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Fluid Phase Equilibria
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thermodynamic study of 1,4-dioxane across cellulose acetate membrane underifferent conditions
irana, D.S. Ranaa, R.L. Balokhraa, A. Umarb, S. Chauhana,∗
Department of Chemistry, Himachal Pradesh University, Shimla 171 005, IndiaCollaborative Research Centre for Sensors and Electronic Devices (CRCSED), Centre for Advanced Materials and Nano-Engineering (CAMNE), Najran University, P.O. Box 1988,ajran-11001, Saudi Arabia
r t i c l e i n f o
rticle history:eceived 2 December 2011eceived in revised form 5 March 2012ccepted 9 March 2012vailable online 20 March 2012
a b s t r a c t
The cellulose membrane used in the present studies was prepared by impregnating cellulose acetatedissolved in acetone and mixed up with aqueous KBr, which has been added through a sintered G2
(porosity) disc. The flow of water, 1,4-dioxane and their different compositions through this membranehas 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–dioxanemixtures across the membrane does not seem to be thermodynamically feasible. However, the dipolarnature of the solvent mixture does affect the membrane structure as shown by the variation in poreradius, number of pores and zeta potential.
. Introduction
Many physiological processes in plants and animals involvedransport through membranes especially water transport throughoots and soil is of particular interest. Exchange of matter andnergy which is the principal function of organisms takes placehrough membranes [1]. Membrane processes are currently beingtudied for numerous applications of practical interest. Mostmportant technological applications of membrane include theirse in industry for chemical and biomedical separations andemineralization by reverse osmosis [2–7]. In this context, non-quilibrium thermodynamics studies have been conducted iniquid mixtures for, e.g. acetone–methanol [8] and methanol–water9] in order to study the concentration dependence of phe-omenological coefficients and to verify Onsagar relations. Inhe present work, we have carried out studies on hydrody-amic flow and electro osmotic flow for aqueous solution of,4-dioxane at different composition, under different electric andagnetic field strengths at different temperatures. From the
alculated hydrodynamic permeability, the electro osmotic perme-
bility coefficients and thermodynamic parameters, i.e. enthalpyf activation (�H*), entropy of activation (�S*), free energy ofctivation (�G*) have been calculated. Further, the number of
pores, pore radius and zeta potential for the membrane crossedby different solution of 1,4-dioxane in water have also beendetermined.
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% fromE. Merck) were used in this study. Ordinary tap water of conductiv-ity range 3–5 × 10−6 S cm−1 at 25 ◦C was distilled with the help ofMillipore (Elix) distillation unit, which was further distilled in thepresence of alkaline potassium permanganate through a 750 mmlong vertical fractionating column. The water so obtained has con-ductitivity value around 1–4 × 10−7 S cm−1 at 25 ◦C and pH in therange 6.5–7.0.
2.2. Membrane
The cellulose acetate was dissolved in acetone in the proportionof 22.2:66.7 and after this mixture was mixed up with aqueous solu-tion of KBr prepared with 10:1.1 of water and KBr, respectively.
The obtained cellulose acetate solution was impregnated into apreviously thoroughly washed and dried sintered G2 disc undervacuum at 0–0.5 ◦C. After impregnation the disc was immersed inhot water at 75–80 ◦C as suggested by Lakshminarayanaih [8]. The
embrane then was treated with water for 24 h before performingxperiments in order to avoid fluctuation in the permeability of theembrane.
.3. Apparatus
The apparatus used for the present investigation and its exper-mental set up is shown in Fig. 1. It consist of a pyrex glass tubef about 20 cm in length having a slight constriction in the middlehere a sintered disc is fixed and the membrane impregnated in it.
he tube has two standard B-24 joints at the end. The main tube haswo side tubes having B-14 standard joints and the pressure headn the other B-14 standard joint is moveable so as to set up any
osition to maintain the desired pressure in the tube. The appara-us is placed in the wooden cradle. The whole assembly was keptn air thermostat.
ig. 2. A plot of volume flux (Jv) versus pressure for water at 303 K at differentagnetic field strength.
electo-osmosis.
3. Results and discussion
3.1. Determination of volume flux (JV) and hydrodynamicpermeability (LP)
According to thermodynamics of irreversible processes [10,11]the dissipation function [12], for the transport processes of liquidsthrough a membrane under the influence of pressure difference canbe written as
˚ = JV · �P + JD · � (1)
where JV is volume flux per unit area of the membrane, JD is thediffusional flow, �P is hydrostatic pressure difference and �П isdifference in osmotic pressure across the membrane. The linearphenomenological equations relating to flow and forces are givenbelow
JV = LP�P + LPd� (2)
JD = LdP�P + Ld�˘ (3)
Fig. 3. A plot of hydrodynamic permeability (Lp) versus pressure for water at 303 Kat different voltage.
Table 2Volume 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)
Table 3Permeability coefficients (Lp) of cellulose acetate membrane at different temperatures, electric and magnetic field strength when crossed by different compositions of1,4-dioxane in water.
Percentage compositionof dioxane
Temperature (K) Voltage (V) Magnetic field strength (KG)
here LP and Ld are the mechanical coefficients of filtration and dif-usion respectively and LPd and LdP represents Onsager coefficients.n experiments where the concentration of solution is same on bothides of membrane, �П = 0 and if pressure difference is maintainedcross the membrane there exists a volume flux JV. The values of
V, i.e. the volume flux of water, dioxane and aqueous solutions ofioxane at different pressure, temperature, electric and magneticeld strengths across cellulose acetate membrane are calculated as
ollows
V =(
dx
dt
)(r2i
R2i
)(6)
here x is distance travelled by the experimental liquid, t is theime taken to travel the distance x, ri is the radius of capillary andi is the radius of the membrane.
The radius of capillary was estimated with the help of the trav-lling microscope supplied by Almicro VM-1. For this purpose,ercury was taken in the capillary, filling a known length of the
apillary, which was measured with the help of the travelling
microscope several times. The weight of mercury (w) filling thecapillary was noted with the help of Eq. (7)
w = �r2i ld (7)
where d is density of mercury and l is length of mercury thread incapillary. Densities (d) of various solutions were determined withthe help of calibrated pycnometer. The values of JV when the mem-brane was crossed by pure water and for the mixture of water and1,4-dioxane are reported in Tables 1 and 2, respectively
When the concentration of solution is the same on both sides ofmembrane the volume flow [from Eq. (2)] can be given [14,15] as
JV = LP�P (8)
where LP is the hydrodynamic permeability or permeability coeffi-cient or simply permeability of the membrane for fluid. LP has thecharacter of mobility and represents the velocity of fluid per unitpressure difference for the unit cross-sectional area of the mem-brane. The values of LP can be estimated from the linear plots of JVand �P for water and aqueous solutions of 1,4-dioxane. A sampleplot for the same has been represented in Fig. 2 at 303 K.
The values of hydrodynamic permeability calculated using Eq.(8) for water and various aqueous–dioxane solutions have beenreported in Table 3. It is clear that LP varies non-linearly with pres-sure as shown in Fig. 3.
Table 4Frictional coefficient (Fwm) of cellulose acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4-dioxane in water.
Percentage compositionof dioxane
Temperature (K) Voltage (V) Magnetic field strength (KG)
The frictional coefficient of the phenomenological coefficient inhe transport processes through membranes has been given byedem and Katchalsky [16]. The explicit treatment of frictional
orces may be approached by considering the simple case of waterltration through membrane. If pure water is placed on both sidesf the membrane, then the driving force provided by a difference inressure which is balanced by mechanical filtration force betweenater and the membrane matrix under the condition of steady flow,
herefore the mechanical filtration force, Xwm is given by
wm = Fwm(Vw − Vm) (9)
here Fwm is the coefficient of friction between water and the mem-rane and it is a measure of the resistance offered by the membraneo water penetration, Vw and Vm are the volume of the water and
ixtures respectively. Under the simple use of translation of ther-odynamic coefficient into frictional coefficient the permeability
oefficient, (LP) can be related to coefficient of friction (Fwm) by aimple relation as
P = ˚wVw
Fwmı(10)
here фw is the water content of the membrane and is expressed
s the volume fraction of the total membrane volume and is numer-cally equal to the fraction of membrane surface available for theermeation of solution. It was determined by the method describedy Ginzberg and Katchalsky [17] and the value obtained was 0.201
in the present case of cellulose acetate membrane, ı is thicknessof membrane and the value in the given case is 4.50 × 10−3 m,Vw is molar volume of water. The values of coefficient of frictioncalculated using Eq. (10) for various aqueous solutions have beenreported in Table 4.
3.3. Determination of �H*, �S* and �G*
Different membranes used in alternate energy devices havebeen characterized in terms of parameters of activation. The vari-ation of hydrodynamic permeability with temperature can bewritten as
log LP = k − En
RT(11)
where k is constant, En is energy of activation, R is gas constant andT is temperature. Energy of activation can be taken as enthalpy ofactivation [18] (�H*). By using Eyring rate Eq. [19] for the flow,entropy of activation is calculated from the equation
� = Nh
Ve�S∗/Re�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
Fig. 6. Variation of free energy of activation (�G*) versus voltage at different composition of dioxane in water–dioxane mixtures.Table 5Enthalpy (�H*), entropy (�S*) and free energy of activation (�G*) of acetate membrane at different electric and magnetic field strengths when crossed by differentcompositions of 1,4-dioxane in water.
Table 6aPore radius (r) across acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4-dioxane in water.
Percentage compositionof dioxane
Temperature (K) Voltage (V) Magnetic field strength (KG)
The free energy of activation (�G*) can be calculated from thequation
G∗ = �H∗ − T · �S∗ (14)
The estimated values of �H*, �S* and �G* have been recordedn Table 5 and the variation of these parameters with voltage at dif-erent composition of dioxane are shown in Figs. 4–6 respectively.
.4. Determination of equivalent pore radius and number of pores
Magnetic field when applied exerts a change in the structure ofhe membrane which has been characterized in terms of its poreadius, number of pores and zeta potential, expressing the electricalharacter of the membrane permeant interface. These parametersan be estimated in the light of capillary model, according to which,
porous membrane is supposed to be composed of a bundle of ‘n’apillaries entering a porous medium on the face and emerging onhe opposite face. Although any structure of the porous mediums not as simple as described by capillary model, yet it has beenuccessfully used by many authors [20,2,21,22]. According to thisodel
22 = (n�r4)8�ı
(15)
2
11 = (n�r k)ı
(16)
here L22 is hydrodynamic permeability, L11 is the electric con-uctance of the membrane, ‘n’ is number of pores, r is equivalent
pore radius, � is the absolute viscosity, and k is specific conduc-tance of the permeant. The equivalent pore radius for differentsystems across cellulose acetate membrane at different magneticfield strength has been calculated by rearranging Eqs. (15) and (16)as
r = (8�kL22)
(L11)1/2(17)
Once the equivalent pore radius of the membrane for differentsystems is known, it is possible to calculate the number of capil-laries. The number of pores for different systems across celluloseacetate membrane has been calculated by rearranging Eq. (15) as
n = (8�ıL22)(�r4)
(18)
The values of r and n thus obtained for membrane have beenrecorded in Tables 6a and 6b.
3.5. Determination of zeta potential
Zeta potential (�) plays important role in various applica-tions such as microfluidics [23–25], colloid chemistry [26,27], andmembrane fouling. The zeta potential is influenced by surface com-position, as well as solution properties such as the nature of theions and ionic strength. Measurement of the streaming potential
in channel geometry is the most commonly used technique forcharacterizing the zeta potential of flat surfaces however somephenomena such as electrophoresis [28] have also been used tocharacterize the zeta potential.
Table 6bNumber of pores (n) of cellulose acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4-dioxanein water.
Percentage compositionof dioxane
Temperature (K) Voltage (V) Magnetic Field Strength (KG)
Electrical character of the membrane interface can be expressedn terms of zeta potential. Zeta-potential is an informative propertyirectly related to the electro kinetic charge density. In the case ofechnical membranes, for example, zeta-potential is believed to beorrelated with the mechanisms of rejection of charged solutes andith the interactions between the membrane surface and various
harged foulants (colloidal and macromolecular). Experimentally,eta-potential of macroscopic surfaces is often obtained from theeasurements of streaming potential. According to double layer
icture and overbeek analysis of electro kinetic effects [29], thelectro osmotic permeability is given by
21 = L12 = (nεr2�)4�ı
(19)
21 = L12 is the electro osmotic permeability, ε is the dielectric con-tant and � is the zeta potential of solid liquid interface. Eq. (19) cane rearrange as
= 4�ıL12
nεr2
The values of � thus obtained for membrane have been recordedn Table 7.
A perusal of the data of JV shows that it decreases with increasen composition of dioxane and magnetic field strength and increase
ith increase in temperature. The addition of dioxane in wateristurbs the dipole distribution and as a result structural rearrange-ent takes place. Further the permeability is inversely proportional
o the viscosity and the effect of magnetic field on permeability
0.55 0.58 0.60 0.64 0.640.59 0.68 0.80 0.83 0.90
coefficient (LP) of membrane is similar to the effect of magneticfield on viscosity [20,21]. The effect of magnetic field on perme-ability coefficient (LP) is much more pronounced than on viscosityof solutions. This suggests that membrane structure under theinfluence of magnetic field also changes. However, the structuralchanges of membrane shall be limited to its porosity and to theelectrostatic charge density, which the membrane may have onits surface or on the inside walls. Under the influence of themembrane, the ions present in the solution get aligned in a par-ticular fashion in the forms of dipoles, parallel to the direction ofmagnetic field. The decrease in permeability coefficient (LP) withthe magnetic field strength may, therefore, be attributed to theincrease in dipole–dipole interactions and structural changes of themembrane. Recently it has been reported in [30] that there is an ori-entation of cellulose micro crystals by magnetic field and the sameeffect may be assumed to affect the structure of the membrane insuch a way that the values of permeability coefficient (LP) decreasesunder a magnetic field strength.
In general, the value of frictional coefficient shows increaseswith increase of electric, as well as, magnetic field strengths.However, with rise in temperature, Fwm values do not show aregular trend. The variation in the value of Fwm can be corre-lated to the structural consequences resulting from interactions ofwater–dioxane dipoles at the given compositions. The membrane
solution interactions also vary with the content of dioxane as wellas viscosity of the medium. The non-linear dependence of Fwm withcompositions shows that Spiegler’s [31] frictional model is not validunder the influence of magnetic field.
Table 7Zeta potential (�) across cellulose acetate membrane at different temperatures, electric and magnetic field strengths when crossed by different compositions of 1,4-dioxanein water.
Percentage compositionof dioxane
Temperature (K) Voltage (V) Magnetic field strength (KG)
The value of �H* increases with increase in magnetic fieldtrength, increase in composition and voltage as well, in all cases.he �S* values also increases with increase in magnetic fieldtrength, increase in composition and voltage and has all negativealues which suggests that the flow through membrane is morerdered due to membrane solution interactions. The values of �G*
how a slight decrease with increase in dioxane composition in theolution and remain almost constant with increase in magnetic fieldtrength. The positive values of �G* in all cases shows that flow isot favoured across the porous medium.
The data suggests that equivalent pore radius decreases with thepplication of magnetic field strength. This may be attributed to thehange in the pore structure of the membrane. On the other hand,umber of pores increase with increase in magnetic field strength.he increase in number of pores with magnetic field strength sug-ests a change in the total physical characteristics of the membrane.he decrease of equivalent pore radius may also suggest that struc-ure of membrane may weaken and diameter of pores vary in the
embrane, which may be attributed to the increase in the numberf pores in the membrane on account of change in its structure.
The data suggests that the values of � decrease with increasen magnetic field strength increase with increase in concentrationnd temperature.
. Conclusion
The results of above study indicate that dipolar interaction ofwo 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 struc-ture of membrane also as reflected by the variation in pore radius,number of pores as well as zeta potential.
List of symbolsFwm frictional coefficientLP permeability coefficientL12 electro osmotic permeability� zeta potentialL22 hydrodynamic permeabilityL11 electric conductance of the membrane‘n’ number of poresr equivalent pore radius� absolute viscosityC dielectric constant of the mediumk specific conductance of the permeant� viscosity of liquidV molar volumeEn energy of activationфw water content of the membraneVw molar volume of waterı thickness of membraneXwm mechanical filtration force
ri radius of the capillaryx distance travelled by the experimental liquidLPd and LdP Onsager coefficientsRi radius of the membrane
1 ibria 3
LJJ�����RT�
A
Dt
R
[
[
[
[
[
[
[[[
[[[[
[[[[
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58 Kiran et al. / Fluid Phase Equil
d mechanical coefficients of diffusionV volume flux per unit area of the membraneD diffusional flow
P hydrostatic pressure differenceП difference in osmotic pressure across the membraneH* enthalpy of activation �H*
S* entropy of activation �S*
G* free energy of activation gas constant
temperature dissipation functionC change in concentration
cknowledgements
Dilbag Singh Rana thanks UGC, New-Delhi for the award of Dr..S. Kothari Postdoctoral Fellowship and S. Chauhan thanks UGC for
he financial assistance under the project (F.No. 32-237/2006/SR).
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