Phase Equilibrium in Polymer Manufacture - American Chemical Society

8 Phase Equilibrium in Polymer Manufacture

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on October 28, 2015 | http://pubs.acs.org Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch008

DAVID C. BONNER Shell Development Company, P. O . Box 1380, Houston, TX 77001

The manufacture of synthetic high polymers involves, in most instances, combined reaction k i n e t i c s , heat transfer, and phase equilibrium. Due to the shortcomings of phase equilibrium computational methods, it has only been possible in the l a s t decade for design engineers to apply rigorous phase equilibrium computations in the design of polymerization processes. In this paper, we discuss some of the computational methods which are now available for use in process design. It i s our hope that this sort of presentation may serve to draw together some of the phase equilibrium work that has been published in the last decade in various journals. In order to begin this presentation in a logical manner, we review in the next few paragraphs some of the general features of polymer solution phase equilibrium thermodynamics. Figure 1 shows perhaps the simplest l i q u i d / l i q u i d phase equilibrium situation which can occur in a solvent(1)/polymer(2) phase equilibrium. In Figure 1, we have assumed for simplicity that the polymer involved i s monodisperse. We will discuss l a t e r the consequences of polymer polydispersity. Conditions of phase equilibrium require that the chemical potential of polymer in each phase and that of solvent in each phase be equal: a _ y

l "

l

y

6

3 2 ~ 2

(1)

a

y

y

The computational problem of polymer phase equilibrium i s to provide an adequate representation of the chemical potentials of each component in solution as a function of temperature, pressure, and composition. A feature of polymer solutions which i s commonly observed in many polymer manufacturing operations i s i l l u s t r a t e d in Figure 2. At a given pressure, a two-phase region exists below a concavedownward locus of temperature-composition points. One of the two 0-8412-0506-x/79/47-104-181$05.00/0 ©

1979 A m e r i c a n C h e m i c a l Society

In Polymerization Reactors and Processes; Henderson, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


182

POLYMERIZATION REACTORS AND PROCESSES

Figure

1. Liquid-liquid equilibria in a polymer/solvent solution: ethylene binary coexistence curve (constant T and molecular

ethylene-polyweight)



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phases i s polymer r i c h , and the other i s solvent r i c h . As the temperature of a solution of constant composition i s raised, a one-phase region i s reached. F i n a l l y , as temperature is i n creased yet more, phase separation occurs again. The higher temperature two-phase region i s bounded by a concave-upward locus of composition-temperature points. The c r i t i c a l point (1) of the two-phase region encountered at reduced temperatures i s called an upper c r i t i c a l solution temperature (UCST), and that of the two-phase region found at elevated temperatures i s c a l l e d , perversely, a lower c r i t i c a l solution temperature (LCST). Figure 2 i s drawn assuming that the polymer in solution i s monodisperse. However, i f the polymer in solution i s polydisperse, generally s i m i l a r , but more vaguely defined, regions of phase separation occur. These are known as "cloud-point" curves. The term "cloud point" results from the visual observation of phase separation - a cloudiness in the mixture. While the shapes of the upper and lower c r i t i c a l l o c i are most usually as shown schematically in Figure 2, a variety of other behaviors has been observed in special cases (2). Another general type of behavior that occurs in polymer manufacture i s shown in Figure 3. In many polymer processing operations, i t i s necessary to remove one or more solvents from the concentrated polymer at moderately low pressures. In such an instance, the phase equilibrium computation can be carried out i f the chemical potential of the solvent in the polymer phase can be computed. Conditions of phase equilibrium require that the chemical potential of the solvent in the vapor phase be equal to that of the solvent in the l i q u i d (polymer) phase. Note that the polymer i s essentially i n v o l a t i l e and i s not present in the vapor phase. Using standard thermodynamics, i t can be shown (3.) that, at modest pressures, the equality of solvent chemical potential in both l i q u i d and vapor phases can be transformed to p = a ^ e x p [ B ^ p * - p^/fRT)] solvent partial pressure 1

where p^ a

i

(2)

a-,(T, w,, p) = solvent a c t i v i t y solvent saturation vapor pressure at solution temperature T = second v i r i a l coefficient of solvent at T

R = gas constant Since the total pressure (p = p,) of the d e v o l a t i l i z a t i o n process i s usually known, computation of weight fraction (w,) of solvent remaining in the polymer at the l i m i t of phase e q u i l i b -




Solvent (I) / Polymer (2) w, « 0

Pure Solvent Vapor (P=p,)

Note ! polymer is essentially involatile

Polymer + Trace Solvent

Question I Given T, P, what is the solvent composition in polymer phase ? Calculations: P| = a,p, exp s

where

EUpf-p.)

RT

a,= a^TjW,,P) = solvent activity p,= solvent vapor pressure at T s

B= solvent 2nd virial coefficient at T P, = y, P = solvent partial pressure Figure

3.

Polymer/solvent

vapor-liquid

equilibrium


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Hum requires formulation of a mathematical expression for computation of solvent a c t i v i t y in the polymer solution. The solvent a c t i v i t y i s a function of temperature, pressure, and composition. Polymer Solution Phase Equilibrium Computations.


Flory-Hugqins Model for Polymer Solutions. We have seen above in two instances, those of l i q u i d - l i q u i d phase separation and polymer d e v o l a t i l i z a t i o n that computation of the phase e q u i l i b r i a involved i s essentially a problem of mathematical formulation of the chemical potential (or a c t i v i t y ) of each component in the solution. The f i r s t q u a l i t a t i v e l y correct attempt to model the r e l e vant chemical potentials in a polymer solution was made independently by Huggins ( 4 , 5 ) and Flory ( 6 J . Their models, which are s i m i l a r except for nomenclature, are now usually called the Flory-Huggins model ( 2 ) . The Flory-Huggins a c t i v i t y expression for solvent in a solvent(l)/polymer(2) solution i s a

1

= exp(

yi

- u°/RT) = ^ e x p [ ( l - r ^ r ^

+

JL _L R

•

P

N

(17)

+

- p*/

- 2p * 12

V

V

= ^

• M

V V l s p

V

2 2s ^ P

There is a similar expression for polymer a c t i v i t y . However, i f the f l u i d being sorbed by the polymer i s a supercritical gas, i t is most useful to use chemical potential for phase equilibrium calculations rather than a c t i v i t y . For example, at equilibrium between the f l u i d phase (gas) and polymer phase, the chemical potential of the gas in the f l u i d phase is equal to that in the l i q u i d phase. An expression for the equality of chemical potentials is given by Cheng (12). To i l l u s t r a t e the use of the gas sorption model, we show in Figure 7 results of the supercritical ethylene sorption in lowdensity polyethylene (12,16). As seen in Figure 7, the theory is capable of f i t t i n g the ethylene sorption data. In this instance, the data at three temperatures can be f i t within experimental precision using interaction parameters (p^>) of 3235 atm, 3178 atm, or 3101 atm at 126°C, 140°C, and ^155 C, respectively. U




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Multicomponent Mixtures - Multiple Solvents. There are two types of multicomponent mixtures which occur in polymer phase equilibrium calculations: solutions with multiple solvents or polymers and solutions containing polydisperse polymers. We w i l l address these situations in turn. There are r e l a t i v e l y few phase equilibrium data relating to concentrated polymer solutions containing several solvents. Nevertheless, in polymer d e v o l a t i l i z a t i o n , such cases are often of prime interest. One of the complicating features of such cases i s that, in many instances, one of the solvents prefere n t i a l l y solvates the polymer molecules, p a r t i a l l y excluding the other solvents from interaction d i r e c t l y with the polymer molecules. This phenomenon i s known as "gathering". Unfortunately, r e l a t i v e l y l i t t l e work has been done on the solution thermodynamics of concentrated polymer solutions with "gathering". The d e f i n i t i v e work on the subject is the a r t i c l e of Yamamoto and White (17). The corresponding-states theory of Flory (1]_) does not account for gathering. We therefore r e s t r i c t our consideration here to multicomponent solutions where the solvents and polymer are nonpolar. For such solutions, gathering i s unlikely to occur. We have recently extended the Flory model to deal with nonpolar, two-solvent, one polymer soltuions (13). We considered sorption of benzene and cyclohexane by polybutadiene. As mentioned e a r l i e r , a binary interaction parameter is required for each pair of components in the solution. In this instance, we required interaction parameters to represent the interactions benzene/cyclohexane, benzene/polybutadiene, and cyclohexane/ polybutadiene. It is clear that much more work should be done on this important subject. Multicomponent Mixtures - Polymer Polydispersity. Essentially a l l industrial polymers are polydisperse. The effect of polymer polydispersity on phase equilibrium has been discussed previously by many authors, but the treatment of Tompa (2) i s one of the most complete. For our purposes, the situation can be summarized as follows. Polydispersity has v i r t u a l l y no effect on vapor-liquid e q u i l i b r i a (as long as the polymer i s non-volatile). However, polymer polydispersity does have an important influence on l i q u i d - l i q u i d e q u i l i b r i a . There i s a large body of experimental l i t e r a t u r e relating to polymer fractionation in l i q u i d - l i q u i d e q u i l i b r i a . In addition, numerous authors have analyzed polymer fractionation using Flory-Huggins theory. We have considered use of the corresponding states theory to model polymer fractionation for the ethylene/ polyethylene system at reactor conditions (18). Results of the




0

4000

8000

POLYETHYLENE

12,000

16,000

20,000

M O L E C U L A R WEIGHT , M

Figure 8. Fractionation of polyethylene owing to phase splitting in ethylene solution: molecular weight distributions in equilibrium phases at 260°C and 900 atm


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calculations are shown in Figure 8 . The algorithm used to generate Figure 8 i s generally applicable to liquid/polydisperse polymer calculations. The algorithm we used for solvent/polydisperse polymer e q u i l i b r i a c a l l s for only one solvent/polymer interaction parameter. The interaction parameter (p* ) used in the algorithm can be determined from essentially any type of ethylene/polyethylene phase equilibrium data. Cloud-point data have been used (18), while Cheng (16) and Harmony (19) have done so from gas sorption data.


2

Conclusion. We have reviewed here, in the brief space available, some recent developments in phase equilibrium representations for polymer solutions. With these recent developments, r e l i a b l e tools have become available for the polymer process designer to use in considering effects of phase equilibrium properly. The corresponding-states theory of polymer solution thermodynamics, developed p r i n c i p a l l y by Prigogine and Flory, has provided a r e l i a b l e predictive tool requiring only minimal information. We have seen here several examples of the use of the corresponding-states theory. We have also seen that the corresponding-states theory is a considerable improvement over the older Flory-Huggins theory. Many further developments can be expected in the use of corresponding-states polymer solution theory in engineering practice. However, the r e l i a b i l i t y and v e r s a t i l i t y of this method i s now well demonstrated for engineering use. Literature Cited 1. Prigogine, I., and Defay, R., "Chemical Thermodynamics", Longmans, Green, London, 1967. 2. Tompa, H., "Polymer Solutions", Butterworths, London, 1957. 3. Bonner, D. C., and Prausnitz, J. M., AIChE J.(1973), 19, 943. 4. Huggins, M. L., J . Chem. Phys.(1941), 9, 440. 5. Huggins, M. L., Ann. N. Y. Acad. Sci.(1942), 43, 9. 6. Flory, P. J., J . Chem. Phys.(1941), 9, 660. 7. Flory, P. J., "Principles of Polymer Chemistry", Cornell University Press, Ithaca, N.Y., 1953.



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8. Bonner, D. C., J. Macromol. S c i . - Revs. Macromol. Chem.(1975), C13, 263. 9. Koningsveld, R., and Staverman, A. J., J. Polym. Sci., Part A-2(1968), 6, 305.


10. Prigogine, I., Trappeniers, N., and Mathot, V., Disc. Faraday Soc.(1953), 15, 93. 11. Flory, P. J., J. Amer. Chem. Soc.(1965), 87, 1833. 12. Cheng, Y. L., and Bonner, D. C., J . Polym. S c i . - Phys. Ed. (1978), 16, 319. 13. Dincer, S . , and Bonner, D. C., Ind. Eng. Chem., Fundam.(1979), in press. 14. Bawn, C. E. H., and Wajid, M. A . , Trans. Farad. Soc.(1956), 52, 1658. 15. Chang, Y. H., and Bonner, D. C., J. Appl. Polym. S c i .(1975), 19, 2457. 16. Cheng, Y. L., and Bonner, D. C., J. Polym. S c i . - Phys. Ed. (1977), 15, 593(1977). 17. Yamamoto, M., White, J . L., and McLean, D. L., Polymer(1971), 12, 290. 18. Bonner, D. C., Maloney, D. P., and Prausnitz, J. M., Ind. Eng. Chem., Proc. Des. Dev.(1974), 13, 91. 19. Harmony, S. C., Bonner, D. C., and Heichelheim, H. R., AIChE J.(1977), 23, 758. RECEIVED F e b r u a r y 1,

1979.


Phase Equilibrium in Polymer Manufacture - American Chemical Society

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