Fluid Phase Equilibria

Transcription

1 Fluid Phase Equilibria (12) Contents lists available at SciVerse ScienceDirect Fluid Phase Equilibria j o ur nal homep age: A thermodynamic study of 1,4-dioxane across cellulose acetate membrane under different conditions Kiran a, D.S. Rana a, R.L. Balokhra a, A. Umar b, S. Chauhan a, a Department of Chemistry, Himachal Pradesh University, Shimla , India b Collaborative Research Centre for Sensors and Electronic Devices (CRCSED), Centre for Advanced Materials and Nano-Engineering (CAMNE), Najran University, P.O. Box 1988, Najran-11001, Saudi Arabia a r t i c l e i n f o Article history: Received 2 December 11 Received in revised form 5 March 12 Accepted 9 March 12 Available online March 12 Keywords: Cellulose acetate membrane Electromosmotic flow Permeation Thermodynamic parameters a b s t r a c t The cellulose membrane used in the present studies was prepared by impregnating cellulose acetate dissolved in acetone and mixed up with aqueous KBr, which has been added through a sintered G 2 (porosity) disc. The flow of water, 1,4-dioxane and their different compositions through this membrane has been measured at different temperatures under different electric and magnetic field strengths. The results are interpreted in terms of a unit rate process. The electro osmotic permeability coefficients, enthalpy of activation ( H * ), entropy of activation ( S * ), free energy of activation ( G * ), number of pores, pore radius and zeta potential have also been calculated. The flow process of various aqueous dioxane mixtures across the membrane does not seem to be thermodynamically feasible. However, the dipolar nature of the solvent mixture does affect the membrane structure as shown by the variation in pore radius, number of pores and zeta potential. 12 Published by Elsevier B.V. 1. Introduction Many physiological processes in plants and animals involved transport through membranes especially water transport through roots and soil is of particular interest. Exchange of matter and energy which is the principal function of organisms takes place through membranes [1]. Membrane processes are currently being studied for numerous applications of practical interest. Most important technological applications of membrane include their use in industry for chemical and biomedical separations and demineralization by reverse osmosis [2 7]. In this context, nonequilibrium thermodynamics studies have been conducted in liquid mixtures for, e.g. acetone methanol [8] and methanol water [9] in order to study the concentration dependence of phenomenological coefficients and to verify Onsagar relations. In the present work, we have carried out studies on hydrodynamic flow and electro osmotic flow for aqueous solution of 1,4-dioxane at different composition, under different electric and magnetic field strengths at different temperatures. From the calculated hydrodynamic permeability, the electro osmotic permeability coefficients and thermodynamic parameters, i.e. enthalpy of activation ( H * ), entropy of activation ( S * ), free energy of activation ( G * ) have been calculated. Further, the number of Corresponding author. Tel.: ; fax: address: chauhansuvarcha@rediffmail.com (S. Chauhan). pores, pore radius and zeta potential for the membrane crossed by different solution of 1,4-dioxane in water have also been determined. 2. Experimental 2.1. Materials Cellulose acetate (AR grade Riedel Germany), acetone (99.0% from E. Merck), KBr (from E. Merck) and 1,4 dioxane (99.5% from E. Merck) were used in this study. Ordinary tap water of conductivity range S cm 1 at 25 C was distilled with the help of Millipore (Elix) distillation unit, which was further distilled in the presence of alkaline potassium permanganate through a 750 mm long vertical fractionating column. The water so obtained has conductitivity value around S cm 1 at 25 C and ph in the range Membrane The cellulose acetate was dissolved in acetone in the proportion of 22.2:66.7 and after this mixture was mixed up with aqueous solution of KBr prepared with 10:1.1 of water and KBr, respectively. The obtained cellulose acetate solution was impregnated into a previously thoroughly washed and dried sintered G 2 disc under vacuum at C. After impregnation the disc was immersed in hot water at C as suggested by Lakshminarayanaih [8]. The /$ see front matter 12 Published by Elsevier B.V. doi: /j.fluid

2 Kiran et al. / Fluid Phase Equilibria (12) Fig. 1. Apparatus for electo-osmosis. membrane then was treated with water for 24 h before performing experiments in order to avoid fluctuation in the permeability of the membrane Apparatus The apparatus used for the present investigation and its experimental set up is shown in Fig. 1. It consist of a pyrex glass tube of about cm in length having a slight constriction in the middle where a sintered disc is fixed and the membrane impregnated in it. The tube has two standard B-24 joints at the end. The main tube has two side tubes having B-14 standard joints and the pressure head on the other B-14 standard joint is moveable so as to set up any position to maintain the desired pressure in the tube. The apparatus is placed in the wooden cradle. The whole assembly was kept in air thermostat. 3. Results and discussion 3.1. Determination of volume flux (J V ) and hydrodynamic permeability (L P ) According to thermodynamics of irreversible processes [10,11] the dissipation function [12], for the transport processes of liquids through a membrane under the influence of pressure difference can be written as = J V P + J D (1) where J V is volume flux per unit area of the membrane, J D is the diffusional flow, P is hydrostatic pressure difference and П is difference in osmotic pressure across the membrane. The linear phenomenological equations relating to flow and forces are given below J V = L P P + L Pd (2) J D = L dp P + L d (3) Fig. 2. A plot of volume flux (J v) versus pressure for water at K at different magnetic field strength. Fig. 3. A plot of hydrodynamic permeability (L p) versus pressure for water at K at different voltage.

3 150 Kiran et al. / Fluid Phase Equilibria (12) Table 1 Volume flux data at different temperatures and magnetic field strengths of cellulose acetate membrane when crossed by pure water. Temperature (K) P 10 3 (N m 2 ) Magnetic field strength (KG) Table 2 Volume flux data at different temperature, concentration and magnetic field strength of cellulose acetate membrane when crossed by the mixtures of 1,4-dioxane and water. Temperature (K) P 10 3 (N m 2 ) Magnetic field strength (KG) % % %

4 Kiran et al. / Fluid Phase Equilibria (12) Table 3 Permeability coefficients (L p) of cellulose acetate membrane at different temperatures, electric and magnetic field strength when crossed by different compositions of 1,4-dioxane in water. Temperature (K) Voltage (V) Magnetic field strength (KG) where = RT C (4) The Onsager reciprocity relation [13] is L Pd = L dp (5) where L P and L d are the mechanical coefficients of filtration and diffusion respectively and L Pd and L dp represents Onsager coefficients. In experiments where the concentration of solution is same on both sides of membrane, П = 0 and if pressure difference is maintained across the membrane there exists a volume flux J V. The values of J V, i.e. the volume flux of water, dioxane and aqueous solutions of dioxane at different pressure, temperature, electric and magnetic field strengths across cellulose acetate membrane are calculated as follows ( dx ) ( ) r 2 i J V = dt R 2 (6) i where x is distance travelled by the experimental liquid, t is the time taken to travel the distance x, r i is the radius of capillary and R i is the radius of the membrane. The radius of capillary was estimated with the help of the travelling microscope supplied by Almicro VM-1. For this purpose, mercury was taken in the capillary, filling a known length of the capillary, which was measured with the help of the travelling microscope several times. The weight of mercury (w) filling the capillary was noted with the help of Eq. (7) w = r 2 i ld (7) where d is density of mercury and l is length of mercury thread in capillary. Densities (d) of various solutions were determined with the help of calibrated pycnometer. The values of J V when the membrane was crossed by pure water and for the mixture of water and 1,4-dioxane are reported in Tables 1 and 2, respectively When the concentration of solution is the same on both sides of membrane the volume flow [from Eq. (2)] can be given [14,15] as J V = L P P (8) where L P is the hydrodynamic permeability or permeability coefficient or simply permeability of the membrane for fluid. L P has the character of mobility and represents the velocity of fluid per unit pressure difference for the unit cross-sectional area of the membrane. The values of L P can be estimated from the linear plots of J V and P for water and aqueous solutions of 1,4-dioxane. A sample plot for the same has been represented in Fig. 2 at K. The values of hydrodynamic permeability calculated using Eq. (8) for water and various aqueous dioxane solutions have been reported in Table 3. It is clear that L P varies non-linearly with pressure as shown in Fig. 3.

5 152 Kiran et al. / Fluid Phase Equilibria (12) Table 4 Frictional coefficient (F wm) of cellulose acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4- dioxane in water. Temperature (K) Voltage (V) Magnetic field strength (KG) Determination of frictional coefficient The frictional coefficient of the phenomenological coefficient in the transport processes through membranes has been given by Kedem and Katchalsky [16]. The explicit treatment of frictional forces may be approached by considering the simple case of water filtration through membrane. If pure water is placed on both sides of the membrane, then the driving force provided by a difference in pressure which is balanced by mechanical filtration force between water and the membrane matrix under the condition of steady flow, therefore the mechanical filtration force, X wm is given by X wm = F wm (V w V m ) (9) where F wm is the coefficient of friction between water and the membrane and it is a measure of the resistance offered by the membrane to water penetration, V w and V m are the volume of the water and mixtures respectively. Under the simple use of translation of thermodynamic coefficient into frictional coefficient the permeability coefficient, (L P ) can be related to coefficient of friction (F wm ) by a simple relation as L P = w V w (10) F wm ı where ф w is the water content of the membrane and is expressed as the volume fraction of the total membrane volume and is numerically equal to the fraction of membrane surface available for the permeation of solution. It was determined by the method described by Ginzberg and Katchalsky [17] and the value obtained was 0.1 in the present case of cellulose acetate membrane, ı is thickness of membrane and the value in the given case is m, V w is molar volume of water. The values of coefficient of friction calculated using Eq. (10) for various aqueous solutions have been reported in Table Determination of H *, S * and G * Different membranes used in alternate energy devices have been characterized in terms of parameters of activation. The variation of hydrodynamic permeability with temperature can be written as log L P = k E n (11) RT where k is constant, E n is energy of activation, R is gas constant and T is temperature. Energy of activation can be taken as enthalpy of activation [18] ( H * ). By using Eyring rate Eq. [19] for the flow, entropy of activation is calculated from the equation = Nh Ve S /R e H /RT (12) where is viscosity of liquid, V is molar volume, N is Avogadro s number and h is Plank s constant. Eq. (12) can be written as ( ) Nh S = H + R log T V (13)

6 Kiran et al. / Fluid Phase Equilibria (12) Fig. 4. Variation of enthalpy of activation ( H * ) versus voltage at different composition in water dioxane mixtures. Fig. 5. Variation of entropy of activation ( S * ) versus voltage at different composition in water dioxane mixtures.

7 154 Kiran et al. / Fluid Phase Equilibria (12) Fig. 6. Variation of free energy of activation ( G * ) versus voltage at different composition in water dioxane mixtures. Table 5 Enthalpy ( H * ), entropy ( S * ) and free energy of activation ( G * ) of acetate membrane at different electric and magnetic field strengths when crossed by different compositions of 1,4-dioxane in water. Thermodynamic parameters at K Enthalpy of activation ( H * ) Entropy of activation ( S * ) Free energy of activation ( G * ) Voltage (V) Magnetic field strength (KG)

8 Kiran et al. / Fluid Phase Equilibria (12) Table 6a Pore radius (r) across acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4-dioxane in water. Temperature (K) Voltage (V) Magnetic field strength (KG) s s The free energy of activation ( G * ) can be calculated from the equation G = H T S (14) The estimated values of H *, S * and G * have been recorded in Table 5 and the variation of these parameters with voltage at different composition are shown in Figs. 4 6 respectively Determination of equivalent pore radius and number of pores Magnetic field when applied exerts a change in the structure of the membrane which has been characterized in terms of its pore radius, number of pores and zeta potential, expressing the electrical character of the membrane permeant interface. These parameters can be estimated in the light of capillary model, according to which, a porous membrane is supposed to be composed of a bundle of n capillaries entering a porous medium on the face and emerging on the opposite face. Although any structure of the porous medium is not as simple as described by capillary model, yet it has been successfully used by many authors [,2,21,22]. According to this model L 22 = (nr4 ) (15) 8ı L 11 = (nr2 k) (16) ı where L 22 is hydrodynamic permeability, L 11 is the electric conductance of the membrane, n is number of pores, r is equivalent pore radius, is the absolute viscosity, and k is specific conductance of the permeant. The equivalent pore radius for different systems across cellulose acetate membrane at different magnetic field strength has been calculated by rearranging Eqs. (15) and (16) as r = (8kL 22) (17) (L 11 ) 1/2 Once the equivalent pore radius of the membrane for different systems is known, it is possible to calculate the number of capillaries. The number of pores for different systems across cellulose acetate membrane has been calculated by rearranging Eq. (15) as n = (8ıL 22) (r 4 (18) ) The values of r and n thus obtained for membrane have been recorded in Tables 6a and 6b Determination of zeta potential Zeta potential () plays important role in various applications such as microfluidics [23 25], colloid chemistry [26,27], and membrane fouling. The zeta potential is influenced by surface composition, as well as solution properties such as the nature of the ions and ionic strength. Measurement of the streaming potential in channel geometry is the most commonly used technique for characterizing the zeta potential of flat surfaces however some phenomena such as electrophoresis [28] have also been used to characterize the zeta potential.

9 156 Kiran et al. / Fluid Phase Equilibria (12) Table 6b Number of pores (n) of cellulose acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4-dioxane in water. Temperature (K) Voltage (V) Magnetic Field Strength (KG) Electrical character of the membrane interface can be expressed in terms of zeta potential. Zeta-potential is an informative property directly related to the electro kinetic charge density. In the case of technical membranes, for example, zeta-potential is believed to be correlated with the mechanisms of rejection of charged solutes and with the interactions between the membrane surface and various charged foulants (colloidal and macromolecular). Experimentally, zeta-potential of macroscopic surfaces is often obtained from the measurements of streaming potential. According to double layer picture and overbeek analysis of electro kinetic effects [29], the electro osmotic permeability is given by L 21 = L 12 = (nεr2 ) (19) 4ı L 21 = L 12 is the electro osmotic permeability, ε is the dielectric constant and is the zeta potential of solid liquid interface. Eq. (19) can be rearrange as = 4ıL 12 nεr 2 The values of thus obtained for membrane have been recorded in Table 7. A perusal of the data of J V shows that it decreases with increase in composition and magnetic field strength and increase with increase in temperature. The addition in water disturbs the dipole distribution and as a result structural rearrangement takes place. Further the permeability is inversely proportional to the viscosity and the effect of magnetic field on permeability coefficient (L P ) of membrane is similar to the effect of magnetic field on viscosity [,21]. The effect of magnetic field on permeability coefficient (L P ) is much more pronounced than on viscosity of solutions. This suggests that membrane structure under the influence of magnetic field also changes. However, the structural changes of membrane shall be limited to its porosity and to the electrostatic charge density, which the membrane may have on its surface or on the inside walls. Under the influence of the membrane, the ions present in the solution get aligned in a particular fashion in the forms of dipoles, parallel to the direction of magnetic field. The decrease in permeability coefficient (L P ) with the magnetic field strength may, therefore, be attributed to the increase in dipole dipole interactions and structural changes of the membrane. Recently it has been reported in [30] that there is an orientation of cellulose micro crystals by magnetic field and the same effect may be assumed to affect the structure of the membrane in such a way that the values of permeability coefficient (L P ) decreases under a magnetic field strength. In general, the value of frictional coefficient shows increases with increase of electric, as well as, magnetic field strengths. However, with rise in temperature, F wm values do not show a regular trend. The variation in the value of F wm can be correlated to the structural consequences resulting from interactions of water dioxane dipoles at the given compositions. The membrane solution interactions also vary with the content as well as viscosity of the medium. The non-linear dependence of F wm with compositions shows that Spiegler s [31] frictional model is not valid under the influence of magnetic field.

10 Kiran et al. / Fluid Phase Equilibria (12) Table 7 Zeta potential () across cellulose acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4-dioxane in water. Temperature (K) Voltage (V) Magnetic field strength (KG) The value of H * increases with increase in magnetic field strength, increase in composition and voltage as well, in all cases. The S * values also increases with increase in magnetic field strength, increase in composition and voltage and has all negative values which suggests that the flow through membrane is more ordered due to membrane solution interactions. The values of G * show a slight decrease with increase in dioxane composition in the solution and remain almost constant with increase in magnetic field strength. The positive values of G * in all cases shows that flow is not favoured across the porous medium. The data suggests that equivalent pore radius decreases with the application of magnetic field strength. This may be attributed to the change in the pore structure of the membrane. On the other hand, number of pores increase with increase in magnetic field strength. The increase in number of pores with magnetic field strength suggests a change in the total physical characteristics of the membrane. The decrease of equivalent pore radius may also suggest that structure of membrane may weaken and diameter of pores vary in the membrane, which may be attributed to the increase in the number of pores in the membrane on account of change in its structure. The data suggests that the values of decrease with increase in magnetic field strength increase with increase in concentration and temperature. 4. Conclusion The results of above study indicate that dipolar interaction of two solvents affects the alignment of dipoles of the membrane under the influence of magnetic as well as electric field strengths. In addition, these interactions manifest their effect on the structure of membrane also as reflected by the variation in pore radius, number of pores as well as zeta potential. List of symbols F wm frictional coefficient L P permeability coefficient L 12 electro osmotic permeability zeta potential L 22 hydrodynamic permeability L 11 electric conductance of the membrane n number of pores r equivalent pore radius absolute viscosity C- dielectric constant of the medium k specific conductance of the permeant viscosity of liquid V molar volume E n energy of activation ф w water content of the membrane V w molar volume of water ı thickness of membrane X wm mechanical filtration force r i radius of the capillary x distance travelled by the experimental liquid L Pd and L dp Onsager coefficients R i radius of the membrane

11 158 Kiran et al. / Fluid Phase Equilibria (12) L d mechanical coefficients of diffusion J V volume flux per unit area of the membrane J D diffusional flow P hydrostatic pressure difference П difference in osmotic pressure across the membrane H * enthalpy of activation H * S * entropy of activation S * G * free energy of activation R gas constant T temperature Ф dissipation function C change in concentration Acknowledgements Dilbag Singh Rana thanks UGC, New-Delhi for the award of Dr. D.S. Kothari Postdoctoral Fellowship and S. Chauhan thanks UGC for the financial assistance under the project (F.No /06/SR). References [1] P.F. Agris, Biomolecular Structure and Function, Academic Press, New York, 19. [2] R.L. Blokhra, S. Kumar, J. Membr. Sci. 43 (1989) [3] R.L. Blokhra, S. Kumar, R.K. Upadhyay, N. Upadhyay, J. Chem. Eng. Data 33 (1988) [4] R.L. Blokhra, C. Prakash, Ind. J. Chem. 28A (1989) [5] R.L. Blokhra, N. Arora, S.K. Aggarwal, J. Ind. Chem. Soc. 66 (1989) [6] V.M. Barragán, C. Ruíz-Bauzá, J.P.G. Villaluenga, B. Seoane, J. Colloid Interf. Sci. 277 (04) [7] L. Shang, S. Zhang, H. Du, S.S. Venkatraman, J. Membr. Sci. 321 (2) (08) [8] R.C. Srivastava, M.G. Abraham, J. Colloid Interf. Sci. 57 (1976) [9] R.C. Srlvastava, M.G. Abraham, A.K. Jain, J. Phys. Chem. 81 (9) (1977) [10] S.R. Degroot, Thermodynamics of Irreversible Processes, Interscience Publishers, New York, 1959, p [11] I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, John Wiley, New York, 1967, p. 63. [12] A. Katchalsky, P.F. Curran, Non Equilibrium Thermodynamics in Biophysics, Harward University Press, Cambridge, 1967, p [13] C. Kalidas, M.V. Sangaranarayanan, Non-Equilibrium Thermodynamics Principals and Applications, Macmillan India Ltd, 02, p. 41. [14] N. Lakshminarayanaiah, Transport Phenomenon in Membranes, Academic Press, New York, 1969, p.. [15] R. Hasse, Thermodynamics of Irreaversible Processes, Reading Massachusetts, 1969, p [16] D.C. Mikulecky, J. Gen. Physiol. 7 (5) (1967) [17] B.Z. Ginzberg, A. Katchalsky, J. Gen. Physiol. 47 (1963) [18] R.L. Blokhra, Activation Parameters of Flow Through Battery Separators NASA TM No , [19] S. Glasston, K.J. Laidler, H. Eyring, Theory of Rate Processes, McGraw-Hill, [] R.L Blokhra, C. Prakash, J. Membr. Sci. 70 (1992) 1 7. [21] K. Singh, R. Kumar, V.N. Srivastava, Indian J. Chem. Soc. 57 (1980) 3 7. [22] R.L Blokhra, S. Kohli, J. Electroanal. Chem. Interf. Electrochem. 124 (1981) [23] J.L. Lin, K.H. Lee, G.B. Lee, J. Micromech. Microengg. 16 (4) (06) [24] Z. Wu, D. Li, Electrochim. Acta 53 (08) [25] D. Erickson, Li, Dongqing, Langmuir 18 (5) (02) [26] H. Reiber, T. Koller, T. Palberg, F. Carrique, E.R. Reina, R. Piazza, J. Colloid Interf. Sci. 309 (07) [27] A.B. Jodar-Reyes, J.L. Ortega-Vinuesa, A. Martín-Rodríguez, J. Colloid Interf. Sci. 297 (06) [28] A.V. Delgado, F.G. Caballero, R.J. Hunter, L.K. Koopal, J. Lyklema, J. Colloid Interf. Sci. 309 (07) [29] O.J. Overbeek, J. Colloid Sci. 8 (1953) [30] J. Sugiyama, H. Chanzy, G. Maret, Macromolecule 25 (1992) [31] K.S Spiegler, Trans. Faraday Soc. 54 (1958)