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Volumetric and ultrasonic studies of the system (water + polypropylene glycol 400) at temperatures from (283.15 to 313.15) K
J. Chem. Thermodynamics 36 (2004) 871–875 www.elsevier.com/locate/jct
Volumetric and ultrasonic studies of the system (water + polypropylene glycol 400) at temperatures from (283.15 to 313.15) K Mohammed Taghi Zafarani-Moattar *, Fatemeh Samadi, Rahmat Sadeghi Physical Chemistry Department, University of Tabriz, Tabriz, Iran Received 28 April 2004; revised 7 June 2004; accepted 9 June 2004 Available online 10 August 2004
Abstract Ultrasonic velocity and density of aqueous solutions of polypropylene glycol have been measured experimentally over the whole range of composition at temperatures T = (283.15 to 313.15) K and atmospheric pressure. From these experimental data, the excess specific volumes, isentropic compressibility, increments of the ultrasonic velocity, and the isentropic compressibility have been determined for each composition. The results have been interpreted in light of polymer–solvent and polymer–polymer interactions. Also, the excess specific volumes, the increments of the ultrasonic velocity, and the isentropic compressibility were fitted to a variable-degree polynomial equation. 2004 Elsevier Ltd. All rights reserved. Keywords: Ultrasonic velocity; Density; Isentropic compressibility; Aqueous solution; Polypropylene glycol
1. Introduction Thermodynamics of water-soluble polymers are of considerable scientific and technological interest. Many research groups have focused their attention to obtain information on the thermodynamics of aqueous polyethylene glycol (PEG), which is often used in biotechnology. Knowledge of acoustical properties of aqueous polymer solutions provides useful information on hydrophobicity or hydrophilicity of polymer in solutions [1–7]. Recently, ultrasonic speed measurements were made on the aqueous PEG solutions to obtain useful information on the unique types of interactions in this system [8]. Polypropylene glycol (PPG) is a polymer that is structurally closely related to PEG. However, * Corresponding author. Tel.: +98-411-339-3135; fax: +98-411-3340191. E-mail address: [email protected] (M. Taghi ZafaraniMoattar).
0021-9614/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2004.06.006
similar information on the aqueous PPG solutions is scarce. With this consideration, the present communication deals with ultrasonic velocity studies and allied parameters of aqueous solutions of polypropylene glycol (PPG) over the whole range of composition at temperatures T = (283.15 to 313.15) K and atmospheric pressure.
2. Experimental PPG (P400) was obtained from Fluka. Double distilled and deionized water was used. The solutions were prepared by mass using an analytical balance (Shimatzu, 321-34553, Shimatzu Co., Japan) with an accuracy of ±1 Æ 104 g. The ultrasonic velocity and density of mixtures were measured at different temperatures with a digital vibrating-tube analyzer (Anton paar DSA 5000, Austria) with proportional temperature controller that kept the samples at working temperature with an accuracy of 0.001 K. The apparatus was calibrated at each
872
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
temperature with distilled water and dry air. Precision of the instrument is reported to be 3 Æ 106 g Æ cm3 for density and 0.1 m Æ s1 for ultrasonic velocity.
5.9
5.4
Du ¼ u ðw2 u2 þ ð1 w2 Þu1 Þ;
ð2Þ
Djs ¼ u ðw2 js;2 þ ð1 w2 Þjs;1 Þ;
ð3Þ
where w is the weight fraction and subscripts 1 and 2 stand for water and polymer, respectively. The increments and excess specific volumes were correlated by means of the Redlich–Kister equation [9], DQ ¼ w2 ð1 w2 Þ
N X
Bp ð2w2 1Þp ;
ð4Þ
p¼0
where Bp represents the fitting coefficients and N is the degree of the polynomic expansion. The root-meansquare deviations, r, between the calculated, DQcalc,
7
Experimental data on density (q) and ultrasonic velocity (u) of various aqueous PPG solutions determined at T = (283.15, 288.15, 293.15, 298.15, 303.15, 308.15, and 313.15) K are given in table 1. At different polymer weight fraction, w2, the isentropic compressibility, js, determined by means of the Laplace equation (js = q1u2) is shown at working temperatures in figure 1. From figure 1, it can be seen that the pure water compressibility at the working temperatures is less than that of the pure PPG and these differences becomes bigger at higher temperatures. This observation is consistent with the previous finding [1,2] that the polymer chains are more compressible. This is due to chain-like structure of the polymer and its greater free volume. Also, it has been shown that [5–7] the increase in u and decrease in js with w2 indicated increase in intermolecular forces forming aggregates of solvent molecules around the solute due to which structural arrangement is affected (polymer–solvent interaction). From figure 1, it can be seen that at the temperature T = 283.15 K for the whole range of polymer composition, the polymer solution compressibility is less than that of the pure water and this indicates that at this temperature the strong polymer–solvent interaction exist. At higher temperatures, this composition range becomes smaller and this indicates that at higher temperatures the polymer–solvent interactions are weakened. The excess specific volumes (VE), ultrasonic velocity increments (Du), and the isentropic compressibility increments (Djs), determined by the following expressions: 1 w2 1 w2 E V ¼ þ ; ð1Þ q q2 q1
10 . k s / (kPa)
-1
3. Results and discussion
4.9
4.4
3.9
3.4 0
0.2
0.4
0.6
0.8
1
w2 FIGURE 1. Isentropic compressibilities, 107 Æ js/(kPa1), plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; ·, T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; and m, T = 313.15 K.
and the experimental, DQexptl, values have been estimated by using 2 !1=2 PnDAT DQexptl DQcalc i¼1 r¼ ; ð5Þ nDAT where nDAT is the number of experimental points. The obtained adjustable parameters, Bp, are summarized in table 2, together with the root-mean-square deviations, r. Figures 2–4 show the values of VE, Du, and Djs obtained experimentally and those calculated using equation (4) plotted against the weight fraction of polymer for the seven studied isotherms. Figure 2 shows that the excess specific volume is negative and decreases in magnitude as temperature increases. Mainly, the behaviour of VE is attributed to the intermolecular interactions between the hydrogen atom of the water and the oxygen atoms of the polypropylene glycol and difference between the size of water and polymer. Strong hydrogen bond interactions between PPG and water at low temperatures are consistent with the obtained negative excess specific volumes. At higher temperatures, hydrogen bond interactions are weakened and hence less negative values of the excess specific volumes are obtained. Thus, we may conclude that the polymer becomes more hydrophobic with increasing temperature. The positive behaviour reflected in figure 3 for the ultrasound velocity increments for the whole range of composition and for all the considered temperatures indicates that the molecular order originated in the mixture process is bigger than the one caused under the ideal behaviour. On the other hand,
w2 0.0000 0.0050 0.0100 0.0199 0.0398 0.0605 0.0991 0.1199 0.1598 0.1992 0.2803 0.3602 0.4328 0.5152 0.6011 0.6781 0.7506 0.8398 0.9128 0.9615 0.9783 1.0000
T = 283.15 K
T = 288.15 K
T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
0.999699 1.000178 1.000621 1.001563 1.003472 1.005514 1.009461 1.011655 1.015953 1.020276 1.029085 1.036840 1.042004 1.045409 1.046376 1.045435 1.042909 1.037298 1.029700 1.022794 1.019902 1.015787
1447.59 1451.84 1455.48 1463.28 1478.26 1494.66 1524.64 1540.37 1570.86 1598.49 1645.19 1666.39 1662.86 1646.47 1617.53 1593.25 1568.12 1529.73 1488.25 1450.9 1437.00 1418.14
0.999099 0.999561 0.999988 1.000894 1.002724 1.004679 1.008444 1.010524 1.014578 1.018618 1.026741 1.033743 1.038339 1.041362 1.042190 1.041283 1.038842 1.033333 1.025651 1.018805 1.015929 1.011860
1466.25 1470.11 1473.48 1480.67 1494.36 1509.39 1536.57 1550.67 1577.77 1601.72 1640.41 1654.37 1647.14 1629.20 1600.33 1576.21 1551.22 1512.83 1471.07 1433.52 1419.56 1400.58
0.998203 0.998649 0.999062 0.999933 1.001695 1.003571 1.007162 1.009133 1.012958 1.016733 1.024199 1.030498 1.034565 1.037238 1.037952 1.037082 1.034722 1.029323 1.021575 1.014882 1.011997 1.007909
1482.66 1486.17 1489.26 1495.87 1508.39 1522.13 1546.70 1559.25 1583.14 1603.61 1634.36 1641.63 1631.18 1612.02 1583.47 1559.62 1534.76 1496.44 1454.40 1416.65 1402.62 1383.51
0.997043 0.997474 0.997874 0.998712 1.000410 1.002209 1.005637 1.007507 1.011110 1.014633 1.021472 1.027100 1.030679 1.033038 1.033661 1.032832 1.030564 1.025254 1.017502 1.010919 1.008031 1.003929
1497.00 1500.21 1503.06 1509.31 1520.57 1533.08 1555.36 1566.23 1587.06 1604.12 1627.20 1628.03 1614.69 1594.69 1566.66 1543.18 1518.59 1480.32 1438.09 1400.11 1385.96 1366.70
0.995645 0.996064 0.996447 0.997246 0.998890 1.000619 1.003889 1.005663 1.009052 1.012328 1.018557 1.023544 1.026679 1.028756 1.029305 1.028541 1.026352 1.021185 1.013765 1.006921 1.004043 0.999941
1509.44 1512.40 1515.02 1520.77 1530.97 1542.33 1562.29 1571.68 1589.51 1603.23 1618.67 1613.36 1597.64 1577.02 1549.75 1526.77 1502.57 1464.38 1421.83 1383.73 1369.55 1350.10
0.994029 0.994430 0.994803 0.995551 0.997163 0.998817 1.001934 1.003613 1.006791 1.009823 1.015455 1.019824 1.022539 1.024383 1.024882 1.024203 1.022131 1.017066 1.009778 1.002900 1.000034 0.995937
1520.12 1522.84 1525.23 1530.56 1539.69 1549.98 1567.67 1575.66 1590.53 1600.87 1608.58 1597.54 1579.86 1559.14 1532.63 1510.34 1486.73 1448.54 1405.82 1367.60 1353.36 1333.64
0.992212 0.992608 0.992974 0.993680 0.995238 0.996830 0.999784 1.001385 1.004363 1.007139 1.012194 1.015922 1.018257 1.019897 1.020375 1.019829 1.017868 1.012934 1.005777 0.998878 0.996026 0.991938
1529.18 1531.64 1533.98 1538.55 1546.88 1556.12 1571.53 1578.21 1590.08 1596.88 1596.62 1580.27 1561.20 1541.55 1515.17 1493.84 1471.05 1432.94 1389.93 1351.65 1337.38 1317.20
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
TABLE 1 The density q and ultrasound velocity u data of aqueous solutions of PPG at different temperatures
873
874
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
TABLE 2 Correlation parameters of equation (4) and root-mean-square deviation, r, at temperatures from T = (283.15 to 313.15) K at five isotherms B0
B1
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.14044 877.41 5.30 Æ 107
0.03187 411.43 1.63 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.13492 807.76 5.00 Æ 107
0.03147 377.83 1.38 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.12964 741.45 4.73 Æ 107
0.03099 341.44 1.10 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.12456 677.54 4.48 Æ 107
0.03067 302.32 0.84 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.11945 615.29 4.25 Æ 107
0.03016 259.78 0.58 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.11444 554.14 4.03 Æ 107
0.03033 212.7 0.29 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.10931 493.91 3.81 Æ 107
0.03081 158.45 0.02 Æ 107
B2
B3
r
0.00918 7.15 1.11 Æ 107
0.03926 586.87 2.77 Æ 107
2.34 Æ 104 2.139 6.796 Æ 1010
0.00293 50.97 1.32 Æ 107
0.03776 533.53 2.75 Æ 107
1.866 Æ 104 2.001 6.275 Æ 1010
0.00336 107.39 1.55 Æ 107
0.03682 476.90 2.59 Æ 107
1.517 Æ 104 1.916 5.697 Æ 1010
0.00951 164.42 1.81 Æ 107
0.03583 416.39 2.43 Æ 107
1.228 Æ 104 1.910 5.471 Æ 1010
0.01672 220.22 2.10 Æ 107
0.03674 351.31 2.28 Æ 107
8.142 Æ 105 1.977 5.637 Æ 1010
0.02317 276.22 2.42 Æ 107
0.03576 281.46 2.06 Æ 107
5.002 Æ 105 2.077 6.155 Æ 1010
0.02989 331.91 2.76 Æ 107
0.03429 204.30 1.81 Æ 107
3.996 Æ 105 2.192 7.171 Æ 1010
T = 283.15 K
T = 288.15 K
T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
250 0
200
-0.005
3
-0.015 -0.02
E
-1
V /( cm .g )
1
∆ u / (m.s )
-0.01
-0.025 -0.03
150
100
50
-0.035 -0.04 0
0.2
0.4
0.6
0.8
1
w2 FIGURE 2. Excess specific volumes, VE/(cm3 Æ g1), plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; ·, T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; m, T = 313.15 K; and ——, calculated from equation (4).
0
0
0.2
0.4
0.6
0.8
1
w2 FIGURE 3. Ultrasonic velocity increments, Du, plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; · , T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; m, T = 313.15 K; and ——, calculated from equation (4).
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
875
mixture is lower as the thermal agitation grows. Strong hydrogen bond interactions between PPG and water at lower temperatures lead to ordered structure of the PPG and water. At higher temperatures, hydrogen bond interactions are weakened and hence the molecular order decreases. Figure 4 shows that Djs behaves in a similar way to the excess specific volume. The behaviour of Djs implies a great difficulty to compress the components of the mixture regarding the impediment that there would be under an ideal behaviour.
References
FIGURE 4. Isentropic compressibility increments, 107 Æ Djs, plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; ·, T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; m, T = 313.15 K; and ——, calculated from equation (4).
the behaviour of Du comes closer to ideal as the temperature increases, and therefore the molecular order in the
[1] [2] [3] [4] [5] [6]
F.D. Karia, P.H. Parsania, Eur. Polym. J. 36 (2000) 519–524. W. Well, R.A. Pethrick, Polymer 23 (1982) 369–373. A. Passynsky, J. Polym. Sci. 29 (1958) 61–65. R. Paladhi, P. Singh, Eur. Polym. J. 26 (1990) 441–444. B. Saraf, K. Samal, Acustica 55 (1984) 60–63. P.C. Bandopadhyay, A.K. Maiti, T.K. Chaki, R.P. Singh, Acustica 50 (1982) 75–79. [7] S. Das, R.P. Singh, S. Maiti, Polym.-Bull. 20 (1980) 403–409. [8] A. Pal, W.J. Singh, Chem. Eng. Data 42 (1997) 234–237. [9] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348.
JCT 04-93
Volumetric and ultrasonic studies of the system (water + polypropylene glycol 400) at temperatures from (283.15 to 313.15) K Mohammed Taghi Zafarani-Moattar *, Fatemeh Samadi, Rahmat Sadeghi Physical Chemistry Department, University of Tabriz, Tabriz, Iran Received 28 April 2004; revised 7 June 2004; accepted 9 June 2004 Available online 10 August 2004
Abstract Ultrasonic velocity and density of aqueous solutions of polypropylene glycol have been measured experimentally over the whole range of composition at temperatures T = (283.15 to 313.15) K and atmospheric pressure. From these experimental data, the excess specific volumes, isentropic compressibility, increments of the ultrasonic velocity, and the isentropic compressibility have been determined for each composition. The results have been interpreted in light of polymer–solvent and polymer–polymer interactions. Also, the excess specific volumes, the increments of the ultrasonic velocity, and the isentropic compressibility were fitted to a variable-degree polynomial equation. 2004 Elsevier Ltd. All rights reserved. Keywords: Ultrasonic velocity; Density; Isentropic compressibility; Aqueous solution; Polypropylene glycol
1. Introduction Thermodynamics of water-soluble polymers are of considerable scientific and technological interest. Many research groups have focused their attention to obtain information on the thermodynamics of aqueous polyethylene glycol (PEG), which is often used in biotechnology. Knowledge of acoustical properties of aqueous polymer solutions provides useful information on hydrophobicity or hydrophilicity of polymer in solutions [1–7]. Recently, ultrasonic speed measurements were made on the aqueous PEG solutions to obtain useful information on the unique types of interactions in this system [8]. Polypropylene glycol (PPG) is a polymer that is structurally closely related to PEG. However, * Corresponding author. Tel.: +98-411-339-3135; fax: +98-411-3340191. E-mail address: [email protected] (M. Taghi ZafaraniMoattar).
0021-9614/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2004.06.006
similar information on the aqueous PPG solutions is scarce. With this consideration, the present communication deals with ultrasonic velocity studies and allied parameters of aqueous solutions of polypropylene glycol (PPG) over the whole range of composition at temperatures T = (283.15 to 313.15) K and atmospheric pressure.
2. Experimental PPG (P400) was obtained from Fluka. Double distilled and deionized water was used. The solutions were prepared by mass using an analytical balance (Shimatzu, 321-34553, Shimatzu Co., Japan) with an accuracy of ±1 Æ 104 g. The ultrasonic velocity and density of mixtures were measured at different temperatures with a digital vibrating-tube analyzer (Anton paar DSA 5000, Austria) with proportional temperature controller that kept the samples at working temperature with an accuracy of 0.001 K. The apparatus was calibrated at each
872
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
temperature with distilled water and dry air. Precision of the instrument is reported to be 3 Æ 106 g Æ cm3 for density and 0.1 m Æ s1 for ultrasonic velocity.
5.9
5.4
Du ¼ u ðw2 u2 þ ð1 w2 Þu1 Þ;
ð2Þ
Djs ¼ u ðw2 js;2 þ ð1 w2 Þjs;1 Þ;
ð3Þ
where w is the weight fraction and subscripts 1 and 2 stand for water and polymer, respectively. The increments and excess specific volumes were correlated by means of the Redlich–Kister equation [9], DQ ¼ w2 ð1 w2 Þ
N X
Bp ð2w2 1Þp ;
ð4Þ
p¼0
where Bp represents the fitting coefficients and N is the degree of the polynomic expansion. The root-meansquare deviations, r, between the calculated, DQcalc,
7
Experimental data on density (q) and ultrasonic velocity (u) of various aqueous PPG solutions determined at T = (283.15, 288.15, 293.15, 298.15, 303.15, 308.15, and 313.15) K are given in table 1. At different polymer weight fraction, w2, the isentropic compressibility, js, determined by means of the Laplace equation (js = q1u2) is shown at working temperatures in figure 1. From figure 1, it can be seen that the pure water compressibility at the working temperatures is less than that of the pure PPG and these differences becomes bigger at higher temperatures. This observation is consistent with the previous finding [1,2] that the polymer chains are more compressible. This is due to chain-like structure of the polymer and its greater free volume. Also, it has been shown that [5–7] the increase in u and decrease in js with w2 indicated increase in intermolecular forces forming aggregates of solvent molecules around the solute due to which structural arrangement is affected (polymer–solvent interaction). From figure 1, it can be seen that at the temperature T = 283.15 K for the whole range of polymer composition, the polymer solution compressibility is less than that of the pure water and this indicates that at this temperature the strong polymer–solvent interaction exist. At higher temperatures, this composition range becomes smaller and this indicates that at higher temperatures the polymer–solvent interactions are weakened. The excess specific volumes (VE), ultrasonic velocity increments (Du), and the isentropic compressibility increments (Djs), determined by the following expressions: 1 w2 1 w2 E V ¼ þ ; ð1Þ q q2 q1
10 . k s / (kPa)
-1
3. Results and discussion
4.9
4.4
3.9
3.4 0
0.2
0.4
0.6
0.8
1
w2 FIGURE 1. Isentropic compressibilities, 107 Æ js/(kPa1), plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; ·, T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; and m, T = 313.15 K.
and the experimental, DQexptl, values have been estimated by using 2 !1=2 PnDAT DQexptl DQcalc i¼1 r¼ ; ð5Þ nDAT where nDAT is the number of experimental points. The obtained adjustable parameters, Bp, are summarized in table 2, together with the root-mean-square deviations, r. Figures 2–4 show the values of VE, Du, and Djs obtained experimentally and those calculated using equation (4) plotted against the weight fraction of polymer for the seven studied isotherms. Figure 2 shows that the excess specific volume is negative and decreases in magnitude as temperature increases. Mainly, the behaviour of VE is attributed to the intermolecular interactions between the hydrogen atom of the water and the oxygen atoms of the polypropylene glycol and difference between the size of water and polymer. Strong hydrogen bond interactions between PPG and water at low temperatures are consistent with the obtained negative excess specific volumes. At higher temperatures, hydrogen bond interactions are weakened and hence less negative values of the excess specific volumes are obtained. Thus, we may conclude that the polymer becomes more hydrophobic with increasing temperature. The positive behaviour reflected in figure 3 for the ultrasound velocity increments for the whole range of composition and for all the considered temperatures indicates that the molecular order originated in the mixture process is bigger than the one caused under the ideal behaviour. On the other hand,
w2 0.0000 0.0050 0.0100 0.0199 0.0398 0.0605 0.0991 0.1199 0.1598 0.1992 0.2803 0.3602 0.4328 0.5152 0.6011 0.6781 0.7506 0.8398 0.9128 0.9615 0.9783 1.0000
T = 283.15 K
T = 288.15 K
T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
q/(g Æ cm3)
u/(m Æ s1)
0.999699 1.000178 1.000621 1.001563 1.003472 1.005514 1.009461 1.011655 1.015953 1.020276 1.029085 1.036840 1.042004 1.045409 1.046376 1.045435 1.042909 1.037298 1.029700 1.022794 1.019902 1.015787
1447.59 1451.84 1455.48 1463.28 1478.26 1494.66 1524.64 1540.37 1570.86 1598.49 1645.19 1666.39 1662.86 1646.47 1617.53 1593.25 1568.12 1529.73 1488.25 1450.9 1437.00 1418.14
0.999099 0.999561 0.999988 1.000894 1.002724 1.004679 1.008444 1.010524 1.014578 1.018618 1.026741 1.033743 1.038339 1.041362 1.042190 1.041283 1.038842 1.033333 1.025651 1.018805 1.015929 1.011860
1466.25 1470.11 1473.48 1480.67 1494.36 1509.39 1536.57 1550.67 1577.77 1601.72 1640.41 1654.37 1647.14 1629.20 1600.33 1576.21 1551.22 1512.83 1471.07 1433.52 1419.56 1400.58
0.998203 0.998649 0.999062 0.999933 1.001695 1.003571 1.007162 1.009133 1.012958 1.016733 1.024199 1.030498 1.034565 1.037238 1.037952 1.037082 1.034722 1.029323 1.021575 1.014882 1.011997 1.007909
1482.66 1486.17 1489.26 1495.87 1508.39 1522.13 1546.70 1559.25 1583.14 1603.61 1634.36 1641.63 1631.18 1612.02 1583.47 1559.62 1534.76 1496.44 1454.40 1416.65 1402.62 1383.51
0.997043 0.997474 0.997874 0.998712 1.000410 1.002209 1.005637 1.007507 1.011110 1.014633 1.021472 1.027100 1.030679 1.033038 1.033661 1.032832 1.030564 1.025254 1.017502 1.010919 1.008031 1.003929
1497.00 1500.21 1503.06 1509.31 1520.57 1533.08 1555.36 1566.23 1587.06 1604.12 1627.20 1628.03 1614.69 1594.69 1566.66 1543.18 1518.59 1480.32 1438.09 1400.11 1385.96 1366.70
0.995645 0.996064 0.996447 0.997246 0.998890 1.000619 1.003889 1.005663 1.009052 1.012328 1.018557 1.023544 1.026679 1.028756 1.029305 1.028541 1.026352 1.021185 1.013765 1.006921 1.004043 0.999941
1509.44 1512.40 1515.02 1520.77 1530.97 1542.33 1562.29 1571.68 1589.51 1603.23 1618.67 1613.36 1597.64 1577.02 1549.75 1526.77 1502.57 1464.38 1421.83 1383.73 1369.55 1350.10
0.994029 0.994430 0.994803 0.995551 0.997163 0.998817 1.001934 1.003613 1.006791 1.009823 1.015455 1.019824 1.022539 1.024383 1.024882 1.024203 1.022131 1.017066 1.009778 1.002900 1.000034 0.995937
1520.12 1522.84 1525.23 1530.56 1539.69 1549.98 1567.67 1575.66 1590.53 1600.87 1608.58 1597.54 1579.86 1559.14 1532.63 1510.34 1486.73 1448.54 1405.82 1367.60 1353.36 1333.64
0.992212 0.992608 0.992974 0.993680 0.995238 0.996830 0.999784 1.001385 1.004363 1.007139 1.012194 1.015922 1.018257 1.019897 1.020375 1.019829 1.017868 1.012934 1.005777 0.998878 0.996026 0.991938
1529.18 1531.64 1533.98 1538.55 1546.88 1556.12 1571.53 1578.21 1590.08 1596.88 1596.62 1580.27 1561.20 1541.55 1515.17 1493.84 1471.05 1432.94 1389.93 1351.65 1337.38 1317.20
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
TABLE 1 The density q and ultrasound velocity u data of aqueous solutions of PPG at different temperatures
873
874
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
TABLE 2 Correlation parameters of equation (4) and root-mean-square deviation, r, at temperatures from T = (283.15 to 313.15) K at five isotherms B0
B1
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.14044 877.41 5.30 Æ 107
0.03187 411.43 1.63 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.13492 807.76 5.00 Æ 107
0.03147 377.83 1.38 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.12964 741.45 4.73 Æ 107
0.03099 341.44 1.10 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.12456 677.54 4.48 Æ 107
0.03067 302.32 0.84 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.11945 615.29 4.25 Æ 107
0.03016 259.78 0.58 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.11444 554.14 4.03 Æ 107
0.03033 212.7 0.29 Æ 107
VE/(cm3 Æ g1) Du/(m Æ s1) Djs/(kPa)1
0.10931 493.91 3.81 Æ 107
0.03081 158.45 0.02 Æ 107
B2
B3
r
0.00918 7.15 1.11 Æ 107
0.03926 586.87 2.77 Æ 107
2.34 Æ 104 2.139 6.796 Æ 1010
0.00293 50.97 1.32 Æ 107
0.03776 533.53 2.75 Æ 107
1.866 Æ 104 2.001 6.275 Æ 1010
0.00336 107.39 1.55 Æ 107
0.03682 476.90 2.59 Æ 107
1.517 Æ 104 1.916 5.697 Æ 1010
0.00951 164.42 1.81 Æ 107
0.03583 416.39 2.43 Æ 107
1.228 Æ 104 1.910 5.471 Æ 1010
0.01672 220.22 2.10 Æ 107
0.03674 351.31 2.28 Æ 107
8.142 Æ 105 1.977 5.637 Æ 1010
0.02317 276.22 2.42 Æ 107
0.03576 281.46 2.06 Æ 107
5.002 Æ 105 2.077 6.155 Æ 1010
0.02989 331.91 2.76 Æ 107
0.03429 204.30 1.81 Æ 107
3.996 Æ 105 2.192 7.171 Æ 1010
T = 283.15 K
T = 288.15 K
T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
250 0
200
-0.005
3
-0.015 -0.02
E
-1
V /( cm .g )
1
∆ u / (m.s )
-0.01
-0.025 -0.03
150
100
50
-0.035 -0.04 0
0.2
0.4
0.6
0.8
1
w2 FIGURE 2. Excess specific volumes, VE/(cm3 Æ g1), plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; ·, T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; m, T = 313.15 K; and ——, calculated from equation (4).
0
0
0.2
0.4
0.6
0.8
1
w2 FIGURE 3. Ultrasonic velocity increments, Du, plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; · , T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; m, T = 313.15 K; and ——, calculated from equation (4).
M. Taghi Zafarani-Moattar et al. / J. Chem. Thermodynamics 36 (2004) 871–875
875
mixture is lower as the thermal agitation grows. Strong hydrogen bond interactions between PPG and water at lower temperatures lead to ordered structure of the PPG and water. At higher temperatures, hydrogen bond interactions are weakened and hence the molecular order decreases. Figure 4 shows that Djs behaves in a similar way to the excess specific volume. The behaviour of Djs implies a great difficulty to compress the components of the mixture regarding the impediment that there would be under an ideal behaviour.
References
FIGURE 4. Isentropic compressibility increments, 107 Æ Djs, plotted against mass fraction of polymer, w2, for aqueous PPG solutions at different temperatures: s, T = 283.15 K; h, T = 288.15 K; n, T = 293.15 K; ·, T = 298.15 K; n, T = 303.15 K; d, T = 308.15 K; m, T = 313.15 K; and ——, calculated from equation (4).
the behaviour of Du comes closer to ideal as the temperature increases, and therefore the molecular order in the
[1] [2] [3] [4] [5] [6]
F.D. Karia, P.H. Parsania, Eur. Polym. J. 36 (2000) 519–524. W. Well, R.A. Pethrick, Polymer 23 (1982) 369–373. A. Passynsky, J. Polym. Sci. 29 (1958) 61–65. R. Paladhi, P. Singh, Eur. Polym. J. 26 (1990) 441–444. B. Saraf, K. Samal, Acustica 55 (1984) 60–63. P.C. Bandopadhyay, A.K. Maiti, T.K. Chaki, R.P. Singh, Acustica 50 (1982) 75–79. [7] S. Das, R.P. Singh, S. Maiti, Polym.-Bull. 20 (1980) 403–409. [8] A. Pal, W.J. Singh, Chem. Eng. Data 42 (1997) 234–237. [9] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348.
JCT 04-93