Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 419
and Skocek of the Geological Survey, Prague, for providing samples of natural carbonate rocks.
Nomenclature C = concentration of reactant gas within pores, mol/cm3 C, = concentration of reactant gas outside spherical particle, mol/cm* D = diffusion coefficient of reactant gas in pores, cm2/s D , = mean particle size, mm Ds = diffusivitiy of reactant gas through product shell of the grain, cm2/s E ( r ) = function defined by eq 6 ec = porosity of calcined limestone eLs = porosity of natural rock ex = porosity of sulfate-loaded particle F ( r ) = function defined by eq 5 K = chemical reaction rate constant, cm/s M = molecular weight, g/mol R = radial coordinate within spherical particle, cm R, = radius of spherical particle, cm r = radius of reaction interface within spherical grain, cm r = radius of grain, cm 9 = sorption capacity of calcine, g of SO,/^ of calcine t = time of exposure of solid to gas, s Vi = molar volume of pure component, cm3/mol V = pore volume of particle, cm3/g x"= conversion of calcium oxide to sulfate, mol/mol Xc = degree of thermal decomposition of calcium carbonate, mol/mol XL 1 - r3/rg3 = local conversion of calcium oxide to sulfate, mol/mol X o 1 3f R; loR* R2XLdR = overall conversion of calcium oxide to sulfate, mol/mol y = content of calcium carbonate in limestone, weight fraction y c = content of calcium oxide in calcine, weight fraction p = true (helium) density of solid reactant, mole/cm3
pi
True (helium) density, g/cm3
Subscripts C = calcine
CC = calcium carbonate CO = calcium oxide CS = calcium sulfate LS = limestone Literature Cited Borgwardt, R. H., Environ. Sci. Technoi., 4, 59 (1970a). Borgwardt, R. H., "Isothermal Reactivity of Selected Calcined Limestones with SO2",International Dry Limestone Injection Process Symposium, Paducah, Ky., 1970b. Borgwardt, R . H., Harvey, R . D., Environ. Sci. Techno/.,6, 350 (1972). Caivelo, A., Smith, J. M., Proc. Chemeca (1970). Falkenberry, H. L., Slack, A. V., Chem. Eng. Prog., 85 (12),62 (1969). Harrington, R . E., Borgwardt, R . H., Potter, A. E., Am. Ind. Hyg. Assoc. J., 29, 52 (1968). Hartman, M., Coughlin, R. W., Ind. Eng. Chem. Process Des. Dev., 13, 248
(1974). Hartman, M., Collect. Czech. Chem. Commun., 40, 1466 (1975). Hartman, M., Int. Chem. Eng., 16 (l),86 (1976). Hartman, M.. Coughlin, R . W., AICHE J . , 22,490 (1976). Hartman, M., Pata, J., Chem. Prum., 27, 230 (1977). Harvey, R. D., Frost, R. R., Thomas, J., Jr., Petrographic Characteristic and Physical Properties of Marls, Chalks, Shells and Their Calcines Related to Desulfurizationof Flue Gases", Final Report No. 68-02-021 2,Illinois State Geological Survey, Urbana, Ill., 1973. MareEek, J., Mocek, K., Erdos, E., Collect. Czech. Chem. Commun., 35, 154
(1970a). MareEek, J., Erdos, E., Collect. Czech. Chem. Commun., 35, 524 (1970b). McClellan, G.H., Hunter, S. R., Scheib, R. M., Spec. Tech. Publ., No. 472,32, Am. SOC.for Testing and Materials (1970). Mullins, R. C.. Hatfieid, J. D., "Effects of Calcination Conditions on the Properties of Lime", Spec. Tech. Publ., No. 472, 117,Am. SOC.for Testing and Materials
(1970). Potter, A. E., Am. Ceram. SOC.Bull., 48,855 (1969). Van den Bosch, P. J. W. M., De Jong, W. A,, The Third International Symposium on Chemical Reaction Engineering, Evanston, Ill., 1974. Yates, J. G.,Best, R. J., I d . Eng. Chem. Process Des. Dev., 15, 239 (1976).
Receiued for reuiew June 15, 1977 Accepted April 19, 1978
Characterization of Membrane Material, Specification of Membranes, and Predictability of Membrane Performance in Reverse Osmosis Takeshi Matsuura and S. Sourlrajan" Division of Chemistry, National Research Counci/ of Canada. Ottawa, Canada K1A OR9
Liquid-solid chromatography (LSC) data on retention volumes of selected reference solutes offer a means of characterizing membrane materials for reverse osmosis. Using tert-butyl alcohol, sec-butyl alcohol, sodium thiocyanate, and raffinose as reference solutes in LSC, four cellulosic and four noncellulosic polymer materials have been characterized by a parameter called the @-parameter. The values of @ exhibit unique correlations with other parameters governing solute separations in reverse osmosis systems where water is preferentially sorbed at the membrane-solution interface. Using data on @-parameterfor the polymer, and only one set of reverse osmosis data for a reference NaCI-H,O feed solution for any membrane made from the above polymer material, reverse osmosis separations obtainable with the membrane for a number of other solutes can be predicted. This is illustrated in this paper with respect to reverse osmosis systems involving 8 polymer membrane materials, 15 membranes of different surface porosities, and 22 organic and inorganic solutes in single-solute dilute aqueous feed solutions.
Introduction In an earlier work (Matsuura et al., 1976a) polar (a,) and nonpolar (a,) parameters characterizing a variety of cellulosic and noncellulosic polymer materials were generated from liquid-solid chromatography (LSC) data on retention times of selected reference solutes in aqueous 0019-7882/78/1117-0419$01.00/0
solutions. The relevance of the above work to reverse osmosis stems from the principle that the solute-solvent-polymer interactions governing the relative retention times of solutes in LSC are analogous to the interactions prevailing a t the membrane-solution interface under reverse osmosis conditions. Following the same principle, @ 1978 American Chemical Society
420
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
depending on the choice of reference solutes, one may also characterize a reverse osmosis membrane material by a number of other LSC generated parameters which may be particularly useful for reverse osmosis process design. This work presents one such parameter, designated as the “@-parameter”,generated from LSC data involving a set of arbitrarily chosen organic and inorganic reference solutes in aqueous solutions; this work is limited to solute-solvent-polymer systems where water is preferentially sorbed a t the polymer material-aqueous solution interface. The experimental results show that both cellulosic and noncellulosic polymer membrane materials can be characterized in terms of numerical values for the P-parameter, and the values of @ exhibit unique correlations with the other parameters governing solute separations in reverse osmosis, discussed earlier (Dickson et al., 1975; Matsuura et al., 1975, 1976b, 197713; Kutowy et al., 1977). Consequently, using the P-parameter for the polymer material, and only one set of reverse osmosis data for a reference NaC1-H20 feed solution for any membrane made out of the above polymer material, the reverse osmosis performance of that membrane for a number of other solutes in aqueous solutions can be predicted using the correlations mentioned above. This is illustrated in this work with particular reference to four cellulosic and four noncellulosic polymer membrane materials, and reverse osmosis separations of alkali metal halides and a number of polar organic solutes (including alcohols, aldehydes, ketones, and ethers containing monofunctional groups in their molecular structure) in single solute dilute aqueous solution systems.
chart I aromatic copolyamide ( 1 7 )
L
-1
r,
1
aromatic copolyamidohydrazide, PPPH 1115 ( 2 0 ) r
1
where R represents a random distribution of
in the mole ratio of 1.54:0.46; aromatic copolyamidohydrazide PPPH 8273 ( 2 3 ) 1
Experimental Section Polymer Materials. Eight polymeric membrane materials were used in this study. These include four cellulosic materials, namely, cellulose acetate E-398-3 (2), cellulose acetate propionate with acetyl content of 30.6% and propionyl content of 14.5% (6), cellulose acetate butyrate E-171-40 (9), and ethyl cellulose phthalate (34), and four noncellulosic materials, namely, an aromatic copolyamide (17),aromatic copolyamidohydrazidesPPPH 1115 (20) and P P P H 8273 (23), and an aromatic copolyhydrazide (22). The numbers in brackets identify the polymer materials used and also the chromatographic columns in which they were used. The molecular structures of the repeat unit for the noncellulosic polymers used are given in Chart I. All the above four noncellulosic polymers were prepared in the laboratory by the methods indicated in the earlier work (Matsuura et al., 1976a). The polymer materials represented by the numbers 2, 6, 9, 17, 20, 22, and 23 are identical with the materials designated by the same numbers in Tables I, 11, and I11 in Matsuura et al. (1976a). The cellulosic materials 2,9, and 34 are Eastman products, and the material 6 was supplied by K & K Laboratories, Jamaica, N.Y. LSC Experiments. The liquid chromatograph model ALC 202 of Waters Associates 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., 1976a). All experiments were carried out a t the laboratory temperature (23-25 “C). The solvent (water) flow rate through the column was fixed a t 0.27 cm3/min. The pressure drop through the column was 150 psi/ft. The reference solutes used were tert-butyl alcohol, sec-butyl alcohol, and sodium thiocyanate; 10 pL of sample solution (solute concentration in the range 1 to 10%) was injected into the column, and the retention time for each solute in each column was determined. Raffinose whose retention time was the least, was used as the unretained
-
80 mol % meta 20 mol % para
70 mol % meta 30 mol % para
aromatic copolyhydrazide (22), a random copolymer consisting of an equimolar ratio of the following repeat units
-I o
O
0
H
II I I -CII
4j-C-N-N
I
H
C-N-N-C
a 0
H
-
H I
W O
H
H
0 C-N-N
component (uc) to establish the position of solvent front in all columns. The retention time measurements were duplicated and the average values obtained were used for computations; in most cases, the results of duplicated measurements were identical. It was already established (Matsuura et al., 1976a) that changes in column length, particle size, and packing density of column material, solvent velocity through the column, operating pressure, and sample size did not affect the retention time ratio for different solutes under otherwise identical experimental conditions. Membranes. The details on membrane preparation using the polymer materials cellulose acetate (2), cellulose acetate propionate (6), aromatic copolyamide (17), and aromatic copolyamidohydrazide (23) have already been reported (Pageau and Sourirajan, 1972; Matsuura et al.,
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 421 Table I. Film Details
membrane material casting solution composition, wt % polymer acetone magnesium perchlorate water N,N-dimethylacetamide calcium chloride diethylene glycol temperature of casting solution, “ C temperature of casting atmosphere, “ C solvent evaporation period gelation period in ice cold water, h film shrinkage temperature, C O
cellulose acetate butyrate ( 9 ) 14.0 72.0 3.5 10.5
23-25 23-25 1 min 1 50
1974,1977b; Kutowy et al., 1977). The casting conditions used for making reverse osmosis membranes with cellulose acetate butyrate (9), ethyl cellulose phthalate (34), aromatic copolyamidohydrazide P P P H 1115 (20), and the aromatic copolyhydrazide (22) materials are given in Table
ethyl cellulose phthalate ( 3 4 ) 17.0 69.2 9.2 4.6
23-25 23-25 CCH,) is equivalent to a hydrocarbon backbone with two vacant bonds, which together with the structural group in the term 2yI(-CH3) + yI,o can complete the hydrocarbon backbone in the molecular structure of the solute under consideration. In
426
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
Table 1V YI
(structural group)
combined y I values shown in Figure 3
o!
d
i;
n
. u h &
a
4
IJI y;(-CHO
j
I
r;(-CHOj - Y I ( -CH3)
order to estimate the AGI value for an alcohol- or aldehyde-solute, one of the -CH3 groups in its hydrocarbon structure may be replaced by the -OH or -CHO group involved in the quantities representing yI(-OH) or TI(CHO), respectively. Likewise, the molecular structure for ketone- and ethersolutes may be constructed by splitting the hydrocarbon structure appropriately and inserting the terms for yI(>C=O) and rI(>O), respectively. The yI values plotted in Figure 3 are applicable for both monofunctional and polyfunctional solute molecules. The following examples illustrate the use of the correlations given in Figure 3 for obtaining AGI values for use in eq 13. Data for @-Parameter = 1.37 (Cellulose Acetate) (Numerical Data from Table V). Propylene glycol, CH20H.CHOHCH3 AGI = ~ I ( - C H J+ 71(>CH2) + ~ I ( + C H+ ) 2rr(-OH) + YI,O = [~YI(-CH~) + ~ 1 , o l+ [TI(>CHJI + [TI(+CH)+ TI(-CHJ] + ~[YI(-OH)- TI(-CH~)I = 7.25 0.24 0.58 + 2(-7.19) = -6.31
+
I
+
Isobutyraldehyde, (CH,),CHCHO AGI = ~ Y I ( - C H ~+) YI(+CH) + YI(-CHO) + YI,O = [2?'I(-CH3) + Y I , ~ ] [TI(+CH) + YI(-CHJI + [YI(-CHO) - 7'1(-CH3)1 = 7.25 0.58 - 5.39 = 2.44 Methyl isobutyl ketone, CH3COCH2CH(CH3)2 AGI = ~ Y I ( - C H ~+) YI(>C=O) + rI(>CH,) + YI(+CH) + YI,O = [~YI(-CH~) + Y1,01 + [yI(+CH) + YI(-CH~)]+ [~~(>c=o)l + [YI(>CH~)I = 7.24 0.58 - 6.32 + 0.24 = 1.75 tert-Butyl isopropyl ether, (CH3)3C-O-CH(CH3)2 AGI = ~ Y I ( - C H ~+) ~ I ( > C O) + YI(+CH) + Y1,O = [~YI(-CH~) + Y1,01 + [ Y I ( > c < ) + 2yI(-CH,)] + [71(>o)l + [YI(+CH)+ YI(-CHJI = 7.25 1.07 - 4.59 + 0.58 = 4.31 The values of yI given in Figure 3 are based on the simple additivity rule expressed by eq 19. It has been shown (Matsuura et al., 1976b) that with respect to four monohydric alcohols, namely, methyl alcohol, ethyl alcohol, n-propyl alcohol, and tert-butyl alcohol, the values of (-AAG/ RT) for cellulose acetate material calculated from experimental reverse osmosis data, (-AAG/RT)Exptl, differ significantly from those calculated by using the 71values obtained from the additivity rule, (-AAG/RT)Fi 3. These deviations occurred only with respect to the a%ovefour alcohols out of 28 different organic solutes (including alcohols, aldehydes, ketones, and ethers) studied for the generation of yI values; similar deviations were also observed with respect to the membrane material tested in this work. The available data on observed deviations are given in Figure 4 in the form (-AAG/RT)Exptl - (-AAG/
+
+
+
I Fl
% h
I
I 'I
&
G. 4
m
Lo.
0
4 I W
:. I rloo
222 Orlo,
Z?? Oat-
"".?
0 0 0
m
CJ Y
a*Q, m
m
k
&
\
ri U
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
RT)Fi .3 vs. @-parameter for the polymer. The value of (-AAh/R7')Exptlis the applicable value for use in eq 18 for purposes of predicting membrane performance. Except for the four specific alcohol-solutes noted in Figure 4, for all other polar organic solutes (both monofunctional and polyfunctional) the data given in Figure 3 are directly applicable for use in eq 18. Figure 3 shows that out of the eight correlations given for the combined -yI values, five appear to be essentially independent of p, two pass through different maxima, and one decreases with increase in @, all changes being relatively small in magnitude. Therefore one might be tempted to treat all the combined yI values as independent of /3 considering the small variations to be within experimental error. Such treatment, however, could lead to too much inaccuracy for the following reasons. The interfacial free energy change AAG is, by its very nature, a small quantity arising from the difference between two near quantities AGI and AGB (eq 13), the latter being fixed by the physical chemistry of the solution independent of reverse osmosis. Consequently even a small change in AGI (and hence in the value of combined 71) makes a significant difference in the resulting value of AAG. Further, the latter quantity, in order to be useful, should be estimated with sufficient accuracy so that the value of DAM/K6 for the solute (eq 18) could be obtained within acceptable error limits indicated earlier. Therefore, for practical purposes, it is necessary to obtain the actual numerical data for combined yI from Figure 3 by interpolation from the best correlations that could be made from the available experimental data without approximating such correlations to constant values for the sake of convenience. Utility of Correlations of @-Parameter. Eight different polymer materials (specified in terms of their @parameters in Table V) and 15 different membrane samples (specified in terms of their A and ( D A M / K ~ ) N , C I values at 250 psig in Table 11) involving the above polymer materials were chosen to test the validity and practical utility of the correlations of @-parametergiven in Figures 1 to 4. While the experimental reverse osmosis data obtained with many membrane samples of different surface porosities, made from one or the other of five of the above eight polymers (namely, cellulose acetate (2), cellulose acetate propionate (6),aromatic copolyamide (17), and aromatic copolyamidohydrazides PPPH 1115 (20) and PPPH 8273 (23)) formed the basis for the correlations given in Figures 1 to 4, these correlations were totally independent of the experimental reverse osmosis data obtained with the five different membrane samples involving the three other polymer materials, namely, cellulose acetate butyrate (9), ethyl cellulose phthalate (34), and aromatic copolyhydrazide (22). The inclusion of the latter polymer materials and membranes in this part of the study constituted a true test of the general validity and utility of the correlations of the @-parametergiven in Figures 1 to 4. The numerical data needed for the quantities combined yI and [(--AAG/RT)Exptl- (-AAG/RT)Fi9,,] for the eight polymer materials obtained by interpolation from Figures 3 and 4 are given in Table V. Using the data on @-parameter for the membrane material, and A and (DAM/ K ~ ) N , for c ~ the membranes (Table 11),the applicable values of C*N,CIand In (C*Nacl/A) for each film were calculated from eq 14 and the correlation of @-parameter vs. (-AAGIRT) for Na+ and C1- ions given in Figure 1b. For the purpose of predicting membrane performance with respect to reverse osmosis separations of other solutes from the above data on @-parameterfor membrane material, and
loo( CELLULOSE ACETATE 12,
I-i
1
14
427
CELLULOSE ACETATE PROPIONATE I61
401
F
a
0
I
I
I
20
40
60
I 80
100 0
I
1
I
I
20
40
60
80
100
SOLUTE SEPARATION. % CALCD.
BUTYRATE IS)
60 J
a
SOLUTE
40
4
NUMBERS
w
z i o t K
20
/
/
o
1
\SOLUTE NUM0ERS
/
PHTHALATE (341 3
/
FILM NO
0
0 1
,
/
I1
u /
0
b
20
40
60
80
100
SOLUTE SEPARATION, % C A L C D
Figure 5. Comparison of calculated solute separations with experimental data for membranes of various polymer materials and surface porosities: operating pressure, 250 psig; feed concentration, 0.001 0.006 rn; feed flow rate, 400 cm3/min. Solute numbers: 1, methyl alcohol; 2, ethyl alcohol; 3, n-propyl alcohol; 4,isopropyl alcohol; 5, n-butyl alcohol; 6,sec-butyl alcohol; 7 , tert-butyl alcohol; 8, acetaldehyde; 9, propionaldehyde; 10, n-butyraldehyde; 11, isobutyraldehyde; 12, acetone; 13, methyl ethyl ketone; 14, methyl isopropyl ketone; 15, diisopropyl ketone; 16, diisopropyl ether; 17, butyl ethyl ether; 18, tert-butyl isopropyl ether; 11, lithium chloride; 12, sodium fluoride; 13, potassium chloride; 14,potassium bromide.
-
A, In C*NaC1and In (C*N,c,/A) for each film, solutes were chosen arbitrarily from 18 polar organic compounds (including methyl alcohol, ethyl alcohol, n-propyl alcohol, isopropyl alcohol, n-butyl alcohol, sec-butyl alcohol, tert-butyl alcohol, acetaldehyde, propionaldehyde, nbutyraldehyde, isobutyraldehyde, acetone, methyl ethyl ketone, methyl isopropyl ketone, diisopropyl ketone, diisopropyl ether, butyl ethyl ether, and tert-butyl ethyl ether), and four alkali metal halides (including lithium chloride, sodium fluoride, potassium chloride, and potassium bromide). Assuming dilute aqueous feed solutions (i.e,, PR = PWP), solute separations were calculated from
428
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
eq 10 using the appropriate values of 12 and DAM/K6for the solute under consideration obtained from the applicable eq 12 to 20 using the data in Figures 1 and 2, and Table V. A total of 141 such solute separation data were calculated and compared with the corresponding experimental data (Figure 5a and b). The comparison showed good agreement between the calculated and experimental results, which confirmed the general validity and practical utility of the correlations of @-parameterestablished in this work. Conclusion This work makes a contribution to the materials science of reverse osmosis membranes. The @-parameteroffers a useful means of characterizing a membrane material on the basis of which membrane performance can be predicted from a minimum of experimental data using the correlations established in this work. Extension of this work and generation of further correlations of the @-parameter can lead to practical techniques for the choice of membrane materials and prediction of membrane performance involving a wide variety of membrane materials and solutes in reverse osmosis. Acknowledgment The authors are grateful to P. Blais for his help in making the noncellulosic membranes, and to R. Scott for his assistance in some reverse osmosis experiments used in this work. Nomenclature A = pure water permeability constant, g-mol of H20/cm2s atm In C * N ~ C = ~constant defined by eq 14 De,(D,&eCI = diffusivities of solute and NaC1, respectively, in water, cm2/s D,M/K6 = solute transport parameter (treated as a single quantity), cm/s EB, EI = constants used in the modified Born equation for AGE and AGI, respectively, kcal &'mol ZE, = Taft's steric parameter for the substituent group in the organic molecule f = fraction solute separation defined by eq 1 AGB, AGI = free energy of hydration of solute in the bulk solution phase, and that at the membrane-solution interface, respectively, kcal/mol AAG = interfacial free energy change defined by eq 13 - A A G / R T = free energy parameter K = equilibrium adsorption coefficient at the polymer material-aqueous solution interface in LSC KBl,K,, = values of K for solutes 1 and 2, respectively k = mass transfer coefficient for the solute on the highpressure side of the membrane, cm/s MB = molecular weight of water P = operating pressure, atm PR = product rate through given area of membrane surface, g/h PWP = pure water permeation rate through given area of membrane surface, g/h
R = gas constant r, rl, r2 = retention time ratios in LSC defined by eq 2 , 4 , and 5, respectively rM+, rx- = radii of alkali metal cation, and halide anion, respectively, A T = absolute temperature, K t = retention time in LSC, s t s l , ts2, tu, = values oft for solute 1, solute 2, and unretained component, respectively, s V,' = retention volume in LSC, cm3 u, = permeation velocity through membrane defined by eq 11
Greek Letters an,aP = nonpolar and polar parameters for polymer material
f l = parameter characterizing polymer material defined by eq 6
(structural group),.yI (structural group) = incremental free energies of hydration for the structural group involved in the organic solute molecule, applicable for the bulk solution phase and the interfacial solution phase, respectively YB,O,YI,O= constants applicable for the bulk solution phase and the interfacial solution phase, respectively In A* = scale factor AB, AI = constants used in the modified Born equation for AGB ann AG1, respectively, 8, 5* = coefficient associated with BE, p = density of water, g/cm3 YB
Subscripts
a- = halide anion c+ = alkali metal cation M+ = a particular alkali metal cation MX = a particular alkali metal halide X- = a particular halide anion Literature Cited Baumann, F., in "Basic Liquid Chromatography", pp 3-9, N. Hadden, F. Baumann, F. MacDonald, M. Munk, R . Stevenson, D. Gere, F. Zarnaroni, R. Majors, Ed., Varian Aerograph, Walnut Creek, Calif., 1971. Dickson. J. M., Matsuura, T., Blais, P., Sourirajan, S.,J . Appl. Polym. Sci., 19, 801 (1975). Dickson, J. M., Matsuura. T.. Blais. P., Souriraian, S.,J . ADD/. Polym. Sci.. 20, 1491 (1976). Kutow, O., Matsuura, T., Sourirayn, S.,J. Appl. Polym. Sci., 21, 2051 (1977). Matsuura, T., Baxter, A. G., Sourirajan, S.,Ind. Eng. Chem. Process Des. Dev., I 6 82 11977al . .. . -, . Matsuura, T., Blais, P., Dlckson, J. M., Sourirajan, S., J . Appl. Polym. Sci., 18. 3671 11974). Matsuura, T.,'Blais: P., Pageau, L.,Sourirajan, S., Ind. Eng. Chem. Process Des. Dev., 16, 510 (1977b). Matsuura, T., Blais, P., Sourirajan, S.,J . Appl. Polym. Sci., 20, 1515 (1976a). Matsuura, T., Dickson, J. M., Sourirajan, S., Ind. Eng. Chem. Process Des. Dev., 15, 149 (1976b). Matsuura, T., Pageau, L.,Sourirajan, S.,J . Appl. Polym. Sci., 18, 179 (1975). Pageau, L.. Sourirajan, S.,J . Appl. Polym. Sci., 16, 3185 (1972). ia7n S.,"Reverse Osmosis," Chapter 3, Academic Press, New Yofk, N.Y., Sourirajan,
__._ _
,-.
I
-.
Sourirajan, s., Matsuura, T., in "Reverse Osmosis and Synthetic Membranes," p 52, S. Sourirajan, Ed., National Research Council Canada, Ottawa, 1977. Taft, R. W., Jr., in "Steric Effects in Organic Chemistry", p 598, M. S. Newman, Ed., Wiley, New York, N.Y., 1956.
Received for review June 20, 1917 Accepted June 7, 1978
Issued as NRC No. 16905.
