a2
20.4537 a3
15.6538 a4
oðLEf Þ
− 0.0974
− 0.0335
− 0.0100
− 0.0052
− 0.0019
0.00010
0.14
Pa − 1
0.23
σ ðVfE Þ:104 m3
0.10 o
A
84
C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
Fig. 1. Plot of the deviation of the speed of sound (Δu) against volume fraction EE (j1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
Fig. 3. Plot of the excess free volume (V Ef ) against mole fraction EE (x1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
The standard deviation values were obtained from:
κ Es ,
V Ef ,
LEf
j
E where F = Δu and κ s
For each mixture, the values Δu, and were smoothed to a Redlich–Kister polynomial regression of the type: F = φ1 · ð1 − φ1 Þ
4 X
aj · ð2φ1 −1Þ
ð8Þ
j=0
G = x1 · ð1 − x1 Þ
4 X
j
aj · ð2x1 −1Þ
E E where G = Vf and Lf :
ð9Þ
j=0
The parameters aj in Eqs. (8) and (9) were evaluated by the leastsquares method. The values of these parameters with standard deviation σ(Δu, κ Es , V Ef , and LEf ), are summarized in Table 4. The plots of these functions are presented in Figs. 1–4.
2P
6 σ =4
Xexptl −Xcalcd N −p
2 31 = 2 7 5
;
ð10Þ
where: N is the number of experimental points, p is the number of parameters, Xexptl and Xcalcd are the experimental and calculated properties, respectively. The values of κEs are negative over the entire composition range for all studied mixtures (see Fig. 2). These values become less negative as the chain length of the glycol molecules (the number of oxyethylene groups OCH2CH2 in the glycol) increases in the following order: E
E
E
κ min ðEE + TETRAEGÞ < κ min ðEE + TEGÞ < κ min ðEE + DEGÞ <
E κ min ðEE
+ EGÞ
The values Δu are showing a similar trend as observed in κ Es (are always negative) but these values become more negative as the chain length of the glycol molecules increases as shown in Fig. 1.
Fig. 2. Plot of the excess isentropic compressibility (κEs ) against volume fraction EE (φ1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
Fig. 4. Plot of the excess intermolecular free length (LEf ) against mole fraction EE (x1) for {(●) EE (1) + EG (2) (▲) EE (1) + DEG (2), (■) EE (1) + TEG (2), and (♦) EE (1) + TETRAEG (2)} binary liquid mixtures, at T = 298.15 K.
C.M. Kinart et al. / Journal of Molecular Liquids 149 (2009) 81–85
The literature review shows, that the deviations of analyzed function provide experimental evidence for the formation of intermolecular complexes, and provide a valuable aid for determining their stoichiometry and relative stability [16–18]. In general, negative κ Es and Δu values indicate the presence of strong intermolecular bonding between the components in the binary mixtures [7–12,16–21]. Ethoxyethanols and the oligomers of ethylene glycol are a very interesting class of solvents, due to the presence of the oxy and hydroxyl groups in the same molecule, which allow self-association via intra- and intermolecular hydrogen bonds. The formation of intramolecular hydrogen bonds in ethoxyethanols is more favourable when the molecules of these solvents are in the gauche conformations. For these molecules 5-, 6-, 7- and 8-membered rings, of quite different properties, are formed [22–29]. In our opinion, in the case of the present binary mixtures at least four different effects can be identified which contribute to Δu and κ Es values: (1) the breaking of homogeneous liquid order on mixing; (2) favorable interactions between polar groups (OH and O) of unlike molecules; (3) unfavorable hydrophobic interactions between OH groups of ethylene glycols and CH2 groups of alkyl chains of EE molecules and (4) geometrical fitting of one component into the other due to differences in the molar volumes and free volume between unlike molecules. This last effect should be significant and of great importance for (EE + TETRAEG) binary mixtures. The presented behaviors of κ Es and Δu are consistent with that of excess molar volume (V E) for {2-ethoxyethanol (EE) + ethylene glycol (EG), 2-ethoxyethanol + diethylene glycol (DEG), 2-ethoxyethanol + triethylene glycol (TEG), and 2-ethoxyethanol + tetraethylene glycol (TETRAEG)} binary mixtures [1]. The values of V E are negative over the entire composition range for all studied mixtures and decrease from EG to TETRAEG. The EE + TETRAEG mixture corresponds to the densest and most packed mixed solvent. Taking into account the literature information concerning the basicity (SB) and acidity (SA) of pure EE and ethylene glycols it seems necessary to assume that the OH group of glycol is the proton donor and the oxygen atom of ether from the molecule of EE is its acceptor [30–33]. Fig. 3 shows that the excess free volume (V Ef ) in the studied binary mixtures becomes more negative when κ Es and Δu decrease. The plot of this function indicates that the excess free volume created in the mixture is not available for the compression. This means that interstitial accommodation plays an important role by influencing the κ Es and Δu of the liquid mixtures containing EE with ethylene glycols. It also indicates that the molecular size and shape of the components are equally important factors in these mixtures. The course of changes LEf also confirms these conclusions (see Fig. 4), because LEf is generally more negative when the structure has high rigidity and it corresponds to the densest and most packed mixed solvent.
85
4. Conclusions In this paper, the speeds of sound were measured at T = 298.15 K over the entire range of composition for binary mixtures of 2ethoxyethanol with ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol. Various calculated excess properties and deviations (κEs , VEf , LEf and Δu) support that there may be intermolecular hydrogen bonding between the components of studied binary solvents and that the interstitial accommodation also plays an important role in these mixtures.
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