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Molecular transport of ketones and nitriles into commercial fluoroelastomeric membranes
Desalination 186 (2005) 165–176
Molecular transport of ketones and nitriles into commercial fluoroelastomeric membranes M.Y. Kariduraganavar,* S.B. Kulkarni, A.A. Kittur, S.S. Kulkarni Department of Chemistry and Center of Excellence in Polymer Science, Karnataka University, Dharwad 580 003, India Tel. +91 (836) 274-7121, ext. 372; Fax: +91 (836) 277-1275; email: [email protected] Received 6 July 2004; accepted 27 April 2005
Abstract The molecular transport of ketones such as acetone, ethyl methyl ketone, methyl isobutyl ketone, cyclohexanone and acetophenone, and nitriles such as acrylonitrile and acetonitrile, through Fluorel 3M membranes (FC-2177 D) was carried out in the temperature range of 30–50°C using the sorption gravimetric method. With the sorption data, the concentration-independent diffusion coefficients were calculated from Fick’s diffusion equation. The liquid concentration profiles were also calculated from the analytical solution of Fick’s diffusion equation with the appropriate initial and boundary conditions, and these were presented as a function of penetration depth of molecular migration and time of immersion. Because of the linearly increasing trend of the diffusion coefficients with temperature, efforts were made to estimate the Arrhenius parameters. Experimental values and the computed quantities were used to determine the membrane solvent interactions and to propose suitable applications in various situations. None of the solvents showed any degradative effects on the polymer membrane. Keywords: Membrane; Diffusion; Barrier; Swelling; Activation energy
1. Introduction A good understanding of molecular transport of small organic molecules into polymer membranes has been the subject of great technological importance in different areas of science and engineering [1,2]. Membrane separation of liquids in the liquid and oil industry has become as widespread as more traditional methods based *Corresponding author.
on absorption, pressure-swing adsorption or cryogenics. The membrane process has certain benefits compared to the cryogenic process, for example, lower investment cost and easier operation. Very important applications in the food industry involve impeding the diffusion of liquids through thin polymer films, commonly used as packaging food wrappers or protective coatings [3,4]. Recently, more applications are anticipated in the burgeoning field of biotechnology [5,6]
0011-9164/06/$– See front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2005.04.060
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such as biosensors, controlled release and bioreactors. The sorption and diffusion of organic molecules in polymers have implications even further afield with such molecules playing important roles in the polymer industry as plasticizers, fillers and biocides [7], paints and varnishes [8], encapsulant of electronic components in polymers that act as barriers to atmospheric gases and moisture [9], polymeric sorbents, hazardous chemical pond lining [10], the removal of residual monomers after the polymerization process, etc. Moreover, the effects of the interaction between glassy polymers and small molecules are of practical interest to chemical engineers due to the inherent sorption and transport of solvents present in most processes they encounter. In all these applications, polymers are exposed to a variety of liquids, and thus, an understanding of molecular interactions of liquids with the membrane materials is important to investigate their transport characteristics. In order to understand membrane transport phenomenon and thereby to develop membranes for suitable applications, the characteristics of membrane and the diffusing constituents must be known. These include molecular states of diffusing constituents, their diffusion coefficients and permeabilities, membrane structure, its history such as method of preparation, annealing etc. [11,12]. Free volume and free volume distribution are the properties of polymer structure that have a major impact on its transport properties. In membrane-related applications of polymers, small organic molecules have been used as probes to study the nature of transport mechanism. The important requirement of membrane material is that it should be chemically resistant to retain its mechanical and dimensional stability, and at the same time the chemical structure of the liquid penetrant is essential for the development of highperformance membranes [13]. Our recent papers [14–16] addressed the different aspects of diffusion anomalies for different polymer-solvent systems. In continuation of these
studies and as a further contribution in this area, we report here the experimental results of sorption kinetics, diffusion and permeation of organic ketones and nitriles through Fluorel copolymer membranes (FC-2177 D) at 30, 40 and 50°C. The concentration-independent diffusion coefficients were calculated from the Fick’s diffusion equation. In addition, the analytical solution of Fick’s equation was used to calculate the liquid concentration profiles at different times and depth of liquids inside the membrane material. The temperature-dependent transport coefficients were used to estimate Arrhenius activation parameters. 2. Experimental 2.1. Reagents/chemicals Organic penetrants such as acetone, acetonitrile, acrylonitrile and cyclohexanone were obtained from S.D. Fine Chemicals (Mumbai, India). Ethyl methyl ketone, acetophenone and methyl isobutyl ketone were procured from Sisco Chemical Industries (Mumbai, India). All the chemicals were of analytical grade and were used without further purification. 2.2. Materials Fluorel FC 2177 D is a medium-viscosityincorporated cure di-polymer of vinylidene fluoride and hexafluoropropylene designed for injection molding and sealing components that meet the major fluoroelastomer O-ring specifications. A gift sample received from Ms. Nina McAllum (3M Company, St. Paul, Minnesota, USA) was used in this study. The typical properties of the fluoroelastomer are: fluorine content, 65.9%; specific gravity, 1.80; color, opaque off-white; solubility, in ketones and esters; Mooney viscosity, approximately 34 MLI + 10 at 121°C. The press-cured sample for 7 min at 177°C has the following mechanical properties: tensile strength, 1865 psi; percentage elongation at break, 240;
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hardness (shore A), 75. The sample was compounded with MT Black (30 phr), MgO (9 phr) and Ca(OH)2 (6 phr). 2.3. Sorption-gravimetric experiments The circularly cut disc-shaped membrane samples of .2 cm in diameter were dried in a vacuum desiccator for 45 h over anhydrous CaCl2 before being used in the sorption experiments. These samples were then immersed in about 15– 20 mL of liquids taken in airtight bottles and were maintained at 30, 40 and 50°C in an electronically controlled oven (WTB Binder, Germany) within an accuracy of ±0.5°C. Mass measurements were made by removing the samples at suitably selected time intervals, then wiping the surface-adhered solvent using smooth tissue paper. These samples were then immediately weighed on a top-loading digital Mettler balance (Model AE 240, Switzerland) with an accuracy of ±0.01 mg. The samples were taken out no longer than 30–40 s outside the temperature-controlled oven. The procedure was continued until no more liquid uptake by the polymer was observed (equilibrium sorption). Three independent readings were taken, and the average value was used in all the calculations. Sorption coefficients were expressed as mol % and are calculated using the equation,
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type of polymer barrier and the nature of the migrating liquids. The dynamic swelling properties of a polymer film include the solvent sorption rate, the rate of approach to equilibrium swelling, the solvent front velocity and the transport mechanism controlling solvent sorption. For the Fickian transport, the rate of equilibrium approach can be characterized by the diffusion coefficient. For plane geometry of the polymer sheet the diffusion coefficient D can be calculated from [17]:
(2)
Here Mt and M4 are the cumulative masses sorbed from the polymer sample at time t and 4, respectively and h is the initial thickness of the polymer sample. Although this equation can be solved readily, it is suitable to consider the short-time limiting expression as well [17]: (3)
(1)
A single curve is obtained from the plot of Mt /M4 vs. the square root of time, which is initially linear. Thus, D can be calculated from the rearrangement of Eq. (3) as [18–22]:
where W0 is the initial mass of the sample; Wt is the mass at time t, that is, the immersion period; and M is the molar mass of the liquid.
(4)
2.4. Diffusion coefficients and concentration profiles Diffusive migration of liquids depends on concentration and temperature, together with the
where M4 is the equilibrium mass uptake at t 6 4 and 2 is the slope of the initial linear portion of the sorption curves. Similarly the permeability coefficient can be calculated using the relation P = D×S, which follows nearly the same pattern
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as those of diffusivities. This simple relation holds for the permeation process when D obeys Fick’s diffusion law and S obeys Henry’s law [23]. For the penetrant-polymer systems used in this study, it is not certain to what degree one or both laws are obeyed. Thus, the P values are considered as estimates of the permeability coefficients. Liquid ingression into polymeric materials is a phenomenon of great technological importance. In many instances it is necessary to know the penetration depth of liquid into polymer. In most application areas, the liquid penetration rates are calculated in terms of liquid concentration profiles. These are extremely useful to predict the self-life of the polymer while in contact with liquids. Liquid concentration profiles can be calculated from Eq. (5) under suitable initial and boundary conditions to yield an equation for solvent uptake C(x,t) inside the membrane thickness h, at time t and distance x as [12,24,25]:
Fig. 1. Plots of Mt vs square-root of time for fluoroelastomer at 30°C with (F) acetone, ()) ethyl methyl ketone, (G) methyl isobutyl ketone, (") acetophenone and (M) cyclohexanone.
(5)
where m is an integer. These data are useful to study the liquid migration as a function of time and penetration depth of the liquids from the face to the middle of the fluoroelastomer along the thickness direction. 3. Results and discussion 3.1. Sorption kinetics Molecular transport of liquid penetrants through the membranes can be studied in terms of sorption/diffusion phenomenon. The equilibrium sorption results measured at three different
Fig. 2. Plots of Mt vs. square-root of time for fluoroelastomer at 30°C with (F) acrylonitrile and ()) acetonitrile.
temperatures are presented in Table 1 whereas the mol percent sorption plots for ketones and nitriles measured at 30°C are displayed in Figs. 1 and 2, respectively. It was observed that among the ketones studied, the sorption values for linear ketones are higher than those of cyclohexanone and acetophenone. Further the sorption values have a systematic trend for linear ketones, and in
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Table 1 Physical properties and equilibrium sorption coefficients of ketones and nitriles through fluoroelastomeric membranes Liquids
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
Molar volume (cm3 mol!1)
Sorption coefficients (mol %) 30°C
40°C
50°C
74.04 90.02 125.8 104.2 117.4 52.9 66.0
2.50 ± 0.02 2.14 ± 0.02 1.69 ± 0.03 0.09 ± 0.02 0.76 ± 0.03 1.65 ± 0.02 1.86 ± 0.02
2.29 ± 0.03 1.86 ± 0.03 1.56 ± 0.03 0.10 ± 0.02 0.72 ± 0.02 1.64 ± 0.03 1.86 ± 0.03
2.20 ± 0.03 1.86 ± 0.03 1.46 ± 0.04 0.11 ± 0.02 0.62 ± 0.03 1.64 ± 0.02 1.86 ± 0.02
accordance, the sorption coefficients decrease with increase in the size of liquid molecules. For instance, acetone with a lower molar volume (74.0 cm3/mol) shows higher equilibrium sorption at all temperatures followed by ethyl methyl ketone and methyl isobutyl ketone, which have higher molar volumes of 90.02 and 125.8 cm3/ mol, respectively. However, in case of cyclohexanone (104.2 cm3/mol) and acetophenone (117.4 cm3/mol), though the molar volumes of these are lower than methyl isobutyl ketone, the equilibrium sorption values are lower than methyl isobutyl ketone; the same trend is observed at higher temperatures as well. This may be due to the fact that cyclohexanone and acetophenone are bulky compared to methyl isobutyl ketone due to its cyclic structure. This clearly implies that sorption not only depends on the molar volume but also on the nature of the liquid structure, which hinders the liquid sorption significantly. On the other hand, acetophenone, which has a higher molar volume than cyclohexanone, shows much higher equilibrium sorption values. This indicates that acetophenone has more interaction with the membrane chosen and thereby exhibits higher liquid sorption. In the case of nitriles, the sorption curves show an overshoot effect as indicated by an abrupt and fast initial penetrant uptake by the
polymer. Such an overshoot effect has been attributed to polymer crosslink density and the increased mobility of the polymer chain segments [26]. Solvent diffuses into the polymer network before its chains have had the time to relax (i.e., diffusion is faster than relaxation) and the fractional uptake reaches a maximum (i.e., the overshoot value). When the chains finally relax, the liquid penetrant is forced out of the network, and hence its uptake eventually reaches the true equilibrium value. Another plausible explanation for the observed overshoot effect is due to the presence of a thin layer formed during the polymer processes, which is morphologically different from the bulk of the polymer. Also, because the solvent diffusion coefficient in the polymer matrix is dependent upon the degree of crosslinking, a sudden initial jump in the uptake is expected if the crosslink density of the polymer is significantly lower in a thin outer layer of the sample. Several studies have addressed different aspects of the overshoot phenomenon when polymers absorb the penetrants [27–31]. Although the molar volumes of the nitriles are smaller than those of ketones, the observed equilibrium sorption values for nitriles are smaller than those of ketones such as acetone and ethyl methyl ketone. At all the investigated temperatures the equili-
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brium sorption values for acetonitrile are lower than acrylonitrile. This is because the magnitude of unsaturation is less compared to acrylonitrile, which decreases the affinity towards the polymer chain segments. In all the cases, except cyclohexanone, sorption coefficients decrease with increasing temperature. As explained above, the sorption coefficient is attributed to the size of the liquid penetrants as well as interactions existing between liquid penetrants and the membrane. As the temperature increases, the interactions between the membrane and liquid molecules decrease due to increased thermal energy, which results in a decrease in the sorption coefficients. On the contrary, the sorption coefficients of cyclohexanone increased with increasing temperature. This may be due to the fact that among ketones, cyclohexanone is a cyclic ketone but the remaining ones are aliphatic ketones, including acetophenone. This suggests that the sorption coefficients of cyclohexanone are mainly attributed to the size of the penetrants, which are not affected by the increase of thermal energy. Instead, it increases due to relaxation of polymer segments as the temperature increases. The results of diffusion coefficients measured at different temperatures are presented in Table 2. It was observed that the values of diffusion coefficients increased systematically from acetone to
methyl isobutyl ketone, and cyclohexanone to acetophenone as the size of the migrating liquids increased at all temperatures. The largest D value of 1.52×10!7 cm2/s was observed for acetophenone at 30°C, whereas the lowest of 0.16× 10!7 cm2/s was observed for acetone, among the ketones studied. In the case of nitriles, the higher value of D was observed for acrylonitrile than acetonitrile. This is in accordance with the size of the molecules. The D values calculated at 30°C vary according to the sequence: acetonitrile < acetone < ethyl methyl ketone < cyclohexanone < acrylonitrile < methyl isobutyl ketone < acetophenone. Permeability coefficients calculated from the kinetic gravimetric sorption experiments are also included in Table 2. It is generally observed that permeability results follow the same pattern as those of diffusion coefficients in the investigated temperature range. In areas where polymeric membranes are used as barriers towards aggressive liquids, it is important to know the liquid penetration rates calculated in terms of liquid concentration profiles. These are calculated from Eq. (5) at different membrane thicknesses (i.e., penetration depth of liquids) and at different time intervals during sorption experiments. However only a few typical graphs are displayed (Figs. 3–6). These plots show a dependence on the temperature, depth of
Table 2 Diffusion (D) and permeation (P) coefficients of ketones and nitriles at different temperatures through fluoroelastomeric membrane Liquids
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
Dipole moment (µ) 2.69 2.76 — 3.08 2.95 3.53 3.67
D (107) cm2/s
P (108) cm2/s
30ºC
40ºC
50ºC
30ºC
40ºC
50ºC
0.16 0.37 1.09 0.45 1.52 0.10 0.90
0.27 0.58 1.29 0.66 2.62 0.30 1.03
0.71 0.91 3.10 1.51 2.78 0.53 1.13
4.00 7.90 18.4 0.40 11.5 1.60 16.70
6.10 10.8 20.1 0.60 18.7 4.90 19.10
15.6 16.9 45.4 1.60 17.2 8.60 20.9
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Fig. 3. Concentration profiles calculated from Eq. (5) for acetone through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
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Fig. 4. Concentration profiles calculated from Eq. (5) for methyl isobutyl ketone through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
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Fig. 5. Concentration profiles calculated from Eq. (5) for acetonitrile through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
Fig. 6. Concentration profiles calculated from Eq. (5) for acrylonitrile through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
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Table 3 Estimated parameters for ketones and nitriles calculated from Eq. (6) at different temperatures for fluoroelastomeric membranes Liquids
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
n
K
30ºC
40ºC
50ºC
30ºC
40ºC
50ºC
0.52 0.53 0.55 0.52 0.51 0.50 0.53
0.54 0.51 0.50 0.55 0.53 0.57 0.59
0.55 0.52 0.54 0.53 0.52 0.55 0.52
1.64 2.52 3.17 2.36 2.89 1.79 4.25
2.95 3.47 4.43 3.73 3.48 3.49 5.34
4.71 5.83 6.06 4.68 5.97 6.28 6.58
penetration as well as on the nature of liquids chosen. For instance, diffusivity of acetone is lower than that of methyl isobutyl ketone and hence, its concentration profiles are lower at all temperatures (see Fig. 3). In case of methyl isobutyl ketone, diffusivity is quite high and so are its concentration profile values (see Fig. 4). Similar effects have been also observed in the case of acetonitrile and acrylonitrile as displayed in Figs. 5 and 6, respectively. From this we could observe a clear-cut dependence of D values on temperature. In addition, the concentration profiles vary according to the diffusion values of the liquids. The same trend was also observed for other liquids, but these plots are not displayed to reduce the number of plots. In order to know the type of diffusion mechanism, the sorption data have been analyzed using the following equation [32,33]: (6) Here, K represents polymer-solvent interaction parameter, while the exponent value n represents the nature of transport mechanism. For instance, if n lies between 0.5 and 0.75, then the transport is anomalous, that is, it slightly deviates from the
Fickian trend. The estimated values of n and K are presented in Table 3. It was observed that the values of n vary from 0.5 to 0.59, thus the transport is found to follow anomalous-type behavior [15,34–36]. Furthermore, the values of n do not show any systematic trend with temperature. In all cases, K increases with increasing temperature, and this suggests increased molecular interaction between the polymer and liquid molecules. Although K values do not show any systematic effects on the dipole moment of the liquids, they do show a systematic effect on the size and nature of liquids as similar to the sorption study. 3.2. Temperature effects The temperature dependency of diffusion was followed by carrying out the sorption experiments at 30, 40 and 50°C. From the typical plots (Figs. 7 and 8), it is clear that mol % uptake increased with the temperatures. From the values of diffusion and permeation coefficients at different temperatures, the corresponding apparent values of activation energy ED, EP were calculated using an Arrhenius-type equation [22]: (7)
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Fig. 7. Arrhenius plots of log D vs. 1/T for fluoroelastomer membranes for (F) acetone, ()) ethyl methyl ketone, (G) methyl isobutyl ketone, (M) acetophenone and (") cyclohexanone.
Fig. 8. Arrhenius plots of log D vs. 1/T for fluoroelastomer membranes for (F) acetonitrile and ()) acrylonitrile.
Table 4 Activation energy for diffusion, permeation and heat of sorption of ketones and nitriles for fluoroelastomeric membranes Liquids
EP (kJ/mol)
ED (kJ/mol)
)Hs (kJ/mol)
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
55.18 ± 0.03 31.34 ± 0.03 36.45 ± 0.02 56.19 ± 0.03 16.63 ± 0.02 68.71 ± 0.03 9.15 ± 0.02
60.47 ± 0.02 36.64 ± 0.02 42.25 ± 0.04 49.09 ± 0.02 24.78 ± 0.02 68.12 ± 0.03 9.29 ± 0.04
!5.29 !5.30 !5.80 7.1 !8.15 0.59 !0.14
where X represents D or P; Xo is a constant representing Do or Po; Ex represents ED or Ep, depending upon the transport process under consideration, and RT is the usual energy term. The mechanism by which small molecules permeate through rubbery or glassy amorphous polymers has been described by many authors [37–41]. From a least square fitting of the linear plots of log X vs. 1/T, the activation energies for diffusivity (ED) and for permeability (Ep) values were estimated. The sorption heat was also cal-
culated from the differences: )HS = EP!ED. These results are given in Table 4. The magnitude of )HS values can be explained in terms of Henry’s law, which states that the heat of sorption will be positive for liquid transport leading to the dissolution of chemical species into that site within the membrane giving an endothermic contribution to the sorption process. However, Langmuir’s sorption requires the pre-existence of a site in which sorption occurs by a hole-filling mechanism, giving an exothermic contribution.
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For ketones, the ED values range from 60 to 25 kJ/mol and for nitriles, they range from 9 to 68 kJ/mol. The results of the heat of sorption, )HS, are negative in most cases, suggesting an exothermic contribution (Langmuir’s mode of sorption), except for cyclohexanone and acetonitrile, whose )HS values are positive, suggesting an endothermic contribution (Henry’s mode of sorption).
4. Conclusions The sorption coefficients determined in the present study decreased with increasing size of the penetrants in most of the linear ketones. However, for cyclohexanone and acetophenone, sorption coefficients not only depend on the size of liquid penetrants but also on the structures of molecules and their molecular interactions with the membrane. Lower equilibrium sorption values were observed for acetonitrile compared to acrylonitrile at all the investigated temperatures. This was explained based on the lower magnitude of unsaturation, which decreases the affinity of penetrants towards the polymer chain segments. In all the cases, except cyclohexanone, sorption coefficients decreased with increasing temperature, and this was discussed based on decreased molecular interaction between the membrane and liquid penetrants due to increased thermal energy. However, the D values show a systematic dependence on the size of the molecules at all temperatures. Acetophenone has the largest D value of 1.52×10!7 cm2/s, whereas acetone has the lowest D value of 0.16×10!7 cm2/s among the ketones studied at 30°C. For nitriles, acrylonitrile had a higher D value than acetonitrile. Permeability coefficients showed the same pattern as those of diffusivity. Molecular transport was found to follow the anomalous-type of behavior in all the cases over the investigated temperature range. The liquid concentration pro-
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files are dependent on the size of liquid molecules and diffusivity values. The ED values range from 60 to 25, and 9 to 68 kJ/mol for ketones and nitriles, respectively. The )HS values are negative in most of the cases, suggesting that sorption is dominated by exothermic contribution and follows Langmuir’s mode of sorption except for cyclohexanone and acetonitrile, whose )HS values are positive, suggesting that the sorption is exothermic and follows Henry’s mode of sorption. The membrane is stable in all the liquids chosen as evidenced by no chemical degradation. Hence, the fluoroelastomeric membrane (FC-2177 D) studied here can be used in field applications containing these liquids. Acknowledgements The authors wish to thank the Department of Science and Technology, New Delhi (Grant No. SP/S1/H-31/2000) for financial support. The authors also express thanks to Dr. M.I. Aralaguppi for his valuable suggestions.
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Molecular transport of ketones and nitriles into commercial fluoroelastomeric membranes M.Y. Kariduraganavar,* S.B. Kulkarni, A.A. Kittur, S.S. Kulkarni Department of Chemistry and Center of Excellence in Polymer Science, Karnataka University, Dharwad 580 003, India Tel. +91 (836) 274-7121, ext. 372; Fax: +91 (836) 277-1275; email: [email protected] Received 6 July 2004; accepted 27 April 2005
Abstract The molecular transport of ketones such as acetone, ethyl methyl ketone, methyl isobutyl ketone, cyclohexanone and acetophenone, and nitriles such as acrylonitrile and acetonitrile, through Fluorel 3M membranes (FC-2177 D) was carried out in the temperature range of 30–50°C using the sorption gravimetric method. With the sorption data, the concentration-independent diffusion coefficients were calculated from Fick’s diffusion equation. The liquid concentration profiles were also calculated from the analytical solution of Fick’s diffusion equation with the appropriate initial and boundary conditions, and these were presented as a function of penetration depth of molecular migration and time of immersion. Because of the linearly increasing trend of the diffusion coefficients with temperature, efforts were made to estimate the Arrhenius parameters. Experimental values and the computed quantities were used to determine the membrane solvent interactions and to propose suitable applications in various situations. None of the solvents showed any degradative effects on the polymer membrane. Keywords: Membrane; Diffusion; Barrier; Swelling; Activation energy
1. Introduction A good understanding of molecular transport of small organic molecules into polymer membranes has been the subject of great technological importance in different areas of science and engineering [1,2]. Membrane separation of liquids in the liquid and oil industry has become as widespread as more traditional methods based *Corresponding author.
on absorption, pressure-swing adsorption or cryogenics. The membrane process has certain benefits compared to the cryogenic process, for example, lower investment cost and easier operation. Very important applications in the food industry involve impeding the diffusion of liquids through thin polymer films, commonly used as packaging food wrappers or protective coatings [3,4]. Recently, more applications are anticipated in the burgeoning field of biotechnology [5,6]
0011-9164/06/$– See front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2005.04.060
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such as biosensors, controlled release and bioreactors. The sorption and diffusion of organic molecules in polymers have implications even further afield with such molecules playing important roles in the polymer industry as plasticizers, fillers and biocides [7], paints and varnishes [8], encapsulant of electronic components in polymers that act as barriers to atmospheric gases and moisture [9], polymeric sorbents, hazardous chemical pond lining [10], the removal of residual monomers after the polymerization process, etc. Moreover, the effects of the interaction between glassy polymers and small molecules are of practical interest to chemical engineers due to the inherent sorption and transport of solvents present in most processes they encounter. In all these applications, polymers are exposed to a variety of liquids, and thus, an understanding of molecular interactions of liquids with the membrane materials is important to investigate their transport characteristics. In order to understand membrane transport phenomenon and thereby to develop membranes for suitable applications, the characteristics of membrane and the diffusing constituents must be known. These include molecular states of diffusing constituents, their diffusion coefficients and permeabilities, membrane structure, its history such as method of preparation, annealing etc. [11,12]. Free volume and free volume distribution are the properties of polymer structure that have a major impact on its transport properties. In membrane-related applications of polymers, small organic molecules have been used as probes to study the nature of transport mechanism. The important requirement of membrane material is that it should be chemically resistant to retain its mechanical and dimensional stability, and at the same time the chemical structure of the liquid penetrant is essential for the development of highperformance membranes [13]. Our recent papers [14–16] addressed the different aspects of diffusion anomalies for different polymer-solvent systems. In continuation of these
studies and as a further contribution in this area, we report here the experimental results of sorption kinetics, diffusion and permeation of organic ketones and nitriles through Fluorel copolymer membranes (FC-2177 D) at 30, 40 and 50°C. The concentration-independent diffusion coefficients were calculated from the Fick’s diffusion equation. In addition, the analytical solution of Fick’s equation was used to calculate the liquid concentration profiles at different times and depth of liquids inside the membrane material. The temperature-dependent transport coefficients were used to estimate Arrhenius activation parameters. 2. Experimental 2.1. Reagents/chemicals Organic penetrants such as acetone, acetonitrile, acrylonitrile and cyclohexanone were obtained from S.D. Fine Chemicals (Mumbai, India). Ethyl methyl ketone, acetophenone and methyl isobutyl ketone were procured from Sisco Chemical Industries (Mumbai, India). All the chemicals were of analytical grade and were used without further purification. 2.2. Materials Fluorel FC 2177 D is a medium-viscosityincorporated cure di-polymer of vinylidene fluoride and hexafluoropropylene designed for injection molding and sealing components that meet the major fluoroelastomer O-ring specifications. A gift sample received from Ms. Nina McAllum (3M Company, St. Paul, Minnesota, USA) was used in this study. The typical properties of the fluoroelastomer are: fluorine content, 65.9%; specific gravity, 1.80; color, opaque off-white; solubility, in ketones and esters; Mooney viscosity, approximately 34 MLI + 10 at 121°C. The press-cured sample for 7 min at 177°C has the following mechanical properties: tensile strength, 1865 psi; percentage elongation at break, 240;
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hardness (shore A), 75. The sample was compounded with MT Black (30 phr), MgO (9 phr) and Ca(OH)2 (6 phr). 2.3. Sorption-gravimetric experiments The circularly cut disc-shaped membrane samples of .2 cm in diameter were dried in a vacuum desiccator for 45 h over anhydrous CaCl2 before being used in the sorption experiments. These samples were then immersed in about 15– 20 mL of liquids taken in airtight bottles and were maintained at 30, 40 and 50°C in an electronically controlled oven (WTB Binder, Germany) within an accuracy of ±0.5°C. Mass measurements were made by removing the samples at suitably selected time intervals, then wiping the surface-adhered solvent using smooth tissue paper. These samples were then immediately weighed on a top-loading digital Mettler balance (Model AE 240, Switzerland) with an accuracy of ±0.01 mg. The samples were taken out no longer than 30–40 s outside the temperature-controlled oven. The procedure was continued until no more liquid uptake by the polymer was observed (equilibrium sorption). Three independent readings were taken, and the average value was used in all the calculations. Sorption coefficients were expressed as mol % and are calculated using the equation,
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type of polymer barrier and the nature of the migrating liquids. The dynamic swelling properties of a polymer film include the solvent sorption rate, the rate of approach to equilibrium swelling, the solvent front velocity and the transport mechanism controlling solvent sorption. For the Fickian transport, the rate of equilibrium approach can be characterized by the diffusion coefficient. For plane geometry of the polymer sheet the diffusion coefficient D can be calculated from [17]:
(2)
Here Mt and M4 are the cumulative masses sorbed from the polymer sample at time t and 4, respectively and h is the initial thickness of the polymer sample. Although this equation can be solved readily, it is suitable to consider the short-time limiting expression as well [17]: (3)
(1)
A single curve is obtained from the plot of Mt /M4 vs. the square root of time, which is initially linear. Thus, D can be calculated from the rearrangement of Eq. (3) as [18–22]:
where W0 is the initial mass of the sample; Wt is the mass at time t, that is, the immersion period; and M is the molar mass of the liquid.
(4)
2.4. Diffusion coefficients and concentration profiles Diffusive migration of liquids depends on concentration and temperature, together with the
where M4 is the equilibrium mass uptake at t 6 4 and 2 is the slope of the initial linear portion of the sorption curves. Similarly the permeability coefficient can be calculated using the relation P = D×S, which follows nearly the same pattern
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as those of diffusivities. This simple relation holds for the permeation process when D obeys Fick’s diffusion law and S obeys Henry’s law [23]. For the penetrant-polymer systems used in this study, it is not certain to what degree one or both laws are obeyed. Thus, the P values are considered as estimates of the permeability coefficients. Liquid ingression into polymeric materials is a phenomenon of great technological importance. In many instances it is necessary to know the penetration depth of liquid into polymer. In most application areas, the liquid penetration rates are calculated in terms of liquid concentration profiles. These are extremely useful to predict the self-life of the polymer while in contact with liquids. Liquid concentration profiles can be calculated from Eq. (5) under suitable initial and boundary conditions to yield an equation for solvent uptake C(x,t) inside the membrane thickness h, at time t and distance x as [12,24,25]:
Fig. 1. Plots of Mt vs square-root of time for fluoroelastomer at 30°C with (F) acetone, ()) ethyl methyl ketone, (G) methyl isobutyl ketone, (") acetophenone and (M) cyclohexanone.
(5)
where m is an integer. These data are useful to study the liquid migration as a function of time and penetration depth of the liquids from the face to the middle of the fluoroelastomer along the thickness direction. 3. Results and discussion 3.1. Sorption kinetics Molecular transport of liquid penetrants through the membranes can be studied in terms of sorption/diffusion phenomenon. The equilibrium sorption results measured at three different
Fig. 2. Plots of Mt vs. square-root of time for fluoroelastomer at 30°C with (F) acrylonitrile and ()) acetonitrile.
temperatures are presented in Table 1 whereas the mol percent sorption plots for ketones and nitriles measured at 30°C are displayed in Figs. 1 and 2, respectively. It was observed that among the ketones studied, the sorption values for linear ketones are higher than those of cyclohexanone and acetophenone. Further the sorption values have a systematic trend for linear ketones, and in
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Table 1 Physical properties and equilibrium sorption coefficients of ketones and nitriles through fluoroelastomeric membranes Liquids
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
Molar volume (cm3 mol!1)
Sorption coefficients (mol %) 30°C
40°C
50°C
74.04 90.02 125.8 104.2 117.4 52.9 66.0
2.50 ± 0.02 2.14 ± 0.02 1.69 ± 0.03 0.09 ± 0.02 0.76 ± 0.03 1.65 ± 0.02 1.86 ± 0.02
2.29 ± 0.03 1.86 ± 0.03 1.56 ± 0.03 0.10 ± 0.02 0.72 ± 0.02 1.64 ± 0.03 1.86 ± 0.03
2.20 ± 0.03 1.86 ± 0.03 1.46 ± 0.04 0.11 ± 0.02 0.62 ± 0.03 1.64 ± 0.02 1.86 ± 0.02
accordance, the sorption coefficients decrease with increase in the size of liquid molecules. For instance, acetone with a lower molar volume (74.0 cm3/mol) shows higher equilibrium sorption at all temperatures followed by ethyl methyl ketone and methyl isobutyl ketone, which have higher molar volumes of 90.02 and 125.8 cm3/ mol, respectively. However, in case of cyclohexanone (104.2 cm3/mol) and acetophenone (117.4 cm3/mol), though the molar volumes of these are lower than methyl isobutyl ketone, the equilibrium sorption values are lower than methyl isobutyl ketone; the same trend is observed at higher temperatures as well. This may be due to the fact that cyclohexanone and acetophenone are bulky compared to methyl isobutyl ketone due to its cyclic structure. This clearly implies that sorption not only depends on the molar volume but also on the nature of the liquid structure, which hinders the liquid sorption significantly. On the other hand, acetophenone, which has a higher molar volume than cyclohexanone, shows much higher equilibrium sorption values. This indicates that acetophenone has more interaction with the membrane chosen and thereby exhibits higher liquid sorption. In the case of nitriles, the sorption curves show an overshoot effect as indicated by an abrupt and fast initial penetrant uptake by the
polymer. Such an overshoot effect has been attributed to polymer crosslink density and the increased mobility of the polymer chain segments [26]. Solvent diffuses into the polymer network before its chains have had the time to relax (i.e., diffusion is faster than relaxation) and the fractional uptake reaches a maximum (i.e., the overshoot value). When the chains finally relax, the liquid penetrant is forced out of the network, and hence its uptake eventually reaches the true equilibrium value. Another plausible explanation for the observed overshoot effect is due to the presence of a thin layer formed during the polymer processes, which is morphologically different from the bulk of the polymer. Also, because the solvent diffusion coefficient in the polymer matrix is dependent upon the degree of crosslinking, a sudden initial jump in the uptake is expected if the crosslink density of the polymer is significantly lower in a thin outer layer of the sample. Several studies have addressed different aspects of the overshoot phenomenon when polymers absorb the penetrants [27–31]. Although the molar volumes of the nitriles are smaller than those of ketones, the observed equilibrium sorption values for nitriles are smaller than those of ketones such as acetone and ethyl methyl ketone. At all the investigated temperatures the equili-
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brium sorption values for acetonitrile are lower than acrylonitrile. This is because the magnitude of unsaturation is less compared to acrylonitrile, which decreases the affinity towards the polymer chain segments. In all the cases, except cyclohexanone, sorption coefficients decrease with increasing temperature. As explained above, the sorption coefficient is attributed to the size of the liquid penetrants as well as interactions existing between liquid penetrants and the membrane. As the temperature increases, the interactions between the membrane and liquid molecules decrease due to increased thermal energy, which results in a decrease in the sorption coefficients. On the contrary, the sorption coefficients of cyclohexanone increased with increasing temperature. This may be due to the fact that among ketones, cyclohexanone is a cyclic ketone but the remaining ones are aliphatic ketones, including acetophenone. This suggests that the sorption coefficients of cyclohexanone are mainly attributed to the size of the penetrants, which are not affected by the increase of thermal energy. Instead, it increases due to relaxation of polymer segments as the temperature increases. The results of diffusion coefficients measured at different temperatures are presented in Table 2. It was observed that the values of diffusion coefficients increased systematically from acetone to
methyl isobutyl ketone, and cyclohexanone to acetophenone as the size of the migrating liquids increased at all temperatures. The largest D value of 1.52×10!7 cm2/s was observed for acetophenone at 30°C, whereas the lowest of 0.16× 10!7 cm2/s was observed for acetone, among the ketones studied. In the case of nitriles, the higher value of D was observed for acrylonitrile than acetonitrile. This is in accordance with the size of the molecules. The D values calculated at 30°C vary according to the sequence: acetonitrile < acetone < ethyl methyl ketone < cyclohexanone < acrylonitrile < methyl isobutyl ketone < acetophenone. Permeability coefficients calculated from the kinetic gravimetric sorption experiments are also included in Table 2. It is generally observed that permeability results follow the same pattern as those of diffusion coefficients in the investigated temperature range. In areas where polymeric membranes are used as barriers towards aggressive liquids, it is important to know the liquid penetration rates calculated in terms of liquid concentration profiles. These are calculated from Eq. (5) at different membrane thicknesses (i.e., penetration depth of liquids) and at different time intervals during sorption experiments. However only a few typical graphs are displayed (Figs. 3–6). These plots show a dependence on the temperature, depth of
Table 2 Diffusion (D) and permeation (P) coefficients of ketones and nitriles at different temperatures through fluoroelastomeric membrane Liquids
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
Dipole moment (µ) 2.69 2.76 — 3.08 2.95 3.53 3.67
D (107) cm2/s
P (108) cm2/s
30ºC
40ºC
50ºC
30ºC
40ºC
50ºC
0.16 0.37 1.09 0.45 1.52 0.10 0.90
0.27 0.58 1.29 0.66 2.62 0.30 1.03
0.71 0.91 3.10 1.51 2.78 0.53 1.13
4.00 7.90 18.4 0.40 11.5 1.60 16.70
6.10 10.8 20.1 0.60 18.7 4.90 19.10
15.6 16.9 45.4 1.60 17.2 8.60 20.9
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Fig. 3. Concentration profiles calculated from Eq. (5) for acetone through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
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Fig. 4. Concentration profiles calculated from Eq. (5) for methyl isobutyl ketone through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
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Fig. 5. Concentration profiles calculated from Eq. (5) for acetonitrile through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
Fig. 6. Concentration profiles calculated from Eq. (5) for acrylonitrile through fluoroelastomer membranes at (A) 30°C, (B) 40°C and (C) 50°C for (F) 25 min, ()) 50 min, (G) 100 min, (") 120 min, (M) 200 min, (•) 300 min and (O) 500 min.
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Table 3 Estimated parameters for ketones and nitriles calculated from Eq. (6) at different temperatures for fluoroelastomeric membranes Liquids
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
n
K
30ºC
40ºC
50ºC
30ºC
40ºC
50ºC
0.52 0.53 0.55 0.52 0.51 0.50 0.53
0.54 0.51 0.50 0.55 0.53 0.57 0.59
0.55 0.52 0.54 0.53 0.52 0.55 0.52
1.64 2.52 3.17 2.36 2.89 1.79 4.25
2.95 3.47 4.43 3.73 3.48 3.49 5.34
4.71 5.83 6.06 4.68 5.97 6.28 6.58
penetration as well as on the nature of liquids chosen. For instance, diffusivity of acetone is lower than that of methyl isobutyl ketone and hence, its concentration profiles are lower at all temperatures (see Fig. 3). In case of methyl isobutyl ketone, diffusivity is quite high and so are its concentration profile values (see Fig. 4). Similar effects have been also observed in the case of acetonitrile and acrylonitrile as displayed in Figs. 5 and 6, respectively. From this we could observe a clear-cut dependence of D values on temperature. In addition, the concentration profiles vary according to the diffusion values of the liquids. The same trend was also observed for other liquids, but these plots are not displayed to reduce the number of plots. In order to know the type of diffusion mechanism, the sorption data have been analyzed using the following equation [32,33]: (6) Here, K represents polymer-solvent interaction parameter, while the exponent value n represents the nature of transport mechanism. For instance, if n lies between 0.5 and 0.75, then the transport is anomalous, that is, it slightly deviates from the
Fickian trend. The estimated values of n and K are presented in Table 3. It was observed that the values of n vary from 0.5 to 0.59, thus the transport is found to follow anomalous-type behavior [15,34–36]. Furthermore, the values of n do not show any systematic trend with temperature. In all cases, K increases with increasing temperature, and this suggests increased molecular interaction between the polymer and liquid molecules. Although K values do not show any systematic effects on the dipole moment of the liquids, they do show a systematic effect on the size and nature of liquids as similar to the sorption study. 3.2. Temperature effects The temperature dependency of diffusion was followed by carrying out the sorption experiments at 30, 40 and 50°C. From the typical plots (Figs. 7 and 8), it is clear that mol % uptake increased with the temperatures. From the values of diffusion and permeation coefficients at different temperatures, the corresponding apparent values of activation energy ED, EP were calculated using an Arrhenius-type equation [22]: (7)
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Fig. 7. Arrhenius plots of log D vs. 1/T for fluoroelastomer membranes for (F) acetone, ()) ethyl methyl ketone, (G) methyl isobutyl ketone, (M) acetophenone and (") cyclohexanone.
Fig. 8. Arrhenius plots of log D vs. 1/T for fluoroelastomer membranes for (F) acetonitrile and ()) acrylonitrile.
Table 4 Activation energy for diffusion, permeation and heat of sorption of ketones and nitriles for fluoroelastomeric membranes Liquids
EP (kJ/mol)
ED (kJ/mol)
)Hs (kJ/mol)
Acetone Ethyl methyl ketone Methyl isobutyl ketone Cyclohexanone Acetophenone Acetonitrile Acrylonitrile
55.18 ± 0.03 31.34 ± 0.03 36.45 ± 0.02 56.19 ± 0.03 16.63 ± 0.02 68.71 ± 0.03 9.15 ± 0.02
60.47 ± 0.02 36.64 ± 0.02 42.25 ± 0.04 49.09 ± 0.02 24.78 ± 0.02 68.12 ± 0.03 9.29 ± 0.04
!5.29 !5.30 !5.80 7.1 !8.15 0.59 !0.14
where X represents D or P; Xo is a constant representing Do or Po; Ex represents ED or Ep, depending upon the transport process under consideration, and RT is the usual energy term. The mechanism by which small molecules permeate through rubbery or glassy amorphous polymers has been described by many authors [37–41]. From a least square fitting of the linear plots of log X vs. 1/T, the activation energies for diffusivity (ED) and for permeability (Ep) values were estimated. The sorption heat was also cal-
culated from the differences: )HS = EP!ED. These results are given in Table 4. The magnitude of )HS values can be explained in terms of Henry’s law, which states that the heat of sorption will be positive for liquid transport leading to the dissolution of chemical species into that site within the membrane giving an endothermic contribution to the sorption process. However, Langmuir’s sorption requires the pre-existence of a site in which sorption occurs by a hole-filling mechanism, giving an exothermic contribution.
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For ketones, the ED values range from 60 to 25 kJ/mol and for nitriles, they range from 9 to 68 kJ/mol. The results of the heat of sorption, )HS, are negative in most cases, suggesting an exothermic contribution (Langmuir’s mode of sorption), except for cyclohexanone and acetonitrile, whose )HS values are positive, suggesting an endothermic contribution (Henry’s mode of sorption).
4. Conclusions The sorption coefficients determined in the present study decreased with increasing size of the penetrants in most of the linear ketones. However, for cyclohexanone and acetophenone, sorption coefficients not only depend on the size of liquid penetrants but also on the structures of molecules and their molecular interactions with the membrane. Lower equilibrium sorption values were observed for acetonitrile compared to acrylonitrile at all the investigated temperatures. This was explained based on the lower magnitude of unsaturation, which decreases the affinity of penetrants towards the polymer chain segments. In all the cases, except cyclohexanone, sorption coefficients decreased with increasing temperature, and this was discussed based on decreased molecular interaction between the membrane and liquid penetrants due to increased thermal energy. However, the D values show a systematic dependence on the size of the molecules at all temperatures. Acetophenone has the largest D value of 1.52×10!7 cm2/s, whereas acetone has the lowest D value of 0.16×10!7 cm2/s among the ketones studied at 30°C. For nitriles, acrylonitrile had a higher D value than acetonitrile. Permeability coefficients showed the same pattern as those of diffusivity. Molecular transport was found to follow the anomalous-type of behavior in all the cases over the investigated temperature range. The liquid concentration pro-
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files are dependent on the size of liquid molecules and diffusivity values. The ED values range from 60 to 25, and 9 to 68 kJ/mol for ketones and nitriles, respectively. The )HS values are negative in most of the cases, suggesting that sorption is dominated by exothermic contribution and follows Langmuir’s mode of sorption except for cyclohexanone and acetonitrile, whose )HS values are positive, suggesting that the sorption is exothermic and follows Henry’s mode of sorption. The membrane is stable in all the liquids chosen as evidenced by no chemical degradation. Hence, the fluoroelastomeric membrane (FC-2177 D) studied here can be used in field applications containing these liquids. Acknowledgements The authors wish to thank the Department of Science and Technology, New Delhi (Grant No. SP/S1/H-31/2000) for financial support. The authors also express thanks to Dr. M.I. Aralaguppi for his valuable suggestions.
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