Anion permeability of cellulosic membranes. Part 1. Porosity of water-swollen membranes

Anion permeability of cellulosic membranes. Part 1. Porosity of water-swollen membranes

Science, 46 (1989) 283-298 Elsevier Science Publishers B.V.. Amsterdam - Printed in The Netherlands 283 Journal of Membrane ANION PERMEABILITY OF C...

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Science, 46 (1989) 283-298 Elsevier Science Publishers B.V.. Amsterdam - Printed in The Netherlands


Journal of Membrane




of Material Systems Engineering, and Technology,


School of Engineering,

Tokyo University


Tokyo 184 (Japan)

RUTH WEBER and PAUL RYS Department of Industrial and Engineering Chemistry, (ETH), ETH-Zentrum, CH-8092 Ziirich (Switzerland)

Swiss Federal Institute

of Technology

(Received February 22,1988; accepted in revised form February 13,1989)

Summary The degree of swelling (S), the hydraulic permeability (J,), and the permeation (D,,,) of 2,4dinitroaniline,p-aminoazobenzene and 1,4-bis(4-hydroxyphenylazo)benzene were measured for nine cellulosic membranes, some of which were modified by a reactive dye. A linear relationship between the porosity (P,), defined as the ratio of water volume in the membrane to the total volume of the swollen membrane, and l/S for eight of the membranes was obtained, where S was defined as the volume of the swollen membrane per unit dry weight of the membrane. Linear relationships were also obtained between J, or Dexp and P, for eight of the membranes. By means of these linear relationships, a reasonable estimation of the absolute value (P) of porosity was made. In the swollen membrane, 0.096 g of water per g of cellulose was shown to be inaccessible for water flow and for permeation of the penetrants. The temperature dependence of the porosity P was investigated by diffusion measurements with 2,4_dinitroaniline in the temperature range between 30 and 80’ C. The activation energies of diffusion in solution and in the membranes are compared. The diffusion behavior of three nonionic penetrants through water-swollen cellulosic membranes has been examined. The results indicate a possible effect of the molecular shape, but show no size effect on the diffusion.

Introduction Cellulosic membranes are used to separate various kinds of solutes. The permeation of water-soluble solutes into cellulose is said to be controlled by both the pore size of the cellulosic material and the size of the penetrants [ 11. Stone and co-workers [ 2,3] made extensive use of solute molecules covering a broad range of both molecular weight and diameter in order to assess the permeability of various cellulosic substances. They showed that, for molecular weights less than 104,the permeability is inversely proportional to the molecular weight of the penetrants [ 31. This result enables us to estimate relative permeabilities


0 1989 Elsevier Science Publishers B.V.

TABLE 1 Membrane properties No. Manufacturer


Thickness of swollen membrane,

Carboxyl group content

Sulfonic Symbol acid group in figures content

1 (cmX 10m3) (meq/kg dry cellulose) 1 2

Union Carbide Co.

36132” modified

3.62 3.32

13.2 13.2

0 18.2


Visking Co.






4 5 6 7

Tokyo Cellophane Co.

No. 300b modified modified modified

3.73 3.33 3.39 3.36

39.0 39.0 39.0 39.0

0 11.0 20.0 40.8

0 v 0


Fukui Chemicals Ltd.

No. 300b 3.73





Asahi Chemical Industry Co. tubular 3.17 Bemberg film





“Seamless cellulose tubing for dialysis. bNo. 300 indicates a weight of 300 g/m’.

glass drying tube. From the values, the volume of the swollen membrane was estimated. The weight of the swollen membranes was measured after pressing the membranes for 10 set between pieces of filter paper at 20’ C. The amount of carboxyl groups in the membranes was determined by a Methylene Blue method [ 111. Hydraulic permeability A microsyringe filter holder equipped with a hose connector (Millipore Corp., XX30 025 14) was used in the pressure range l-3 x lo5 Pa; the pressure was applied by nitrogen. A filter paper was put between the swollen cellulose film and a stainless steel filter support screen. The flow rate of water was determined by weighing the amount of water passed through the membrane at given time intervals. Permeation experiments The permeation of 2,4-dinitroaniline ( 1 ), p-aminoazobenzene (2 ) and 1,4bis (4-hydroxyphenylazo)benzene (3) was determined by the steady state method. All the chemicals were of reagent grade. The permeation cell consisted of two thermostatted compartments which were separated by the membranes,


set horizontally [ 121. The concentration of the penetrant in the solution in the higher concentration compartment was kept constant at 2.0~ lop4 mol/ dm3 for penetrant 1,at 1.34 x lop4 mol/dm3 for penetrant 2 and at 6.79x 10e5 mol/dm3 for penetrant 3. The solution in the other compartment was renewed at definite time intervals of permeation, and the concentration of the penetrated substance was measured by using a UVIDEC-505 spectrophotometer (Japan Spectroscopic Co. Ltd. ) . NOi





(I )


In order to eliminate the stagnant layer effect, the multiple membrane method was used, and both the upper and lower solutions were stirred. The rate of permeation or flux, J,,, (mol/sec-cm2), through the membranes is given by [13]: AC

-=J -P

+h___ +d2+ (n-116 Dexp Dw DW nl

where AC ( mol/cm3) is the concentration difference of the penetrant between the two compartments, n is the number of membranes, S, and 8, (cm) are the thicknesses of the stagnant layers at the membrane surface in the lower and upper compartment, respectively, 6 (cm) is the thickness of the intermembrane stagnant layer, D, ( cm2/sec ) is the diffusion coefficient of the penetrant in the bulk solution and Dexp (cm”/sec) is the apparent diffusion coefficient within the membrane. A plot of AC/J,,, - (n - 1)6/D, against n should be linear, with an intercept equal to (6, + 6,) /D,. In the present study, the multiple membrane was pressed before setting in order to minimize the thickness S. Tsimboukis and Petropou10s estimated the value of 6 to be 3.4 pm [ 131. By preliminary experiments, linear relationships between AC/J,,, - (n- 1)6/D, and n could be demonstrated, as shown in Fig. 1. Up to now, no exact knowledge is available of the stagnant layer properties and their influence on the measurable membrane permeabilities for the dyes investigated. In order to minimize such an influence but, at the same time, tolerating the uncertainty of the magnitude of 6, a multiple membrane with n = 10 was applied.


Fig. 1. Permeability of 2,4_dinitroaniline as a function of n for some membranes, according to eqn. (1) (I=O.l mol/dm3, 80°C). The other membranes showed a similar relationship.

With this experimental set-up, under steady state conditions, eqn. (1) becomes:

Neglecting surface diffusion, there are also the following relationships between De,,, and D,: D


_$ =kiP, -





Here, P is the porosity of the membrane, b is the tortuosity factor for the membrane and lzi is a constant given by the relation D, = kiD,, where D, is the diffusion coefficient of the ith penetrant in the pore solution [i=1:2,4-dinitroaniline, i= 2: p-aminoazobenzene and i= 3: 1,4-bis (4-hydroxyphenylazo)benzene] . The values of JeXpwere averaged from 4 or more measurements. The experimental results were reproducible to about 3%, and they were obtained at various ionic strengths at 80’ C. The pH of the solution was adjusted with HCl and was measured by a Hitachi-Horiba pH meter at 80’ C. The ionic strengths of the solution were adjusted with NaCl. Diffusion in aqueous solution The diffusion coefficient D, of the penetrants in aqueous solution were measured at 80°C by using a diaphragm cell of the same type as the permeation cell in which the membrane was replaced by a glass filter. The cell constant was determined by using KC1 [ 141. Stirring was carried out slowly at a defined rate.


Results and discussion

Porosity of the membranes The porosity of various membranes was first estimated by measuring the degree of swelling. Taking the volume expansion by swelling into account, the total volume ( Vtot) of the membrane was regarded as a first approximation to be the sum of the volumes of cellulose ( V,) and of water ( VW) in the membrane and the expansion by swelling ( V,): Vtot= v, + VW+ v,


From the measured total volume of the water-swollen membrane and the dry weight (G,) of the membrane, the degree of swelling (S) defined by S = V,,/ G, was calculated. The weight of expansion (G,) is zero. The difference between the weights of the swollen and the dry membrane gives the weight (G,) of imbibed water in the membrane. Assuming that the density of the water in the membrane is equal to the density of bulk water at the same temperature, the porosity P, defined by P,= Vw/Vtotcan be calculated. The values of S, S’ (swelling ratio: swollen wt./dry wt.) and P, for membranes l-8 are given in Table 2. The change in the size of various membranes in the repeated swelling-drying processes is shown in Table 3. The values of S, S’ and swelling ratio by volume were similar to each other. But membrane 9 showed a smaller swelling ratio in thickness and a larger one in area than those for the other membranes. This indicates that membrane 9 must have a larger porosity than the others, as mentioned later. TABLE 2 Degree of swelling, porosity and flow rate of water for the membranes at 20°C No.

1 2 3 4 5 6 7 8 9

S (dm3/kg cellulose)

S’ (kg swollen cellulose/ kg cellulose)

p, (- )

1.48 1.44 1.56 1.57 1.36 1.39 1.47 1.58 1.55

1.51 1.50 1.60 1.59 1.38 1.42 1.54 1.61 1.64

0.362 0.343 0.397 0.395 0.329 0.318 0.360 0.406 (0.666)

“P= Nnr’.





( X 10V5cm/sec)


N” (X10’2cm-2)

1.17 1.16 1.21 1.20 1.20 1.16 1.17 1.18 (1.15)

6.38 6.04 6.73 6.76 5.35 5.42 6.31 7.22 (13.9)

Yr,, ( X lo5 Pa) 1.0 2.0 3.0 0.274 0.255 0.309 0.307 0.241 0.230 0.272 0.318 (0.578)

1.32 1.28 1.59 1.50 1.26 1.15 1.37 1.47 3.03

2.63 2.60 3.24 2.94 2.55 2.22 2.81 3.03 6.11

3.74 4.81 4.48 4.07 3.53 4.49 8.87


TABLE 3 Swelling ratios for various membranes in the repeated swelling-drying processes (dried at 110 ’ C in vacuum) Swelling ratio (swollen/dry)


1 3 4 8 9


by length

by width or circumference

by thickness

by area

by volume

1.077 1.078 1.088 1.085 1.145

1.157 1.167 1.169 1.136 1.285

1.882 1.700 1.854 1.773 1.585

1.246 1.258 1.271 1.232 1.471

2.345 2.138 2.358 2.185 2.332

Apparent density (g/cm3 dry cellulose) 1.473 1.456 1.517 1.421 1.414

-_I 0.7






Fig. 2. Relationship between P, and l/S slope = - 0.940.

for various membranes, according to eqn. (5);

The following relationship can be derived:

From the plot of P, vs. l/S in Fig. 2 it can be concluded that membranes 1-8 have approximately the same value for V,/ V,. This value was calculated from the slope to be 0.44-0.46. The density of cellulose, pC,was assumed to be 1.531.55 g/cm3 [ 151. A change in pCdue to modification of the membrane with the reactive dye was neglected, since the amount of dye fixed was less than 1% of the membrane weight. The density of the dye was assumed to be 1.6 g/cm3 1161. Hydraulic permeability The flow rates of water, J, (cm/set ) , which were measured at 20’ C and at three pressure levels for the nine membranes, are given in Table 2. Under the


Fig. 3. Pressure dependence of water flow for some membranes at 20” C. As J, of the membrane 9 shows scattering in the experimental data, the standard deviation is included. The other membranes showed the same relationship.

67 (0 E



“0 x




1 -



0.2 Ps





Fig. 4. Hydraulic permeability for various membranes Pa, (b) 2X105Paand (c) 3x105Pa.

at 20°C and at three pressures:

(a) 1 X lo5

conditions examined, there is a linear relationship between J, and the applied pressure, 9$:, (Pa), for all the membranes, as Fig. 3 shows. According to Poiseuille’s law [ 17,181:

(6) where r (cm) is the mean pore radius of the membrane, v (Pa-set) is the viscosity of water and P (dimensionless) is the porosity, a linear relation between the flow rate J, and the pressure L?&is expected for cylindrical pores. In the following it will be assumed that the pores in the membranes investigated are cylinders with a constant mean radius. The cylindrical pores form a statistical, three-dimensional network in the membrane. This is taken into account by the tortuosity factor b in eqn. (3 ).


A linear relationship between J, and P, was found, as shown in Fig. 4. The lines intersect the abscissa at P, = 0.090. Permeability of nonionic penetrant The value of D, for 2,4-dinitroaniline obtained at 80°C (I&,= 2.78~ 10W5 cm’/sec) was confirmed as being constant over the range of ionic strengths and pH values examined (Fig. 5 ) . The values of D, for p-aminoazobenzene


+ 0

-3 I




Fig. 5. (a) Relationships between D,, of 2,4-dinitroaniline and Z at 80°C and (b) those between D, of 2,4-dinitroaniline and Zor pH at 80°C. The pH dependence was examined at Z=O.Ol. TABLE 4 Permeation of 2,4-dinitroaniline ( i= 1), p-aminoazobenzene ( i = 2 ) and 1,4-bis (4-hydroxyphenylazo ) benzene (i = 3 ) through various membranes at 80” C No.

1 2 3 4 5 6 7 8 9



D ew ( X low6 cm’/sec)


2.81 2.61 3.26 3.35 2.59 2.65 3.06 3.36 5.71

0.369 0.369 0.379 0.394 0.386 0.413 0.404 0.381 (0.355)




Dexp ( X 10-a cm’/sec)


2.50 2.32 2.87 2.84 2.21 2.22 2.64 2.89 5.09

0.391 0.388 0.398 0.394 0.390 0.413 0.415 0.390 (0.377)

De, (X


10e6 cm’/sec)

2.16 2.06 2.58 2.49 1.94 1.93 2.30 2.56 4.22

k,b 0.405 0.416 0.430 0.417 0.415 0.430 0.438 0.415 (0.377) 0.421




0.1 0.2 Ps





Fig. 6. Relationship between (a) D,, of 2,4_dinitroaniline, (b) Derp of p-aminoazobenzene (c) De_, of 1,4-bis(4-hydroxyphenylazo)benzeneandP, (T=80”C, Z=O.l mol/dm3).


and 1,4-bis(4-hydroxyphenylazo)benzene at 80°C were 2.34~ 10U5 cm2/sec and 1.94 x lop5 cm2/sec, respectively. These are approximately equal to the values estimated by the Wilke-Chang method [ 191 [viz., 2.34~ 10V5 cm’/sec for 2,4-dinitroaniline, 1.93 x lop5 cm2/sec for p-aminoazobenzene and 1.50 x 10m5 cm2/sec for 1,4-bis (4-hydroxyphenylazo)benzene], where the molar volume of penetrant at its boiling point was estimated by the Kopp rule [201. The permeations at steady state were usually measured with 10 sheets of membrane. In order to check for constancy in swelling with an increase in the ionic strength, the permeations of 2,4_dinitroaniline at various ionic strengths were measured (Fig. 5 ) . All the membranes used showed no change in the swelling under the conditions examined, and the averaged values of De._, are given in Table 4. The relationships between De_, and P, are shown in Fig. 6 and will be discussed later. Relationship between permeation and porosity The plots of Dexp for penetrants 1 to 3, with various membranes, against P, are straight lines intersecting the abscissa at P,=O.O86 (Fig. 6). This value corresponds to the same amount of inaccessible water in the pores as was found by the flow rate experiments (Fig. 4). The mean value of P, was calculated from Figs. 4 and 6 to be 0.088 t 0.018. From the definition of P,, the following equation is derived:





( > VS




From eqn. (7 ), the P, value corresponds to VW/V, = 0.139-0.141, or to 0.096 g of water per g of cellulose. This part of the water may penetrate into the cellulose phase to give a large expansion. As eqn. (6) predicts a linear relationship between J, and P passing through the origin, it may be concluded from Fig. 4 that P, encloses a portion of the water to make it inaccessible for water flow. Assuming that this portion (0.096 g per g of cellulose) is the same for all the membranes used, the absolute values of P can be obtained by subtracting it from P,. It seems that this amount of inaccessible water corresponds to the socalled bound water. This bound water has so far been estimated by various methods, for instance, the differential heat of water sorption by cellulose [ 211, the amounts of freezing and nonfreezing water in moist cellulose [22], the thermal expansion coefficients of water-swollen pellets of cellulose [23] and NMR spectroscopy [ 24-281. Ogiwara et al. reported that the content of bound water was 0.10 g per g of cotton, and that it was influenced greatly by the type and the state of the fibers [ 26,271. Froix and Nelson, using a pulsed NMR technique, suggested four types of water in the cellulose, namely primary and secondary bound water, free water and bulk water [ 281. They gave values for the primary bound water up to 0.09 g per g of cotton, and 0.09 to 0.15-0.20 g/g as the secondary bound water. The amount of inaccessible water for permeation in cellulosic membranes l-8 coincided with the primary bound water mentioned above. The values of P and r [ eqn. (6) 1, as well as the number, N, of pores (calculated from P and r) per unit area of the membrane, are listed in Table 2. Indirect estimation ofporosity for membrane 9 The plots of De_, against J, gave linear relationships for all the membranes used, although the figures have been omitted, showing that the values of De.+ and J, for membrane 9 were not exceptional compared with those for the other membranes. Another method for estimating P for membrane 9 was then tried. The plots of values of De+, for the investigated penetrants l-3 against those of P,, as well as plots of J, against P,, gave linear relationships for membranes l-8, as shown by Figs. 4 and 6. By extrapolating these straight lines in Figs. 4 and 6 and plotting the values of J, and D,, for membrane 9 on the lines, the values of P, were estimated, from which the mean value of P, was determined to be 0.666. Membrane 9, manufactured by a cuprammonium process from cotton linter, shows a quite different swelling behavior from membranes l-8, which are cellophane films (cf. Fig. 2 and Table 3). The values of P, r and N for membrane 9 were estimated by using the same relationships as for the other membranes. These values for membrane 9 obtained from the P, value as estimated above are shown in parentheses in Tables 2 and 4. The experimental values of S, J, and D,,, for membrane 9 from direct


measurements in the present study are shown in the figures and tables without parentheses. As expected from the large values of II,, and J, for membrane 9, the value of P is very large compared with those for the other membrane, but the radius r of the pores is very similar for all membranes. This means that membrane 9 has a larger number of pores per unit area than membranes l-8, which is in agreement with the large swelling ratio by area (Table 3). The diffusion behavior of penetrants l-3 in membrane 9 is similar to that in membranes 1-8, according to the values of kJb in Table 4. Effect of temperature An inference as to whether the diffusion mechanism in water-swollen substrates is similar to that in bulk water may be drawn from the variation of De_, with temperature. The activation energy, E, of the diffusion of co-ions in ionexchange resins was measured as being in close agreement with that in bulk water [ 4,5]. An Arrhenius plot of De._, for 2,4_dinitroaniline in some cellulosic membranes and that of D, in the bulk solution are shown in Fig. 7. All the values of E in the cellulosic membranes were approximately the same (Table



3.0 3.1 T-' x 103(K-')

Fig. 7. Arrhenius



plots of D,, for 2,4-dinitroaniline

in various membranes

and of D, in bulk water.

TABLE 5 Activation

energies, E, of diffusion for 2,4-dinitroaniline Membrane

E (kJ/mol)

in various membranes

and in bulk water




















Average value of E= 19.7 rt0.3 kJ/mol. E in bulk water = 19.5 kJ/mol.



Values of k,P/b for the diffusion of 2,4-dinitroaniline


k,P/b (- ) at a temp. (“C) 30

50 0.101 0.094 0.122



0.102 0.092

3 4

0.096 0.123 0.122

5 6 7 8 9

(klP/b= D&D,)




in various membranes









0.092 0.126 0.123 0.093 0.095 0.111 0.121

0.094 0.117 0.121

0.094 0.124 0.123 0.094 0.097 0.112 0.121


0.093 0.096 0.110 0.116

0.123 0.121 0.093 0.097 0.111 0.127

0.122 0.094 0.098 0.114 0.117

0.095 0.130 0.128 0.100 0.098 0.113 0.126





0.093 0.095 0.110 0.120 0.205


5). No differences in E were observed between the original cellulosic membranes and the cellulosic membranes that had been reactively dyed with C.I. reactive Blue 2. These values of E were approximately equal to that of E in the bulk solution. This implies that no measurable difference exists between the structural properties of bulk water and those of water in the membrane. The values of &P/b defined by the relationship De_, = &PD,/b were calculated as shown in Table 6. Since it was confirmed that the values of kiP/b were constant over the temperature range examined, the kiP values must be constant within the same temperature range. Estimation of P by using the diffusion coefficient of nonionic penetrant may be a useful method for characterizing cellulosic membranes. Structure effect of penetrants The values of kiP/b were estimated for membranes l-9 at 80 oC, as shown in Table 7, where suffixes 1,2 and 3 of ki denote the penetrants 2,4-dinitroaniline, p-nitroaniline and 1,4-bis (4-hydroxyphenylazo)benzene, respectively. Assuming that the values of b are the same for each of penetrants, the values of k2/k1, k3/k1 and k3/k2 can be calculated (Table 7). Within experimental error, each of the ratios kp/kl, k,/k, and k,/k, is equal to 1. Furthermore, the inaccessible portion of the porosity, P,, is the same for all membranes, as is shown in Fig. 6. This means that there is no indication of molecular size hindrance for the permeation of penetrants l-3 through the membranes examined. P represents only that part of the water in the membrane which is accessible for the diffusion process, and since the activation energy for diffusion of 2,4_dinitroaniline through these membranes was the same as for diffusion in bulk solution, it was concluded that this pore water has the same viscosity as



Values of k,P/b and their ratios for nonionic


@‘lb (- 1 i=l


3 4 5

0.101 0.093 0.117 0.120 0.093

6 7 8 9

0.094 0.110 0.120 0.205

0.107 0.098 0.121 0.120 0.096 0.096 0.112 0.122 0.216

1 2



at 80°C

b/k, t--j


1.06 1.05 1.03 1.00 1.03 1.02 1.01 1.01

1.10 1.12 1.11 1.08 1.08


Wk, t-1

i=3 0.111 0.104 0.130 0.130 0.101 0.099 0.119 0.131 0.218

1.04 1.07 1.08 1.08 1.05 1.03 1.06


1.05 1.08 1.09 1.06

1.03 + 0.03

1.08 k 0.03

1.05 k 0.03

1.07 1.04

the bulk water; one is thus inclined to assume that ki=l. Therefore, for an isotropic membrane for which b= fi, the value of $/b is expected to be 0.577. However, the experimental values of ki/b for all three penetrants are considerably smaller, namely 0.387,0.397 and 0.421, respectively. The reason might be that the membranes are anisotropic, with a tortuosity factor b greater than $L These results may imply also that, although there is no size effect of penetrants in permeation through cellulosic membranes, a shape effect does exist, since the slenderer the molecule of the penetrant, the larger is the value of ki/ b obtained [291. List of symbols

b AC

D exP DP




tortuosity factor of the membrane (- ) concentration difference of penetrant between two compartments ( mol/cm3) apparent diffusion coefficient in the membrane (cm’/sec) diffusion coefficient in the pore solution (cm2/sec) diffusion coefficient of penetrant in an aqueous solution (cm2/sec) activation energy (kJ/mol) dry weight of membrane weight of expansion during swelling weight of the imbibed water in the membrane ionic strength amount of substance penetrated through membrane per unit area of the membrane and time ( mol/sec-cm2)


hydraulic permeability or flow rate of water (cm/set) constant given by the relation: D, = kiD, thickness of membrane (cm ) number of membranes ( - ) number of pores per unit area of membrane ( cmW2) porosity of membrane ( cm3 accessible water/cm3 swollen cellulose ) porosity defined by the degree of swelling ( - ) applied pressure (Pa) pore radius of the membrane (cm) degree of swelling ( cm3 swollen cellulose/g dry cellulose ) swelling ratio defined by swollen weight/dry weight ( - ) volume of cellulose volume of expansion by swelling volume of water viscosity of water (Pa-set) density of cellulose (g/cm”) density of water ( g/cm3)

References 1

2 3 4

8 9 10

11 12

S.P. Rowland, Cellulose: Pores, internal surfaces, and the water interface, in: J.C. Arthur (Ed.), Textile and Paper Chemistry and Technology, ACS Symp. Ser., No. 49, American Chemical Society, Washington, DC, 1977, p, 20. J.E. Stone and A.M. Scallan, A structural model for the cell wall of water-swollen wood pulp fibres based on their accessibility to macromolecules, Cellul. Chem. Technol., 2 (1968) 343. J.E. Stone, E. Treiber and B. Abrahamson, Accessibility of regenerated cellulose to solute molecules of molecular weight of 180 to 2 x 106,TAPPI, 52 (1969) 108. P. Meares, The diffusion of co-ions, in: J. Crank andG.S. Park (Eds.), Diffusion in Polymers, Academic Press, London, 1968, p. 405. R. Schlogl and B. Stein, Zur Diffusion in riiumlich vernetzten Gelen, Untersuchungen an einem Kationenaustauscher, Z. Elektrochem., 62 (1958) 340. R. Schlijgl, Ionenbeweglichkeiten in Austauschern, Z. Elektrochem., 57 (1953) 195. E. Glueckauf and R.E. Watts, The Donnan law and its application to ion exchanger polymers, Proc. R. Sot. London, Ser. A, 268 (1962) 339. E. Glueckauf, A new approach to ion exchange polymers, Proc. R. Sot. London, Ser. A, 268 (1962) 350. J.M. Crabtree and E. Glueckauf, Structural analysis of ion semi-permeable membranes by co-ion uptake and diffusion studies, Trans. Faraday Sot., 59 (1963) 2639. S. Uematsu, 0. Egami and Y. Kaneko (Asahi Kasei Kogyo K.K.), Selektiv permeable Membran und Verfahren zur ihrer Herstellung, Ger. Offen, 3,002,438,31 July, 1980, to Asahi Kasei Kogyo KK; Jpn. Kokai Tokkyo Koho, 79 7,049,26 January, 1979. 0. Samuelson, Determination of carboxyl groups, in: R.L. Whister et al. (Eds.), Methods in Carbohydrates Chemistry, Vol. III, Academic Press, New York, NY, 1963, p. 31. T. Hori, R.J. Ott and P. Rys, Sorption and diffusion of ionic dyes in anionic cellophane membranes, Polym. Eng. Sci., 20 (1980) 264.



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