Phase Equilibria for Polymer Systems

416 石油学会誌 Sekiyu Gakkaishi, 34, (5), 416-426 (1991)

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 components 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

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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. molecular interaction term. These are explained The definition of the weight-fraction Henry as follows. constant of solute H1 is lnγ1C=(1-1/m)φ2 (10) H1=limw1→0(f1/w1) (5) lnγ1FV=p1*M1v1*/RT1* where w1 is the weight fraction of solute. The fugacity of vapor phase f1 can be approximated by the partial pressure at low pressures. The ×{3ln(v11/3-1)/(v1/3-1)+1/T1(1/v1-1/v)} solubility of monomer or solute in polymer can be (11) calculated by Eq. (6).

w1=py1/H1 (6) lnγ1H=φ22M1v1*/RTv(p1*+p2*-2p12*) (12) where y1 is the mole fraction of solute in the vapor phase. The weight-fraction Henry constant is where M is the molecular weight, p*, v*, and T* are required to calculate the solubilities of gases and the characteristic pressure, the hard-core volume, vapors in polymers. The weight-fraction Henry and the characteristic temperature, respectively, constant is given by Eq. (7). and v=v/v*, T=T/T*. The activity of solute in polymer solutions can be predicted roughly by the H1=γ1∞(v1/v2)p1° (7) free volume theory. The parameter of mixture in p12* should be determined to fit the solubility data where v is the specific volume, γ1∞ is the infinite of solute. dilution activity coefficient of solute. Furthermore, according to the idea of Beret and (2) Flory-Huggins equation Prausnitz34), Cheng and Bonner35) modified the The Flory-Huggins equation29),30) was derived partition function of Flory and proposed an based on the assumptions that the Gibbs energy of equation of state which satisfied the limitation of mixing was given by the contribution of entropy of ideal gas at V→∞. mixing due to the differences in the molecular size (4) Group contribution method and enthalpy of mixing due to molecular Oishi and Prausnitz36) first applied a group interaction. The activity is given as follows. contribution method to polymer solutions. They proposed the following expression for the activity lna1=lnφ1+(1-1/m)φ2+χφ22 (8) of solute in polymer. where m is the ratio of the volumes of polymer and lna1=lna1C+lna1R+lna1FV (13) solute, and χ is the interaction parameter. The Flory-Huggins equation is very important for where lna1C and lna1R are calculated with understanding the nature of polymer solutions. UNIFAC37) which is a group contribution method, Parameter χ is theoretically independent of the and lna1FV is calculated with the free volume concentration of solute; however, it usually de- derived by Flory. pends on the concentration of solute when it is determined with the experimental data. The vapor-liquid equilibria can be correlated with the

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Table 1 Group Parameters for UNIFAC-FV Model44) -C1(v1/v-1)/(1-1/v11/3) (14) where

v1=v1/(15.17br1) (15)

v=(w1v1+w2v2)/(15.17b(w1r1+w2r2)) (16) where r is the UNIFAC volume parameter. The external degrees of freedom for solute C1 and parameter b for the modification of hard-core volume are introduced in the free volume term. The activity of solute in polymer can be predicted with C1=1.1 and b=1.28. Furthermore, the model has been applied to polymer solution systems directly or with modification38)-43). Iwai et al.44),45) reexamined the free volume term and proposed a new free volume expression as follows.

lna1FV=C1[lnvf,1/vf,M+v15.66/(v1-1)4exp(0.3v1)

×1/(1.66-0.3v1)

×{exp(0.3v1)/v11.66-exp(0.3vM)/vM1.66}] (17)

p=pressure, w=weight fraction in liquid phase. where Fig. 1 Solubilities of m-Xylene (1) in Polystyrene (2)44) vf=(v-1)

×exp{-18(v-1)2+9(v-1)+2/6(v-1)3} (18)

v1=v1/v1* (19)

vM=v1w1+v2w2/v1*w1+v2*w2 (20)

The group parameters for calculation of the free volume term are shown in Table 1. The hard- core volume of molecule vi* and the external degrees of freedom of solute C1 can be calculated with the following equations.

vi*=1/Mi∑kνk(i)Vk* (21)

H=Henry constant. C1=∑kνk(1)Ck (22) Fig. 2 Henry Constants of Hydrocarbons (1) in where vk(i) is the number of group k in molecule i, Polypropylene(2)44)

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Mi is the molecular weight of component i, Vk* is q(alkanes)=0.08164×106Vw+0.4766 the hard-core volume of group k, and Ck is the (26) external degrees of freedom of group k. If a component is not included in the group listed in Table 1, one can calculate the hard-core volume q(aromatics)=0.08156×106Vw+1.017 and the external degrees of freedom of solute from (27) the properties of the pure component. The solubilities of several solutes in polymers can be Henry constant can be well correlated with the well predicted with the combination of the free adjustable parameter k12 determined for binary volume term and UNIFAC46) as shown in Figs. 1 systems. An example of calculation is shown in and 2. The free volume given by Eq. (18) can be Fig. 3. adopted to predict the pVT behavior of poly- (2) Vapor-Liquid equilibria at high pressures mers47). Polymer can usually be considered as a Misovich et al.48) applied ASOG to correlate the nonvolatile component; however, the solubility of activities of solutes in polymers. polymer under high gas pressures (ethylene at Holten-Anderson et al.49) proposed a new group 1,000-2,000 atm) is considerable. An equation contribution model which was an extension of the of state, which can be applied to both the liquid work of Prigogine33), Patterson32), and Flory50). and vapor phases for solute and polymer mixture, 2.2.3 Equation of State is necessary for calculating the vapor-liquid The equation of state given by Flory can be equilibria at high pressures. applied to the liquid phase, but not to the gas Schotte51) modified the equation of state of phase, because it was proposed based on the lattice Bonner and Prausnitz56) and Harmony et al.57). theory to calculate the activity only in the liquid The following equation was proposed. phase. There are a few examples showing that equation pv/T=RT*/p*Mv*(1-1/v1/3) of state to be applicable to polymer systems. Schotte51), Ohzono et al.52), and Kubic53) have applied their equation of state. The methods of Ohzono et al. and Schotte are explained in the (28) following sections. (1) Henry constant Ohzono et al.52) correlated the weight-fraction Henry constants of hydrocarbon vapors in molten polymers with the Perturbed-Hard-Chain(P-H-C) theory54),55). According to the P-H-C theory, the Henry constant of solute is given by

H1=limx1→0RT/M1v2exp(μ1HS+μ1Att+μ1SV/kT)

(23)

where, μ1HS, μ1Att, and, μ1SV are the chemical potential of hard-chain part, attraction part, and second virial coefficient part, respectively, k is the Boltzmann constant, and x is the mole fraction. The pure component parameters in the chemical potentials are the hard-core volume V*, the external degrees of freedom C, and the surface area q. These parameters are correlated with the hard- core volume of Bondi Vw as follows.

V*=0.9034Vw+2.8679×10-6 (24) H=Henry constant.

C=0.01759×106Vw+0.7908 (25) Fig. 3 Henry Constants of Hydrocarbons(1) in Polypropylene(2)52)

石油学会誌 Sekiyu Gakkaishi, Vol. 34, No. 5, 1991 421 where pressure, volume, and temperature are explained by reduced properties.

p=p/p*, v=v/v*, T=T/T* (29)

Equation (28) is applicable to subcritical solutes, supercritical solutes, and liquid polymers. Vaporization of polymer should be considered at elevated pressures and temperatures. The lower molecular weight fractions will begin to vaporize first, and the mean molecular weight fraction in the vapor phase will increase with pressure. Low-density polyethylene is produced by a high p=pressure, Mn=number-average molecular weight of polyethylene. pressure method. Schotte divided low-density polyethylene into 33 fractions according to Fig. 5 Mean Molecular Weight of Polyethylene in molecular weight and calculated the vapor-liquid Liquid and Vapor51) equilibria of the ethylene-polyethylene systems based on the condition that the fugacity of each component in the vapor phase was equal to that in two-phase system containing water soluble the liquid phase. The results of calculation, polymers, which have recently arrested much which seem satisfactory, are shown in Fig. 4, and attention will be briefly discussed in the following the average molecular weights in both phases are sections. shown in Fig. 5. 3.1 Measurements 3.1.1 Type of Experimental Technique 3. Liquid-Liquid Equilibria Liquid-liquid equilibria (LLE), i. e., tie lines, of Features of liquid-liquid equilibria for polymer polymer systems can be determined by observing systems have been reviewed in detail58),59). The cloud points or by measuring concentrations of the cyclopentane-polystyrene system and the aqueous phases in equilibrium. For a binary system, solubility curves can be obtained by observing cloud points60),61). The LLE (tie line) at a given temperature is determined by interpolation. For multicomponent systems, however, the concentration of each phase must be analyzed to determine the LLE (tie lines), though solubility curves can be determined by observing cloud points. 3.1.2 Binary System Iwai et al.62) determined solubility curves of cyclopentane-polystyrene system by measuring the cloud points. A proper amount of polystyrene was weighed in a cylindrical cell. A desired amount of cyclopentane was poured into the cell in a dry bag filled with nitrogen. The cell was immersed in a bath whose temperature was changed slowly (less than 0.1℃/min). The cell was shaken continuously to maintain its temperature and uniformity of concentration. During this operation, a beam of light was passed through the cell, and both the intensity of the transmitted light and the temperature of the bath were monitored. The intensity of the transmitted light decreased sharply when the temperature passed through the cloud point which was determined from the breakpoint. The experi- p=pressure, w=weight fraction. mental data thus obtained are shown in Fig. 6. Fig. 4 Vapor-Liquid Equilibria of Ethylene(1)- 3.1.3 Multicomponent System Polyethylene(2) System51) Concentrations of both phases must be analyzed

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3.2 Correlation and Prediction

○ Exp. 3.2.1 Fundamental Equation

- Calc. The LLE can be calculated by solving the following equations.

ΔμiI=ΔμiII, (aiI=aiII) (30)

∑iwiI=∑iwiII=1,(∑iφiI=∑iφiII=1) (31)

where I and II denote phases I and II, respectively. 3.2.2 Binary System The solution models shown in 2. 2. 2 can in principle be applied to correlate the LLE. How- ever, the quantitative calculation of LLE is more difficult than that of vapor-liquid equilibria. Only qualitative explanation can be attempted by the Flory-Huggins equation, Eq. (8) below the upper critical solution temperature (UCST). To understand the nature of liquid-liquid equilibria above the lower critical solution temperature (LCST), the free volume model shown in 2.2.2 (3) tcp=cloud point temperature, w=weight fraction. was proposed. Fig. 6 Cloud Point Curves for Cyclopentane(1)-Poly- Iwai et al.62) correlated the solubility curves of styrene(2) Systems62) the cyclopentane-polystyrene system. The interaction parameter X12 contained in p12* in Eq. (12) was assumed to be a function of the volume fraction of polystyrene. ○---,● Exp.

- Flory-Huggins Eq. X12=aexp(bφ2) (32) -・- Osmotic virial Eq.

The chemical potentials can be derived as follows.

Δμ1=RT[lnφ1+(1-r1/r2)φ2]

Fig. 7 Liquid-Liquid Equilibria for Dextran T40(1)-PEG4000(2)-Water (3) System at 20℃63)

to obtain the LLE (tie lines). For example, Furuya et al.63) measured the LLE of an aqueous +V1*θ22/v(θ2-bφ1φ2)X12 (33) two-phase system containing dextran, polyethylene glycol, and water. The two phases were agitated for 6 hours to bring them into equi- Δμ2=RT[lnφ2+(1-r2/r1)φ1] librium, and the system was then settled for 24 hours. After the phase separation, each phase was withdrawn, and the polymer concentrations were measured by gel-permeation liquid chromato- graphy (GPC). In addition to measure the partition coefficients of enzymes in aqueous two- +(1/v2-1/v)] phase systems, concentrations of the enzymes were measured spectrophotometrically with a UV spectrophotometer. The experimental data are +V2*θ12/vS2/S1(θ1+bφ1φ2)X12 (34) shown in Fig. 7.

石油学会誌 Sekiyu Gakkaishi, Vol. 34, No. 5, 1991 423 where r is the number of segments per molecule, V* aqueous two-phase systems using both the is the molar hard-core volume, θ is the surface Flory-Huggins model and the osmotic virial fraction, and s is the unit-volume surface area per equation. The result of correlation of the osmotic molecular weight. It was found that parameters a virial equation is better than that of the and b in Eq. (32) seemed to be a function of Flory-Huggins model as shown in Fig. 7. temperature and molecular weight of polystyrene as follows to correlate the solubility curves. 4. Volume-phase Transition of Gel The recently observed volume-phase transition a=a1Ta2M2a3 (35) of polymeric gels is very interesting and is considered to be applicable to various fields of b=b1Tb2M2b3 (36) industry, etc. Saito58),59) reviewed in detail the volume-phase transition of hydrogels. A cor- The correlation results are good as shown in Fig. 6. relation method for the volume-phase transition is The quantitative representation for LLE above briefly discussed here. the lower critical solution temperature (LCST) is Tanaka et al.70) used the mean field theory for much more difficult. Shigematsu et al.65) have representing the phase transition of ionic gels. attempted to correlate the LLE above LCST for the The osmotic pressure of a gel is described by the cyclopentane-polystyrene system using the Flory-Huggins formula as follows. UNIFAC-FV model44),45)and fairly good results have been obtained. 3.2.3 Multicomponent System π=-RT/V[φ+ln(1-φ)+ΔF/2kTφ2] Aqueous two-phase system is one of the most interesting topics for study in the field of liquid-liquid equilibria containing polymers. +νkT[φ/2φo-(φ/φo)1/3]+fνkT(φ/φo) (40) The Flory-Huggins model29),30) and the UNIQUAC model have been used to calculate the where V is the molar volume of the solvent, φ is the liquid-liquid equilibria for the system containing volume fraction of the netwrork, ΔF is the free- dextran, polyethylene glycols, and water66),67). energy decrease associated with the formation of a However, the Flory-Huggins model is not suitable contact between polymer segments, φo is the for such systems that exhibit specific interactions volume fraction of the network at random walk of such as hydrogen bonding68), and the UNIQUAC configurations, ν is the number of constituent equation requires many adjustable parameters. chains per unit volume at φ=φo, and f is the A more suitable description of dilute aqueous two- number of dissociated counterions per effective phase systems has been provided by Edmond and chain. The osmotic pressure difference between Ogston69). They have developed a theory based inside and outside of a gel must be zero in order that on the osmotic virial equation truncated at the the gel to be in equilibrium with the surrounding second virial coefficient term. King et al.68)have solvent. If selective absorption of one of the extended the Edmond and Ogston's equation to solvent components to polymer network is aqueous two-phase system containing proteins neglected, the excess free energy ΔF can be (four components system). According to King et described by Eq. (41) al., the chemical potentials of dextran(1)-polyethylene(2)-water(3) systems are written as a function ΔF=x1ΔF1+x2ΔF2-x1x2ΔF12 (41) of molality by the following equations. where x denotes the mole fraction of each sur- Δμ1=RT(lnm1+a11M1+a12m2) (37) rounding solvent, ΔF1, ΔF2, and ΔF12 are the parameters defining the free energy of association Δμ2=RT(lnm2+a22m2+a12m1) (38) between solvent 1 and polymer segment, solvent 2 and polymer segment, and solvent 1 and solvent 2, Δμ3=RTV3ρ3(m1+m2+(a11/2)(m1)2 respectively. Ishidao et al.71)applied the model to alcohol(1)-water(2)-vinyl alcohol-sodium acry- +(a22/2)(m2)2+a12m1m2) (39) late copolymer (Sumikagel S-50) (3) systems. The volume change of the gel can be correlated as where mi is the molality of component i, aij is the shown in Fig. 8 by using the parameters listed in interaction coefficient between components i and j, Table 2. On the other hand, the reentrant type V3 is the molar volume of water, and ρ3 is the volume-phase transition, observed in the density of water. Furuya et al.63),64) correlated the methanol-water-N-isopropylacrylamide gel

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Table 2 Parameters for Sumikagel S-5071)

* Optimum parameters.

selective absorption of one of the solvent components to polymer network can be neglected. However, the alcohol concentration inside the gel in shrunken state is much smaller than that outside the gel as shown in Fig. 972). A successful model considering the difference between concentrations outside and inside a gel should be proposed in the future work.

5. Conclusion ○ Methanol

○ Ethanol Some recent topics on phase equilibria for ● Propanol polymer systems have been described. Solubilities of volatile hydrocarbons in polymers at low pressures have been studied sufficiently to provide a fundamental knowledge to design

x°=mole fraction in fluid phase, V=volume of gel, equipment for monomer or solvent recovery. On -; results calculated using parameters listed in Table 2, the other hand, interests in vapor-liquid equilibria ----; results calculated using optimum parameters in at high pressures have been augmented as Table 2. fundamental data for supercritical gas extraction and membrane separation of gases. In general, Fig. 8 Volumes of Sumikagel S-50 in Mixed Solvents of Alcohol(1) and Water(2)71 membrane materials are fine polymers, so the solubilities of gases in such polymers should be of increasing importance. It is difficult to quantitatively correlate the

● Methanol liquid-liquid equilibria (LLE) for polymer

○ Ethanol systems, especially, for the LLE above LCST.

●Propanol The LLE of aqueous two-phase systems containing strong hydrogen bonding components and biological components is difficult to be correlated by using the Flory-Huggins type equation. A better correlation seems to be possible by using the osmotic virial equation. A quantitative model to represent the volume- phase transition behaviors of polymeric gels should be developed especially for reentrant type polymer systems. In general, it is difficult to explain the phase behavior of polymer systems, especially the LLE x1°=mole fraction of alcohol in fluid phase, x1i=mole and volume-phase transition of polymeric gels. fraction of alcohol in gel. Thus, there still remains the nature of polymer

Fig. 9 Equilibrium Distribution of Alcohol between systems to be further studied. Sumikagel S-50 and Fluid Phase72) References

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要旨

ポリマー系の相平衡

岩井芳夫, 荒井康彦

九州大学工学部化学機械工学科, 812 福岡市東区箱崎 6-10-1

ポリマー系の相平衡すなわち気液平衡, 液液平衡, およびポのポリエチレンの平均分子量も計算可能になっている (Fig. リマーゲルの体積相転移についてレビューした。 5)。まず, ポリマー系の気液平衡すなわちポリマーに対する気体液液平衡の2成分系の測定例として, 岩井らによるシクロペや蒸気の溶解度の測定法として, 圧力法, 重量法, ガスクロマンタン-ポリスチレン系の曇点法による測定を解説した (Fig. トグラフ法, および透過法について簡単に述べた。さらに, 気 6)。さらに, 古屋らによって行われたデキストラン-ポリエチ液平衡の推算および相関法として対応状態原理, 溶液モデル, レングリコール-水の水性2相系の測定結果を多成分系の例とおよび状態方程式について解説した。対応状態原理に基づく方して示した (Fig. 7)。液液平衡の相関は気液平衡の相関に比べ法は, 溶質の臨界値を用いて相関するものであり, ポリマーがて困難である。岩井らは, 溶液モデルのパラメーターの一つがポリスチレン, ポリエチレン, ポリイソブチレン, ポリジメチポリマーの分子量および温度の関数であるとすることで, シクルシロキサンなど, 溶解度のデータが多い系に適用可能であロペンタン-ポリスチレン系のUCST以下の温度での液液平衡る。溶液モデルによる方法は, Flory-Huggins 式が基本となっが良好に相関可能であることを示した (Fig. 6)。また, 古屋らているが, この式では気液平衡を良好に相関することは困難なは, ビリアル展開式と Flory-Huggins 式の両者で水性2相系ので自由容積寄与項を付加したモデルが提案されている。さらの液液平衡の相関を行い, ビリアル展開式の方が良好な相関結に, Oishi と Prausnitz によって, UNIFAC に自由容積寄与項果を与えることを示した (Fig. 7)。を付加したUNIFAC-FVモデルが提案された。Iwai と Arai 最後に, ポリマーゲルの体積相転移の例として, スミカゲルは自由容積寄与項として新しい式を提案し, UNIFAC-FVモ S-50 (ビニルアルコール-アクリル酸ナトリウム共重合体) のデルで気液平衡が良好に推算可能であることを示した (Table アルコール水溶液中における体積測定の結果および Tanaka の 1および Figs. 1, 2)。気液平衡を状態方程式を用いて相関す式による相関結果を示した (Fig. 8およびTable 2)。Tanaka る試みは少ないが, Ohzono らは Perturbed-Hard-Chain 理論の式では, ポリマーゲルに対する溶媒の選択的吸収は無いとしにより, 溶質のヘンリー定数が良好に相関できることを示したているが, スミカゲルS-50は水を選択的に吸収する (Fig. 9) (Fig. 3)。さらに, Schotte は高圧におけるエチレン-ポリエチため, このことを考慮にいれたモデルの開発が今後の重要な課レン系の気液平衡を状態方程式により相関した (Fig. 4)。ポリ題となる。エチレンを33の成分に分割することにより, 液相および気相

Keywords Polymer, Polymer solution, Vapor liguid equilibrium, Liquid liquid equilibrium, Polymeric gel, Volume phase transition

石油学会誌 Sekiyu Gakkaishi, Vol. 34, No. 5, 1991