Wypych Handbook of Solvents

78A. L. Jones, Trans. Faraday Soc., 52, 1408 (1956).

79E. C. Baughan, A. L. Jones, K. Stewart, Proc. Roy. Soc., London, Ser. A, 225, 478 (1954).

80G. N. Malcolm, C. E. Baird, G. R. Bruce, K. G. Cheyne, R. W. Kershaw, M. C. Pratt, J. Polym. Sci., Pt. A-2, 7, 1495 (1969).

81W. R. Moore, R. Shuttleworth, J. Polym. Sci., Pt. A, 1, 733 (1963).

82K. H. Meyer, E. Wolff, Ch. G. Boissonnas, Helv. Chim. Acta, 23, 430 (1940).

83S. G. Canagratna, D. Margerison, J. P. Newport, Trans. Faraday Soc., 62, 3058 (1966).

84H. Ochiai, K. Gekko, H. Yamamura, J. Polym. Sci., Pt. A-2, 9, 1629 (1971).

85R. C. Osthoff, W. T. Grubb, J. Amer. Chem. Soc., 76, 399 (1954).

86A. A. Tager, A. I. Suvorova, Yu.S. Bessonov, A. I. Podlesnyak, I.A. Koroleva, L. V. Adamova, Vysokomol. Soedin., Ser. A, 13, 2454 (1971).

87A. A. Tager, L. V. Adamova, Yu.S. Bessonov, V. N. Kuznetsov, T. A. Plyusnina, V. V. Soldatov,

Vysokomol. Soedin., Ser. A, 14, 1991 (1972).

88T. V. Gatovskaya, V. A. Kargin, A. A. Tager, Zh. Fiz. Khim., 29, 883 (1955).

89J. Leonard, Van Tam Bui, Polymer, 28, 1041 (1987).

90A. Hamdouni, J. Leonard, Van Tam Bui, Polymer Commun., 31, 258 (1990).

91Van Tam Bui, J. Leonard, J. Chem. Soc., Faraday Trans. I, 82, 899 (1986).

92Van Tam Bui, J. Leonard, J. Chem. Soc., Faraday Trans. I, 81, 1745 (1985).

93A. H. Abdel-Alim, J. Appl. Polym. Sci., 22, 3597 (1978).

94U. Messow, Inst. Phys. Chem., Univ. Leipzig, personal communication.

95F. Cordt, Dissertation, TU Muenchen, 1985.

96F. Moeller, Dissertation, TU Muenchen, 1989.

97G. Luengo, G. Rojo, R. G. Rubio, M. G. Prolongo, R. M. Masegosa, Macromolecules, 24, 1315 (1991).

98N. H. Wang, K. Hattori, S. Takashima, H. Masuoka, Kagaku Kogaku Ronbunshu, 17, 1138 (1991).

99A. J. Ashworth, G. J. Price, Macromolecules, 19, 362 (1986).

100A. J. Ashworth, G. J. Price, J. Chem. Soc., Faraday Trans. I, 81, 473 (1985).

101A. J. Ashworth, G. J. Price, Macromolecules, 19, 358 (1986).

102I. Noda, Y. Higo, N. Ueno, T. Fujimoto, Macromolecules, 17, 1055 (1984).

103H. W. Starkweather, Jr., J. Appl. Polym. Sci., 2, 129 (1959).

104M. Herskowitz, M. Gottlieb, J. Chem. Eng. Data, 30, 233 (1985).

105Van Tam Bui, J. Leonard, Polym. J., 21, 185 (1989).

106Y. Iwai, Y. Arai, J. Chem. Eng. Japan, 22, 155 (1989).

107H. Masuoka, N. Murashige, M. Yorizane, Fluid Phase Equil., 18, 155 (1984).

108Y. C. Bae, J. J. Shim, D. S. Soane, J. M. Prausnitz, J. Appl. Polym. Sci., 47, 1193 (1993).

109Ch. Wohlfarth, Plaste & Kautschuk, 40, 272 (1993).

110G. Luengo, R. G. Rubio, I. C. Sanchez, C. G. Panayiotou, Macromol. Chem. Phys., 195, 1043 (1994).

111J. Gaube, A. Pfennig, M. Stumpf, J. Chem. Eng. Data, 38, 163 (1993).

112J. Zhu, Dissertation, Univ. Kaiserslautern, 1991.

113Y. Iwai, S. Miyamoto, K. Nakano, Y. Arai, J. Chem. Eng. Japan, 23, 508 (1990).

114Y. Iwai, T. Ishidao, S. Miyamoto, H. Ikeda, Y. Arai, Fluid Phase Equil., 68, 197 (1991).

115K. Gekko, K. Matsumara, Bull. Chem. Soc. Japan, 46, 1554 (1973).

116Ch. Wohlfarth, Plaste & Kautschuk, 41, 163 (1994).

117M. Koester, Diploma Paper, TH Darmstadt, 1994.

118Ch. Wohlfarth, ELDATA: Int. Electron. J. Phys.-Chem. Data, 1, 113 (1995).

119C. Grossmann, R. Tintinger, G. Maurer, Fluid Phase Equil., 106, 111 (1995).

120S. P. V. N. Mikkilineni, D.A. Tree, M. S. High, J. Chem. Eng. Data, 40, 750 (1995).

121R. B. Gupta, J. M. Prausnitz, J. Chem. Eng. Data, 40, 784 (1995).

122J. S. Choi, K. Tochigi, K. Kojima, Fluid Phase Equil., 111, 143 (1995).

123S. Behme, G. Sadowski, W. Arlt, Chem.-Ing.-Techn., 67, 757 (1995).

124H.-M. Petri, N. Schuld, B. A. Wolf, Macromolecules, 28, 4975 (1995).

125H.-M. Petri, Dissertation, Univ. Mainz, 1994.

126Ch. Wohlfarth, ELDATA: Int. Electron. J. Phys.-Chem. Data, 2, 13 (1996).

127K. Wang, Y. Chen, J. Fu, Y. Hu, Chin. J. Chem. Eng., 1, 65 (1993).

128D.-Q. Lin, L.-H. Mei, Z.-Q. Zhu, Z.-X. Han, Fluid Phase Equil., 118, 241 (1996).

129L.R. Ochs, M. Kabri-Badr, H. Cabezas, AIChE-J., 36, 1908 (1990).

130Ch. Wohlfarth, ELDATA: Int. Electron. J. Phys.-Chem. Data, 2, 163 (1996).

131K. Wang, Q. Xue, J. Fu, Y. Hu, Huadong Ligong Daxue Xuebao, 22, 330 (1996).

132K. Wang, Q. Xue, Y. Hu, Huadong Ligong Daxue Xuebao, 23, 109 (1997).

133J. O. Tanbonliong, J. M. Prausnitz, Polymer, 38, 5775 (1997).

134Ch. Wohlfarth, Macromol. Chem. Phys., 198, 2689 (1997).

135Ch. Wohlfarth, ELDATA: Int. Electron. J. Phys.-Chem. Data, 3, 47 (1997).

136K. Tochigi, S. Kurita, M. Ohashi, K. Kojima, Kagaku Kogaku Ronbunshu, 23, 720 (1997).

137R. K. Surana, R. P. Danner, A. B. De Haan, N. Beckers, Fluid Phase Equil., 139, 361 (1997).

138H. C. Wong, S. W. Campbell, V. R. Bhetnanabotla, Fluid Phase Equil., 139, 371 (1997).

139G. Sadowski, L. V. Mokrushina, W. Arlt, Fluid Phase Equil., 139, 391 (1997).

140C. Mio, K. N. Jayachandran, J. M. Prausnitz, Fluid Phase Equil., 141, 165 (1997).

141J. S. Aspler, D. G. Gray, Macromolecules, 12, 562 (1979).

142K. N. Jayachandran, P. R. Chatterji, J. M. Prausnitz, Macromolecules, 31, 2375 (1998).

143Benczedi, D., Tomka, I., Escher, F., Macromolecules, 31, 3062 (1998).

144C. Mio, S. Kiritsov, Y. Thio, R. Brafman, J. M. Prausnitz, C. Hawker, E. E. Malmstroem, J. Chem. Eng. Data, 43, 541 (1998).

145S. Hwang, J. Kim, K.-P. Yoo, J. Chem. Eng. Data, 43, 614 (1998).

146F. Wie, W. Wenchuan, F. Zhihao, J. Chem. Ind. Eng. China, 49, 217 (1998).

147J. Kim, K. C. Joung, S. Hwang, W. Huh, C. S. Lee, K.-P. Yoo, Korean J. Chem. Eng., 15, 199 (1998).

148N. H. Kim, S. J. Kim, Y. S. Won, J. S. Choi, Korean J. Chem. Eng., 15, 141 (1998).

149Y. Dahong, S. Jibin, L. Xiaohui, H. Ying, J. East China Univ. Sci. Technol., 23, 608 (1997).

150W. Hiyan, W. Kun, L. Honglai, H. Ying, J. East China Univ. Sci. Technol., 23, 614 (1997).

151A. Eliassi, H. Modarress, G. A. Mansoori, J. Chem. Eng. Data, 44, 52 (1999).

152C. Mio, J. M. Prausnitz, Polymer, 39, 6401 (1998).

153Ch. Wohlfarth, ELDATA: Int. Electron. J. Phys.-Chem. Data, 4, 83 (1998).

154H.-P. Kany, H. Hasse, G. Maurer, J. Chem. Eng. Data, 44, 230 (1999).

155J. G. Lieu, M. Liu, J. M. J. Frechet, J. M. Prausnitz, J. Chem. Eng. Data, 44, 613 (1999).

156J. G. Lieu, J. M. Prausnitz, Polymer, 40, 5865 (1999).

157J. Kim, E. Choi, K.-P. Yoo, C. S. Lee, Fluid Phase Equil., 161, 283 (1999).

158L. Ninni, M. S. Camargo, A. J. A. Meirelles, Thermochim. Acta, 328, 169 (1999).

159K. Wang, Y. Hu, D. T. Wu, J. Chem. Eng. Data, 39, 916 (1994).

160D.-Q. Lin, Y.-T. Wu, Z.-Q. Zhu, L.-H. Mei, S.-J. Yao, Fluid Phase Equil., 162, 159 (1999).

161R. N. French, G. J. Koplos, Fluid Phase Equil., 158-160, 879 (1999).

*) all data from the Merseburg group before 1994 have been published in Ref. Ch. Wohlfarth, Vapor-liquid equilibrium data of binary polymer solutions, Physical Science Data 44, Elsevier, Amsterdam, 1994

5

Solubility of Selected Systems

and Influence of Solutes

5.1EXPERIMENTAL METHODS OF EVALUATION AND CALCULATION OF SOLUBILITY PARAMETERS OF POLYMERS AND SOLVENTS. SOLUBILITY PARAMETERS DATA.

Valery Yu. Senichev, Vasiliy V. Tereshatov

Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia

5.1.1EXPERIMENTAL EVALUATION OF SOLUBILITY PARAMETERS OF LIQUIDS

The value of solubility parameter can be calculated from the evaporation enthalpy of liquid at given temperature:1

Vmolar volume

5.1.1.1Direct methods of evaluation of the evaporation enthalpy

For measurement of the evaporation enthalpy of volatile substances, adiabatic apparatuses were developed. They require significant quantities of highly purified substances. The accuracy is determined to a large degree by equipment design and precision of measurement.

Most calorimeters that measure a latent heat of vaporization work under isobaric conditions. The measurement of a latent heat of vaporization requires monitoring heat input into calorimeter and the amount of liquid evaporated during measurement time.2-4

In calorimeters of a flowing type,5-6 a liquid evaporates from a separate vessel of a calorimeter. The vapors are directed into the second calorimeter where the thermal capacity of gas is measured. The design of such calorimeters ensures a precise measurement of the stream rate. Heaters and electrical controls permit control of heat flow with high precision and highly sensitive thermocouples measure temperature of gas. There are no excessive

thermal losses, thus single-error corrections for the heat exchange can be used to increase precision of measurement.

The calorimeters used for the measurement of the heat of reaction can also be used for a measurement of the latent heat of vaporization. These are calorimeters for liquids, mi- cro-calorimeters, mass calorimeters, and double calorimeters.7

The calorimeters with carrier gas are also used.8-9 Evaporation of substance is accelerated by a stream of gas (for example, nitrogen) at reduced pressure. The heat loss by a calorimeter, due to evaporation, is compensated by an electrical current to keep temperature of calorimeter constant and equal to the temperature of the thermostating bath.

5.1.1.2 Indirect methods of evaluation of evaporation enthalpy

Because the calorimetric methods of measurement of enthalpy of vapor formation are very difficult, the indirect methods are used, especially for less volatile substances. The application of generalized expression of the first and second laws of thermodynamics to the heterogeneous equilibrium between a condensed phase in isobaricthermal conditions is given in the Clausius-Clapeyron equation that relates enthalpy of a vapor formation at the vapor pressure, P, and temperature, T. For one component system, the Clausius-Clapeyron equation has the form:7

where:

Vdifference between molar volumes of vapor and liquid

The ratio that neglects volume of a condensed phase with assumption that vapor at low pressure is ideal can be derived from the above equation:

where:

Zdifference between compressibility factors of gas and liquids

The value Z includes corrections for volume of liquid and non-ideality of a vapor

Approximate dependence of a vapor pressure on inverse temperature is frequently linear but the dependence may also be non-linear because of changing ratio of Hp/ Z on heating. The mathematical expressions of the dependence lnP on 1/T of real substances in a wide range of temperatures should be taken into account. If Hp/ Z = a + bT, it results in an equation with three constants:

Accepting that Eq. [5.1.12] represents a valid means of assignment of a constant δ2 to polymer, the rearrangement of this equation gives:

Now it is assumed that χS is of the order of magnitude suggested above and that, in accordance with the Huggins equation, it is not a function of δ2. Therefore χS/V1 is only about 3% or less of δ22 /RT for reasonable values of δ2 of 10-20 (MJ/m3)1/2. Hence Eq. [5.1.14] gives δ2 from the slope and intercept on plot against δ1 (see Figure 5.1.1).

This method was improved21 by using calculations that exclude strong deviations of χ. When (χSRT/V1 ≈const), Eq. [5.1.14] is close to linear (y = A + Bx), where

y = δ2 − χ (RT / V ), A = -χS(RT/V1) - δ2 ,

1 S 1 2

B = 2δ2, x = δ1.

But δ2 enters into expression for a tangent of a slope angle and intercept which is cut off on the ordinates axes. This can be eliminated by introduction of a sequential

approximation of χS(RT/V1) and grouping of experimental points in areas characterized by a definite interval of values χS(RT/V1). Inside each area χS(RT/V1) →const and Eq. [5.1.14] becomes more precise.

The intervals of values χS(RT/V1) are reduced in the course of computations. For n experimental points, the files X (x1, x2,.... xn) and Y (y1, y2, .... yn) are gathered. Tangent of the slope angle is defined by the method of least squares and the current value (at the given stage) of a solubility parameter of a polymer is:

where:

ja stage of computation

χS(RT/V1) is then calculated using the equation derived from Eqs. [5.1.13] and [5.1.14]:

mediate position between solubility parameters of solvents. Assumption is made that the maximum polymer swelling occurs when the solubility parameters of the solvent mixture and polymer are equal. This is the case when the solubility parameter of polymer is lower than the solubility parameter of the primary solvent and the solubility parameter of the secondary solvent is higher. The dependence of the swelling ratio on the composition of solvent mixture has a maximum (see Figure 5.1.2). Such mixed solvents are called symmetric liquids. The reliability of the method is examined by a narrow interval of change of the solubility parameter of a binary solvent. The data obtained by this method in various mixtures differ by no more than 1.5% with the data obtained by other methods. Examples of results are given in Tables 5.1.2, 5.1.3.

Table 5.1.2. Values of solubility parameters for crosslinked elastomers from swelling in symmetric liquids. [Adapted, by permission, from V.V. Tereshatov, V.Yu. Senichev, A.I. Gemuev, Vysokomol. soed., B32, 412 (1990).]

Table 5.1.3. Values of solubility parameters of crosslinked elastomers from swelling in individual solvents and symmetric liquids. [Adapted, by permission, from

V.V. Tereshatov, V.Yu. Senichev, A.I. Gemuev, Vysokomol. soed., B32, 412 (1990).]

The calculations were made using equation:

If there are no volume changes, V12 can be calculated using the additivity method:

Attempts25 were made to relate intrinsic viscosity [η] to solubility parameters of mixed solvents. δ2 of polymer was calculated from the equation: [η] = f(δ1). The authors assumed that the maximum value of [η] is when δ1 = δ2 of polymer. However, studying [η] for polymethylmethacrylate in fourteen liquids, the authors found a large scatter of experimental points through which they have drawn a curve with a diffusion maximum. Thus the pre-

cision of δ2 values was affected by 10% scatter in experimental data.

This method was widely used by Mangaray et al.26-28 The authors have presented [η] as

the Gaussian function of (δ1 - δ2 )2. Therefore, dependence {(1/ V1 ) ln[η]max / [η]}1/ 2 = f (δ1 ) can be expressed by a straight line intersecting the abscissa at a point for which δ1 = δ2 . For

natural rubber and polyisobutylene, the paraffin solvents and ethers containing alkyl chains of a large molecular mass were studied.26 For polystyrene, aromatic hydrocarbons were used. For polyacrylates and polymethacrylates esters (acetates, propionates, butyrates)

were used.27,28 The method was used for determination of δ2 of many polymers.29-31 In all cases, the authors observed extrema in the dependence of [η] = f(δ1), and the obtained values of δ2 coincided well with the values determined by other methods. But for some polymers it was not possible to obtain extremum in dependence of [η] = f(δ1).32

A method of the evaluation [η] in one solvent at different temperatures was used for polyisobutylene33 and polyurethanes.34

For polymers soluble in a limited range of solvents, more complex methods utilizing [η] relationship are described.35-37

In addition to the above methods, δ2 of polymer can be determined from a threshold of sedimentation38 and by critical opalescence.39 In recent years the method of inverse gas-liq- uid chromatography has been used to evaluate δ2 of polymers.40,41 One may also use some empirical ratios relating solubility parameters of polymers with some of their physical properties, such as, surface tension42-44 and glass transition temperature.45

The solubility parameters for various polymers are given in Table 5.1.3.

Table 5.1.4. Solubility parameters of some polymers36,46