Section: 13 | Vapor Pressures (Solvent Activities) for Binary Polymer Solutions |

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VAPOR PRESSURES (SOLVENT ACTIVITIES) FOR BINARY POLYMER SOLUTIONS

Christian Wohlfarth

The vapor pressure of a binary polymer solution is determined by the activity of the solvent A, a_A. Solvent activities in polymer solutions are measured either by the isopiestic method applying a reference system whose solvent activity is precisely known or by determining the solvent partial pressure, P_A, and calculating the activity of the solvent by equation (1):

<math xmlns= "http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>a</mtext><mtext>A</mtext></msub><mtext>=</mtext><mrow><mo>(</mo><mrow><msub><mi>P</mi><mtext>A</mtext></msub><mtext>/</mtext><msubsup><mi>P</mi><mtext>A</mtext><mtext>s</mtext></msubsup></mrow><mo>)</mo></mrow><mtext>exp</mtext><mrow><mo>[</mo><mrow><mfrac><mrow><mrow><mo>(</mo><mrow><msub><mi>B</mi><mrow><mtext>AA</mtext></mrow></msub><mtext>–</mtext><mi>V</mi><mmultiscripts><mrow></mrow><mprescripts/><mtext>A</mtext><mtext>L</mtext></mmultiscripts></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mi>P</mi><mo>–</mo><msubsup><mi>P</mi><mtext>A</mtext><mtext>s</mtext></msubsup></mrow><mo>)</mo></mrow></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></math> (1)

where B_AA is the second virial coefficient, P_A^s is the saturation vapor pressure, and V_A^L is the molar volume of the pure solvent A at the measuring temperature T. The exponential term is neglected in quite a lot of original papers, however, and only the reduced vapor pressures are given (such data are indicated by an asterisk in the table below). Vapor pressures of polymer solutions have been measured since the 1940s, but the amount of experimental data for polymer solutions is still relatively small in comparison to low-molecular mixtures and solutions. The data scatter with respect to temperature, concentration, molar mass, and other polymer characterization variables. Furthermore, the concentration range for measuring vapor pressures in good thermodynamic quality is often limited to the polymer mass fraction range between 0.4 and 0.85. A recent review on methods for the measurement of vapor pressures/solvent activities of polymer solutions and on related problems is given in Ref.1. Experimental data have been collected in several books Refs. 2-6.

The table below provides data for a number of polymer solutions as smoothed values over the complete range of solvent activities between 0 (polymer mass fraction = 1) and 1 (polymer mass fraction = 0). For this purpose, the data were selected from data books Refs. 4-6 as well as from a number of original sources Refs. 7-22, which are not included in these books. The appropriate data were smoothed. The final table provides the polymer mass fractions at given fixed solvent activities between 0.1 and 0.9. Of course, the user must keep in mind that the activity vs. concentration range of the experimental data is sometimes smaller than the complete range given below, thus the smoothed data should be used with sufficient care.

Generally, vapor pressures or solvent activities of binary polymer solutions depend on molar mass. However, for high molecular weight polymers (well above the oligomer region), this molar-mass dependence can be neglected in many cases. Therefore, the table below presents only data for polymer solutions where the number average molar mass M_n is in the order of 10⁵ g/mol or even higher; therefore, the molar mass is not specified. The temperature is stated, even though the temperature dependence of a_A is relatively small for the temperature ranges where most of the experimental data exist.

References

Wohlfarth, C., Methods for the measurement of solvent activity of polymer solutions, in Handbook of Solvents, Wypych, G., Ed., ChemTec Publishing, Toronto, 2000, 146.
Wen, H., Elbro, H. S., and Alessi, P., Polymer Solution Data Collection. I. Vapor-liquid equilibrium; II. Solvent activity coefficients at infinite dilution; III. Liquid-liquid equilibrium, Chemistry Data Series, Vol. 15, DECHEMA, Frankfurt am Main, 1992.
Danner, R. P. and High, M. S., Handbook of Polymer Solution Thermodynamics, American Institute of Chemical Engineers, New York, 1993. [https://doi.org/10.1002/9780470938232]
Wohlfarth, C., Vapour-Liquid Equilibrium Data of Binary Polymer Solutions: Physical Science Data, 44, Elsevier, Amsterdam, 1994.
Wohlfarth, C., CRC Handbook of Thermodynamic Data of Copolymer Solutions, CRC Press, Boca Raton, FL, 2001. [https://doi.org/10.1201/9781420040968]
Wohlfarth, C., CRC Handbook of Thermodynamic Data of Aqueous Polymer Solutions, CRC Press, Boca Raton, FL, 2003. [https://doi.org/10.1201/9780203998205]
Wang, K., Hu, Y., and Wu, D. T., J. Chem. Eng. Data, 39, 916, 1994. [https://doi.org/10.1021/je00016a063]
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Wong, H. C., Campbell, S. W., and Bhethanabotla, V. R., Fluid Phase Equil., 139, 371, 1997. [https://doi.org/10.1016/S0378-3812(97)00158-1]
Kim, J., Joung, K. C., Hwang, S., Huh, W., Lee, C. S., and Yoo, K.-P., Korean J. Chem. Eng., 15, 199, 1998. [https://doi.org/10.1007/BF02707073]
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Fornasiero, F., Halim, M., and Prausnitz, J. M., Macromolecules, 33, 8435, 2000. [https://doi.org/10.1021/ma000739t]
Wong, H. C., Campbell, S. W., and Bhethanabotla, V. R., Fluid Phase Equil., 179, 181, 2001. [https://doi.org/10.1016/S0378-3812(00)00499-4]
Wibawa, G., Takahashi, M., Sato, Y., Takishima, S., and Masuoka, H., J. Chem. Eng. Data, 47, 518, 2002. [https://doi.org/10.1021/je010310c]
Wibawa, G., Hatano, R., Sato, Y., Takishima, S., and Masuoka, H., J. Chem. Eng. Data, 47, 1022, 2002. [https://doi.org/10.1021/je025518s]
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Jung, J. K., Joung, S. N., Shin, H.Y., Kim, S. Y., Yoo, K.-P., Huh, W., Lee, C. S., Korean J. Chem. Eng., 19, 296, 2002. [https://doi.org/10.1007/BF02698417]
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Go to interactive table

Mobile-friendly table

Solvent Activity a_A as a Function of Temperature and Mass Fraction

Polymer/Solvent	T/K	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
Continued on next page...
Acrylonitrile/Styrene Copolymer (28 wt% Acrylonitrile)
Benzene *	343.15	0.982	0.962	0.940	0.915	0.886	0.851	0.809	0.753	0.670
1,2-Dimethylbenzene *	398.15	0.983	0.964	0.942	0.918	0.890	0.857	0.817	0.764	0.685
1,3-Dimethylbenzene *	398.15	0.983	0.965	0.944	0.921	0.893	0.861	0.821	0.769	0.690
1,4-Dimethylbenzene *	398.15	0.983	0.964	0.942	0.918	0.890	0.857	0.817	0.763	0.684
Propylbenzene *	398.15	0.987	0.972	0.955	0.935	0.913	0.885	0.851	0.804	0.732
Toluene *	343.15	0.982	0.962	0.940	0.915	0.886	0.851	0.809	0.753	0.669
Butadiene/Styrene Copolymer (41 wt% Styrene)
Benzene *	343.15	0.968	0.934	0.896	0.853	0.805	0.748	0.680	0.591	0.461
Cyclohexane *	343.15	0.978	0.953	0.925	0.893	0.856	0.811	0.754	0.678	0.556
Ethylbenzene *	398.15	0.974	0.945	0.912	0.875	0.831	0.779	0.713	0.625	0.491
Mesitylene *	398.15	0.977	0.950	0.921	0.887	0.847	0.799	0.738	0.656	0.526
Toluene *	343.15	0.970	0.936	0.899	0.857	0.808	0.751	0.682	0.591	0.456
Cellulose Triacetate
Dichloromethane	298.15	0.979	0.956	0.930	0.899	0.863	0.819	0.762	0.683	0.554
Trichloromethane	298.15	0.978	0.953	0.924	0.892	0.853	0.806	0.747	0.665	0.533
Dextran
Water	313.15	0.988	0.975	0.960	0.942	0.921	0.894	0.860	0.810	0.725
Hydroxyethylcellulose
Water	368.15	0.988	0.974	0.958	0.939	0.915	0.884	0.841	0.775	0.650
Hydroxypropylstarch
Water	293.15	0.989	0.977	0.963	0.947	0.927	0.903	0.872	0.827	0.749
Nitrocellulose
Ethyl acetate	293.15	0.938	0.885	0.835	0.786	0.737	0.685	0.627	0.560	0.471
Ethyl formate	293.15	0.958	0.916	0.873	0.828	0.780	0.728	0.668	0.595	0.494
Ethyl propionate	293.15	0.941	0.889	0.839	0.789	0.739	0.685	0.625	0.555	0.460

^* a_A = P_A/P_A^S.

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VAPOR PRESSURES (SOLVENT ACTIVITIES) FOR BINARY POLYMER SOLUTIONS

References