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Excess molar volumes and excess molar heat capacities of (polyethylene glycols + water) at temperatures betweenT = 278 K andT = 328 K
J. Chem. Thermodynamics 1999, 31, 289–300 Article No. jcht.1998.0458 Available online at http://www.idealibrary.com on
Excess molar volumes and excess molar heat capacities of (polyethylene glycols + water) at temperatures between T = 278 K and T = 328 K C. Aucouturier, G. Roux-Desgranges,a and A. H. Roux Lab Thermodynamique et G´enie Chimique, UPRES A CNRS 6003, Universit´e Blaise Pascal, 63177 Aubi`ere cedex, France Densities of aqueous solutions of the following polyethylene glycols (PEGs) of average molar mass (300, 400, and 600) g·mol−1 have been measured over the entire mass fraction range at T = 298.15 K, using a vibrating-tube densimeter. In the case of PEG 300, heat capacities have been determined at T = 298.15 K in dilute solutions with a flow microcalorimeter. In addition, densities and heat capacities of (PEG 300 + water) have been measured over the entire composition range using a differential scanning microcalorimeter in the temperature interval T = (278 to 328) K. Excess molar volumes and excess molar heat capacities as functions of mole fraction have been deduced therefrom for the selected temperatures. Excess volumes are found to be negative, and become more negative as the molar mass of PEG increases and/or the temperature decreases. In contrast, excess heat c 1999 Academic Press capacities are always positive, and increase with temperature. KEYWORDS: polyethylene glycols; excess volumes; excess heat capacities; excess thermal expansivities; densimeter; microcalorimeter; d.s.c.
1. Introduction Polyethylene glycols (PEG) are neutral polymers that have a well-defined molecular structure. Whatever their molar mass, they exhibit a high solubility over a wide range of temperatures in water as well as in different types of organic solvents. As a consequence, they have found a wide variety of applications in numerous industrial processes from petroleum, or textiles to pharmaceutical and biochemical technologies. On the fundamental aspect, due to their interesting characteristics, they can be considered as model polymers for study by various experimental methods. The possibility of having a wide range of polymers of increasing molar mass makes these compounds particularly interesting for the correlation of thermodynamic properties of polymer solutions or mixtures and the prediction of phase diagrams. The peculiar structures of PEGs in aqueous solutions have been investigated using different techniques(1–5) in order to ascertain their high solubility as compared to other polyethers (methylene, propylene, butylene oxides) for which a very low solubility is observed only with the shorter oligomers. Despite their importance, it is surprising that relatively little a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/99/020289 + 12 $30.00/0
c 1999 Academic Press
290
C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
attention has been paid to the determination of the thermodynamic properties of aqueous mixtures of PEGs over a wide range of molar masses and a wide range of temperatures.(5–9) Apart from the data of Malcolm and Rowlinson,(6) and those of M¨uller and Rasmussen(9) for the excess volumes of several PEGs, no data are available in the literature. To our knowledge, only few data by Andersson and Olofsson(8) on the heat capacities of aqueous polymer mixtures where concentration and temperature effects have been investigated exist. In fact, the determination of thermodynamic properties have mainly centered upon aqueous solutions of oligomers where the number of repeat units of ethoxyl groups is lower than six. The aim was essentially to derive information about solute–solvent or molecular interactions and to correlate thermodynamic properties using group contribution theories or thermodynamic models of interactions.(10–15) In the present work, we have investigated polymers that are intermediate between oligomers and true polymers to provide useful data for the development of theories for testing or predicting the behaviour of aqueous polymer solutions when conformational changes are induced by size. We have undertaken measurements of densities and heat capacities of mixtures of water with a series of polymers of increasing molar mass, covering the mole fraction range x = (0 to 0.6) and the temperature range (278 to 328) K. Accurate excess molar volumes and excess molar heat capacities have been deduced therefrom.
2. Experimental The different polyethylene glycols (PEG 300, PEG 400, and PEG 600) were purchased from Aldrich and used as supplied, without further purification. For these low molar mass compounds the polydispersity is small. The associated number is relative to the average molar mass of the polymer and does not generally correspond to an entire number of units of ethoxyl groups. A rounded number was chosen for each polymer: six for PEG 300, nine for PEG 400, and 13 for PEG 600. The corresponding calculated molar masses are close to the maximum of the polydispersity curve of the polymer.(16) All solutions were prepared gravimetrically using deionized and degassed water at least one day before the measurements to ensure equilibrium in the relatively high viscosity mixtures. Densities ρ were obtained using a Picker vibrating-tube densimeter (Sodev, 03D),(17) whose calibration constants were determined under vacuum and with water for which the variation of density with temperature is well known.(18) At T = 298.15 K, the densities were measured as a function of composition. The measurement of the reference period of water was repeated between solutions to ensure that the difference in the density between the solution and water is determined with an accuracy of ±5·10−6 g·cm−3 . The procedure was somewhat different for densities determined as a function of temperature. First, starting with the lowest temperature and, at selected temperature steps at which equilibrium was achieved, the reference periods were recorded for water. Then, a solution with a given composition was introduced into the tube of the densimeter while keeping the flow rate extremely low, and using the stepwise procedure to record the solution periods at each selected temperature. The determination of the reference periods of water at the selected temperatures was repeated between solutions to monitor the shifts in the reference periods. Although less precise than
Thermodynamics of (polyethylene glycols + water)
291
TABLE 1. Densities ρ and molar heat capacities C p,m of pure PEGs at different temperatures ρ/(g·cm−3 )
C p,m /(J·K−1 ·mol−1 )
PEG
T /K
This work
PEG 300
298.15
1.12175
PEG 400
298.15
1.12162
PEG 600
298.15
1.12177
PEG 300
278.15
1.13727
606.9
PEG 300
288.15
1.12984
607.8
PEG 300
308.15
1.11350
612.1
PEG 300
318.15
1.10529
615.8
PEG 300
328.15
1.09717
619.7
Literature
This work 609.4
1.1223(9)
Note: the densities and the heat capacities of water used as the reference liquid for the selected temperatures are from Kell.(18)
the procedure used at constant temperature, this method, nevertheless, ensures an accuracy in the density measurements of about ±1·10−5 g·cm−3 . Heat capacities per volume unit were mainly determined with a differential scanning microcalorimeter (d.s.c. 2) from Setaram. Volumetric heat capacity measurements were obtained between T = (278 and 328) K with an accuracy of ±1·10−4 J·K−1 ·cm−3 using a continuous scanning mode at a fixed rate. This rate was chosen slow enough as to be close to thermodynamic equilibrium while allowing a sufficient sensitivity. Calibration curves were established to convert thermal flux into volumetric heat capacities (the cell being completely filled), and water was chosen as the reference liquid for which the heat capacity values are taken from the recommended values of Kell.(18) The apparatus was described previously.(19) The scanning procedure was similar to that published recently.(20) In addition, a series of measurements were also performed at T = 298 K with a Picker flow microcalorimeter,(21) in order to compare the two instruments and to check the accuracy of the d.s.c. microcalorimeter. Since the viscosity of the aqueous solutions of the PEGs increases rapidly with concentration, the use of the Picker Cp-microcalorimeter was limited to the case of relatively dilute solutions. The volumetric heat capacities interpolated at the chosen temperatures were converted into specific heat capacities using the densities of the solutions.
3. Results Densities were measured for the aqueous mixtures of PEG 300, 400, and 600 at T = 298.15 K, and in the case of PEG 300 at the temperatures (278, 288, 298, 308, 318, and 328) K. In parallel, heat capacities at the same temperatures were obtained for PEG 300. The densities and molar heat capacities of the pure PEGs at the different temperatures are given in table 1 together with the scarce literature data available for comparison. The excess molar volumes and excess molar heat capacities of the PEG solutions derived, respectively, from the densities and specific heat capacities are reported in table 2 for the
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C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
TABLE 2. Excess molar volumes VmE for {PEG (300, or 400, or 600) + water} and excess molar heat capacities C Ep,m for (PEG 300 + water) at T = 298.15 K and mole fraction x of PEG C Ep,m −1 J·K ·mol−1
x
−2.1·10−3
0.05
3.46·10−3
−6.43·10−2
9.1·10−4
−2.51·10−2
1.87·10−3
−2.13·10−2
0.45
4.97·10−3
1.93·10−3
−2.22·10−2
3.83·10−3
−4.49·10−2
5.74·10−3
x
VmE 3 cm ·mol−1
1.94·10−4
PEG 300
VmE 3 cm ·mol−1 PEG 400
VmE 3 cm ·mol−1
x
PEG 600
−9.30·10−2
1.84·10−3
−5.08·10−2
8.61·10−3
−0.1654
5.47·10−3
−0.1563
0.89
1.005·10−2
−0.1934
9.04·10−3
−0.2638
−6.80·10−2
1.30
2.002·10−2
−0.3950
1.353·10−2
−0.3993
9.47·10−3
−0.1143
2.07
5.015·10−2
−0.8918
1.794·10−2
−0.5284
1.133·10−2
−0.1387
2.42
7.345·10−2
−1.1214
2.239·10−2
−0.6505 −0.7566
1.415·10−2
−0.1752
2.93
9.994·10−2
−1.2660
2.655·10−2
1.862·10−2
−0.2324
3.62
0.1151
−1.3183
3.096·10−2
−0.8586
2.062·10−2
−0.2598
3.94
0.1993
−1.3746
3.515·10−2
−0.9450
2.789·10−2
−0.3545
4.90
0.3011
−1.2579
4.358·10−2
−1.0915 −1.2039 −1.3403
3.243·10−2
−0.4119
5.41
0.3974
−1.1280
5.201·10−2
3.505·10−2
−0.4423
5.67
0.5020
−0.9529
6.638·10−2
3.792·10−2
−0.4770
5.97
8.375·10−2
−1.4422
4.213·10−2
−0.5287
6.36
0.1124
−1.5247
4.576·10−2
−0.5670
6.68
0.1534
−1.5457
5.593·10−2
−0.6762
7.42
0.2214
−1.5035
7.105·10−2
−0.8107
8.49
0.3154
−1.3455
8.764·10−2
−0.9272
9.20
0.3912
−1.2101
0.1177
−1.0675
10.29
0.4480
−1.1070
0.1598
−1.1633
10.87
0.4982
−1.0216
0.2232
−1.1919
0.2764
−1.1636
12.99 a
0.3610
−1.0686
14.30 a
0.4332
−0.9617
13.41 a
0.4817
−0.8863
12.62 a
0.5255
−0.8145
0.5951
−0.7082
0.6147
−0.674
0.7018
−0.524
0.8110
−0.332
0.8949
−0.181
11.33 a
a Data from d.s.c. microcalorimeter.
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293
TABLE 3. Excess molar volumes VmE for (PEG 300 + water) at temperature T and mole fraction x of PEG 300 VmE /(cm3 ·mol−1 )
x T /K:
278.15
288.15
298.15
308.15
318.15
328.15
9.5·10−3
−0.131
−0.120
−0.115
−0.112
−0.108
−0.105
1.88·10−2
−0.267
−0.245
−0.234
−0.226
−0.218
−0.212
2.79·10−2
−0.409
−0.375
−0.356
−0.343
−0.328
−0.318
5.41·10−2
−0.758
−0.696
−0.655
−0.623
−0.594
−0.567
8.73·10−2
−1.060
−0.975
−0.920
−0.871
−0.828
−0.772
0.1254
−1.233
−1.134
−1.070
−1.016
−0.964
−0.920
0.1607
−1.336
−1.250
−1.204
−1.146
−1.089
−1.030
0.2232
−1.356
−1.251
−1.192
−1.143
−1.096
−1.047
0.2764
−1.314
−1.191
−1.134
−1.099
−1.054
−1.008
0.3610
−1.201
−1.096
−1.047
−1.007
−0.964
−0.920
0.4332
−1.107
−1.012
−0.970
−0.932
−0.894
−0.846
0.4817
−1.040
−0.939
−0.901
−0.879
−0.839
−0.808
0.5255
−0.975
−0.860
−0.833
−0.808
−0.782
−0.754
0.5951
−0.860
−0.724
−0.708
−0.693
−0.677
−0.652
TABLE 4. Excess molar heat capacities C Ep,m for (PEG 300 + water) at temperature T and mole fraction x of PEG 300 C Ep,m / (J·K−1 ·mol−1 )
x T /K:
278.15
288.15
298.15
308.15
318.15
328.15
9.5·10−3
1.42
1.83
2.14
2.34
2.50
2.53
1.88·10−2
2.10
3.06
3.73
4.16
4.49
4.61
2.79·10−2
2.36
3.86
4.80
5.59
6.10
6.43
5.41·10−2
3.28
5.61
7.36
8.73
9.75
10.45
8.72·10−2
4.61
7.28
9.34
11.00
12.30
13.34
0.1254
5.53
8.10
10.11
11.73
12.99
13.91
0.1607
7.19
9.46
11.30
12.80
14.09
15.03
0.2232
9.90
11.86
13.38
14.65
15.72
16.59
0.2764
10.21
11.88
12.99
13.85
14.79
15.43
0.3610
12.55
13.50
14.30
14.99
15.64
16.16
0.4332
11.83
12.49
13.41
13.58
13.95
14.00
0.4817
11.55
11.93
12.62
12.62
12.20
12.84
0.5951
10.96
11.27
11.33
11.38
11.43
11.18
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C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
series of PEGs at T = 298.15 K, and in tables 3 and 4 at the selected temperatures for PEG 300. Generally these quantities are expressed on a mole fraction scale, according to the relationships: VmE = {x M1 + (1 − x)M2 }/ρ − x M1 /ρ1 − (1 − x)M2 /ρ2 , C Ep,m = {x M1 + (1 − x)M2 }c p − x M1 c p1 − (1 − x)M2 c p2 .
(1) (2)
However, when relatively high molar mass compounds are studied, specific excess properties can be defined on a mass fraction scale, to compare easily the effect of the chain length over the entire range: v E = 1/ρ − w/ρ1 − (1 − w)/ρ2 , cEp = c p − wc p1 − (1 − w)c p2 .
(3) (4)
The excess molar quantities YmE are related to the specific quantities y E by: YmE = y E {x M1 + (1 − x)M2 }.
(5)
In these relations, M1 and M2 are the molar masses of the pure PEG and water, ρ1 and ρ2 their densities, and c p1 and c p2 their specific heat capacities, respectively; ρ and c p are the density and the specific heat capacity of the PEG solution for which w and x represent the mass fraction and the mole fraction of PEG, respectively. Excess molar properties have been reported against mole fraction in tables 2 to 4. However, by using the mole fraction scale, the fitting of all the data proved to be quite difficult, leading to abnormal shape, or requiring too high a number of parameters because of the lack of data at high mole fractions. Fortunately, the specific excess quantities cover the entire mass fraction range and are easily fitted using a least-squares method to determine the coefficients of the Redlich–Kister equation, which is expressed as follows: y E = w(1 − w)
3 X
ai (2w − 1)i .
(6)
i=0
The coefficients ai are given in table 5 for the excess specific volumes and specific heat capacities with the corresponding standard deviations estimated according to the relation: X 1/2 n E E (ycalc − yexpt )2 /(n − p) , (7) s(y E ) = i=1
where n is the number of experimental points and p the number of selected fitting coefficients. The composition dependence of the excess molar volumes and excess molar heat capacities are represented as a function of the mole fraction in figures 1 to 4. Figures 1 and 2 illustrate the effect of the chain length of the different PEGs on VmE at T = 298.15 K. For PEG 300, the temperature effect on VmE is shown in figure 3, and that on C Ep,m in figure 4. The only reliable data for comparison are those obtained by M¨uller and Rasmussen(9) on the excess volumes of PEG 400. These values are in good agreement with our results as shown in figures 1 and 2. In contrast, good quality data exist for the lower PEGs containing
Thermodynamics of (polyethylene glycols + water)
295
TABLE 5. Coefficients ai and standard deviations s(y E ) for the representation of the specific excess quantities expressed on a mass fraction scale at temperature T by equations (6) and (7) T /K
102 ·a0
102 ·a1
102 ·a2
102 ·a3
102 ·s
y E = v E /(cm3 ·g−1 ) PEG 300 a
298.15
−8.4499
−4.9188
1.4374
2.2417
4.7·10−3
PEG 400
298.15
−9.0097
−5.3313
1.4381
2.3470
5.3·10−3
PEG 600
298.15
−9.4807
−5.7513
1.4316
2.6385
5.2·10−3
PEG 300
278.15
−9.7114
−5.3343
1.8332
1.8744
1.6·10−2
288.15
−8.9421
−5.1479
1.7199
2.3481
1.8·10−2
298.15
−8.4309
−4.8990
1.3937
2.2639
2.5·10−2
308.15
−8.0049
−4.5355
1.0739
1.9239
2.3·10−2
318.15
−7.6198
−4.2146
0.9249
1.6348
2.2·10−2
328.15
−7.2643
−3.8024
0.7395
1.2605
2.0·10−2
y E = cEp / (J·K−1 ·g−1 ) PEG 300 a
298.15
90.010
2.942
29.910
40.270
0.41
PEG 300
278.15
39.401
1.796
74.003
52.479
0.56
288.15
68.428
−2.680
48.643
53.781
0.53
298.15
89.508
−1.603
30.967
48.831
0.59
308.15
106.689
1.121
13.135
43.167
318.15
118.213
17.689
10.574
328.15
126.921
21.690
0.63 0.84 0.79
a Series measured separately at T = 298.15 K with a densimeter and a Picker microcalorimeter.
1 to 4 ethoxyl groups.(9, 10, 13) In the figures, the solid lines correspond to values obtained by fitting the excess specific quantities to equation (6) using the parameters given in table 5. The excess thermal molar expansivities of PEG 300 obtained by a finite difference approximation (1VmE /1T ) of: (αp Vm )E = (∂ VmE )/(∂ T ) p ,
(8)
are presented in figure 5. They were calculated at T = (298 and 318) K from the temperature dependence of the experimental excess volumes of PEG 300 for each concentration. In fact, the use of the smoothed values leads to artefacts in the variations of (α p Vm )E as VmE varies slightly with temperature. The excess thermal molar expansivities of PEG 400 and triethylene glycol at T = 308 K deduced from the data of M¨uller and Rasmussen(9) are also reported in figure 5 for comparison purposes.
4. Discussion When a solute in a hydro-organic mixture shows an amphiphilic and/or polar character, negative excess volumes and positive excess heat capacities are observed. On a molar scale,
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C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
0
VmE/(cm3.mol–1)
–0.5
–1
–1.5
–2 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 1. Excess molar volumes VmE of {xPEG + (1 − x)H2 O} at T = 298.15 K. M , {xPEG300 + (1 − x)H2 O}; N , from temperature scanning measurements; , {xPEG 400 + (1 − x)H2 O}; , M¨uller and Rasmussen;(9) ¤ , {xPEG 600 + (1 − x)H2 O}; —, using equation (6).
◦
•
VmE/x (cm3.mol–1)
–5
–15
–25
–35
0
0.05
0.1
0.15
x FIGURE 2. Variation of VmE /x of {xPEG + (1 − x)H2 O} at T = 298.15 K. M , {xPEG 300 + (1 − x)H2 O}; N , from temperature scanning measurements; , {xPEG 400 + (1 − x)H2 O}; , M¨uller and Rasmussen;(9) ¤ , {xPEG 600 + (1 − x)H2 O}; —, using equation (6).
◦
•
Thermodynamics of (polyethylene glycols + water)
297
VmE/(cm3.mol–1)
0
–0.5
–1.0
–1.5 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 3. Excess molar volumes VmE of {xPEG 300+(1− x)H2 O} at temperature T : ¥ , T = 278 K; ¤ , T = 288 K ; M , T = 298 K; , T = 308 K ; , T = 318 K ; ¨ , T = 328 K; —, using equation (6).
•
◦
20
Cp,E m/(J.K–1.mol–1)
15
10
5
0
0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 4. Excess molar heat capacities C Ep,m of {xPEG 300 + (1 − x)H2 O} at temperature T : ¥ , T = 278 K; ¤ , T = 288 K; M , T = 298 K; , T = 308 K; , T = 318 K ; ¨ , T = 328 K ; N , T = 298 K, with a Picker calorimeter; —, using equation (6).
•
◦
298
C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
(αpVm)E/(cm3.mol–1.K–1)
0.008
0.006
0.004
0.002
0 0
0.2
0.4
0.6
0.8
1.0
x FIGURE 5. Excess thermal molar expansivities (α p Vm )E of {xPEG + (1 − x)H2 O} at temperature T . , {xPEG 300 + (1 − x)H2 O} at T = 298 K; , {xPEG 300 + (1 − x)H2 O} at T = 318 K; N , {xPEG 400 + (1 − x)H2 O} at T = 308 K from M¨uller and Rasmussen;(9) ¤ , {xHO(EO)3 H + (1 − x)H2 O} at T = 308 K from M¨uller and Rasmussen.(9)
◦
•
as shown in figures 1 to 5, the extrema of these excess quantities are generally skewed towards low x values. Excess volumes become more negative with increase in the chain length of the PEG (figure 1), and the minimum, situated near x = 0.2, is slightly shifted towards lower x values. Furthermore, in the dilute region, the variations of VmE /x against mole fraction, shown in figure 2 for the three PEGs, point clearly to hydrophobic interactions between the PEG and water. The resulting increase in the water structure is expressed by the deeper minimum situated close to x = 2·10−2 , when the chain length of PEG increases. The minima of the excess volumes are also deeper when the temperature decreases (figure 3), but the variation is relatively weak, leading to small positive excess thermal expansivities. Within the uncertainty of the measurements, this quantity seems to be mostly independent of the number of ethoxyl units of the PEG (except perhaps for the lowest oligomers where the proximity effect of the hydroxyl groups plays a more marked role) and the temperature. The excess heat capacities, reported in figure 4, show large positive values; their maxima are shifted to lower x values, and an increase in temperature results in an increase in the excess values. When comparing the different polyether–water mixtures, the specific intermolecular interactions result mainly from the hydration of the ethoxyl units through hydrogen bonding between oxygen ether and the hydrogen atom of water, and/or the enhancement of the water structure (iceberg formation) around the hydrophobic hydrocarbon groups (ethyl) of the polymer chains. In the particular case of the PEGs chains, the repeating distance between the oxygen atoms in the PEG chain fits between the oxygen atoms of water,
Thermodynamics of (polyethylene glycols + water)
299
this conformation being the most favourable condition for insertion into the net of water clusters. Thus, when interacting with water, the PEGs give rise to a well-defined structure(3) in which the hydrogen bonding becomes the preponderant interaction.(1, 4) Several structural models have been suggested in order to explain the high solubility of the PEGs. In the case of the lower molar mass PEGs, the oxygen ether can be directly involved through hydrogen bonds in the water lattice,(14) and the hydrophobic interaction mainly controls the solution behaviour.(5) In general, it is assumed that a (water + PEG) complex is formed resulting in hydrogen bond formation between three water molecules and an ether oxygen, favouring an increase of the structure of the water surrounding the chains.(3, 4) Thus, with an increase in the PEG concentration, aggregates coexisting with free molecular polymer chains are formed.(2) However, it has been stated that the PEG chains keep partially the conformation of their crystalline state and form helical structures able to fit into the hexagonal lattice of water.(3, 4) For the lower molar mass PEGs the structure is certainly less ordered; the more extended chains allow the formation of trihydrates around each ethoxyl unit(1, 4, 8) resulting, for example, in the ethoxyl group having a constant increment on the volume, independently of the degree of polymerization.(11) Consequently, the negative excess volumes become more negative with chain length. With an increase in temperature, hydrogen bonds are weakened, thus favouring the progressive dehydration of oxygen ethers and the release of the water structure. However, this effect is counterbalanced by an increase of hydrophobic interactions(5) leading to more compact conformations, and the growth of aggregates into microgels(2, 7) is enhanced until the cloud point is reached. This results in less negative excess volumes and increasing positive excess heat capacities as the temperature increases. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
}Liu, K.-J.; Parsons, J. L. Macromolecules 1969, 2, 529–533. }Polik, F.; Burchard, W. Macromolecules 1983, 16, 978–982. }Kjellander, R.; Florin, E. J. Chem. Soc. Faraday Trans. 1981, 77, 2053–2077. }Graham, N. B.; Zulfiquar, M.; Nwachuku, N. E.; Rashid, A. Polymer 1989, 30, 528–533. }Eagland, D.; Crowther, N. J.; Butler, C. J. Polymer 1993, 34, 2804–2808. }Malcolm, G. N.; Rowlinson, J. S. Trans. Faraday Soc. 1957, 33, 921–931. }Daoust, H.; St-Cyr, D. Macromolecules 1984, 17, 596–601. }Andersson, B.; Olofsson, G. J. Solution Chem. 1989, 18, 1019–1035. }Mu¨ ller, E. A.; Rasmussen, P. J. Chem. Eng. Data 1991, 36, 214–217. }Mor´enas, M.; Douh´eret, G. Thermochim. Acta 1978, 25, 217–224. }Lepori, L.; Mollica, V J. Polym. Sci. Polym. Phys. Ed. 1978, 16, 1123–1134. }Harada, S.; Nakajima, T.; Komatsu, T.; Nakagawa, T. J. Solution Chem. 1978, 7, 463–474. }Dethlefsen, C.; Hvidt, A. J. Chem. Thermodynamics 1985, 17, 193–199. }Biros, J.; Pouchly, J.; Zivny, A. Makromol. Chem. 1987, 188, 379–394. }Ambrosone, L.; Sartorio, R.; Vescio, A.; Vitagliano, V. J. Chem. Soc. Faraday Trans. 1996, 92, 1163–1166. 16. }Bailey, F. E. Jr.; Koleske, J. V. Nonionic Surfactants. Schick M.J.: editor. Dekker: New York. 1967, Chap. 23. 17. }Picker, P.; Tremblay, E.; Jolicoeur, C. J. Solution Chem. 1974, 3, 377–384. 18. }Kell, G. S. Water—a comprehensive treatise, Vol 1. Franks, F.: editor. Plenum: New York. 1972.
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19. }Cobos, J. C.; Garcia, I.; Casanova, C.; Roux, A. H.; Roux-Desgranges, G.; Grolier, J.-P. E. Fluid Phase Equilib. 1991, 69, 223–233. 20. }Ballerat-Busserolles, K.; Rassinoux, S.; Roux-Desgranges, G.; Roux, A. H. J. Thermal Anal. 1998, 51,161–171. 21. }Picker, P.; Leduc, P.-A.; Philip, P. R.; Desnoyers, J. E. J. Chem. Thermodynamics 1971, 3, 631– 641. (Received 21 May 1998; in final form 29 October 1998)
WA98/026
Excess molar volumes and excess molar heat capacities of (polyethylene glycols + water) at temperatures between T = 278 K and T = 328 K C. Aucouturier, G. Roux-Desgranges,a and A. H. Roux Lab Thermodynamique et G´enie Chimique, UPRES A CNRS 6003, Universit´e Blaise Pascal, 63177 Aubi`ere cedex, France Densities of aqueous solutions of the following polyethylene glycols (PEGs) of average molar mass (300, 400, and 600) g·mol−1 have been measured over the entire mass fraction range at T = 298.15 K, using a vibrating-tube densimeter. In the case of PEG 300, heat capacities have been determined at T = 298.15 K in dilute solutions with a flow microcalorimeter. In addition, densities and heat capacities of (PEG 300 + water) have been measured over the entire composition range using a differential scanning microcalorimeter in the temperature interval T = (278 to 328) K. Excess molar volumes and excess molar heat capacities as functions of mole fraction have been deduced therefrom for the selected temperatures. Excess volumes are found to be negative, and become more negative as the molar mass of PEG increases and/or the temperature decreases. In contrast, excess heat c 1999 Academic Press capacities are always positive, and increase with temperature. KEYWORDS: polyethylene glycols; excess volumes; excess heat capacities; excess thermal expansivities; densimeter; microcalorimeter; d.s.c.
1. Introduction Polyethylene glycols (PEG) are neutral polymers that have a well-defined molecular structure. Whatever their molar mass, they exhibit a high solubility over a wide range of temperatures in water as well as in different types of organic solvents. As a consequence, they have found a wide variety of applications in numerous industrial processes from petroleum, or textiles to pharmaceutical and biochemical technologies. On the fundamental aspect, due to their interesting characteristics, they can be considered as model polymers for study by various experimental methods. The possibility of having a wide range of polymers of increasing molar mass makes these compounds particularly interesting for the correlation of thermodynamic properties of polymer solutions or mixtures and the prediction of phase diagrams. The peculiar structures of PEGs in aqueous solutions have been investigated using different techniques(1–5) in order to ascertain their high solubility as compared to other polyethers (methylene, propylene, butylene oxides) for which a very low solubility is observed only with the shorter oligomers. Despite their importance, it is surprising that relatively little a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/99/020289 + 12 $30.00/0
c 1999 Academic Press
290
C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
attention has been paid to the determination of the thermodynamic properties of aqueous mixtures of PEGs over a wide range of molar masses and a wide range of temperatures.(5–9) Apart from the data of Malcolm and Rowlinson,(6) and those of M¨uller and Rasmussen(9) for the excess volumes of several PEGs, no data are available in the literature. To our knowledge, only few data by Andersson and Olofsson(8) on the heat capacities of aqueous polymer mixtures where concentration and temperature effects have been investigated exist. In fact, the determination of thermodynamic properties have mainly centered upon aqueous solutions of oligomers where the number of repeat units of ethoxyl groups is lower than six. The aim was essentially to derive information about solute–solvent or molecular interactions and to correlate thermodynamic properties using group contribution theories or thermodynamic models of interactions.(10–15) In the present work, we have investigated polymers that are intermediate between oligomers and true polymers to provide useful data for the development of theories for testing or predicting the behaviour of aqueous polymer solutions when conformational changes are induced by size. We have undertaken measurements of densities and heat capacities of mixtures of water with a series of polymers of increasing molar mass, covering the mole fraction range x = (0 to 0.6) and the temperature range (278 to 328) K. Accurate excess molar volumes and excess molar heat capacities have been deduced therefrom.
2. Experimental The different polyethylene glycols (PEG 300, PEG 400, and PEG 600) were purchased from Aldrich and used as supplied, without further purification. For these low molar mass compounds the polydispersity is small. The associated number is relative to the average molar mass of the polymer and does not generally correspond to an entire number of units of ethoxyl groups. A rounded number was chosen for each polymer: six for PEG 300, nine for PEG 400, and 13 for PEG 600. The corresponding calculated molar masses are close to the maximum of the polydispersity curve of the polymer.(16) All solutions were prepared gravimetrically using deionized and degassed water at least one day before the measurements to ensure equilibrium in the relatively high viscosity mixtures. Densities ρ were obtained using a Picker vibrating-tube densimeter (Sodev, 03D),(17) whose calibration constants were determined under vacuum and with water for which the variation of density with temperature is well known.(18) At T = 298.15 K, the densities were measured as a function of composition. The measurement of the reference period of water was repeated between solutions to ensure that the difference in the density between the solution and water is determined with an accuracy of ±5·10−6 g·cm−3 . The procedure was somewhat different for densities determined as a function of temperature. First, starting with the lowest temperature and, at selected temperature steps at which equilibrium was achieved, the reference periods were recorded for water. Then, a solution with a given composition was introduced into the tube of the densimeter while keeping the flow rate extremely low, and using the stepwise procedure to record the solution periods at each selected temperature. The determination of the reference periods of water at the selected temperatures was repeated between solutions to monitor the shifts in the reference periods. Although less precise than
Thermodynamics of (polyethylene glycols + water)
291
TABLE 1. Densities ρ and molar heat capacities C p,m of pure PEGs at different temperatures ρ/(g·cm−3 )
C p,m /(J·K−1 ·mol−1 )
PEG
T /K
This work
PEG 300
298.15
1.12175
PEG 400
298.15
1.12162
PEG 600
298.15
1.12177
PEG 300
278.15
1.13727
606.9
PEG 300
288.15
1.12984
607.8
PEG 300
308.15
1.11350
612.1
PEG 300
318.15
1.10529
615.8
PEG 300
328.15
1.09717
619.7
Literature
This work 609.4
1.1223(9)
Note: the densities and the heat capacities of water used as the reference liquid for the selected temperatures are from Kell.(18)
the procedure used at constant temperature, this method, nevertheless, ensures an accuracy in the density measurements of about ±1·10−5 g·cm−3 . Heat capacities per volume unit were mainly determined with a differential scanning microcalorimeter (d.s.c. 2) from Setaram. Volumetric heat capacity measurements were obtained between T = (278 and 328) K with an accuracy of ±1·10−4 J·K−1 ·cm−3 using a continuous scanning mode at a fixed rate. This rate was chosen slow enough as to be close to thermodynamic equilibrium while allowing a sufficient sensitivity. Calibration curves were established to convert thermal flux into volumetric heat capacities (the cell being completely filled), and water was chosen as the reference liquid for which the heat capacity values are taken from the recommended values of Kell.(18) The apparatus was described previously.(19) The scanning procedure was similar to that published recently.(20) In addition, a series of measurements were also performed at T = 298 K with a Picker flow microcalorimeter,(21) in order to compare the two instruments and to check the accuracy of the d.s.c. microcalorimeter. Since the viscosity of the aqueous solutions of the PEGs increases rapidly with concentration, the use of the Picker Cp-microcalorimeter was limited to the case of relatively dilute solutions. The volumetric heat capacities interpolated at the chosen temperatures were converted into specific heat capacities using the densities of the solutions.
3. Results Densities were measured for the aqueous mixtures of PEG 300, 400, and 600 at T = 298.15 K, and in the case of PEG 300 at the temperatures (278, 288, 298, 308, 318, and 328) K. In parallel, heat capacities at the same temperatures were obtained for PEG 300. The densities and molar heat capacities of the pure PEGs at the different temperatures are given in table 1 together with the scarce literature data available for comparison. The excess molar volumes and excess molar heat capacities of the PEG solutions derived, respectively, from the densities and specific heat capacities are reported in table 2 for the
292
C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
TABLE 2. Excess molar volumes VmE for {PEG (300, or 400, or 600) + water} and excess molar heat capacities C Ep,m for (PEG 300 + water) at T = 298.15 K and mole fraction x of PEG C Ep,m −1 J·K ·mol−1
x
−2.1·10−3
0.05
3.46·10−3
−6.43·10−2
9.1·10−4
−2.51·10−2
1.87·10−3
−2.13·10−2
0.45
4.97·10−3
1.93·10−3
−2.22·10−2
3.83·10−3
−4.49·10−2
5.74·10−3
x
VmE 3 cm ·mol−1
1.94·10−4
PEG 300
VmE 3 cm ·mol−1 PEG 400
VmE 3 cm ·mol−1
x
PEG 600
−9.30·10−2
1.84·10−3
−5.08·10−2
8.61·10−3
−0.1654
5.47·10−3
−0.1563
0.89
1.005·10−2
−0.1934
9.04·10−3
−0.2638
−6.80·10−2
1.30
2.002·10−2
−0.3950
1.353·10−2
−0.3993
9.47·10−3
−0.1143
2.07
5.015·10−2
−0.8918
1.794·10−2
−0.5284
1.133·10−2
−0.1387
2.42
7.345·10−2
−1.1214
2.239·10−2
−0.6505 −0.7566
1.415·10−2
−0.1752
2.93
9.994·10−2
−1.2660
2.655·10−2
1.862·10−2
−0.2324
3.62
0.1151
−1.3183
3.096·10−2
−0.8586
2.062·10−2
−0.2598
3.94
0.1993
−1.3746
3.515·10−2
−0.9450
2.789·10−2
−0.3545
4.90
0.3011
−1.2579
4.358·10−2
−1.0915 −1.2039 −1.3403
3.243·10−2
−0.4119
5.41
0.3974
−1.1280
5.201·10−2
3.505·10−2
−0.4423
5.67
0.5020
−0.9529
6.638·10−2
3.792·10−2
−0.4770
5.97
8.375·10−2
−1.4422
4.213·10−2
−0.5287
6.36
0.1124
−1.5247
4.576·10−2
−0.5670
6.68
0.1534
−1.5457
5.593·10−2
−0.6762
7.42
0.2214
−1.5035
7.105·10−2
−0.8107
8.49
0.3154
−1.3455
8.764·10−2
−0.9272
9.20
0.3912
−1.2101
0.1177
−1.0675
10.29
0.4480
−1.1070
0.1598
−1.1633
10.87
0.4982
−1.0216
0.2232
−1.1919
0.2764
−1.1636
12.99 a
0.3610
−1.0686
14.30 a
0.4332
−0.9617
13.41 a
0.4817
−0.8863
12.62 a
0.5255
−0.8145
0.5951
−0.7082
0.6147
−0.674
0.7018
−0.524
0.8110
−0.332
0.8949
−0.181
11.33 a
a Data from d.s.c. microcalorimeter.
Thermodynamics of (polyethylene glycols + water)
293
TABLE 3. Excess molar volumes VmE for (PEG 300 + water) at temperature T and mole fraction x of PEG 300 VmE /(cm3 ·mol−1 )
x T /K:
278.15
288.15
298.15
308.15
318.15
328.15
9.5·10−3
−0.131
−0.120
−0.115
−0.112
−0.108
−0.105
1.88·10−2
−0.267
−0.245
−0.234
−0.226
−0.218
−0.212
2.79·10−2
−0.409
−0.375
−0.356
−0.343
−0.328
−0.318
5.41·10−2
−0.758
−0.696
−0.655
−0.623
−0.594
−0.567
8.73·10−2
−1.060
−0.975
−0.920
−0.871
−0.828
−0.772
0.1254
−1.233
−1.134
−1.070
−1.016
−0.964
−0.920
0.1607
−1.336
−1.250
−1.204
−1.146
−1.089
−1.030
0.2232
−1.356
−1.251
−1.192
−1.143
−1.096
−1.047
0.2764
−1.314
−1.191
−1.134
−1.099
−1.054
−1.008
0.3610
−1.201
−1.096
−1.047
−1.007
−0.964
−0.920
0.4332
−1.107
−1.012
−0.970
−0.932
−0.894
−0.846
0.4817
−1.040
−0.939
−0.901
−0.879
−0.839
−0.808
0.5255
−0.975
−0.860
−0.833
−0.808
−0.782
−0.754
0.5951
−0.860
−0.724
−0.708
−0.693
−0.677
−0.652
TABLE 4. Excess molar heat capacities C Ep,m for (PEG 300 + water) at temperature T and mole fraction x of PEG 300 C Ep,m / (J·K−1 ·mol−1 )
x T /K:
278.15
288.15
298.15
308.15
318.15
328.15
9.5·10−3
1.42
1.83
2.14
2.34
2.50
2.53
1.88·10−2
2.10
3.06
3.73
4.16
4.49
4.61
2.79·10−2
2.36
3.86
4.80
5.59
6.10
6.43
5.41·10−2
3.28
5.61
7.36
8.73
9.75
10.45
8.72·10−2
4.61
7.28
9.34
11.00
12.30
13.34
0.1254
5.53
8.10
10.11
11.73
12.99
13.91
0.1607
7.19
9.46
11.30
12.80
14.09
15.03
0.2232
9.90
11.86
13.38
14.65
15.72
16.59
0.2764
10.21
11.88
12.99
13.85
14.79
15.43
0.3610
12.55
13.50
14.30
14.99
15.64
16.16
0.4332
11.83
12.49
13.41
13.58
13.95
14.00
0.4817
11.55
11.93
12.62
12.62
12.20
12.84
0.5951
10.96
11.27
11.33
11.38
11.43
11.18
294
C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
series of PEGs at T = 298.15 K, and in tables 3 and 4 at the selected temperatures for PEG 300. Generally these quantities are expressed on a mole fraction scale, according to the relationships: VmE = {x M1 + (1 − x)M2 }/ρ − x M1 /ρ1 − (1 − x)M2 /ρ2 , C Ep,m = {x M1 + (1 − x)M2 }c p − x M1 c p1 − (1 − x)M2 c p2 .
(1) (2)
However, when relatively high molar mass compounds are studied, specific excess properties can be defined on a mass fraction scale, to compare easily the effect of the chain length over the entire range: v E = 1/ρ − w/ρ1 − (1 − w)/ρ2 , cEp = c p − wc p1 − (1 − w)c p2 .
(3) (4)
The excess molar quantities YmE are related to the specific quantities y E by: YmE = y E {x M1 + (1 − x)M2 }.
(5)
In these relations, M1 and M2 are the molar masses of the pure PEG and water, ρ1 and ρ2 their densities, and c p1 and c p2 their specific heat capacities, respectively; ρ and c p are the density and the specific heat capacity of the PEG solution for which w and x represent the mass fraction and the mole fraction of PEG, respectively. Excess molar properties have been reported against mole fraction in tables 2 to 4. However, by using the mole fraction scale, the fitting of all the data proved to be quite difficult, leading to abnormal shape, or requiring too high a number of parameters because of the lack of data at high mole fractions. Fortunately, the specific excess quantities cover the entire mass fraction range and are easily fitted using a least-squares method to determine the coefficients of the Redlich–Kister equation, which is expressed as follows: y E = w(1 − w)
3 X
ai (2w − 1)i .
(6)
i=0
The coefficients ai are given in table 5 for the excess specific volumes and specific heat capacities with the corresponding standard deviations estimated according to the relation: X 1/2 n E E (ycalc − yexpt )2 /(n − p) , (7) s(y E ) = i=1
where n is the number of experimental points and p the number of selected fitting coefficients. The composition dependence of the excess molar volumes and excess molar heat capacities are represented as a function of the mole fraction in figures 1 to 4. Figures 1 and 2 illustrate the effect of the chain length of the different PEGs on VmE at T = 298.15 K. For PEG 300, the temperature effect on VmE is shown in figure 3, and that on C Ep,m in figure 4. The only reliable data for comparison are those obtained by M¨uller and Rasmussen(9) on the excess volumes of PEG 400. These values are in good agreement with our results as shown in figures 1 and 2. In contrast, good quality data exist for the lower PEGs containing
Thermodynamics of (polyethylene glycols + water)
295
TABLE 5. Coefficients ai and standard deviations s(y E ) for the representation of the specific excess quantities expressed on a mass fraction scale at temperature T by equations (6) and (7) T /K
102 ·a0
102 ·a1
102 ·a2
102 ·a3
102 ·s
y E = v E /(cm3 ·g−1 ) PEG 300 a
298.15
−8.4499
−4.9188
1.4374
2.2417
4.7·10−3
PEG 400
298.15
−9.0097
−5.3313
1.4381
2.3470
5.3·10−3
PEG 600
298.15
−9.4807
−5.7513
1.4316
2.6385
5.2·10−3
PEG 300
278.15
−9.7114
−5.3343
1.8332
1.8744
1.6·10−2
288.15
−8.9421
−5.1479
1.7199
2.3481
1.8·10−2
298.15
−8.4309
−4.8990
1.3937
2.2639
2.5·10−2
308.15
−8.0049
−4.5355
1.0739
1.9239
2.3·10−2
318.15
−7.6198
−4.2146
0.9249
1.6348
2.2·10−2
328.15
−7.2643
−3.8024
0.7395
1.2605
2.0·10−2
y E = cEp / (J·K−1 ·g−1 ) PEG 300 a
298.15
90.010
2.942
29.910
40.270
0.41
PEG 300
278.15
39.401
1.796
74.003
52.479
0.56
288.15
68.428
−2.680
48.643
53.781
0.53
298.15
89.508
−1.603
30.967
48.831
0.59
308.15
106.689
1.121
13.135
43.167
318.15
118.213
17.689
10.574
328.15
126.921
21.690
0.63 0.84 0.79
a Series measured separately at T = 298.15 K with a densimeter and a Picker microcalorimeter.
1 to 4 ethoxyl groups.(9, 10, 13) In the figures, the solid lines correspond to values obtained by fitting the excess specific quantities to equation (6) using the parameters given in table 5. The excess thermal molar expansivities of PEG 300 obtained by a finite difference approximation (1VmE /1T ) of: (αp Vm )E = (∂ VmE )/(∂ T ) p ,
(8)
are presented in figure 5. They were calculated at T = (298 and 318) K from the temperature dependence of the experimental excess volumes of PEG 300 for each concentration. In fact, the use of the smoothed values leads to artefacts in the variations of (α p Vm )E as VmE varies slightly with temperature. The excess thermal molar expansivities of PEG 400 and triethylene glycol at T = 308 K deduced from the data of M¨uller and Rasmussen(9) are also reported in figure 5 for comparison purposes.
4. Discussion When a solute in a hydro-organic mixture shows an amphiphilic and/or polar character, negative excess volumes and positive excess heat capacities are observed. On a molar scale,
296
C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
0
VmE/(cm3.mol–1)
–0.5
–1
–1.5
–2 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 1. Excess molar volumes VmE of {xPEG + (1 − x)H2 O} at T = 298.15 K. M , {xPEG300 + (1 − x)H2 O}; N , from temperature scanning measurements; , {xPEG 400 + (1 − x)H2 O}; , M¨uller and Rasmussen;(9) ¤ , {xPEG 600 + (1 − x)H2 O}; —, using equation (6).
◦
•
VmE/x (cm3.mol–1)
–5
–15
–25
–35
0
0.05
0.1
0.15
x FIGURE 2. Variation of VmE /x of {xPEG + (1 − x)H2 O} at T = 298.15 K. M , {xPEG 300 + (1 − x)H2 O}; N , from temperature scanning measurements; , {xPEG 400 + (1 − x)H2 O}; , M¨uller and Rasmussen;(9) ¤ , {xPEG 600 + (1 − x)H2 O}; —, using equation (6).
◦
•
Thermodynamics of (polyethylene glycols + water)
297
VmE/(cm3.mol–1)
0
–0.5
–1.0
–1.5 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 3. Excess molar volumes VmE of {xPEG 300+(1− x)H2 O} at temperature T : ¥ , T = 278 K; ¤ , T = 288 K ; M , T = 298 K; , T = 308 K ; , T = 318 K ; ¨ , T = 328 K; —, using equation (6).
•
◦
20
Cp,E m/(J.K–1.mol–1)
15
10
5
0
0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 4. Excess molar heat capacities C Ep,m of {xPEG 300 + (1 − x)H2 O} at temperature T : ¥ , T = 278 K; ¤ , T = 288 K; M , T = 298 K; , T = 308 K; , T = 318 K ; ¨ , T = 328 K ; N , T = 298 K, with a Picker calorimeter; —, using equation (6).
•
◦
298
C. Aucouturier, G. Roux-Desgranges, and A. H. Roux
(αpVm)E/(cm3.mol–1.K–1)
0.008
0.006
0.004
0.002
0 0
0.2
0.4
0.6
0.8
1.0
x FIGURE 5. Excess thermal molar expansivities (α p Vm )E of {xPEG + (1 − x)H2 O} at temperature T . , {xPEG 300 + (1 − x)H2 O} at T = 298 K; , {xPEG 300 + (1 − x)H2 O} at T = 318 K; N , {xPEG 400 + (1 − x)H2 O} at T = 308 K from M¨uller and Rasmussen;(9) ¤ , {xHO(EO)3 H + (1 − x)H2 O} at T = 308 K from M¨uller and Rasmussen.(9)
◦
•
as shown in figures 1 to 5, the extrema of these excess quantities are generally skewed towards low x values. Excess volumes become more negative with increase in the chain length of the PEG (figure 1), and the minimum, situated near x = 0.2, is slightly shifted towards lower x values. Furthermore, in the dilute region, the variations of VmE /x against mole fraction, shown in figure 2 for the three PEGs, point clearly to hydrophobic interactions between the PEG and water. The resulting increase in the water structure is expressed by the deeper minimum situated close to x = 2·10−2 , when the chain length of PEG increases. The minima of the excess volumes are also deeper when the temperature decreases (figure 3), but the variation is relatively weak, leading to small positive excess thermal expansivities. Within the uncertainty of the measurements, this quantity seems to be mostly independent of the number of ethoxyl units of the PEG (except perhaps for the lowest oligomers where the proximity effect of the hydroxyl groups plays a more marked role) and the temperature. The excess heat capacities, reported in figure 4, show large positive values; their maxima are shifted to lower x values, and an increase in temperature results in an increase in the excess values. When comparing the different polyether–water mixtures, the specific intermolecular interactions result mainly from the hydration of the ethoxyl units through hydrogen bonding between oxygen ether and the hydrogen atom of water, and/or the enhancement of the water structure (iceberg formation) around the hydrophobic hydrocarbon groups (ethyl) of the polymer chains. In the particular case of the PEGs chains, the repeating distance between the oxygen atoms in the PEG chain fits between the oxygen atoms of water,
Thermodynamics of (polyethylene glycols + water)
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this conformation being the most favourable condition for insertion into the net of water clusters. Thus, when interacting with water, the PEGs give rise to a well-defined structure(3) in which the hydrogen bonding becomes the preponderant interaction.(1, 4) Several structural models have been suggested in order to explain the high solubility of the PEGs. In the case of the lower molar mass PEGs, the oxygen ether can be directly involved through hydrogen bonds in the water lattice,(14) and the hydrophobic interaction mainly controls the solution behaviour.(5) In general, it is assumed that a (water + PEG) complex is formed resulting in hydrogen bond formation between three water molecules and an ether oxygen, favouring an increase of the structure of the water surrounding the chains.(3, 4) Thus, with an increase in the PEG concentration, aggregates coexisting with free molecular polymer chains are formed.(2) However, it has been stated that the PEG chains keep partially the conformation of their crystalline state and form helical structures able to fit into the hexagonal lattice of water.(3, 4) For the lower molar mass PEGs the structure is certainly less ordered; the more extended chains allow the formation of trihydrates around each ethoxyl unit(1, 4, 8) resulting, for example, in the ethoxyl group having a constant increment on the volume, independently of the degree of polymerization.(11) Consequently, the negative excess volumes become more negative with chain length. With an increase in temperature, hydrogen bonds are weakened, thus favouring the progressive dehydration of oxygen ethers and the release of the water structure. However, this effect is counterbalanced by an increase of hydrophobic interactions(5) leading to more compact conformations, and the growth of aggregates into microgels(2, 7) is enhanced until the cloud point is reached. This results in less negative excess volumes and increasing positive excess heat capacities as the temperature increases. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
}Liu, K.-J.; Parsons, J. L. Macromolecules 1969, 2, 529–533. }Polik, F.; Burchard, W. Macromolecules 1983, 16, 978–982. }Kjellander, R.; Florin, E. J. Chem. Soc. Faraday Trans. 1981, 77, 2053–2077. }Graham, N. B.; Zulfiquar, M.; Nwachuku, N. E.; Rashid, A. Polymer 1989, 30, 528–533. }Eagland, D.; Crowther, N. J.; Butler, C. J. Polymer 1993, 34, 2804–2808. }Malcolm, G. N.; Rowlinson, J. S. Trans. Faraday Soc. 1957, 33, 921–931. }Daoust, H.; St-Cyr, D. Macromolecules 1984, 17, 596–601. }Andersson, B.; Olofsson, G. J. Solution Chem. 1989, 18, 1019–1035. }Mu¨ ller, E. A.; Rasmussen, P. J. Chem. Eng. Data 1991, 36, 214–217. }Mor´enas, M.; Douh´eret, G. Thermochim. Acta 1978, 25, 217–224. }Lepori, L.; Mollica, V J. Polym. Sci. Polym. Phys. Ed. 1978, 16, 1123–1134. }Harada, S.; Nakajima, T.; Komatsu, T.; Nakagawa, T. J. Solution Chem. 1978, 7, 463–474. }Dethlefsen, C.; Hvidt, A. J. Chem. Thermodynamics 1985, 17, 193–199. }Biros, J.; Pouchly, J.; Zivny, A. Makromol. Chem. 1987, 188, 379–394. }Ambrosone, L.; Sartorio, R.; Vescio, A.; Vitagliano, V. J. Chem. Soc. Faraday Trans. 1996, 92, 1163–1166. 16. }Bailey, F. E. Jr.; Koleske, J. V. Nonionic Surfactants. Schick M.J.: editor. Dekker: New York. 1967, Chap. 23. 17. }Picker, P.; Tremblay, E.; Jolicoeur, C. J. Solution Chem. 1974, 3, 377–384. 18. }Kell, G. S. Water—a comprehensive treatise, Vol 1. Franks, F.: editor. Plenum: New York. 1972.
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19. }Cobos, J. C.; Garcia, I.; Casanova, C.; Roux, A. H.; Roux-Desgranges, G.; Grolier, J.-P. E. Fluid Phase Equilib. 1991, 69, 223–233. 20. }Ballerat-Busserolles, K.; Rassinoux, S.; Roux-Desgranges, G.; Roux, A. H. J. Thermal Anal. 1998, 51,161–171. 21. }Picker, P.; Leduc, P.-A.; Philip, P. R.; Desnoyers, J. E. J. Chem. Thermodynamics 1971, 3, 631– 641. (Received 21 May 1998; in final form 29 October 1998)
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