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Permeation of aromatic compounds in aqueous solutions through thin, dense cellulose acetate membranes
Journal of Membrane Science, 1’7 (1984) 275-288 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
275
PERMEATION OF AROMATIC COMPOUNDS IN AQUEOUS SOLUTIONS THROUGH THIN, DENSE CELLULOSE ACETATE MEMBRANES SETSUJI TONE, MITSUO DEMIYA,* Department of Chemical Engineering, Toyonaka, Osaka 560 (Japan)
KOUICHI SHINOHARA** Faculty
of Engineering
and TSUTAO OTAKE
Science,
Osaka University,
(Received April 28, 1983; accepted in revised form July 29, 1983)
The partition and diffusion coefficients of aqueous solutions of aromatic compounds through a thin, dense cellulose acetate membrane were measured at 20” C. The water content and the thickness of the prepared membranes varied from 0.121 to 0.610 by volume fraction and from 17 to 88 pm, respectively. The aromatic solutes used were phenol, aniline, hydroquinone and p-chlorophenol. The solute concentration ranged between 9.0 x 10“ and 1.0 x 10e3 mol/l. The partition coefficients had the following order: p-chlorophenol, phenol, aniline, hydroquinone; they were experimentally correlated with the water content of the swollen membranes. The dependence of the diffusion coefficients on the water content of the membrane was examined using as basis a pore model and a free volume model, respectively. The diffusion coefficients were adequately correlated with the water content of the membrane according to the relation given by the free volume model.
Introduction Separation processes using semipermeable cellulose acetate (CA) membranes have played a significant role in the fields of sea water desalination, hemodialysis and food processing. When they are employed in the rejection of organic substances from aqueous solutions by a reverse osmosis process, aromatic solutes like phenol and its substituted compounds usually are enriched in the permeate solution [l-4] . To understand the transport mechanism of aromatic solutes across a cellulose acetate membrane, it is necessary to describe the permeation characteristics quantitatively in terms of both partition equilibrium and diffusion coefficient of the aromatic solute. The object of the present study is to examine the permeability coefficients of aromatic solutes through a thin, dense CA membrane by measuring both the partition and the diffusion coefficients. A thin, dense CA membrane is used in this study because it has a physically uniform structure. *Present address: Kyowa Hakko Kogyo Co., Osaka 560, Japan. **Present address: Kawasaki Steel Corp., Kurashiki 712, Japan.
0376-7388/84/$03.00
0 1984 Elsevier Science Publishers B.V.
276
The partition and diffusion coefficients of the solute in the membrane are significantly influenced by the water content of the membrane. The authors will examine the measured partition and diffusion coefficients with respect to the water content of the hydrated CA membrane. The transport mechanism of the solute will be inspected using a pore diffusion model approach and a free volume model approach, according to whether or not clearly distinct pores exist in the membrane. Experimental Materials The cellulose acetate used was Eastman-Kodak CA (E398-3) with 39.8 wt.% acetyl content, supplied by Daicel Chemical Industry Co. Ltd. The membrane was cast on a polished glass plate with an adjustable casting blade at room temperature. After very slow evaporation (for at least two full days) to prevent formation of a skin on the surface of the membrane, it was immersed in distilled water at 0°C for 24 hours. Some membranes were used in the permeation experiments without annealing, but most were annealed for a given period (between 60 and 90 min in a hot water bath) at a predetermined temperature between 80’ and 90°C. The water content of the membrane increased with an increasing ratio of weight fraction of formamide to cellulose acetate in the casting soIution under the same annealing conditions. At any fixed composition of the casting solution, the water content of the membrane decreased with increasing temperature. Opaque membranes equilibrated in water were discarded, and only clearly transparent membranes were adopted for the test runs. The thickness of the wet membranes was measured to + 0.5 pm with a Peacock dial thickness gauge, and their specifications are summarized in Table 1. Each membrane sample was cut with a circular edge knife to have a cross-sectional area of 38.5 cm*, and a check of its characteristics was performed by observing whether or not leakage of Eosin Y dye into the permeate took place using reverse osmosis from an aqueous dye solution at 60 atm and 2O’C. If there was no leakage into the permeate, it was assumed that the CA membranes were virtually free of pinholes. Measurement of the water content of the membrane After the CA membrane had been equilibrated with distilled water for a full day, it was removed and quickly blotted between sheets of filter paper. It was then dried in a thermostated drier at 60°C for at least two days. There was no appreciable change in the weight of dry membrane after 24 hours. After the weight of dry membrane reached a constant value, the water lost from the membrane was calculated from the weight loss. Water content, e,, based on the volume fraction, was given as follows: e,
=
(w m,wet W m.dry/&n
+
Wm,dry)/Pw
(Wm,wet
-
Wm,dry
)/Pw
(1)
25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
CA
10 10 20 20 8 8 30 30 20 20 10 10 10 10 10
FA
65 65 55 55 67 67 45 45 55 55 65 65 65 65 65
AC
Composition of casting solutions (wt. %)b
80 90 80
90 80
90 90 90 90 80
tzmp. ( C)
Annealing
60
90 60 60 60 60 60 90 90 60
time (min)
a Superscript ’ on film no. refers to unannealed membrane. bCA = cellulose acetate, FA = formamide, AC = acetone. ‘Dry membrane density, pm = weight of dry membrane/volume
2 3 8 10 11’ 13 16’ 16 17’ 17 18’ 19 22 23’ 27
Film a no.
Specifications of thin, dense cellulose acetate membranes used
TABLE 1
17 20 76 46 29 19 81 88 35 41 31 34 22 40 30
Wet membrane thickness (pm)
of wet membrane; water density, pw = 1 g/cm3.
0.155 0.257 0.380 0.333 0.238 0.315 0.610 0.525 0.498 0.448 0.274 0.197 0.225 0.312 0.121
cm3 wet membrane
Water content cm3 Ha0
1.24 1.24 1.25 1.25 1.24 1.24 1.30 1.30 1.25 1.25 1.24 1.24 1.24 1.24 1.24
Dry membrane densit ’ B (g/cm )
278
where Wm.dry and K,wet are the weights of dry and wet membranes (g), respectively; pm and p,,, are the densities (g/cm3 ) of dry membrane and water, respectively; the observed values of pm are listed in Table 1. Measurement of partition coefficients Organic reagent grade phenol, p-chlorophenol, aniline and hydroquinone used were from Wako Pure Chemical Industries Ltd. First, the wet membrane was soaked in an aqueous solution of the organic substance of concentration, Co, at a temperature of 20 f O.l’C until equilibrium was maintained for 24 hours. When equilibrium was first attained the concentration, Cel, of desorbed solution was determined by high speed liquid chromatography (HSLC). Secondly, after removal of the equilibrated membrane from the solution, it was blotted, and added to a known volume of distilled water. When a second equilibrium was established after a 24-hour desorption period, the concentration, Ce2, of the desorbed solution was also determined by HSLC. The surface area of the membranes used was 24.5 cm2. The partition coefficient, K,, was defined as follows: K, =
moles of solute in membrane/cm3 of wet membrane moles of solute in solution/cm3 of solution
(2)
K, was calculated from the following equation: R
=
s
(Co-ct?1 ‘G2)Vw Ce2VIII
where Co is the concentration of the original soaking solution (mol/l); Cel is the concentration of desorbed solution at first equilibrium (mol/l); VW is the volume of distilled water used (cm3); and V, is the volume of the wet membrane (cm3 ). The R, values determined were independent of solution concentration, which ranged between 9.0 x 10m5 and 1.0 x low3 mol/l. The concentration .of solutes was chosen as 4 x 10m4 mol/l in all subsequent experiments. Desorp tion rate measurement The desorption cell shown in Fig. 1 consists of a Teflon support with a circular passage at its centre. The solutions can be freely circulated and mixed well owing to the circular passage between both glass cells. The organic substances used, phenol, p-chlorophenol, aniline and hydroquinone, were of concentrations varying between 9.6 x lo-’ and 9.18 x 10m4 mol/l. The membrane sample equilibrated with the prescribed concentration of an aqueous organic solution was removed from the solution, and blotted with sheets of filter paper. The membrane was placed in the centre of the support and fixed between the two halves of the glass cell. 4 ml samples of solution were removed from the cell at each time interval, and were analyzed by ultraviolet spectroscopy. After analysis of each sample, it was returned to
279
the original solution in order to keep the solution volume constant at 200 ml. The stirring speed of the impeller was high enough to eliminate the effect of concentration polarization near the membrane surface. All runs were carried out at 20 f O.l’C. The effective surface area of the membrane was 23.8 cm2.
@ upper cell lid
@
paddle
@ upper
@
membrane
@
stirrer
@
circulation
cell
@ support
plate
@
lower
cell
@
sampling
stirrer
hole
port
Fig. 1. Schematic diagram of desorption cell.
tXW3 Fig. 2. Plots of log (C, -
C,)/(C,
[sl - C O) vs. time in desorption rate measurement.
The desorption rate of solute from a plane sheet of membrane into the solution has been treated by assuming Fick’s second law [l-3]. At longer times, when _ZISr2t/a& > 0.1, the relative concentration of the solute in the plane sheet can be expressed approximately by the following equation [ 51 :
where D, is the diffusion coefficient of solute in the membrane (cm2 /set); E, is the membrane thickness (cm); t is the time (set); C_ is the final concentration of solute (mol/l); C,, is the initial concentration (mol/l); and Ct is the concentration at time t (mol/l). According to eqn. (4), a plot of log]Cco - C, MC_ - C, )] against t yields a straight line of slope - T~D,/~&. In Fig. 2, typical logarithmic plots of the experimental relative concentration versus time are shown. The diffusion coefficient, D,, was determined by matching the straight line to eqn. (4) and by obtaining its slope. D, was independent of variations of the solute concentration. Dialysis rate measurement The dialysis cell is shown in Fig. 3. The membrane was kept for 24 hours in distilled water and then removed and blotted. It was placed into the membrane holder of the dialysis cell, all in a thermostated water bath at 2O’C. Cell compartment 1 was filled with the solution of prescribed concentration and cell compartment 2 with distilled water. The solutions in both cell compartments were stirred well. The impeller speed was chosen to eliminate concentration polarization on the surface of the membrane. The concentrations of the solutions in both cell compartments were measured by taking 4 ml samples from their respective compartment at each time interval; these were then analyzed as in the desorption rate measurements. During measurement, the concentration of aqueous organic solution in compartment 1 was maintained at its initial value owing to the transport of a very small amount of solute from compartment 1 to compartment 2. No volume flow across the membrane by osmotic flow was observed in the dialysis cell.
@flask @ cell @ @
bolt paddle
stirrer
@
membrane
@
membrane
@ @
sampling port thermostated bath
Fig. 3. Schematic diagram of dialysis cell.
support
plate
283
membrane:
solute:
_
film no.17
aniline
Cl =4.0x1 d4 molll Ds=4.06x1decm2/s
-
Ks=14.5
, 2
0
4
1 6
I
I
I
8
I
,
10
,
_
12
tX10-3 [s-j Fig. 4. Plot of Qf vs. time in dialysis
rate measurement.
Each compartment of the dialysis cell had a volume of 200 ml; the effective surface area of the membrane in the dialysis cell was 18.5 cm’. In the dialysis rate measurements, the initial concentration of solute in the membrane is equal to zero, as the membrane is equilibrated with distilled water. One face of the membrane in cell compartment 1 is kept at a constant solution concentration, Ci , and the other face in cell compartment 2 is kept initially in distilled water at zero concentration. We will assume that the dialysis process obeys Fick’s second law. For longer time, t, the total amount, Qt, of diffusing solute which has passed through membrane in time t becomes linearly dependent on time t [ 51 :
Qt =
DsC,K L
(5)
A typical plot of observed Qt values against t is shown in Fig. 4. From the slope of the straight line in Fig. 4, and by matching eqn. (5), D, was evaluated by using known values of K,, Cl and 1, . The determined D, values were independent of solute concentrations in the range 9.6 x lo-’ to 9.18 x 10V4 mol/l. The concentration of solute was chosen as 4 x 1O-4 mol/l in all subsequent experiments. Results and discussion Partition coefficient in the membrane KS was dependent on E, in the membrane as is shown in Fig. 5. K, of the aromatic solute decreases with increasing c, . This trend is opposite to that of
282
the partition coefficient of inorganic solutes with e,, reported by Yasuda et al. [ 6, 71 and Kimura et al. [ 81. In the NaCl-water system, the experimental partition coefficient increases with increasing eV. Recently, Burghoff et al. [4] measured the partition coefficient of phenol in homogeneous cellulose acetate membranes of varying acetyl content and reported that K, decreased with increasing E, , Similar to the results obtained in this study. 50
250
40
200
30
150
20
100
10
50
0 0
0.2
0.4
0.6 &v
0.6
n 1. -
L-1
Fig. 5. Dependence of partition coefficients of aromatic solutes on water content at 2o"c.
In the partition equilibrium between an aromatic solute and a highly hydrated polymer membrane, water molecules in the solution strongly adsorb on the site of the hydrophilic ester group on the CA polymer chains [ 3, 91, and KS decreases as the water content of the membrane increases. However, in the case of a lowly hydrated membrane, a hydrophobic interaction between the aromatic ring of the solute and the carbon-hydrogen bond of the CA polymer will become significant. As a result, K, may increase as E, decreases. On the other hand, in the case of aqueous salt solution, the CA polymer chains expe1 salt ions from the polymer matrix, owing to the high hydrogen bonding strength of water. This will be the reason why the trend of the equilibrium relation between aromatic solute and polymer membrane with varying water content is quite different from that of the equilibrium relation between salt and polymer membrane. We will attempt to demonstrate the correlation of KS with E, . Assumptions will be made so that the partition coefficient consists of the sum of two terms, one contributed by the effect of solute solubility in the water volume fraction, f, , in the membrane phase and another by the hydrophobic interaction between the organic solute and the polymer volume fraction, 1 .- E, . Thus, K, can be expressed by
K, = ae, + b(1 -E,)
(6)
283
TABLE
2
Values of experimental parameter b and parameters a and fl in partition and diffusion coefficients Solute
b
a
P
Phenol Aniline Hydroquinone p-Chlorophenol Watera NaClb
36.5 25.3 20.0 264
0.5 0.5 0.5 0.5
14.0 14.5 14.5 15.5 4.5 0.985
a Date from Yasuda et al., [ 6, 7 1. ba’ = 1, [6,7].
where a and b are experimental constants, depending on the aromatic solute used. When e, + 1, KS is assumed to approach unity, and we hence obtain a = 1. Equation (7) can then be obtained: K, = b + (1 -- b)ev Matching eqn. (7) to plots of KS vs. E, in Fig. 5, the value of b was determined and listed in Table 2 for four kinds of aromatic solutes used. The constant, b, was influenced by changes in the substituents of phenol, and its value decreased in the following order: p-chlorophenol, phenol, aniline, hydroquinone. As suggested by Matsuura and Sourirajan [9], it can be considered that hydroquinone molecules have an electron-releasing group (the OH group) and are not adsorbed easily on to the CA polymer chains because of the electron-releasing site, similar to an ester or an ether bond, but p-chlorophenol molecules have a strong electron-attractive group (the Cl group), and can easily be adsorbed on to the polymer chain (sorption site). Diffusion coefficient in the membrane Values of D, obtained by both desorption rate and dialysis rate measurements were in good agreement. D, decreased with decreasing E, . Using a parameter, X, related to water content such that x = (1 - E, )/ev , we obtained plots of D, against x which are shown in Figs. 6-9, each for a different aromatic solute. Recently, Burghoff et al. [4] determined D, of phenol in a homogeneous CA membrane using an immersion experiment for the partition coefficient and a reverse osmosis experiment for the permeability coefficients; they reported a value of 1.2 x 10m9 cm2 /set at 25°C for a homogeneous CA membrane with an acetyl content 39.1% by wt.
284
(E, = 0.15). This value was very close to D, = 1.0 x lo-9 cm2 /set (E, = 0.158) at 20°C obtained for the thin, dense CA membrane used in the present study.
solute:
,
Fig.
=
(i”U
012345670
0
X=(1 -WE,
aniline
1
2
[ -1
3
4
5
6
X=(1 -E&E,
6. Relation
between
D, and x in the phenol-water
system.
Fig. ‘7. Relation
between
D, and x in the aniline--water
system.
7
6
I-1
‘GE ” Y
012345678
0 x =(l
-G)/
E” [ - 1
Fig.
8. Relation
between
D, and x in the hydroquinonewater
Fig.
9. Relation
between
D, and x in the p-chlorophenol-water
1
2
3 X=(1
system. system.
4
5
-&)I&
6 [
7
-1
8
285
To describe the diffusion process of a solute through a hydrated membrane, depending on whether or not fine, small pores exist in the polymer matrix, two discrete approaches have been developed, the pore model relation of Mackie and Meares [lo] and the free volume model relation of Yasuda et al. [6, 71. In the pore model relation of Mackie and Meares, the influence of water content on the diffusion coefficient can be analyzed by relating the penetrating distance of water molecules to a tortuosity factor, r, of the membrane, including a twisted small pore. The tortuosity factor is related to the water content by assuming a path length for solute diffusion in a macromolecular lattice array where the solute moves from one lattice point to one of its nearest neighbours as a result of a random jump. Mackie and Meares presented the following relation for the diffusion coefficient: D,
= DSO /T2 = D,, (1 + 2x)-2
(8)
where r = e, /(2 - E, ), and DS,, is the molecular diffusivity in free solution. Osterhoudt [ll] reported that eqn. (8) could be applied to predict the diffusion coefficient of chain-like molecules such as ethanol and glycerol in lowly hydrated membranes with x less than 1.45. The D, values calculated from eqn. (8), however, showed a considerable deviation, even in the range of low hydration in the membrane, i.e., x < 2, when D,, was evaluated using the relation of Wilke and Chang [12] . Yasuda et al. [6, 71 assumed that, as a consequence of the plasticizing effect of water in a swollen membrane, the polymer segments in the waterswollen membrane exhibit a fair degree of mobility, so that the size and shape of the pores or channels may continually change, and the movement of diffusant can be visualized as occurring by activated diffusion in a free volume through fixed channels. Osterhoudt suggested that the free volume model treatment of Yasuda et al. is more appropriate for a diffusant of appreciable size in a swollen, random polymer matrix. Based on the approach of Yasuda et al., the equation for the diffusion coefficient is expressed by D,
= DSO exp [-
V*(I/Vf
-
l/V,,,
)I
(9)
where Vf is the total free volume per unit volume of the membrane, and V* is a characteristic volume required to accommodate the diffusant in the membrane, namely the critical volume proportional to the cross-section of the diffusing entity multiplied by the diffusional jump distance. Assuming additivity of free volume contributions of water and polymer, Vf can be described by Vf
=
E” Vf,,
+
(10)
(1 - E")Vf,rn
where V,,, is the free volume of pure water per unit volume of the phase, and Vf,, is the free volume of randomly coiled macromolecules having some unoccupied space per unit volume of phase. Combination of eqns. (9) and (10) gives the following:
D,
= Dso exp[-@x(1
-or)/(l
-t ox)]
(11)
286
where the parameters cyand 6 are denoted by LX= Vfa, /V,,, and P = vV%,, * Yasuda et al. measured the diffusion coefficients of water and salt in homogeneous membranes of hydrogels, cross-linked copolymer films and CA polymers cast from acetone solution. Applying eqn. (11) to experimental data, they reported that (x = 0.5 and /3 = 4.0 for water diffusion, and that o( = 0 and /3 = 0.986 for salt diffusion. We will assume that the dense CA membranes prepared in this study are very close to having a symmetrical structure [8] and that water in the hydrated polymer matrix behaves similarly to that in the homogeneous membrane. Matching eqn. (11) with the plots of log D, vs. x shown in Figs. 6-9 gave (Yvalues of around 0.5 and so o( was fixed at this value. The estimated p values then ranged between 14 and 16 for aromatic solutes; they are listed in Table 2. The fl values in the case of aromatic solutes are about four times those in the case of water. In membranes of high hydration, the aromatic solute can diffuse primarily in the free volume of water and macromolecules in the polymer matrix. However, when hydration of the membrane is low, an appreciably larger molecule than water would be expected to encounter a greater tortuosity or steric hindrance in small pores or channels. The movement of solute will be greatly affected by physicochemical interactions between aromatic solute and polymer segments. As a result, the value of 0 becomes larger, owing to the high barrier to transport. Further, the size distribution of pores in the membrane limits the critical pore size for aromatic solutes of larger molecular size than water. From the complicated geometry of the polymer network, the free volume concept will describe the transport characteristics for the diffusion of an aromatic solute in the hydrated membrane adequately. Conclusion Investigations were made of the mechanism of transport of aromatic substances from aqueous solutions through a thin, dense CA membrane of close to uniform structure. The two factors influencing the permeability of the membrane to the solute were found to be the partition and diffusion coefficients. The partition coefficient, measured by the immersion method, was greatly dependent on the water content of the hydrated membrane, and increased as the water content decreased. By considering a hydrophobic interaction between the aromatic ring of the solute and the CA polymer chains, the partition coefficient could be experimentally correlated with water content. The diffusion coefficient was also greatly dependent on the water content of the membrane and becomes very low in case of low water content. Two treatments, the pore model relation of Mackie and Meares and the free volume model relation of Yasuda et al., were tested to describe the dependence of the diffusion coefficient on the water content. Consequently, for a varying water content of the hydrated membrane, the free volume model relation could be applied to adequately correlate the diffusion coefficient with the water content.
287
List of symbols
a, b CO C ‘21 C e2 ct
C,
L
Qt V*
Experimental parameters used in eqn. (6). Concentration of original soaking solution (mol/l). Concentration of desorbed solution at first equilibrium (mol/l). Concentration of desorbed solution at second equilibrium (mol/l). Concentration of desorbed solution at time t (mol/l). Concentration of desorbed solution at infinite time or at equilibrium (mol/l). Diffusion coefficient of solute in the membrane (cm2 /set). Diffusion coefficient of solute in free solution (cm2 /set). Partition coefficient of solute in the membrane (mol solute per cm3 membrane/m01 solute per cm3 solution). Thickness of wet membrane (cm). Total amount of diffusing solute which passed through the membrane at time t (mol/cm2 membrane). Characteristic volume required to accommodate the diffusant in the membrane (cm3 ). Free volume of randomly coiled macromolecules having some unoccupied space per unit volume phase (cm3 ). Free volume of pure water per unit volume of the phase (cm3 ). Volume of wet membrane (cm3 )_ Volume of a distilled water for second desorption procedure (cm3 ). (1 - G)/G Parameters used in eqn. (11). Volume fraction of water in the membrane. Tortuosity of pore in the membrane.
References H.K. Lonsdale, U. Merten and M. Tagami, Phenol transport in cellulose acetate membranes, J. Appl. Polym. Sci., 11 (1967) 1807. H.K. Lonsdale, B.P. Cross, F.M. Graber and C.E. Milstead, Permeability of cellulose acetate membranes to selected solutes, J. Macromol. Sci., Phys., B5, (1) (1971) 16’7. J.E. Anderson, S.J. Hoffman and CR. Peters, Factors influencing reverse osmosis rejection of organic solutes from aqueous solution, J. Phys. Chem., 76 (1980) 4006. H.-G. Burghoff, K.L. Lee and W. Pusch, Characterization of transport across cellulose acetate membranes in the presence of strong solute-membrane interacterions, J. Appl. Polym. Sci., 25 (1980) 323. J. Crank, The Mathematics of Diffusion, 2nd edn., Clarendon Press, Oxford, 1978, pp. 49 and 56. H. Yasuda, C.E. Lamase and L.D. Ikenberry, Permeability of solutes through hydrated polymer membranes, Part I. Diffusion of sodium chloride, Makromol. Chem., 118 (1968) 19. H. Yasuda, C.E. Lamaze and A. Peterlin, Diffusive and hydraulic permeabilities of water in water-swollen polymer membranes, J. Polym. Sci., A-2, 9 (1971) 1117. S. Kimura, J. Irie and T. Miyauchi, Characteristics of cellulose acetate membranes used for the reverse osmosis process: The case of symmetric membranes, MAKU(Membrane), 1 (1976) 231.
288 9
10 11
12
T. Matsuura and S. Sourirajan, Reverse osmosis separation of phenols in aqueous solutions using porous cellulose acetate membranes, J. Appl. Polym. Sci., 16 (1972) 2531. J.S. Mackie and P. Meares, The diffusion of electrolytes in a cation-exchange resin membrane. I. Theoretical, Proc. Royal Sot., Ser. A, 232 (1955) 498. H.W. Osterhoudt, Transport properties of hydrophilic polymer membranes. The influence of volume fraction polymer and tortuosity on permeability, J. Phys. Chem., 78 (1974) 408. C.R. Wilke and P. Chang, Correlation of diffusion coefficients in dilute solutions, AIChE J., 1 (1955) 264.
275
PERMEATION OF AROMATIC COMPOUNDS IN AQUEOUS SOLUTIONS THROUGH THIN, DENSE CELLULOSE ACETATE MEMBRANES SETSUJI TONE, MITSUO DEMIYA,* Department of Chemical Engineering, Toyonaka, Osaka 560 (Japan)
KOUICHI SHINOHARA** Faculty
of Engineering
and TSUTAO OTAKE
Science,
Osaka University,
(Received April 28, 1983; accepted in revised form July 29, 1983)
The partition and diffusion coefficients of aqueous solutions of aromatic compounds through a thin, dense cellulose acetate membrane were measured at 20” C. The water content and the thickness of the prepared membranes varied from 0.121 to 0.610 by volume fraction and from 17 to 88 pm, respectively. The aromatic solutes used were phenol, aniline, hydroquinone and p-chlorophenol. The solute concentration ranged between 9.0 x 10“ and 1.0 x 10e3 mol/l. The partition coefficients had the following order: p-chlorophenol, phenol, aniline, hydroquinone; they were experimentally correlated with the water content of the swollen membranes. The dependence of the diffusion coefficients on the water content of the membrane was examined using as basis a pore model and a free volume model, respectively. The diffusion coefficients were adequately correlated with the water content of the membrane according to the relation given by the free volume model.
Introduction Separation processes using semipermeable cellulose acetate (CA) membranes have played a significant role in the fields of sea water desalination, hemodialysis and food processing. When they are employed in the rejection of organic substances from aqueous solutions by a reverse osmosis process, aromatic solutes like phenol and its substituted compounds usually are enriched in the permeate solution [l-4] . To understand the transport mechanism of aromatic solutes across a cellulose acetate membrane, it is necessary to describe the permeation characteristics quantitatively in terms of both partition equilibrium and diffusion coefficient of the aromatic solute. The object of the present study is to examine the permeability coefficients of aromatic solutes through a thin, dense CA membrane by measuring both the partition and the diffusion coefficients. A thin, dense CA membrane is used in this study because it has a physically uniform structure. *Present address: Kyowa Hakko Kogyo Co., Osaka 560, Japan. **Present address: Kawasaki Steel Corp., Kurashiki 712, Japan.
0376-7388/84/$03.00
0 1984 Elsevier Science Publishers B.V.
276
The partition and diffusion coefficients of the solute in the membrane are significantly influenced by the water content of the membrane. The authors will examine the measured partition and diffusion coefficients with respect to the water content of the hydrated CA membrane. The transport mechanism of the solute will be inspected using a pore diffusion model approach and a free volume model approach, according to whether or not clearly distinct pores exist in the membrane. Experimental Materials The cellulose acetate used was Eastman-Kodak CA (E398-3) with 39.8 wt.% acetyl content, supplied by Daicel Chemical Industry Co. Ltd. The membrane was cast on a polished glass plate with an adjustable casting blade at room temperature. After very slow evaporation (for at least two full days) to prevent formation of a skin on the surface of the membrane, it was immersed in distilled water at 0°C for 24 hours. Some membranes were used in the permeation experiments without annealing, but most were annealed for a given period (between 60 and 90 min in a hot water bath) at a predetermined temperature between 80’ and 90°C. The water content of the membrane increased with an increasing ratio of weight fraction of formamide to cellulose acetate in the casting soIution under the same annealing conditions. At any fixed composition of the casting solution, the water content of the membrane decreased with increasing temperature. Opaque membranes equilibrated in water were discarded, and only clearly transparent membranes were adopted for the test runs. The thickness of the wet membranes was measured to + 0.5 pm with a Peacock dial thickness gauge, and their specifications are summarized in Table 1. Each membrane sample was cut with a circular edge knife to have a cross-sectional area of 38.5 cm*, and a check of its characteristics was performed by observing whether or not leakage of Eosin Y dye into the permeate took place using reverse osmosis from an aqueous dye solution at 60 atm and 2O’C. If there was no leakage into the permeate, it was assumed that the CA membranes were virtually free of pinholes. Measurement of the water content of the membrane After the CA membrane had been equilibrated with distilled water for a full day, it was removed and quickly blotted between sheets of filter paper. It was then dried in a thermostated drier at 60°C for at least two days. There was no appreciable change in the weight of dry membrane after 24 hours. After the weight of dry membrane reached a constant value, the water lost from the membrane was calculated from the weight loss. Water content, e,, based on the volume fraction, was given as follows: e,
=
(w m,wet W m.dry/&n
+
Wm,dry)/Pw
(Wm,wet
-
Wm,dry
)/Pw
(1)
25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
CA
10 10 20 20 8 8 30 30 20 20 10 10 10 10 10
FA
65 65 55 55 67 67 45 45 55 55 65 65 65 65 65
AC
Composition of casting solutions (wt. %)b
80 90 80
90 80
90 90 90 90 80
tzmp. ( C)
Annealing
60
90 60 60 60 60 60 90 90 60
time (min)
a Superscript ’ on film no. refers to unannealed membrane. bCA = cellulose acetate, FA = formamide, AC = acetone. ‘Dry membrane density, pm = weight of dry membrane/volume
2 3 8 10 11’ 13 16’ 16 17’ 17 18’ 19 22 23’ 27
Film a no.
Specifications of thin, dense cellulose acetate membranes used
TABLE 1
17 20 76 46 29 19 81 88 35 41 31 34 22 40 30
Wet membrane thickness (pm)
of wet membrane; water density, pw = 1 g/cm3.
0.155 0.257 0.380 0.333 0.238 0.315 0.610 0.525 0.498 0.448 0.274 0.197 0.225 0.312 0.121
cm3 wet membrane
Water content cm3 Ha0
1.24 1.24 1.25 1.25 1.24 1.24 1.30 1.30 1.25 1.25 1.24 1.24 1.24 1.24 1.24
Dry membrane densit ’ B (g/cm )
278
where Wm.dry and K,wet are the weights of dry and wet membranes (g), respectively; pm and p,,, are the densities (g/cm3 ) of dry membrane and water, respectively; the observed values of pm are listed in Table 1. Measurement of partition coefficients Organic reagent grade phenol, p-chlorophenol, aniline and hydroquinone used were from Wako Pure Chemical Industries Ltd. First, the wet membrane was soaked in an aqueous solution of the organic substance of concentration, Co, at a temperature of 20 f O.l’C until equilibrium was maintained for 24 hours. When equilibrium was first attained the concentration, Cel, of desorbed solution was determined by high speed liquid chromatography (HSLC). Secondly, after removal of the equilibrated membrane from the solution, it was blotted, and added to a known volume of distilled water. When a second equilibrium was established after a 24-hour desorption period, the concentration, Ce2, of the desorbed solution was also determined by HSLC. The surface area of the membranes used was 24.5 cm2. The partition coefficient, K,, was defined as follows: K, =
moles of solute in membrane/cm3 of wet membrane moles of solute in solution/cm3 of solution
(2)
K, was calculated from the following equation: R
=
s
(Co-ct?1 ‘G2)Vw Ce2VIII
where Co is the concentration of the original soaking solution (mol/l); Cel is the concentration of desorbed solution at first equilibrium (mol/l); VW is the volume of distilled water used (cm3); and V, is the volume of the wet membrane (cm3 ). The R, values determined were independent of solution concentration, which ranged between 9.0 x 10m5 and 1.0 x low3 mol/l. The concentration .of solutes was chosen as 4 x 10m4 mol/l in all subsequent experiments. Desorp tion rate measurement The desorption cell shown in Fig. 1 consists of a Teflon support with a circular passage at its centre. The solutions can be freely circulated and mixed well owing to the circular passage between both glass cells. The organic substances used, phenol, p-chlorophenol, aniline and hydroquinone, were of concentrations varying between 9.6 x lo-’ and 9.18 x 10m4 mol/l. The membrane sample equilibrated with the prescribed concentration of an aqueous organic solution was removed from the solution, and blotted with sheets of filter paper. The membrane was placed in the centre of the support and fixed between the two halves of the glass cell. 4 ml samples of solution were removed from the cell at each time interval, and were analyzed by ultraviolet spectroscopy. After analysis of each sample, it was returned to
279
the original solution in order to keep the solution volume constant at 200 ml. The stirring speed of the impeller was high enough to eliminate the effect of concentration polarization near the membrane surface. All runs were carried out at 20 f O.l’C. The effective surface area of the membrane was 23.8 cm2.
@ upper cell lid
@
paddle
@ upper
@
membrane
@
stirrer
@
circulation
cell
@ support
plate
@
lower
cell
@
sampling
stirrer
hole
port
Fig. 1. Schematic diagram of desorption cell.
tXW3 Fig. 2. Plots of log (C, -
C,)/(C,
[sl - C O) vs. time in desorption rate measurement.
The desorption rate of solute from a plane sheet of membrane into the solution has been treated by assuming Fick’s second law [l-3]. At longer times, when _ZISr2t/a& > 0.1, the relative concentration of the solute in the plane sheet can be expressed approximately by the following equation [ 51 :
where D, is the diffusion coefficient of solute in the membrane (cm2 /set); E, is the membrane thickness (cm); t is the time (set); C_ is the final concentration of solute (mol/l); C,, is the initial concentration (mol/l); and Ct is the concentration at time t (mol/l). According to eqn. (4), a plot of log]Cco - C, MC_ - C, )] against t yields a straight line of slope - T~D,/~&. In Fig. 2, typical logarithmic plots of the experimental relative concentration versus time are shown. The diffusion coefficient, D,, was determined by matching the straight line to eqn. (4) and by obtaining its slope. D, was independent of variations of the solute concentration. Dialysis rate measurement The dialysis cell is shown in Fig. 3. The membrane was kept for 24 hours in distilled water and then removed and blotted. It was placed into the membrane holder of the dialysis cell, all in a thermostated water bath at 2O’C. Cell compartment 1 was filled with the solution of prescribed concentration and cell compartment 2 with distilled water. The solutions in both cell compartments were stirred well. The impeller speed was chosen to eliminate concentration polarization on the surface of the membrane. The concentrations of the solutions in both cell compartments were measured by taking 4 ml samples from their respective compartment at each time interval; these were then analyzed as in the desorption rate measurements. During measurement, the concentration of aqueous organic solution in compartment 1 was maintained at its initial value owing to the transport of a very small amount of solute from compartment 1 to compartment 2. No volume flow across the membrane by osmotic flow was observed in the dialysis cell.
@flask @ cell @ @
bolt paddle
stirrer
@
membrane
@
membrane
@ @
sampling port thermostated bath
Fig. 3. Schematic diagram of dialysis cell.
support
plate
283
membrane:
solute:
_
film no.17
aniline
Cl =4.0x1 d4 molll Ds=4.06x1decm2/s
-
Ks=14.5
, 2
0
4
1 6
I
I
I
8
I
,
10
,
_
12
tX10-3 [s-j Fig. 4. Plot of Qf vs. time in dialysis
rate measurement.
Each compartment of the dialysis cell had a volume of 200 ml; the effective surface area of the membrane in the dialysis cell was 18.5 cm’. In the dialysis rate measurements, the initial concentration of solute in the membrane is equal to zero, as the membrane is equilibrated with distilled water. One face of the membrane in cell compartment 1 is kept at a constant solution concentration, Ci , and the other face in cell compartment 2 is kept initially in distilled water at zero concentration. We will assume that the dialysis process obeys Fick’s second law. For longer time, t, the total amount, Qt, of diffusing solute which has passed through membrane in time t becomes linearly dependent on time t [ 51 :
Qt =
DsC,K L
(5)
A typical plot of observed Qt values against t is shown in Fig. 4. From the slope of the straight line in Fig. 4, and by matching eqn. (5), D, was evaluated by using known values of K,, Cl and 1, . The determined D, values were independent of solute concentrations in the range 9.6 x lo-’ to 9.18 x 10V4 mol/l. The concentration of solute was chosen as 4 x 1O-4 mol/l in all subsequent experiments. Results and discussion Partition coefficient in the membrane KS was dependent on E, in the membrane as is shown in Fig. 5. K, of the aromatic solute decreases with increasing c, . This trend is opposite to that of
282
the partition coefficient of inorganic solutes with e,, reported by Yasuda et al. [ 6, 71 and Kimura et al. [ 81. In the NaCl-water system, the experimental partition coefficient increases with increasing eV. Recently, Burghoff et al. [4] measured the partition coefficient of phenol in homogeneous cellulose acetate membranes of varying acetyl content and reported that K, decreased with increasing E, , Similar to the results obtained in this study. 50
250
40
200
30
150
20
100
10
50
0 0
0.2
0.4
0.6 &v
0.6
n 1. -
L-1
Fig. 5. Dependence of partition coefficients of aromatic solutes on water content at 2o"c.
In the partition equilibrium between an aromatic solute and a highly hydrated polymer membrane, water molecules in the solution strongly adsorb on the site of the hydrophilic ester group on the CA polymer chains [ 3, 91, and KS decreases as the water content of the membrane increases. However, in the case of a lowly hydrated membrane, a hydrophobic interaction between the aromatic ring of the solute and the carbon-hydrogen bond of the CA polymer will become significant. As a result, K, may increase as E, decreases. On the other hand, in the case of aqueous salt solution, the CA polymer chains expe1 salt ions from the polymer matrix, owing to the high hydrogen bonding strength of water. This will be the reason why the trend of the equilibrium relation between aromatic solute and polymer membrane with varying water content is quite different from that of the equilibrium relation between salt and polymer membrane. We will attempt to demonstrate the correlation of KS with E, . Assumptions will be made so that the partition coefficient consists of the sum of two terms, one contributed by the effect of solute solubility in the water volume fraction, f, , in the membrane phase and another by the hydrophobic interaction between the organic solute and the polymer volume fraction, 1 .- E, . Thus, K, can be expressed by
K, = ae, + b(1 -E,)
(6)
283
TABLE
2
Values of experimental parameter b and parameters a and fl in partition and diffusion coefficients Solute
b
a
P
Phenol Aniline Hydroquinone p-Chlorophenol Watera NaClb
36.5 25.3 20.0 264
0.5 0.5 0.5 0.5
14.0 14.5 14.5 15.5 4.5 0.985
a Date from Yasuda et al., [ 6, 7 1. ba’ = 1, [6,7].
where a and b are experimental constants, depending on the aromatic solute used. When e, + 1, KS is assumed to approach unity, and we hence obtain a = 1. Equation (7) can then be obtained: K, = b + (1 -- b)ev Matching eqn. (7) to plots of KS vs. E, in Fig. 5, the value of b was determined and listed in Table 2 for four kinds of aromatic solutes used. The constant, b, was influenced by changes in the substituents of phenol, and its value decreased in the following order: p-chlorophenol, phenol, aniline, hydroquinone. As suggested by Matsuura and Sourirajan [9], it can be considered that hydroquinone molecules have an electron-releasing group (the OH group) and are not adsorbed easily on to the CA polymer chains because of the electron-releasing site, similar to an ester or an ether bond, but p-chlorophenol molecules have a strong electron-attractive group (the Cl group), and can easily be adsorbed on to the polymer chain (sorption site). Diffusion coefficient in the membrane Values of D, obtained by both desorption rate and dialysis rate measurements were in good agreement. D, decreased with decreasing E, . Using a parameter, X, related to water content such that x = (1 - E, )/ev , we obtained plots of D, against x which are shown in Figs. 6-9, each for a different aromatic solute. Recently, Burghoff et al. [4] determined D, of phenol in a homogeneous CA membrane using an immersion experiment for the partition coefficient and a reverse osmosis experiment for the permeability coefficients; they reported a value of 1.2 x 10m9 cm2 /set at 25°C for a homogeneous CA membrane with an acetyl content 39.1% by wt.
284
(E, = 0.15). This value was very close to D, = 1.0 x lo-9 cm2 /set (E, = 0.158) at 20°C obtained for the thin, dense CA membrane used in the present study.
solute:
,
Fig.
=
(i”U
012345670
0
X=(1 -WE,
aniline
1
2
[ -1
3
4
5
6
X=(1 -E&E,
6. Relation
between
D, and x in the phenol-water
system.
Fig. ‘7. Relation
between
D, and x in the aniline--water
system.
7
6
I-1
‘GE ” Y
012345678
0 x =(l
-G)/
E” [ - 1
Fig.
8. Relation
between
D, and x in the hydroquinonewater
Fig.
9. Relation
between
D, and x in the p-chlorophenol-water
1
2
3 X=(1
system. system.
4
5
-&)I&
6 [
7
-1
8
285
To describe the diffusion process of a solute through a hydrated membrane, depending on whether or not fine, small pores exist in the polymer matrix, two discrete approaches have been developed, the pore model relation of Mackie and Meares [lo] and the free volume model relation of Yasuda et al. [6, 71. In the pore model relation of Mackie and Meares, the influence of water content on the diffusion coefficient can be analyzed by relating the penetrating distance of water molecules to a tortuosity factor, r, of the membrane, including a twisted small pore. The tortuosity factor is related to the water content by assuming a path length for solute diffusion in a macromolecular lattice array where the solute moves from one lattice point to one of its nearest neighbours as a result of a random jump. Mackie and Meares presented the following relation for the diffusion coefficient: D,
= DSO /T2 = D,, (1 + 2x)-2
(8)
where r = e, /(2 - E, ), and DS,, is the molecular diffusivity in free solution. Osterhoudt [ll] reported that eqn. (8) could be applied to predict the diffusion coefficient of chain-like molecules such as ethanol and glycerol in lowly hydrated membranes with x less than 1.45. The D, values calculated from eqn. (8), however, showed a considerable deviation, even in the range of low hydration in the membrane, i.e., x < 2, when D,, was evaluated using the relation of Wilke and Chang [12] . Yasuda et al. [6, 71 assumed that, as a consequence of the plasticizing effect of water in a swollen membrane, the polymer segments in the waterswollen membrane exhibit a fair degree of mobility, so that the size and shape of the pores or channels may continually change, and the movement of diffusant can be visualized as occurring by activated diffusion in a free volume through fixed channels. Osterhoudt suggested that the free volume model treatment of Yasuda et al. is more appropriate for a diffusant of appreciable size in a swollen, random polymer matrix. Based on the approach of Yasuda et al., the equation for the diffusion coefficient is expressed by D,
= DSO exp [-
V*(I/Vf
-
l/V,,,
)I
(9)
where Vf is the total free volume per unit volume of the membrane, and V* is a characteristic volume required to accommodate the diffusant in the membrane, namely the critical volume proportional to the cross-section of the diffusing entity multiplied by the diffusional jump distance. Assuming additivity of free volume contributions of water and polymer, Vf can be described by Vf
=
E” Vf,,
+
(10)
(1 - E")Vf,rn
where V,,, is the free volume of pure water per unit volume of the phase, and Vf,, is the free volume of randomly coiled macromolecules having some unoccupied space per unit volume of phase. Combination of eqns. (9) and (10) gives the following:
D,
= Dso exp[-@x(1
-or)/(l
-t ox)]
(11)
286
where the parameters cyand 6 are denoted by LX= Vfa, /V,,, and P = vV%,, * Yasuda et al. measured the diffusion coefficients of water and salt in homogeneous membranes of hydrogels, cross-linked copolymer films and CA polymers cast from acetone solution. Applying eqn. (11) to experimental data, they reported that (x = 0.5 and /3 = 4.0 for water diffusion, and that o( = 0 and /3 = 0.986 for salt diffusion. We will assume that the dense CA membranes prepared in this study are very close to having a symmetrical structure [8] and that water in the hydrated polymer matrix behaves similarly to that in the homogeneous membrane. Matching eqn. (11) with the plots of log D, vs. x shown in Figs. 6-9 gave (Yvalues of around 0.5 and so o( was fixed at this value. The estimated p values then ranged between 14 and 16 for aromatic solutes; they are listed in Table 2. The fl values in the case of aromatic solutes are about four times those in the case of water. In membranes of high hydration, the aromatic solute can diffuse primarily in the free volume of water and macromolecules in the polymer matrix. However, when hydration of the membrane is low, an appreciably larger molecule than water would be expected to encounter a greater tortuosity or steric hindrance in small pores or channels. The movement of solute will be greatly affected by physicochemical interactions between aromatic solute and polymer segments. As a result, the value of 0 becomes larger, owing to the high barrier to transport. Further, the size distribution of pores in the membrane limits the critical pore size for aromatic solutes of larger molecular size than water. From the complicated geometry of the polymer network, the free volume concept will describe the transport characteristics for the diffusion of an aromatic solute in the hydrated membrane adequately. Conclusion Investigations were made of the mechanism of transport of aromatic substances from aqueous solutions through a thin, dense CA membrane of close to uniform structure. The two factors influencing the permeability of the membrane to the solute were found to be the partition and diffusion coefficients. The partition coefficient, measured by the immersion method, was greatly dependent on the water content of the hydrated membrane, and increased as the water content decreased. By considering a hydrophobic interaction between the aromatic ring of the solute and the CA polymer chains, the partition coefficient could be experimentally correlated with water content. The diffusion coefficient was also greatly dependent on the water content of the membrane and becomes very low in case of low water content. Two treatments, the pore model relation of Mackie and Meares and the free volume model relation of Yasuda et al., were tested to describe the dependence of the diffusion coefficient on the water content. Consequently, for a varying water content of the hydrated membrane, the free volume model relation could be applied to adequately correlate the diffusion coefficient with the water content.
287
List of symbols
a, b CO C ‘21 C e2 ct
C,
L
Qt V*
Experimental parameters used in eqn. (6). Concentration of original soaking solution (mol/l). Concentration of desorbed solution at first equilibrium (mol/l). Concentration of desorbed solution at second equilibrium (mol/l). Concentration of desorbed solution at time t (mol/l). Concentration of desorbed solution at infinite time or at equilibrium (mol/l). Diffusion coefficient of solute in the membrane (cm2 /set). Diffusion coefficient of solute in free solution (cm2 /set). Partition coefficient of solute in the membrane (mol solute per cm3 membrane/m01 solute per cm3 solution). Thickness of wet membrane (cm). Total amount of diffusing solute which passed through the membrane at time t (mol/cm2 membrane). Characteristic volume required to accommodate the diffusant in the membrane (cm3 ). Free volume of randomly coiled macromolecules having some unoccupied space per unit volume phase (cm3 ). Free volume of pure water per unit volume of the phase (cm3 ). Volume of wet membrane (cm3 )_ Volume of a distilled water for second desorption procedure (cm3 ). (1 - G)/G Parameters used in eqn. (11). Volume fraction of water in the membrane. Tortuosity of pore in the membrane.
References H.K. Lonsdale, U. Merten and M. Tagami, Phenol transport in cellulose acetate membranes, J. Appl. Polym. Sci., 11 (1967) 1807. H.K. Lonsdale, B.P. Cross, F.M. Graber and C.E. Milstead, Permeability of cellulose acetate membranes to selected solutes, J. Macromol. Sci., Phys., B5, (1) (1971) 16’7. J.E. Anderson, S.J. Hoffman and CR. Peters, Factors influencing reverse osmosis rejection of organic solutes from aqueous solution, J. Phys. Chem., 76 (1980) 4006. H.-G. Burghoff, K.L. Lee and W. Pusch, Characterization of transport across cellulose acetate membranes in the presence of strong solute-membrane interacterions, J. Appl. Polym. Sci., 25 (1980) 323. J. Crank, The Mathematics of Diffusion, 2nd edn., Clarendon Press, Oxford, 1978, pp. 49 and 56. H. Yasuda, C.E. Lamase and L.D. Ikenberry, Permeability of solutes through hydrated polymer membranes, Part I. Diffusion of sodium chloride, Makromol. Chem., 118 (1968) 19. H. Yasuda, C.E. Lamaze and A. Peterlin, Diffusive and hydraulic permeabilities of water in water-swollen polymer membranes, J. Polym. Sci., A-2, 9 (1971) 1117. S. Kimura, J. Irie and T. Miyauchi, Characteristics of cellulose acetate membranes used for the reverse osmosis process: The case of symmetric membranes, MAKU(Membrane), 1 (1976) 231.
288 9
10 11
12
T. Matsuura and S. Sourirajan, Reverse osmosis separation of phenols in aqueous solutions using porous cellulose acetate membranes, J. Appl. Polym. Sci., 16 (1972) 2531. J.S. Mackie and P. Meares, The diffusion of electrolytes in a cation-exchange resin membrane. I. Theoretical, Proc. Royal Sot., Ser. A, 232 (1955) 498. H.W. Osterhoudt, Transport properties of hydrophilic polymer membranes. The influence of volume fraction polymer and tortuosity on permeability, J. Phys. Chem., 78 (1974) 408. C.R. Wilke and P. Chang, Correlation of diffusion coefficients in dilute solutions, AIChE J., 1 (1955) 264.