Density, Speed of Sound, and Viscosity of Some ... - ACS Publications

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Density, Speed of Sound, and Viscosity of Some Binary and Ternary Aqueous Polymer Solutions at Different Temperatures Sharmin Ebrahimi and Rahmat Sadeghi* Department of Chemistry, University of Kurdistan, Sanandaj, Iran S Supporting Information *

ABSTRACT: Density, speed of sound and viscosity measurements at (288.15, 293.15, 298.15, 303.15 and 308.15) K were carried out on several binary (water + polymer) and ternary (water + polymer (1) + polymer (2)) systems. Polymers were polyethylene glycol 600 (PEG600), polyethylene glycol 10000 (PEG10000), polypropylene glycol 400 (PPG400), polyethylene glycol dimethyl ether 250 (PEGDME250), and polyvinylpyrrolidone 10000 (PVP10000). The measured density and speed of sound data were used to determine the excess specific volume, isentropic compressibility, and isentropic compressibility increment of the investigated solutions as well as the apparent specific volume, limiting apparent specific volume, limiting apparent specific expansibility, apparent isentropic compressibility, and limiting apparent isentropic compressibility of each polymer in the aqueous solutions of 1 % and 3 % (w/w) other investigated polymers. The intrinsic viscosities for the investigated binary and ternary systems were calculated from the experimental viscosity data. Finally, the ability of polymer (1) in varying the volumetric, compressibility, and viscometric properties of polymer (2) in aqueous solutions was discussed on the basis of the polymer−water and polymer (1)−polymer (2) interactions. extensively studied4−27 very limited information has been reported for these properties of ternary aqueous polymer− polymer solutions.28−32 In continuation of our previous work on ternary aqueous polymer solutions,33 in the present report, volumetric, acoustic, and viscometric properties of aqueous solutions of each of the polymers polyethylene glycol 600 (PEG600), polypropylene glycol 400 (PPG400), polyvinylpyrrolidone 10000 (PVP10000), and polyethylene glycol dimethylether 250 (PEGDME250) in pure water, in the aqueous solutions of 1 % w/w PEG10000, PPG400, PEGDME250, and PVP10000 and in the aqueous solutions of 3 % w/w PEG10000 have been studied through the density, speed of sound, and viscosity measurements at different temperatures.

1. INTRODUCTION Ternary aqueous solutions of two structurally different water soluble polymers are separated into a polymer (1)-rich aqueous phase and a polymer (2)-rich aqueous phase above a certain concentration. These aqueous two-phase systems (ATPSs) have a widespread use in biotechnology and biochemistry for purification of biological materials such as cells, organelles, enzymes, proteins,1−3 etc. Since the equilibrium phases of these systems contain 70 % to 90 % water, (thus reducing the risk of denaturation of labile biomolecules) they are suitable for purification of biological materials. Both the equilibrium phases of ATPSs have the same components with different concentrations and therefore the formation of the ATPSs is an unusual phenomenon. Although this phenomenon is well documented and has been extensively investigated in the literature, its mechanism at the molecular level is still unclear. One way to the clarification of the mechanism of phase separation in the polymer (1)−polymer (2) ATPSs is investigation of the thermodynamic properties of aqueous solutions of polymer (1) in the absence and presence of polymer (2). On the other hand, knowledge of volumetric, viscometric, and acoustical properties of polymer solutions has been proven to be a very useful tool in evaluating the molecular interactions occurring in these solutions. Therefore, investigation of volumetric, compressibility, and viscometric properties of aqueous solutions of one polymer in the absence and presence of the other polymer can be a very useful tool for the study of the phase separation mechanism. Although volumetric, compressibility, and viscometric behaviors of binary aqueous polymer solutions have been © 2015 American Chemical Society

Table 1. Sample Description of the Used Chemicals chemical

source

lot number

purification method

PPG400 PEGDME250 PEG600 PEG10000 PVP10000 water

Fluka Merck Merck Merck Merck

101378417 S27703 446 S5125586 944 S5190581 835 K38734343016

none none none none none distillation and deionization

Received: March 27, 2015 Accepted: October 9, 2015 Published: October 22, 2015 3132

DOI: 10.1021/acs.jced.5b00290 J. Chem. Eng. Data 2015, 60, 3132−3147

Journal of Chemical & Engineering Data

Article

Table 2. Density, ρ, and Speed of Sound, u, against Polymer Weight Molality, mwp, for Different Binary and Ternary Aqueous Polymer Solutions at Different Temperatures, Ta T = 288.15 K 10−3ρ mwp

kg·m

−3

T = 293.15 K 10−3ρ

u −1

m·s

kg·m

−3

0.00604 0.00806 0.01006 0.02041 0.03089 0.04714 0.06388 0.08715 0.11132 0.24978 0.42880 0.66656

1.000091 1.000419 1.000746 1.002407 1.004069 1.006596 1.009136 1.012582 1.016047 1.033953 1.052778 1.071836

1470.33 1471.65 1472.91 1479.25 1485.55 1495.30 1505.09 1518.42 1531.84 1600.67 1669.84 1731.43

0.999173 0.999494 0.999813 1.001438 1.003061 1.005533 1.008015 1.011382 1.014764 1.032207 1.050497 1.068986

0.00603 0.00807 0.02044 0.03090 0.04716 0.06371 0.08703 0.11099 0.24917 0.42741 0.66497

1.001796 1.002127 1.004105 1.005757 1.008272 1.010780 1.014215 1.017641 1.035387 1.054027 1.072903

1476.54 1477.88 1485.48 1491.88 1501.48 1511.19 1524.58 1537.92 1606.24 1674.13 1734.56

1.000838 1.001162 1.003097 1.004711 1.007170 1.009619 1.012972 1.016307 1.033594 1.051708 1.070019

0.00601 0.00805 0.01009 0.02038 0.03091 0.06384 0.08684 0.11089 0.24963 0.42598 0.66597

1.005101 1.005432 1.005757 1.007388 1.009033 1.014036 1.017387 1.020787 1.038396 1.056493 1.075027

1488.74 1489.93 1491.26 1497.61 1503.96 1523.52 1536.52 1549.74 1617.36 1682.86 1743.14

1.004066 1.004391 1.004706 1.006303 1.007911 1.012797 1.016067 1.019382 1.036524 1.054114 1.071865

0.00603 0.00807 0.01010 0.02038 0.03085 0.04715 0.08627 0.11102 0.25019 0.42818 0.66639

1.000989 1.001319 1.001645 1.003302 1.004964 1.007504 1.013372 1.016924 1.034867 1.053490 1.072441

1477.50 1478.79 1480.01 1486.28 1492.56 1502.35 1524.78 1538.38 1606.72 1674.20 1734.15

1.000039 1.000362 1.000682 1.002302 1.003924 1.006408 1.012138 1.015602 1.033072 1.051162 1.069547

0.00601 0.00806 0.02043 0.03093 0.04716 0.06373 0.08689

1.001124 1.001456 1.003446 1.005107 1.007638 1.010161 1.013591

1477.40 1478.60 1486.19 1492.56 1502.18 1511.81 1525.07

1.000171 1.000493 1.002440 1.004066 1.006540 1.009000 1.012352

T = 298.15 K 10−3ρ

u m·s

−1

kg·m

−3

T = 303.15 K 10−3ρ

u −1

m·s

kg·m

−3

PEG600 in Pure Water 1486.10 0.997993 1500.02 0.996577 1487.31 0.998306 1501.15 0.996883 1488.47 0.998620 1502.21 0.997192 1494.33 1.000212 1507.59 0.998755 1500.19 1.001803 1513.00 1.000314 1509.14 1.004225 1521.27 1.002691 1518.15 1.006653 1529.59 1.005072 1530.45 1.009947 1540.88 1.008300 1542.75 1.013255 1552.18 1.011539 1605.84 1.030278 1609.89 1.028180 1668.89 1.048074 1667.24 1.045522 1724.77 1.066039 1717.63 1.062997 PEG600 in the Aqueous Solutions of 1 % (w/w) PEG10000 1491.85 0.999622 1505.34 0.998174 1493.08 0.999938 1506.45 0.998487 1500.12 1.001837 1512.95 1.000346 1506.01 1.003417 1518.39 1.001897 1514.84 1.005824 1526.55 1.004258 1523.84 1.008223 1534.81 1.006611 1536.13 1.011504 1546.10 1.009824 1548.35 1.014771 1557.31 1.013026 1610.94 1.031619 1614.54 1.029444 1672.84 1.049250 1670.80 1.046669 1727.59 1.067040 1720.17 1.063971 PEG600 in the Aqueous Solutions of 3 % (w/w) PEG10000 1503.09 1.002782 1515.71 1.001268 1504.25 1.003099 1516.78 1.001581 1505.42 1.003410 1517.83 1.001885 1511.24 1.004971 1523.24 1.003416 1517.12 1.006546 1528.62 1.004961 1535.15 1.011326 1545.18 1.009645 1547.07 1.014524 1556.17 1.012779 1559.23 1.017764 1567.29 1.015949 1621.08 1.034481 1623.78 1.032278 1680.75 1.051588 1677.96 1.048942 1735.51 1.068314 1726.98 1.064499 PEG600 in the Aqueous Solutions of 1 % (w/w) PPG400 1492.68 0.998829 1506.05 0.997384 1493.87 0.999146 1507.14 0.997694 1495.00 0.999459 1508.17 0.998003 1500.85 1.001045 1513.60 0.999559 1506.63 1.002635 1518.95 1.001119 1515.58 1.005065 1527.19 1.003502 1536.26 1.010672 1546.15 1.008995 1548.74 1.014057 1557.62 1.012310 1611.34 1.031098 1614.83 1.028963 1672.78 1.048697 1670.66 1.046106 1727.10 1.066558 1719.62 1.063483 PEG600 in the Aqueous Solutions of 1 % (w/w) PEGDME250 1492.57 0.998958 1505.94 0.997514 1493.70 0.999275 1506.96 0.997825 1500.71 1.001181 1513.41 0.999695 1506.54 1.002773 1518.83 1.001258 1515.42 1.005195 1527.01 1.003632 1524.36 1.007606 1535.23 1.005993 1536.49 1.010881 1546.36 1.009204 3133

T = 308.15 K 10−3ρ

u m·s

−1

−3

kg·m

u m·s−1

1512.11 1513.13 1514.10 1519.10 1524.14 1531.73 1539.40 1549.73 1560.13 1612.85 1664.87 1710.09

0.994944 0.995246 0.995550 0.997085 0.998619 1.000952 1.003290 1.006458 1.009633 1.025921 1.042847 1.059865

1522.52 1523.46 1524.36 1528.97 1533.57 1540.63 1547.61 1557.14 1566.66 1614.73 1661.85 1702.15

1517.09 1518.07 1524.10 1529.11 1536.65 1544.21 1554.59 1564.89 1617.11 1668.05 1712.37

0.996513 0.996819 0.998648 1.000170 1.002489 1.004797 1.007950 1.011087 1.027210 1.043961 1.060813

1527.08 1528.01 1533.58 1538.18 1545.07 1552.09 1561.62 1570.97 1618.54 1664.61 1704.15

1526.59 1527.61 1528.57 1533.52 1538.47 1553.70 1563.79 1573.96 1625.53 1674.52 1718.47

0.999551 0.999855 1.000155 1.001659 1.003175 1.007772 1.010842 1.013951 1.029922 1.046170 1.060539

1535.85 1536.82 1537.64 1542.22 1546.79 1560.76 1570.02 1579.28 1626.22 1670.45 1709.51

1517.65 1518.66 1519.70 1524.63 1529.58 1537.10 1554.57 1565.09 1617.28 1667.84 1711.75

0.995726 0.996031 0.996334 0.997863 0.999394 1.001735 1.007121 1.010373 1.026668 1.043400 1.060314

1527.60 1528.55 1529.43 1533.99 1538.56 1545.50 1561.50 1571.11 1618.67 1664.34 1703.54

1517.57 1518.48 1524.45 1529.42 1536.97 1544.53 1554.74

0.995854 0.996159 0.997997 0.999530 1.001861 1.004181 1.007329

1527.56 1528.37 1533.86 1538.40 1545.36 1552.27 1561.68



Article

Table 2. continued T = 288.15 K −3

T = 293.15 K −3

T = 298.15 K −3

T = 303.15 K −3

T = 308.15 K −3

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

mwp

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

0.11137 0.25027 0.42882 0.65128

1.017096 1.034970 1.053639 1.071384

1538.49 1606.73 1674.48 1731.72

1.015773 1.033178 1.051315 1.068526

1565.22 1617.28 1668.14 1710.02

1.010537 1.026776 1.043554 1.059345

1571.22 1618.69 1664.62 1701.99

0.00605 0.00804 0.01009 0.02039 0.03093 0.04718 0.06384 0.08683 0.11130 0.25016 0.42949 0.65824

1.002216 1.002532 1.002873 1.004518 1.006177 1.008689 1.011206 1.014586 1.018074 1.035861 1.054531 1.072708

1474.97 1476.24 1477.55 1483.84 1490.39 1500.05 1509.83 1523.05 1536.67 1605.59 1674.35 1733.56

1.001272 1.001582 1.001917 1.003524 1.005143 1.007602 1.010059 1.013362 1.016765 1.034086 1.052222 1.069734

1516.00 1516.97 1518.01 1523.07 1528.11 1535.75 1543.30 1553.56 1564.10 1616.86 1668.46 1711.86

0.996986 0.997277 0.997593 0.999110 1.000641 1.002956 1.005272 1.008374 1.011570 1.027728 1.044470 1.058548

1526.20 1527.08 1528.09 1532.76 1537.38 1544.33 1551.30 1560.75 1570.38 1618.48 1665.13 1703.80

0.00200 0.00807 0.00984 0.02042 0.03092 0.06383 0.08687 0.11112 0.24930 0.42643 0.66750

0.999276 0.999812 0.999964 1.000889 1.001805 1.004615 1.006536 1.008508 1.018604 1.028410 1.036146

1468.01 1472.41 1473.58 1480.93 1487.96 1509.39 1523.55 1537.66 1602.95 1647.20 1654.36

0.998373 0.998889 0.999036 0.999929 1.000807 1.003507 1.005343 1.007222 1.016719 1.025725 1.032653

1510.24 1513.61 1514.53 1520.21 1525.68 1541.86 1552.25 1562.41 1604.14 1620.82 1608.64

0.994181 0.994647 0.994780 0.995582 0.996371 0.998764 1.000366 1.001989 1.009822 1.016571 1.021384

1520.75 1523.83 1524.72 1529.91 1534.87 1549.46 1558.74 1567.67 1601.78 1609.39 1591.72

0.00604 0.01010 0.02042 0.03092 0.04713 0.06381 0.08681 0.11102 0.24961 0.42816 0.66578

1.001349 1.001701 1.002598 1.003500 1.004884 1.006284 1.008184 1.010122 1.020123 1.029737 1.037193

1477.02 1479.87 1486.99 1494.05 1504.74 1515.38 1529.36 1543.36 1608.01 1650.44 1655.18

1.000392 1.000735 1.001596 1.002464 1.003792 1.005134 1.006947 1.008792 1.018187 1.027014 1.033566

1517.31 1519.51 1525.02 1530.51 1538.53 1546.43 1556.72 1566.77 1607.63 1622.61 1608.71

0.996068 0.996379 0.997151 0.997927 0.999103 1.000284 1.001863 1.003450 1.011157 1.017721 1.022280

1527.29 1529.30 1534.32 1539.33 1546.63 1553.69 1562.79 1571.59 1604.81 1610.76 1591.68

0.00200 0.00604 0.00805 0.01006 0.02038 0.03098 0.06372 0.08694 0.11109 0.25019 0.41993 0.66661

1.004306 1.004649 1.004830 1.005001 1.005879 1.006772 1.009489 1.011358 1.013265 1.022996 1.031815 1.038905

1486.35 1489.26 1490.73 1492.12 1499.17 1506.12 1527.17 1541.13 1554.97 1617.64 1655.00 1656.53

1.003287 1.003615 1.003790 1.003956 1.004798 1.005655 1.008254 1.010037 1.011846 1.020963 1.029006 1.035138

1524.73 1526.90 1528.04 1529.11 1534.51 1539.82 1555.44 1565.61 1575.35 1614.18 1625.84 1609.39

0.998805 0.999101 0.999259 0.999405 1.000156 1.000916 1.003196 1.004738 1.006278 1.013680 1.019571 1.023520

1534.12 1536.10 1537.13 1538.10 1543.00 1547.81 1561.85 1570.83 1579.32 1610.44 1613.62 1592.13

0.00603 0.01011

1.000653 1.001012

1477.75 1480.58

0.999701 1.000047

1517.72 1519.94

0.995389 0.995701

1527.61 1529.68

PEG600 in the Aqueous Solutions of 1 % (w/w) PEGDME250 1548.85 1.014225 1557.75 1.012476 1611.31 1.031207 1614.82 1.029071 1673.06 1.048854 1670.93 1.046262 1724.90 1.065568 1717.67 1.062499 PEG600 in the Aqueous Solutions of 1 % (w/w) PVP10000 1490.48 1.000070 1504.18 0.998635 1491.64 1.000374 1505.21 0.998934 1492.84 1.000700 1506.36 0.999255 1498.74 1.002277 1511.75 1.000800 1504.66 1.003866 1517.26 1.002359 1513.62 1.006269 1525.50 1.004716 1522.62 1.008676 1533.77 1.007074 1534.78 1.011903 1544.95 1.010239 1547.27 1.015230 1556.43 1.013495 1610.39 1.032121 1614.13 1.030007 1673.08 1.049755 1671.09 1.047160 1727.06 1.066570 1719.67 1.062645 PPG400 in Pure Water 1483.92 0.997206 1498.00 0.995801 1487.93 0.997703 1501.69 0.996284 1489.07 0.997848 1502.73 0.996421 1495.81 0.998707 1508.90 0.997253 1502.28 0.999555 1514.83 0.998071 1521.88 1.002146 1532.70 1.000560 1534.72 1.003902 1544.29 1.002238 1547.42 1.005692 1555.68 1.003942 1604.67 1.014618 1605.09 1.012319 1639.57 1.022849 1630.79 1.019797 1639.87 1.029041 1624.69 1.025301 PPG400 in the Aqueous Solutions of 1 % (w/w) PEG10000 1492.27 0.999178 1505.69 0.997732 1494.88 0.999509 1508.08 0.998050 1501.43 1.000340 1514.09 0.998851 1507.92 1.001174 1520.04 0.999656 1517.67 1.002450 1528.95 1.000881 1527.37 1.003736 1537.73 1.002114 1540.05 1.005467 1549.17 1.003767 1552.67 1.007222 1560.47 1.005437 1609.16 1.016039 1609.04 1.013695 1642.29 1.024088 1633.09 1.020991 1640.34 1.029898 1624.90 1.026183 PPG400 in the Aqueous Solutions of 3 % (w/w) PEG10000 1500.93 1.002014 1513.66 1.000514 1503.53 1.002331 1516.08 1.000821 1504.89 1.002500 1517.32 1.000985 1506.16 1.002660 1518.50 1.001138 1512.62 1.003470 1524.40 1.001918 1519.03 1.004293 1530.25 1.002708 1538.15 1.006781 1547.58 1.005090 1550.78 1.008481 1558.98 1.006709 1563.25 1.010195 1570.00 1.008336 1617.69 1.018727 1616.60 1.016296 1646.36 1.026026 1636.71 1.022884 1641.48 1.030910 1625.70 1.027049 PPG400 in the Aqueous Solutions of 1 % (w/w) PEGDME250 1492.89 0.998491 1506.20 0.997047 1495.50 0.998826 1508.60 0.997371 3134



Article


T = 293.15 K −3

T = 298.15 K −3

T = 303.15 K −3

T = 308.15 K −3

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

mwp

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

0.02035 0.03083 0.04713 0.06375 0.08709 0.11105 0.25011 0.42884 0.66539

1.001910 1.002822 1.004222 1.005641 1.007585 1.009526 1.019633 1.029336 1.036762

1487.59 1494.64 1505.31 1515.84 1529.98 1543.75 1608.12 1650.12 1655.06

1.000912 1.001791 1.003136 1.004491 1.006347 1.008194 1.017693 1.026583 1.032557

1525.44 1530.83 1538.83 1546.69 1557.04 1566.89 1607.51 1622.21 1608.53

0.996476 0.997261 0.998452 0.999643 1.001261 1.002848 1.010650 1.017281 1.021895

1534.64 1539.56 1546.76 1553.81 1563.03 1571.63 1604.60 1610.39 1591.68

0.00603 0.00805 0.01009 0.02043 0.03094 0.04707 0.06373 0.08709 0.11084 0.24981 0.42818 0.66656

1.001716 1.001895 1.002075 1.002966 1.003866 1.005250 1.006631 1.008558 1.010456 1.020461 1.030091 1.037617

1475.40 1476.87 1478.25 1485.54 1492.63 1503.29 1513.65 1528.03 1541.86 1607.24 1650.26 1655.29

1516.32 1517.44 1518.54 1524.13 1529.60 1537.67 1545.44 1555.98 1565.95 1607.37 1622.69 1609.15

0.996495 0.996649 0.996803 0.997576 0.998347 0.999526 1.000691 1.002295 1.003845 1.011557 1.018110 1.022688

1526.47 1527.49 1528.53 1533.63 1538.55 1545.86 1552.84 1562.28 1570.97 1604.72 1610.98 1592.08

0.00200 0.00604 0.01519 0.02042 0.03094 0.06381 0.08693 0.11112 0.17619 0.24984 0.42769 0.66797

0.999310 0.999729 1.000667 1.001196 1.002255 1.005527 1.007776 1.010067 1.015965 1.022204 1.034832 1.047090

1467.97 1471.00 1477.43 1481.02 1487.96 1509.65 1524.15 1538.66 1574.77 1610.60 1674.09 1721.13

1510.27 1512.53 1517.46 1520.22 1525.53 1541.94 1552.81 1563.65 1590.23 1616.10 1660.20 1689.79

0.994214 0.994581 0.995407 0.995870 0.996795 0.999639 1.001574 1.003533 1.008516 1.013710 1.024017 1.033670

1520.83 1522.89 1527.39 1529.89 1534.73 1549.59 1559.44 1569.22 1593.03 1616.07 1654.37 1678.70

0.00805 0.01009 0.02037 0.03096 0.04690 0.06381 0.08697 0.11122 0.25027 0.42725 0.66550

1.001650 1.001856 1.002898 1.003968 1.005568 1.007239 1.009482 1.011764 1.023787 1.036249 1.048098

1478.56 1479.79 1486.90 1494.13 1504.69 1515.62 1529.95 1544.43 1615.33 1678.64 1723.41

1518.34 1519.43 1524.82 1530.33 1538.37 1546.53 1557.29 1568.10 1619.55 1663.27 1690.98

0.996343 0.996522 0.997436 0.998370 0.999760 1.001204 1.003133 1.005079 1.015132 1.025254 1.031473

1528.21 1529.22 1534.11 1539.13 1546.36 1553.83 1563.54 1573.17 1619.11 1657.12 1679.74

0.00602 0.00807 0.01009 0.02035 0.03094 0.06383 0.08681 0.11098 0.25028

1.004744 1.004947 1.005139 1.006174 1.007227 1.010415 1.012596 1.014833 1.026612

1489.25 1490.75 1492.14 1499.26 1506.13 1527.57 1541.86 1556.19 1626.07

1526.99 1528.10 1529.21 1534.55 1539.77 1555.88 1566.52 1577.08 1627.61

0.999190 0.999366 0.999537 1.000435 1.001352 1.004097 1.005958 1.007853 1.017642

1536.23 1537.23 1538.19 1543.07 1547.81 1562.40 1571.96 1581.46 1626.32

PPG400 in the Aqueous Solutions of 1 % (w/w) PEGDME250 1501.95 0.999658 1514.51 0.998174 1508.47 1.000503 1520.46 0.998989 1518.14 1.001796 1529.33 1.000229 1527.76 1.003093 1538.03 1.001473 1540.56 1.004867 1549.56 1.003167 1552.97 1.006625 1560.69 1.004838 1609.19 1.015540 1608.99 1.013190 1641.94 1.023651 1632.68 1.020555 1640.03 1.029295 1624.58 1.025765 PPG400 in the Aqueous Solutions of 1 % (w/w) PVP10000 1.000778 1490.88 0.999578 1504.49 0.998144 1.000949 1492.23 0.999743 1505.73 0.998304 1.001121 1493.71 0.999911 1507.00 0.998464 1.001980 1500.21 1.000740 1512.98 0.999262 1.002847 1506.66 1.001571 1518.97 1.000064 1.004175 1516.45 1.002847 1527.91 1.001293 1.005496 1525.95 1.004115 1536.50 1.002507 1.007338 1538.95 1.005873 1548.24 1.004189 1.009143 1551.45 1.007590 1559.45 1.005821 1.018542 1608.58 1.016412 1608.65 1.014076 1.027363 1642.27 1.024453 1633.11 1.021369 1.034079 1640.63 1.030393 1625.20 1.026611 PEGDME250 in Pure Water 0.998407 1483.92 0.997237 1498.03 0.995834 0.998810 1486.64 0.997629 1500.49 0.996213 0.999719 1492.56 0.998507 1505.89 0.997063 1.000228 1495.85 0.999002 1508.88 0.997542 1.001248 1502.22 0.999988 1514.71 0.998496 1.004400 1522.00 1.003028 1532.75 1.001435 1.006558 1535.22 1.005105 1544.77 1.003438 1.008757 1548.40 1.007219 1556.76 1.005473 1.014397 1581.11 1.012621 1586.29 1.010658 1.020340 1613.41 1.018297 1615.23 1.016082 1.032322 1670.06 1.029680 1665.40 1.026910 1.043850 1711.07 1.040534 1700.48 1.037135 PEGDME250 in the Aqueous Solutions of 1 % (w/w) PEG10000 1.000685 1493.54 0.999464 1506.82 0.998010 1.000883 1494.81 0.999655 1507.98 0.998194 1.001891 1501.29 1.000631 1513.91 0.999138 1.002924 1507.86 1.001627 1519.94 1.000103 1.004463 1517.55 1.003111 1528.75 1.001539 1.006069 1527.49 1.004661 1537.80 1.003035 1.008223 1540.54 1.006731 1549.64 1.005032 1.010411 1553.72 1.008834 1561.58 1.007051 1.021879 1617.69 1.019791 1619.07 1.017542 1.033661 1674.03 1.030811 1668.90 1.028173 1.044680 1712.76 1.040422 1701.93 1.035955 PEGDME250 in the Aqueous Solutions of 3 % (w/w) PEG10000 1.003709 1503.58 1.002424 1516.12 1.000911 1.003906 1504.93 1.002614 1517.37 1.001095 1.004092 1506.17 1.002792 1518.53 1.001268 1.005087 1512.68 1.003754 1524.46 1.002198 1.006101 1519.01 1.004732 1530.19 1.003145 1.009164 1538.54 1.007682 1547.92 1.005989 1.011254 1551.49 1.009690 1559.72 1.007920 1.013397 1564.49 1.011742 1571.44 1.009891 1.024615 1627.45 1.022448 1627.93 1.020120 3135



Article


T = 293.15 K −3

T = 298.15 K −3

T = 303.15 K −3

T = 308.15 K −3

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

mwp

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

0.42878 0.66753

1.038719 1.049665

1687.04 1729.54

1669.63 1695.05

1.027383 1.029311

1662.75 1683.25

0.00604 0.00805 0.01012 0.02038 0.03099 0.04711 0.06364 0.08702 0.11070 0.24966 0.42867 0.65511

1.000622 1.000826 1.001042 1.002096 1.003177 1.004799 1.006433 1.008716 1.010970 1.023049 1.035604 1.046894

1478.00 1479.41 1480.76 1487.83 1494.94 1505.58 1516.13 1530.64 1544.67 1615.30 1678.15 1721.52

1517.98 1518.99 1520.08 1525.45 1530.92 1538.89 1546.82 1557.65 1568.10 1619.26 1662.67 1689.39

0.995356 0.995539 0.995726 0.996652 0.997592 0.998999 1.000409 1.002367 1.004291 1.014383 1.024590 1.029212

1527.83 1528.80 1529.77 1534.36 1539.54 1546.83 1554.00 1563.79 1573.14 1618.68 1656.41 1678.23

0.00604 0.00805 0.01010 0.02040 0.03093 0.04713 0.06388 0.08700 0.11114 0.24983 0.42888 0.66088

1.001855 1.002061 1.002270 1.003312 1.004366 1.005968 1.007620 1.009844 1.012118 1.024058 1.036560 1.048174

1475.40 1476.87 1478.21 1485.41 1492.57 1503.38 1514.26 1528.69 1543.13 1614.43 1678.36 1723.10

1516.17 1517.26 1518.36 1523.83 1529.30 1537.54 1545.69 1556.49 1567.37 1619.11 1663.41 1691.24

0.996624 0.996807 0.996988 0.997899 0.998822 1.000211 1.001641 1.003549 1.005488 1.015466 1.025611 1.032788

1526.35 1527.33 1528.30 1533.32 1538.23 1545.72 1553.10 1562.87 1572.62 1618.78 1657.26 1680.10

0.00806 0.01007 0.03086 0.04731 0.06373 0.08782 0.11122 0.17635 0.25052

1.000773 1.001182 1.005373 1.008606 1.011774 1.016336 1.020647 1.031842 1.043443

1470.11 1471.02 1480.22 1487.44 1494.83 1505.54 1515.80 1543.63 1574.13

1512.07 1512.79 1520.53 1526.62 1532.80 1541.64 1550.16 1573.09 1598.03

0.995635 0.996027 1.000049 1.003156 1.006196 1.010577 1.014710 1.025435 1.036541

1522.53 1523.22 1530.57 1536.25 1542.05 1550.36 1558.36 1579.84 1603.19

0.00804 0.01007 0.02035 0.03008 0.04662 0.06403 0.08622 0.11140 0.17684 0.24953

1.002340 1.002761 1.004866 1.006829 1.010101 1.013455 1.017569 1.022078 1.033171 1.044121

1475.88 1476.73 1481.46 1485.85 1493.21 1501.04 1510.81 1521.51 1549.47 1577.98

1516.68 1517.46 1521.34 1525.06 1531.14 1537.59 1545.71 1554.58 1577.59 1600.92

0.997076 0.997479 0.999503 1.001388 1.004530 1.007748 1.011679 1.016024 1.026694 1.037147

1526.90 1527.61 1531.24 1534.66 1540.39 1546.44 1554.07 1562.42 1583.96 1605.81

0.00604 0.00807 0.01010 0.02042 0.06378 0.11116 0.25009

1.005386 1.005825 1.006252 1.008392 1.017051 1.025959 1.048846

1487.84 1488.84 1489.76 1494.46 1514.46 1536.23 1595.69

1526.06 1526.91 1527.70 1531.59 1548.19 1566.15 1614.66

0.999860 1.000280 1.000691 1.002744 1.011059 1.019595 1.041502

1535.43 1536.24 1536.97 1540.62 1556.22 1573.06 1618.42

PEGDME250 in the Aqueous Solutions of 3 % (w/w) PEG10000 1.036068 1681.84 1.033228 1676.02 1.030409 1.043657 1718.14 1.037648 1706.63 1.032262 PEGDME250 in the Aqueous Solutions of 1 % (w/w) PPG400 0.999670 1493.14 0.998459 1506.41 0.997016 0.999868 1494.40 0.998651 1507.58 0.997202 1.000076 1495.69 0.998853 1508.75 0.997397 1.001095 1502.12 0.999838 1514.62 0.998350 1.002135 1508.61 1.000842 1520.59 0.999322 1.003697 1518.30 1.002347 1529.43 1.000775 1.005266 1527.95 1.003862 1538.16 1.002236 1.007460 1541.10 1.005970 1550.11 1.004268 1.009621 1553.85 1.008045 1561.67 1.006266 1.021139 1617.54 1.019048 1618.86 1.016790 1.033039 1673.55 1.030346 1668.36 1.027529 1.042766 1710.89 1.037724 1700.24 1.033249 PEGDME250 in the Aqueous Solutions of 1 % (w/w) PVP10000 1.000913 1490.82 0.999711 1504.40 0.998274 1.001111 1492.14 0.999904 1505.62 0.998462 1.001313 1493.42 1.000098 1506.76 0.998651 1.002319 1499.97 1.001069 1512.79 0.999591 1.003333 1506.51 1.002052 1518.75 1.000542 1.004876 1516.42 1.003538 1527.83 1.001979 1.006465 1526.33 1.005069 1536.81 1.003456 1.008600 1539.45 1.007124 1548.71 1.005435 1.010778 1552.61 1.009217 1560.64 1.007447 1.022164 1616.93 1.020088 1618.46 1.017859 1.033999 1674.01 1.031324 1669.01 1.028531 1.044736 1712.90 1.041094 1702.12 1.036796 PVP10000 in Pure Water 0.999858 1485.94 0.998677 1499.93 0.997265 1.000259 1486.78 0.999079 1500.73 0.997661 1.004403 1495.49 1.003178 1508.89 1.001721 1.007600 1502.31 1.006341 1515.32 1.004855 1.010731 1509.26 1.009439 1521.88 1.007922 1.015246 1519.30 1.013906 1531.34 1.012344 1.019502 1528.97 1.018117 1540.40 1.016515 1.030560 1555.05 1.029051 1564.86 1.027340 1.042030 1583.57 1.040397 1591.53 1.038564 PVP10000 in the Aqueous Solutions of 1 % (w/w) PEG10000 1.001388 1491.33 1.000176 1504.91 0.998735 1.001802 1492.18 1.000588 1505.71 0.999138 1.003886 1496.58 1.002649 1509.83 1.001182 1.005826 1500.71 1.004570 1513.74 1.003085 1.009060 1507.60 1.007770 1520.22 1.006253 1.012375 1514.92 1.011050 1527.14 1.009501 1.016485 1524.12 1.015114 1535.77 1.013514 1.020903 1534.22 1.019487 1545.21 1.017854 1.031870 1560.43 1.030343 1569.77 1.028603 1.042680 1587.06 1.041022 1594.70 1.039174 PVP10000 in the Aqueous Solutions of 3 % (w/w) PEG10000 1.004361 1502.33 1.003081 1515.04 1.001575 1.004793 1503.28 1.003507 1516.08 1.002000 1.005216 1504.16 1.003926 1516.78 1.002414 1.007328 1508.57 1.006018 1520.93 1.004484 1.015892 1527.39 1.014490 1538.60 1.012874 1.024693 1547.76 1.023198 1557.74 1.021493 1.047300 1603.34 1.045549 1609.65 1.043610 3136



Article


T = 293.15 K −3

T = 298.15 K −3

T = 303.15 K −3

T = 308.15 K −3

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

10 ρ

u

mwp

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

kg·m−3

m·s−1

0.42857

1.072381

1662.58

1.070573

1668.65

1.064028

1668.75

0.00604 0.01007 0.02044 0.04745 0.06412 0.08680 0.11119 0.17648 0.25075

1.001272 1.002114 1.004257 1.009674 1.012918 1.017190 1.021646 1.032877 1.044583

1476.53 1478.40 1483.05 1495.07 1502.47 1512.44 1523.11 1550.94 1581.42

1517.03 1518.56 1522.49 1532.49 1538.67 1546.93 1555.71 1578.59 1603.47

0.996034 0.996842 0.998901 1.004100 1.007213 1.011311 1.015585 1.026346 1.037534

1527.07 1528.51 1532.17 1541.59 1547.40 1555.15 1563.39 1584.81 1608.09

0.00606 0.00804 0.02042 0.03083 0.04713 0.06374 0.08683 0.11022 0.17650 0.25027

1.001429 1.001842 1.004389 1.006491 1.009723 1.012929 1.017280 1.021517 1.032957 1.044663

1476.56 1477.42 1483.06 1487.68 1494.91 1502.28 1512.45 1522.62 1551.03 1581.50

1516.96 1517.70 1522.36 1526.24 1532.32 1538.41 1546.83 1555.25 1578.61 1603.47

0.996179 0.996577 0.999025 1.001042 1.004139 1.007220 1.011392 1.015459 1.026426 1.037607

1526.98 1527.67 1532.06 1535.72 1541.42 1547.15 1555.05 1562.95 1584.84 1608.08

PVP10000 in the Aqueous Solutions of 3 % (w/w) PEG10000 1665.61 1.068558 1667.62 1.066376 PVP10000 in the Aqueous Solutions of 1 % (w/w) PPG400 1.000331 1491.86 0.999127 1505.35 0.997688 1.001160 1493.60 0.999948 1506.96 0.998502 1.003279 1497.99 1.002045 1511.08 1.000579 1.008634 1509.25 1.007343 1521.73 1.005826 1.011841 1516.28 1.010515 1528.35 1.008967 1.016065 1525.68 1.014696 1537.15 1.013106 1.020470 1535.62 1.019051 1546.48 1.017418 1.031558 1561.72 1.030020 1570.91 1.028279 1.043120 1590.20 1.041444 1597.54 1.039578 PVP10000 in the Aqueous Solutions of 1 % (w/w) PEGDME250 1.000483 1491.85 0.999275 1505.29 0.997835 1.000890 1492.68 0.999680 1506.06 0.998237 1.003408 1497.95 1.002169 1511.04 1.000702 1.005485 1502.31 1.004227 1515.13 1.002740 1.008681 1509.10 1.007386 1521.57 1.005869 1.011850 1516.04 1.010523 1528.09 1.008975 1.016150 1525.60 1.014778 1537.05 1.013186 1.020344 1535.13 1.018927 1545.99 1.017293 1.031644 1561.78 1.030105 1570.95 1.028361 1.043200 1590.22 1.041522 1597.55 1.039657

The standard uncertainties for polymer weight molality, density, speed of sound and temperature were estimated to be ± 2·10−5, ± 5·10−3 kg·m−3, ± 0.5 m·s−1, and ± 1·10−3 K, respectively.

a

of nominal diameter 1.6·10−3 and 1.8·10−3 m, respectively. The viscosity of each sample was measured at 75° angle. The uncertainty of viscosity measurements was ± 2·10−7 Pa·s.

2. EXPERIMENTAL SECTION 2.1. Materials. The specifications of chemicals used in this work were listed in Table 1. The polymers were used without further purification. Double distilled and deionized water was used. 2.2. Experimental Procedures. All the solutions were prepared by mass on a Sartorius CP124S balance precisely within ± 1·10−7 kg. The density and speed of sound of the mixtures were measured at different temperatures with a digital vibrating-tube analyzer (Anton Paar DSA 5000, Austria). The temperature of the instrument is controlled by a Peltier device within a precision of ± 10−3 K. The apparatus was calibrated with double distilled deionized, and degassed water, and dry air at atmospheric pressure. Densities and speeds of sound can be measured to ± 10−3 kg·m−3 and ± 10−2 m·s−1, respectively, under the most favorable conditions. The uncertainties of density and speed of sound measurements were ± 5·10−3 kg·m−3 and ± 0.5 m·s−1, respectively. The viscosities of the mixtures were measured at different temperatures using an Anton Paar AMVn microviscometer. This viscometer is based on the concept of a falling sphere inside a capillary of known diameter. Two laser sensors at the two ends of the capillary detect the small metal sphere and allow the determination of the time elapsed during its fall between the two positions. An average time is automatically recorded for the desired number of successive runs. The apparatus can be operated in a wide range of temperatures and angles. The temperature of the capillary is controlled by a Peltier device within a precision of ± 0.01 K. The average time for the different angles has been used to calculate the kinematic viscosity of each compound. The measurements at low and high polymer concentration range were made in two different capillaries

3. RESULTS AND DISCUSSION Tables 2 and 3 show the experimental density, speed of sound and viscosity data of the investigated polymer solutions at different temperatures. It should be mentioned that, although aqueous solutions of PPG400 form aqueous two-phase systems with PEG600, PEG10000, PEGDME250, and PVP10000 in the high polymers concentration range (other investigated ternary systems do not form aqueous two-phase systems), in the low concentration range studied in this work all the investigated systems were completely miscible. 3.1. Apparent Specific Volumes. From the experimental density data, the apparent specific volumes of the polymers in the investigated binary and ternary aqueous solutions were calculated using the following equation: Vϕ =

1 + m wp m wpρ

−

1 m wpρ0

(1)

where ρ and ρ0 are the densities of the solution and solvent, respectively, mwp is the weight molality of polymer (kg polymer per kg of solvent). For ternary systems (polymer (1) in the aqueous solutions of 1 or 3 % (w/w) polymer (2)), the polymer (2) + water is considered as the solvent. Figure 1 shows the variations of Vϕ of different polymers (1) in pure water and in the aqueous solutions of 1 % w/w PEG10000 (2) as a function of the weight molality of polymer (1) at 288.15 K and 308.15 K. From this figure, we note that the values of Vϕ show a shallow minimum. For the low concentration of 3137



Article

Table 3. Viscosity, η, against Polymer Weight Molality, mwp, for Different Binary and Ternary Aqueous Polymer Solutions at Different Temperatures, Ta 103η/(Pa·s) mwp 0.0000 0.0019 0.0059 0.0080 0.0100 0.0151 0.0203 0.0308 0.0637 0.0870 0.1111 0.1750 0.2500

0.0040 0.0081 0.0100 0.0417 0.0837 0.1100 0.2484 0.4284

103η/(Pa·s)

303.15 K

308.15 K

mwp

PEG600 in Pure Water 0.9078 0.8168 0.9126 0.8202 0.9270 0.8340 0.9336 0.8397 0.9422 0.8475 0.9657 0.8693 0.9878 0.8867 1.0335 0.9275 1.1917 1.0642 1.3171 1.1720 1.4544 1.2904 1.8610 1.6408 2.4313 2.1281 PPG400 in Pure Water

0.7441 0.7458 0.7578 0.7625 0.7690 0.7881 0.8020 0.8382 0.9570 1.0520 1.1547 1.4596 1.8788

0.0019 0.0060 0.0080 0.0100 0.0151 0.0204 0.0309 0.0637 0.0868 0.1111 0.1762 0.2497

298.15 K

0.9126 0.9214 0.9280 1.0286 1.1765 1.2724 1.9251 3.1489

0.8211 0.8344 0.8408 0.9290 1.0405 1.1176 1.6515 2.6167

0.7443 0.7574 0.7556 0.8291 0.9185 0.9775 1.4070 2.1568

PVP10000 in the Aqueous Solutions of 1 % (w/w) PEG10000 0.0019 1.1909 1.0626 0.9553 0.0059 1.2958 1.1536 1.0354 0.0081 1.3452 1.1964 1.0726 0.0101 1.4014 1.2450 1.1149 0.0203 1.7121 1.5151 1.3509 0.0309 2.0435 1.8026 1.6032 0.0636 3.4060 2.9799 2.6268 0.0868 4.8486 4.2178 3.6998 0.1110 6.4792 5.5895 4.8676 0.2502 26.4285 22.4018 19.3229

PEG600 in the Aqueous Solutions of 3 % (w/w) PEG10000 0.0019 1.7388 1.5382 1.3712 0.0060 1.7693 1.5636 1.3936 0.0081 1.7800 1.5737 1.4017 0.0101 1.7982 1.5863 1.4135 0.0204 1.8670 1.6500 1.4691 0.0308 1.9354 1.7093 1.5196 0.0637 2.1802 1.9212 1.7070 0.0870 2.3639 2.0813 1.8452 0.1110 2.5608 2.2478 1.9931 0.2500 4.0494 3.5232 3.1062 0.4278 6.4651 5.4991 4.7388 0.6661 10.7452 9.0286 7.6370

298.15 K

303.15 K

PEGDME250 in Pure Water 0.9034 0.8135 0.9200 0.8277 0.9253 0.8329 0.9339 0.8409 0.9512 0.8549 0.9706 0.8738 1.0066 0.9025 1.1321 1.0096 1.2239 1.0894 1.3260 1.1749 1.6252 1.4316 2.0011 1.7467

103η/(Pa·s) 308.15 K

mwp

0.7388 0.7523 0.7551 0.7624 0.7745 0.7904 0.8173 0.9091 0.9772 1.0514 1.2693 1.5406

0.0020 0.0059 0.0080 0.0101 0.0151 0.0204 0.0308 0.0637 0.0865 0.1111 0.1765

PEG600 in the Aqueous Solutions of 1 % (w/w) PEG10000 0.0000 1.1412 1.0193 0.9179 0.0020 1.1495 1.0267 0.9240 0.0059 1.1706 1.0452 0.9405 0.0080 1.1803 1.0536 0.9486 0.0100 1.1908 1.0620 0.9550 0.0203 1.2497 1.1151 1.0007 0.0308 1.3099 1.1673 1.0480 0.0638 1.4944 1.3253 1.1867 0.0870 1.6351 1.4498 1.2943 0.1111 1.8051 1.5958 1.4942 0.2500 2.9319 2.5597 2.2524 0.4286 4.9649 4.2650 3.7095 0.6669 8.6163 7.2205 6.1393 PPG400 in the Aqueous Solutions of 1 % (w/w) PEG10000 0.0019 1.1797 1.0546 0.9521 0.0060 1.1805 1.0531 0.9486 0.0080 1.1864 1.0583 0.9515 0.0101 1.1959 1.0666 0.9593 0.0203 1.2500 1.1133 0.9984 0.0309 1.3042 1.1593 1.0391 0.0637 1.4919 1.3183 1.1756 0.0870 1.6370 1.4442 1.2829 0.1110 1.8279 1.5803 1.3972 0.2498 2.9769 2.5534 2.2158 0.4286 5.7838 4.8039 4.0435 0.6667 9.0338 7.3537 6.0858 PVP10000 in the Aqueous Solutions of 3 % (w/w) PEG10000 0.0020 1.8100 1.6017 1.4252 0.0060 1.9403 1.7131 1.5225 0.0081 2.0026 1.7658 1.5692 0.0100 2.0687 1.8231 1.6211 0.0204 2.4671 2.1694 1.9236 0.0308 2.9186 2.5615 2.2585 0.0637 4.7682 4.1450 3.6435 0.0868 6.4732 5.5791 4.8570 0.1111 8.7144 7.5204 6.5280 0.2500 32.6019 27.4867 23.5408 0.4286 119.5661 97.0123 80.5050

3138

298.15 K

303.15 K

PVP10000 in Pure Water 0.9277 0.8345 0.9903 0.8889 1.0231 0.9179 1.0547 0.9524 1.1417 1.0212 1.2376 1.1047 1.4483 1.2874 2.2610 1.9917 3.0062 2.6336 4.1205 3.5858 7.8941 6.7881

308.15 K 0.7636 0.8045 0.8301 0.8612 0.9208 0.9923 1.1535 1.7851 2.3261 3.1899 5.8803

PEGDME250 in the Aqueous Solutions of 1 % (w/w) PEG10000 0.0020 1.1571 1.0366 0.9317 0.0060 1.1762 1.0502 0.9457 0.0081 1.1839 1.0566 0.9505 0.0101 1.1915 1.0635 0.9563 0.0204 1.2332 1.0987 0.9872 0.0309 1.2787 1.1395 1.0230 0.0637 1.4243 1.2652 1.1316 0.0870 1.5366 1.3617 1.2143 0.1111 1.6486 1.4551 1.2947 0.2498 2.4111 2.1021 1.8471 0.6658 5.3353 4.4801 3.8110

PEGDME250 in the Aqueous Solutions of 3 % (w/w) PEG10000 0.0000 1.7317 1.5307 1.3644 0.0019 1.7533 1.5504 1.3803 0.0059 1.7598 1.5557 1.3871 0.0081 1.7721 1.5662 1.3944 0.0100 1.7822 1.5750 1.4026 0.0203 1.8363 1.6229 1.4443 0.0309 1.8944 1.6730 1.4871 0.0637 2.0867 1.8389 1.6300 0.0867 2.2332 1.9626 1.7368 0.1109 2.3740 2.0808 1.8431 0.2502 3.3146 2.8752 2.5166 0.4288 4.7844 4.0891 3.5276 0.6675 6.8171 5.7037 4.8057 PPG400 in the Aqueous Solutions of 3 % (w/w) PEG10000 0.0040 1.4633 1.2989 1.1393 0.0081 1.4848 1.3079 1.1436 0.0100 1.4915 1.3188 1.1520 0.0416 1.6488 1.4554 1.2709 0.0866 1.9117 1.6619 1.4321 0.1111 2.0477 1.7839 1.5220 0.2497 3.0334 2.5683 2.1473 0.0040 1.4633 1.2989 1.1393 0.0081 1.4848 1.3079 1.1436 0.0100 1.4915 1.3188 1.1520 0.0416 1.6488 1.4554 1.2709



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Table 3. continued 103η/(Pa·s) mwp

298.15 K

303.15 K

103η/(Pa·s) 308.15 K

mwp

298.15 K

303.15 K

103η/(Pa·s) 308.15 K

PEGDME250 in the Aqueous Solutions of 1 % (w/ w) PPG400 0.0000 0.9309 0.8431 0.7556 0.0040 0.9357 0.8457 0.7596 0.0081 0.9450 0.8552 0.7674 0.0100 0.9514 0.8599 0.7714 0.0416 1.0281 0.9234 0.8236 0.0870 1.1486 1.0289 0.9079 0.1111 1.2198 1.0830 0.9531 0.2489 1.6640 1.4473 1.2511 0.4271 2.3466 1.9947 1.6892 PPG400 in the Aqueous Solutions of 1 % (w/w) PVP10000 0.0039 1.0594 0.9477 0.8448 0.0081 1.0607 0.9541 0.8503 0.0101 1.0743 0.9643 0.8579 0.0416 1.1850 1.0583 0.9357 0.0870 1.3658 1.2045 1.0557 0.1106 1.4850 1.2959 1.1286 0.2505 2.2605 1.9332 1.5613 0.4205 3.5636 2.9650 2.4216

PVP10000 in the Aqueous Solutions of 1 % (w/w) PPG400 0.0039 0.9783 0.8834 0.7927 0.0081 1.0485 0.9396 0.8365 0.0100 1.0744 0.9653 0.8572 0.0308 1.4555 1.2789 1.1197 0.0525 1.9171 1.7248 1.4983 0.0868 3.1090 2.6850 2.2592 0.1115 4.0540 3.4788 2.9211 0.1762 8.0406 6.7129 5.5415 PEGDME250 in the Aqueous Solutions of 1 % (w/w) PVP10000 0.0039 1.0417 0.9380 0.8373 0.0080 1.0577 0.9581 0.8500 0.0101 1.0675 0.9618 0.8528 0.0417 1.1541 1.0281 0.9165 0.0868 1.2857 1.1338 0.9991 0.1110 1.3501 1.1974 1.0482 0.2500 1.8525 1.6128 1.3851 0.4284 2.5648 2.1789 1.8399

PPG400 in the Aqueous Solutions of 1 % (w/w) PEGDME250 0.0039 0.9435 0.8520 0.7664 0.0081 0.9477 0.8617 0.7665 0.0100 0.9530 0.8598 0.7707 0.0416 1.0486 0.9415 0.8355 0.0866 1.2149 1.0766 0.9417 0.1112 1.3009 1.1509 1.0067 0.2503 1.9925 1.7102 1.4493 0.4298 3.2301 2.6814 2.2073

PVP10000 in the Aqueous Solutions of 1 % (w/w) PEGDME250 0.0020 0.9378 0.8485 0.7630 0.0081 1.0304 0.9261 0.8230 0.0100 1.0608 0.9507 0.8505 0.0307 1.4145 1.2524 1.1104 0.0471 1.8217 1.5896 1.3769 0.0868 3.0164 2.5837 2.2096 0.1110 3.9795 3.4042 2.8318 0.1765 7.8307 6.6974 5.5399

mwp

298.15 K

303.15 K

308.15 K

PEG600 in the Aqueous Solutions of 1 % (w/w) PVP10000 0.0000 1.0366 0.9348 0.8335 0.0039 1.0514 0.9458 0.8431 0.0080 1.0681 0.9593 0.8555 0.0100 1.0670 0.9659 0.8562 0.0417 1.1754 1.0466 0.9319 0.0867 1.3427 1.1929 1.0546 0.1107 1.4470 1.2826 1.1210 0.2500 2.1658 1.8937 1.6041 0.4284 3.4110 2.8682 2.4106 PEG600 in the Aqueous Solutions of 1 % (w/w) PEGDME250 0.0000 0.9159 0.8328 0.7466 0.0040 0.9241 0.8388 0.7533 0.0080 0.9408 0.8531 0.7649 0.0100 0.9497 0.8550 0.7678 0.0414 1.0435 0.9361 0.8361 0.0870 1.1965 1.0729 0.9472 0.1111 1.2847 1.1458 1.0076 0.2500 1.9380 1.6895 1.4581 0.4280 3.0764 2.6103 2.1950

a The standard uncertainties for polymer weight molality, viscosity and temperature were estimated to be ± 1·10−4, ± 2·10−7 Pa·s and ± 1·10−2 K, respectively.

Figure 1. (a) Apparent specific volumes of different polymers in pure water at 288.15 K (solid lines) and 308.15 K (dotted lines). (b) Apparent specific volumes of different polymers in aqueous solutions of 1 % (w/w) of PEG10000 at 288.15 K (solid lines) and 308.15 K (dotted lines): ○, PPG400; ×, PEGDME250; △, PEG600; ●, PVP10000; solid and dotted lines, calculated by equation 2.

are a typical characteristic of amphiphile-water systems.20,34 Assuming that the polymer intrinsic volume and shape do not depend on the polymer amount in solution, the Vϕ dependence

polymer (1), the values of Vϕ decrease with the increase in the concentration of polymer (1), this is completely opposite to that for high polymer (1) concentrations. Minima of this type 3139



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Figure 2. (a) Apparent specific volumes of PEG600 in aqueous solutions of 1 % (w/w) of different polymers at 298.15 K: ○, pure water; ×, PEG10000; ▲, PVP10000; □, PEGDME250; ■, PPG400. (b) Apparent specific volumes of PEGDME250 in aqueous solutions of 1 % (w/w) of different polymers at 298.15 K: ○, pure water; ×, PEG10000; ▲, PVP10000; □, PPG400. (c) Apparent specific volumes of PVP10000 in aqueous solutions of 1 % (w/w) of different polymers at 298.15 K: ○, pure water; ×, PEG10000; ▲, PEGDME250; □, PPG400. (d) Apparent specific volumes of PPG400 in aqueous solutions of 1 % (w/w) of different polymers at 298.15 K: ○, pure water; ×, PEG10000; ▲, PVP10000; □, PEGDME250.

(2) at 298.15 K has been shown. As can be seen, for the low polymer (1) concentration range, the values of Vϕ in pure water are larger than those in the presence of polymer (2) and the ability of polymer (2) in decreasing Vϕ of the polymer (1) in this region follows the order: PPG400 > PEGDME250 > PEG10000 > PVP10000. However, for the high polymer (1) concentration range, the values of Vϕ of polymer (1) increased in the presence of polymer (2). As can be seen from Figure 3, the values of Vϕ in the low and high polymer (1) concentration ranges respectively decrease and increase by increasing the polymer (2) (PEG10000) concentration. In all cases, an equation in the form,

on polymer concentration can be interpreted as due to the change of amount of water in the polymer hydration shells.22 At low polymer concentration, the addition of polymer promotes a structuring effect on water (the water molecules inside the hydration shells of polymers have an ice-like structure whose specific volume is larger than the corresponding liquid water specific volume) and then a drop of Vϕ value. A further increase of the polymer concentration implies a redistribution of water molecules between the bulk and the hydration shells (due to overlap of the polymer hydration cospheres and subsequent release of water to the bulk). Therefore the number of icestructured water molecules in the hydration shells decreases and then a subsequent Vϕ rise is observed.22 The values of Vϕ of the investigated polymers decrease in the order: PPG400 > PEGDME250 > PEG600 > PVP10000, and in all cases Vϕ values increase by increasing temperature. In Figure 2, the concentration dependence of the apparent specific volumes of PEG600, PEGDME250, PVP10000, and PPG400 in pure water and in aqueous solutions of 1 % (w/w) of different polymers

2 Vϕ = V ϕ0 + B V m wp + C Vm wp

(2)

was used to obtain V0ϕ, the limiting apparent specific volume of polymer (1) in the investigated solutions. The V0ϕ data extend the knowledge of thermodynamic behavior of aqueous polymer solutions: They help to give some insight into the solvation 3140



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characteristic property of aqueous solutions of hydrophobic hydration. Upon heating, due to the increase of their motion, the polymer chains increase their size. This produces a slight increase of the Vϕ°, and so Eϕ° would be positive. 3.2. Excess Specific Volume. The excess specific volume, VE, of the investigated solutions can be calculated using the relation: VE =

⎛m ⎞ 1 1 ⎜ wp + 1 ⎟ − ρ ρ0 ⎟⎠ 1 + m wp ⎜⎝ ρp

(4)

where ρp is density of pure polymer. The variation of V for the solutions of different polymers (1) in pure water and that of PPG400 (1) in the aqueous solutions of 1 % w/w of different polymers (2) as a function of the weight molality of polymer (1) are shown in Figure 4 at 288.15 K and 308.15 K. It was found that for the systems studied in this work, the excess specific volumes have negative values and become more negative as temperature decreases. Similar to the Vϕ values, the magnitude of VE of the investigated solutions decrease in the order: PPG400 > PEGDME250 > PEG600 (Figure 4a). Although the obtained values of VE for the solutions of polymer (1) in pure water are very close to that in polymer (2) + water solutions (Figure 4b), close examinations of the obtained data shows that the concentration dependence of VE values in both low and high polymer (1) concentration range is similar to that of Vϕ shown in Figures 2 and 3. Mainly, the behavior of VE is attributed to the breakdown of the H2O self-associated molecules from each other (a positive volume), the breakdown of the polymers self-associated molecules from each other (a positive volume), the breakdown of the polymer (2)−water interaction as a consequence of preferential polymer (1)− polymer (2) interactions (a positive volume) or vice versa (a negative volume), and the negative contributions of VE due to the intermolecular polymer−water interactions and difference between the size of water and polymer molecules (the relatively small water molecules fit in the available free volume of polymer upon mixing). The obtained negative values of VE show that the effects due to the polymer−water hydrogen-bond E

Figure 3. Apparent specific volumes of PPG400 in the aqueous solutions of PEG10000 at 298.15 K: ○, pure water; ×, aqueous solutions of 1 % (w/w) of PEG10000; ▲, aqueous solutions of 3 % (w/w) of PEG10000.

phenomenon and, indirectly, into conformational features of these macromolecules in aqueous solutions. In this equation, BV and CV are the empirical parameters which depend on solute, solvent and temperature. The coefficients of eq 2 are given in Table S1 of the Supporting Information. The values of the limiting apparent specific expansibility, E0ϕ, were calculated using the following equation:

⎛ ∂V 0 ⎞ ϕ ⎟⎟ Eϕ0 = ⎜⎜ T ∂ ⎠P ⎝

(3)

E0ϕ

The obtained values of the investigated systems are also given in Table S2 of the Supporting Information. As can be seen, the obtained values of E0ϕ for all the investigated polymers are positive and decrease in the order: PEGDME250 ≈ PEG600 > PPG400 ≫ PVP10000. Positive expansibility is a

Figure 4. (a) Apparent specific excess volumes for solutions of different polymers in pure water at 288.15 K (solid lines) and 308.15 K (dotted lines): ○, PPG400; ×, PEGDME250; △, PEG600. (b) Apparent specific excess volumes of PPG400 in aqueous solutions of 1 % (w/w) of different polymers at 288.15 K (solid lines) and 308.15 K (dotted lines): ○, pure water; △, PEG10000; ×, PVP10000; ●, PEGDME250. 3141



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Figure 5. (a) Isentropic compressibility for solutions of different polymers in pure water at 288.15 K (solid lines) and 308.15 K (dotted lines). (b) Isentropic compressibility for solutions of different polymers in aqueous solutions of 3 % (w/w) of PEG10000 at 288.15 K (solid lines) and 308.15 K (dotted lines): ○, PPG400; ×, PEGDME250; △, PEG600; ●, PVP10000.

interactions along with the packing effect may be the predominant factors. At higher temperatures, hydrogen-bond interactions may be weakened and hence less negative values of the excess specific volume are obtained. The packing effect increases by increasing the differences between the volumes of polymer and water molecules which in turn leads to the more negative values of VE. 3.3. Isentropic Compressibility. Isentropic compressibilities, κs, of solutions were obtained using the following Laplace equation:

κs =

1 u 2ρ

(5)

As an example, the variation of κs values with the weight molality of polymer for solutions of different polymers (1) in pure water and in the aqueous solutions of 3 % w/w PEG10000 (2) are shown in Figure 5 at 288.15 K and 308.15 K. The similar behavior was obtained for other systems studied in this work. The variations of κs values with temperature for pure water, pure liquid polymers, and aqueous solutions of 1 % or 3 % w/w PEG10000 have been shown in Figure 6. That is to say, at each temperature the values of κs for aqueous solutions of 1 % w/w all the investigated polymers are almost similar to that shown in Figure 6 for PEG10000. Figure 6 shows that the values of κs for pure water and for aqueous solutions of 1 or 3 % w/w polymers decrease by increasing temperature. However those for pure liquid polymers (PEG600, PPG400 and PEGDME250) increase with increasing temperature. From Figure 5, we note that the values of κs for the investigated aqueous polymer solutions show a shallow minimum at high polymer concentration. This minimum becomes more distinct as temperature is lowered. For low polymer (1) concentrations, the values of κs decrease with the increase in the concentration of polymer (1), this is completely opposite to that for high polymer (1) concentrations. In fact, in aqueous polymer solutions the isentropic compressibility is the sum of two contributions, κs (solvent intrinsic) and κs (solute intrinsic). Figure 5 shows that, similar to the solvents (pure water and binary aqueous solutions of 1 or 3 % w/w polymer (2)), the values of κs for ternary solutions with low concentration of polymers (1) decrease by

Figure 6. Isentropic compressibility of pure water, polymers and binary aqueous solutions of 1 % and 3 % (w/w) of PEG10000 against temperature: ○, pure water; ●, PEG600; △, PEGDME250; ▲, PPG400; ×, aqueous solutions of 1 % (w/w) of PEG10000; ◊, aqueous solutions of 3 % (w/w) of PEG10000.

increasing temperature. However, the values of κs for both ternary solutions with high polymers (1) concentrations and pure polymers increase by increasing temperature. The results show that the values of κs (solvent intrinsic) are the dominant contribution to the total value of κs from pure solvent up to the converging concentration, and beyond that the values of κs (solute intrinsic) is the substantial contribution. Figure 5 also shows that at low polymer concentration the values of κs for different polymers are almost identical. However, at high polymer (1) concentrations the values of κs for aqueous polymer solutions have the same order as that for pure polymers (PPG400 > PEGDME250 > PEG600). This behavior also supports our idea that κs (solvent intrinsic) and κs (solute intrinsic) are the dominant contributions to the total value of κs respectively at low and high polymer (1) concentrations. The compressibility isotherms for all the measured temperatures 3142



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Figure 7. (a) Isentropic compressibility increments for solutions of different polymers in pure water at 288.15 K (solid lines) and 308.15 K (dotted lines): ○, PPG400; ×, PEGDME250; △, PEG600. (b) Isentropic compressibility increments for solutions of PPG400 in aqueous solutions of 1 % (w/w) of different polymers at 288.15 K (solid lines) and 308.15 K (dotted lines): ○, pure water; △, PEG10000; ×, PVP10000; ●, PEGDME250.

solutions. The behavior of Δκs implies a great difficulty to compress the components of the mixture regarding those can be expected under an ideal behavior. This is due to a closer approach of unlike molecules and stronger interaction between components of mixtures that lead to decreasing compressibility. 3.4. Apparent Specific Isentropic Compressibility. The apparent specific isentropic compressibilities κs,ϕ of the investigated systems were computed from the density and speed of sound experimental data according to the following equation:

intersect each other approximately at a fixed polymer (1) molality which shifts to low polymer (1) molality as concentration of polymer (2) increases. Therefore, one can assume that the isentropic compressibilities for the corresponding concentration are independent of temperature and at this concentration dκs (solute intrinsic)/dT + dκs (solvent intrinsic)/ dT = 0. In fact for polymer (1) molality smaller than the intersection concentration, the compressibility of a solution is mainly due to the effect of pressure on the bulk (unhydrated) water molecules. Therefore in this concentration region, as the concentration of the polymer increases and a large portion of the water molecule is hydrated, the amount of bulk water decreases causing the compressibility to decrease. Also, Figure 5 shows that the concentration dependence of κs becomes greater as temperature decreases. This is because at higher temperatures, polymer−water interactions are weakened and therefore the number of water molecules affected by the segment of polymer decreases. The experimental isentropic compressibility increments, △κs, were obtained using the relation: Δκs = κs −

1 (m wpκsp + κs0) 1 + m wp

κs, ϕ =

(1 + m wp)κs ρm wp

−

κs0 ρ0 m wp

(7)

where κs and κs0 are the isentropic compressibility of the solution and solvent, respectively. The negative values of κs,ϕ (loss of compressibility of the medium) indicate that the water molecules surrounding the polymer molecules would present greater resistance to compression than the bulk water molecules. On the other hand, the positive values of κs,ϕ indicate that the water molecules around the polymer molecules are more compressible than the water molecules in the bulk solution. The variation of κs,ϕ as a function of the weight molality of the investigated polymers in pure water is shown in Figure 8a at 288.15 K and 308.15 K. The similar behavior was obtained for solutions of different polymers (1) in the aqueous solutions of polymer (2). Figure 8 panels b and c, respectively, show the effect of type and concentration of polymer (2) on the apparent specific isentropic compressibility of PEG600 (1) in aqueous solutions at 298.15 K. From Figure 8, it can be seen that the apparent specific isentropic compressibility of the polymers (1) in water and in aqueous polymer (2) solutions increased (changed from negative to positive values) by increasing temperature, polymer (1) (except for PVP10000) and polymer (2) concentration. In the presence of polymer (2) as well as by increasing temperature, polymer (1)−water interactions are weakened and therefore some water molecules are released into the bulk, thereby making the medium more compressible and therefore the values of κs,ϕ increase. As can be seen from Figure 8, the polymer (1) concentration dependence of κs,ϕ for

(6)

where κsp and κs0 are the values of isentropic compressibility of pure polymer (1) and solvent (polymer (2) + water is considered as the solvent), respectively. As an example, Figure 7 shows the variation of Δκs values with the molality of polymer (1) for solutions of different polymers (1) in pure water and for solutions of PPG400 (1) in the aqueous solutions of 1 % w/w of different polymers (2) at 288.15 K and 308.15 K. Similar behavior was obtained for other systems studied in this work. From Figure 7a, it can be seen that similar to the VE values, the values of Δκs are negative and become more negative as temperature decreases. Furthermore, the magnitudes of Δκs for the solutions of the investigated polymers in aqueous solutions decrease in the order: PPG400 > PEGDME250 > PEG600. Figure 7b shows that the values of Δκs for solutions of polymer (1) in pure water are very close to that in polymer (2) + water 3143



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Figure 8. (a) Apparent specific isentropic compressibility of different polymers in pure water at 288.15 K (solid lines) and 308.15 K (dotted lines). ○, PPG400; ×, PEGDME250; △, PEG600; ●, PVP10000; solid and dotted lines, calculated by equation 6. (b) Apparent specific isentropic compressibility of PEG600 in aqueous solutions of 1 % (w/w) of different polymers at 298.15 K: ◊, pure water; ○, PPG400; ×, PEGDME250; △, PEG10000; ●, PVP10000. (c) Apparent specific isentropic compressibility of PEG600 in the aqueous solutions of PEG10000 at 298.15 K: ○, pure water; ×, aqueous solutions of 1 % (w/w) of PEG10000; ▲, aqueous solutions of 3 % (w/w) of PEG10000.

different polymers (1) in pure water and in the aqueous solutions of 3 % w/w PEG10000 (2) at 298.15 K and 308.15 K. The values of η for solutions of different polymers (1) in pure water and in the aqueous solutions of 3 % w/w PEG10000 (2) decrease in the order: PVP10000 > PEG600 > PEGDME250 > PPG400 and in all cases they increase by decreasing temperature. This trend for the viscosity of the pure polymers is PVP10000 > PEG600 > PPG400 > PEGDME250. Figure 10 shows the concentration dependence of the viscosities for solutions of PEG600 (1) in pure water and in the aqueous solutions of 1 % w/w PEG10000, PVP10000, PPG400, and PEGDME250 at 298.15 K. As can be seen, for the low PEG600 concentration range, the values of η for solutions of PEG600 in pure water are smaller than those in the aqueous solutions of 1 % w/w polymers (2) and the abilities of polymers (2) in increasing the viscosity follow the order: PEG10000 > PVP10000 > PPG400 > PEGDME250. However, for the high PEG600 concentration range, the values of η decrease in the order: PEG10000 > pure water > PVP10000 > PPG400 > PEGDME250.

the investigated polymers increased in the order: PVP10000 < PEG600 < PEGDME250 < PPG400. Although the κs,ϕ values of polymer (1) in pure water are very close to that in polymer (2) + water solutions, close examinations of Figure 8b show that the abilities of polymer (2) in the increasing the κs,ϕ values of polymer (1) in aqueous solutions decrease in the order: PPG400 > PEGDME250 > PEG10000 > PVP10000 which is the same order of the polymer (1) concentration dependence of κs,ϕ. Similar to the apparent specific volume, in all cases, the following equation was used for the correlation of κs,ϕ data and the coefficients of this equation for κs,ϕ are given in Table S2 of the Supporting Information. 2 κs, ϕ = κs,0ϕ + Bκ m wp + Cκm wp

(8)

As can be seen, the infinite dilution apparent specific isentropic compressibilities κ0s,ϕ of the investigated systems at low and high temperatures, respectively, have negative and positive values. 3.5. Viscosity. Figure 9 shows the variations of η as a function of the weight molality of polymer (1) for solutions of 3144



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Figure 9. (a) Viscosity for solutions of different polymers in pure water at 298.15 K (solid lines) and 308.15 K (dotted lines). (b) Viscosity for solutions of different polymers in aqueous solutions of 3 % (w/w) of PEG10000 at 298.15 K (solid lines) and 308.15 K (dotted lines): ○, PPG400; ×, PEGDME250; △, PEG600; ●, PVP10000.

3 % w/w PEG10000). In the most cases, the values of [η] in the aqueous solutions of 1 % w/w investigated polymers (2) increase in the order: PPG400 < PVP10000 < PEGDME < PEG10000.

■

CONCLUSIONS Volumetric, acoustic, and viscometric behavior of aqueous solutions of each of the polymers PEG600, PEGDME250, PPG400, and PVP10000 in the aqueous solutions of 0 % and 1 % w/w PEG10000, PPG400, PEGDME250, and PVP10000 and in the aqueous solutions of 3 % w/w PEG10000 have been studied through the density, speed of sound, and viscosity measurements at different temperatures. It was found that the values of Vϕ as well as the concentration dependence of κs,ϕ for each of the investigated polymers in pure water and in the polymer (2)−water solutions decrease in the order: PPG400 > PEGDME250 > PEG600 > PVP10000 and the values of both Vϕ and κs,ϕ increase by increasing temperature. The abilities of polymer (2) in increasing the κs,ϕ values (in the whole polymer (1) concentration range) and decreasing the Vϕ values (in the low polymer (1) concentration range) of polymer (1) in aqueous solutions decrease in the order: PPG400 > PEGDME250 > PEG10000 > PVP10000. In the case of high polymer (1) concentration range, the values of Vϕ increased in the presence of polymer (2). It was also found that, the VE values of the investigated systems are negative and become more negative as temperature decreases. The magnitude of the VE values for the investigated polymers in aqueous solutions as well as the concentration dependence of VE values in both low and high polymer (1) concentration range is similar to that of Vϕ. From the experimental viscosity data, the values of intrinsic viscosities for the investigated binary and ternary systems were calculated. It was found that the values of [η] for solutions of different polymers (1) in pure water and in the aqueous solutions of PEG10000 (2) decrease in the order PVP10000 > PEG600 > PEGDME250 (1 % w/w PEG10000) > PPG400 > PEGDME250 (pure water and 3 % w/w PEG10000) and they decrease by increasing temperature.

Figure 10. Viscosity for solutions of PEG600 in aqueous solutions of 1 % (w/w) of different polymers at 298.15 K: ○, pure water; ×, PEG10000; ▲, PVP10000; □, PEGDME250; ■, PPG400.

The intrinsic [η] viscosities for the investigated binary and ternary systems were calculated by using the following equation35 ηsp = [η] + kH[η]2 c + kH′ [η]3 c 2 (9) c where kH and kH′ are empirical parameters, ηsp is specific viscosity (ηrel − 1, where ηrel is ratio of solution viscosity to solvent viscosity) and c is polymer concentration (kg·m−3). In Table S3 of the Supporting Information the obtained values of [η], kH and kH′ for the investigated systems have been given. The results show that the intrinsic viscosity of the investigated systems reduced with increasing temperature. It means that, with increasing temperature, polymer−solvent interaction is decreased and polymer−polymer interaction is increased; therefore polymers chains may be coiled by increasing temperature. The values of [η] for solutions of different polymers (1) in pure water and in the aqueous solutions of PEG10000 (2) decrease in the order: PVP10000 > PEG600 > PEGDME250 (1 % w/w PEG10000) > PPG400 > PEGDME250 (pure water and 3145



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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00290. Tables of limiting apparent specific volume, limiting apparent specific expansibility, limiting apparent specific isentropic compressibility, intrinsic viscosity, and fitting parameters of equations 2, 8, and 9 for different binary and ternary aqueous polymer solutions examined in this study (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. [email protected]. Tel./Fax: +98-871-6624133. Notes

The authors declare no competing financial interest.

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REFERENCES

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