Diffusion and sorption of simple ions in cellulose acetate—semipermeability

Diffusion and Sorption of Simple Ions in Cellulose AcetatemSemipermeability M. BENDER, B. KHAZAI AND T. E. DOUGHERTY Chemistry Department, Fairleigh Dickinson University, Teaneck, New Jersey 07666 Received January 22, 1976; accepted June 10, 1977 The diffusion and sorption properties of NaC1, NaI, KC1 and KI have been studied in cellulose acetate (CA) membrane. Sorption is not reversible. Residual solute remains which can only be removed by ion exchange. Thus H +, K + and Na ÷ membranes were prepared. The sorption of K was almost twice that of Na in which connection the biological difference between K and Na is of interest. Both K and Na sorption decrease with decreasing pH. The diffusion of NaC1 was much less in the CA than in cellulose and decreased with decreasing concentration. At the higher concentrations the diffusion concentration gradient data implies a single barrier across the membrane as with cellulose but this becomes multibarrier at lower concentration. The observations are understandable according to electrokinetic theory. Salt retention properties in reverse osmosis are thus explained including the decreasing of the semipermeability with increasing solute concentrations. The much greater effectiveness of cellulose acetate vs cellulose is evident in terms of the reduced absorption and diffusion in the more compact less swollen molecular chain network of lower average dielectric constant. INTRODUCTION

latter, while the possibility of the presence of a small concentration of ionizable carboxyl groups is acknowledged giving the CA weak ion-exchange character and its electrical charge, dielectric exclusion of ions seems to be the most important factor in the rejection of salts. Ullman's mathematical treatment (4, 5) utilizes the Debye-Hiickel shielded potential concept in interionic attraction theory. His relationships show that under conditions of lower concentration there should be a greater range of ionic atmosphere, the salt rejection by the membrane being greater; salt solubility is less in membranes of lower dielectric constant; and membranes with smaller pores should exclude salt more effectively. Spiegler's (6) observations of a streaming potential for CA membrane as a result of reverse osmosis or hyperfiltration are evidence of its electrokinetic nature. Interpretation of the electrokinetic properties of the CA membrane through its (weak) ion-exchange character was given

Following the work in these laboratories on diffusion and sorption of simple ions in cellulose (1), a parallel approach of investigation is carried out with cellulose acetate (CA). 1 This membrane has a lower average dielectric constant so that its swelling in water is appreciably less and the restrictions to salts are greater. As is the case with cellulose, observations are explainable via an electrokinetic approach. In the literature, Sourirajan (19) suggested the negative salt adsorption due to dielectric exclusion as being responsible for the rejection of salts by CA membrane. Dresner (18) included the screening of salt by ionic atmospheres also as a factor. Partition coefficient and diffusion constant studies were reported by Anderson et al. (2) and by Heyde et al. (3) for CA. According to the 1 B. Khazai, M.S. thesis, May 1974; B. Khazai, B.S. thesis, May 1972; T.E. Dougherty, B.S. thesis, May 1968. 346 0021-9797/78/0632-0346502.00/0 Copyright © 1978by AcademicPress,Inc. All rightsof reproductionin any formreserved.

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SEMIPERMEABILITY

much attention by Demisch and Pusch (20) and Schmid and Schwarz (22). Demisch and Pusch showed the difficulty of comparison of the evaluation of "fixed charges" in weak ion-exchange membranes by titration vs by measuring transport coefficients and/ or streaming potentials. Thus they have to refer to an "effective" fixed charge with respect to the transport phenomena and this is shown to depend strongly on pH, on outside solution concentration and the valency of the counterions. EXPERIMENTAL METHODS

The essential experimental methodology is described for previous work done on cellulose (1). Temperature was 303.6°K and the pH of the water 7.0. A Perkin-Elmer Model 303 atomic absorption spectrophotometer was employed to evaluate cation concentrations. Potassium was determined at 384 and sodium at 295 nm wavelength. The margin of error of this instrument is less than 1% absorption transmittance which corresponds to less than 0.2 ppm. CA membrane film was obtained from Sargent-Welch Scientific Co. It is listed as Catalogue No. S-14825. Infrared analysis identified it as having the same spectrum as Eastman Kodak Co. cellulose acetate powder E-394-45 grade which has an acetyl content of 39.4%. The film is symmetric (in contradistinction to the asymmetric membrane generally used in reverse osmosis). Its dry (to atmosphere) thickness was 2.70 x 10-s m as measured by Zeiss micrometer. This swelled to 3.08 x 10-s m whether in water or the solutions employed in this work. There was relatively little change in the length and width. Dry density was 1.23 x 10~ kg m-q Na + was found present in the original membrane (and also a trace of K+). Part of this Na + content was leachable in water while the remainder could only be extracted by ion exchange. Thus H +, Na +, K +, etc., CA membranes could be prepared. Hydrogen membranes were used in the experimentation. They were prepared by placing

the original membrane in 0.1 N HCI. In this treatment as well as in the sorption experiments the amount of membrane was about V3 g, the quantity of solution 200 ml, and the duration of exposure 1.5 hr. The degree of acidity in the hydrogen membranes used for experimentation is identified by the pH of the last wash water in which they were prepared. Generally the first wash was pH 5.7-5.8 and the second 6.2-6.3. In the sorption experiments, previously dried hydrogen membranes were allowed to equilibrate in solutions of NaC1, NaI, KC1 and KI, respectively, the original solution concentrations being varied from 2 x 10-4 t o 6 0 X 10 -4 N . The pH was followed. That amount of salt absorbed (per kilogram of dry membrane) which could be leached out with pure water was measured, one wash usually being sufficient in this connection. Remaining cations were removed by immersion of the CA in 0.1 N HC1. Symbols used here and their definitions are: Cu CMc

C~ - CMc Cs

Total moles salt/kg dry to atmosphere membrane. Moles salt remaining/kg dry to atmosphere membrane after leaching with water. Water leachables/kg membrane. Solution concentration (moles liter-I).

The steady state diffusion experiments involved NaC1 only. In each run the diffusion membrane consisted of six layers of the CA the total wet thickness (x) as immersed in water or the solutions utilized, being 1.85 x 10-4 m. Both hydrogen membrane and original (Na) material were considered, respectively. The accumulation with time of Na in the receiving compartment was followed through measurements on 5 ml aliquots over 1200 sec intervals. RESULTS

As is the case for cellulose, the leaching, ion exchange and absorption measurements show that for a given salt, desorption is not Journal of Colloid and Interface Science, Vol. 63, No. 2, February 1978

BENDER, KHAZAIAND DOUGHERTY

348

reversible with absorption. Analysis for N a in the original m e m b r a n e gave 4.88 × 10 -3 mole kg 1 ( C M - CMC) leachable with water. Three different techniques were considered for the total N a analysis. One method used concentrated perchloric acid (25 ml) to dissolve about 1 g of the CA, the solution being diluted with w a t e r to 1 liter. This showed CM = 8.29 X 10 -3 mole kg -1. In the other methods which are based on the ion-exchange nature of the CA, 0.1 N HC1 and 0.01 N KC1 were used, respectively (200 ml vol) on film samples (½ g). The values obtained were 8.18 × 10 z and 8.06 × 10 -3 mole kg -1. Thus the nonleachable portion of 3 . 2 - 3 . 4 × 10 -3 mole kg -1 (CMc) was essentially r e m o v a b l e by r e p l a c e m e n t with the H + or the K +, the K + appearing not quite so effective as the H +. Total equilibrium absorption isotherms (C:~ vs Cs) and the corresponding non leachables (CMc) vs Cs in moles liter -a for NaCI, N a I , KC1 and K I in CA p H 5.7 hydrogen m e m b r a n e s are plotted in Fig. 1. Values for CM of NaC1 not shown, obtained by extrapolation of the diffusion concentration gradient data (vide infra) are 5.73, 6.50, 6.60 and 7.36 mole kg -1 × 10~ at Cs equal to 100,300, 500 and 1000 mole liter-! × 104,

9.0

respectively. These values increase slowly with concentration much as might be exp e c t e d o f t h e i s o t h e r m b e y o n d Cs = 0.0060 M. F o r all four salts the ratio of the concentration in the m e m b r a n e to that in solution decreases with increasing salt concentration. Leveling off o f the isotherms begins in the range of Cs = 50 × 10 -4 M. This is the case, essentially, for cellulose. CMc likewise begins to level in this Cs range. The total absorption is seen to c o r r e s p o n d in magnitude with the values reported by H e y d e et al. (3). On c o m p a r i s o n of this data (at p H 5.7) with that for cellulose at p H 4 . 5 - 5 . 2 (it was shown for cellulose that absorption increased with pH) it is seen that the total absorption is one-fifth to one-third that for the cellulose on the basis of dry membrane. Nonleachables in the CA are only 75% that for the cellulose and are about double the leachables in the CA. T h e y c o m p a r e in magnitude with the "fixed c h a r g e s " reported by Demisch and Pusch (20). CMc N a + absorbed in the CA checks with that found in the original material although the leachables are about half that in the original. CM for K salts is seen to be almost double

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FIG. 1. Total equilibrium absorption and nonleachables for NaCI, NaI, KC1 and KI on hydrogen cellulose acetate: NaCI CM (×) and CMc ([]); NaI CM (-X-) and CMC (11); KCI CM (Q) and CCM (A); KI CM (0) and CMC (A). Chlorides ( ), iodides ( - - - ) , abscissa = Cs (mole liter-1 × 104), ordinate = CM, CMc (mole kg-1 × 103). Journal of Colloid and Interface Science,

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SEMIPERMEABILITY TABLE I

here for con)parison and it is seen for the most part that the H + released corresponds to the nonleachable content going in. The difference between Na and K is apparent. The steady state diffusion flux measurements (J) were converted to integral diffusion coefficients (Ds and DM') based on the overall concentration drop across the whole membrane, utilizing the Fick's first law concept. Ds is in terms of the contiguous solutions, the concentration of the solution in the receiving compartment being taken as zero:

pH D e p e n d e n c e o f NaI Absorption in CA Absorption (mole kg-1 x 103) pH

Total

Nonleachable

6.24 6.00 5.80 5.40 5.10 5.08

6.94 6.14 5.69 4.38 4.18 4.17

4.92 4.16 3.65 2.28 1.88 1.87

that for the Na salts. This is likewise so for the nonleachable sorption CMc KC1 is even greater than CM NaC1. In cellulose CM KC1 was only about 10% greater than CM NaC1. The effect of pH on the sorption in CA is shown by the NaI data given in Table I. CM and CMC are seen to decrease appreciably with decreasing pH. Heyde et al. (3) show such pH dependence for NaC1 and NaBr at 0.05 molarity of the soak solution. Values for the total H + released during absorption of the four salts are plotted in Fig. 2 vs Cs. The CMC values are replotted

J = -DsCs/x. D M' was calculated from the overall concentration drop in the membrane, that on the low side being taken as zero: J

CM' (moles m -3) is obtained from that CM which is the absorption equilibrium value corresponding to the contiguous solution concentration utilizing the dry thickness of the CA, its increase in thickness due to its swelling and its dry density. Namely,

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FIG. 2. Total H + e x c h a n g e for nonleachable NaCI, NaI, KCI and KI: NaC1, CMC ([]) and H + desorbed (B), NaI, CMC (X) and H + desorbed (-x-); KC1, CMC (~X) and H + desorbed (A); KI, CMC (Q) and H + desorbed (Q). CMC ( ) , H + desorbed ( - - - ) , abscissa = Cs (mole liter -1 × 104), ordinate = C u e , H + desorbed (mole kg -1 x 103). Journal of Colloid and Interface Science, Vol. 63, No. 2, February 1978

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BENDER,

KHAZAI

CM' = CM X 1.08 X 10a. Results are summarized in Table II. These integral diffusion coefficients are much less than in the case o f cellulose. They are in the range of values reported by Hyde et al. (3) and Lonsdale et al. (16, 17). Although Ds decreases with increase in Cs, D:~/ based on concentrations in the membrane is seen to increase appreciably. Figure 3 represents plots for the hydrogen membrane diffusion runs, of the Na concentration of individual layers vs wet diffusion membrane distance. An estimate of the positioning of each concentration point along the X axis within its layer has been made by trial and error graphical integration in order to approximate the actual concentration gradient in the diffusion membrane. For each layer the area under the curve is proportional to the salt content of that layer. This was the technique utilized in the work with cellulose. The vertical broken lines represent the interfaces between layers. In the Cs = 0.005 M run the curve is seen to extrapolate on the high side to the measured absorption equilibrium value. At the higher concentrations the gradient curves point to the CM values reported above in connection with the sorption isotherm. While the cellulose diffusion concentration gradient points to one barrier, the CA runs indicate a multibarrier situation. This could be part explanation of the much lower integral diffusion coefficient observed for CA (and the better reverse osmosis properties). For each Cs there is a barrier on the low concentration side. This was the case for cellulose. The other barriers move with increasing Cs towards the low side and tend to disappear so that the gradient approaches constant D linearity ( C s = 0.05 M) except for the low side barrier. At C s = 0.1 M the gradient for cellulose is approached. DISCUSSION

AND

DOUGHERTY

TABLE

D i f f u s i o n o f N a C 1 in C e l l u l o s e A c e t a t e

Concn of diffusing solutions

Cs (mole liter -a)

CM (mole kg ' x 10~)

0.005 0.010 0.010 a 0.030 0.030 a 0.050 0.10

5.36 5.73 -6.50 -6.60 7,36

Journal of Colloid and Interface Science, Vol. 63, No. 2, February 1978

Steady state diffusion flux J (mole sec ' m ~ x 10s)

2.00 4.76 3.80 5.44 3.94 7.35 10.5

Diffusion flux/unit overal concentratient gradient Ds D~/ (m2 sec -~ x 10'8)

7.40 8.80 7.03 3.35 2.43 2.72 1.95

6.40 14.2 14.40 -19.1 24.4

a Original CA membrane. bone dry membrane is estimated to contain 11.3 × 1023 acetylated cellobiose units. Absorption to the extent of about 9 × 10-3 moles (5 × 1021 cations) kg -1 amounts to 1 cation per some 200 units. As in the case for cellulose such large spacing per cation makes it difficult to conch]de that there are specific solute sites.

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Based on the cellobiose molecular weight 324 and the 39.4% aeetyl content, 1 kg of

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at

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and 0.10 M (A). Abscissa=x = C M ( m o l e k g -1 x 103).

SEMIPERMEABILITY For K + the total absorption (CM') in CA at Cs = 0.006 M is estimated at 10 moles m -3 and in cellulose at 20 moles m -3. The concentration of water in the wet CA is estimated at 6.8 x 103 moles m -3 and in cellulose at 26.6 x 103. The preferential solubility of water vs the salt whether in CA or cellulose, is very striking and is an important factor contributing to the membrane semipermeability. The greater semipermeability for the CA vs the cellulose is associated with the lower salt solubility in this medium. These solubility differences are understandable according to the respective dielectric constants (3, 5) of salt, water, and membrane. Likewise, the semipermeability is explainable in terms of differences in diffusion of salt and water in the CA and cellulose according to the "dielectric exclusion." For instance, the self diffusion coefficient of water is 2 x 10 -9 m 2 sec -1 (21). In CA the coefficient for water is 1.5 × 10-1° (4, 17), and it is expected that the value in cellulose is somewhere in between. Meanwhile NaC1 in water has a coefficient of 1.5 x 10.9 which is close to that of water in water. In cellulose DM' of KC1 at Cs = 0.01 M is 2.86 x 10-11 m z sec -1 while in CA the DM' of NaC1 at Cs = 0.01 is seen to be 14.2 x 10-12. An electrokinetic barrier system is apparently present in the cellulose acetate much as was concluded for cellulose. 2 The diffuse electrical double layer network may be regarded radiating out from the membrane molecular chains as a core. See Ullman (4, 5) and Jacazio et al. (15) for mathematical approximations. The potential is a function of the electronegative nature of the oxygen atoms in the cellulose acetate and "potential determining" ions, like H +, O H - , absorbed (strongly, i.e., 2 Strazdins (13) in an electrokinetic study of cellulose refers to its electronegative charge, the negative charge capacity being less when acidic. Flowers et al. (14) in work with graphitic oxide as reverse osmosis membrane point to its being electrically charged, its salt rejection decreasing with decreased pH.

351

by hydrogen bonding) at the chains adjacent to the Stern layer. Absorbed H + neutralizes electronegativity and the overall absorption is lessened. In the same vein, the cations absorbed decrease the negative potential and the decrease in the ratio of CM to Cs with increasing concentration is thus explained. This is deduced by Ullman on the basis of electrostatics (5). Any " a c c i d e n t a l " carboxyl groups present in the cellulose acetate, the ionization of these groups being pH dependent, would be involved. Membrane absorbed water molecules are part of the layer as well as solute ions. On a general basis the double layer thickness is greatest and the electrical (negative) potential highest at low membrane electrolyte content. Higher concentration tends toward swamping. At increased membrane concentrations, the cations are held less strongly in the double layer and desorption can take place. But at less concentration the coulombic attraction is sufficient to counteract the random translational energy of the cation, interfering with its migration to contiguous solution despite the concentration difference in the membrane vs solution. Thus the irreversibility of desorption vs absorption is understood, given species at low concentration being only removable by cation exchange where the increased ionic strength which is applied with introduction of the exchanging ion enables redistribution of the cations by lowering their double layer interaction. The preferential sorption observed for H vs K vs N a in the CA (and less exaggeratedly in cellulose) follows the " l y o t r o p i c " series? Smaller (hydrated) ions having a stronger electrostatic force field should be more closely attracted into the vicinity of the electronegative molecular chain network. H e y d e et al. (3) report that their various 3 The preferential sorption of K vs Na correlates with reported ionic and membrane pore sizes. The hydrated ion size of K is given as 5.3 x 10-'° m and of Na 7 x 10-'° m, (7) while the pore size of cellulose is reported to be 16 x 10-~° m in water (8, 9) and that for CA, 8-10 x 10-'° m (2, 10). Journal of Colloid and Interface Science, Vol. 63, No. 2, February 1978

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BENDER, KHAZAI AND DOUGHERTY

partition coefficients in CA correlate with the lyotropic series. It is of interest in this connection that biological cells are high in K content vs Na. With respect to the diffusion results, D ~t' decreases with decrease in concentration due to the greater interaction of ions with the double layer at lower concentration. The barriers indicated by the diffusion concentration gradients and the change in barrier location in the membrane with concentration are explainable in this manner. Electrokinetics periodicity such as is indicated by the ~'multibarrier" diffusion gradients has been observed by Bender (12) in the case of the cataphoretic velocity of zinc sulfide particles vs AIC13 concentration in pure water and in 0.002 N H ~ S O 4 , respectively. The decreased D s in the original CA vs in hydrogen membrane at C s = 0.01 is understood to be due to the greater electronegativity field in the membrane molecular chains since less of the potential determining H ÷ is absorbed. Thus there is greater interaction with the Na. The interpretation of D s into D M' utilizing the absorption isotherm is an application of activity coefficients. Such activity considerations have been utilized in the sorption and diffusion of an anionic organic salt in cellulose (11). Thus the salt retention properties of cellulose acetate in reverse osmosis may be understood as due to an electrokinetic barrier system superimposed on its dielectric restriction properties, the semipermeability decreasing with increasing solute concentrations. The much greater effectiveness of cellulose acetate vs cellulose is evident in the reduced absorption and diffusion of salt in the more compact less swollen molecular chain network of lower average dielectric constant in which electrostatic barriers can exist on a "multi" basis.

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REFERENCES 1. Bender, M., Moon, J. K., Stine, J., Fried, A., Klein, R., and Bonjouklian, R., J. Chem. Sac., Faraday Transactions 1 71,491 (1975). 2. Anderson, J. E., Hoffman, S. J., and Peters, C. R., J. Phys. Chem. 76, 4006 (1972). 3. Heyde, M. E., Peters, C. R., and Anderson, J. E., J. Colloid hTterface Sci. 50, 467 (1975). 4. Ullman, R., "The Rejection of Salt by Microporous Membranes" of the Sci. Res. Staff, Ford Motor Co., Dearborn, Mich. 5. Ullman, R., "Electrostatic Models of Salt Solubility in Membranes", Feb. 7, 1974. of the Sci. Res. Staff, Ford Motor Co., Dearborn, Mich. 6. Spiegler, K. S., Preprint of Paper Presented at 155th ACS National Meeting, San Francisco, Calif., Div. of Water, Air and Waste Chem., (Spring), 8(1), 79 (1968). 7. Wiklander, L., Ann. Royal Agr. Coll., Sweden 14, 1 Reference table 17 (1946). 8. Peterson, C. M., and Livingston, E. M., J. Appl. Polym. Sci. 8, 1429 (1964). 9. Madras, S., Mclntosh, R. L., and Mason, S. E., Canad. J. Res. 27(8), 764 (1949). 10. Thau, G., Bloch, R., and Kedem, O., Desalination 1, 129 (1966). 11. Bender, M., and Foster, W. H., Jr., Trans. F a r a d a y Soc. 61, 159 (1965). 12. Bender, M., J. Phys. Chem. 57, 466 (1953). 13. Strazdins, E., Abstr. No. 7, Div. of Cellulose, Wood and Fiber Chem., t57th ACS Nat. Meet., Minneapolis, Minn., Apr. 14, 1969. 14. Flowers, L. C., Sestrich, D. E., and Berg, D., Abstr. No. 26, Div. of Cellulose, Wood and Fiber Chem., 157th ACS Nat. Meet., Minneapolis, Minn., Apr. 14, 1969. 15. Jacazio, G., Probstein, R. F., Sonin, A. A., and Yung, D., J. Phys. Chem. 76, 4015 (1972). 16. Lonsdale, H. K., Cross, B. P., Graber, F. M., and Milstead, C. E., J. Macromol. Sci. (Phys.) BS(1), 167 (1971). 17. Lonsdale, H. K., Merten, U., and Riley, R. L. J. Appl. Polym. Sci. 9, 1341 (1965). 18. Dresner, L., Desalination 15, 39 (1974). 19. Sourirajan, S., Ind. Eng. Chem., Fundam. 2, 51 (1963). 20. Demisch, H.-U., and Pusch, W., J. Electrochem. Soc. 123, 370 (1976). 21. Wang, J. H . , J . Amer. Chem. Soc. 73, 510 (1951). 22. Schmid, G., Z. Elektrochem. 54, 424 (1950); 55, 229 (1951); 56, 181 (1952); Schmid, G., and Schwarz, H., Z. Elektrochem. 55, 295 (1951); 55, 684 (1951); 56, 35 (1952).