goes from the methyl to the octyl group is certainly due to steric factors (examples 1 to 8 of Table I). In contrast to y-picoline complexes, the substituted benzylamine complexes are not able to form clathrates by simple contact with the compound to be clathrated. Clathration takes place only when the complex is allowed to crystallize in the presence of the compound to be clathrated. Preliminary x-ray studies have shown that the complexes and the clathrates have different crystalline forms. The process works as though there were an interaction between the molecules of complex and of aromatic compounds inducing the formation of a special crystalline form which permits clathration. Sometimes, this crystalline form is unstable and collapses when the clathrated compounds are removed. Probably, some conflict exists in many cases between steric and electronic factors, making selectivities hard to foresee. Further experiments are necessary to elucidate the clathration mechanism and then to predict a priori which complex is able to perform a specific separation. Nevertheless, numerous practical applications may be deduced from the examples and clathration with the new complexes has already permitted recovery of pure aromatic compounds from petroleum cuts and from synthesis effluents ( 3 ) . Conclusions
Almost any desired aromatic isomer may be selectively trapped by the proper Werner complex. One clathration stage is often as efficient as a distillation in a column with hundreds of theoretical plates. This clathration process can be successfully applied not only to xylenes but also to mono- or polysubstituted benzenes and naphthalenes. Clathration can be carried out as a cyclic process without complex consumption.
Hydrocarbon capacities of the new clathrates are higher than with conventional solid adsorption processes. Acknowledgment
The authors express their thanks to the directors of Petrofina and Labofina for permission to publish this work and to numerous Labofina personnel who actively participated in this research. literature Cited
(1) Buu-Hoi’, N. P., Jaquignon, P., Bull. ioc. chzm. France 4, 488 (1957). (2) Christensen, E. R., Francis, S. A . (to Texaco, Inc.), U. S. Patent 2,914,581 (Nov. 24, 1959). (3) de Radzitzky, P., Hanotier, J., Brandly, J., Hanotier-Bridoux, M., Rec. inst.franG.pttrole 16, 886 (1961). (4) Ferstanding, L. L., Toland, W. G., Heaton, C. D., J . Am. Chem. Soc. 83, 1151 (1961). (5) Foreman, R. W. [to Standard Oil Co. (Ohio)], U. S. Patent 2,941,018 (June 14, 1960). (6) Fritsche, J., J . prakt. Chem. 73, 282 (1858). (7) Heaton, C. D., Toland, W. G. (to California Research Co.), U. S. Patent 2,900,428 (Aug. 18, 1959). (8) Labofina, S. A , , Belg. Patents 591,872 (Dec. 14, 1960), 595,746 (April 5, 1961). (9) Pfeiffer, P., Ber. 5 5 , 413 (1922) ; “Organische Molekulverbindungen,” 2nd ed., Ferdinand Enke, Stuttgart, 1927. (10) Schaeffer, W. D. (to Union Oil Co. of Calif.), U. S. Patent 2,789,891 (July 9, 1957). (11) Schaeffer, W. D., Dorsey, LV. S., Skinner, D. A , , Christian, C. G., J . A m . Chem. Sod. 79, 5870 (1957). (12) Schaeffer, LV. D., Wordie, J. D. (to Union Oil Co. of Calif.), U. S. Patents 2,798,103 (July 2, 1957), 2,951,104 (Aug. 30, 1960). (13) Williams, F. V., J . A m . Chcm. Sod. 79, 5876 (1957). RECEIVED for review April 24, 1961 ACCEPTEDAugust 21, 1961 Division of Petroleum Chemistry, 139th Meeting, ACS, St. Louis, Mo., March 1961. Work partly supported by Belgian Institut pour 1’Encouragementde la Recherche Scientifique dans 1’Industrie et 1’Agriculture (I.R.S.I.A.).
CONDITIONED POLYETHYLENE A S A PERMSELECTIVE M E M B R A N E Separation of Isomeric Xylenes ALAN S . M I C H A E L S , R A Y M O N D F . BADDOUR, H A R R I S J . B I X L E R , A N D C. Y . C H O O Department of Chemical Engineering, Massachusetts Institute of Technology. Cambridge 39, Mass.
By swelling polyethylene film i n p-xylene and annealing the film at elevated temperature in the swollen state, it has been possible t o increase the xylene liquid permeation rate
-
throuah the film and the permselectivity of the film t o p- with respect to m- and o-xylenes.
Permeability and permselec-
tivity changes are highly dependent on degree o f swelling, treatment temperature, compound.
polymer crystallinity, and treating
Alteration o f crystalline texture of the polymer
is believed responsible for the observed effects.
This
technique of tailoring a polymeric membrane to render it more effective as a separation barrier appears to open new prospects for utilization o f membrane permeation as a practical mixture-separation method. 14
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
HE ABILITY O F POLYMERIC MEMBRANES to show selective to various gases and vapors has been well Tpermeability documented in the literature, and the possibility of utipractical separations lizing this phenomenon to carry has been more than casually suggested (3, 6, 7 1 , 75). More recently, Binning (3) reported that, by evaporation of liquid mixtures through plastic films, efficient separation of azeotropes and hydrocarbon isomers has been effected and that a staged membrane separation technique appears economically competitive with conventional mixture resolution methods. Differences in rates of transmission of various penetrants through a specific polymeric membrane have usually been ascribed either to differences in solubility of the penetrants in the polymer or differences in diffusivity arising from differences in size or configuration of the penetrant molecule. Evidence that the morphology of the amorphous polymer
matrix plays a part in the transmission process is scanty, although studies of gas permeation through cross-linked elastomers implicate this as a variable. Studies by Dickey (tS)? and more recently by McKee ( g ) , have demonstrated that polymeric networks formed in the presence of a foreign (nonpolymerizing) compound, when suitably extracted to remove the entrapped solute, exhibit sorptive selectivity- for that compound relative to others of similar molecular structure. These results have been interpreted to mean that “holes” or “pockets” are formed by the foreign solute molecules in this matrix which can accommodate that solute more easily than other, even quite similar molecular species. Application of this principle of tailoring a polymeric network to membrane systems, in a n effort to develop transmissive permselectivity to a compound of choice, has evidently not been explored and thus seemed a desirable subject for investigation. Polyethylene appeared to be a n attractive material for this study for several reasons: The polymer is, in effect, a network structure, wherein the crystalline phase serves to cross link and immobilize chains in the amorphous phase. Since the crystallite cross links can be reversibly destroyed and reformed by suitably elevating or lowering the temperature, alteration 01 the matrix morphology in the presence of foreign solutes can be accomplished simply by thermal treatment. Furthermore, the molecular and crystalline structure of polyethylene is reasonably well defined and amenable to examination by readily available analytical tools. Much is now known about the mechanism of transport of both fixed gases (7, 9-77) and condensable vapors 172) through polyethylene, in terms of which new information can be interpreted. Finally, polyethylene is commercially available in the form of thin films at a cost which would make it economically attractive for use in a practical separation process. Bent (2) has reported that ordinary polyethylene is somewhat more permeable to p-xylene than to the other xylene isomers. Inasmuch as the molecular structural differences between the three xylenes are quite small and separation of xylene mixtures represents a practical problem of considerable magnitude, a study of the transmission of these isomers through normal and structurally modified polyethylene films appeared to be both a timely and a severe test of the “tailoring” principle. The objectives of this investigation, therefore, were as follows: to measure the rates of transmission of xylene isomers through conventional polyethylene films under controlled conditions; to condition polyethylene films by heating the polymer in the presence of selected isomers, followed by cooling; and, by measuring the isomer transmission characteristics of the conditioned films, to establish whether the conditioning process had any significant effect on either film permeability or permselectivity to the isomer:;.
Theoretical
Condensable Vapor Transport through Polymers. For fixed gas permeation through polymer films, it is usually assumed [and in most instances, experimentally confirmed (7)] that the permeability coefficient, p, defined by J = P- -*P
I
can be related to a diffusional process occurring within the film substance by the expression:
p
=
kD
Since k and D are essentially independent of pressure (as low to moderate pressures)? the permeability coefficient it similarly pressure-independent . For microcrystalline polymers such as polyethylene, Michaels and Parker (72) have proposed that Equation 2 be modified to:
The quantities cy and 7 are uniquely determined by the crystallinity and crystalline texture of the polymer; k* and D* are uniquely determined by the properties of the penetrant molecules; and p, which arises from restrictions imposed by crystallites on mobility of chains in the amorphous phase, is a function both of the polymer morphology and the diffusing molecule size and shape. For highly crystalline polyethylenes, Michaels and Bixler (70) have presented data suggesting that p increases rapidly with the diameter of the penetrant molecule. For condensable and, in particular, for solvating vapor transport through amorphous polymers, the solubility of the penetrant is not linear with pressure, and the diffusivity of the penetrant is concentration-dependent. Consequently, the permeability coefficient is also pressure dependent. Under steady flow conditions, however, p as defined by Equation 1 can be written :
(4)
If the exit boundary condition is specified by p a = 0, Equation
4 can be simplified to: PO
(5) Since kl can be calculated from static sorption measurements and p measured directly from flow measurements, can be determined indirectly. Independent examination of k1 and D for a particular penetrant can thus throw some light on the solution and diffusion contributions to the permeation process. In crystalline polymers such as polyethylene, the problem of interpreting permeation data is further complicated by the fact that solvating vapors swell the polymer and therefore are likely to alter the crystallite arrangement. The most obvious consequence of swelling is a reduction in the volume fraction of crystalline phase, with consequent reduction in both 7 and p in Equation 3. T h e concentration average diffusivity, 0, is thus a rather complex quantity, influenced by polymer and permeant properties not many of which are amenable to direct experimental measurement. Equations 3 and 5 show that measurement of the permeability coefficient p, the equilibrium sorption of permeant by polymer a t the permeant pressure upstream of the film, 61, and the volume fraction of amorphous phase in the unswollen polymer, cy, should provide the basic information needed to undertake a n analysis of the vapor transmission process. If we define the permselectivity of the membrane for component A with respect to component B as the ratio of the flux of A relative to that of B through the film under equal partial pressure driving forces (for the conditionp, = 0). then:
(2) VOL.
1
NO. 1
JANUARY
1962
15
Equation 6 shows that permselectivity may arise from either solubility differences or diffusivity differences between components. This further emphasizes the need for sorption as well as permeation measurements to clarify the origins of permselectivity of polymer films. For fixed gas permeation of amorphous polymers, the variations of permeability and solubility with temperature provide further insight into the transport mechanism, since such variations permit estimates of the heat of solution and activation energy for diffusion of the permeant. This approach has also been fruitful for analysis of fixed gas permeation in linear polyethylene near room temperature (9-7 7). For solvating vapors permeating either amorphous or crystalline polymers, however, this simple analysis is not particularly informative. because of the dependence of both diffusivity and crystallinity upon the concentration of the permeant. Thus. while there is no objection to plotting variations in p. D.or k l with temperature in the conventional Arrhenius form, it may be difficult to attach physical significance to the slopes of such lines with terms such as activation energies, heats of solution, or the like. Vapor-Permeation us. Pervaporation through Membranes. A condensible permeant may be transmitted through a membrane by exposing one face of the membrane to a higher pressure of the component in the gaseous state than is maintained on the opposite face; such a process is termed vapor transmission and is analogous to fixed-gas permeation. O n the other hand, the membrane may be contacted on one face with permeant in the liquid state and the permeant transmitted through the membrane by maintaining the downstream face in contact with a gas phase below saturation in permeant vapor. Such a process is herein referred to as "pervaporation." Theoretically, it would be expected that the rate of transmission of a component through a polymer film when the upstream face of the film is in contact with liquid should be identical with that measured with saturated vapor upstream, other things being equal. This is. however, not the case: The pervaporative transport rate is found usually to be higher (and often far higher) than the vapor permeation rate. The reasons for this anomaly remain obscure. Measurements made in the course of this investigation indicated that the apparent equilibrium sorption of xylene by polyethylene from the liquid phase was much higher than sorption from the saturated vapor at the same temperature; yet, differences in transmission rates for vapor permeation and pervaporation were considerably greater than the observed solubility differences. No effort is made to reconcile these differences here. although the subject merits further investigation. Table I compares vapor permeation and pervaporation permeability coefficients for the three xylenes through a lowdensity polyethylene film a t room temperature. S o t only
Table 1. Vapor Transmission and Pervaporative Perrneabilities of low-Density Polyethylene at 30' C.
P , Gram/(Hr.) (Sq. Cm.) Pervaporation 13.4 15.9 19.7 a upstream vapor phase at pressure corresponding to saturation at 25' C.
16
Permeant
Vapor transmissiona
o-Xylene m-Xylene p-Xylene
1.36 1.39 1.58
I&EC PROCESS DESIGN A N D DEVELOPMENT
are the permeabilities manyfold higher for pervaporation but the permselectivity of the film with respect to any pair of isomers is similarly higher for pervaporation. In view of these differences. pervaporative transport appeared to merit primary attention, since the motive for this study was to develop membranes of practical utility in separation processes. \Vir11 saturated liquid on one side of a membrane and subsaturated vapor on the other, there is a question regarding the proper driving force for the transmission process. For reasons of convenience, and since it appeared justifiable on thermodynamic grounds, it \vas decided to use the vapor pressure of the liquid a t the permeation temperature as the upstream boundary condition, thereby defining the permeability coefficient by the relation : (9)
For most of the measurements made in this study, p?was maintained effectively at zero. Under these conditions, Equation 9 reduces to:
which. combined with Equation 5, yields:
Independent measurement of c L and J thus permits a semiquantitative interpretation of the solute transport mechanism. Experimental
LMaterials. Two commercially available polyethylenes, obtained as air-blown film. were examined: Bakelite polyethylene (Union Carbide Corp.) ; density 0.918 gram per cc. a t 25" C.; nominal thickness, 1.0 mil. Grex olefin polymer (W. R. Grace and Co.); density 0.957 gram per cc. a t 25' C. ; nominal thickness, 2.0 mils. Reagent grade 0-, rn-, and p-xylene (Eastman Kodak Co.) \rere used; no effort was made to purify these compounds further. The infrared absorption spectrum of each \vas determined with a Perkin-Elmer Infracord spectrophotometer and the specific absorption at the dominant xvave length calculated. These values were used subsequently for determination of the composition of isomer mixtures. Xylene Solubility Measurements. Film samples weighing benveen 0.25 and 0.5 gram were completely immersed in liquid xylene in ground glass-stoppered vials, the vials sealed and transferred to a thermostatted water bath, and the samples allowed to equilibrate with the liquid for a period of at least three days. After equilibration, the films were removed from the liquid, quickly blotted free of adhering solvent, transferred to tared, glass-stoppered vials, and weighed. The film samples were then allowed to dry in air a t ambient conditions and reweighed to detect any weight loss because of extraction of polymer by the solvent. Despite the likelihood of inaccuracies arising from solvent loss during transfer of the films from the equilibrating liquid to the weighing bottles. solubility measurements were found to be reproducible to . t l O % . Measurement of solvent uptake as a function of equilibration time at room temperature indicated that equilibrium absorption by 1- to 2-mil films is attained in less than 24 hours. Transmission Rate Measurements. Determination of the rate of transport of the xylenes through polymer films was
VACUUN PUUP
I
RI
Figure 1. Schematic diagram of apparatus for pervaporation studies
carried out in the apparatus diagrammed in Figure 1. T h e permeation cell consisted of a stainless steel cylinder ( R ) about 8 cm. in diameter, fitted with a flanged base (C) which served as the film holder. A disk of film, supported on its lower surface by a smaller disk of 200-mesh stainless steel screen, was clamped between these two flanges. T h e cylindrical chamber was filled with liquid and the chamber then closed with a tight fitting cap to prevent evaporation. Contents of the chamber were constantly stirred during a run to eliminate temperature and/or concentration gradients. The entire assembly was submerged in a thermostatted water bath ( R , )maintained within 0.1 O C. of the preset temperature. The outlet tube from the cell was connected (via glass tubing) to the two glass traps in series ( T I , T ? )and thence to a mechanical vacuum pump capable of maintaining a pressure of less than 0.1 mm. of Hg. After mounting a film in the cell, the downstream section of the system was evacuated and trap T1 chilled with liquid air. The cell chamber was then filled with liquid xylene and pervaporation through the film alloived to proceed for about 6 hours to assure attainment of steady-state flow conditions. T r a p T 2was then chilled with liquid air and xylene transport allowed to proceed for a measured period of time. At the end of this period, trap T z was isolated from the system. allowed to warm to room temperature, and the weight of xylene collected in the trap determined gravimetrically. \\:hen mixtures of xylene isomers were used as the permeants, the trap contents were also subjected to infrared spectrophotometric analysis with a Perkin-Elmer Infracord spectrophotometer. Reproducibility of xylene transmission rates determined by this technique was established to be about 7%. Film thicknesses were measured \vith a supermicrometer to 1.0.002 mm., an average of about .30 random measurements being used to estimate a suitable me,m value. Film Conditioning. Five-inch disks of film were placed in an excess of liquid xylene isomer in a borosilicate glass test tube, and the tube and its contents were then immersed in a constant temperature water bath for periods of from 12 to 24 hours. This equilibration step was conducted a t temperatures between SO" and 60" C . for low density polyethylene films and between 90" and 100' C. for the high density polymer. In most instances, the tubes containing film and liquid were then transferred to a water bath maintained a t 25' C. and allowed to cool without disturbance to this temperature. After cooling, the films were removed from the xylene, quickly wiped free of adhering liquid, and weighed in sealed containers; they were then allolved to dry completely in air under ambient conditions. In some cases, tubes were transferred instead to an
ice bath or a dry ice-acetone bath, the contents allowed to cool to bath temperature, and the films vacuum-dried under these conditions. T o limit the quantity of xylene absorbed by the po1)mer during conditioning, the follolving procedure \vas employed with a number of linear polyethylene films: .4 sample of film was allowed to equilibrate with liquid n l e n e a t either 30", SOo.or 70' C. Following equilibration. the film \cas removed from the xylene, quickly wiped free of adhering liquid. and transferred to a clean glass vial which \vas then sealed. The vial and its contents were then placed in a water bath a t 100" C.. allowed to equilibrate for 24 hours, and then cooled to room temperature. The vial was opened and the film alloLved to dry a t room temperature. Results and Discussion
Solubility of Xylenes in Polyethylene. Table I1 shows the solubilities of the three xylenes in both high- and low-density polyethylene in the temperature range 25 to 10.5 C. Figure 2 presents the temperature variation of solubility for o- and p-xylene in low-density polyethylene and for p-xylene in highdensity polyethylene. The solubility of a given isomer was over twice as great in the low-density polymer as in the high-density polymer; in a given polymer, the solubilities of the isomers increased in the order p < m < 0; and the rate of increase of solubility Lcith temperature of p-xylene in low-density polyethylene was significantly higher than that in the high-densitv polymer. Equation 3 shows, by analogy with fixed-gas solution in polyethylene, that xylene would be expected to dissolve only in the amorphous phase of the polymer and that the observed solubility differences are due solely to differences in crystallinity of the two polymers. From the measured polymer densities, and assuming the specific volumes of the crystalline and amorphous phases in polyethylene a t 25" C . to be 1.003 and 1.171 cc. per gram, respectively, the volume fractions of amorphous phase in the low- and high-density polymers studied here were calculated to be CY = 0 . 3 and 0.28. respectively. Using the data of Table 11, the solubilities of the xylene isomers, expressed as
Table II. Solubility of liquid Xylene in Polyethylene
Solubility, Grams &lene/ 100 Grams Dry Polymer
o-Xylene m-Xylene )-Xylene $-Xylene p-Xylene p-Sylene p-Xylene p-Sylene o-Xylene o-Xylene o-Xylene
Temp., C. LowDensity Polyethylene 25 16.9 25 13.6 25 11.8 35 17.3 45 22.5 50 28.2 55 36.0 65 Polymer dissolves 35 21 . o 45 29.3 50 33.5
o-Xylene m-Xylene p-Xylene p-Xylene $-Xylene $-Xylene p-Xylene p-Sylene
High-Density Polyethylene 25 6.5 25 5.8 25 5.1 30 6.3 50 9.8 70 14.3 100 25 . O 105 Polymer dissolves
Isomer
VOL.
1
NO. 1
JANUARY
1962
17
30
20
5
.
l-
Figure 2. films
I
I
I
I
1
Solubility of xylene in unconditioned
grams per 100 grams of amorphous phase, have been calculated for each polymer. Results appear in Table 111. Per unit weight of amorphous phase, the solubilities are higher for the low-density polymer, the differences decreasing in the same order as the solubilities. A simple linear relation between solubility and crystallinity is evidently not obeyed by solvating penetrants; solvation of the amorphous phase is evidently restricted by the presence of the crystalline phase. Differences in solubilities of the three xvlene isomers are not large but consistently suggest that solubility increases in the order p < m < o. Since this order is also that of decreasing vapor pressure, and evaporative losses from the film samples during transfer to weighing bottles could not be estimated with accuracy, no theoretical significance is attached to these solubility differences; suffice it to say that these differences are small and are probably even smaller than the reported solubility values indicate From Figure 2, the apparent heats of solution of p-xylene in low- and high-density polyethylene are estimated to be approximately +7.1 and $4.1 kcal. per gram mole. respectively. For the process of dissolution of an aromatic in a n aliphatic hydrocarbon, true heats of solution of this magnitude are clearly unreasonable; further, a difference of 3 kcal. in the molar heats of solution in the two polymers seems equally unlikely. One must. therefore, seek another explanation for the marked temperature dependence of solubility in these systems. A partial explanation is to be found in the observation that the low-density polymer swells without limit (Le., dissolves) in p-xylene a t 65' C. while with the high-density polymer. dissolution takes place a t 105' C. These temperatures evidently represent the first-order transition temperatures for the two polymers in liquid xylene and, thus, the temperatures a t which the crystalline phase vanishes. (These temperatures are, respectively, about 45' and 30" C. below the normal first-order transition temperatures for the unsolvated polymers.) I t therefore appears likely that the observed solubility increases with temperature are to some degree attributable to a loss in crystallinity with increasing temperature and that the rate of decrease of crystallinity with temperature is considerably greater for the low-density polymer. Dilatometric studies on low- and high-density (unsolvated) polyethylenes (5, 74) 18
l & E C PROCESS DESIGN A N D DEVELOPMENT
have established that, indeed, crystalline melt-out begins at temperatures well below the first-order transition temperature and becomes appreciable at much lower temperatures for low-density than for high-density polymer. I t is, nevertheless, clear that mere increase in amorphous phase content with increasing temperature is hardly adequate to explain the observed solubility increases. For example, since the amorphous content of the low-density polymer is 55 volume % a t room temperature, the maximum solubility increase because of loss of crystallinity alone would be less than twofold, whereas the observed increase between 25' and only 50' C. is more nearly threefold. However, polyethylene may be regarded as a quasinetwork polymer, with the crystallites functioning as the chain cross links. In all likelihood, polyethylene, as is true of virtually all other amorphous hydrocarbon thermoplasts, would be infinitely miscible with xylene at all temperatures if the crystalline phase were absent. In other words, the extent of solvation of the amorphous phase of polyethylene can be expected to be limited by the degree of crystallinity; thus, a reduction in crystallinity by elevation of temperature will not only increase the amount of amorphous phase available for solvation, but will also allow additional solvation of the amorphous phase already present. The observed solubilitytemperature dependence may therefore be analogized to the variation in the equilibrium solvation of an elastomer by a good solvent, as cross-link density is varied. Furthermore, this argument serves to explain the trends observed in Table 111, wherein the xylene solubilities in lowdensity polyethylene are substantially higher than would be predicted from the measured solubilities in high density polymer under similar conditions. As shown below, the degree of solvation of polyethylene by the xylenes is also highly sensitive to the thermal history of the polymer, a phenomenon which further supports the concept that both the degree of crystallinity and crystallite morphology are of prime importance in determining absorption of the penetrant. Permeability and Diffusivity of Xylenes in Polyethylene. The permeability coefficients for the pervaporation of isomeric xylenes through low- and high-density polyethylenes as a function of increasing temperature are presented in Figure 3. (These coefficients have been calculated on the basis of the thickness of the dry polymer film.) The permeability to any one isomer of the low density polymer was nearly tenfold greater than that of the high density polymer; both polymers showed significant permselectivity in the order p > m > o, the high density polymer having the greater permselectivity a t low temperatures ; permeabilities increased and permselectivities decreased rapidly with increasing temperature, effect of temperature being greater for the low density polymer. Using Equation 10 and the data of Figure 2 , values of the concentration average diffusivity, 0, were calculated for p. xylene in both polymers, and for o-xylene in the low-density
Table 111.
Xylene Solubilities in Polyethylenes at 25" C. Based on amorphous phase content
Isomer
o-Xylene m-Xylene p-Xylene
Solubility, Grams/ 700 Grams Amorphous Phase High-density Low-density 32.8 26.0 26.5 23.2 23.0 22.8
2 9
28
1/T
I lo'
JO
J /
J2
33
54
Ileoiprooai Permeation Temperature ( O S . - ' l
Figure 3. Pervaporative permeability coefficients of xylenes in high- and lowdensity polyethylene
285
295 icclp-oca
305 Tr-npcrsnre.
315
325
335
T I 0 ' 1 '&'I
Figure 4. (Concentration average d i f fusivity o f xylenes in untreated polyethylene
polymer (Figure 4). The diffusivity of p-xylene in the lowdensity polymer was about three times that in the high density polymer, the diffusivity (at 30' C.) of o-xylene was about one third that of p-xylene in the low-density polymer, and the temperature dependence of the diffusivity of o-xylene was significantly greater than that ofp-xylene in either polymer. The marked differences in both permeabilities and diffusivities of the isomeric: xylenes in either polymer are evidently due to differences in the molecular configuration of the three isomers. These differences cannot logically be traced to variations in molecular size since, from the densities of the liquid isomers, molecular volume appears to increase in the order o < m < p. O n the other hand, the isomers differ significantly in shape, as molecular models easily illustrate. If it is assumed that the molecules move through the polymer matrix with their major axes aligned with the diffusion direction, the important configurational parameter controlling the
diffusion rate is the molecular cross-sectional area normal to the major axis. The differences in these diffusional cross sections for the three isomers are estimated in Table IV, where the apparent molecular volume calculated from the molar refraction (20' C.) is divided by the maximum dimension of the molecule as determined from Stuart model measurements. These values increase in the order p = 1, m = 1.04, o = 1.10, consistent with the observed permeability differences, and the temperature coefficients of permeability increase in the same order. One is, therefore, tempted to postulate an activated diffusional process for the transport of xylenes through polyethylene, with diffusivity decreasing and activation energy for diffusion increasing as molecular cross section increases. Certain other observations are not entirely consistent with the simple activated diffusional mechanism of transport, however. Permeabilities and diffusivities are much lower and permselectivities higher in the high-density polymer, while the temperature variation of permeability is lower in this film, relative to the low density polymer. Furthermore, the appaxent activation energy for diffusion of p-xylene in the lowdensity polymer is in excess of 8 kcal. per mole, a value which seems abnormally large for activated diffusion in a polymer matrix which is swollen to the extent of 30 to 60% by volume with the permeating solute. These results can be more satisfactorily explained in terms of variations of a, 7, and 0 (Equation 3) brought about by changes in temperature. As the temperature is raised, a reduction in crystallinity (increase in a ) causes a reduction in both geometric impedance offered by the crystallites (7) and in restriction to chain mobility ( p ) . These changes cooperate in causing an increase in permeability, the effect being more marked for the low density polymer. Since the molecule with the smallest cross section (p-xylene) will experience the least obstruction to diffusion offered by chain segment immobility, any alteration in 0 with level of crystallinity will have less influence on the transport rate of this isomer than upon its larger cross-section counterparts; as a result, permselectivity will increase with increasing crystallinity and decrease with increasing temperature, as the data indicate. Effects of Xylene Conditioning on Permeability and Permselectivity. Inasmuch as p-xylene exhibited the highest permeability of the three isomers through both high- and lowdensity polyethylenes, the consequences of solvating the films with liquid p-xylene a t elevated temperature, followed by cooling and drying, were examined. Lowdensity films were heated to 50" and 55" C. in p-xylene, cooled to 0 " C., and dried a t that temperature; high-density films were heated to 95" and 100" C., cooled to 25" C., and dried a t that temperature. Permeation rates for the three isomers were then measured with the conditioned films (at 40" C. for the lowdensity, and 30" C. for the high-density polymer). Results are presented in Table V.
Table IV.
Apparent Diffusion Cross Seciions of Xylene Isomers
Molecular Volume,a
a
Compound o-Xylene m-Xylene p-Xylene From molar refraction
Maximum Length of Stuart Model,
Apparent Cross Section,
A. 7.80 8.33 8.67
7.65 7.20 6.92
A.3 59.7 59.8 59.9 at 20' C.
VOL. 1
NO. 1
.4.2
JANUARY 1 9 6 2
19
Table V. Effect of Conditioning Temperature upon Permeability Coefficient and Permselectivity
Permeant
o-Xylene m-Xylene p-Xylene o-Xylene m-Xylene p-Xylene o-Xylene m-Xylene p-Xylene
Conditioning Permselectioity Temp., "C. P X lo5 p/o Low-Denrity Polyethylenes (Permeation Temp. = 40' C.) Unconditioned 19.4 Unconditioned 22.4 1,35 1.17 1.15 Unconditioned 26.2 50 26.1 50 29.1 1.39 1.25 1.12 50 36,3 55 31.1 55 34.4 1.23 1.13 1.10 55 38.8
High-Density Polyeth.vleneb (Permeation Temp. = 30aC . ) +Xylene Unconditioned 1 .81c m-Xylene Unconditioned 2.12c 1 , 6 2 1.39 1.17 p-Xylene Unconditioned 2.94~ +Xylene 95 17 1 m-Xylene 95 16.6 1.20 1.23 0.97 p-Xylene 95 20.5 o-Xylene 100 18.2 m-Xylene 100 24.8 1.62 1.18 1.36 p-Xylene 100 29.3 a Films conditioned in liquidp-xylene, cooled and dried at 0' C. Films conditioned in $-xylene, cooled and dried at 25' C. c Extrapolated data from Figure 3.
Table VI.
Permeant
o-Xylene m-Xylene p-Xylene +Xylene m-Xylene ,&Xylene o-Xylene m-Xylene p-Xylene o-Xylene m-Xylene p-Xylene
Effect of Conditioning Compound upon Permeability Coefficient and Permseleclivity
Conditioning Compound
Permeation Temp.. O
c.
P
X
105
Low-Density Polyethylenea Unconditioned 45 24.0 Unconditioned 45 26.4 Unconditioned 45 30 6 o-Xylene 45 32 3 o-Xylene 45 32 0 o-Xylene 45 36 9 rn-Xvlene 45 25 6 rn-xj-lene 45 30.2 m-Xylene 45 35.7 p-Xylene 45 25.6 p-Xylene 45 28.9 p-Xylene 45 35.8
Permselectivitv p/m m/o-
P/O
1.28
1.16
1.10
1.14 1.15 0.99 1.39
1.18
1.18
1.40
1.24 1.13
High-Density Polyethyleneh o-Xylene Unconditioned 30 1 ,81c 30 2,12c 1 . 6 2 1 . 3 9 1 . 1 7 m-Xylene Unconditioned p-Xylene Unconditioned 30 2.94c 50 2,86 o-Xylene Unconditioned m-Xylene Unconditioned 50 3.15 1.38 1.26 1.10 p-Xylene Unconditioned 50 3.96 o-Xylene o-Xylene 30 24.3 m-Xylene o-Xylene 30 25.1 1.30 1.25 1.04 p-Xylene o-Xylene 30 31.4 50 16.1 o-Xylene o-Xylene m-Xylene o-Xylene 50 16.9 1.24 1.18 1 . 0 5 50 19.9 p-Xylene o-Xylene 30 18.2 o-Xylene $-Xylene m-Xylene $-Xylene 30 24.8 1.62 1 . 1 8 1.36 p-Xylene p-Xylene 30 29.3 50 12.9 o-Xylene $-Xylene 50 16.1 1.50 1.20 1.26 m-Xylene $-Xylene p-Xylene p-Xylene 50 19.2 a Films conditioned in spectfied isomer at 50" C., cooled and dried at 0" C. b Films conditioned in speciJied isomer at 100' C., cooled and dried at 25" C. c Extrapolatedfrom Figure 3.
20
l & E C PROCESS DESIGN A N D DEVELOPMENT
Other film samples were then subjected to conditioning nith and m-xylene under identical conditions and permeabilities measured for comparison with p-xylene-treated films. Results are given in Table VI. Finally, films treated with p-xylene (at 50' C. for the lowdensity polymer, 100' C. for the high) were submitted to pervaporation rate measurement a t various temperatures ; results are summarized in Figures 5 and 6. For the low-density polymer (Table \-), treatment with p xylene at 50" C. results in a roughly 40% increase in permeability (at 40" C.) to all isomers, a slight (perhaps insignificant) increase in permselectivity toward para with respect to ortho, and a some\shat larger increase in selectivity toward meta with respect to ortho. Conditioning at 55' C. causes a roughly 60% increase in permeability to all isomers, but a general loss in permselectivity. It is significant that, with unconditioned polymer, to obtain a permeability coefficient for pxylene of 36.3 would necessitate conducting the pervaporative process at a temperature of 50" C.?where the permselectivity of the film toward p- with respect to o-xylene would be about 1.2. Thus, conditioning with p-xylene produces a substantial increase in film permeability at the lower temperatures, without sacrificing permselectivity. Lt'ith high-density polymer (Table V), the effects of conditioning with p-xylene are even more marked. Treatment at 95" C. produces a greater than eightfold increase in permeability to all isomers (at 30" C.) but a substantial loss in permselectivity with respect to all three pairs. Treatment at 100' C., however, produces a slight further increase (to about tenfold) in permeability, restores the p/o permselectivity to its value (at 30' C.) for the untreated film, increases the m/o selectivity substantially above that of the control, and further depresses the p/m selectivity. With unconditioned film? a p-xylene permeability coefficient of 29.3 can be realized only at temperatures of about 100' C., where the permselectivity of the film to any isomer pair is very small indeed. The effects of substitution of m- and o-xylenes for p-xylene in the conditioning process are striking (Table VI). With lowdensity polymer, the highest mean permeability (at 45' C.) is achieved by conditioning with o-xylene and the lowest with the p-xylene. However, the highest permselectivity to\vard para with respect to either meta or ortho is achieved by p-xylene treatment; highest permselectivity toward meta with respect to ortho, by rn-xylene treatment; and lowest permselectivity for all three pairs, by ortho treatment. With the high-density polymer, the trends are quite similar, with the exception that para conditioning improves m/o selectivity and depresses p/rn selectivity relative to the untreated film. The effect of mxylene conditioning of this polymer remains to be determined. The variations of permeability of p-xylene-conditioned films with temperature (Figures 5 and 6) are even more provocative. \t'ith low-density polymer, the permeability coefficients of conditioned film to all three isomers are virtually temperature independent, at least up to the conditioning temperature (50' C.), That is to say, the pervaporation rates of the xylenes through these films are nearly directly proportional to the vapor pressures of the penetrants in the range 25" to 50" C. \liith the high-density polymer, on the other hand, the permeability coefficients for the conditioned film actually decrease rapidly with increasing temperature (although the pervaporation rates increase with temperature). For both polymers. the permeability coefficients for conditioned and unconditioned films tend to converge a t roughly the conditioning temperature. 0-
11 1 I 2.
I
I
I
9.9s
L6
I
1
I ' I
39.
30
3 4
I fT x l o ' [ ' K;'l
Figure 6. Pervaporative permeability coefficients in high-density polyethylene
Figure 5. Pervaporative permeability coefficients iri low-density polyethylene
The observation that both the temperature a t which conditioning was carried out and the specific compound employed for this treatment exerted a very marked effect on the pervaporative transport rates and the permselectivities of the polymers suggested that the concentration of sorbed xylene in the polymer a t the time of exposure to elevated temperature might also be an important variable. To evaluate this factor. samples of high-density polyethylene film were allowed first to equilibrate with liquid p-xylene a t 30'. 50', and 70' C . ; the swollen films were then removed from the xylene, quickly blotted free of excess liquid. placed in sealed tubes, and heated to 100' C. for 24 hours. Following heat treatment. they were cooled slowly to room temperature and allowed to dry thoroujghly under ambient conditions. These films were then subjected to pervaporative transmission rate
measurements with each of the xllene isomers a t 30'. 59'. and 70' C. Results are summarized in Figures 7 and 8. Xylene permeability coefficients measured a t 30" C. increased rapidly as the concentration ofp-xylene in the polymer during conditioning increased. What is perhaps more significant are the observations that p-xylene permeability increased and the temperature coefficient of permeability to p-xylene decreased much more rapidly with this variable than did the corresponding quantities for the 0- and m-xylenes. Consequently, the concentration of p-xylene during conditioning has a very important influence on the permselectivity of the membrane, as Figure 8 clearly demonstrates. The permselectivity of the film t o p - relative to o-xylene passed through a maximum \\ ith increasing xylene concentration during conditioning, the location of this maximum shifting to higher xylene concentrations and its magnitude decreasing as the temperature of permeation increased. Maximum p/o selectivity of 1.80'is exhibited by film containing 9.8 grams xylene per 109 grams of polymer a t conditioning. when permeated at
/
I20
I
I
1
1 I d
9j-2 7
rl
emme-*
I
J'i re
11
. ! 2 ("K
'x
1'4
i.'
I
/A
I
I
I
I I
J'6
131,
Figure. 7 Xylene permeability coefficients in high-density polyethylene annealed a t 100" C. in presence of variable concentrations of p-xylene VOL.
1
NO. 1
JANUARY
1962
21
Table VII.
Isomer 0-Xylene m-Xylene )-Xylene
Xylene Solubilities in Conditioned Polyethylene Film Solubility, Grams/?00 Grams Dry Polymer Low-Density Polyethylene 25" C. 35" c. 45O U* Clb C2c Lra Cp Ua 16.9 22.7 21.8 21.0 23.5 29.3 13.6 17.6 17.3 ... 19.8 11.8 2 1 . 0 1 7 . 5 1 7 . 3 2 1 . 9 2 2 . 5
c. Cz 30.2 30.1 30.0
High Density Polyethylene 30" C. 50" C. 70" C. ua Cd c'" Cd D'n Cd o-Xylene , . . 16.9 ... 17.5 , . . 18.2 m-Xylene , . . 14.5 .., 17.3 , , , 18.0 +Xylene 6.3 14.9 9.8 17.0 14.3 18.2 a Untreated film. Conditioned in liquid $-xylene at 50' C. Conditioned in liquid$-xylene at 50' C., cooled to 25' C., and dried. d Conditioned in liquid$-xylene at 700' C., cooled and dried at 25' C.
30' C. These results establish beyond little doubt that the concentration of sorbate in the polymer during heat treatment is of crucial importance in determining permselectivity of the film; furthermore, they raise the very important practical question of whether appropriate selection of the type and concentration of sorbate species can develop extremely high permselectivity of polyethylene toward any selected pair of permeants. Effects of Conditioning on Solubility. Table VI1 compares the equilibrium solubilities of the xylenes in p-xyleneconditioned polyethylene with corresponding values for untreated polymer. For low-density polymer, conditioning a t 50' C. followed by cooling to 25 ' C. yields a product in which thep-xylene solubility is nearly twice that in untreated polymer a t this temperature. (Conditioning a t 55 ' C. raises the solubility a t 25" C. to a value about threefold greater than that of untreated polymer.) If, however, the 50" C. conditioned polymer is cooled and thoroughly dried, re-equilibration with p-xylene a t 25 ' C. yields a solubility roughly 20y0 lower than that measured prior to drying but still substantially greater than that of untreated polymer. The response of high-density polyethylene to the conditioning process (with p-xylene a t 100' C.) is analogous, although the changes are even more marked : Conditioning followed by cooling and drying yields film in which xylene solubility (at 25' C.) is more than twice that in untreated polymer. Relative solubilities of the individual xylene isomers seem to be little, if a t all, altered by the conditioning process. This sorption hysteresis throws considerable light upon the structural and morphologic changes which evidently take place in polyethylene consequent to conditioning. It was pointed out that the observed limited swelling of polyethylene in the xylenes is probably due to the cross-linking action of the crystallites upon the amorphous phase of the polymer. When polyethylene is heated in xylene to a temperature just short of the critical solution temperature in the solvent, a large fraction of the crystallinity of the polymer is melted out. When the highly swollen polymer is cooled, recrystallization takes place, but under conditions where the mobility of the polymer molecules is greatly enhanced by the solvent. Such conditions can be expected to favor the growth of larger, more nearly perfect crystals than could conceivably have been grown from the unsolvated polymer melt, particularly for low-branchingindex (i.e., linear) polymer. 22
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
If it is postulated that the effective cross-link density in polyethylene (i.e., the volume density of intercrystallite bridging by disordered chain segments) decreases with increasing crystallite perfection and size, then conditioned polymer will be less tightly cross linked (and thus more readily solvated) than untreated polymer. Furthermore, the size of the crystallites grown by cooling of the hot, solvated polymer will in large measure be determined by the number of residual crystalline elements present prior to cooling, since these elements undoubtedly serve as primary nuclei during recrystallization. Since the concentration of these residual crystallites will decrease as the conditioning temperature is increased, higher conditioning temperatures should therefore favor formation of larger (and/or less imperfect) crystallites on cooling and hence greater swelling a t room temperature. The data appear to be consistent with this mechanistic model. Additional support for the foregoing argument is provided by density measurements on conditioned polymer and x-ray diffraction analyses. Conditioned high-density polymer is slightly more crystalline than untreated polymer (by roughly 3 9 3 , and the mean a-axis crystallite dimension appears to increase significantly, as evidenced by a sharpening of the corresponding diffraction band. X-ray diffraction analysis of conditioned high-density films prior to drying, or resolvated after having been dried, shows essentially the same degree of crystallinity as that of the corresponding films in the dry state. This observation suggests that there is no significant loss in crystallinity in conditioned linear polyethylene because of xylene solvation at room temperature and indicates that the enhancement of xylene solubility in polyethylene by conditioning is due to rearrangement of crystalline and amorphous components of the matrix, rather than to mere reduction in crystallinity. As the concentration of p-xylene in high density polymer during heat-treatment (at 100' C.) is increased, the equilibrium solubility of p-xylene in the treated film (measured a t 30' C.) is similarly increased. as shown in Table V I I I . The equilibrium solubility a t 30" C. is in all but one case greater than the concentration of xylene present during heat treatment, although the difference between the two quantities decreases as solubility increases. This behavior is in marked contrast to that of polymer allowed to equilibrate with p-xylene at 100" C. which, after cooling and drying, imbibes much less xylene a t 30" C. than a t 100' C. This difference in behavior is interpreted to indicate that two processes occur concurrently when xylene-swollen polyethylene is heated: One is a reversible decrease in crystallinity, which provides more amorphous phase in which additional xylene may dissolve, and the other is a largely irreversible change in crystallite morphology which results in a reduction in intercrystallite cross linkage. Both processes contribute to increased xylene solubility a t elevated temperature, the former becoming of greater importance as the melting point of the crystalline phase is approached; only the latter, however, contributes to increased xylene solvation at lower temperatures. Table VIII. Effect of pXylene Content during Annealing on p-Xylene Solubility in High-Density Polyethylene Grams/?00 Grams Dry Polymer Xvlene Content $-Xylene Solubility during Annealin! at 30' C . at 700' C. 6.3 0. 0. ~ 9.2 6.3 13.5 9.8 16.3 14.3 14.9 25.0
These observations c,trongly support the hypothesis that changes in crystallite morphology during heat treatment of solvated polymer are fundamentally responsible for changes in sorption behavior; it thus appears desirable to consider these morphologic changes in greater detail as a possible means of explaining the unusual permeation properties of conditioned polymer films. Effect of Conditioning on Apparent Diffusion Constants. Concentration average diffusivities (Equation 5) for p - and o-xylene in conditioned high-density polymer have been estimated from measured permeabilities and interpolated solubilities, for films annealed a t 100" C. containing variable amounts of p-xylene (Figure 9). Polymer solvated a t 30" C. and annealed a t 100' C. differs in no important respects from untreated polymer, as regards xylene diffusivities and their temperature dependency; this treatment has, however, already been shown to increase xylene solubility a t low temperatures, and thus permeability Solvation a t SO", 7 0 " , or 100' C . prior to anntaling, on the other hand, causes a striking increase in difiusivities a t low temperatures and reduction in their temperature dependency: In effect, the log D us. T lines for these conditioned films are rotated about a point on the line for untreated film, corresponding roughly to the temperature at which the film was xylene-solvated prior to annealing. Evidently, the process of annealing solvated polymer stabilizes a special morphologic configuration of the polymer matrix which is established by the solvation process itself. New and important light is thrown on the mechanism of the conditioning process by examining the apparent activation energies (E,) for diffusion of the xylenes through the solvated and annealed films as a function of the level of p-xylene solvation. These values are summarized in Table I X . For p xylene, E , drops very rapidly from a value of about 8.5 to 5.9 kcal. as the solvation temperature is increased from 30" to 50" C. and undergoes a n additional decrease to 4.7 kcal. as the solvation temperature is raised to 100" C . With o-xylene, on the other hand. the corresponding decreases in E, are both smaller and more gradual. T h e greatest difference in diffusion activation energies for the two isomers (of roughly 2 kcal.) is exhibited by polymer solvated at SO" C., this polymer also displaying the highest p/o permselectivity. The latent heat of vaporization for both 0- and p-xylene is approximately 10 kcal., whence the activation energies for self diffusion are estimated to be of the order of 3 kcal. Thus, polymer which has been solvated and annealed a t 100' C. offers a much smaller energetic barrier to p-xylene diffusion than to o-xylene diffusion. The magnitude by which the E, values in Table I X exceed 3 kcal. is, therefore, a measure of the extent to which restricted chain segment mobility
Table IX. Apparent Diffusion Activation Energies in Conditioned High-Density Polyethylene p-Xylene Content during Annealing. Grams/?80 Grams Polymer
Solvation Temp. before Annealing at 100' C., C.
I00
100
IC
. 0
i
26
1
'
2 7
1
!
2 6
I
29
I/T
.I3
30
lo3 OK
-'
32
33
Figure 9. Average diffusivities of xylenes in high-density polyethylene annealed a t 100" C. in the presence of variable concentrations of p-xylene
in the microcrystalline polymer interferes with diffusion of xylene molecules through the amorphous matrix. Since this excess activation energy is much smaller for p xylene than o-xylene i n conditioned polyethylene, it is deduced that the conditioning process alters the intercrystalline or interlamellar spacings in such a way that p-xylene molecules can pass relatively unimpeded, while o-xylene molecules must distort or displace polymer chain segments to make a successful diffusion step. I n terms of the model depicted by Equation 3, the chain immobilization factor ( p ) forp-xylene in high density polyethylene decreases rapidly toward unity with increasing solvation, while /3 for o-xylene decreases less rapidly, maintaining a value far in excess of unity under all conditions studied. I t therefore appears likely that molecular transport of liquids through swollen polyethylene is controlled primarily by the configuration and spatial distribution of the impermeable crystalline phase. X y l e n e Mixture Separation w i t h Polyethylene Membranes
Measurements were made of the changes in composition which resulted from allowing xylene mixtures to pervaporate through a conditioned high-density polyethylene film, and the experimentally measured changes were compared with those calculated from individual permeability coefficients, using the ideal relationship : J,
E D , Kcal./Gram Adole p-Xylene o-Xylene
P,p:x:
= 7
T h e ratio of any two components in the (vapor) mixture leaving the film is then related to the feed liquid composition by the expression :
VOL.
1
NO. 1
JANUARY
1962
23
7 MELT- QUENCHED POLYMER
2 ANNEALED WITHOUT SOLVLNT
3 IDEALLY ANNEALED WITH S O L V E N ~
4 OVER -SOL V A ~ L D WHEN ANNEALED
suitable for confining liquid in contact with as little as 2000 square feet of film would not present major obstacles, particularly if the film Lvere fabricated in the form of smalldiameter, thin-walled tubing. The major advantage of using conditioned polymer in this illustration is the nearly tenfold reduction in film area required for a given throughput, relative to unmodified polymer. Since the permselectivity of unmodified polymer to p- with respect to o-xylene is already quite high, moderate increases in permselectivity brought about by conditioning do not effect much change in the number of cascades required. For more difficultly separable mixtures, however, where the permeability ratio in unmodified polymer is close to unity, even small permselectivity increases brought about by conditioning can greatly reduce the staging required for a given separation and thereby significantly reduce the cost of the operation. Thus, if Binning’s ( 3 ) estimate of the economic prdcticability of staged membrane separation processes is sound, suitable conditioning of the membranes offers promise of making such processes even more economically attractive.
Origins of Permrelectivity-A
Figure 10. membrane
Schematic model of permselective polymer
Results are presented in Table X. The film shows a pronounced ability to discriminate between the isomers in mixtures and the agreement between the experimental and calculated enrichment factors is surprisingly good. Thus, the xylenes form essentially ideal solutions in the polymer phase, and the transport rate for any isomer within the polymer is directly proportional to the mole fraction of that isomer present in the imbibed solution. If this trivial relation proves to hold true for the transport of any pair of closely related compounds penetrating through a polymer film, prediction of the barrier properties of a membrane will be vastly simplified. To illustrate the potential practicability of employing conditioned 1-mil polyethylene films in a cascaded barrier separation scheme, consider the problem of separating 10,000 pounds per day of an equimolal mixture of o- and p-xylene into products containing 98 mole 70 of one or the other isomer. Using the data of Table X and the permeability values from Figure 6, at 30’ C. six cascade stages would be required, each containing a film area of 2000 square feet. Design of units
Table X.
Separation of Xylene Mixtures with Conditioned High-Density Polyethylene Film Film annealed in liquid p-xylene at 100’ C.
‘Yylene Isomer 0
m
P 0
m
P
24
Upstream Concn., .Mole % 30.0 65.0 5.0 90.0 5.0 5.0
Downstream Concn., Mole 70 Exptl. Calcd. 20.9 20.7 72.1 72.4 7.0 6.9 83.4 83.3 7.4 7.3 9.2 9.4
I&EC PROCESS DESIGN A N D DEVELOPMENT
Physical Model
The accumulated experimental evidence on the macroscopic transmission properties of polyethylene and its interpretation in terms of the t\vo-phase microstructure of the polymer are consistent \vith a model presented schematically in Figure 10. This model considers the polymer as a simple molecular “sieve” or screen, wherein the intercrystalline amorphous regions (be they intra- or interlamellar) constitute the ‘‘holes,” and the extensively interconnected crystalline elements, the “mesh.” In ordinary melt-quenched polymer, there is a broad distribution of crystallite sizes and a high degree of intercrystalline cross linking, whereupon the amorphous “holes” in the sisollen polymers are similarly broadly distributed as to size and are quite small, on the average. In such a structure, the xylenes will find relatively few holes available for unobstructed passage, although the smaller para isomer will have the greater statistical probability of making successful transit; hence, this polymer will exhibit lo\\ permeability but some degree of permselectivity. If the polymer is annealed and recrystallized in the presence of a solvating liquid, growth of larger and more perfect crystals is strongly favored but under conditions where the crystals are rather widely separated by intervening solvent. S o t only isill the number of intercrystalline bridging molecules then be drastically reduced, but the mean lengths of those chain segments which do participate in bridging will be greatly increased. Ll’hen such a structure is resolvated with xylene at low temperature, the matrix expands greatly, and the resulting mean intercrystalline spaces become much larger than in unmodified polymer. The result of this conditioning, therefore? is both a narrowing of the “hole” size distribution and an increase in mean “hole” size. Clearly, the mean ‘.hole” size will increase with the volume concentration of solvent during annealing and with the extent of crystalline melt-out preceding recrystallization. The latter variable increases rapidly with solvent content during annealing and with annealing temperature. Obviously, an increase in mean ”hole” size will result in an increase in permeability; a major increase in permselectivity will, however, result only if the hole size distribution is sharply peaked, and only if the most prevalent “hole” size is slightly smaller than the diffusion diameter of the smaller diffusing molecule.
It is. therefore, no surprise to find that the permselectivity of polyethylene to the isomeric xylenes is extraordinarily sensitive to the level of crystallinity in the polymer, the temperature a t which annealing is carried out? and the solvent content of the polymer during annealing. It is entirely probable that the optimal treatment conditions for maximum permselectivity for the xylene isomers have not been struck in this investigation and the need for a much more detailed study of conditioning variables is evident. The observation that the permselectivity of polyethylene to the xylenes is also dependent on the configuration of the solvating molecule present during annealing is provocative, in that it implies that these molecules function are templates which control the ultimate intercrystalline spacing or "hole" size. Although the evidence supporting such a conclusion is a t present not overwhelming, the possibility that the effect may be real has an immense impact upon the prospects of tailoring polyethylene to render it permselective to a compound of choice. Further study of this phenomenon is now under way. The model proposed here does not invoke any properties peculiar to ethylene polymers; it should apply with equal defensibility to any microcrystalline thermoplast. I n fact, a n entirely analogous model can be developed for an amorphous polymer \vhich is subjected to cross linking in the presence of a solvating. inert diluent. Furthermore, there is no feature of the model which restricts its applicability to the process of pervaporation studied here: Similar behavior may be expected in such processes as gas or vapor transmission and dialysis. T h e authors feel that the surface of a new and very important aspect of polymer physics, with its attendant engineering implications, has barely been scratched by this investigaton. N o r e extensive study of the phenomena involved and of their practical utilization is clearly in order. Nomenclature c1
= penetrant concentration a t upstream film boundary = penetrant concentration at downstream film boundary
cL
=
D
= = = =
e* D En
J = J, =
k k*
= =
ki
=
equilibrium concentration of solute in film in contact with pure liquid solute at permeation temperature apparent diffusivity of gas in polymer diffusivity of permeant in amorphous polyethylene concentration average diffusivity apparent activation energv for diffusion of xylene through film. kcal. transmission flux. grams '(sq. cm.) (hr.) transmission flux of component i through film, grams/ (sq. cm ) (hr.) solubilitv (Bunsm) coefficient for gas in polymer solubility coeffirient of permeant in amorphous polyeth) lene pseudosolubility coefficient, referred to upstream face of film
1
= thickness of unswollen film, cm.
= permeability coefficient P , = permeability coefficient for
i
p pl
= partial pressure, cm. Hg = partial pressure of gas phase at upstream film boundary,
pz
= partial
cm. H g pressure of gas phase at downstream film boundary, cm. Hg p L = liquid vapor pressure, cm. Hg pp = vapor pressure of pure i at permeation temperature, cm. Hg S = permselectivity of membrane xp = mole fraction of i in feed liquid = volume fraction of amorphous phase CY p = chain immobilization factor = geometric impedance to diffusion offered by crystallites 7 where Acknowledgment
T h e invaluable assistance of A. J. Buselli. A. G. Foglia, J. Fogerty. F. 121. Mitchell, and G. E. Ashby, LV. R. Grace and Co., and of Turner Alfrey and D. R Petersen. Dol\ Chemical Co., in connection with property measurements on film samples and interpretation of the results, is l\arml\ appreciated. References
(1) Amerogen, G. .J. van, J . Polymer Sci.5 , 207 (1950). (2) Bent, H. A , . Pinsky, J., WADC Tech. Rept. 53-113, Pt. 2 , August 1955. (3) Binning, R. C., Lee, R. J., Jennings, J. F., Martin, E. C., IND.EXG.CHEM.53, 45 (1961). (4) Brubaker. D. \V.. Kammermever. K.. Zbzd.. 45. 733 (1954). (5j Charlesby, .\., Callaghan, L., 'Ji-.; J . Phys. Chem Solihs 4, '227 I1 958). (6)' Dickey. F. H., J . Phys. Chem. 59, 635 (1955). (7) Kammermeyer, K.: IND.ENG.CHEM.50, 697 (1958). (8) Klute, C. H., J . Appl. Polymer Scz. 1, 340 (1959). (9) McKee, R. G., S;. D.. thesis. Massachusetts Institute of Technology, Cambridge, Mass.. 1957. (10) Michaels, .4.S., Bixler, H. J., J . Polymer Sci. 50, 393 (1961).
(11) Zbid.: p. 413.
(12) Michaels, A. S., Parker, R. B., Jr., Ibid.,41, 53 (1959). (13) Rogers, C. E., Stannett, V.: Swarc: M., J . Phys. ChPm. 63, 1406 (1959). (14) Tung, L. H., Buckser, S., Ibid.,62, 1530 (1958). (15) \Yeller, S., Steiner, \V. .4.: ChPm. Eng. Pray. 46, 585 (1950). (16) Weller, S., Steiner! \$'. '4.:J. '4ppl. Phy's. 21, 279 (1950).
RECEIVED for review March 30. 1961 ACCEPTED .4ugust 10, 1961 Symposium on Less Common Separation Methods, 139th Meeting, ACS, St. Louis, Mo., March 1961. Condensation of Sc. D. thesis of C. Y . Choo, Department of Chemical Engineering, Massachusetts Institute of Technolow. Cambridge. 1Iass.. January 1960. Work supported by Scientific Design "CO. fellow: ship (1957-1958) and National Science Foundation (Grant G-7373, 1958-1960).
VOL.
1
NO. 1
JANUARY
1962
25
