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Phase Equilibria for Polymer Systems

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Phase Equilibria for Polymer Systems 416 石 油 学 会 誌 Sekiyu Gakkaishi, 34, (5), 416-426 (1991) Phase Equilibria for Polymer Systems Yoshio IWAI and Yasuhiko ARAI* Dept. of Chem. Eng., Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812 (Received February 6, 1991) Phase equilibria for polymer systems were reviewed. The authors briefly described such methods as barometric method, gravimetric method, gas chromatographic method, and permeation method used as experimental techniques to measure the vapor-liquid equilibria of polymer systems, i.e., solubilities of gases and vapors in polymers. Furthermore, the corresponding state principle, solution models, and equation of state for prediction and correlation of vapor-liquid equilibria were described. For liquid-liquid equilibria, the experimental results obtained using the cloud point method and the correlated results obtained using a solution model for cyclopentane-polystyrene system were shown as an example of binary systems. The experimental and correlated results for the aqueous two-phase systems were shown as an example of multicomponent systems. Finally, the results of correlation for the volume-phase transition of polymeric gels were presented. than moderate pressure (about 50 atm) or (b) 1. Introduction higher than moderate pressure. Up to moderate In the chemical industry, it is very important to pressure, polymers do not exist in the vapor phase; design appropriate separation equipment, because then the vapor-liquid equilibria can be considered its cost can be from about 40 to 60% of the total as the solubilities of gases in polymers. If the initial and running costs. To design such equip- solute gas is pure, its solubility in polymer can be ment, the knowledge of phase equilibria is determined by measuring the change in pressure or necessary. Solubilities of gases and vapors in the concentration of the solute in polymer after the polymers are important for designing equipment solute gas has been contacted with the polymer. for recovering monomers and solvents and drying This method is used essentially for the system polymers. Liquid-liquid equilibria are also consisting of several polymers (blend polymers) as important in the selection of a solvent for solution well as of single polymers. polymerization. There are not many data avail- If a multisolute is used, the solubility of each able for phase equilibria, and a successful cor- solute cannot be obtained by either measurement relation or prediction method has not yet been of the pressure or the weight change of the developed for polymer systems as it has been for polymer. The concentration of the solute in the low molecular weight component systems. Fur- vapor phase or in the polymer must be analyzed. thermore, aqueous two-phase systems containing As the density of the vapor phase becomes close water soluble polymers have recently received to that of the liquid phase at high pressures, the much attention for separating bio-products. The polymer exists in both vapor and liquid phases volume-phase transition of polymeric gels has been because it is solvated in the high-pressure vapor found, and its applications have been considered to phase. There is a scarcity of data at high various fields of industry, etc. In this review, the pressures; however, vapor-liquid equilibria at phase equilibria of mixtures containing low- high pressures have been measured, for example, molecular weight components and polymers will for ethylene-polyethylene system5)-7). These be described. data are necessary for designing equipment for production of low-density polyethylene. 2. Vapor-Liquid Equilibria1),2) 2.1.2 Barometric Method 2.1 Measurements3),4) Solubilities of gases in polymer are determined 2.1.1 Type of Experimental Technique from the change in pressure in a sorption cell. Measurement of vapor-liquid equilibria of Pressures are usually measured with a mercury polymer systems can be classified by one of the manometer8) or a gage9),10);sometimes a pressure following conditions: one solute system or difference from that of the pure solute vapor multisolute system with (a) the pressure being less pressure is observed11). Limitations of these experiments are found when they become inac- * To whom correspondence should be addressed. curate at very small vapor pressures and are affected 石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 34, No. 5, 1991 417 by the presence of small amounts of noncondensa- general. If other reducing parameters than ble gases or solute impurities; moreover, lengthy critical constants are used, the method can be periods of time are required for attaining applied; however, there are no examples in which equilibrium. it has been applied for the calculation of vapor- 2.1.3 Gravimetric Method liquid equilibria for polymer systems. However, The change in weight of the polymer film due to there are some examples in which solubilities of gas sorption is measured by using a quartz solutes in polymers were correlated with the spring12),13) or an electromicrobalance14) or a quartz critical constants of the solutes. They can be crystal15),16). The method is commonly used considered as one of the applications of the because the principle involved is simple, and corresponding state principle. Method (2) is accurate measurements can be expected; however, accepted widely; moreover, there are many studies. lengthy periods are required for attaining To apply method (3) for polymer systems, an equilibrium. equation of state applicable to the polymers should 2.1.4 Gas Chromatographic Method be developed. In order to obtain a new equation A polymer sample is coated on the support and of state, virial coefficients, pVT (vapor and liquid packed in a column. The infinite-dilution phase), and vapor pressure as fundamental data are solubility of the solute in polymer is determined necessary. However, only the specific volume at from its retention time using the column. molten state can be adopted for polymers, because Smidsrod and Guillet17) showed that the method they are not volatile at moderate temperatures and could be successfully used, and it has been used by decompose at high temperatures, making it many researchers18). Solubility data can be difficult to develop a good equation of state for obtained readily. However, it should be noted polymers. The three methods mentioned above that the data are affected by method of column will be further elaborated. preparation, flow rate of carrier gas, and sample 2.2.1 Corresponding State Principle size. In general, the gas chromatographic method Stern et al.24) showed that solubilities of several can be used for gum or molten polymers, because gases in amorphous polyethylene (i.e., Henry the diffusion coefficients of the solutes in glassy constants) So could be explained by polymers are very small. 2.1.5 Permeation Method19),20) logSo=-5.64+1.14(Tc/T)2 (1) This method is usually used for measuring solubilities of gases in membrane. The pressures where T is the absolute temperature, and Tc is the of gas at upstream and downstream faces of the critical temperature of the gas. Similar methods polymer film are held constant. The amount of were applied for polystyrene25), low-density gas that permeates through the membrane is polyethylene26-28), polyisobutylene26)-28), and determined as a function of time, and the solubility polydimethylsiloxane27),28) systems. The method can be obtained from the permeation curve. can be applied only to the systems for which 2.1.6 Measurements at High Pressures sufficient data are available. The solubility of a The quartz-spring balance method and the solute can be predicted approximately using the electromicrobalance method are not used at high above correlation equation based on the pressures. Solubilities at high pressures are experimental data of other solutes. usually measured by using a high pressure vessel or 2.2.2 Solution Model piezoelectric quartz crystal5),21). (1) Fundamental equation 2.2 Correlation and Prediction22),23) Vapor-liquid equilibria at low pressures can be There are three methods for predicting phase explained by Eq. (2). equilibria in general. (1) Application of corresponding state principle. pi=aipi° (2) The corresponding state principle for pure com- ponents is extended to multicomponent systems. where pi is the partial pressure of component i, ai is (2) Application of solution model. Nonideality the activity of component i in the liquid phase, and in the liquid phase is explainable in terms of pi° is the saturated vapor pressure of pure com- activity coefficient. ponent i. Therefore, the vapor-liquid equilibria (3) Application of equation of state. The fugacity can be calculated from activity. The activity is can be obtained thermodynamically from an calculated from chemical potential as follows. equation of state. Critical constants of polymers are not available, ai=(μi-μi°)/RT=Δμi/RT (3) so the application of method (1) is difficult in 石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 34, No. 5, 1991 418 where μi is the chemical potential of component i, values of χ adjusted to fit the experimental data. μi° is that of pure component i, and R is the gas (3) Free volume model constant. The noncombinatorial contribution to the The use of mole fraction is incovenient in a configurational partition function for a pure solute (1)-polymer(2) system because the molecular component was proposed by Flory et al.31),32) based weight of polymer can be very large compared to on the partition function of Prigogine33). The that of solute. The volume fraction or weight activity coefficient of solute can be explained with fraction is usually used as a concentration scale. the free volume theory as The activity coefficient based on the volume fraction γi is defined by lnγ1=lnγ1C+lnγ1FV+lnγ1H (9) γi=ai/φi (4) where lnγ1C is the athermal combinatorial term, lnγ1FV is the free volume term, and lnγ1H is the where φi is the volume fraction.
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