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Formation of hydrophilic microporous membranes via thermally induced phase separation
Journal of Membrane Science 142 (1998) 213±224
Formation of hydrophilic microporous membranes via thermally induced phase separation Hideto Matsuyama, Stephane Berghmans, Douglas R. Lloyd* Department of Chemical Engineering, Center for Polymer Research, The University of Texas at Austin, Austin, TX 78712, USA Received 1 August 1997; received in revised form 2 December 1997; accepted 4 December 1997
Abstract Hydrophilic microporous membranes were produced via the TIPS process using two hydrophilic ethylene±acrylic acid copolymers (zinc salt) with different co-unit contents. These co-polymers were con®rmed to be hydrophilic by contact angle measurements. Low density polyethylene homopolymer was also used in this work as a reference to investigate the effect of polymer properties on the membrane structures. First, dynamic phase diagrams for these three polymer systems were determined. The cloud point curves shifted to higher temperatures and the crystallization temperature curves shifted to lower temperatures as the acrylic acid content of the co-polymer increased. The membrane structures were investigated and related to the initial polymer concentration and cooling rate. Increasing either the polymer concentration or the cooling rate decreased the pore size. Furthermore, structures with smaller pores and a skin layer at the top surface were obtained by introducing an evaporation process before the cooling to generate a polymer concentration gradient in the melted polymer solution. # 1998 Elsevier Science B.V. Keywords: Thermally induced phase separation; Microporous membranes; Hydrophilic membranes; Ethylene acrylic acid copolymer; Polyethylene
1. Introduction Many micro®ltration (MF) and ultra®ltration (UF) membranes are made from hydrophobic polymers such as polypropylene (PP), polyethylene (PE), poly(vinylidene ¯uoride), and polysulfone. These so-called engineering plastics or commodity plastics are suitable for sterilization with hot water for use in the food, medical, and biological industries [1]. However, hydrophobic membranes have a disadvantage in that *Corresponding author. Fax: +1 512 471 9643; e-mail: [email protected] 0376-7388/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved. PII S0376-7388(97)00330-X
the ¯ux is likely to decline during operation due to solute adsorption and pore blocking [1±3]. This fouling is especially signi®cant in the case of protein separation because hydrophobic interactions between proteins and the membrane surface bring about nonselective irreversible adsorption of proteins on the membrane surface. Moreover, since hydrophobic membranes are non-wettable by water, a pressure gradient is needed in order to pass water through the membrane pores. Thus, hydrophilic microporous membranes are desirable. The surfaces of hydrophobic membranes have been made hydrophilic by physical and chemical post-
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treatment processes. For example, methods of altering surface chemistries include adsorption of surfactant on the membrane surface [4], plasma treatment [5±7], and the surface grafting of hydrophilic species [8,9]. However, instabilities in the treated sections can cause problems in the practical use of the membranes [10]. An alternative way to make stable hydrophilic microporous membranes is to use co-polymers with both hydrophobic and hydrophilic components [10]. Although hydrophilic homopolymer membranes made of polymers such as cellulose acetate, poly(vinyl alcohol), and polyacrylonitrile are low-fouling, they usually do not have good thermal stability or chemical resistance [1]. In order to avoid fouling but still obtain durable membranes, co-polymers with hydrophobic and hydrophilic components must be used. Thermally induced phase separation (TIPS) is a method of making microporous membranes [11± 16]. TIPS is applicable to a wide range of polymers that could not be used in the traditional phase inversion membrane formation due to the solubility problems. However, few studies have reported on the formation of porous membranes from co-polymers via TIPS. Castro ®rst produced microporous membranes from styrene±butadiene co-polymers and ethylene± acrylic acid co-polymer salts [11]. Chung and Lee produced a hydroxylated polypropylene (PP±OH) copolymer and prepared a hydrophilic PP/PP±OH blend membrane [17]. This membrane had good selectivity and ¯ux as well as excellent antifouling properties. In both cases, the preparation method was the TIPS process, although the authors did not refer to it as such. In the TIPS process, a concentration gradient across the nascent membrane results in an anisotropic membrane. Prior and current work in our laboratories [18± 27] plus work conducted elsewhere [12,28±34] has demonstrated that the droplet growth rate in liquid± liquid TIPS is: dependent on the polymer±diluent interfacial tension, increases with increasing volume fraction of the droplet phase and decreases with increasing viscosity of the polymer-rich matrix phase. Smaller cells are obtained when the polymer concentration is higher (that is, lower diluent concentration), whereas larger cells result when the polymer concentration is lower. Thus, inducing a concentration gra-
dient across the thickness of the membrane, by evaporating the diluent from one side of the nascent membrane, prior to phase separation will result in a gradation in structure development kinetics and thus a gradient in cell size across the thickness of the membrane. In this work, hydrophilic microporous membranes were prepared from two ethylene±acrylic acid copolymers (zinc salt) with different co-unit content via the TIPS process. The effects of the initial polymer concentration and cooling rate on the resultant membrane structures were investigated. Polyethylene homopolymer was also used as a membrane material for comparison to the co-polymeric structures. Studies on the effects of various diluents on the TIPS process have been reported already [35,36]. However, as far as we know, the effects of polymer properties on membrane morphology have not yet been studied. 2. Experimental materials and methods 2.1. Materials Two ethylene±acrylic acid co-polymer salts (Iotek 7030 and Iotek 4200, Exxon) and low density polyethylene homopolymer (Aldrich) were used. The properties of these polymers are summarized in Table 1. Iotek 7030 has a higher acrylic acid content than Iotek 4200. The melt index values for all the polymers are similar, which means that they have similar molecular weights. Diphenyl ether (DPE, Aldrich, 99% purity) was used as the diluent without further puri®cation. 2.2. Methods Homogeneous polymer±diluent samples were prepared by a method previously described [35]. Each Table 1 Polymer properties
Melt index (g/10 min) Density (g/cm3) Cation type Acrylic acid content Type of PE
Iotek 7030
Iotek 4200
PE
2.5 0.964 Zn 15 wt% low density
3.0 0.946 Zn 11 wt% low density
7.0 0.918 ± ± low density
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solid sample was chopped into small pieces and placed between a pair of microscope cover slips. To prevent diluent loss by evaporation during TIPS, a Te¯on ®lm of 130 mm thickness with a square opening in the center was inserted between the cover slips. Each sample was heated on a hot stage (Linkam, HFS91) at 453.2 K for 5 min. Then each sample was cooled to 298.2 K at a controlled rate (usually 10 K/min) on the hot stage. The temperature of the stage was manipulated by a Linkam TMS-91 controller. Initial polymer concentrations were varied and for the Iotek 7030 experiments, different cooling rates were used (2.5, 10, and 100 K/min) in order to obtain diverse membrane morphologies. Anisotropic membranes with smaller pores on one surface and larger pores on the other surface were created by a method previously described [37]. Anisotropic (gradation in pore size) and asymmetric (integrally skinned) membranes were produced by inducing a polymer concentration gradient in the membrane solution prior to cooling. After placing the polymer±diluent sample (20 wt% Iotek 4200, initial thickness: about 550 mm) in a glass bottle as previously described [37], the sample was sealed and heated at 433.2 K. The glass cap was then taken off and some diluent was allowed to evaporate from one side, thereby creating a polymer concentration gradient in the sample before cooling. After a certain evaporation period (up to 3 min), the glass cap was replaced and the glass bottle containing the sample was cooled in room temperature air (approximately 298 K). For scanning electron micrograph (SEM) observation, diphenyl ether was extracted from each sample with methanol. The resulting microporous membrane was fractured in liquid nitrogen and mounted vertically on a sample holder. The surface of the sample was coated with gold±palladium using a sputter coater (Commonwealth Model 3, Pelco). A SEM (JEOL, JSN-35 C) with an accelerating voltage of 25 kV was used to examine the membrane cross-sections. Cloud point curves for the three polymer±diluent systems were determined as follows. The sample was sealed with two cover slips as described above and placed on the hot stage. The hot stage was placed on the platform of an optical microscope (Nikon Optiphot 2-POL). The sample was heated to 453.2 K for 5 min to assure homogeneity and cooled at a controlled rate
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of 10 K/min. Cloud points were determined visually by noting the appearance of turbidity under the microscope. A DSC (Perkin Elmer DSC-7) was used to determine the crystallization temperature (Tc) for the dynamic phase diagram. A 3 to 5 mg sample was sealed in an aluminum DSC pan, melted at 473.2 K for 5 min and then cooled at a controlled rate of 10 K/ min to 298.2 K (for Iotek 7030, different cooling rates were used in order to observe their effect on the crystallization temperature). After keeping the sample at 298.2 K for 5 min, the sample was reheated at the same rate. The onset of the exothermic peak during the cooling was taken as the crystallization temperature. The enthalpy of fusion Hu was determined from the endothermic peak area during heating. The contact angle of water on surfaces of Iotek 7030, Iotek 4200, and polyethylene homopolymer was measured with a contact angle meter (Rame-Hart, Contact Angle Goniometer) at room temperature. The contact angles were measured by two methods. Method A involved placing a 1 ml water droplet on the surface of the polymer and method B involved placing a 3 ml water droplet on the surface and then removing 2 ml. Method A gives the contact angle between water and the dry polymer. Method B gives the contact angle between water and the polymer after it has been wetted. 3. Results and discussion Table 2 shows the contact angle data for the three polymers. For low density polyethylene (PE), the contact angle measured by method A (958) was nearly equal to that measured by method B (948) and these values are in agreement with the literature [38]. For Iotek 7030, the advancing contact angle measured by method A (738) was lower than that of PE because of the presence of hydrophilic acrylic acid in the coTable 2 Measured contact angles (degrees)
PE Iotek 7030 Iotek 4200
Method A
Method B
950 732 751
941 323 341
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polymer. The receding contact angle determined by method B (328) was much lower than that measured by method A. Holly and Refojo also observed advancing angles greater than receding angles while studying the wettability of poly(2-hydroxyethylmethacrylate) [39]. This behavior was attributed to structural changes in the polymer. That is, the hydrophilic groups were buried in the polymer when the surface was exposed to air, but they were able to reorient quickly in a water environment and appeared at the polymer±water interface. The low contact angle obtained by method B for Iotek 7030 may be explained by such a reorientation of the hydrophilic acrylic acid parts of the co-polymers. In practical operation, micro®ltration or ultra®ltration membranes are usually wetted by the water being treated. Therefore, the receding contact angle determined by method B is of greater signi®cance. This data indicates that Iotek 7030 is certainly a hydrophilic polymer. The contact angles measured by both methods for Iotek 4200 were approximately the same as those for Iotek 7030, indicating that the difference in acrylic acid content was not suf®cient to signi®cantly alter the hydrophilic nature of the polymers. Fig. 1 shows the dynamic phase diagrams of the three polymer±diluent systems. These are typical phase diagrams for semi-crystalline polymers with liquid±liquid phase separation occurring below the cloud point curve and solid±liquid phase separation occurring below Tc. The cloud point curve shifts to higher temperatures as the acrylic acid content increases in the order PE, Iotek 4200, Iotek 7030. The shift in the location of the cloud point curve (which represents the binodal curve) can be explained in terms of the polymer±diluent compatibility. The shape and location of the binodal can be calculated from the Gibbs free energy of mixing Gmix based on the Flory±Huggins lattice model. p Gmix d ln d ln p d p (1) RT xd xp where d and p are the volume fractions of the diluent and polymer, respectively, xd and xp are the numbers of lattice sites occupied by the diluent molecules and polymer molecules and is the Flory±Huggins interaction parameter. As becomes more positive (that is, the polymer±diluent system becomes less compatible), the binodal shifts to higher temperatures at a ®xed polymer concentration [16]. The interaction
Fig. 1. Dynamic phase diagrams of three polymer±diluent systems. Cooling rates in all cases were 10 K/min except for (5) and (}). Cloud point curve of (*) Iotek 7030-DPE, (~) Iotek 4200-DPE, (&) PE±DPE. Crystallization curve of (*) Iotek 7030-DPE, (~) Iotek 4200-DPE, (&) PE±DPE, (5) Iotek 7030-DPE at 2.5 K/min cooling rate, (}) Iotek 7030-DPE at 40 K/min cooling rate.
parameter has been related to the difference between the solubility parameters of the polymer and the diluent. The solubility parameters of polyethylene and diphenyl ether (DPE) were reported as 17.6 and 20.7 MPa1/2, respectively [40]. The solubility parameter of poly(acrylic acid) is estimated as 24.6 MPa1/2 by the group contribution method [41]. Because the acrylic acid units in the co-polymers are zinc salt and therefore more polar than normal acrylic acid units, the solubility parameter of the acrylic acid component in this co-polymer is expected to be larger than 24.6 MPa1/2. As the acrylic acid content in the copolymer increased from PE to Iotek 4200 to Iotek 7030, the solubility parameter of the polymer increased. Therefore, the polymer±diluent system becomes less compatible as the acrylic acid content in the polymer increases. This is why the cloud point curves shift to higher temperatures in the order PE, Iotek 4200, Iotek 7030, as shown in Fig. 1. The crystallization curves in the dynamic phase diagrams shifted to lower values in the order PE, Iotek 4200, Iotek 7030. This tendency is opposite to that for the cloud point curve. Therefore, the liquid±liquid phase separation region is smallest for the PE±DPE
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system and increases in size for Iotek 4200 and Iotek 7030. According to Flory's equilibrium theory, the melting temperature of a copolymer, Tm, relative to that of the homopolymer, Tm0 , can be expressed as 1 1 R ln p (2) ÿ ÿ Tm Tm0 HuM where HuM is the enthalpy of fusion per repeating unit and p is the probability that a randomly selected crystallization unit will be succeeded by another such unit [42,43]. For a random copolymer, p is less than unity, which results in a melting point depression. Although the Tc in Fig. 1 are dynamic data and not equal to the equilibrium melting temperature Tm, the tendency for Tm is similar to that for Tc. Therefore, a decrease in Tc in the order PE, Iotek 4200, Iotek 7030 can be explained by the decrease in p due to an increase in the amorphous acrylic acid content. The effect of the cooling rate on Tc for the Iotek 7030±DPE system is also shown in Fig. 1. The cooling rate had a signi®cant effect on Tc: Tc decreased as the cooling rate increased. However, the cloud points were independent of the cooling rate within the range 2.5 to 40 K/min. Fig. 2 shows the relationship between the degree of crystallinity of the polymer±diluent sample and the polymer weight fraction for the three polymers. The
Fig. 2. Relations between the degree of crystallinity of the polymer±diluent sample and polymer weight fractions for (*) Iotek 7030, (~) Iotek 4200, (&) PE.
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degree of crystallinity was evaluated from the enthalpy of fusion by taking the enthalpy of fusion of the perfect polyethylene crystal to be 69 kcal/g at Tm0 and heat capacity difference between liquid and crystal, Cp of 0.0713 cal/(gK) [43,44]. Crystallinity decreases in the order PE, Iotek 4200, Iotek 7030 because crystallization is less likely to occur as the amorphous acrylic acid content increases. For all the three systems, crystallinity is nearly constant up to a certain polymer weight fraction in the polymer±diluent blend and then decreases with increasing polymer weight fraction. This downturn for each system occurs roughly at the respective polymer weight fraction corresponding to the monotectic point, which is the intersection of the cloud point curve and Tc curve in Fig. 1. When polymer±diluent samples with a polymer concentration less than the monotectic point are cooled below Tc, the polymer weight fraction in the polymer-rich phase generated after the liquid±liquid phase separation is equal to the monotectic values for all samples, regardless of the initial polymer weight fractions. Because crystallization occurs almost entirely in the polymer-rich phase, crystallinity is almost constant in this region. On the other hand, when the initial polymer weight fraction is greater than the monotectic value, crystallization occurs prior to the liquid±liquid phase separation. In this situation, the polymer weight fraction in the crystallizing solution depends on the initial polymer concentration. It is well known that crystallization from dilute solution enhances crystallinity [45]. Therefore, the decrease in crystallinity with increasing polymer weight fraction shown in Fig. 2 is reasonable. Fig. 3 shows cross-sections of membranes formed at a cooling rate of 10 K/min and with varying initial weight fractions of Iotek 7030. Because the monotectic point in this system exists between 50 and 60 wt% polymer as shown in Fig. 1, liquid±liquid TIPS occurs prior to crystallization in the case of 10 to 40 wt%. On the other hand, the crystallization occurs ®rst in the case of 60 wt%. In the 10 and 30 wt% samples, spherical pores are well connected so that these structures are suitable for membrane separation applications. In the 40 and 60 wt% samples, the spherical pores are isolated so that the membranes are not suitable for membrane separation applications. The decrease in pore size with increasing polymer content from 10 to 30 to 40 wt% is due to two
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Fig. 3. Micrographs of the cross-sections of Iotek 7030 membranes. Cooling rate10 K/min. Polymer concentration(a) 10 wt%; (b) 30 wt%; (c) 40 wt%; (d) 60 wt%.
factors. Firstly, as the polymer concentration increases, there is less time for coarsening of droplets due to the shorter time interval while going from the binodal to Tc as shown in Fig. 1. Secondly, coarsening of the droplets is slower for higher polymer concentrations due to the higher viscosity of the polymer-rich matrix phase and the smaller polymer-lean droplet phase volume fraction. The porosity in the 40 wt% sample is smaller than in the 10 and 30 wt% samples. This can be explained by the smaller volume fraction of polymer-lean phase in the 40 wt% sample (see the phase diagram in Fig. 1). Despite the fact that the 60 wt% sample underwent solid±liquid TIPS prior to droplet formation, no spherulites were detected. The amorphous acrylic acid in the copolymer may have prevented the formation of visible spherulites. Fig. 4 shows the membrane structures when PE homopolymer was used. Well-connected pores were obtained in the 10 wt% sample. The mean pore size is larger than that of the 10 wt% co-polymer sample in Fig. 3. The higher melt index for PE shown in Table 1
corresponds to a lower viscosity of the polymer solution, which enhances coarsening of the droplets. The monotectic point exists between 40 and 50 wt% for PE. As expected in the 50 wt% sample, crystallization occurred prior to the liquid±liquid separation and spherulites were formed [46]. The structures of the Iotek 4200 membranes are shown in Fig. 5. The pores in the 20 wt% sample are well-connected and the mean pore size is similar to those of the 10 and 30 wt% samples of Iotek 7030. The pores in the 30 wt% samples of Iotek 4200 are smaller and the pores are less connected than in the 30 wt% sample of Iotek 7030. The smaller pore size is probably attributable to the shorter time for coarsening of the droplets due to the smaller area between the binodal and Tc curve shown in Fig. 1. The relative isolation of the Iotek 4200 pores can be explained by the smaller droplet phase volume fraction upon phase separation, as given by the lever rule at Tc in the phase diagram. The effect of the cooling rate on membrane structure is shown in Fig. 6 for Iotek 7030. The morphol-
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Fig. 4. Micrographs of cross-sections of PE membranes. Cooling rate10 K/min. Polymer concentration(a) 10 wt%; (b) 30 wt%; (c) 40 wt%; (d) 50 wt%.
Fig. 5. Micrographs of cross-sections of Iotek 4200 membranes. Cooling rate10 K/min. Polymer concentration(a) 20 wt%; (b) 30 wt%; (c) 40 wt%; (d) 60 wt%.
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Fig. 6. Effect of cooling rate on Iotek 7030 membrane structures. Polymer weight fraction 20 wt%. Cooling rate (a) 2.5 K/min; (b) 10 K/ min; (c) 100 K/min; (d) quenched in water.
Fig. 7. Micrographs of the whole cross-sections of Iotek 4200 membranes. Polymer weight fraction20 wt%. Evaporation time(a) 0 min; (b) 1 min; (c) 2 min; (d) 3 min.
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Fig. 8. Detail structures at the top and bottom surfaces of Iotek 4200 membrane. (a) evaporation time0, (b) evaporation time1 min, (c) evaporation time2 min, (d) evaporation time3 min.
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ogy that was obtained when the melt-blended sample between two cover slips was directly quenched in water at 298.2 K is also included in this ®gure. This quenching technique induces faster cooling than 100 K/min. As the cooling rate was increased, the pore size decreased, a tendency which agrees with results previously reported [47]. The connectivity of pores also became more extensive with an increase in cooling rate. Mostly isotropic structures have been produced by TIPS process so far; that is, the pore sizes do not vary with the position in the membrane. However, anisotropic and asymmetric membranes are highly desirable for some MF and UF applications [3]. In this work, anisotropic and asymmetric membranes were produced by introducing a polymer concentration gradient in the melted polymer solution prior to phase separation. As explained above, smaller pores are expected in the high polymer concentration region, while larger pores are expected in the lower polymer concentration region. Fig. 7 shows whole membrane cross-sections when the melted polymer solutions were allowed to evaporate from one side (air-facing surface) before cooling. In all micrographs, the right side corresponds to the air-facing top surface, while the left side corresponds to the glass-facing bottom surface. Fig. 8 shows the corresponding cross-sections near the top and bottom surfaces at a higher magni®cation. In the case of no evaporation, an almost isotropic membrane was obtained (Fig. 7 (a) and Fig. 8 (a)). On the other hand, upon evaporation, the pore sizes at the top surface clearly became smaller and a skin layer was formed, while the pore sizes at the bottom surfaces did not change for up to 3 min of evaporation. As the evaporation time was increased, the pore sizes at the top surface decreased and the pores were more isolated due to the increase in polymer concentration. The experimental result that the pore sizes at the bottom surface did not change for up to 3 min of evaporation indicates that the polymer concentration at the bottom surface essentially remained constant during evaporation. The existence of such a polymer concentration gradient was con®rmed by the simulation of the evaporation process for the iPP±DPE system, where similar changes in the mean pore sizes at both surfaces were observed [37].
4. Conclusion Hydrophilic microporous membranes were prepared from two ethylene±acrylic acid co-polymers (zinc salt) with different co-unit contents via the TIPS process. Polyethylene homopolymer was used in this work as a reference. The hydrophilicity of these copolymers was con®rmed by the contact angle measurements. Dynamic phase diagrams for these three polymer± diluent systems were determined. As the acrylic acid content in the co-polymer increased, the cloud point curve shifted to higher temperatures, while the crystallization curve shifted to lower temperatures. This created a larger liquid±liquid phase separation region and in¯uenced the membrane morphology. The degree of crystallinity decreased with increasing acrylic acid content in the co-polymers. The effects of the initial polymer concentration and cooling rate on the membrane structures were investigated. For hydrophilic polymers, well-connected pore structures were obtained when the initial polymer concentration was low. The pore sizes decreased with the increase of both the polymer concentration and the cooling rate. No spherulites were detected in the copolymer membranes, probably because the amorphous acrylic acid in the co-polymers prevents spherulites from growing. Spherulites were observed in membranes formed from solutions with high polyethylene concentrations. Asymmetric structures with smaller pores and a skin layer at the top surface were successfully obtained by introducing an evaporation process before the cooling. As the evaporation time was increased, the pore sizes at the top surface decreased, while those at the bottom surface did not change signi®cantly. 5. List of symbols Cp Gmix Hu HuM p
heat capacity difference between liquid and crystal (cal/(gK)) Gibbs free energy of mixing (J) enthalpy of fusion (J/g) enthalpy of fusion per repeating unit (J/ mol) probability that a randomly selected crystallization unit is succeeded by another such unit
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R T Tc Tm Tm0 xd xp d p
gas constant (J/(mol K)) temperature (K) crystallization temperature (K) melting temperature of copolymer (K) melting temperature of homopolymer (K) number of lattice sites occupied by a diluent molecule number of lattice sites occupied by a polymer molecule Flory±Huggins interaction parameter volume fraction of diluent volume fraction of polymer
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[29] T. Nose, T.V. Tan, Interfacial tension of demixed polystyrene± methylcyclohexane solution, J. Polym. Sci. Polym. Lett. 14 (1976) 705±712. [30] J.H. Aubert, Structural coarsening of demixed polymer solutions, Macromolecules 23 (1990) 1446±1452. [31] A. Laxminarayan, Polymer membrane formation via thermal inversion, Thesis, Michigan Technical University, 1990. [32] J. Lal, R. Bansil, Light-scattering study of kinetics of spinodal decomposition in a polymer solution, Macromolecules 24 (1991) 290±297. [33] S.-W. Song, J.M. Torkelson, Coarsening effects on microstructure formation in isopycnic polymer solutions and membranes produced via thermally induced phase separation, Macromolecules 27 (1994) 6389±6397. [34] S.-W. Song, J.M. Torkelson, Coarsening effects on the formation of microporous membranes produced via thermally induced phase separation of polystyene±cyclohexanol solutions, J. Membr. Sci. 98 (1995) 209±222. [35] S.S. Kim, D.R. Lloyd, Microporous membrane formation via thermally-induced phase separation. III. Effect of thermodynamic interactions on the structure of isotactic polypropylene membranes, J. Membr. Sci. 64 (1991) 13±29. [36] H.C. Vadalia, H.K. Lee, A.S. Myerson, K. Levon, Thermally induced phase separation in ternary crystallizable polymer solutions, J. Membr. Sci. 89 (1994) 37±50. [37] H. Matsuyama, S. Berghmans, D.R. Lloyd, Formation of anisotropic membrane structure via thermally induced phase separation, Polymer (1997) in press. [38] D.K. Owens, Estimation of the surface free energy of polymers, J. Appl. Polym. Sci. 13 (1969) 1741±1747.
[39] F.J. Holly, M.F. Refojo, Wettability of hydrogels. I. Poly(2hydroxyethyl methacrylate), J. Biomed. Mater. Res. 9 (1975) 315±326. [40] A.F.M. Barton, CRC Handbook of Solubility Parameters and other Cohesion Parameters, CRC Press, Boca Raton, FL, 1983. [41] D.W. van Krevelen, Properties of Polymers, 3rd ed, Elsevier, New York, 1990. [42] P.J. Flory, Thermodynamics of crystallization in high polymers. IV. A theory of crystalline states and fusion in polymers, co-polymers and their mixtures with diluents, J. Chem. Phys. 17 (1949) 223±240. [43] R. Alamo, R. Domszy, L. Mandelkern, Thermodynamic and structural properties of co-polymers of ethylene, J. Phys. Chem. 88 (1984) 6587±6595. [44] P.J. Flory, A. Vrij, Melting points of linear-chain homologs. The normal paraffin hydrocarbons, J. Am. Chem. Soc. 85 (1963) 3548±3553. [45] R.C. Domszy, R. Alamo, C.O. Edwards, L. Mandelkern, Thermoreversible gelation and crystallization of homopolymers and co-polymers, Macromolecules 19 (1986) 310± 325. [46] W. Li, Y. Yuan, I Cabasso, Formation and microstructure of polyethylene microporous membranes through thermally induced phase separation, Chin. J. Polym. Sci. 13 (1995) 7±19. [47] S. Berghmans, H. Berghmans, H.E.H. Meijer, Spinning of hollow porous fibres via the TIPS mechanism, J. Membr. Sci. 116 (1986) 171±189.
Formation of hydrophilic microporous membranes via thermally induced phase separation Hideto Matsuyama, Stephane Berghmans, Douglas R. Lloyd* Department of Chemical Engineering, Center for Polymer Research, The University of Texas at Austin, Austin, TX 78712, USA Received 1 August 1997; received in revised form 2 December 1997; accepted 4 December 1997
Abstract Hydrophilic microporous membranes were produced via the TIPS process using two hydrophilic ethylene±acrylic acid copolymers (zinc salt) with different co-unit contents. These co-polymers were con®rmed to be hydrophilic by contact angle measurements. Low density polyethylene homopolymer was also used in this work as a reference to investigate the effect of polymer properties on the membrane structures. First, dynamic phase diagrams for these three polymer systems were determined. The cloud point curves shifted to higher temperatures and the crystallization temperature curves shifted to lower temperatures as the acrylic acid content of the co-polymer increased. The membrane structures were investigated and related to the initial polymer concentration and cooling rate. Increasing either the polymer concentration or the cooling rate decreased the pore size. Furthermore, structures with smaller pores and a skin layer at the top surface were obtained by introducing an evaporation process before the cooling to generate a polymer concentration gradient in the melted polymer solution. # 1998 Elsevier Science B.V. Keywords: Thermally induced phase separation; Microporous membranes; Hydrophilic membranes; Ethylene acrylic acid copolymer; Polyethylene
1. Introduction Many micro®ltration (MF) and ultra®ltration (UF) membranes are made from hydrophobic polymers such as polypropylene (PP), polyethylene (PE), poly(vinylidene ¯uoride), and polysulfone. These so-called engineering plastics or commodity plastics are suitable for sterilization with hot water for use in the food, medical, and biological industries [1]. However, hydrophobic membranes have a disadvantage in that *Corresponding author. Fax: +1 512 471 9643; e-mail: [email protected] 0376-7388/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved. PII S0376-7388(97)00330-X
the ¯ux is likely to decline during operation due to solute adsorption and pore blocking [1±3]. This fouling is especially signi®cant in the case of protein separation because hydrophobic interactions between proteins and the membrane surface bring about nonselective irreversible adsorption of proteins on the membrane surface. Moreover, since hydrophobic membranes are non-wettable by water, a pressure gradient is needed in order to pass water through the membrane pores. Thus, hydrophilic microporous membranes are desirable. The surfaces of hydrophobic membranes have been made hydrophilic by physical and chemical post-
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treatment processes. For example, methods of altering surface chemistries include adsorption of surfactant on the membrane surface [4], plasma treatment [5±7], and the surface grafting of hydrophilic species [8,9]. However, instabilities in the treated sections can cause problems in the practical use of the membranes [10]. An alternative way to make stable hydrophilic microporous membranes is to use co-polymers with both hydrophobic and hydrophilic components [10]. Although hydrophilic homopolymer membranes made of polymers such as cellulose acetate, poly(vinyl alcohol), and polyacrylonitrile are low-fouling, they usually do not have good thermal stability or chemical resistance [1]. In order to avoid fouling but still obtain durable membranes, co-polymers with hydrophobic and hydrophilic components must be used. Thermally induced phase separation (TIPS) is a method of making microporous membranes [11± 16]. TIPS is applicable to a wide range of polymers that could not be used in the traditional phase inversion membrane formation due to the solubility problems. However, few studies have reported on the formation of porous membranes from co-polymers via TIPS. Castro ®rst produced microporous membranes from styrene±butadiene co-polymers and ethylene± acrylic acid co-polymer salts [11]. Chung and Lee produced a hydroxylated polypropylene (PP±OH) copolymer and prepared a hydrophilic PP/PP±OH blend membrane [17]. This membrane had good selectivity and ¯ux as well as excellent antifouling properties. In both cases, the preparation method was the TIPS process, although the authors did not refer to it as such. In the TIPS process, a concentration gradient across the nascent membrane results in an anisotropic membrane. Prior and current work in our laboratories [18± 27] plus work conducted elsewhere [12,28±34] has demonstrated that the droplet growth rate in liquid± liquid TIPS is: dependent on the polymer±diluent interfacial tension, increases with increasing volume fraction of the droplet phase and decreases with increasing viscosity of the polymer-rich matrix phase. Smaller cells are obtained when the polymer concentration is higher (that is, lower diluent concentration), whereas larger cells result when the polymer concentration is lower. Thus, inducing a concentration gra-
dient across the thickness of the membrane, by evaporating the diluent from one side of the nascent membrane, prior to phase separation will result in a gradation in structure development kinetics and thus a gradient in cell size across the thickness of the membrane. In this work, hydrophilic microporous membranes were prepared from two ethylene±acrylic acid copolymers (zinc salt) with different co-unit content via the TIPS process. The effects of the initial polymer concentration and cooling rate on the resultant membrane structures were investigated. Polyethylene homopolymer was also used as a membrane material for comparison to the co-polymeric structures. Studies on the effects of various diluents on the TIPS process have been reported already [35,36]. However, as far as we know, the effects of polymer properties on membrane morphology have not yet been studied. 2. Experimental materials and methods 2.1. Materials Two ethylene±acrylic acid co-polymer salts (Iotek 7030 and Iotek 4200, Exxon) and low density polyethylene homopolymer (Aldrich) were used. The properties of these polymers are summarized in Table 1. Iotek 7030 has a higher acrylic acid content than Iotek 4200. The melt index values for all the polymers are similar, which means that they have similar molecular weights. Diphenyl ether (DPE, Aldrich, 99% purity) was used as the diluent without further puri®cation. 2.2. Methods Homogeneous polymer±diluent samples were prepared by a method previously described [35]. Each Table 1 Polymer properties
Melt index (g/10 min) Density (g/cm3) Cation type Acrylic acid content Type of PE
Iotek 7030
Iotek 4200
PE
2.5 0.964 Zn 15 wt% low density
3.0 0.946 Zn 11 wt% low density
7.0 0.918 ± ± low density
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solid sample was chopped into small pieces and placed between a pair of microscope cover slips. To prevent diluent loss by evaporation during TIPS, a Te¯on ®lm of 130 mm thickness with a square opening in the center was inserted between the cover slips. Each sample was heated on a hot stage (Linkam, HFS91) at 453.2 K for 5 min. Then each sample was cooled to 298.2 K at a controlled rate (usually 10 K/min) on the hot stage. The temperature of the stage was manipulated by a Linkam TMS-91 controller. Initial polymer concentrations were varied and for the Iotek 7030 experiments, different cooling rates were used (2.5, 10, and 100 K/min) in order to obtain diverse membrane morphologies. Anisotropic membranes with smaller pores on one surface and larger pores on the other surface were created by a method previously described [37]. Anisotropic (gradation in pore size) and asymmetric (integrally skinned) membranes were produced by inducing a polymer concentration gradient in the membrane solution prior to cooling. After placing the polymer±diluent sample (20 wt% Iotek 4200, initial thickness: about 550 mm) in a glass bottle as previously described [37], the sample was sealed and heated at 433.2 K. The glass cap was then taken off and some diluent was allowed to evaporate from one side, thereby creating a polymer concentration gradient in the sample before cooling. After a certain evaporation period (up to 3 min), the glass cap was replaced and the glass bottle containing the sample was cooled in room temperature air (approximately 298 K). For scanning electron micrograph (SEM) observation, diphenyl ether was extracted from each sample with methanol. The resulting microporous membrane was fractured in liquid nitrogen and mounted vertically on a sample holder. The surface of the sample was coated with gold±palladium using a sputter coater (Commonwealth Model 3, Pelco). A SEM (JEOL, JSN-35 C) with an accelerating voltage of 25 kV was used to examine the membrane cross-sections. Cloud point curves for the three polymer±diluent systems were determined as follows. The sample was sealed with two cover slips as described above and placed on the hot stage. The hot stage was placed on the platform of an optical microscope (Nikon Optiphot 2-POL). The sample was heated to 453.2 K for 5 min to assure homogeneity and cooled at a controlled rate
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of 10 K/min. Cloud points were determined visually by noting the appearance of turbidity under the microscope. A DSC (Perkin Elmer DSC-7) was used to determine the crystallization temperature (Tc) for the dynamic phase diagram. A 3 to 5 mg sample was sealed in an aluminum DSC pan, melted at 473.2 K for 5 min and then cooled at a controlled rate of 10 K/ min to 298.2 K (for Iotek 7030, different cooling rates were used in order to observe their effect on the crystallization temperature). After keeping the sample at 298.2 K for 5 min, the sample was reheated at the same rate. The onset of the exothermic peak during the cooling was taken as the crystallization temperature. The enthalpy of fusion Hu was determined from the endothermic peak area during heating. The contact angle of water on surfaces of Iotek 7030, Iotek 4200, and polyethylene homopolymer was measured with a contact angle meter (Rame-Hart, Contact Angle Goniometer) at room temperature. The contact angles were measured by two methods. Method A involved placing a 1 ml water droplet on the surface of the polymer and method B involved placing a 3 ml water droplet on the surface and then removing 2 ml. Method A gives the contact angle between water and the dry polymer. Method B gives the contact angle between water and the polymer after it has been wetted. 3. Results and discussion Table 2 shows the contact angle data for the three polymers. For low density polyethylene (PE), the contact angle measured by method A (958) was nearly equal to that measured by method B (948) and these values are in agreement with the literature [38]. For Iotek 7030, the advancing contact angle measured by method A (738) was lower than that of PE because of the presence of hydrophilic acrylic acid in the coTable 2 Measured contact angles (degrees)
PE Iotek 7030 Iotek 4200
Method A
Method B
950 732 751
941 323 341
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polymer. The receding contact angle determined by method B (328) was much lower than that measured by method A. Holly and Refojo also observed advancing angles greater than receding angles while studying the wettability of poly(2-hydroxyethylmethacrylate) [39]. This behavior was attributed to structural changes in the polymer. That is, the hydrophilic groups were buried in the polymer when the surface was exposed to air, but they were able to reorient quickly in a water environment and appeared at the polymer±water interface. The low contact angle obtained by method B for Iotek 7030 may be explained by such a reorientation of the hydrophilic acrylic acid parts of the co-polymers. In practical operation, micro®ltration or ultra®ltration membranes are usually wetted by the water being treated. Therefore, the receding contact angle determined by method B is of greater signi®cance. This data indicates that Iotek 7030 is certainly a hydrophilic polymer. The contact angles measured by both methods for Iotek 4200 were approximately the same as those for Iotek 7030, indicating that the difference in acrylic acid content was not suf®cient to signi®cantly alter the hydrophilic nature of the polymers. Fig. 1 shows the dynamic phase diagrams of the three polymer±diluent systems. These are typical phase diagrams for semi-crystalline polymers with liquid±liquid phase separation occurring below the cloud point curve and solid±liquid phase separation occurring below Tc. The cloud point curve shifts to higher temperatures as the acrylic acid content increases in the order PE, Iotek 4200, Iotek 7030. The shift in the location of the cloud point curve (which represents the binodal curve) can be explained in terms of the polymer±diluent compatibility. The shape and location of the binodal can be calculated from the Gibbs free energy of mixing Gmix based on the Flory±Huggins lattice model. p Gmix d ln d ln p d p (1) RT xd xp where d and p are the volume fractions of the diluent and polymer, respectively, xd and xp are the numbers of lattice sites occupied by the diluent molecules and polymer molecules and is the Flory±Huggins interaction parameter. As becomes more positive (that is, the polymer±diluent system becomes less compatible), the binodal shifts to higher temperatures at a ®xed polymer concentration [16]. The interaction
Fig. 1. Dynamic phase diagrams of three polymer±diluent systems. Cooling rates in all cases were 10 K/min except for (5) and (}). Cloud point curve of (*) Iotek 7030-DPE, (~) Iotek 4200-DPE, (&) PE±DPE. Crystallization curve of (*) Iotek 7030-DPE, (~) Iotek 4200-DPE, (&) PE±DPE, (5) Iotek 7030-DPE at 2.5 K/min cooling rate, (}) Iotek 7030-DPE at 40 K/min cooling rate.
parameter has been related to the difference between the solubility parameters of the polymer and the diluent. The solubility parameters of polyethylene and diphenyl ether (DPE) were reported as 17.6 and 20.7 MPa1/2, respectively [40]. The solubility parameter of poly(acrylic acid) is estimated as 24.6 MPa1/2 by the group contribution method [41]. Because the acrylic acid units in the co-polymers are zinc salt and therefore more polar than normal acrylic acid units, the solubility parameter of the acrylic acid component in this co-polymer is expected to be larger than 24.6 MPa1/2. As the acrylic acid content in the copolymer increased from PE to Iotek 4200 to Iotek 7030, the solubility parameter of the polymer increased. Therefore, the polymer±diluent system becomes less compatible as the acrylic acid content in the polymer increases. This is why the cloud point curves shift to higher temperatures in the order PE, Iotek 4200, Iotek 7030, as shown in Fig. 1. The crystallization curves in the dynamic phase diagrams shifted to lower values in the order PE, Iotek 4200, Iotek 7030. This tendency is opposite to that for the cloud point curve. Therefore, the liquid±liquid phase separation region is smallest for the PE±DPE
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system and increases in size for Iotek 4200 and Iotek 7030. According to Flory's equilibrium theory, the melting temperature of a copolymer, Tm, relative to that of the homopolymer, Tm0 , can be expressed as 1 1 R ln p (2) ÿ ÿ Tm Tm0 HuM where HuM is the enthalpy of fusion per repeating unit and p is the probability that a randomly selected crystallization unit will be succeeded by another such unit [42,43]. For a random copolymer, p is less than unity, which results in a melting point depression. Although the Tc in Fig. 1 are dynamic data and not equal to the equilibrium melting temperature Tm, the tendency for Tm is similar to that for Tc. Therefore, a decrease in Tc in the order PE, Iotek 4200, Iotek 7030 can be explained by the decrease in p due to an increase in the amorphous acrylic acid content. The effect of the cooling rate on Tc for the Iotek 7030±DPE system is also shown in Fig. 1. The cooling rate had a signi®cant effect on Tc: Tc decreased as the cooling rate increased. However, the cloud points were independent of the cooling rate within the range 2.5 to 40 K/min. Fig. 2 shows the relationship between the degree of crystallinity of the polymer±diluent sample and the polymer weight fraction for the three polymers. The
Fig. 2. Relations between the degree of crystallinity of the polymer±diluent sample and polymer weight fractions for (*) Iotek 7030, (~) Iotek 4200, (&) PE.
217
degree of crystallinity was evaluated from the enthalpy of fusion by taking the enthalpy of fusion of the perfect polyethylene crystal to be 69 kcal/g at Tm0 and heat capacity difference between liquid and crystal, Cp of 0.0713 cal/(gK) [43,44]. Crystallinity decreases in the order PE, Iotek 4200, Iotek 7030 because crystallization is less likely to occur as the amorphous acrylic acid content increases. For all the three systems, crystallinity is nearly constant up to a certain polymer weight fraction in the polymer±diluent blend and then decreases with increasing polymer weight fraction. This downturn for each system occurs roughly at the respective polymer weight fraction corresponding to the monotectic point, which is the intersection of the cloud point curve and Tc curve in Fig. 1. When polymer±diluent samples with a polymer concentration less than the monotectic point are cooled below Tc, the polymer weight fraction in the polymer-rich phase generated after the liquid±liquid phase separation is equal to the monotectic values for all samples, regardless of the initial polymer weight fractions. Because crystallization occurs almost entirely in the polymer-rich phase, crystallinity is almost constant in this region. On the other hand, when the initial polymer weight fraction is greater than the monotectic value, crystallization occurs prior to the liquid±liquid phase separation. In this situation, the polymer weight fraction in the crystallizing solution depends on the initial polymer concentration. It is well known that crystallization from dilute solution enhances crystallinity [45]. Therefore, the decrease in crystallinity with increasing polymer weight fraction shown in Fig. 2 is reasonable. Fig. 3 shows cross-sections of membranes formed at a cooling rate of 10 K/min and with varying initial weight fractions of Iotek 7030. Because the monotectic point in this system exists between 50 and 60 wt% polymer as shown in Fig. 1, liquid±liquid TIPS occurs prior to crystallization in the case of 10 to 40 wt%. On the other hand, the crystallization occurs ®rst in the case of 60 wt%. In the 10 and 30 wt% samples, spherical pores are well connected so that these structures are suitable for membrane separation applications. In the 40 and 60 wt% samples, the spherical pores are isolated so that the membranes are not suitable for membrane separation applications. The decrease in pore size with increasing polymer content from 10 to 30 to 40 wt% is due to two
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Fig. 3. Micrographs of the cross-sections of Iotek 7030 membranes. Cooling rate10 K/min. Polymer concentration(a) 10 wt%; (b) 30 wt%; (c) 40 wt%; (d) 60 wt%.
factors. Firstly, as the polymer concentration increases, there is less time for coarsening of droplets due to the shorter time interval while going from the binodal to Tc as shown in Fig. 1. Secondly, coarsening of the droplets is slower for higher polymer concentrations due to the higher viscosity of the polymer-rich matrix phase and the smaller polymer-lean droplet phase volume fraction. The porosity in the 40 wt% sample is smaller than in the 10 and 30 wt% samples. This can be explained by the smaller volume fraction of polymer-lean phase in the 40 wt% sample (see the phase diagram in Fig. 1). Despite the fact that the 60 wt% sample underwent solid±liquid TIPS prior to droplet formation, no spherulites were detected. The amorphous acrylic acid in the copolymer may have prevented the formation of visible spherulites. Fig. 4 shows the membrane structures when PE homopolymer was used. Well-connected pores were obtained in the 10 wt% sample. The mean pore size is larger than that of the 10 wt% co-polymer sample in Fig. 3. The higher melt index for PE shown in Table 1
corresponds to a lower viscosity of the polymer solution, which enhances coarsening of the droplets. The monotectic point exists between 40 and 50 wt% for PE. As expected in the 50 wt% sample, crystallization occurred prior to the liquid±liquid separation and spherulites were formed [46]. The structures of the Iotek 4200 membranes are shown in Fig. 5. The pores in the 20 wt% sample are well-connected and the mean pore size is similar to those of the 10 and 30 wt% samples of Iotek 7030. The pores in the 30 wt% samples of Iotek 4200 are smaller and the pores are less connected than in the 30 wt% sample of Iotek 7030. The smaller pore size is probably attributable to the shorter time for coarsening of the droplets due to the smaller area between the binodal and Tc curve shown in Fig. 1. The relative isolation of the Iotek 4200 pores can be explained by the smaller droplet phase volume fraction upon phase separation, as given by the lever rule at Tc in the phase diagram. The effect of the cooling rate on membrane structure is shown in Fig. 6 for Iotek 7030. The morphol-
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Fig. 4. Micrographs of cross-sections of PE membranes. Cooling rate10 K/min. Polymer concentration(a) 10 wt%; (b) 30 wt%; (c) 40 wt%; (d) 50 wt%.
Fig. 5. Micrographs of cross-sections of Iotek 4200 membranes. Cooling rate10 K/min. Polymer concentration(a) 20 wt%; (b) 30 wt%; (c) 40 wt%; (d) 60 wt%.
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Fig. 6. Effect of cooling rate on Iotek 7030 membrane structures. Polymer weight fraction 20 wt%. Cooling rate (a) 2.5 K/min; (b) 10 K/ min; (c) 100 K/min; (d) quenched in water.
Fig. 7. Micrographs of the whole cross-sections of Iotek 4200 membranes. Polymer weight fraction20 wt%. Evaporation time(a) 0 min; (b) 1 min; (c) 2 min; (d) 3 min.
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Fig. 8. Detail structures at the top and bottom surfaces of Iotek 4200 membrane. (a) evaporation time0, (b) evaporation time1 min, (c) evaporation time2 min, (d) evaporation time3 min.
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ogy that was obtained when the melt-blended sample between two cover slips was directly quenched in water at 298.2 K is also included in this ®gure. This quenching technique induces faster cooling than 100 K/min. As the cooling rate was increased, the pore size decreased, a tendency which agrees with results previously reported [47]. The connectivity of pores also became more extensive with an increase in cooling rate. Mostly isotropic structures have been produced by TIPS process so far; that is, the pore sizes do not vary with the position in the membrane. However, anisotropic and asymmetric membranes are highly desirable for some MF and UF applications [3]. In this work, anisotropic and asymmetric membranes were produced by introducing a polymer concentration gradient in the melted polymer solution prior to phase separation. As explained above, smaller pores are expected in the high polymer concentration region, while larger pores are expected in the lower polymer concentration region. Fig. 7 shows whole membrane cross-sections when the melted polymer solutions were allowed to evaporate from one side (air-facing surface) before cooling. In all micrographs, the right side corresponds to the air-facing top surface, while the left side corresponds to the glass-facing bottom surface. Fig. 8 shows the corresponding cross-sections near the top and bottom surfaces at a higher magni®cation. In the case of no evaporation, an almost isotropic membrane was obtained (Fig. 7 (a) and Fig. 8 (a)). On the other hand, upon evaporation, the pore sizes at the top surface clearly became smaller and a skin layer was formed, while the pore sizes at the bottom surfaces did not change for up to 3 min of evaporation. As the evaporation time was increased, the pore sizes at the top surface decreased and the pores were more isolated due to the increase in polymer concentration. The experimental result that the pore sizes at the bottom surface did not change for up to 3 min of evaporation indicates that the polymer concentration at the bottom surface essentially remained constant during evaporation. The existence of such a polymer concentration gradient was con®rmed by the simulation of the evaporation process for the iPP±DPE system, where similar changes in the mean pore sizes at both surfaces were observed [37].
4. Conclusion Hydrophilic microporous membranes were prepared from two ethylene±acrylic acid co-polymers (zinc salt) with different co-unit contents via the TIPS process. Polyethylene homopolymer was used in this work as a reference. The hydrophilicity of these copolymers was con®rmed by the contact angle measurements. Dynamic phase diagrams for these three polymer± diluent systems were determined. As the acrylic acid content in the co-polymer increased, the cloud point curve shifted to higher temperatures, while the crystallization curve shifted to lower temperatures. This created a larger liquid±liquid phase separation region and in¯uenced the membrane morphology. The degree of crystallinity decreased with increasing acrylic acid content in the co-polymers. The effects of the initial polymer concentration and cooling rate on the membrane structures were investigated. For hydrophilic polymers, well-connected pore structures were obtained when the initial polymer concentration was low. The pore sizes decreased with the increase of both the polymer concentration and the cooling rate. No spherulites were detected in the copolymer membranes, probably because the amorphous acrylic acid in the co-polymers prevents spherulites from growing. Spherulites were observed in membranes formed from solutions with high polyethylene concentrations. Asymmetric structures with smaller pores and a skin layer at the top surface were successfully obtained by introducing an evaporation process before the cooling. As the evaporation time was increased, the pore sizes at the top surface decreased, while those at the bottom surface did not change signi®cantly. 5. List of symbols Cp Gmix Hu HuM p
heat capacity difference between liquid and crystal (cal/(gK)) Gibbs free energy of mixing (J) enthalpy of fusion (J/g) enthalpy of fusion per repeating unit (J/ mol) probability that a randomly selected crystallization unit is succeeded by another such unit
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R T Tc Tm Tm0 xd xp d p
gas constant (J/(mol K)) temperature (K) crystallization temperature (K) melting temperature of copolymer (K) melting temperature of homopolymer (K) number of lattice sites occupied by a diluent molecule number of lattice sites occupied by a polymer molecule Flory±Huggins interaction parameter volume fraction of diluent volume fraction of polymer
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