J Solution Chem (2007) 36: 997–1022 DOI 10.1007/s10953-007-9165-y O R I G I N A L PA P E R
Some Thermodynamic Properties of the Binary Systems of Toluene with Butyl Methacrylate, Allyl Methacrylate, Methacrylic Acid and Vinyl Acetate at 20, 30 and 40 °C Jaime Wisniak · Gladis Cortez · René D. Peralta · Ramiro Infante · Luis E. Elizalde Received: 30 October 2006 / Accepted: 21 February 2007 / Published online: 12 June 2007 © Springer Science+Business Media, LLC 2007
Abstract Densities of the binary systems of toluene with butyl methacrylate, allyl methacrylate, methacrylic acid, and vinyl acetate have been measured as a function of composition at 20, 30 and 40 °C at atmospheric pressure, using an Anton Paar DMA 5000 oscillating U-tube densimeter. The excess molar volumes are negative for the system toluene + butyl methacrylate and positive for the three other binaries, and become more so as the temperature increases from 20 to 40 °C. The system toluene + allyl methacrylate presents near ideal behavior. The apparent volumes were used to calculate values of the partial excess molar volumes at infinite dilution. The excess coefficient of thermal expansion is positive for the four binary systems. The calculated excess molar volumes were correlated with the Redlich–Kister equation and with a series of Legendre polynomials. An explanation of the results is given based by the FT-IR (ATR) and 13 C NMR spectra of equimolar mixtures of the different systems. Keywords Densities · Excess molar volumes · Apparent properties · Monomers · Toluene · Methacrylates · Vinyl acetate · Densimeter
1 Introduction The mixing of different compounds gives rise to solutions that generally do not behave ideally. The deviation from ideality is expressed by many thermodynamic properties, particularly activity coefficients and excess or residual properties. Activity coefficients are valuable for describing phase equilibria whereas excess thermodynamic properties are useful in the study of molecular interactions and arrangements. In particular, they reflect the interactions J. Wisniak () Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel e-mail:
[email protected] G. Cortez · R.D. Peralta · R. Infante · L.E. Elizalde Centro de Investigación en Química Aplicada, Saltillo 25253, Coahuila, México
998
J Solution Chem (2007) 36: 997–1022
that take place between solute-solute, solute-solvent and solvent-solvent species. In general, positive excess molar volumes may be due to compensation between strong like interactions (such as those present in alcohols) and equally strong unlike H-bond interactions (such as those present between alcohols and ether). Negative excess molar volumes will occur when the unlike interactions prevail over self-association. Binary mixtures are an important class of solvents and solutions, and the behavior of some of their physical properties is still unclear. The effect of temperature on the molar volume and excess molar volume can be expressed by the coefficient of isobaric thermal expansion: α = (1/Vm )(∂Vm /∂T )P . This work is part of our program to provide data for the eventual characterization of the molecular interactions between solvents and commercially important monomers, in particular, the influence of the chemical structure of the solute in the systems under consideration. So far we have studied the volumetric behavior of several monomers with cyclic hydrocarbons [1], aromatic solvents [2–4], and aliphatic and cyclic ethers [5–7]. Toluene is a powerful solvent, hardly soluble in water, useful in polymerization, synthesis of aromatic derivatives and other chemical reactions, in the cleaning of polymer surfaces, electronic materials, etc. The monomers considered in this study are important industrial chemicals used in the large-scale preparation of useful polymers; acrylic acids and its esters are some of the most used monomers for improving the performance characteristics of a large number of polymer formulations. These monomers are also interesting for structural studies because they contain both one or more double bonds and an ester group. A monomer–dimer equilibrium has been found among the acid groups of methacrylic acid; at room temperature the acid is present almost completely in the form of hydrogen-bonded dimers [8]. The solvent has a π electron cloud that can interact with the solute. Here we report experimental values for the excess molar volumes for the binary systems of toluene (1) with butyl methacrylate (2), allyl methacrylate (3), methacrylic acid (4) and vinyl acetate (5). Resa et al. [9] measured the excess volumes of toluene and other alkyl benzenes + vinyl acetate at 25 °C and found them to be positive over the whole composition range and to increase with the alkyl chain size of the aromatic compound. Peralta et al. [10, 11] measured the excess volumes of m-xylene and ethyl benzene with ethyl acrylate, butyl acrylate and methyl methacrylate at 25 °C and found that they were positive for the binaries of alkyl benzene with methyl methacrylate and ethyl acrylate but showed a sigmoid behavior with butyl acrylate. Peralta et al. [4] found that the excess volumes at 25 °C of the system toluene + butyl acrylate were negative whereas those of toluene + methyl methacrylate were positive. Gong et al. [12] measured the excess volumes of toluene with methyl acrylate at 20 °C and found them to be positive. George et al. [13] measured the excess molar volumes for the system toluene + methyl methacrylate in the range 25–45 °C and found that they followed a sigmoid behavior. Wisniak et al. [14] determined the values of the excess molar volumes of the ternary system ethylbenzene + styrene + ethyl acrylate and its binaries at 25 °C and found that they were negative for the system toluene + butyl methacrylate and positive for the two other binaries. To the best of our knowledge no additional literature data are available that relate to the excess molar volumes of the systems reported here.
2 Experimental Section 2.1 Materials Toluene (TOL), mass fraction 0.9989; butyl methacrylate (BM), mass fraction 0.995 (stabilized with 10 ppm of monomethyl ether of hydroquinone); allyl methacrylate (AMA),
J Solution Chem (2007) 36: 997–1022
999
mass fraction 0.998 (stabilized with 50–185 ppm of hydroquinone monomethyl ether); methacrylic acid (MA), mass fraction 0.999 (stabilized with 100–250 ppm of hydroquinone); and vinyl acetate (VA), mass fraction 0.999 (stabilized with 3–5 ppm of hydroquinone), were purchased from Aldrich. The supplier certified the purity of all the reagents. BM, AMA, MA and VA were vacuum distilled prior to being used to eliminate the stabilizer. The purity of the solvents was further ascertained by comparing their densities at 25 and 35 °C with the values reported in the literature. 2.2 Density Measurements The densities of the pure components and their mixtures were measured with an Anton Paar model DMA 5000 oscillating U-tube densimeter, provided with automatic viscosity correction, and two integrated Pt 100 platinum thermometers (DKD traceable) with a stated accuracy of 5 × 10−6 g·cm−3 . The temperature of the densimeter was regulated to ±0.001 °C with a solid-state thermostat. The densimeter was calibrated daily with both dry air and bidistilled degassed water. All liquids were boiled or heated to remove dissolved air. Solutions of different compositions were prepared by mass in a 10 cm3 rubber-stoppered vial (PTFE/silicone, Supelco) to prevent evaporation, using a Mettler AG 204 balance accurate to ±10−4 g. To minimize the errors in composition, the heavier component was charged first and the sample was kept in ice water. The total absolute uncertainty (ISO 9001) in the mole fraction is ±9.44 × 10−5 , precision of the density (duplicate) measurement ±2 × 10−5 g·cm−3 , and of the temperature to ±0.002 °C. The total absolute uncertainty in the density measurement, as reported by the equipment manufacturer, was 5 × 10−6 g·cm−3 . Proper safety measures were taken when handling all the materials.
3 Results and Discussion For every binary system twenty-one density measurements were performed (with repetition) at 20, 30 and 40 °C in the full mole fraction range (0 < x < 1). In addition, the density of the pure components was also measured at 25 and 35 °C. The values of the density of the pure components given in Table 1 serve as an indication of the relative intensity of the attractive forces operating within the given molecule: The density of methacrylic acid is substantially larger than that of the other pure compounds due to the presence of a strong H-bond interaction between the acid and the carbonyl groups; the densities of allyl methacrylate and vinyl acetate are similar because of the presence of one double bond in the side chain and an ester group; and toluene has the lowest density due to the absence of interacting groups (as reflected by its very low dipole moment, 0.36 D). The density, ρ, of the pure materials was correlated with the absolute temperature with the simple linear equation ρ = a + bT .
(1)
The values of the adjustable coefficients a and b, and the standard deviation s of the fit appear in Table 2 and are valid within the temperature range studied here. A secondorder polynomial did not improve the statistical quality of the fit. Equation 1 can be used for interpolation, differentiation or integration purposes, for example, to calculate the coefficient of thermal expansion, α = (1/v)(∂v/∂T )T = −(1/ρ)(∂ρ/∂T )T , at any desired temperature.
99.89
99.5
99.8
99.9
99.9
Toluene (1)
Butyl methacrylate (2)
Allyl methacrylate (3)
Methacrylic acid (4)
Vinyl acetate (5)
Purity (mass%)
Component
0.932238
1.014261
0.933288
0.895266
0.866787
0.93235 [23]
1.01413 [22]
0.93365 [22]
0.89526 [23]
0.86684 [22]
0.925775
1.009127
0.927997
0.890438
0.862055
25 °C Meas.
Meas.
Lit.
20 °C
Density/g·cm−3
Table 1 Purity and densities of pure components from 20 ° to 40 °C
0.92567 [9]
0.92623 [23]
1.012 [24]
1.00940 [23]
0.9287 [24]
0.92866 [23]
0.891 [24]
0.89090 [23]
0.86220 [22]
Lit.
30 °C
0.919387
1.003868
0.922776
0.885805
0.857463
Meas.
0.92004 [23]
1.00475 [23]
0.92364 [23]
0.88652 [23]
0.85753 [22]
Lit.
35 °C
0.9139.94
0.998641
0.917423
0.880857
0.852703
Meas.
0.91384 [23]
0.99993 [23]
0.91860 [23]
0.88210 [23]
0.8528 [22]
Lit.
40 °C
0.906508
0.993524
0.912164
0.876171
0.848086
Meas.
0.90747 [23]
0.99519 [23]
0.91351 [23]
0.87765 [23]
0.84820 [22]
Lit.
1000 J Solution Chem (2007) 36: 997–1022
J Solution Chem (2007) 36: 997–1022
1001
Table 2 Coefficients of Eq. 1 a g·cm−3
b × 105
s × 105
3.41
g·cm−3 ·K−1
g·cm−3
Toluene
1.14105
−0.935621
Butyl methacrylate
1.17591
−0.957300
6.04
Allyl methacrylate
1.24260
−1.05517
5.84
Methacrylic acid
1.31954
−1.04127
3.74
Vinyl acetate
1.30916
−1.28568
7.83
The excess molar volumes, VmE , of the solutions of molar composition x were calculated from the densities of the pure liquids and their mixtures according to the following equation [15]: VmE = [x1 M1 + x2 M2 ]/ρ − [x1 M1 /ρ1 + x2 M2 /ρ2 ]
(2)
where ρ and ρi are the densities of the solution and pure component i in g·cm−3 , and Mi is the molar mass of pure component i in g·mol−1 . The corresponding values of ρ and VmE are reported in Table 3 and Figs. 1–3. The first term in Eq. 2 represents the actual molar volume of the solution and the second, the molar volume it would occupy if the mixture behaved ideally. In general, while these two molar volumes are similar in size (usually larger than 100 cm3 ·mol−1 ) their difference is usually smaller by two to three orders of magnitude and thus may carry a significantly larger error. Partial molar volumes for each binary system were calculated using the relations [15]: V¯m1 = Vm + x2 (dVm /dx1 )
(3)
V¯m2 = Vm − x1 (dVm /dx1 ).
(4)
The pertinent values are reported in Table 4 and are necessarily consistent. Partial volumes can also be calculated using the concept of apparent volume, φV , defined for the solute as φV =
V − n1 V1 M2 (ρ1 − ρ) + = n2 ρ mρ1 ρ
(5)
where n1 and V1 represent the number of moles and molar liquid volume of component 1 (the solvent in this case), n2 and M2 are the number of moles and the molar mass of the solute, and m is the molality (moles of solute per kg of solvent) of the solution, respectively [16]. The pertinent values of φV are reported in Table 3. As defined, the apparent volume represents the apparent contribution of one mole of solute to the volume of the mixture. If the apparent volumes were strictly additive for both components then the value of φV would be exactly equal to the partial molar volume. The partial volume of the solute can be calculated from Eq. 5 using the relation, V¯2 = (∂V /∂n2 )P ,T ,n1 , yielding [16]: dφV ∂φV V¯2 = n2 + φV . + φV = m ∂n2 n1 dm
(6)
1002
J Solution Chem (2007) 36: 997–1022
Table 3 Experimental densities, molar volumes, calculated excess molar volumes, apparent volumes and deviations δV E for binary mixtures at 20, 30 and 40 °C x1
ρ/(g·cm−3 )
Va
103 × V E a
ϕV a
t = 20 °C xC6 H5 CH3 + (1 − x)CH2 C(CH3 )CO2 C4 H9 0
0.895266
158.8326
0.0252
0.894826
157.5009
0
0.0509
0.894381
156.1413
−17.75
158.8118
0.1002
0.893482
153.5353
−32.92
158.7939
0.1515
0.892507
150.8259
−47.53
158.7745
0.2005
0.891548
148.2359
−62.47
158.7524
0.2503
0.890517
145.6107
−73.94
158.7319
0.3004
0.889417
142.9685
−81.86
158.7135
0.3500
0.888299
140.3573
−91.13
158.6903
0.4006
0.887101
137.6913
−98.75
0.4503
0.885857
135.0737
−103.1
158.6429
0.5003
0.884534
132.4472
−104.0
158.6223
0.5501
0.883169
129.8287
−105.9
158.5951
0.6002
0.881704
127.1980
−102.8
158.5733
0.6502
0.880180
124.5749
−99.58
158.5458
0.6999
0.878597
121.9724
−95.55
158.5122
0.7500
0.876892
119.3482
−86.61
158.4841
0.8000
0.875095
116.7314
−75.19
158.4546
0.8499
0.873197
114.1241
−60.75
158.4257
0.9003
0.871177
111.4967
−44.14
158.3880
0.9499
0.869043
108.9089
−22.17
158.3878
0.9749
0.867931
107.6086
−11.02
158.3916
1
0.866787
106.3009
0
−7.808
158.8225
158.6658
xC6 H5 CH3 + (1 − x)CH2 C(CH3 )CO2 CH2 CHCH2 0
0.933288
135.1724
0.0253
0.931940
134.4452
2.693
135.1734
0.0501
0.930607
133.7321
4.995
135.1759
0.1000
0.927883
132.2949
0.1501
0.925092
130.8506
0
8.904 12.12
135.1805 135.1849
0.2001
0.922252
129.4090
14.44
135.1887
0.2500
0.919356
127.9701
16.49
135.1926
0.3002
0.916388
126.5236
17.49
135.1956
0.3499
0.913379
125.0889
18.23
135.1987
0.4001
0.910275
123.6402
18.41
135.2013
0.4496
0.907142
122.2101
18.27
135.2038
0.5002
0.903870
120.7495
17.66
135.2059
0.5500
0.900569
119.3099
16.82
135.2080
0.5995
0.897209
117.8785
15.76
135.2100
0.6493
0.893753
116.4398
14.27
135.2113
J Solution Chem (2007) 36: 997–1022
1003
Table 3 (Continued) x1
ρ/(g·cm−3 )
Va
103 × V E a
ϕV a
0.6991
0.890213
115.0013
12.59
135.2125
0.7497
0.886525
113.5393
10.72
135.2135
0.8000
0.882758
112.0826
8.549
135.2134
0.8497
0.878948
110.6469
6.416
135.2133
0.8997
0.875012
109.2018
4.258
135.2131
0.9500
0.870940
107.7463
2.174
135.2142
0.9740
0.868962
107.0527
1.052
135.2111
1
0.866787
106.3009
0
xC6 H5 CH3 + (1 − x)CH2 C(CH3 )COOH 0
1.014261
84.8797
0.0250
1.009351
85.4422
27.82
0 84.9073
0.0499
1.004521
86.0030
55.23
84.9369
0.0999
0.995014
87.1290
109.3
85.0002
0.1499
0.985814
88.2493
157.6
85.0642
0.1999
0.976974
89.3574
194.7
85.1221
0.2491
0.968508
90.4456
229.9
85.1849
0.3000
0.960108
91.5577
251.3
85.2379
0.3502
0.952066
92.6501
268.2
85.2916
0.4035
0.943768
93.8066
282.5
85.3524
0.4499
0.936767
94.8072
289.6
85.4053
0.4995
0.929534
95.8677
287.8
85.4539
0.5495
0.922434
96.9331
283.4
85.5079
0.5993
0.915564
97.9899
272.3
85.5583
0.6495
0.908831
99.0498
257.6
85.6137
0.7002
0.902237
100.1140
234.6
85.6616
0.7500
0.895965
101.1507
206.0
85.7027
0.8001
0.889825
102.1893
171.3
85.7359
0.8499
0.883799
103.2271
141.8
85.8237
0.8998
0.878025
104.2498
95.51
0.9495
0.872385
105.2685
49.37
85.8320 85.8566
0.9752
0.869529
105.7928
23.98
85.8444
1
0.866787
106.3009
0
xC6 H5 CH3 + (1 − x)CH3 CO2 CHCH2 0
0.932238
92.3479
0.0249
0.930219
92.7100
15.25
0 92.3625
0.0499
0.928167
93.0780
34.29
92.3829
0.0998
0.924162
93.8083
67.73
92.4221
0.1502
0.920260
94.5374
93.63
92.4570
0.1999
0.916509
95.2522
115.4
92.4911
0.2499
0.912847
95.9659
131.0
92.5215
0.2999
0.909235
96.6798
147.2
92.5572
0.3499
0.905716
97.3897
159.0
92.5914
1004
J Solution Chem (2007) 36: 997–1022
Table 3 (Continued) x1
ρ/(g·cm−3 )
Va
103 × V E a
ϕV a
0.4002
0.902281
98.0973
165.7
92.6230
0.4499
0.898970
98.7929
168.1
92.6525
0.5001
0.895677
99.4954
169.8
92.6865
0.5496
0.892508
100.1846
167.5
92.7189
0.6002
0.889332
100.8862
164.0
92.7570
0.6499
0.886287
101.5725
155.9
92.7922
0.6991
0.883349
102.2471
144.4
92.8269
0.7499
0.880397
102.9386
128.0
92.8586
105.3
92.8731
0.7999
0.877578
103.6144
0.8493
0.874812
104.2833
85.62
92.9149
0.8996
0.872077
104.9594
59.66
92.9410
0.9501
0.869384
105.6359
31.61
92.9800
0.9723
0.868237
105.9302
16.01
92.9248
1
0.866787
106.3009
0
t = 30 °C xC6 H5 CH3 + (1 − x)CH2 C(CH3 )CO2 C4 H9 0
0.885805
160.5290
0.0267
0.885348
159.1029
0
0.0506
0.884932
157.8250
−18.44
160.5075
0.1002
0.884045
155.1778
−36.01
160.4869
0.1499
0.883103
152.5245
−50.06
160.4680
0.2001
0.882120
149.8467
−64.48
160.4463
0.2504
0.881086
147.1619
−76.99
160.4242
0.3005
0.880001
144.4946
−86.39
160.4034
0.3500
0.878885
141.8567
−95.27
160.3804
0.4001
0.877696
139.1947
−101.29
160.3581
0.4499
0.876460
136.5480
−106.1
160.3340
0.5000
0.875148
133.8832
−108.4
160.3101
0.5498
0.873779
131.2411
−108.5
160.2859
0.6000
0.872333
128.5788
−107.3
160.2586
0.6500
0.870809
125.9291
−102.9
160.2329
0.7000
0.869207
123.2828
−96.60
160.2050
0.7501
0.867514
120.6299
−88.17
160.1741
0.8001
0.865730
117.9877
−76.99
160.1418
0.8499
0.863844
115.3617
−61.98
160.1141
0.8999
0.861834
112.7244
−43.62
160.0911
0.9500
0.859718
110.0873
−24.11
160.0449
0.9749
0.858608
108.7770
−12.05
160.0468
1
0.857463
107.4568
0
−9.677
xC6 H5 CH3 + (1 − x)CH2 C(CH3 )CO2 CH2 CHCH2 0
0.922776
136.7123
0
160.5170
J Solution Chem (2007) 36: 997–1022
1005
Table 3 (Continued) x1
ρ/(g·cm−3 )
Va
103 × V E a
ϕV a
0.0254
0.921447
135.9701
2.288
136.7128
0.0499
0.920156
135.2573
4.587
136.7153
0.1000
0.917471
133.7970
0.1501
0.914727
132.3318
8.975 12.29
136.7204 136.7249
0.2002
0.911929
130.8704
15.56
136.7299
0.2498
0.909106
129.4225
17.56
136.7338
0.2993
0.906224
127.9750
19.09
136.7377
0.3499
0.903215
126.4941
19.82
136.7409
0.3997
0.900193
125.0396
20.23
136.7442
0.4501
0.897062
123.5636
19.76
136.7464
0.5000
0.893891
122.1046
19.47
136.7494
0.5499
0.890645
120.6412
17.99
136.7504
0.6004
0.887282
119.1642
17.09
136.7532
0.6501
0.883898
117.7096
15.14
136.7537
0.6996
0.880437
116.2590
13.41
136.7551
0.7498
0.876837
114.7875
11.64
136.7570
0.7991
0.873219
113.3425
9.080
136.7557
0.8500
0.869387
111.8520
6.666
136.7549
0.8997
0.865540
110.3959
4.642
136.7568
0.9499
0.861550
108.9246
2.426
136.7589
0.9750
0.859514
108.1885
1.233
136.7599
1
0.857463
107.4568
0
xC6 H5 CH3 + (1 − x)CH2 C(CH3 )COOH 0
1.003868
85.7585
0.0251
0.998938
86.3337
30.65
0 85.7890
0.0500
0.994144
86.9014
58.70
85.8193
0.0998
0.984791
88.0332
108.1
85.8777
0.1502
0.975596
89.1750
158.0
85.9434
0.1999
0.966902
90.2882
191.4
85.9968
0.2499
0.958395
91.4052
223.6
86.0557
0.3000
0.950155
92.5167
248.7
86.1128
0.3495
0.942280
93.6076
265.9
86.1663
0.3996
0.934507
94.7109
280.9
86.2255
0.4498
0.927008
95.8042
286.6
86.2784
0.5001
0.919681
96.8986
288.8
86.3353
0.5498
0.912681
97.9714
282.6
86.3853
0.5994
0.905871
99.0389
274.8
86.4435
0.6502
0.899138
100.1228
255.0
86.4867
0.7000
0.892684
101.1841
236.1
86.5446
0.7499
0.886408
102.2409
210.6
86.5996
0.7994
0.880347
103.2851
180.5
86.6575
0.8498
0.874386
104.3378
139.9
86.6894
1006
J Solution Chem (2007) 36: 997–1022
Table 3 (Continued) x1
ρ/(g·cm−3 )
Va
103 × V E a 100.1
ϕV a
0.9000
0.868560
105.3874
0.9496
0.862961
106.4187
55.85
86.7591 86.8655
0.9752
0.860136
106.9484
29.64
86.9531
1
0.857463
107.4568
0
xC6 H5 CH3 + (1 − x)CH3 CO2 CHCH2 0
0.919387
93.6387
0.0249
0.917432
94.0022
19.89
93.6580
0.0500
0.915475
94.3691
39.79
93.6795
0.1001
0.911685
95.0939
0.1503
0.907985
95.8161
0
72.35 100.3
93.7180 93.7558
0.1997
0.904440
96.5223
123.5
93.7920
0.2503
0.900927
97.2381
141.0
93.8257
0.3002
0.897531
97.9425
155.5
93.8599
0.3500
0.894232
98.6408
165.7
93.8925
0.3997
0.891028
99.3328
171.2
93.9228
0.4502
0.887834
100.0341
175.0
93.9560
0.4997
0.884791
100.7167
173.5
93.9844
0.5495
0.881787
101.4014
170.2
94.0154
0.6001
0.878807
102.0940
162.8
94.0448
0.6501
0.875918
102.7759
154.2
94.0784
0.6996
0.873142
103.4456
140.0
94.1037
0.7497
0.870376
104.1228
124.5
94.1349
106.0
94.1665
0.7996
0.867684
104.7937
0.8499
0.865026
105.4671
85.12
94.2046
0.8998
0.862447
106.1332
60.37
94.2405
0.9494
0.859947
106.7902
32.97
94.2890
0.9744
0.858711
107.1200
17.42
94.3173
1
0.857463
107.4568
0
t = 40 °C xC6 H5 CH3 + (1 − x)CH2 C(CH3 )CO2 C4 H9 0
0.876171
162.2941
0.0245
0.875749
160.9695
0
0.0503
0.875307
159.5801
−17.67
162.2734
0.1004
0.874408
156.8718
−34.11
162.2541
0.1501
0.873494
154.1891
−51.67
162.2312
0.1998
0.872536
151.5093
−67.14
162.2081
0.2506
0.871500
148.7674
−79.78
162.1856
0.3002
0.870453
146.0978
−91.93
162.1607
0.3500
0.869333
143.4174
−99.59
0.3999
0.868175
140.7338
−108.2
162.1118
0.4503
0.866933
138.0207
−113.1
162.0863
0.5000
0.865652
135.3547
−116.2
162.0597
−7.939
162.2839
162.1388
J Solution Chem (2007) 36: 997–1022
1007
Table 3 (Continued) x1
ρ/(g·cm−3 )
Va
103 × V E a
ϕV a
0.5505
0.864280
132.6454
−116.8
162.0322
0.6002
0.862863
129.9787
−115.9
162.0021
0.6497
0.861367
127.3260
−111.3
161.9742
0.7000
0.859758
124.6370
−103.0
161.9488
0.7501
0.858077
121.9591
−93.58
161.9176
0.8000
0.856305
119.2957
−81.03
161.8870
0.8440
0.854656
116.9457
−67.62
161.8585
0.9000
0.852419
113.9626
−45.02
161.8417
0.9500
0.850310
111.3043
−23.15
161.8292
0.9748
0.849218
109.9858
−11.34
161.8423
1
0.848086
108.6449
0
xC6 H5 CH3 + (1 − x)CH2 C(CH3 )CO2 CH2 CHCH2 0
0.912164
138.3028
0.0245
0.910912
137.5766
0 1.561
138.3025
0.0503
0.909585
136.8154
3.230
138.3043
0.0981
0.907083
135.4003
5.809
138.3073
0.1499
0.904307
133.8652
8.820
138.3113
0.1999
0.901574
132.3839
10.97
138.3146
0.2500
0.898778
130.9018
13.06
138.3183
0.3000
0.895919
129.4195
15.01
138.3224
0.3503
0.892989
127.9307
16.03
138.3256
0.3999
0.890028
126.4583
16.53
138.3285
0.4497
0.886993
124.9824
16.73
138.3399
0.4997
0.883872
123.4990
16.64
138.3342
0.5501
0.880653
122.0040
16.20
138.3369
0.6002
0.877381
120.5173
14.89
138.3382
0.6498
0.874061
119.0459
13.73
138.3401
11.66
0.6999
0.870625
117.5568
0.7498
0.867118
116.0750
9.650
138.3398 138.3395
0.7999
0.863503
114.5869
7.812
138.3400
0.8502
0.859787
113.0944
5.462
138.3374
0.8998
0.856016
111.6211
3.646
138.3373
0.9496
0.852128
110.1415
1.749
138.3356
0.9749
0.850117
109.3916
0.8227
138.3337
1
0.848086
108.6449
0
xC6 H5 CH3 + (1 − x)CH2 C(CH3 )COOH 0
0.993524
86.6514
0.0248
0.988647
87.2304
34.24
0 86.6855
0.0500
0.983795
87.8158
64.49
86.7183
0.1000
0.974437
88.9698
118.1
86.7816
0.1497
0.965506
90.1042
159.4
86.8379
0.1995
0.956813
91.2376
197.9
86.8976
1008
J Solution Chem (2007) 36: 997–1022
Table 3 (Continued) x1
ρ/(g·cm−3 )
Va
103 × V E a
ϕV a
0.2497
0.948311
92.3758
232.2
86.9599
0.3000
0.940123
93.5043
253.8
87.0130
0.3500
0.932224
94.6207
271.7
87.0684
0.3999
0.924572
95.7305
283.4
87.1227
0.4500
0.917117
96.8390
290.6
87.1788
0.4998
0.909943
97.9339
289.2
87.2287
0.5491
0.903038
99.0129
284.4
87.2812
0.5999
0.896099
100.1225
277.0
87.3429
0.6502
0.889478
101.2095
259.0
87.3907
0.7001
0.883071
102.2861
236.9
87.4403
0.7494
0.876939
103.3410
208.8
87.4835
0.8001
0.870763
104.4266
178.1
87.5413
0.8499
0.864886
105.4843
141.4
87.5924
0.8993
0.859171
106.5337
104.6
87.6883
0.9498
0.853553
107.5932
52.32
87.6928
0.9745
0.850819
108.1148
30.02
87.8294
1
0.848086
108.6449
0
xC6 H5 CH3 + (1 − x)CH3 CO2 CHCH2 0
0.906508
94.9690
0.0252
0.904588
95.3389
25.77
94.9944
0.0498
0.902777
95.6955
44.92
95.0153
0.1002
0.899136
96.4217
0.1501
0.895633
97.1362
0
82.79 114.2
95.0600 95.1024
0.1994
0.892300
97.8333
137.1
95.1392
0.2500
0.889004
98.5401
152.5
95.1713
0.2999
0.885805
99.2372
166.3
95.2055
0.3500
0.882685
99.9311
175.6
95.2381
0.4003
0.879631
100.6242
180.4
95.2688
0.4502
0.876665
101.3086
183.2
95.3012
0.4998
0.873784
101.9861
182.2
95.3323
0.5496
0.870960
102.6628
177.7
95.3626
0.5991
0.868250
103.3285
165.8
95.3815
0.6500
0.865477
104.0150
156.9
95.4164
0.7003
0.862755
104.6964
149.5
95.4668
0.7497
0.860207
105.3537
131.6
95.4939
0.7994
0.857681
106.0142
113.1
95.5319
0.8502
0.855175
106.6842
88.57
95.5591
0.8998
0.852771
107.3371
62.60
95.5928
0.9501
0.850385
107.9960
33.83
95.6457
0.9745
0.849260
108.3990
16.92
95.6315
1
0.848086
108.6449
a Units: cm3 ·mol−1
0
J Solution Chem (2007) 36: 997–1022
1009
Fig. 1 Excess molar volumes at 20 °C: " toluene + allyl methacrylate; F toluene + butyl methacrylate; ∗ toluene + methacrylic acid; Q toluene + vinyl acetate
Fig. 2 Excess molar volumes at 30 °C: " toluene + allyl methacrylate; F toluene + butyl methacrylate; ∗ toluene + methacrylic acid; Q toluene + vinyl acetate
1010
J Solution Chem (2007) 36: 997–1022
Fig. 3 Excess molar volumes at 40 °C: " toluene + allyl methacrylate; F toluene + butyl methacrylate; ∗ toluene + methacrylic acid; Q toluene + vinyl acetate
The left-hand side of Eq. 6 is a result of the fact that the calculation of V¯2 is carried out at n1 constant so that m = n2 . If the apparent molar volume, φV , is determined at various molalities, then the partial molar volume can be calculated from the slope, at any composition, of the plot of φV against n2 or against m. An important characteristic of this plot for the systems studied here is that at molalities below 0.015 it becomes a straight line (containing at least the last eleven experimental points); a fact that can be used to calculate the partial volumes at infinite dilution. The values of this parameter for the different systems at the three temperature levels are reported in Table 5. Once again, the values of the partial excess volumes at infinite dilution are calculated as the difference between two numbers that are necessarily of the same magnitude. Hence, the result is prone to carry more error than each of the terms. The values of VmE of the binary systems were correlated for the composition using two procedures: (a) The Redlich–Kister expression [17] VmE = x1 x2
n
Ak (x1 − x2 )k
(7)
k=0
where the Ak ’s are the adjustable parameters of the empirical equation. The Redlich–Kister equation, developed originally to correlate activity coefficients, has proven to be such a powerful and versatile correlating tool that its use has been extended to the description of other properties, particularly, excess molar volumes and excess enthalpies of mixing. Nevertheless, it suffers from the important drawback that the values of its adjustable parameters change as the number of terms in the series is increased, so that no physical interpretation can be attached to them.
J Solution Chem (2007) 36: 997–1022
1011
Table 4 Partial molar volumes V¯mi , cm3 ·mol−1
x1
Toluene (1) + BM (2)
Toluene (1) + AMA (3)
Toluene (1) + MA (4)
Toluene (1) + VA (5)
V¯m1
V¯m1
V¯m1
V¯m1
V¯m2
V¯m3
V¯m4
V¯m5
t = 20 °C 0
105.938
158.833
106.411
135.172
107.473
84.8797
107.043
92.3479
0.05
105.965
158.832
106.391
135.173
107.404
84.8817
106.966
92.3499
0.10
105.991
158.830
106.374
135.174
107.303
84.8896
106.885
92.3562
0.15
106.017
158.826
106.360
135.176
107.186
84.9048
106.807
92.3664
0.20
106.042
158.821
106.349
135.179
107.064
84.9264
106.734
92.3792
0.25
106.066
158.814
106.339
135.181
106.946
84.9523
106.667
92.3932
0.30
106.090
158.805
106.331
135.184
106.833
84.9805
106.606
92.4071
0.35
106.113
158.794
106.325
135.187
106.728
85.0091
106.551
92.4202
0.40
106.136
158.780
106.320
135.191
106.631
85.0372
106.499
92.4323
0.45
106.157
158.764
106.315
135.194
106.541
85.0650
106.450
92.4444
0.50
106.178
158.745
106.311
135.197
106.459
85.0942
106.403
92.4582
0.55
106.198
158.723
106.308
135.201
106.386
85.1275
106.360
92.4760
0.60
106.217
158.698
106.306
135.204
106.321
85.1689
106.320
92.5008
0.65
106.234
158.669
106.304
135.207
106.269
85.2226
106.287
92.5355
0.70
106.250
158.635
106.303
135.210
106.231
85.2923
106.262
92.5824
0.75
106.265
158.598
106.302
135.213
106.211
85.3803
106.247
92.6426
0.80
106.277
158.556
106.301
135.215
106.208
85.4861
106.244
92.7149
0.85
106.287
158.508
106.301
135.216
106.224
85.6045
106.253
92.7945
0.90
106.294
158.455
106.301
135.216
106.253
85.7238
106.270
92.8720
0.95
106.299
158.396
106.301
135.215
106.285
85.8231
106.290
92.9316
1
106.301
158.330
106.301
135.212
106.301
85.8701
106.301
92.9493
t = 30 °C 0
107.082
160.529
107.563
136.714
108.709
85.7585
108.304
93.6387
0.05
107.103
160.528
107.548
136.714
108.564
85.7622
108.184
93.6417
0.10
107.128
160.526
107.534
136.715
108.431
85.7729
108.079
93.6502
0.15
107.157
160.523
107.522
136.717
108.310
85.7902
107.987
93.6632
0.20
107.186
160.517
107.511
136.719
108.200
85.8136
107.908
93.6801
0.25
107.216
160.510
107.501
136.722
108.100
85.8426
107.838
93.7001
0.30
107.245
160.501
107.492
136.725
108.009
85.8771
107.778
93.7229
0.35
107.273
160.491
107.484
136.729
107.927
85.9167
107.726
93.7479
0.40
107.300
160.480
107.478
136.733
107.852
85.9611
107.681
93.7749
0.45
107.325
160.468
107.473
136.737
107.786
86.0102
107.642
93.8037
0.50
107.350
160.453
107.468
136.741
107.727
86.0640
107.608
93.8343
0.55
107.374
160.435
107.464
136.745
107.674
86.1222
107.579
93.8668
0.60
107.396
160.413
107.462
136.749
107.627
86.1850
107.554
93.9012
0.65
107.415
160.386
107.460
136.752
107.587
86.2524
107.531
93.9380
0.70
107.432
160.352
107.458
136.755
107.552
86.3245
107.512
93.9776
0.75
107.445
160.312
107.457
136.758
107.523
86.4014
107.496
94.0203
0.80
107.454
160.265
107.457
136.759
107.499
86.4833
107.483
94.0670
0.85
107.459
160.210
107.457
136.760
107.481
86.5706
107.472
94.1184
0.90
107.460
160.150
107.457
136.760
107.467
86.6635
107.464
94.1753
1012
J Solution Chem (2007) 36: 997–1022
Table 4 (Continued) Toluene (1) + BM (2)
Toluene (1) + AMA (3)
Toluene (1) + MA (4)
Toluene (1) + VA (5)
x1
V¯m1
V¯m2
V¯m1
V¯m3
V¯m1
V¯m4
V¯m1
V¯m5
0.95
107.458
160.087
107.457
136.759
107.459
86.7624
107.459
94.2388
1
107.457
160.026
107.457
136.756
107.457
86.8677
107.457
94.3099
t = 40 °C 0
108.315
162.294
108.708
138.303
110.054
86.6514
109.666
94.9690
0.05
108.294
162.295
108.706
138.303
109.817
86.6572
109.479
94.9737
0.10
108.300
162.294
108.702
138.303
109.638
86.6719
109.327
94.9859
0.15
108.322
162.292
108.697
138.304
109.499
86.6932
109.205
95.0034
0.20
108.352
162.288
108.691
138.305
109.387
86.7207
109.106
95.0243
0.25
108.386
162.284
108.685
138.307
109.294
86.7554
109.026
95.0474
0.30
108.422
162.279
108.679
138.309
109.215
86.7983
108.961
95.0718
0.35
108.460
162.274
108.673
138.312
109.148
86.8503
108.908
95.0971
0.40
108.497
162.270
108.667
138.316
109.091
86.9118
108.865
95.1232
0.45
108.535
162.266
108.662
138.320
109.043
86.9820
108.828
95.1501
0.50
108.573
162.260
108.657
138.324
109.003
87.0590
108.797
95.1782
0.55
108.608
162.250
108.653
138.328
108.970
87.1400
108.770
95.2081
0.60
108.641
162.234
108.650
138.333
108.940
87.2213
108.746
95.2406
0.65
108.669
162.208
108.647
138.337
108.911
87.2991
108.725
95.2764
0.70
108.690
162.170
108.646
138.340
108.881
87.3699
108.706
95.3163
0.75
108.701
162.119
108.645
138.343
108.846
87.4316
108.689
95.3612
0.80
108.702
162.056
108.644
138.345
108.805
87.4851
108.674
95.4118
0.85
108.692
161.983
108.644
138.345
108.757
87.5353
108.662
95.4689
0.90
108.675
161.910
108.644
138.343
108.707
87.5931
108.653
95.5329
0.95
108.655
161.849
108.645
138.338
108.664
87.6779
108.647
95.6041
1
108.645
161.822
108.645
138.330
108.645
87.8195
108.645
95.6826
(b) A series of Legendre polynomials, Lk (x1 ) VmE = x1 x2
n
ak Lk (x1 )
(8)
k=0
which for the four first terms (k = 0, 1, 2, 3) become VmE = x1 x2 [a0 + a1 (2x1 − 1) + a2 (6x12 − 6x1 + 1) + a3 (20x13 − 30x12 + 12x1 − 1)].
(9)
Legendre polynomials belong to the category of orthogonal functions, such as Fourier, Bessel and Chebyshev, which have the valuable property that for a continuous series of observations (infinite) the values of the coefficients do not change as the number of terms in the series is increased. This is an important property because if a physical explanation can be attached to one of its coefficients, its value remains constant. For the case of discrete measurements, such as determination of molar volumes of mixing, the values of the coefficients will vary, but only slightly. In addition, the series of Legendre polynomials have the important characteristic that the structure of its first four terms is the same as that of the
J Solution Chem (2007) 36: 997–1022
1013
Table 5 Partial volume, molar volume of pure component and excess partial volume at infinite dilution, calculated from the apparent volume. All values in cm3 ·mol−1 V¯i∞
o Vmi
273.15
158.3933
158.8305
−0.4372
303.15
160.9772
160.5269
−0.4497
313.15
161.8306
162.2920
−0.4614
293.15
135.2152
135.1706
0.04458
303.15
136.7584
135.7104
0.04804
313.15
138.3393
138.3009
0.03844
293.15
85.8558
84.8787
0.9798
303.15
86.7872
85.7575
1.0297
313.15
87.6714
86.6504
1.0210
293.15
92.9588
92.3468
0.6120
303.15
94.2494
93.6376
0.6118
313.15
95.6077
94.9680
0.6397
T /K
V¯iE,∞
Butyl methacrylate (2)
Allyl methacrylate (3)
Methacrylic acid (4)
Vinyl acetate (5)
first four terms of the Redlich–Kister expression. The mathematical procedure to transform a power expansion, such as that of Redlich–Kister, into an orthogonal series has been described in detail by Tomiska [18, 19], who also provides the iteration formulas for Legendre or Chebyshev’s series of any order as well as the proof that the procedure is independent of the conversion coefficients from the actual excess property. Equations 7 and 8 were fitted using a least squares optimization procedure, with all points weighted equally and minimizing the following objective function, OF, defined by OF =
N (VmEi ,expt − VmEi ,calc )2 /N
(10)
1
where N is the number of observations. The values of the different adjustable parameters, Ak of Eq. 7 and ak , of Eq. 8 are reported in Tables 6 and 7 for different values of k, together with the pertinent statistics. The standard deviation s was calculated from s=
N [(VmEi ,expt − VmEi ,calc )2 /(N − k)]
(11)
i
where N is the number of observations and k is the number of adjustable parameters. The statistical significance of adding one or more terms after the third was examined using a χ 2 -based test, with the simultaneous requirement that the residues (given by the difference between the calculated and experimental value of the molar excess volume) be randomly distributed, as suggested by Wisniak and Polishuk [20]. Randomness of the residues was tested using the Durbin–Watson statistic. It was not deemed necessary to perform a stepwise regression. Figure 4 shows the residuals distribution of the Redlich–Kister fit for the
0.6812
Toluene + VA (1 + 5)
0.6946
Toluene + VA (1 + 5)
u=2 (eu − eu−1 )/
b Units: cm3 ·mol−1
ad =
−0.1135
−0.09857
−0.01765
−0.07627
−0.08790
−0.07147
−0.03225
−0.06007
−0.01578
−0.1117
−0.028589
−0.06999
A1
0.1444
0.002283
−0.02130
−0.02092
0.06447
0.03028
−0.002956
−0.02787
0.07606
0.06406
0.003921
−0.01222
A2
E E 2 u=1 eu ; eu = Vm,u,calc − Vm,u,exptl
0.7231
Toluene + VA (1 + 5)
N
1.163
Toluene + MA (1 + 4)
N
0.06664
Toluene + AMA (1 + 3)
Toluene + BM (1 + 2)
−0.4642
1.150
Toluene + MA (1 + 4)
t = 40 °C
0.07742
Toluene + BM (1 + 2)
Toluene + AMA (1 + 3)
−0.4334
1.153
Toluene + MA (1 + 4)
t = 30 °C
0.07029
−0.4203
A0
Toluene + AMA (1 + 3)
Toluene + BM (1 + 2)
t = 20 °C
System
−0.4045
−0.02185
0.005092
−0.004404
−0.05479
0.02088
−0.006348
A3
0.1229
0.08366
0.02248
−0.08526
−0.1355
A4
15.9
16.3
1.41
6.07
5.52
16.2
2.22
4.15
14.3
19.3
0.679
9.58
s × 104
E,∞ E ) Table 6 Coefficients, Ak , Eq. 7, standard deviation, s, Eq. 11, Durbin–Watson statistic, d a , (V¯mi x=0.5 , and V¯mi
1.91
2.47
2.21
2.40
2.15
2.40
1.72
2.75
1.86
2.32
2.52
1.81
da
18.0779
29.0829
1.66603
−11.6040
17.3650
28.7612
1.93548
−10.8340
17.0290
28.8160
1.77322
−10.5070
E) b 102 (V¯mi x=0.5
102.142
140.895
6.29947
−33.0245
84.6984
125.220
10.6710
−37.4267
74.2529
117.198
10.9786
−36.2509
E,∞ b 102 V¯m1
71.3599
116.810
2.76852
−47.2600
67.1167
110.926
4.22164
−50.3224
60.1389
99.0331
3.99134
−50.2499
E,∞ b 102 V¯m2
1014 J Solution Chem (2007) 36: 997–1022
0.6895
Toluene + VA (1 + 5)
0.7161
Toluene + VA (1 + 5)
u=2 (eu − eu−1 )/
b Units: cm3 ·mol−1
ad =
−0.1377
−0.1117
−0.01765
−0.07321
−0.08791
−0.07147
−0.03224
−0.06271
−0.04865
−0.09917
−0.03240
−0.06999
a1
0.09626
0.07176
−0.01420
0.03385
0.04298
0.02018
−0.001971
−0.005734
0.001983
−0.03475
0.002613
−0.008149
a2
E E 2 u=1 eu ; eu = Vm,u,calc − Vm,u,exptl
0.7712
Toluene + VA (1 + 5)
N
1.189
Toluene + MA (1 + 4)
N
0.05954
Toluene + AMA (1 + 3)
Toluene + BM (1 + 2)
−0.4544
1.160
Toluene + MA (1 + 4)
t = 40 °C
0.07643
Toluene + BM (1 + 2)
Toluene + AMA (1 + 3)
−0.4381
1.147
Toluene + MA (1 + 4)
t = 30 °C
0.07223
−0.4243
a0
Toluene + AMA (1 + 3)
Toluene + BM (1 + 2)
t = 20 °C
System
−0.01618
−0.008739
0.002038
−0.001762
−0.02191
0.008354
−0.002539
a3
0.02810
0.01912
0.005139
−0.01949
−0.03098
a4
16.4
16.8
1.45
6.26
5.68
16.6
2.28
4.28
14.7
19.9
0.699
9.84
s × 104
E,∞ b E ) Table 7 Coefficients, ak , Eq. 8, standard deviations s, Eq. 11, Durbin–Watson statistic d a , (V¯mi x=0.5 , and V¯m2
1.91
2.47
2.21
2.40
2.15
2.40
1.72
2.75
1.86
2.32
2.52
1.81
da
18.0792
29.0837
1.66628
−11.6039
17.3664
28.7609
1.93552
−10.8341
17.0290
28.8187
1.77298
−10.5081
E) b 102 (V¯mi x=0.5
102.142
140.894
6.29940
−33.0251
84.6982
125.220
10.6709
−37.4269
74.2528
117.197
10.9786
−36.2510
E,∞ b 102 V¯m1
71.3596
116.810
2.76846
−47.2602
67.7116
110.925
4.22158
−50.3228
60.1383
99.0326
3.99125
−50.2501
E,∞ b 102 V¯m2
J Solution Chem (2007) 36: 997–1022 1015
1016
J Solution Chem (2007) 36: 997–1022
Fig. 4 Residual distribution plot for the system toluene + allyl methacrylate at 40 °C, according to the fit given in Table 6
binary system toluene + allyl methacrylate at 40 °C, which is random as shown by the Durbin–Watson statistic. The fit of the remaining three binary systems also exhibits a random distribution of the residuals. The variation of VmE /x1 xi (i = 2, 3, 4, 5) with composition was used to test the quality of the binary data; this function is extremely sensitive to experimental errors, particularly in the dilute ranges and helps to detect outliers. In addition, its values at infinite dilution represent [15], which can be the values of the partial excess molar volume at infinite dilution, VmE,∞ i also calculated from the adjustable parameters using V¯mE,∞ = A0 − A1 + A2 − . . . = V¯m∞1 − Vmo1 1
(12)
= A0 + A1 + A2 + . . . = V¯m∞2 − Vmo2 V¯mE,∞ 2
(13)
for the Redlich–Kister expression and = a0 − a1 + a2 − . . . = V¯m∞1 − Vmo1 V¯mE,∞ 1
(14)
= a0 + a1 + a2 + . . . = V¯m∞2 − Vmo2 V¯mE,∞ 2
(15)
for the Legendre polynomials. In Eqs. 12–15, Vmoi is the molar volume of pure component i. In addition, it should be realized that in the absence of self-association, the value of the partial excess molar volume at infinite dilution reflects the true solute-solvent interaction. . The values of this property Equations 12 and 14 or 13 and 15 yield the same values of VmE,∞ i for the different systems are reported in Tables 6 and 7 and compare well with the ones calculated using apparent volumes. It should be realized that the values of the property at
J Solution Chem (2007) 36: 997–1022
1017
infinite dilution are probably less accurate because the data have been fitted with a technique that assigns equal statistical weight to all the points. Inspection of the results in Table 3 and Figs. 1–3 indicates that the excess molar volumes are negative for the binary of toluene + butyl methacrylate, positive for the other three binaries, and that the system toluene + allyl methacrylate presents near ideal behavior. The magnitude and sign of VmE is a reflection of the type of interactions taking place in the mixture. This is well exhibited by the mixtures studied here where the acrylate solutes are characterized by the simultaneous presence of one or two double bonds and an ester group. In addition, methacrylic acid has a free –COOH group, which can lead to H bonding. Hence, the relative magnitude of VmE is a result of the effect of breaking the ester’s dipole–dipole association; the negative sign indicates a net packing effect contributed by structural effects arising from interstitial accommodation. The excess volume curves are almost symmetrical indicating the absence of association effects. The maximum value of the excess molar volume for the system toluene + methacrylic acid is almost fifteen times that for toluene + allyl methacrylate, reflecting a substantial breaking of the self-packing structure of the acid, caused by intercalation of toluene molecules. The fact that the excess volumes of the system toluene + allyl methacrylate are slightly positive is indicative of the strong effect of the presence of a second double bond in the molecule of the monomer. First of all, this fact leads to a substantially packed monomer molecule, as shown by the large difference in density between pure butyl methacrylate and pure allyl methacrylate, in spite of a small difference in molecular weights. Second, when the monomer is dissolved in toluene, the intercalation effect caused by steric effects and the added attraction between the two dipole moments of the monomer with the π -cloud electron of the solvent is strong enough to overcome the internal self-attraction of the two dipole moments of the allyl methacrylate molecule. Vinyl acetate is weakly polar and alkyl benzenes are nearly non-polar. When these compounds are mixed, the non-polar hydrocarbon molecules intersperse among the vinyl acetate molecules, resulting in a decreased interaction between the dipoles of the acetate moiety. As polar interactions diminish, the excess volume becomes positive; that is, the change in intermolecular forces is stronger than the packing caused by geometrical effects. Table 3 and Figs. 1–3 describe the effect of temperature on the density and excess molar volumes of the four binary systems studied here. It is seen that the binary systems of toluene + butyl acrylate, + methacrylic acid and + vinyl acetate behave similarly, their VmE curves are shifted in a regular way with increasing temperature, and the excess molar volume becoming more positive (or more negative) as the temperature increases from 20 to 40 °C. Figure 5 shows that the system toluene + allyl methacrylate appears to present the unusual feature that although the density of its solutions decreases systematically as the temperature increases, the corresponding excess volumes behave differently: their values increase as the temperature goes from 20 to 30 °C and then decrease as the temperature increases to 40 °C. The interpretation of this behavior is not based on the effect of temperature on the interactions taking place within a given molecule or between two different molecules. It is simply the statistical effect of changing the dependent variable from density to excess volume, with the accompanying change in error distribution [21]. The latter can become very significant in systems like toluene + allyl methacrylate where the excess molar volumes are very small, indicating that the actual volume of the solution is almost identical to that of the ideal one. The general result for the four binary systems of the systematic decrease of the density with temperature is probably due to the net result of two opposing effects: increase of kinetic energy of the molecules of the solvent and the solute, which facilitates intercalation of one species into the other, and interaction between the dipole moments of the esters and the π electron cloud of the solvent.
1018
J Solution Chem (2007) 36: 997–1022
Fig. 5 Variation with temperature of density (empty symbols) and excess volume (full symbols) for the system toluene + allyl methacrylate. 20 °C: E,F; 30 °C: P, Q; 40 °C: !, "
Since the change of VmE with temperature and the temperature interval are small, the excess isobaric thermal coefficient of expansion can be calculated by following the finite difference approximation: E E E E + V1m )][(V2m − V1m )/(T2 − T1 )] α E = (1/VmE )(∂VmE /∂T )P = [2/(V2m
(16)
E E E E α E = (1/5)(V2m − V1m )/(V2m + V1m ).
(17)
For both the Redlich–Kister and the Legendre expansion the value of VmE at x = 0.5 is equal to A0 , and a0 , respectively, so that Eq. 17 becomes: α E (x = 0.5) = (1/5)(A02 − A01 )/(A01 + A02 ).
(18)
In Eqs. 16–18 the indexes 1 and 2 represent the values of the parameter at the corresponding absolute temperature (T1 and T2 ). In order to avoid the problems caused by a change in the distribution of the error, the isobaric thermal coefficient of expansion can be calculated directly from the measured density values, as follows: α E = −(1/ρ)(∂ρ/∂T )P − (1/2)[−(1/ρ)(∂ρ/∂T )P ,solvent − (1/ρ)(∂ρ/∂T )P ,solute ]
(19)
α = (1/5)(ρ2 − ρ1 )/(ρ2 + ρ1 ) + (1/2)[(1/ρ)(dρ/dT )solvent + (1/ρ)(dρ/dT )solute ]. (20) E
The value of dρ/dT corresponds to the value of coefficient b given in Table 2. The values of α E (x = 0.5) calculated for the two temperature intervals 20 to 30 °C and 30 to 40 °C are given in Table 8 for the four binary systems studied here and show that the excess expansion coefficients are of almost the same order of magnitude.
J Solution Chem (2007) 36: 997–1022 Table 8 Isobaric thermal expansion coefficient at x = 0.5
System
Toluene + BM (1 + 2) Toluene + AMA (1 + 3) Toluene + MA (1 + 4) Toluene + VA (1 + 5)
1019 α E (x = 0.5), K−1 20–30 °C
30–40 °C
1.08·10−3
1.10·10−3
1.12·10−3
1.14·10−3
6.88·10−4
1.08·10−3
1.42·10−3
1.26·10−3
3.1 Spectroscopic Study of the Mixtures In order to explain the results obtained at the molecular level, it was decided to study the spectra of the four binary mixtures, at equimolar compositions, by infrared spectroscopy (FT-IR model Magna 550, manufactured by Nicolet) coupled with an attenuated total reflectance device (ATR) and operating with a resolution of 0.5 wave numbers, under the assumption that the possible molecular interactions will alter the spectroscopic characteristics of the mixtures when compared to those of the pure components. The test was focused on the absorption of the C=O carbonyl group, which is particularly sensitive to electronic interactions and presents a symmetric stretch in the range 1760 to 1630 wave numbers. Any interaction affecting the electronic density of this group will enlarge or shorten the bond and change the characteristic wave number. Interactions that enlarge the bond (caused, for example, by the presence of a charged complex) will absorb at lower wave numbers causing a displacement towards the red, while those that shorten the bond will cause the absorption to take place at higher wave numbers with a displacement towards the blue. Another possibility to study the possible structural effects that can affect the C=O group is the use of the 13 C NMR spectrum: the magnetic environment resulting from an attractive or repulsive interaction with another functional group will cause a change in the chemical shift of the carbonyl group. The C=O group of butyl methacrylate presents an IR absorption at 1717.36 wave numbers that increases to 1718.24 when mixed with toluene. The change in 0.88 wave numbers is not significant and would seem to indicate that no interactions exist between the components that result in the displacement of the absorption band. Nevertheless, the system toluene + butyl methacrylate presents negative excess volumes, suggesting that the molecular orbitals of toluene do interact with those of the acrylic group. The following figure, obtained by an optimized molecular mechanics model (Chem 3D pro 8.0 Molecular Modeling and Analysis© , Cambridge Software), shows a possible transfer complex between the two compounds (see Scheme 1). The existence of such a complex was investigated by determining the 13 C NMR spectrum of an equimolar mixture at 20.7 and 39.9 °C, using a Gemini 200 apparatus, manufactured by Varian, operating at 50.289 MHz, using methanol as an internal standard (the alcohol was introduced separately in a 150 µL glass tube and assigned a displacement of 43.109 ppm), and the fact that at 20.7 °C the C=O group of pure butyl methacrylate presents a displacement band at 160.191 ppm (Table 9). As shown in the table, the increase in chemical shift of 2.694 ppm at 20.7 °C and 2.897 ppm at 39.9 °C for the mixture of toluene + butyl methacrylate, can be attributed to a deshielding effect of the induced magnetic field, Bi, over the C=O group caused by the nearness of the aromatic ring of toluene, as illustrated by Scheme 2. The C=O group of pure vinyl acetate presents an IR absorption band at 1758.32 cm−1 , which in an equimolar mixture with toluene moves to 1759.25 cm−1 . This small displace-
1020
J Solution Chem (2007) 36: 997–1022
Scheme 1
Table 9 Chemical shift of 13 C NMR C=O band for equimolar solutions of toluene + monomer Temperature, °C
Chemical shift, ppm Pure monomer
Mixture
Difference
20.7
162.885
160.191
2.694
39.9
163.287
160.390
2.897
20.7
167.149
167.642
0.493
30.9
167.316
167.422
0.106
Butyl methacrylate
Methacrylic acid
Scheme 2
ment can be attributed to the fact that the C=O group of vinyl acetate is prevented from conjugation with the double bond by the presence of an oxygen atom. As shown in Scheme 3, to access the electronic density required by the aromatic ring, the vinyl group requires the difficult-to-achieve assistance of the free electron pair of oxygen. The excess volume of the mixture being positive verifies that this phenomenon does not take place.
J Solution Chem (2007) 36: 997–1022
1021
Scheme 3
Scheme 4
The IR spectrum of the solution of toluene + allyl methacrylate shows that there is a very weak interaction between the functional groups of the components, as evidenced by the displacement of the absorption band of the C=O group of allyl methacrylate from 1717.35 cm−1 for the pure component to 1717.39 cm−1 when dissolved in toluene. The small difference of 0.04 wave numbers implies that the C=O group does not experience an attractive interaction with the aromatic group of toluene, as reflected in the very small positive values of the excess volume. In the case of the toluene + methacrylic acid system it should be noticed that the acid is capable of forming dimers through hydrogen bridges. These dimers exert attractive forces that will influence the displacement of the C=O band, as shown in Scheme 4. Solutions of toluene + methacrylic acid show an increase of 6.37 cm−1 in the position of the absorption band of the C=O group, an increase that can be attributed instead of a repulsive interaction between the molecules, to a decrease in the strength of the hydrogen bond by a dilution effect caused by toluene. This possibility was further studied using the technique of 13 C NMR, with the results given in Table 9. At 20.7 °C the chemical shift of the C=O group of pure methacrylic acid appears at 167.642 ppm and can be attributed to the dimer of the acid. In an equimolar mixture with toluene the chemical shift of the carbonyl group appears at 167.149 ppm; the decrease of 0.493 ppm points to a decrease in the degree of association of the acid since a higher frequency will be required by the resonance of the carbon nucleus of the C=O group at lower degrees of association. The same effect is observed at 39.9 °C. A further remark is the influence of the solvent on the excess molar volume of the mixture. For example, at 25 °C solutions of methacrylate with benzene present positive values of the excess molar volume with a maximum of about 105 cm3 ·mol−1 [3], which decreases to about 65 cm3 ·mol−1 in cyclohexane [1], and becomes negative when the solvent is toluene. For vinyl acetate in toluene the maximum molar excess volume is about 140 cm3 ·mol−1 in benzene [3] 100 cm3 ·mol−1 in cyclohexane [1] and 18.5 in toluene. References 1. Peralta, R.D., Infante, R., Cortez, G., Villarreal, L., Wisniak, J.: Volumetric properties of cyclohexane with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene at 298.15 K. Thermochim. Acta 390, 47–53 (2002)
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2. Peralta, R.D., Infante, R., Cortez, G., Torres-Lubián, J.R., Wisniak, J.: Volumetric properties of 1,2dimethylbenzene + ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene at 298.15 K. Thermochim. Acta 402, 247–252 (2003) 3. Peralta, R.D., Infante, R., Cortez, G., Cisneros, A., Wisniak, J.: Densities and excess volumes of benzene with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene at 298.15 K. Thermochim. Acta 398, 39–46 (2003) 4. Peralta, R.D., Infante, R., Cortez, G., Rodríguez, O., Wisniak, J.: Volumetric properties of toluene with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene at 25 °C. J. Solution Chem. 31, 175–186 (2002) 5. Peralta, R.D., Infante, R., Cortez, G., López, R.G., Wisniak, J.: Volumetric properties of 1,1dimethylethyl methyl ether with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene at 298.15 K. Int. J. Thermophys. 24, 173–183 (2003) 6. Peralta, R.D., Infante, R., Cortez, G., Ramírez, R.R., Wisniak, J.: Densities and excess volumes of binary mixtures of 1,4-dioxane with either ethyl acrylate, or styrene at T = 298.15 K. J. Chem. Thermodyn. 35, 239–250 (2003) 7. Peralta, R.D., Infante, R., Cortez, G., Ramos, L.F., Wisniak, J.: Excess molar volumes of tetrahydrofuran with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene at 298.15 K. Phys. Chem. Liq. 41, 361–369 (2003) 8. MacKnight, W.J., McKenna, L.W., Read, B.E., Stein, R.S.: Properties of ethylene–methacrylic acid copolymers. J. Phys. Chem. 72, 1122–1126 (1968) 9. Resa, J.M., Iglesias, M., González, C., Lanz, J., Mtz. de Ilarduya, J.A.: Excess volumes of binary mixtures of vinyl acetate and aromatic hydrocarbons. J. Chem. Thermodyn. 33, 723–732 (2001) 10. Peralta, R.D., Infante, R., Cortez, G., Cadenas, G., Wisniak, J.: Densities, excess volumes, and partial molar volumes of m-xylene + ethyl acrylate, + butyl acrylate, + methyl methacrylate, and + styrene at 298.15 K. Int. J. Thermophys. 24, 1061–1071 (2003) 11. Peralta, R.D., Infante, R., Cortez, G., Angulo, J.L., Wisniak, J.: Volumetric properties of ethylbenzene with ethyl acrylate, butyl acrylate, methyl methacrylate, and styrene at 298.15 K. Phys. Chem. Liq. 40, 649–660 (2003) 12. Gong, H., Chen, W., Chou, Y., Chen, M., Zheng, G.: Excess volumes of the mixing of benzene and toluene with some polar solvents at 293.15 K. Wuli Huaxue Xuebao 1, 293–298 (1985) 13. George, J., Sastry, N.V., Prasad, D.H.L.: Excess molar enthalpies and excess molar volumes of methyl methacrylate + benzene, + toluene, + p-xylene, + cyclohexane and + aliphatic diethers (diethyl, diisopropyl and dibutyl). Fluid Phase Equilib. 214, 39–51 (2003) 14. Wisniak, J., Sandoval, L.E., Peralta, R.D., Infante, R., Cortes, G., Elizalde, L.E., Soto, H.: Density and volumes of mixing of the ternary system ethylbenzene + styrene + ethyl acrylate and its binaries at 298.15 K. J. Solution Chem. 36, 135–152 (2007) 15. Van Ness, H.C., Abbott, M.M.: Classical Thermodynamics of Nonelectrolyte Solutions. McGraw-Hill, New York (1982) 16. Glasstone, S.: Textbook of Physical Chemistry. Van Nostrand, New York (1946) 17. Redlich, O., Kister, A.T.: Thermodynamics of nonelectrolytic solutions. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 40, 345–348 (1948) 18. Tomiska, J.: Zur Konversion der Anpassungen Thermodynamischer Funktionen Mittels einer Reihe Legendre’scher Polynome und der Potenzreihe. CALPHAD 5, 93–102 (1981) 19. Tomiska, J.: Mathematical conversions of the thermodynamic excess functions represented by the Redlich–Kister expansion, and by the Chebyshev polynomial series to power series representations and vice-versa. CALPHAD 8, 283–294 (1984) 20. Wisniak, J., Polishuk, A.: Analysis of residues—A useful tool for phase equilibrium data analysis. Fluid Phase Equilib. 164, 61–82 (1999) 21. Shacham, M., Wisniak, J., Brauer, N.: Error analysis of linearization methods in regression of data for the van Laar and Margules equations. Ind. Eng. Chem. Res. 32, 2820–2825 (1993) 22. TRC Thermodynamic Tables—Hydrocarbons. Thermodynamics Research Center, The Texas A&M University System, College Station, Texas, extant 2004; Table db-3220-0 (October 31, 2000) 23. DIPPR 801 Database, Properties for Industrial Process Design. Design Institute for Physical Properties (DIPPR), American Institute of Chemical Engineers, New York, extant 2006 24. Yaws, C.: Chemical Properties Handbook. McGraw-Hill, New York (1999)
