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Pervaporation separation of aqueous mixtures using crosslinked polyvinyl alcohol membranes. III. Permeation of acetic acid-water mixtures
Journal of Membrane Science, 58 (1991) 33-47 Elsevier Science Publishers B.V., Amsterdam
33
Pervaporation separation of aqueous mixtures using crosslinked polyvinyl alcohol membranes. III. Permeation of acetic acid-water mixtures R.Y.M. Huang and C.K. Yeom Department of Chemical Engineering, University of Waterloo, Waterloo, Ont. N2L 3Gl (Canada) (Received February 21,199O; accepted in revised form November 15,199O)
Abstract The pervaporation separation of acetic acid-water mixtures was carried out over the full range of compositions at temperatures varying from 30 to 70’ C, using chemically crosslinked poly (vinyl alcohol) (PVA) membranes which had been developed in our laboratory. For the preparation of these membranes, PVA was crosslinked with amic acid and then the crosslinking agent, amic acid was imidized for an additional one hour at 150°C. The best condition for preparing the crosslinked PVA was found to be ca. 12 wt.% amic acid content. Pervaporation separation of acetic acid-water mixtures using the crosslinked PVA membrane containing 12 wt.% crosslinking agent gave separation factors of 13-42 and permeation rates of 79-2285 g/ (m2-hr) depending on the operating temperature and feed mixture composition. Deviation of permeation rates from ideal rates was discussed through the permeation ratio concept. These phenomena were explained in terms of both the plasticizing effect of permeants and the interaction between permeants in the polymer membrane. We have also defined a new term, the pervaporation separation index (PSI) as the product of permeation rate and separation factor, which could be a measure of the pervaporation separation ability of a membrane for a binary mixture under the specified experimental conditions. The temperature dependence of the permeation rate for binary mixtures was expressed by the Arrhenius-type relation and activation energies of 5.73-8.21 kcal/mol were calculated for acetic acid-water mixtures through the crosslinked PVA with 12 wt.% crosslinking agent. The pre-exponential factor as well as the activation energy were found to be functions of the permeant concentrations. Keywords: pervaporation; polyvinyl alcohol membranes; acetic acid/water mixtures, separation of; pervaporation separation index; Arrhenius activation energy
Introduction
The introduction of crosslinked structures into the polymer membrane to improve the pervaporation separation properties of the membrane for aqueous solutions has recently been reported [ 1,2].
0376-7388/91/$03.50
0 1991-
Elsevier Science Publishers B.V.
34
In the previous papers of this series [ 3,4], the characterization of the crosslinking reaction between PVA and amic acid was discussed in detail for the purposes of new membrane development for pervaporation and the pervaporation separation of ethanol-water mixtures was reported. The PVA membranes were prepared by the crosslinking reaction of PVA and amic acid which is composed of two steps: (1) the crosslinking reaction between hydroxyl groups of PVA and carboxylic acid groups of amic acid, and (2 ) imidization of the amic acid. The best condition for preparing the crosslinked PVA was found to be with ca. 12 wt.% of amic acid content. The membranes produced by this technique had excellent mechanical and thermal properties. This paper deals with the pervaporation separation of acetic acid-water mixtures with various concentrations using the chemically crosslinked polyvinyl alcohol membranes previously reported [ 31. Theory
A permeation ration, 19,which is a measure of the deviation of the actual permeation rate, Q, from the ideal rate, Q”, has been defined to explain interactions between polymer and permeants.
Q/Q"
8=
(1)
The ideal permeation rate in binary liquid permeation is defined as the permeation rate of a component which is proportional to the concentration of the component in feed mixture, without coupling of fluxes, i.e. in the absence of the effect of the presence of the other component. For ideal binary liquid permeation, the component rates in the mixture can be expressed in terms of the pure component permeation ratios as follows: q; zxiQP
(2)
q;
(3)
=x,QJ’
(4)
Q;=qP+qr
where i andj denote the individual components in the binary mixture, x is the weight fraction in feed mixture, superscript, o, denotes ideal permeation, Q0 pure component permeation rates, q component permeation rate in binary mixture, and Qt, total permeation rate. In actual permeation, the permeation rate can be expressed in terms of 13as follows: Oi =
qilq
Oj =
qj/qp
P
Q,=qi+qj=BiqP+6,Q~=e,Q,”
(5) (6)
(7)
35
&= teiqP+ejqj))/(qP
+4p)
(8)
The membrane selectivity of a binary system consisting of two components i and j can be expressed in terms of a separation factor a!, defined as the concentration ratio yi/Yj in the permeate divided by the ratio Xi/Xi in the feed side. ‘Yi/j= (YilYj)l(xi/xj)
= (eil6’j)
(QP/Qj')
(9)
Thus, the permeation ratio should be equal to unity and ~i/j= QP/QP when the system exhibits ideal permeation behaviour. When 15 1, the interactions between polymer and permeants give positive effect on permeation, and when 0< 1, the interactions affect permeation negatively. The separation ability of a membrane can be expressed in terms of permeation and selectivity which usually take place in the opposite way, that is, when one factor increases, the other decreases, but both of them are important factors in the separation process. We define a new pervaporation separation index (PSI), which is a relative measure of the separation ability of a membrane, as the product of the separation factor and the permeation rate. PSI = Q, cYi/j
(10)
Introducing eqns. (7) and (9) into eqn. (10) gives PSI=
[ (BiQP)“XJ/(OjQ~)
+eiQpXj
(11)
When the membrane has a high selectivity to component i, the second term in eqn. (11) is negligible, thus PSI=((eiQP)“]xi/(ejQp)
(12)
Equations (11) and (12) show the relationship between PSI and the individual permeation ratios. The permeation at various operating temperatures was described as being governed by three factors, namely (a) change in the free volume of the polymer membrane swollen by pure components which can affect QP and Qj, (b) change in the interactions between the permeants in the membrane, and (c) change in the free volume due to the plasticizing effect. Experimental Materials 3,3’,4,4’-benzophenone tetracarboxylic dianhydride (BTDA) andp-phenylene diamine were obtained from Polysciences Inc., Philadelphia, PA. PVA (99-100% hydroloyzed, viscosity of 4% aqueous solution at 20’ C = 55-68 cp ) and dimethylsulfoxide (analytical reagent) were obtained from the J.T. Baker Chemical Co. Methyl alcohol was analytical reagent from B.D.H. Chemicals.
36
Membrane preparation PVA ( 10 wt.% ) and amic acid solution (51 wt.% ) (the procedures of amic acid synthesis have been reported elsewhere [ 31) both in dimethyl sulfoxide were mixed together with stirring for 12 hr to form a homogeneous casting solution. The resulting casting solution was cast onto a perspex plate with the aid of a Gardner casting knife and dried for 4 hr at 40’ C under vacuum and then reacted by heat (reaction temperature= 150°C for 1.5 hr). Membranes with crosslinking agent contents of 8,12,16 wt.% were prepared. The thickness of membranes ranged from 1.4 to 1.8 mil. Pervaportion The apparatus used to obtain pervaporation data is illustrated in Fig. 1, which is a continuously feeding type. The pervaporation experiments were performed employing two stainless steel pervaporation cells (Fig. 2 ) . The feed mixture enters the cell through the center opening, flows radially through the thin channel and leaves the cell through the side opening. This allows relatively higher fluid viscosity parallel to the membrane surface. The effective membrane area in each cell is 14.2 cm’. The Pyrex glass feed tank had a feed solution
2
3
1
3
1
t
+
7 u
Fig. 1. Schematic presentation of pervaporation apparatus. 1. water bath, 2. feed tank, 3. pump, 4. membrane cells, 5. collection tubes, 6. vent to atmosphere, 7. cold trap, 8. vacuum pump.
37 membrane
-_-feed mixture
.xture
Fig. 2. Schematic presentation of permeation cell.
capacity of approximately 1000 ml. From the feed tank, which was kept at a constant temperature by a water bath, the feed mixture was circulated through the two cells. The pressure at the downstream side was kept below 5 mmHg by two vacuum pumps. Pervaporation experiments were conducted at 30,45,60 and 75°C with the same membrane being used for a complete composition range study of a given binary pair. Upon reaching steady state flow conditions, product samples were collected for timed intervals, isolated from the vacuum system, and weighed. The analysis of the permeates was done using an Anton-Parr DMA 60 digital density meter at 18”C. A calibration curve of density vs. composition of acetic acid-water mixtures was prepared using known quantities of the two components. The following relationship was used to calculate the separation factor: c&/j=
1
where x is the feed composition, y is the permeate composition, and component i is the preferentially permeating component. Results and discussion
Effect of feed mixture composition It is well known that the molecular structure of a permselective membrane has a strong influence on the permeation and separation of binary mixtures [ 41. This is especially true when one of the components is a plasticizing agent
38
for the polymer, as is the case with water in hydrophilic membranes. Usually, hydrophilic membranes have groups that have a relatively high polarity and strong interaction with water through hydrogen bonding and thereby the selectivity of the membrane to water can be enhanced. The permeation and separation of binary mixtures were investigated over the full range of compositions at temperatures varying from 30 to 75°C. The effect of composition of the feed mixture on the permeation rate at different temperatures is shown in Fig. 3. Interesting “permeation enhancement” was observed, and the maximum permeation rates were found at a concentration of ca. 10 wt.%. This indicates that mixtures permeated faster than either of the pure components. This phenomena can be explained in terms of the plasticizing effects of water and acetic acid on the membrane. In the permeation rate of individual components (Figs. 4,5 ), the permeation rates of both components show positive deviation from ideal rate, having maximum points at ca. 10 wt.% for the water component and at ca. 70 wt.% for the acetic acid component. This can be explained assuming that the plasticizing actions of water and acetic acid operate more or less independently to supplement each other, resulting in the enhancement of the permeation rates. These plasticizing effects could be observed from the separation curve which is concave upward having minimum points between 50 and 70 wt.%, depending on temperature, as shown in Fig. 6. This phenomenon can be qualitatively ex-
Acetlc
Acid
Content
in
0
: 30°C
0
: 45°C
+
: 60°C
Feed
Fig. 3. Effects of temperature and feed composition membrane with 12 wt.% crosslinking agent.
on total permeation
rate for a crosslinked
PVA
39
Water
0
Permeation
0 + *
Acetic
Acid
0.‘5 Content
in
: : : :
30 ‘c 45 ‘C 60-C 75°C
Feed
Fig. 4. Permeation rate of water component in water-acetic acid mixture.
Acetic
Acid
Permeation
0 + *
Acetic
Acid
0.5 Content
3oT
q
in
: : :
45’C 6O’C 75’C
Feed
Fig. 5. Permeation rate of acetic acid component in water-acetic acid mixture.
40
0 /
0.0 Acetic
Acid
/ 0.5 Content
in
Feed
Fig. 6. Effects of temperature and feed composition on separation factor.
plained by using the concept of the permeation ratio which will be discussed in the next section. In Figs. 3 and 6, it can be seen that a higher separation factor and a lower permeation rate were observed at lower temperatures regardless of the feed composition. According to the free volume theory [ 51, the thermal motion of polymer chains in the amorphous regions randomly produces free volume. As temperature increases, the frequency and amplitude of the chain jumping (i.e. thermal agitation) increase and the resulting free volumes become larger. In pervaporation, the permeating molecules can diffuse through these free volumes. Thus, when the temperature is high, the diffusion rates of both of the isolated permeating molecules and associated permeating molecules are high, so that the total permeation rate could be high and the separation factor low. Permeation ratio The permeation ratio of a component can be interpreted as a measure of the effect of the other component on its permeation rate. Permeation enhancement refers to a permeation ratio higher than unity, while permeation depression refers to a permeation ratio less than one. The permeation ratio is thought to be governed by the combined effects of the plasticizing action and the attractive interactions between permeates in the membrane which affect the permeation rate in opposite ways. The relationship between the total permeation ratio, S,, and the composition
41
of feed mixture is shown in Fig. 7. All of 0, values are higher than unity, which means the plasticizing effect on the polymer membrane predominates over any interaction between permeants. It is also shown that as separation temperature increases, the 0, value increases. It is suggested that increases in 0, with temperature can be due to the following two factors: (a) increasing free volume which allows the amorphous region to be loosened up and to allow to some extent diffusion of the incorporated molecules, and (b) decreasing interactions between permeants. More details can be obtained through the analysis of the permeation ratio of the individual components (Figs. 8 and 9). The value of 0, over the full range of compositions is almost the same as that of 13,because the permeation rate of water is much higher than that of acetic acid. This permeation enhancement of the water component is thought to be due mainly to the plasticizing effect of acetic acid on the polymer membrane. Especially, the maximum permeation was found between 50 and 70 wt.% and at the same time the maximum variation of 0, value with increasing temperature was also found in this region. This is because the strongest interaction between the permeants might be formed at low temperature which reduces the plasticizing effect to a relatively high extent compared with the case of other compositions in the feed mixture; however, as temperature increases, the interactions decrease, and thus the plasticizing effect can be restored to some extent. In the case of the permeation ratio of acetic acid component, all of the t9, values, except those in the range of O-20 wt.% compositions are higher than
00 0.0
Acetic
Acid
0.5 Content
in
0
: 30°C
0
: 45°C
+
: 60°C
*
: 75°C
Feed
Fig. 7. Plot of total permeation ratio vs. feed composition with varying temperature.
42
Water
0
Permeotion
0 +
: : :
*
30°C 45°C 60°C 75 “C
I
Aceilc
Acid
0.5 Content
1 in
Feed
Fig. 8. Plot of the permeation ratio of water component vs. feed composition with varying temperature.
Acetic
Acid
Permeotlon
0
:
o
: 45°C
30°c
+
60°C
*
75°C
J 00 Acetlc
Acid
0.5 Content
in
Feed
Fig. 9. Plot of the permeation ratio of acetic acid component vs. feed composition with varying temperature.
43
unity. As in the case of the water component, 0, values in the range of 50-70 wt.% increase rapidly with temperature, having a maximum that is higher than that for the case of water component. This is why the separation factor has a minimum value in this range of compositions. In the range of O-20 wt.% compositions, the 6’, value is less than one, indicating that there is a strong interaction between permeants which results in the depression of the acetic acid permeation. The reason for this is thought to be that since water content in the feed mixture is very large compared to the acetic acid content, a large portion of acetic acid may be associated with water molecules, so that acetic acid could hardly diffuse through membrane. Therefore, the separation factors in this region of compositions have high values as shown in Fig. 6. It is very interesting to note that the slope of the separation factor curve decreases with temperature in this range of compositions. This decrease in the slope is due to an increase in the free volume of the polymer membrane with increasing temperature and a decrease in the interaction, which causes the enhancement of acetic acid permeation. The effect of the composition of feed mixture on the pervaporation separation index (PSI) at different temperature is shown in Fig. 10. According to eqn. (12 ), the PSI curve shifts upward with increasing temperature due to an increase in Qg (Qz > Qz ), depending on the feed composition, and the shape of the curve is determined mainly by the values of 0, and & where PSI is proportional to (0,)” and l/0, terms. The resulting PSI value decreases mo-
0 : 30°c 0 : 45’C + *
: 60% : 75-c
I
0.5 Acetic
Fig. 10. Effects of temperature
Acid
Content
in
Feed
and feed composition
on pervaporation
separation
index (PSI).
44
notonously with the composition because 0, and 0, values similarly change with the composition. From Fig. 10, it can be seen that the lower the composition of feed mixture and the higher the separation temperature, the better is the separation capability of the membrane. Arrhenius plot of permeation rate Figure 11 shows the Arrhenius plots of total permeation rates which were used to calculate the permeation activation energy (Fig. 12) and the pre-exponential factor (Fig. 13 ) for the binary mixture. On the whole, each activation curve shows a positive deviation which in turn affects diffusivity negatively. This coincides with the idea of immobilization of the membrane due to interaction as discussed in previous work [ 41. On matching these activation energy data with the analysis of the permeation ratio data, it can be seen that when the activation energy is high, the interaction between permeants is strong, which means that the permeation rate is sensitive to the temperature because of the interaction. Therefore, the activation energy could be related with the interactions between permeants in the membrane. The pre-exponential factor may be strongly related to the plasticizing effect because it is the characteristic of permeation at infinite temperature where interaction effect is not important any more. In the case of total permeation, as an example, the pre-exponential factor has a maximum in the range of 50-
10.’ ~ 0.0028
8” feed
mixture
I
0.0030
I 0.0032
l/Temperature,
l/K
0.0034
Fig. 11. Arrhenius plot of total permeation rate vs. temperature.
45
0 : Acetic
: :
0 *
10.0
Acid
Perme
Water Permeation Total Permeation
F 0 y” 2 b I=
7.5
6 ._ 2 ti
5.0
I
C Acetic
Acid
0.5 Content
1 in
Feed
Fig. 12. Effect of feed composition on activation energy.
22.5 q
o t
12.5
: Total Permeation : Water Permeation : Acetic Acid Permeat
(1.b
1
0.5 Acetic
Acid
Content
in
Feed
Fig. 13. Effect of feed composition on pre-exponential factor.
46
70 wt.% composition showing a maximum plasticizing effect, while the interaction between permeants is also maximum in this region as discussed in Figs. 7 and 12. Through this analysis, it can be seen that, at low temperatures, 13,has a low value because of the strong interactions, while at high temperatures, 0, has a high value because of the weak interactions and high plasticizing effects. From Figs. 12 and 13, it can be seen that both the activation energy and the pre-exponential factor are not constant but should be functions of permeant concentrations:
where wi and wj are the concentrations of components i and j in a membrane, respectively. These functions can include the free volume, the plasticizing effect, and the interaction between permeants and the polymer membrane. At present, the study of model equations containing the concept of the above functions to predict the permeation behavior of aqueous solutions is underway and will be reported in a separate paper. Conclusions
The results of the pervaporation separation of acetic acid-water mixtures using a crosslinked PVA membrane with 12 wt.% crosslinking agent are as follows: (1) Separation factor of 13-42 and permeation rate of 79-2285 g/m’-hr over the full range of composition at temperatures varying from 30 to 75 ‘C. (2) There exist complex interactions between the permeants as well as plasticizing effects of both components on the membrane, which enhance the total permeation rate, reaching maximum values at ca. 10 wt.% of acetic acid. The permeation rate of the water component has a maximum at ca. 10 wt.% composition due to the plasticizing effect of acetic acid, while that of acetic acid has a maximum value at ca. 70 wt.% composition mainly due to the plasticizing effect of water. The strongest interaction between permeants is shown in the range of 50-70 wt.% composition. The membrane shows a good separation capability at high temperature and low composition. (3) The results of the analysis with the newly defined pervaporation separation index (PSI) indicate it to be a good relative measure to estimate the pervaporation performance of a membrane for the specified experimental conditions. (4) Information on the interaction between permeants can be obtained from the activation energy curve and gives information on the pre-exponential curve the plasticizing effect. Activation energies of 5.73-8.21 Kcal/mol were calculated for water-ethanol mixtures. The pre-exponential factor as well as the
47
activation energy of the permeation were found to be functions of permeant concentrations. Acknowledgement The authors wish to thank the Natural Science and Engineering Research Council of Canada (NSERC ) for their support of this research. List of symbols
A
Ek
PSI 9 Q”
Q" QZ Qt x
Y ai/j 8
pre-exponential factor for permeation (g-m-2-h-1 ) activation energy for permeation (kcal/mol) pervaporation separation index (g-mP2-h-l) real permeation rate of a component for a binary mixture (g-mP2-h-’ ) ideal permeation rate of a component for a binary mixture (g-m-2-h-’ ) permeation rate of pure component (g-m-‘-h-’ ) ideal total permeation rate for a binary mixture (g-m-2-h-1) real total permeation rate for a binary mixture (g-m-2-h-’ ) weight fraction of a component in feed mixture weight fraction of a component in permeate separation factor referred to the preferential permeation of component i permeation ratio
Subscripts components i and j in binary mixture, respectively i,.i References R.Y.M. Huang, A. Moreira, R. Notarfonzo and Y.F. Xu, Pervaporation separation of acetic acid-water mixtures using modified membranes. I. Blended polyacrylic acid (PAA)-nylon membranes, J. Appl. Polym. Sci., 35 (1989) 1191. Y.F. Xu and R.Y.M. Huang, pervaporation separation of ethanol-water mixtures using ionitally crosslinked blended polyacrylic (PAA)-nylon 6 membranes, J. Appl. Polym. Sci., 36 (1988) 1121. C.K. Yeom and R.Y.M. Huang, pervaporation separation of aqueous mixtures using crosslinked poly(viny1 alcohol) (PVA). I. Characterization of the reaction between PVA and amic acid, Angew. Macromol. Chem., 1989, accepted for publication. R.Y.M. Huang and C.K. Yeom, Pervaporation separation of aqueous mixtures using crosslinked polyvinyl alcohol (PVA) membranes. II. Permeation of ethanol-water mixtures, J. Membrane Sci., 51 (1990) 273. J.E. Mark, A. Eisenberg, W.W. Grtaessly, L. Mandelkern and J.L. Koenig, Physical Properties of Polymers, American Chemical Society, Washington, DC, 1984, Chap. 2.
33
Pervaporation separation of aqueous mixtures using crosslinked polyvinyl alcohol membranes. III. Permeation of acetic acid-water mixtures R.Y.M. Huang and C.K. Yeom Department of Chemical Engineering, University of Waterloo, Waterloo, Ont. N2L 3Gl (Canada) (Received February 21,199O; accepted in revised form November 15,199O)
Abstract The pervaporation separation of acetic acid-water mixtures was carried out over the full range of compositions at temperatures varying from 30 to 70’ C, using chemically crosslinked poly (vinyl alcohol) (PVA) membranes which had been developed in our laboratory. For the preparation of these membranes, PVA was crosslinked with amic acid and then the crosslinking agent, amic acid was imidized for an additional one hour at 150°C. The best condition for preparing the crosslinked PVA was found to be ca. 12 wt.% amic acid content. Pervaporation separation of acetic acid-water mixtures using the crosslinked PVA membrane containing 12 wt.% crosslinking agent gave separation factors of 13-42 and permeation rates of 79-2285 g/ (m2-hr) depending on the operating temperature and feed mixture composition. Deviation of permeation rates from ideal rates was discussed through the permeation ratio concept. These phenomena were explained in terms of both the plasticizing effect of permeants and the interaction between permeants in the polymer membrane. We have also defined a new term, the pervaporation separation index (PSI) as the product of permeation rate and separation factor, which could be a measure of the pervaporation separation ability of a membrane for a binary mixture under the specified experimental conditions. The temperature dependence of the permeation rate for binary mixtures was expressed by the Arrhenius-type relation and activation energies of 5.73-8.21 kcal/mol were calculated for acetic acid-water mixtures through the crosslinked PVA with 12 wt.% crosslinking agent. The pre-exponential factor as well as the activation energy were found to be functions of the permeant concentrations. Keywords: pervaporation; polyvinyl alcohol membranes; acetic acid/water mixtures, separation of; pervaporation separation index; Arrhenius activation energy
Introduction
The introduction of crosslinked structures into the polymer membrane to improve the pervaporation separation properties of the membrane for aqueous solutions has recently been reported [ 1,2].
0376-7388/91/$03.50
0 1991-
Elsevier Science Publishers B.V.
34
In the previous papers of this series [ 3,4], the characterization of the crosslinking reaction between PVA and amic acid was discussed in detail for the purposes of new membrane development for pervaporation and the pervaporation separation of ethanol-water mixtures was reported. The PVA membranes were prepared by the crosslinking reaction of PVA and amic acid which is composed of two steps: (1) the crosslinking reaction between hydroxyl groups of PVA and carboxylic acid groups of amic acid, and (2 ) imidization of the amic acid. The best condition for preparing the crosslinked PVA was found to be with ca. 12 wt.% of amic acid content. The membranes produced by this technique had excellent mechanical and thermal properties. This paper deals with the pervaporation separation of acetic acid-water mixtures with various concentrations using the chemically crosslinked polyvinyl alcohol membranes previously reported [ 31. Theory
A permeation ration, 19,which is a measure of the deviation of the actual permeation rate, Q, from the ideal rate, Q”, has been defined to explain interactions between polymer and permeants.
Q/Q"
8=
(1)
The ideal permeation rate in binary liquid permeation is defined as the permeation rate of a component which is proportional to the concentration of the component in feed mixture, without coupling of fluxes, i.e. in the absence of the effect of the presence of the other component. For ideal binary liquid permeation, the component rates in the mixture can be expressed in terms of the pure component permeation ratios as follows: q; zxiQP
(2)
q;
(3)
=x,QJ’
(4)
Q;=qP+qr
where i andj denote the individual components in the binary mixture, x is the weight fraction in feed mixture, superscript, o, denotes ideal permeation, Q0 pure component permeation rates, q component permeation rate in binary mixture, and Qt, total permeation rate. In actual permeation, the permeation rate can be expressed in terms of 13as follows: Oi =
qilq
Oj =
qj/qp
P
Q,=qi+qj=BiqP+6,Q~=e,Q,”
(5) (6)
(7)
35
&= teiqP+ejqj))/(qP
+4p)
(8)
The membrane selectivity of a binary system consisting of two components i and j can be expressed in terms of a separation factor a!, defined as the concentration ratio yi/Yj in the permeate divided by the ratio Xi/Xi in the feed side. ‘Yi/j= (YilYj)l(xi/xj)
= (eil6’j)
(QP/Qj')
(9)
Thus, the permeation ratio should be equal to unity and ~i/j= QP/QP when the system exhibits ideal permeation behaviour. When 15 1, the interactions between polymer and permeants give positive effect on permeation, and when 0< 1, the interactions affect permeation negatively. The separation ability of a membrane can be expressed in terms of permeation and selectivity which usually take place in the opposite way, that is, when one factor increases, the other decreases, but both of them are important factors in the separation process. We define a new pervaporation separation index (PSI), which is a relative measure of the separation ability of a membrane, as the product of the separation factor and the permeation rate. PSI = Q, cYi/j
(10)
Introducing eqns. (7) and (9) into eqn. (10) gives PSI=
[ (BiQP)“XJ/(OjQ~)
+eiQpXj
(11)
When the membrane has a high selectivity to component i, the second term in eqn. (11) is negligible, thus PSI=((eiQP)“]xi/(ejQp)
(12)
Equations (11) and (12) show the relationship between PSI and the individual permeation ratios. The permeation at various operating temperatures was described as being governed by three factors, namely (a) change in the free volume of the polymer membrane swollen by pure components which can affect QP and Qj, (b) change in the interactions between the permeants in the membrane, and (c) change in the free volume due to the plasticizing effect. Experimental Materials 3,3’,4,4’-benzophenone tetracarboxylic dianhydride (BTDA) andp-phenylene diamine were obtained from Polysciences Inc., Philadelphia, PA. PVA (99-100% hydroloyzed, viscosity of 4% aqueous solution at 20’ C = 55-68 cp ) and dimethylsulfoxide (analytical reagent) were obtained from the J.T. Baker Chemical Co. Methyl alcohol was analytical reagent from B.D.H. Chemicals.
36
Membrane preparation PVA ( 10 wt.% ) and amic acid solution (51 wt.% ) (the procedures of amic acid synthesis have been reported elsewhere [ 31) both in dimethyl sulfoxide were mixed together with stirring for 12 hr to form a homogeneous casting solution. The resulting casting solution was cast onto a perspex plate with the aid of a Gardner casting knife and dried for 4 hr at 40’ C under vacuum and then reacted by heat (reaction temperature= 150°C for 1.5 hr). Membranes with crosslinking agent contents of 8,12,16 wt.% were prepared. The thickness of membranes ranged from 1.4 to 1.8 mil. Pervaportion The apparatus used to obtain pervaporation data is illustrated in Fig. 1, which is a continuously feeding type. The pervaporation experiments were performed employing two stainless steel pervaporation cells (Fig. 2 ) . The feed mixture enters the cell through the center opening, flows radially through the thin channel and leaves the cell through the side opening. This allows relatively higher fluid viscosity parallel to the membrane surface. The effective membrane area in each cell is 14.2 cm’. The Pyrex glass feed tank had a feed solution
2
3
1
3
1
t
+
7 u
Fig. 1. Schematic presentation of pervaporation apparatus. 1. water bath, 2. feed tank, 3. pump, 4. membrane cells, 5. collection tubes, 6. vent to atmosphere, 7. cold trap, 8. vacuum pump.
37 membrane
-_-feed mixture
.xture
Fig. 2. Schematic presentation of permeation cell.
capacity of approximately 1000 ml. From the feed tank, which was kept at a constant temperature by a water bath, the feed mixture was circulated through the two cells. The pressure at the downstream side was kept below 5 mmHg by two vacuum pumps. Pervaporation experiments were conducted at 30,45,60 and 75°C with the same membrane being used for a complete composition range study of a given binary pair. Upon reaching steady state flow conditions, product samples were collected for timed intervals, isolated from the vacuum system, and weighed. The analysis of the permeates was done using an Anton-Parr DMA 60 digital density meter at 18”C. A calibration curve of density vs. composition of acetic acid-water mixtures was prepared using known quantities of the two components. The following relationship was used to calculate the separation factor: c&/j=
1
where x is the feed composition, y is the permeate composition, and component i is the preferentially permeating component. Results and discussion
Effect of feed mixture composition It is well known that the molecular structure of a permselective membrane has a strong influence on the permeation and separation of binary mixtures [ 41. This is especially true when one of the components is a plasticizing agent
38
for the polymer, as is the case with water in hydrophilic membranes. Usually, hydrophilic membranes have groups that have a relatively high polarity and strong interaction with water through hydrogen bonding and thereby the selectivity of the membrane to water can be enhanced. The permeation and separation of binary mixtures were investigated over the full range of compositions at temperatures varying from 30 to 75°C. The effect of composition of the feed mixture on the permeation rate at different temperatures is shown in Fig. 3. Interesting “permeation enhancement” was observed, and the maximum permeation rates were found at a concentration of ca. 10 wt.%. This indicates that mixtures permeated faster than either of the pure components. This phenomena can be explained in terms of the plasticizing effects of water and acetic acid on the membrane. In the permeation rate of individual components (Figs. 4,5 ), the permeation rates of both components show positive deviation from ideal rate, having maximum points at ca. 10 wt.% for the water component and at ca. 70 wt.% for the acetic acid component. This can be explained assuming that the plasticizing actions of water and acetic acid operate more or less independently to supplement each other, resulting in the enhancement of the permeation rates. These plasticizing effects could be observed from the separation curve which is concave upward having minimum points between 50 and 70 wt.%, depending on temperature, as shown in Fig. 6. This phenomenon can be qualitatively ex-
Acetlc
Acid
Content
in
0
: 30°C
0
: 45°C
+
: 60°C
Feed
Fig. 3. Effects of temperature and feed composition membrane with 12 wt.% crosslinking agent.
on total permeation
rate for a crosslinked
PVA
39
Water
0
Permeation
0 + *
Acetic
Acid
0.‘5 Content
in
: : : :
30 ‘c 45 ‘C 60-C 75°C
Feed
Fig. 4. Permeation rate of water component in water-acetic acid mixture.
Acetic
Acid
Permeation
0 + *
Acetic
Acid
0.5 Content
3oT
q
in
: : :
45’C 6O’C 75’C
Feed
Fig. 5. Permeation rate of acetic acid component in water-acetic acid mixture.
40
0 /
0.0 Acetic
Acid
/ 0.5 Content
in
Feed
Fig. 6. Effects of temperature and feed composition on separation factor.
plained by using the concept of the permeation ratio which will be discussed in the next section. In Figs. 3 and 6, it can be seen that a higher separation factor and a lower permeation rate were observed at lower temperatures regardless of the feed composition. According to the free volume theory [ 51, the thermal motion of polymer chains in the amorphous regions randomly produces free volume. As temperature increases, the frequency and amplitude of the chain jumping (i.e. thermal agitation) increase and the resulting free volumes become larger. In pervaporation, the permeating molecules can diffuse through these free volumes. Thus, when the temperature is high, the diffusion rates of both of the isolated permeating molecules and associated permeating molecules are high, so that the total permeation rate could be high and the separation factor low. Permeation ratio The permeation ratio of a component can be interpreted as a measure of the effect of the other component on its permeation rate. Permeation enhancement refers to a permeation ratio higher than unity, while permeation depression refers to a permeation ratio less than one. The permeation ratio is thought to be governed by the combined effects of the plasticizing action and the attractive interactions between permeates in the membrane which affect the permeation rate in opposite ways. The relationship between the total permeation ratio, S,, and the composition
41
of feed mixture is shown in Fig. 7. All of 0, values are higher than unity, which means the plasticizing effect on the polymer membrane predominates over any interaction between permeants. It is also shown that as separation temperature increases, the 0, value increases. It is suggested that increases in 0, with temperature can be due to the following two factors: (a) increasing free volume which allows the amorphous region to be loosened up and to allow to some extent diffusion of the incorporated molecules, and (b) decreasing interactions between permeants. More details can be obtained through the analysis of the permeation ratio of the individual components (Figs. 8 and 9). The value of 0, over the full range of compositions is almost the same as that of 13,because the permeation rate of water is much higher than that of acetic acid. This permeation enhancement of the water component is thought to be due mainly to the plasticizing effect of acetic acid on the polymer membrane. Especially, the maximum permeation was found between 50 and 70 wt.% and at the same time the maximum variation of 0, value with increasing temperature was also found in this region. This is because the strongest interaction between the permeants might be formed at low temperature which reduces the plasticizing effect to a relatively high extent compared with the case of other compositions in the feed mixture; however, as temperature increases, the interactions decrease, and thus the plasticizing effect can be restored to some extent. In the case of the permeation ratio of acetic acid component, all of the t9, values, except those in the range of O-20 wt.% compositions are higher than
00 0.0
Acetic
Acid
0.5 Content
in
0
: 30°C
0
: 45°C
+
: 60°C
*
: 75°C
Feed
Fig. 7. Plot of total permeation ratio vs. feed composition with varying temperature.
42
Water
0
Permeotion
0 +
: : :
*
30°C 45°C 60°C 75 “C
I
Aceilc
Acid
0.5 Content
1 in
Feed
Fig. 8. Plot of the permeation ratio of water component vs. feed composition with varying temperature.
Acetic
Acid
Permeotlon
0
:
o
: 45°C
30°c
+
60°C
*
75°C
J 00 Acetlc
Acid
0.5 Content
in
Feed
Fig. 9. Plot of the permeation ratio of acetic acid component vs. feed composition with varying temperature.
43
unity. As in the case of the water component, 0, values in the range of 50-70 wt.% increase rapidly with temperature, having a maximum that is higher than that for the case of water component. This is why the separation factor has a minimum value in this range of compositions. In the range of O-20 wt.% compositions, the 6’, value is less than one, indicating that there is a strong interaction between permeants which results in the depression of the acetic acid permeation. The reason for this is thought to be that since water content in the feed mixture is very large compared to the acetic acid content, a large portion of acetic acid may be associated with water molecules, so that acetic acid could hardly diffuse through membrane. Therefore, the separation factors in this region of compositions have high values as shown in Fig. 6. It is very interesting to note that the slope of the separation factor curve decreases with temperature in this range of compositions. This decrease in the slope is due to an increase in the free volume of the polymer membrane with increasing temperature and a decrease in the interaction, which causes the enhancement of acetic acid permeation. The effect of the composition of feed mixture on the pervaporation separation index (PSI) at different temperature is shown in Fig. 10. According to eqn. (12 ), the PSI curve shifts upward with increasing temperature due to an increase in Qg (Qz > Qz ), depending on the feed composition, and the shape of the curve is determined mainly by the values of 0, and & where PSI is proportional to (0,)” and l/0, terms. The resulting PSI value decreases mo-
0 : 30°c 0 : 45’C + *
: 60% : 75-c
I
0.5 Acetic
Fig. 10. Effects of temperature
Acid
Content
in
Feed
and feed composition
on pervaporation
separation
index (PSI).
44
notonously with the composition because 0, and 0, values similarly change with the composition. From Fig. 10, it can be seen that the lower the composition of feed mixture and the higher the separation temperature, the better is the separation capability of the membrane. Arrhenius plot of permeation rate Figure 11 shows the Arrhenius plots of total permeation rates which were used to calculate the permeation activation energy (Fig. 12) and the pre-exponential factor (Fig. 13 ) for the binary mixture. On the whole, each activation curve shows a positive deviation which in turn affects diffusivity negatively. This coincides with the idea of immobilization of the membrane due to interaction as discussed in previous work [ 41. On matching these activation energy data with the analysis of the permeation ratio data, it can be seen that when the activation energy is high, the interaction between permeants is strong, which means that the permeation rate is sensitive to the temperature because of the interaction. Therefore, the activation energy could be related with the interactions between permeants in the membrane. The pre-exponential factor may be strongly related to the plasticizing effect because it is the characteristic of permeation at infinite temperature where interaction effect is not important any more. In the case of total permeation, as an example, the pre-exponential factor has a maximum in the range of 50-
10.’ ~ 0.0028
8” feed
mixture
I
0.0030
I 0.0032
l/Temperature,
l/K
0.0034
Fig. 11. Arrhenius plot of total permeation rate vs. temperature.
45
0 : Acetic
: :
0 *
10.0
Acid
Perme
Water Permeation Total Permeation
F 0 y” 2 b I=
7.5
6 ._ 2 ti
5.0
I
C Acetic
Acid
0.5 Content
1 in
Feed
Fig. 12. Effect of feed composition on activation energy.
22.5 q
o t
12.5
: Total Permeation : Water Permeation : Acetic Acid Permeat
(1.b
1
0.5 Acetic
Acid
Content
in
Feed
Fig. 13. Effect of feed composition on pre-exponential factor.
46
70 wt.% composition showing a maximum plasticizing effect, while the interaction between permeants is also maximum in this region as discussed in Figs. 7 and 12. Through this analysis, it can be seen that, at low temperatures, 13,has a low value because of the strong interactions, while at high temperatures, 0, has a high value because of the weak interactions and high plasticizing effects. From Figs. 12 and 13, it can be seen that both the activation energy and the pre-exponential factor are not constant but should be functions of permeant concentrations:
where wi and wj are the concentrations of components i and j in a membrane, respectively. These functions can include the free volume, the plasticizing effect, and the interaction between permeants and the polymer membrane. At present, the study of model equations containing the concept of the above functions to predict the permeation behavior of aqueous solutions is underway and will be reported in a separate paper. Conclusions
The results of the pervaporation separation of acetic acid-water mixtures using a crosslinked PVA membrane with 12 wt.% crosslinking agent are as follows: (1) Separation factor of 13-42 and permeation rate of 79-2285 g/m’-hr over the full range of composition at temperatures varying from 30 to 75 ‘C. (2) There exist complex interactions between the permeants as well as plasticizing effects of both components on the membrane, which enhance the total permeation rate, reaching maximum values at ca. 10 wt.% of acetic acid. The permeation rate of the water component has a maximum at ca. 10 wt.% composition due to the plasticizing effect of acetic acid, while that of acetic acid has a maximum value at ca. 70 wt.% composition mainly due to the plasticizing effect of water. The strongest interaction between permeants is shown in the range of 50-70 wt.% composition. The membrane shows a good separation capability at high temperature and low composition. (3) The results of the analysis with the newly defined pervaporation separation index (PSI) indicate it to be a good relative measure to estimate the pervaporation performance of a membrane for the specified experimental conditions. (4) Information on the interaction between permeants can be obtained from the activation energy curve and gives information on the pre-exponential curve the plasticizing effect. Activation energies of 5.73-8.21 Kcal/mol were calculated for water-ethanol mixtures. The pre-exponential factor as well as the
47
activation energy of the permeation were found to be functions of permeant concentrations. Acknowledgement The authors wish to thank the Natural Science and Engineering Research Council of Canada (NSERC ) for their support of this research. List of symbols
A
Ek
PSI 9 Q”
Q" QZ Qt x
Y ai/j 8
pre-exponential factor for permeation (g-m-2-h-1 ) activation energy for permeation (kcal/mol) pervaporation separation index (g-mP2-h-l) real permeation rate of a component for a binary mixture (g-mP2-h-’ ) ideal permeation rate of a component for a binary mixture (g-m-2-h-’ ) permeation rate of pure component (g-m-‘-h-’ ) ideal total permeation rate for a binary mixture (g-m-2-h-1) real total permeation rate for a binary mixture (g-m-2-h-’ ) weight fraction of a component in feed mixture weight fraction of a component in permeate separation factor referred to the preferential permeation of component i permeation ratio
Subscripts components i and j in binary mixture, respectively i,.i References R.Y.M. Huang, A. Moreira, R. Notarfonzo and Y.F. Xu, Pervaporation separation of acetic acid-water mixtures using modified membranes. I. Blended polyacrylic acid (PAA)-nylon membranes, J. Appl. Polym. Sci., 35 (1989) 1191. Y.F. Xu and R.Y.M. Huang, pervaporation separation of ethanol-water mixtures using ionitally crosslinked blended polyacrylic (PAA)-nylon 6 membranes, J. Appl. Polym. Sci., 36 (1988) 1121. C.K. Yeom and R.Y.M. Huang, pervaporation separation of aqueous mixtures using crosslinked poly(viny1 alcohol) (PVA). I. Characterization of the reaction between PVA and amic acid, Angew. Macromol. Chem., 1989, accepted for publication. R.Y.M. Huang and C.K. Yeom, Pervaporation separation of aqueous mixtures using crosslinked polyvinyl alcohol (PVA) membranes. II. Permeation of ethanol-water mixtures, J. Membrane Sci., 51 (1990) 273. J.E. Mark, A. Eisenberg, W.W. Grtaessly, L. Mandelkern and J.L. Koenig, Physical Properties of Polymers, American Chemical Society, Washington, DC, 1984, Chap. 2.