Ind. Eng. Chem. Prod. Res. Dev. 1984, 23,501-508
501
Effect of Shrinkage on Pore Size and Pore Size Distribution of Different Cellulosic Reverse Osmosis Membranes Thanh D. Nguyen, Kam Chan, Takeshl Matsuura, and S. SourIraJan' Dlvlsion of ChemIStv, National Research Council of Canada, Ottawa, Ontario K1A OR9, Canada
The average pore size and pore size distribution on the surface of membranes made from cellulose and different cellulose acetate materials, and obtained by shrinkage in hot water at different temperatures, were determined on the basis of the surface force-pore flow model for reverse osmosis transport. I t was found that the two Gaussian normal distributionsmodel applled to the pore size distributions of membranes involved in this study. From data on the change in pore radius at different Shrinkage temperatures, the relative variations in the free energy changes involved could be quantitatlvely ascertained as a function of the pore radius and the acetyl content of the membrane material; such variations could be further related to the regularity in the macromolecular structure of the cellulosic membrane materials used.
Introduction The control of the average pore size and the pore size distribution on the membrane surface in the membrane formation process has a major effect on the performance data of the membrane produced, such as pure water permeation rate, product rate, solute separation, fractionation of different solutes, and membrane fouling in the RO/UF processes (Chan et al., 1982,1984a, 1984b; Liu et al., 1984; Matsuura et al., 1984; Matauura and Sourirajan, 1983; Sourirajan and Matauura, 1982; Taketani et al, 1983). In view of its importance, the changes of the average pore size and the pore size distribution during the shrinkage process of cellulose acetate (CA-398) membranes and also during the solvent evaporation process of aromatic polyamidohydrazide membranes were studied in our earlier work (Chan et al., 1984a,b) by determining the average pore sue and the pore size distribution of membranes on the basis of the surface force-pore flow model for reverse osmosis transport. Such studies have given rise to a concept of bimodal pore size distribution. According to this concept, two Gaussian normal distributions of pores are produced on the surface (skin) layer of the untreated membranes (untreated membranes are defined as those formed immediately before the shrinkage process in the case of cellulose acetate membranes and those formed immediately before the solvent evaporation process in the case of aromatic polyamidohydrazidemembranes). The existence of such bimodal pore size distribution is consistent with the existence of two kinds of pores on the membrane surface, namely the polymer network pores and the polymer aggregate pores;the former kind arises from the spaces among the polymer segments constituting the polymer network in each supermolecular polymer aggregate in the film casting solution, and the latter kind arises from the spaces among the neighboring such supermolecular polymer aggregates themselves (Sourirajan, 1983). The aggregate pore is larger than the network pore, and it accounts for less than a few percent of the total number of pores, while the network pore constitutes the majority of pores. Further, it has been shown (Chan et al., 1984a,b) that a free energy barrier which is associated with the entropy decrease accompanying the realignment of the polymer network in a higher order should be overcome when aggregate pores are transformed to network pores. According to our view, therefore, the shrinkage as well as the evaporation processes constitute a process of heat 0198-432116411223-0501$01.50/0
energy input, whereby a sufficient energy is supplied to the polymer material to overcome the above energy barrier, thus enabling the transition of aggregate pores into network pores. Whereas by solvent evaporation the entire aggregate pores may turn into network pores, it is hard to eliminate the aggregate pores entirely by shrinkage process only. Probably, this is due to the higher mobility of polymer segments in the presence of solvent liquid. As a result of the transition of a portion of aggregate pores into network pores, a reduction of the average pore size takes place during the shrinkage as well as the solvent evaporation processes. In this work, the average pore size and pore size distribution on the surface of membranes made from cellulose and different cellulose acetate materials and obtained by shrinkage in hot water at different temperatures have been determined on the basis of the surface force-pore flow model for reverse osmosis transport (Matsuura and Sourirajan, 1981; Matauura et al., 1981). In analogy to the foregoing works the free energy diagram as a function of pore radius is obtained for each cellulosic material. Such free energy diagrams may be expected to depend on the acetyl content of the membrane material. In particular, our attention is focussed on the height and the shape of the energy barrier, since they determine the effectiveness of the shrinkage process. The free energy diagram so obtained is further related to the molecular structure of the polymer repeat unit of cellulose and cellulose acetate materials. In summary the objects of this paper are (1) to determine the pore size distribution of cellulose and cellulose acetate membranes produced by different shrinkage temperatures, (2) to determine the functional relationship of a pore radius of a shrunk membrane to the shrinkage temperature and the pore radius of the corresponding unshrunk membrane from which the former pore originates, (3) to generate a free energy diagram as a function of the pore radius, (4) to obtain an insight into the movement of cellulose and cellulose acetate polymers during the shrinkage process, and (5) to find the relationship between such a movement and the structure of the polymer repeat unit, particularly the regularity of polymer structure.
Experimental Section Liquid Chromatography (LC) Experiments. The liquid chromatograph Model ALC 202 of Waters Associ-
Published 1984 by the American Chemical Society
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Table I. Details of Film Casting Conditions polymers and batches polymer acetone dichloromethane dimethylsulfoxide magnesium perchlorate formamide paraformaldehyde water methanol
CTA 10.0
CA-398 batch 316 batch 18 CA-383 Casting Solution Compositions, wt % 17.0 17.0 17.0 69.2 68.0 73.6
17.0 69.2
1.45
1.45
CA-376
CA-318
CE
15.0 38.9
8.0
9.7
70.5
70.0 6.0
1.5
1.5
36.4 21.5 12.35
13.5
7.9
12.35
14.0
Film Casting Conditions temperature of casting ambient 10 -10 10 solution, "C temperature of casting ambient 30 24 30 atmosphere, "C humidity of casting ambient 50-60 50-60 65 atmosphere, % solvent evaporation time, 0.5 1 4 1 min gelation medium MeOH/H20" ice cold water ice cold water ice cold water Immersion in methyl alcohol for 15 min followed by immersion in water for 1 h at room
ates fitted with a differential refractometer was used in this work. The method of column preparation and the general experimental technique used were the same as those reported earlier (Matsuura et al., 1976). Briefly, solutes were injected into the solvent water stream which flows through a column packed with membrane polymer powder. The particle size was kept in the range 38-53 pm by sieving and the column length was 60 cm. Ten microliters of sample solution (1wt % solute) was injected into the column and retention volume was determined. In the case of heavy water, 10 w t % solution was used as the sample. Eight cyclic ether solutes were used as reference solutes and retention volumes were determined for all reference solutes. Reverse Osmosis Experiments. All the chemicals used for the reference solutes are of reagent grade. Cellulae triacetate (CTA),cellulae acetate materials of acetyl content 39.8% (CA-398),38.3% (CA-383),37.6% (CA-376), and 31.8% (CA-318), and cellulose (CE) were used to produce laboratory made membranes. CTA, CA-398, CA-383, and CA-376 were supplied from Eastman Chemicals, CA-318 was laboratory produced by partial hydrolysis of CA-376, and CE was supplied from Baker Chemicals Co. Details of the casting solution compositions and the film casting conditions used are listed in Table I. The membranes so produced were further shrunk in hot water at temperatures from 60 to 98 "C. The shrinkage temperature ("C) is indicated in the last part of the membrane code in Tables 11, IV, and V. All membranes were subjected to a pressure of 2068 kPag (= 300 psig) for 2 h with pure water as feed to minimize compaction effects. The specifications of all the c l membranes in terms of (DAM/K8)NaCI, A, and k ~ ~ are given in Table 11. These were determined by the Kimura-Sourirajan analysis of experimental data with sodium chloride solution at a feed concentration of 0.06 m (Sourirajan, 1970). The apparatus and the experimental details are the same as reported elsewhere (Kunst and Sourirajan, 1970). All reverse osmosis experiments were carried out at laboratory temperature (23-26 "C) at the operating pressure of 1724 kPag (250 psig) and feed concentrtion of 100 ppm, using a feed flow rate of >400 cm3/min. In each experiment the fraction solute separation, f is defined as
10
ambient
ambient
30
ambient
ambient
65
ambient
ambient
1
1
5
ice cold water ice cold water ice cold water temperature.
Table 11. Membrane SDecifications" product rate X 103, kg/h
(DM/KS) NaCl membranes A X IO7* X sepn, % CTA membranes 3.141 506.1 8.3 48.28 -unshrunk 2.052 262.7 30.6 31.56 -60 1.264 43.8 18.72 -70 53.87 1.020 74.5 14.16 9.561 -77 0.651 85.5 -85 2.824 8.79 CA-398 membranes 9.948 525.2 36.5 148.2 batch 316-unshrunk batch 316-67 2.792 79.6 35.6 12.07 2.114 90.0 27.4 4.916 batch 316-77 batch 316-82 2.120 96.1 26.8 1.684 batch 18-unshrunk 13.63 1380 7.0 206.0 batch 18-77.5 7.127 111.2 32.5 92.5 batch 18-85.0 3.452 55.2 46.8 47.27 2.044 26.1 12.27 batch 18-87.5 71.9 0.964 12.4 1.456 93.2 batch 18-90 CA-383 membranes -60 4.436 98.08 39.5 61.59 60.1 -70 3.690 48.07 48.85 1.424 79.0 18.40 -77 6.808 -80 1.234 80.1 15.83 5.383 86.1 2.86 -82 0.228 0.658 CA-376 membranes 14.1 -unshrunk 5.614 431.9 84.00 39.3 -60 4.356 117.4 61.80 73.4 14.12 27.15 -70 2.056 24.72 80.1 -75 1.992 7.359 88.7 12.42 2.275 -80 0.982 CA-318 membranes 21.8 94.29 -unshrunk 6.116 969.5 3.405 843.7 -60 27.7 53.76 249.1 37.2 46.32 3.047 -63 2.727 193.4 -65 41.6 41.34 -68 54.6 13.90 0.944 29.80 -70 CE membranes 3.6 13.28 0.240 98.14 -unshrunk 0.361 26.64 6.7 5.43 -80 - 98 266.8 0.853 8.4 3.75 Operating pressure, 1724 kPag (= 250 psig); feed NaCl concentration, 0.06 m; k = 22 X lo4 m/s. *Dimension of A, kg-mol H20/(m2s kPa). cDimension of ( D ~ / K S ) N . Cm/s. I,
f = [(ppm of solute in feed) -
(ppm of solute in product)]/(ppm of solute in feed)
Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, No. 3, 1984 503 7--
1
CA-378 MEMBRANES
1
SHRUNK AT 7 0 ' t
99.2
I
I
I
40
PORE RADIUS x 1010,
60
m
transport equations based on the surface force-pore flow model, the procedure for the calculation of solute separation, pure water permeation rate, and product rate which are obtainable by the reverse osmosis experiment, the procedure for the determination of the interaction force constanb from the liquid chromatography data, and the procedure for calculating the average pore size and the pore size distribution on the surface layer of asymmetric reverse osmosis membranes have all been described elsewhere (Matsuura and Sourirajan, 1981; Matsuura et al., 1981; Chan et al., 1982,1984a). For the clarification of symbols used in this paper, however, the framework of the theory is outlined below. The quantities obtainable from reverse osmosis experiments such as solute separation, f , and product rate, (PR), can be calculated when data on (PWP), pore size distribution and interaction force constants are given under the operating conditions of the experiment such as feed concentration, operating pressure, and feed flow rate (Chan et al., 1984a). The pore size distribution is expressed in terms of one or more normal distributions. For describing such pore size distributions the distribution function of the ith distribution, given as
v2 CAP(-
2ai2
]
and a quantity defined as
are necessary, where &, ui,and ni indicate the average pore size, standard deviation, and the number of pores which belong to the ith distribution (Chan et al., 1984a). We also define that Rb,i becomes progressively larger as the number i increases. The integral pore size distribution can be defined on the basis of the pore size distribution given by eq 1 and 2 as
and product rate (PR) and pure water permeation rate (PWP) in kg/h for given area of film surface (13.2 cm2in this work) were determined under the specified experimental conditions. The data on (PR) and (PWP) are corrected to 25 OC using the relative viscosity data for pure water. Reverse osmosis experiments were conducted with respect to sodium chloride and eight reference organic solutes. Concentrations of NaCl were determined by conductivity measurements and those of organic solutes by Beclunan Total Carbon Analyzer Model 915-A. In addition to the data obtained by experiments described above, the data obtained in our previous work (Chan et al., 1984a) from Batch 316 and Batch 18 membrane series, both produced in the laboratory from cellulose acetate material of acetyl content 39.8% (CA-398),were further used in this study. The details of the membrane formation procedure and the membrane specifications of CA-398 membranes are included in Tables I and 11.
Theory Determination of Pore Size Distribution. The
where n(Rb) and nt indicate the number of pores whose radii are less than or equal to R b and the total number of pores, respectively (Chan et al., 1984a). The interaction force constants were introduced, on the other hand, as constants which define the interfacial potential function by $(d) = very large (when d ID) (44 4 ( d ) = -(B/d3) R T
(when d > D)
(4b)
where d is the distance between the polymer surface and the center of the solute molecule, D is a constant associated with the steric hindrance (distance of steric repulsion), and B expresses the nature and magnitude of the van der Waals force. The quantity D is approximated by the Strokes law radius of the solute molecule. The quantity B can be determined from the surface excess r / C A , b which is further obtainable from the retention volume data of LC experiments by the method described earlier (Chan et al., 1984a). The quantity B depends both on the solute and the membrane polymer material, while the quantity D is approximated such that it depends only on the solute. Conversely, one can determine the average pore size and the pore size distribution on the membrane surface by
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obtaining experimental solute separation data with respect to a series of reference organic solutes and from the known intraction force constants for all combinations of reference solutes and membrane polymer materials involved. The procedure involved is also described fully in our previous paper (Chan et al., 1984a). Generation of Free Energy Diagram as Function of Pore Radius. The procedure for generating the profile of free energy changes (free energy diagram) as a function of pore radius is similar to the one established earlier (Chan et al., 1984b). There are three steps involved in the procedure and they are outlined below by using a CA-376 unshrunk membrane (abbreviated as CA-376-unshrunk) and a CA-376 membrane shrunk at 70 "C (abbreviated as CA-376-70) as examples. First, we draw the integral pore size distribution curve defined by eq 3 using Rb,&,ui,and h, determined by the method given in the foregoing section. Such integral distribution curves are given in Figure l a for both CA-376-unshrunk and CA-376-70 membranes. This figure shows that the pore of 60 X 10-lo m radius on the CA-376-unshrunkmembrane, corresponding to point a in the figure, was reduced to the pore of 43 X m radius on the CA-376-70 membrane (point b) after shrinkage at 70 OC on the basis of the following assumptions: (1)the total number of the pore does not change during shrinkage, and (2) the shrinkage process does not alter the order of pore radii. On the above basis, one can produce the correlation of the pore radius on the CA-376-70 membrane, (&)70, vs. that on the CA-376-unshrunk membrane, as illustrated in Figure lb. Further, on the basis of Figure l b the free energy diagram is generated in the following way. Let us first recall our earlier statement that a decrease in pore size results by the energy input, or the work supplied, from outside during shrinkage. In other words, a smaller pore is considered to be at a higher energy level than a larger pore. Then, our task is to assign a definite energy level to a given pore radius. Further, the elevation of energy level accompanying the pore size reduction at temperature Tis some multiple of RT;this is evident from the theoretical calculation made earlier for the case of solvent evaporation process applied for the polyamidohydrazide membrane formation, which showed that the
-
80
I I C -
c
I
I
40r -
I
I 1
I
I
1.
1
100
200
300
400
500
80°C
0
2 n
r
n
100
0
I00
1
CE
-16Oc
ix.
80
1
-
L!.
z
o!,
100
1
200
300
400
500
(Rb), x lo'', m
Figure 2. The pore size of membranes shrunk a t different temperatures vs. the pore size of unshrunk membranes with respect to CTA, CA-398, CA-376, CA-318, and CE membranes.
energy change involved in the pore size reduction from 3 min to 6 min evaporation was RT In (6/3) (Chan et al., 1984b). However, since the shrinkage experiment does not supply any information of the rate process, it is not possible to determine the precise energy input involved in pore size reduction. The energy input made during the reduction of pore radius a t the shrinkage temperature of T is arbitrarily fixed as RT. Fixing the energy input in this manner simply seta an arbitrary scale for the energy level of the pore. For the purpose of producing a free energy diagram, the energy level of the largest pore obtained in
Table 111. Some S u r f a c e Force Parameters Pertinent to Reference Solute a n d Cellulose Acetyl Contents solute CTA CA-398 CA-383 1,3-dioxolane (74.1)" 48.89 45.98 59.61 43.02 42.43 43.14 1.96 1.96 1.96 24.07 trimethylene oxide (58.1)' 9.96 41.46 31.52 1.83 1.83 28.22 9.66 p-dioxane (88.1)" -0 38.61 53.87 -0 2.23 2.23 2.23 tetrahydropyran (86.1)" 32.44 6.36 39.64 67.05 2.38 2.38 51.14 4.24 oxepane (100.2)' 88.25 39.67 2.53 2.53 12-crown-4 (176.2)' -5.57 -0.608 -9.54 -108.3 -449.1 28.68 3.19 3.19 3.19 15-crown-5 (220.3)' -5.64 -7.98 -13.14 -107.8 -321.8 -1509 3.77 3.77 3.77 18-crown-6 (264.3)" -7.08 -5.85 -117.3 -202.6 4.29 4.29 Molecular weight.
Acetate Materials of Different CA-376 41.38 41.43 1.96 9.41 30.88 1.83 1.46 18.65 2.23 5.02
33.72 2.38 -0 16.76 2.53 -9.61 -456 3.19 -13.17 -1498 3.77 -16.93 -2400 4.29
CA-318 36.27 40.14 1.96 5.46 25.16 1.83 12.29 42.00 2.23 9.36 45.57 2.38 10.14 54.86 2.53 -2.54 -4.5 3.19 -13.26 -1561 3.77 -17.94 -2739 4.29
CE 13.92 30.74 1.96 1.40 14.63 1.83 9.83 38.74 2.23 -3.86 -44.13 2.38 0.70 21.92 2.53 -3.04 -15.00 3.19 -5.50 -100.0 3.77 -11.7 -807.8 4.29
Ind. Eng. Chem. Prod. Res. Dev., Vol. 23,No. 3, 1984
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Table IV. Pore Size Distributions of Membranes
CTA membranes -unshrunk -60 -70 -77 -85 CA-398 membranes batch 316unshrunk batch 316-67 batch 316-77 batch 316-82 batch 18unshrunk batch 18-77.5 batch 18-85.0 batch 18-87.5 batch 18-90 CA-383 membranes -60 -70 -77 -80 -82 CA-376 membranes -unshrunk -60 -70 -75 -80 CA-318 membranes -unshrunk’ -60 -63 -65 -68 -70 CE membranes anshrunk -80
0.300 0.450 0.100 0.100 0.050
0.006 0.005 0.003 0.002 0.001
8.7 8.7 8.6 8.3 7.3
0.002 0.002 0.001 0.002 0.001
330 300 110 59 51
10.4
0.002
51
0.196 0.050
9.2 8.4 7.5 10.4
0.002 0.002 0.002 0.002
42 40 36 61
0.196 0.195 0.195 0.160
0.005 0.003 0.001 0.080
8.4 7.3 7.2 7.2
0.004 0.003 0.003 0.002
48 45 44 42
0.147 0.098 0.098 0.098
0.030 0.010 0.005 0.001
9.7 9.1 9.0 8.7 8.5
0.014 0.013 0.009 0.063 0.027
61 51 41
0.155 0.120 0.100
0.006 0.003 0.002 0 0
9.9 9.8 8.8 8.6 8.1
0.004 0.002 0.001 0.001 0.001
51 46 43 42 41
0.120 0.100 0.090 0.070
0.050
0.024 0.011 0.002 0.002 0.001
8.5 8.5 8.3 8.3 8.2 8.1
0.005 0.001 0.001 0.001 0.001 0.001
47 46 44 43 43 41
0.320 0.250 0.250 0.200 0.200 0.070
0.260 0.010 0.007 0.007 0.008 0.006
151 0.009 0.250 0.043 0.190 0.015 121 0.009 -98 7.6 __ 0.005 101 0.160 0.016 “Reconstructed from data of shrunk membranes (Chan et al., 1984a). 8.0 7.6
the unshrunk membrane is arbitrarily fixed as a datum energy level for each cellulosic material. The above means enable us to produce free energy diagrams which can be compared for different cellulosic materials at least on a relative scale at constant shrinkage temperature. The above method, however, prevents the comparison of free energy diagrams at different temperatures on the same energy scale. Therefore, an attempt was made to produce such free energy diagrams at a fixed temperature of 70 “C, except for cellulose material for which shrinkage temperature of 80 “C was used. In order to illustrate the method, we go back to Figure lb, where (Rb),O is plotted vs. According to the figure, (Rb),,of 62 X 1W0m (point A) was reduced to of 48 X m (point B). Setting the free energy level of the pore with (Rb),, = 62 X m as the datum point (point A’ in Figure IC),the energy level of the pore with (Rb)= 48 X 10-lo m is calculated to be R T = (8.3147 X 10-3)(273.2 70) = 2.85 kJ/mol; therefore the point is plotted at (48 X 10-lom, 2.85 kJ/mol)(point B’ in Figure IC).The pore with (Rb) of 48 X m is further reduced to 8.6 X 10-lo m (point C in Figure lb), the energy gain being another 2.85 kJ/mol. This means that the latter pore & (a,),
+
-2
W
0
I
I
0
100
I
I
200 300 (Rb)xldo, m
I
I
400
500
Figure 3. Free energy profiles as a function of pore radius with respect to CTA, CA-398, CA-376, CA-318, and CE membranes at 70 OC (CE membranes at 80 “C). STERIC HINDRANCE
1 CONTRIBUTION
,
CONTRIBUTION
Figure 4. Shift in contributions to the free energy as the regularity of polymer structure increases: -, shift to the higher regularity of the polymer structure.
Figure 5. Shift in free energy diagrams as the regularity of polymer structure increases. Number increases with the regularity in the polymer structure.
possesses the energy level of 5.70 kJ/mol. Therefore, the point is plotted at (8.6 X 10-lo m, 5.70 kJ/mol)(point C’ in Figure IC).We also know from Figure l b that the pore of 58 X m on the unshrunk membrane (point D) was reduced to 37.5 X m (point E in Figure lb), or the pore is drastically reduced to 8.6 X 10-lo m (point F in Figure lb). There is a marked discontinuity between these two points. Going to Figure IC,we can assign 0.85 kJ/mol for the pore of 58 X 10-lo m (point D’ in Figure IC)by interpolation; therefore, both pores of 37.5 X 10-lom and 8.9 X m possess the energy level of 0.85 + 2.85 = 3.70 kJ/mol. They are plotted as point E’ and point F’ in Figure IC. (Actually the interpolation of point D’ is conducted iteratively so that points A’-D’-B’-E’ form a smooth curve). Obviously, these two points cannot be connected, because of the discontinuity between points E and F in Figure lb. It is reasonable to consider that the unfilled region between E’ and F’ corresponds to the potential well of the general free energy diagram presented in Figure 9 of our earlier paper (Chan et al., 1984a). The vertical line F’-C’ corresponds to the potential wall associated with the steric hindrance, and this width determines Rtvl.The curve which connects points E’-B’-D’-A’ constitutes the right shoulder of the free energy barrier associated with the entropy contribution to the free energy curve (also Figure 9 of Chan et al., 1984a).
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Table V. Comparison of Experimental (in Parentheses) a n d Calculated Separations" solute separation, % trimethytetra(PWP) x lene hydromembranes lo3, kg/h 1,3-dioxolane oxide p-dioxane pyran oxepane 12-crown-4 15-crown-5 CTA membranes -unshrunk 49.2 3.3 5.3 5.9 7.5 13.7 19.7 29.5 (10.0) (26.7) (28.9) (1.4) (3.1) (6.6) (8.4) 33.9 5.4 -60 5.9 12.6 11.7 14.8 35.5 40.7 (4.3) (13.6) (9.0) (11.1) (39.3) (36.0) (2.0) 22.7 -70 8.1 6.0 15.7 16.9 21.7 49.2 53.3 (16.1) (19.1) (22.8) (53.7) (56.4) (4.0) (8.1) -77 11.3 16.5 9.1 33.9 29.9 80.1 35.6 86.6 (15.8) (28.0) (31.9) (84.2) (36.4) (85.5) (8.8) -85 24.1 10.1 17.8 45.0 44.3 54.4 86.0 90.6 (28.0) (20.1) (41.7) (43.0) (89.2) (45.8) (90.1) CA-398 membranes batch 316-unshrunk 156.8 0 0 21.5 35.2 (-1.3 1) (-1.31) (26.0) (38.0) 44.0 5.2 batch 316-67 16.1 75.3 86.1 (16.1) (75.3) (88.5) (3.3) batch 316-77 33.3 9.8 21.4 92.3 78.3 (27.2) (91.4) (80.8) (9.4) 33.4 21.0 batch 316-82 38.5 89.2 96.9 (21.0) (38.7) (89.6) (97.3) batch 18-unshrunk batch 18-77.5 112.3 0 11.3 35.5 41.1 (10.2) (33.8) (3.0) (43.9) batch 18-85.0 8.8 54.4 31.5 63.8 65.5 (14.4) (27.0) (59.5) (68.8) batch 18-87.5 32.2 12.0 41.8 76.4 77.1 (20.3) (34.2) (73.4) (82.0) batch 18-90 15.2 13.4 53.1 89.9 92.5 (25.2) (42.2) (88.7) (96.2) CA-383 membranes -60 69.9 4.0 3.5 8.7 10.4 17.2 50.0 65.6 (11.1) (56.9) (16.6) (59.0) (0.1) (2.0) (9.5) 58.8 7.5 -70 8.0 13.6 20.7 74.0 28.6 84.6 (19.4) (28.1) (19.9) (79.3) (81.9) (2.2) (5.5) 21.3 -77 9.1 10.4 31.6 32.2 45.4 93.0 97.9 (30.8) (42.1) (31.2) (93.6) (4.1) (95.5) (9.6) 18.2 -80 9.4 10.7 40.8 48.4 36.4 98.0 100 (14.5) (37.9) (37.4) (99.0) (48.5) (6.6) (100) 13.9 3.3 -82 20.9 39.3 56.6 48.7 100 100 (19.6) (46.1) (45.6) (56.7) (99.4) (9.6) (100) CA-376 membranes -unshrunk 86.2 0.89 1.3 5.9 6.8 8.1 25.9 35.5 (10.6) (30.4) (33.6) (-0.5) (0.8) (3.6) (5.4) 66.4 -60 2.6 2.2 11.3 13.4 19.1 57.8 69.3 (19.8) (11.0) (59.6) (63.7) (0.1) (7.1) (1.8) 31.1 -70 6.1 27.4 8.8 44.7 30.6 90.5 95.5 (25.6) (47.4) (33.5) (92.0) (94.0) (4.7) (9.8) -75 7.3 29.0 31.1 9.6 36.4 54.8 93.8 96.8 (29.1) (36.5) (13.8) (92.4) (52.1) (94.3) (6.4) 11.6 14.5 -80 43.8 16.5 50.3 95.9 67.9 97.7 (13.9) (22.0) (39.6) (47.4) (96.5) (63.1) (97.5) CA-318 membranes -unshrunk 89.8 2.8 6.2 7.9 11.1 13.8 21.7 27.1 (10.5) (19.4) (29.1) (1.3) (3.6) (8.3) (5.9) -60 53.0 4.7 7.6 10.8 18.0 21.0 48.6 60.4 (14.3) (20.2) (24.8) (49.7) (63.7) (9.0) (3.9) 48.1 -63 14.1 5.8 8.9 20.2 57.6 26.5 74.2 (24.7) (18.0) (11.9) (29.6) (59.6) (73.9) (5.5) -65 45.5 8.2 16.4 9.9 22.6 59.6 79.1 31.0 (12.9) (25.2) (17.9) (31.3) (61.9) (76.2) (6.2) -70 17.0 14.4 26.5 15.5 30.4 78.4 40.3 85.2 (11.8) (26.8) (20.0) (37.3) (43.5) (74.6) (86.6) CE membranes -unshrunk 13.8 0.8 3.1 3.2 6.2 9.1 6.8 6.3 (0.6) (1.9) (1.5) (5.1) (4.1) (4.1) (6.9) -80 4.2 5.6 8.0 6.9 17.4 21.7 17.4 17.6 (14.9) (18.6) (12.3) (21.8) (3.3) (6.2) (7.0) -98 3.8 11.3 8.4 5.5 26.4 21.5 21.8 25.7 (7.9) (8.7) (4.5) (17.9) (14.3) (20.0) (22.5) "Solute concentration in feed, 100 ppm; operating pressure, 1724 kPag (= 250 psig); (PR) = (PWP).
18-crown6 34.4 (30.5) 42.4 (42.0) 57.9 (59.1) 88.3 (86.0) 91.6 (90.4) 42.7 (36.0) 90.5 (88.1) 92.4 (91.1) 96.7 (97.2) 46.6 (42.1) 67.8 (67.5) 80.5 (81.3) 92.6 (96.0)
-
-
41.6 (33.6) 77.7 (64.4) 97.6 (94.4) 98.4 (94.7) 98.9 (97.7) 33.9 (30.2) 72.8 (65.4) 87.6 (75.6) 87.9 (78.0) 92.1 (88.3) 9.6 (8.6) 27.3 (26.0) 30.8 (26.8)
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Results and Discussion Liquid Chromatography Experiments. The numerical values r/CA,b, B, and D obtained from LC experiments are all listed in Table I11 with respect to eight reference solutes and six cellulosic materials used in this study. The data on r / C A , b and those on B as well do not show any definitive trend with the increase in the molecular weight of cyclic ethers and the decrease in the acetyl content of cellulosic polymers, except r / C A , b is negative (indicating solutes are rejected from the polymer surface) when their sizes are larger than that of 12-Crown-4molecule. One might suspect that the rejective force working on large reference solutes is due to the size exclusion effect. This can,however, be denied by the pore size distributions of the polymer particles in the LC columns determined in our earlier work (Matsuura et al., 1983), which showed that more than 90% of pores possessed radii greater than 7 X W0m. Reverse Osmosis Experiments. The pore size distributions obtained for membranes made from cellulose and cellulose acetate materials of different acetyl contents shrunk at different temperatures are summarized in Table IV. The solute separation data calculated on the basis of the pore size distribution given in Table IV are listed in Table V together with those experimentally obtained. The agreement of calculated and experimental data is satisfactory, indicating that the transport model and the numerical parameters used in the calculation are practically valid. On the Pore Size Distribution. When Table IV is examined in detail, several features of the pore size distribution data become obvious. They are as follows: (1) The applicable pore size distribution is characterized by two normal distributions. (2) While the first distribution is very narrow, the second distribution is significantly broader. (3) As the shrinkage temperature increases, both R b , l and Rb.2 decrease. (4) As the shrinkage temperature increases, h2 (the ratio of the number of pores in the second distribution to that of pores in the first distribution) decreases. In some cases (CA-383-80 and CA-383-82) h2 becomes zero, indicating the total disappearance of the second normal distribution. The only exception is cellulose membranes for which the second distribution continues to exist. (5) There is some correlation between the average pore radius and the acetyl content. As far as the unshrunk membranes are concerned, value of CTA (8.72 X lo-'' m) increasses to that of CA-398 (10.37 X m) and then gradually decreases to that of CE (7.97 X lo-'' m). Therefore, there is a maximum in R b , l as acetyl content decreases. On the other hand, &,,2 value decreases drasm of CTA to 51 X to 61 X tically from 330 X lo-'' m of CA-398 and remains at about the same level up to CA-318 and finally increases to 151 X m for CE. Therefore, there is a minimum in Rb,2 as the acetyl content decreases. Although numerical values quoted above do not represent the limits for each cellulosic material since the porosity of unshrunk membranes may naturally be expected to depend on the casting procedure, the general tendency may be expected to remain unaltered. The pore radius after the shrinkage, (&,)a, as a function of the initial pore radius before shrinkage, (&,)ut is illustrated in Figure 2 for CTA, CA-398, CA-376, CA-318, and CE materials on the basis of the pore size distribution given in Table IV. The data for CA-383 material were omitted since the pore size distributions of unshrunk membranes were not available. The main features of this graph indicated below are the same as those reported in our earlier paper (Chan et al., 1984a); i.e., regardless of the
acetyl content: (1) At a given temperature there is a moderate decrease in the pore size when the initial pore size on the surface of the unshrunk membrane is large. (2) There is a drastic decrease in the pore size when a threshold pore radius is reached. This corresponds to the transition of a pore belonging to the second distribution to a pore belonging to the first distribution. (3) The pore radius below the threshold value is reduced to an almost constant value. (4) With increase in the shrinkage temperature the moderate decrease of the large initial pore is intensified. ( 5 ) With increase in the shrinkage temperature, the threshold pore radius also increases. (6) With increase in the shrinkage temperature the small pore radius also is reduced. Despite the similarity in the above features, the shape of the graphs depends very much on the acetyl content. The difference is caused mainly by the large Rb.2 values for unshrunk CTA and CE membranes which are ultimately reduced to R b , l , by shrinkage. Thus, CTA and CE materials cover significantly wider ranges of pore radius on the membrane surface than the rest of cellulose acetate materials. The free energy diagrams as functions of R b were further produced on the basis of (Rb),, vs. curves following the method described in the theoretical section. The results corresponding to the shrinkage temperature of 70 "C are illustrated in Figure 3. The data for CE correspond to the shrinkage temperature of 80 "C, however, since data for 70 "C are not available for this material. The general features of the free energy diagrams in Figure 3 are essentially the same as those produced for the polyamidohydrazide membranes reported earlier (Chan et al., 1984b). They resemble the free energy curve presented schematically in Figure 9 of our earlier paper (Chan et al., 1984a), though the part representing the potential well is missing, since the experimental data do not allow the generation of this particular part of the energy diagram. As for the effect of the acetyl content, both CE and CTA materials cover significantly wider range of pore radius than the other cellulose acetate materials studied, reflecting the existence of large pores in the unshrunk membranes of CE and CTA. Particularly, cellulose material demonstrates the highest energy barrier among all cellulosic materials, corresponding to the least susceptibility of the above material to shrinkage. Though CTA material covers an even wider range of pore radius than CE, the energy barrier is not as high as that of CE, resulting in greater susceptibility for shrinkage than CE. With respect to the rest of the polymer materials with intermediate levels of acetyl content, the range of pore radius covered is small and the energy barrier also is low. Therefore, membranes with relatively small pores are easy to produce and they are susceptible to shrinkage in hot water for the latter materials. The above features can be further related to the susceptibility of the cellulosic macromolecules to their regular geometrical close packing. Both cellulose triacetate and cellulose are known to form highly ordered and rigid systems by close packing due to the regularity of their molecular structures, which are often manifested in the higher crystallinity and the greater tensile strength of these materials (Wakeham, 1955). Any partial acetylation reduces such properties significantly because of the increased irregularity. The greater close packing of polymer molecules results in the narrow potential wall associated with the steric hindrance due to closeness of polymer molecules, deeper potential well due to the stronger van der Waals force, and the shift of the entropy contribution to the free energy toward the higher (Rb) region and toward the higher
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free energy region due to the larger entropy decrease accompanying decrease in pore radius even when the radius is large. These shifts in the steric hindrance, van der Waals force and entropy contributions are schematically illustrated in Figure 4. Since such shifts are toward all directions on the two-dimensional illustration, we are able to expect a variety of changes in the shape of the free energy curve. One of such changes is illustrated in Figure 5 as a function of the regularity of the polymer molecule (The increasing order of regularity is indicated by increase in number assigned to the free energy curve.). It is obvious that Figure 5 is entirely consistent with the direction of change given in Figure 4. Furthermore, if we assume the increasing order in regularity of cellulose and cellulose acetate polymer structures as CA-398 = CA-376 = CA-318 C CE C CTA, the parts of free energy curves in Figure 5 indicated by solid lines are consistent wtih the experimentally produced free energy diagrams of Figure 3. A note here is in order on the regularity of cellulose and cellulose acetate polymer structure. The reason for assigning the highest regularity to CTA polymer material is the free energy barrier of the material stretching over the widest range of Rb as shown in Figure 3. The largest pore achievable for a polymer material, which was set as a datum energy point, however, depends on the method of producing the unshrunk membrane. Therefore, it may be possible to bring the largest pore of CTA membrane into m and 200 X 10-l" m by the range between 100 X suitable adjustment of membrane making method. The inflection point observed at 126 X 10-lom of CTA curve in Figure 3 suggests such possibility. Then, the increasing order of molecular regularity changes to CA-398 = CA-376 = CA-318 < CTA < CE. In any case the higher regularity of CTA and CE materials than that of the cellulosic materials in the intermediate range of acetyl content is unaltered.
Conclusion The effectiveness of shrinkage process is closely related to the height of free energy barrier by entropy decrease in polymer realignment. Cellulose material possesses the highest potential barrier due to regularity in macromoleular structure and is least susceptible to shrinkage. Cellulose triacetate material possesses the second largest potential barrier and hence second least susceptibility to shrinkage. This is also due to the high regularity of CTA polymer material. Cellulose acetate materials of intermediate acetyl content are more irregular and the free energy barrier is low, resulting in the formation of small aggregate pores in unshrunk membranes and also in greater susceptibility for shrinkage. Nomenclature A = pure water permeability constant, kg-mol/(m2s kPa) B = constant characterizing the van der Waals attraction force, m3 = bulk solute concentration, mol/m3 d = distance between polymer material surface and the center of the solute molecule, m D = constant characterizing the steric repulsion at the interface, m
( D A M / K 6 ) N , a = transport parameter of reference sodium
chloride in water (treated as a single quantity), m/s f = fraction solute separation based on the feed concentration hi = ratio defined by eq 2 kNGl= mass transfer coefficient for NaCl on the high pressure side of the membrane, m/s ni= number of pores belonging to the ith normal distribution n, = total number of pores on the membrane n(Rb) = number of pores whose radii are less than or equal to Rb (PR)= product rate through given area of membrane surface, kglh (PWP) = pure wate permeation rate through given area of membrane surface, kg/h Rb = pore radius, m R b , i = average pore radius of ith distribution, m R = gas constant T = absolute temperature, K Yi(Rb)= normal pore size distribution function, l / m Greek Letters r = surface excess of the solute, mol/m2 ui= standard deviation of ith normal pore size distribution, m 4 = potential function of interaction force exerted on the solute from the pore wall, J/mol
NO.CTA, 9012-09-3;CA, 9004-35-7; CE, 9004-34-6; 1,3-dioxolane,646-06-0;trimethylene oxide, 503-30-0;p-dioxane, 123-91-1; tetrahydropyran, 142-68-7; oxepane, 592-90-5; 12crown-4,294-93-9;15-crown-5,33100-27-5;l&crown-6,17455-13-9. Literature Cited Chan, K.; Liu, T.; Matsuura, T.; Sourlrajan, S. Ind. Eng. Chem. Prod. Res. Dev. 1984a, 23, 124. Chan, K.; Matsuura, T.; Sourirajan, S. Ind. Eng. Chem. Prod. Res. Dev. 1982, 21, 605. Chan, K.; Matsuura, T.; Sourlrajan, S. Ind. Eng. Chem. Prod. Res. Dev. I984b, accompanying article In thls issue. Kunst, B.; SourIraJan, S. J. Appl. Po!vm. Sci. 1870, 14, 2559. Llu, T.; Chan, K.; Matsuura, T.; Sourirajan, S. Ind. Eng. Chem. Prod. Res. Dev. 1984, 23, 116. Matsuura, T.; Biais, P.; Dlckson, J. M.; Sourirajan, S. J . Appl. Po/ym. Sci. 1978, 20, 1515. Matsuura, T.; Sourirajan, S. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 273. Matsuura, T.; Sourirajan, S. "On the Predlctabillty of RO/UF Performance from Interfacial Interactlon Forces and Membrane Pore Structure", paper presented at the Symposlum on Membrane Processes for Water Reuse and Material Recovery in the AIChE Annual Meetlng (Diamond Jubllee), Oct 30-Nov 4, 1983, Washington, DC. Matsuura, T.; Taketani, Y.; Sourirajan, S. "Synthetic Membranes", Vol. 11, Turbak, A. F., Ed.; ACS Symposlum Series No. 154, 1981; p 315. Matsuura, T.; Taketanl, Y.; Sourlrajao, S. J . ColkM Interface Sd.1983, 95, 10. Matsuura, T.; Tweddle, T. A.; Sourirajan, S. Ind. Eng . Chem. Process Des. Dev. 1984, In press. Sourlrajan, S. "Reverse Osmosis"; Academlc Press: New York. 1970; Chapter 3. Sourlrajan, S. "Lectures on Reverse Osmosis"; Natlonal Research Council of Canada: Ottawa, 1983; Chapter 6. Sourlrajan. S.; Matsuura, T. The Chem. Eng. oct 1982, 359. Taketani, Y.; Matsuura, T.; Sourirajan, S. DesallnaNon 1983, 48, 455. Wakeham. H. "Celluiose and Cellulose Derlvathes", Ott. E.; Spurlln, H. M.; Grafflin, M. W.. Ed.; Part 111; Intersclence: New York, 1955; Chapter X I .
CA,b
Received for review January 16, 1984 Accepted April 26, 1984
Issued as N.R.C. No. 23541.
