Modelling of the pervaporation separation of ethanol-water mixtures through crosslinked poly(vinyl alcohol) membrane

Journal of Membrane Sczence, 67 (1992) 39-55 Elsevler Science Publishers B V , Amsterdam

39

Modelling of the pervaporation separation of ethanolwater mixtures through crosslinked poly (vinyl alcohol) membrane C K. Yeom and R.Y.M. Huang Department of Chemtcal Engmeermng, Unwersrty of Waterloo, Waterloo, Ont N2L 3Gl (Canada) (Received December 13,1990, accepted m revrsed form September 30,1991)

Abstract A mathematical model for the permeation of hquld mixtures through polymeric membranes takmg mto account the coupling of fluxes has been developed The model is based on the extension of FuJ&~‘s free volume theory and Flory-Huggms thermodynamics and 1s apphed to the pervaporatlon separation of the full range of ethanol-water mixtures through crosslmked poly(vmy1 alcohol) (PVA) The model mcludes the dlffuslon coefficient of the mdlvldual penetrants and terms that explam the plastlclzatlon action of a penetrant and the couplmg effect of the permeation through the membrane of one penetrant on permeation of the other penetrant Dlffuslvlty data havmg practical values for the pervaporatlon process weredetermmed from steady-state pervaporatlon expenments of smgle components Coupling parameters were also introduced to explam the coupling behavior and plastrcmatlon action of the penetrants Comparisons were made between the simulated and calculated permeablhtres obtained from the model and the expenmental values, respectively Keywords pervaporatlon mixtures

separation, poly(vmy1

Introduction For pervaporation membrane separation processes as well as module design, model equations for the description of mass transport in a membrane at different operatmg conditions are necessary. For a description of a pervaporatlon transport model, one should distinguish between single component and multicomponent permeations. There are several model equaCorrespondence to, R Y M Huang, Department of Chemical Engmeenng, Umverslty of Waterloo, Waterloo, Ont N2L 3Gl (Canada)

alcohol)

membranes, separation of ethanol/water

tions [2-4,251 for single component permeation which show more or less good agreement between theory and experiment. In the case of the separation of a mixture no satisfactory theory exists because the transport phenomenon is more complicated due to the coupling of fluxes, both in the solution and the diffusion processes. Greenlaw et al [ 61, Lee [ 41 and Long [5] investigated models which hold for liquid mixtures that behave almost ideally, but it is uncertain whether these will hold for non-ideal mixtures such as aqueous mixtures. Brun et al. [ 71 proposed a “six coefficients exponential model” which is based on the free

0376-7388/92/$05 00 0 1992 Elsevler Science Publishers B V All rights reserved

40

volume theory. Their model gives a relatively correct description for the pervaporation behavior, and they tried a phenomenological approach to obtain practical values for their system. Mulder and Smolders [8,9] proposed a modified solution-diffusion model which describes the transport and concentration profiles of water and ethanol in dense membranes In their model the exponential relationship between diffusion coefficient and concentration was used, and the dissolving ablhty of the mixture has also been mcluded. They simply studied the permeation behavior when applymg arbitrary parameters in their models without determuung their absolute values. Fels and Huang [1,25] developed a model for the pervaporation process by employing Fujita’s free volume theory which is generally accepted for determuung diffusion coefficients from unsteady-state desorption experiments. They used the simplified Flory-Huggins thermodynamic theory to explain the interaction between permeant and membrane material but they did not consider the mutual mteractions of the mdlvldual permeants m the membrane which may be sign&ant m non-ideal solutions. Recently, Rhlm and Huang [19,26] modified Fels and Huang’s model by introducing the Flory-Huggms interaction parameters, which are functions of the concentration of the individual components in a membrane and the operatmg temperature. However, the coupling behavior of fluxes m a membrane could not be explained with their model, and an overestimation of the diffusion coefficients m the simulation was made by takmg the diffuslvity at the upstream side of a membrane as the diffuslvity across the membrane although the local diffusivity can change with the concentration profile developed within the membrane during permeation. In both of the above studies, the free volume parameters and the diffusion coefficients at zero concentration were determmed from the unsteady-state desorption experiment which is

C K YEOM AND R Y M HUANG

highly complicated. These experimental results are very sensitive to the accuracy of the measurements and are of hmited practical value for application to the steady-state pervaporation process. In a previous paper [lo], we have reported a new technique for the determination of the diffusion coefficient and free volume parameter of a penetrant through a membrane from the steady-state pervaporation experiments of smgle components. The purpose of the present study is to develop a mathematical model for the pervaporation separation of binary liquid mixtures through a polymer membrane taking mto account the coupling of fluxes. The model is based on the extension of Fujita’s free volume theory and Flory-Huggms thermodynamics and is applied to the pervaporation separation of the full range of ethanol-water mixtures through a crosshnked PVA membrane (type II) which has been developed m our laboratory [ 161. The type II crosshnked poly (vinyl alcohol ) membrane is poly(vmy1 alcohol) crosslmked to varying degrees with amlc acid where amic acid based mphenylene dlamine was used as the crosshnking agent. Descrtptton of the model The model follows the prmclple of the solution-diffusion model but the following assumptions have been made to simplify the procedure: l impermeable crystalhtes, not contributing to the free volume of the polymer. l no effect of swelling on the polymer morphology [ 111. l isothermal conditions of pervaporation process due to thin membrane thickness exists during l equilibrium sorption pervaporation. l zero concentration of the penetrants at the permeate side of the membrane. The steady state permeation of a single component through a membrane can be described

41

PERVAPORATION SEPARATION OF ETHANOL-WATER MIXTURES THROUGH CROSSLINKED POLY (VINYL ALCOHOL)

by Fick’s first law with a concentration dependent diffusion coefficient

where J, 1sthe flux of single component z, D, is the concentration dependent diffusion coefficient of component zm the polymer fixed frame of reference, and dC,/& is the concentration gradient across the membrane. According to FuJita’sfree volume theory [ 201 and Kreltuss and Frrsch [22], the thermodynamic diffusion coefficient of z component, ( DT) z, is defined as the followmg expression:

further (3) where Adz and Bdc are constants characteristic of the given polymer-penetrant pair, u, is the volume fraction of component zin a membrane, f(u,,T) the free volume fraction of the system, & the crystallimty of a polymeric membrane, R the gas constant, T the operating temperature, and a, is the chemical activity of component z in the membrane which can be calculated by Flory-Huggins thermodynamics. The free volume parameter, BdZ, is a characteristic parameter of an amorphous polymer. In order to get BdZapplicable to semi-crystalline polymers as well as amorphous polymers, we define a new generalized parameter B, as

&r

B”=m

(4)

Thus, the measurement of crystallimty is not necessary because the generahzed parameter, B,, already includes the effect of crystallmlty. The free volume of the bmary system (pure hquld-membrane ) is given by

(5)

f(u,,T) =f(O,T) +P(Th

where f(O,T) is the free volume fraction of the polymer itself and p(T) 1s a proportional constant relating the amount of free volume m creased by the diffusing species z. When u,=O in eqn. (2), the diffusion coefficient at zero concentration, Q,, , 1s given by Dlo = RT

&,eXP

Combmmg eqns. (2) and (6) leads to the expression for the ratio of ( DT) I to DC0 B,B,(T)u, ,noL = [F(O,T) 1”+PSVW’)~, DLO

(7)

In the case of a binary liquid permeations through a membrane, the system will consist of three components, that LS,the free volume of the polymer itself plus the increase m free volume due to the plastlclzmg actions of the two llquldswhlchareequalto~,(T)@,+~,(T)@,(@,: the volume fraction of component z m a ternary system). Therefore, based on the free volume theory, the thermodynamic diffusion coefficient of component 1, (DT) 1,in the ternary system can be expressed as (%)I =RT(Ad),exp

- (B), c (O,T)+P,(TM

+/32(5%2

(8) where (Ad)l and (B), are free volume parameters in a ternary system (Ad) 1and (B) 1should be determined to evaluate (DT) 1.If component 1 were removed, the resulting free volume would be equal to the free volume of the polymer plus the amount added by the presence of component 2 In other words, considering one liquid m a ternary system the free volume at zero concentration of this liquid IS not f(O,T) but an increased free volume due to the presence of the second liquid. The new free volume fraction at

CK YEOMANDRYM

42

zero concentration of component 1 can be expressed accordmg to [ 251:

Extending eqn. (6) into the ternary system, the diffusion coefficient at zero concentration of component 1 will be related to the free volume fraction at zero concentration of component 1, f( $,T) as follows:

(10)

From eqn. (7), the thermodynamic diffusion coefficrent of component 1 can be given as

WI(WI [f(b.,T) 12+f(h2,WdTh

tDT)l

=exp

DIO

(11)

=RTAdw

+

c

-B1 (@2,T)

W1(TM1 W$2,T)

=RT

1”+f(~2,WMW~1

AdleXp

Comparing eqn. (8) with eqn. (12), (Ad)1 =&I,

(&)I =RT &leXp

(9)

f(&?,T) =f(O,T) + P2&

D IO =RT &exP

(B), =BI

(13)

Therefore, the resultmg (DT) 1 can be written as (DT)~

Actually, B, is an arbitrary parameter corresponding to the minimum “hole” required for a given penetrant molecule z to permit drffusional displacement, so that it could be related to the size of the penetrant molecule [ 201. The first term in the exponential of eqn. (15)) f (0,T) /B,, indicates the effect of pure polymer chain on the diffusion of component 1, which is responsible for the diffusion coefficient of component 1 at zero concentration. The second term, /-G(7’) &/BI, 1s assigned to the self-plasticizatlon action of component 1 on Its own permeation through the membrane. The last term, b2 ( T)qJ2/B1, represents the cross-plastrcizatlon action of component 2 on the permeation of component 1, which is related to the coupling of fluxes. However, components 1 and 2 have different dlffusional sizes and are based on diffusion behaviours. Thus, m order to consrder the cross-plastlcization action of component 2 m the component 1 fixed frame of reference, l/B, should be replaced with the ratio, B2/B1, whrch is the ratro of B values corresponding to that of the drffusronal sizes of penetrants 1 and 2. The final form of thermodynamic diffusion coefficient of component 1 can be given by

(DT)~=RT

c

HUANG

-& t&T) +/h(T)@1 +P2(T)$z

=RT Adlexp

&eXp (16)

(14)

From eqn. (13 ) , it can be seen that the free volume parameters of (DT) 1in the ternary system IS identical wrth those in the binary system. Equation (14) can be rewrrtten as follows:

The concentration of component z m the membrane, C,, can be expressed at isothermal condition in terms of the volume fraction, d,,

PERVAPORATION SEPARATION OF ETHANOL-WATER MIXTURES THROUGH CROSSLINKED POLY (VINYL ALCOHOL)

cz=P&

(17)

de, =psd@,

(18)

wherep, is the density of component t Combmmg eqns. (1) through (18) and integrating with boundary conditions, the resulting permeabllity of component t, P,, gives P,=

LJLdx s0

(19)

where @Lois the volume fraction of component L at the feed side interface of the membrane, which can be obtained from the equilibrium sorption experiments. The derivation of the dlna,/dln@, term is shown elsewhere [ 191. In order to analyze the plasticization action of permeants, some parameters are needed. As discussed earlier, parameter, p(T), is closely related to the plasticization action of a permeant and parameter, B,, is a constant for a given polymer-permeant pair, so that the combination of these two parameters can explain the plasticization action of a permeant on a membrane. Thus, we define a new plasticizing coefficient, 0, which is a measure of plasticization action of a component, from eqn. (16) as follows:

where O,, is a self-plasticizmg coefficient of component z on its own flux and 0, which represents the coupling effect as a cross-plasticizmg coefficient of component J on the flux of component L.Hence, the amount of plasticization action can be expressed as the product of the volume fraction of individual component and its plasticizing coefficient: O,&, O,$,.

43

Determmatzon of free volume parameters In a previous paper [lo], a new method was reported by which the diffusion coefficient and free volume parameters of a penetrant could be determined from steady-state pervaporation experiments of single components. The method consists of fitting a numerical solution of the diffusion equation to experimental pervaporation data For the determmation of the free volume parameters and diffusivity, free volume data are needed. In pure hquid permeation, the parameter, p( T), can be computed with the followmg defimtion (in eqn. 5, when I$~=1): f(l,T)=f(O,T)+P*(T)

(22)

The free volume fraction in a hquid, f (l,T), can be defined as [ 211 f(l,T)=

7

(23)

where vf is the specific volume of the liquid at any temperature and v. is the specific volume of the liquid extrapolated to the temperature T at 0’ K without phase change. It was considered that the most obvious method of extrapolating density to 0°K would be to set up a density function m the form of a Taylor expansion [ 231 For the free volume fraction of a polymer at temperature below the glass transition temperature, Tg, Robert and White [ 121 reported that the free volume is an essential pre-requisite for molecular motion by rotation or translation to occur. The mobility of polymer chains is primarily affected by the barrier to rotation around backbone carbon-carbon bonds. No backbone mobihty is found upto Tg for most polymers. A muumum level for the free volume will fix the point at which a glass structure will be frozen into the matrix. Therefore, in the glassy state, the free volume will be frozen in and will remain at a constant value below Tg. In his model Rhim [ 261 used a constant value, 0.025, for the value off (0,T) at temperatures below Tq How-

C K YEOM AND R Y M HUANG

44

ever, it was reported [ 131 that f( 0,T) is a function of temperature even at temperatures below Tg According to the free volume definition, the free volume of a polymer is zero at 0’ K, and as temperature increases from O”K, free volume can be formed and increased. At Tg,f( 0,T) was mostly estimated as a universal value, 0.025 Unfortunately, there is no quantitative information on the free volumes of polymers below Tc Thus, we approximately assume that f(O,T) IS proportional to temperature in the temperature range just below Tg with a slope of (O.O25/T,)/2 which is a average value of the above extreme cases. f(O,T)=O025-O.O25(T,-T)/2T,

(24)

Concentratton profile m a membrane In the case of the permeation of liquid mixtures, coupling phenomena should be taken mto account If flux or permeabihty data are available, the concentration profiles can be calculated from eqn. (19). However, since the purpose of the modelling m the present study is to predict the permeabihties of individual components by using the least possible number of material properties, the calculation of concentration profiles can be done without any permeability data of binary liquid mixtures. It is very difficult to determine the exact concentration profile from limited conditions, i.e. the condition without mformation on the real pervaporation data of binary mixtures, so that one cannot but use more or less an approxlmatlon for the calculation of the profile. In the approximation, it IS assumed that both components diffuse independently, that is, there are two independent binary systems (component l-polymer and component 2-polymer) m the membrane during the diffusion process But the real sorption data of a ternary system which are thermodynamically coupled can be determined from swelling experiments to be used as the boundary comhtlons at the upstream side of the

membrane. For each binary system, the flux of component z can be expressed by

;ly;Ldz

Jz= -pm,),

)

El,2

(25)

where u,= @,/ (& + &,p)and subscript, p, refers to polymer. The partial differential equation, dlna,/dlnv, yields [ 141

alna,=ldlnv,

(

-1-v

l-;

P>

v,-2x,v,v,

?-2x&&(1-v,)

(26)

where up= 1 -u, After combining eqns. (25) and (26) and integrating across the membrane using the boundary conditions, the permeability of component z is given by J,L=

=P,

s 0

“‘O(l -v,)

(i-2Xlp)~,(Dr),dvZ

(27)

where v. is the v, value corresponding to & at equlhbrmm sorption as described in the assumptions. Definmg a relative distance in the membrane (XR=x/L), a substitution of this quantity in to eqn (27) gives *,=L

L

Thus, v, and xn can be calculated from eqn. (28) by a numerical method. The volume fractions, v1 and up,which are determined at a given position xn within the membrane, can be transformed into those in a ternary system, fll and @2 (from u,=@I/(@L+&,) andA+$2+&,=1) as follows:

PERVAPORATION SEPARATION OF ETHANOL-WATER MIXTURES THROUGH CROSSLINKED POLY (VINYL ALCOHOL)

#22=

Ul -U1U2

@1= l-u1u‘J

’

u2-u1u2 l-UlU2

(29)

Swellzng measurement The traditional method for solubility measurements which consists of weighing a polymeric membrane before and after swelling may cause some errors m the weighing step, especially, when using highly volatile liquids. Hauser et al. [ 151 have developed a simple method for the determination of the solubihty of a hquld in a membrane m terms of weight fraction The method consists of measuring the change m membrane length due to swelling and precisely measuring the density of the liquid mixture surrounding the swollen membrane, which allows determination of solubllities of single components in polymeric membranes in the presence of a binary liquid mixture It is assumed that the system involves isotropic swelhng (or isotropic membrane structure) and neglects the difference between molar volumes of the pure solvents and their partial molar volumes m the membrane. However, in this study, solubihty in terms of volume fraction is needed rather than weight fraction. Smce length changes in an isotopic material are the same in all directions, the ratio of the swollen volume to the dry volume of the membrane, R,, can be given by

where aP is the volume of dry membrane, Acx the volume change in the membrane due to swelling, and 2 the membrane length in any direction. A series of density measurement has to be performed m addition to the swelling experiments in order to determine single component solublhty. A sample of membrane having a volume of LY,is added to a binary mixture having a volume of &j, and the volume fractions, U1b and UZb, of components 1 and 2, respectively After the swelhng equilibrium has been established, the density of the liquid mixture surrounding the swollen membrane is determined The volume fractions, ula and uZa,of the binary mixture surroundmg the membrane can be determined from a calibration curve of the density as a function of the composition of the binary mixture. In this system, the volumes of components 1 and 2, &$,Ulband c&u‘&,can be written m the following form: abulb

=hUla

+

abu2b

= %Uz,

+

(lo/l+ @12=

Aa

a,+Aa=

U”/03

1

(31)

(Aa+qJ$l

(32)

(33)

W+a,M2

where cy, is the volume of the liquid mixture surroundmg the membrane. Combmmg eqns (31)-(33), two equations are obtained that provide algebraic solutions for $I and qj2:

@1= where Z,, 2,,,and Z,are the dimensions of the dry membrane m the X, y, and z directions, respectively, and superscript o, denotes the swollen membrane. Thus, R, can be expressed m terms of a length ratio in any direction The volume fraction of liquid components, $12( = $1 + @2), can be written m the following form:

45

ab@p

(Ulb

-ula)

+@lZapUla

(34)

a,

$2 =

ab@p

(u2b

-UZa)

+@12apUZa

(35)

a,

Experimental Materzals 3,3 ’ ,4,4’ -benzophenone tetracarboxyhc dianhydride (BTDA) and m-phenylene dia-

C K YEOM AND R Y M HUANG

mine were obtained from Polysciences Inc Philadelphia, PA. PVA (99-100% hydrolyzed, viscosity of 4% aqueous solution at 20 oC = 55 68 cP) and dimethyl sulfoxide (analytical reagent) were obtained from the J.T. Baker Chemical Co. Methyl alcohol was analytical reagent from BDH Chemicals The synthesis and preparation of the crosslinked [A(vinyl alcohol) (type II) membranes has been reported in a previous paper [ 161. Solub&y measurement A slab of membrane is suspended on a hook immersed m a thermostated glass tube which contams a binary mixture at a certain composition. The length of the dry membrane, 1,and the length of the swollen membrane, l”, were measured by using a cathetometer which has a scale with an accuracy of ? 10m3mm. The dimension of the slab were 7 x 89 (mm). The densities of binary m;xtures were measured by usmg an Anton-Paar ‘DMA 60 digital density meter with an accuracy of t 10m5g/cm3. The volume fractions of each component m the binary mixture were determined by a cahbratlon curve of density vs. composition of ethanolwater mixtures and then the volume fractions, @I and &, in the membrane can be calculated from eqns. (34) and (35). The measurements were carried out at 30,40,50, and 60°C. Pervaporatton The pervaporation experiments were performed as described previously [ 241. Vacuum at the downstream side was maintained at a pressure below 5 mmHg The experiments were carried out at 30,45, and 60’ C, respectively, in a complete range of feed compositions. The analysis of the permeates was done by using an Anton-Paar DMA 60 digital density meter. Evaluatum of bznary tnteractzonparameters Usually, binary mixtures show deviations from ideal behavior due to mteractlon between

two components. A measure for the deviation can be given by the excess functions. The xl2 can be determined from the excess free energy of mixing data, AGE, by using Flory-Huggins thermodynamics [ 141 x12 =

1 mu2

m,lnm,

+m,lnm,

Vl

v2

AGE + RT

(36)

where m, and m2 are the mole fractions of components 1 and 2, respectively. AGE data were calculated by the following equation: AGE=RT(m,lny,

+m21ny2)

(37)

The activity coefficients, y1 and 1/2,were determined by means of the Van Laar equation using fittmg parameters which were taken from the literature [ 171. Interaction parameters of a polymer and a non-solvent, xLp,can be expressed as an approximate form of eqn. [8] m terms of the volume fraction of the polymer, v,. x&p= -

ln(l-v,)+v, 2 VP

(38)

the volume fraction, v, or v,, can be determmed from eqn. (31). Results and discussion Swellrng behavror The solubihty of liquids (ethanol and water) m the membrane were determined in terms of the volume fraction of the liquids from eqn (31) by using the data of the length change in the membrane slab at equilibrium swelling. The result is shown m Fig. 1. The solubility is a function of temperature and the composition of the feed mixture, having a maximum value at about 30 wt.% of ethanol content in the feed mixture. In addition to the swelling experiments, a series of density measurements gives the single component solubilities m the membrane, cal-

PERVAPORATION SEPARATION OF ETHANOL-WATER MIXTURES THROUGH CROSSLINKED POLY (VINYL ALCOHOL)

47

of interactions between the components and the polymeric membrane, i.e. because of coupled sorptlons, that is, the enhancement of the solublhty of a component due to the presence of the bmary hquid mixture These solublhties were used as the boundary conditions at the upstream side of the membrane in simulatmg the permeation of the liquid mixtures through the membrane

Fig 1 Experimental swelhng curves of crosshnked PVA m ethanol-water mixture 015

,

1 0

0 *

30 ‘c 45 ‘C 60 “C

-4.

000

__

05

00

Ethanol

C&nt

10

m

Feed

_

Fig 2 Solublhty of mdlvldual liquid components m crosslinked PVA membrane (-_) ethanol, (---) water

culated from eqns (34) and (35). The single component solublhties show positive deviations from the ideal values as shown m Fig 2, mdicating that the solubility of a component in the presence of the liquid mixture is higher than the solubility of the pure components because

B&nary uateractronparameters The binary mteractlon parameter, x12, between ethanol( 1) and water(2) with varymg mixture composition at 30, 45, and 60°C respectively were determined from eqn. (36) Here, the excess Gibbs free energies were calculated from the Van Laar equation by using given Van Laar parameters [ 171 for the system m question Table 1 shows the values for AGE and xl2 which are obviously functions of the mixture composition. For the calculation of the first- and second order derivatives m the model equations, xl2 was fit mto the fourth order polynomial relation as a function of the volume fraction of ethanol, ul. Table 2 presents the coefficients of each term m the polynomial equation at various temperatures as found by using a least squares method From eqn. (38)) the mteractlon parameters between each liquid and the polymeric membrane, xlP and x2P,can be determined by usmg the solubllity data for the single components as shown m Table 3 In this study, these mteractlon parameters are assumed to be concentration independent. Free volume parameters The free volume or density data of the pure liquids (ethanol and water) are needed to calculate the free volume fractions of the liquids from eqn (23) given by Doohttle [ 211. Fortunately, the free volumes of water, vf - v,, in the temperature range of 0-150°C are given m the literature [ 181 The density of specific volume of ethanol is also given as a function of temper-

48

C K YEOM AND R Y M HUANG

TABLE 1 Binary mteractlon parameters for ethanol( 1)-water(e) Vol fraction of ethanol

mixtures at 30,45, and 60°C

0 013 0 075 0 136 0 253 0 364 0 470 0 570 0 666 0 712 0 757 0 845 0 928 0 968

30

45

60

30

45

60

3 59 2156 39 50 74 97 109 01 140 17 166 17 183 50 187 29 186 59 166 38 107 63 56 11

3 64 2183 39 94 75 53 109 42 140 11 165 34 18165 184 89 183 66 162 72 104 50 54 27

4 21 25 14 45 78 85 74 122 92 155 63 18141 196 67 198 75 195 96 170 85 107 79 55 44

80 25 82 52 84 89 89 91 95 36 10132 107 87 115 10 119 01 123 14 132 14 142 33 147 93

78 58 80 75 83 01 87 78 92 93 98 52 104 61 11128 114 86 118 62 126 77 135 86 140 82

83 14 85 29 87 51 92 14 97 06 102 32 107 94 113 97 117 16 120 48 127 52 135 17 139 27

TABLE 2 Coefficients of each terms m 4th order polynomial xIz ( ul) Coefficients”

a0

a1 a2 o3 a4

xtz X 10’ at temperature ( ‘C)

AGE (cal/mol) at temperature ( “C)

Temperature ( ’ C ) 30

45

60

0 8020 0 2905 0 4319 -0 3695 0 3717

0 7820 0 3139 0 2654 - 0 1557 0 2433

0 8274 0 3145 0 2061 - 0 0752 0 1532

“Coefficients of x12(u1) ,&(ul)=aO+alul+~u~ +U,U:

+a,~;

ature in the form of a Taylor expansion [23] The Tg of the membrane was found to be 145 oC by differential scannmg calorimetry (DSC). Thus, the free volume parameters, /3( 2’)) f(O,T), and f(l,T) can be computed with eqns. (22)(24) and are summarized m Table 4. In the previous study [lo], the &ffuslvitles and free volume parameters (B, and Adz) of several hydrocarbon organic liquids have been successfully determined from the pervaporation experiments of single liquid components. TABLE 4 Free volume parameters of each penetrant m crosslmked PVA membrane Penetrant

TABLE 3 Bmary interaction parameter between mdlvldual hquld and membrane at vanous temperatures Temperature ( ’ C )

XlP

X!&

30 45 60

6 7351 5 9977 5 3141

18712 18064 17229

Temp

(“Cl

p,(T)

f@,T)

f(l,T)

Ethanol (1)

30 45 60

0 2098 0 2222 0 2350

0 0215 0 0220 0 0224

0 2313 0 2442 0 2574

Water (2)

30 45 60

0 2783 0 3079 0 3374

0 0215 0 0220 0 0224

0 2998 0 3299 0 3598

PERVAPORATION SEPARATION OF ETHANOL-WATER MIXTURES THROUGH CROSSLINKED POLY (VINYL ALCOHOL)

In this work, the same method was also applied to determine the diffusivities and free volume parameters of ethanol and water having + 5% deviation of the simulated permeability (see Table 7) from the experimental value. The results are shown in Table 5. As expected, the B, value of water is smaller than that of ethanol because water has a smaller diffusional size D$fu.sron coeffment For the permeation of pure hqmds, the diffusion coefficients, D,, and diffusion coefficients at zero concentration, D,,, of pure ethanol and pure water were determined from eqns. (3 ) and (6) and are presented in Table 6. In fact, the diffusivity of a penetrant through a membrane is a strong function of the size and shape of the penetrant. In a homologous series the molecules with a smaller molecular srze permeate faster. As can be seen m Table 6, the water molecule diffuses much faster than the ethanol because the size of the water molecule is smaller. TABLE 5 Free volume parameters, B, and Ad,, of ethanol and water m crosshnked PVA membrane Penetrant

B&

RX&,

Ethanol Water

0 4074 0 1677

5 4434x 10-5 5 1827 x 1O-8

49

For the permeation of bmary liquid mixtures, the thermodynamic &ffusion coefficients, (DT),, and diffusion coefficients, D,, of ethanol and water components across the membrane can be calculated from eqns. (3 ) and (15)) respectrvely. These &ffusivities havmg a self-plasticizatlon term and a cross-plasticization term are functions of the temperature and the concentrations of the liquids in membrane as described earlier For example, diffusion coefficients of ethanol and water at the upstream side of the membrane are shown in Fig. 3. In the middle range of the feed composition, the plasticizmg effect of water on the permeation of ethanol is found to be pronounced, resultmg m a maximum diffusion coefficient of ethanol. Figure 4 shows the dependence of the diffusion coefficient, D,, on temperature to have an Arrhenius relationship. Usually, the activation energy of diffusion can be evaluated from the plot of lnD, vs. l/T. Figure 4 mdicates that the plot 1slinear which confirms that the activation energy is independent of temperature m the given temperature range. It can be seen that the slope of the line, i.e. the activation energy, is higher for diffusion of ethanol than for diffusion of water; this indicates that the activation energy for diffusion depends on the value of B,.

TABLE 6 Dlffuslon coeffclenta, D,” and 0,” of pure ethanol and pure water on the upstream side of membrane at vanous temperatures Temp (“C) 30 45 60

Water (m”/sec )

Ethanol (m’/sec)

D,

&

Q

&

6 375 x lo-” 9 528x lo-” 1415x lo-‘0

1874x lo--” 2 306 x lo-l2 2811x1O-‘2

3 361x1O-‘4 5 644x10-I4 1006 x lo-l3

3 125x 10-14 4 832 x lo-l4 7 314x 10-14

“D, = Dlffuslon coefficient of penetrant I m polymer fixed frame of reference bD, = Dlffuslon coeffclent of penetrant zat zero concentration

CK YEOMANDRYM

50

0

0

4-

&

-

10 -” Ethanol

-

*a $3-

\

0 0 *

30 “c 45 ‘c 60 ‘C

I

00

30 “c 45 “C 60 “c

\\’

10 -“y

10 -‘I

l

z

HUANG

05

Content

10 m Feed

Fig 3 Dlffuslon coefficients, D,, of ethanol (-_) and water (---) on the upstream side of the membrane at various temperatures

Ethanol

I 05 Content

1 m Feed

Fig 5 Calculated concentration profiles of ethanol and water m crosshnked PVA membrane at 50 wt % ethanol content m the feed mixture at 45 ’ C

the concentration profiles in the ii.111 range of feed mixture compositions at various temperatures, the profiles at 50 wt.% feed composition and 45 ’ C are given as a typical example m Fig. 5. These concentration profiles were used to calculate the permeablhtles of the mdlvidual components taking into account the couphng fluxes and plastlcization actions The variation of the coupling fluxes and plasticizatlon actions with the position in the membrane can be determined from the local concentration profile. The detals will be dscussed in next section.

lo -‘n l/temperature.

0 00

l/K

Fig 4 Temperature dependence of dtifuslon coefficients at 50 wt % ethanol content m the feed murture (-_) ethanol, (---) water

Concentrattonprofiles In membrane The concentration profiles of ethanol and water m the crosslinked PVA have been calculated from eqns. (28) and (29 ) by using the parameters sven m the previous sections. Among

Predrctwn of the permeabhty of lndtvlduul llquld For the permeations of single liquid components, the model shows excellent agreement with the experiments because the free volume parameters and lffusivity of the liquid component were determined by the regression method, 1 e. fitting the relevant equations to experimental pervaporatlon data of the single liquid component (Table 7). Knowing the equllibrmm sorption data, the binary interaction parameters, the concentra-

51

PERVAPORATION SEPARATION OF ETHANOL-WATER MIXTURES THROUGH CROSSLINKED POLY(VINYL ALCOHOL)

TABLE 7 Comparison of calculated and expenmental permeablhtles of pure penetrant m membrane at various temperatures Temp

Permeability (g-cm-cm-‘-hr-‘)

("C)

Experimental

Model

30 45 60

Rat.10"

W”

Eb

W

E

W

E

0 739

3 91x10-6 9 87x10-6 2 49x10-5

0 759 1230 1988

4 10x lo+ 9 23 x 1O-6 2 37 x 10-5

0 973 1020 1036

0 952 1069 1048

1255

2 059

“W water permeabhty bE ethanol permeablhty ‘Ratlo = model permeablhty /expenmental

permeablhty

tlon dependent diffusion coefficients, and the concentration profiles it is possrble to calculate the mdividual permeablhties m the permeation of a binary liquid mixture by usmg eqn (19). The results of the calculations are presented in Table 8 in comparison with experimental permeabilitles m the full range of feed compositions at 30,45, and 60” C, respectively As can be seen in Table 8, the water permeabilitres from the model are very close to the experimental data (Fig. 6), m spite of the fact that there may be some inaccuracies in the assumptions used m this study. There are some deviations from the experimental values at 10 and 90 wt.% ethanol content m the feed mixture. The reason for the deviations is not clear, but this may arise from maccuracles m the swellmg measurement In the ethanol part, the comparison shows a more or less significant deviation between the values from the model and the experimental data. This deviation can be considered as being caused by sensitivity to the error that may occur m the total system. Actually, the permeability of ethanol is quite small compared wrth that of water or with total permeability. Even though the measuring error of the total system is trivial, it may be magnified when the result is applied to a small part of the system.

More detailed analysis of the permeation of a binary liquid mixture can be made by using the newly defined plasticizing coefficients. Generally, the permeation of a binary liquid mixture is characterized by the couplmg and plasticizing actions of permeants. From this point of view, the plasticizing coefficient can be said to provide a measure of the coupling and plasticizing actions for analyzing the transport properties of a membrane. Since coupling and plastlcizmg take place durmg the diffusion step, the coefficients should be involved m eqn (16) for the diffusion term. The plasticizmg coefficients were computed from eqns. (20) and (21) by using the free volume parameters (Table 9). The self-plasticizing coefficient of water, 0Z2,is much higher than that of ethanol, O,,. That is why the permeability of pure water (i e 0 wt.% ethanol content in feed mixture) is higher than that of pure ethanol (100 wt.% ethanol content in feed mixture). This self-plasticizing coefficient seems to be strongly related to the mteractlon between liquid and membrane material. The cross-plasticlzmg coefficient of ethanol, OZ1,has a higher value than that of ethanol, O,, This suggests that the enhancement of water permeation by the presence of ethanol is more pronounced than that of ethanol due to the pres-

52

C K YEOM AND R Y M HUANG

TABLE 8 Companson of calculated and experimental permeablhtles of mdlvldual components m binary hqulds mixture through crosslmked PVA membrane Temp

Comp a

("Cl

(wt%)

Permeablhty (g-cm-cm-*&r-‘) Model

30

45

60

Ratlod

Expenmental

Wb

EC

W

E

W

E

10 30 50 70 90

0 7345 0 6095 0.3305 0 1787 0 0190

3 46x 1O-4 3 19x 10-3 9 38X 1O-3 4 97x10-3 3 59 x 10-4

0 5681 0 4971 0 2898 0 1729 0 0322

7 77x 10-4 2 51 x 10-3 2 68X 10-3 2 12x 10-3 6 05~10-~

1293

1266 1 140 1034 0 590

0 444 1274 3 506 2 347 0 594

10 30 50 70 90

13004 10250 0 6406 0 3881 0 0419

106x 1O-3 704x10-3 199x 10-z 109x 10-2 969x1O-4

0 9857 0 9007 0 5710 0 3495 0 0660

177 x 10-3 7 38x 1O-3 7 60~10-~ 6 10x 1O-3 133x10-3

1319 1 138 1122 1110 0 634

0 598 0 953 2 625 1792 0 724

10 30 50 70 90

2 7305 19839 12208 0 6688 0 0914

2 89x 1O-3 3 32x lo-* 605x10-* 2 67x lo-* 3 05x10-3

17652 16488 1 1215 0 7121 0 1344

177x 138x 159x 156X 3 07 x

1547 1203 1089 0 939 0 680

10-3 lo-* 10-2 lo-’ 10-3

1 ’

1632 2 412 3 797 1712 0 993

“Camp ethanol content m feed mixture bW water permeability % ethanol permeability dFtatlo model permeablhty/expenmental permeability

ence of water. Thus, crosshnked PVA membranes have an excellent selectivity to water. Hence, the amount of individual plasticization action can be expressed as the product of the volume fraction of the individual permeant and its plasticizmg coefficient (Table 10 ). In the water permeation part, the amount of self-plasticrzation action decreases with increasing ethanol content in the feed mixture because of decreasing &. The cross-plastlclzation action has a maximum value at 50 wt.% composition due to maximum & in the equilibrium sorption. However, the amount of the cross-plasticlzation action is very small over the complete range of feed compositions compared to that of the self-plasticlzation action. Therefore, the permeation of water is mainly affected

by the self-plasticization action of water. In the ethanol permeation part, the self-plasticization action ~3more significant at 50 wt.% composition, mainly due to the maximum sorption of ethanol while the cross-plasticlzation action decreases with the composition, the amount being comparable to that of the self-plasticization action. In the high ethanol content region in the feed mixture, the cross-plasticization action surpasses the self-plastlcization action. Therefore, one can say that the crossplasticization action of water contributes to the permeation of ethanol to the same extent as the self-plasticization action of ethanol. As a result of the analysis of the plastlclzmg coefficients, the total permeability and water permeability through the crosslinked PVA

PERVAPORATIONSEPARATIONOF ETHANOL-WATER MIXTURES THROUGH CROSSLINKEDPOLY (VINYL ALCOHOL)

53

membrane can be determined by only using the self-plasticization action of water The selectivity or separation factor of the membrane can be affected by both the cross-plasticization action of water and the self-plastlclzation action of ethanol. Conclusions

05

Relative Distance Fig 6 Companson of theoretical permeability with experimental values (for the water component)

TABLE 9 Plastlclzmg coefficients of mdlvldual components Temp (“C)

Water 0 22

0 21

011

0 12

30

1660 1836 2 012

0 510 0 540 0 571

0 512 0 545 0 577

0 115 0 127 0 139

45 60

Ethanol

TABLE 10 The amount of plastlclzatlon action of mdlvldual component on the upstream side of membrane at 45°C Compontion” (wt%) 0

10 30 50 70 90 100

Ethanol

Water &X022

41x0,,

@lXOI1

&!XOIZ

0 1658 0 1665 0 1482 0 1201 0 1000 0 0358 0

0 0 0025 0 0093 0 0165 0 0143 0 0068 0 0005

0 0 0 0 0 0 0

0 0115 0 0115 0 0102 0 0083 0 0069 0 0025 0

0025 0094 0166 0144 0068 0005

“Compoatlon ethanol content m feed mixture

A modification of existing models based on the free volume theory for the prediction of the permeation of binary liquid mixtures (ethanolwater) through a crosshnked poly(viny1 alcohol) (type II) membrane has been developed. For more correct simulation and calculation of the permeation behavior, the solubihty data of the individual components present in the liquid mixture directly measured from equllibrium sorption experiments were used as the boundary conditions at the upstream side of membrane. The determination of solubility in terms of the volume fraction of liquid was made by measuring the change m the length of the membrane due to swelling. By calculation of the concentration profile in the membrane it was also tried to provide local concentration data to the model. On the whole, the new model successfully works for predicting the permeation of ethanolwater mixtures through crosslmked poly (vinyl alcohol) membrane, in spite of the fact that there may be some inaccuracies m the assumptions used m this study. Good agreement between the model and the experimental data is partly due to the estimation of the diffuslvlties and free volume parameters having real practical values. The measurement of diffuslvity was done by using the same membrane and the same process conditions as in the real experiment during pervaporation. The introduction of the plasticizing coefficient to the model equation allows one to explain the plastlcization action and the coupling fluxes, making possible the

54

C K YEOM AND R Y M HUANG

detailed analysis of the pervaporatlon behaviour of the system. Acknowledgement The authors wish to thank the Natural SOence and Engineering Research Council of Canada (NSERC) for their support of this research.

density ( g-cmm3)

P

Subsmpts ethanol 1 water 2 component 2 z polymer P References 1

List of symbols

B C D

DO

AGE J

1 I” L

0 P T

Ts u

V n

activity free volume parameters for amorphous region in polymer generalized Bd concentratron m membrane ( g-cmm3) &ffusion coefficrent in the polymer fixed frame of reference (m2-set-‘) drffusion coefficient at zero concentratron (m2-set-l) thermodynamic diffusion coefficrent ( m2-sec-l ) excess free energy of mixing (J-mol-l ) permeation rate (g-m-2-hr-1) drmenslon of dry membrane (m) dimension of swollen membrane (m) membrane thickness (m) plasticizing coefficient permeability (g-cm-cm-2-hr-1) operating temperature (K) glass transition temperature (K) volume fraction in the binary system molar volume ( m3-mol-l ) distance along which diffusion takes place (m )

Greek letters volume of system ( m3 ) proportional constant a” volume fraction in the ternary system crystallmity of polymer L Flory-Huggins interaction parameter x

2

3

4

5 6

7

8

9

10

11

12

M Fels and R Y M Huang, Diffusion coefficients of hqmds m polymer membranes by a desorptlon method, J Appl Polym Scl ,14 (1970) 523 R Y M Huang and V J C Lm, Separation of liquid mixtures by usmg polymer membranes I Permeation of binary organic hqmd mixtures through polyethylene, J Appl Polym Scl ,12 (1968) 2615 S N Kim and K Kammermeyer, Actual concentration profiles m membrane separation, Sep Scl, 5 (1970) 679 C H Lee, Theory of reverse osmosis and some other membrane operations, J Appl Polym Scl ,19 (1975) 83 R B Long, Liquid permeation through plastic films, Ind Eng Chem , Fundam ,4 (1965) 445 F W Greenlaw, R A Shelden and E V Thompson, Dependence of diffusive permeation rates on upstream and downstream pressures II Two component permeant, J Membrane Scl ,2 (1977) 333 J -P Brun, C Larchet, R Melet and G Bulvestre, Modehng of the pervaporatlon of bmary mixtures through moderately swelling, non-reacting membranes, J Membrane Scl ,23 (1985) 257 M H V Mulder and C A Smolders, On the mechanism of separation of ethanol/water mixtures by pervaporatlon I Calculations of concentration profiles, J Membrane Scl ,17 (1984) 289 M H V Mulder, A C M Franken and C A Smolders, On the mechanism of separation of ethanol water mixtures by pervaporatlon II Expenmental concentration profiles, J Membrane Scl ,23 (1985) 41 C K Yeom and R Y M Huang, A new method for determining the diffusion coefficient of penetrant through polymenc membrane from steady state pervaporatlon, J Membrane Scl , m press (1992) A F Asfour, M Saleem and D D Kee, Diffusion of saturated hydrocarbon m low density polyethylene (LDPE) films, J Appl Polym Scl ,38 (1989) 1503 G E Robert and E F T White, The thermodynamics of the glassy state, m R N Howard (Ed ), The PhysICSof Glassy Polymers, Applied Science Publications, London, 1973, Chap 1, pp 54-66

PERVAPORATION SEPARATION OF ETHANOL-WATER MIXTURES THROUGH CROSSLINKED POLY (VINYL ALCOHOL)

13

J S Vrentas and J L Duda, Diffusion m polymer-solvent systems I Reexammation of the free volume theory, J Polym Sci , Polym Phys Ed, 15 (1977) 403 14 P J Flory, Prmciples of Polymer Chemistry, Cornell Umverslty Press, Ithaca, NY, 1953 15 J Hauser, G A Remhardt, F Stumm and A Hemtz, Non-ideal solublhty of hquld mixtures m poly (vinyl alcohol) and its influence on pervaporatlon, J Membrane !%I, 47 (1989) 261 16 C K Yeom and R Y M Huang, Development of crosslmked poly(vmy1 alcohol) (type II) and permeation of acetic acid-water mixtures, J Membrane Scl , 62 (1991) 59-73 17 D Behrens and R Eckermann, Vapor-Liquid Eqmhbrmm Data Collection, Vol 1, Part 6C, Dechema, Frankfurt, 1983 18 A A Miller, Free volume and the viscosity of hqmd water, J Chem Phys ,38(7) (1963) 1568 19 J -W Rhlm and R Y M Huang, On the prediction of separation factor and permeabihty m the separation of binary mixtures by pervaporatlon, J Membrane Scl ,46 (1989) 335

20 21

22

23 24

25

26

55

H FuJita, Diffusion m polymer-chluent systems, Fortschr Hochpolym -Forsch ,3 (1961) 1 A K Doohttle, Studies m newtoman flow II The dependence of the viscosity of hqulds on free-space, J Appl Phys ,22( 12) (1951) 1471 A Kreltuss and H L Fnsch, Free-volume estimates m heterogeneous polymer systems I Dlffuaon m crystalline ethylene-propylene copolymers, J Polym Scl , Polym Phys Ed, 19 (1981) 889 International CrItical Tables, McGraw Hill Book Co Inc , New York, NY, 1933 R Y M Huang and C K Yeom, Pervaporatlon separation of aqueous mixtures usmg crosshnked poly (vinyl alcohol) (PVA) II Permeation of ethanolwater mixtures, J Membrane SCI,51 (1990) 273 M Fels and R Y M Huang, TheoretIcal mterpretatlon of the effect of mixtures composltlon on separatlon liquid m polymers, J Macromol Scl -Phys , B5 ( 1) (1971) 89 J W Rhlm, Pervaporatlon separation of binary orgame-aqueous liquid mixtures usmg modified blended polymer membranes A theoretical and expenmental mvestigatlon, Ph D Dlssertatlon, Umvers&.y of Waterloo, Waterloo, Ont , Canada, 1989