Surface charges and zeta potentials on polyethersulphone heteroporous membranes

journal of MEMBRANE

SCIENCE

ELSEVIER Journal of Membrane Science 137 (19971 109 119

Surface charges and zeta potentials on polyethersulphone heteroporous membranes

R. Pastor, J.I. Calvo, P. Pr~idanos, A. Hernfindez* l)epartamento de Termodin(tmica y F[sica Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071 Valhulolid. Spain

Received 26 May 1997: received in revised form 18 July 1997: accepted 22 July 1997

A b s t r a c t

Two microporous polyethersulphone filters are studied. The pore size distributions are obtained by an air-liquid displacement method. These distributions are narrow Gaussians with mean pore sizes over the nominal ones. The membranes are bathed by several diluted aqueous solutions of NaCI at 298 K. The equations of transport through the Gaussian distributed capillary pores of these membranes (Nemst-Planck, Navier-Stokes. Poisson, and charge and mass conservation laws) are numerically solved with the adequate limit conditions and used to obtain the electrokinetic coefficients for an assumed pore charge. The streaming potential is measured allowing to obtain the adsorbed surface charge density as a function of concentration (adsorption isotherm). The so obtained results are seen to deviate only slightly from those that should be obtained if all the pores were assumed equal to the most probable one (homoporous membrane). A Langmuir chloride adsorption mechanism fits well to the complete adsorption isotherm obtained: while a Freundlich or heterogeneous adsorption pattern could be assumed for low concentrations. Moreover, by an adequate correction of both the Langmuir and Freundlich equations to take into account the complex structure of the electrical double layer, the proper charges of lhe membranes arc evaluated. These proper charges seem to be negligible in our case. Whereas, lhe average adsorption free energy and the maximum number of accessible sites are evaluated being relatively small, according to the hydrophillic character assumed for the membranes. ~' 1997 Elsevier Science B.V.

Kevw,,r&: Heteroporous membranes: Micropores; Pore size: Streaming potential: Adsorption

1. I n t r o d u c t i o n subject undergoing rapid progression. Such projec-

tions ul t imately rest on the deve lopment and applica-

Membrane microf i l t ra t ion is used for the process ing tion of effect ive procedures tbr membrane

of small particles, col loids and bio-mater ia ls such as characterizat ion. A range of methods is avai lable

protein precipi tates and microorgan isms [1]. Such for assessing the physical propert ies of the mere-

membranes are c o m m o n l y po lymer ic materials having branes, such as porosity, surface area, pore size dis-

pore d iameters in the range 0. l - 1 0 . 0 p m . The predic- tribution, and pore structure 12-51. Also several

tion of the separat ion propert ies o f microf i l t ra t ion is a models for the membrane structure are used to relate

structural parameters and functional per formance ~:Corresponding author. Fax: +34 83 42 30 13. [6,7].

0376-7388/97/$17.00 :~' 1997 Elsevier Science B.V, All righls reserved. PI I S0376-7388(97)0111 86-5

110 R. Pastor et al./Journal of Membrane Science 137 (1997) 109-119

The proper charge which is present on the surfaces The structural characterization techniques for of a microporous material along with the number of microporous membranes now available cover a broad accessible sites per surface unit are parameters of real range of physical methods. They can be included into interest if we want to study, from a microscopic point two main groups, some of these methods giving of view, the fouling mechanism. The knowledge of the parameters related with the membrane permeation adsorption mechanism acting and the analysis of the while others directly obtain morphological properties solution-material interaction, are highly significant [13]. Those techniques related with permeation para- for example in microporous membranes, whose sur- meters (liquid and gas flux measurements, solute face properties will be studied when they are in contact retention test, liquid displacement method, permporo- with a chloride solution in order to help to characterize metry, etc.) allow to determine the pore size distribu- and explain the specific performances and fouling tions for the pores open to flux. limits. Here we will study two microporous membranes,

A microporous membrane is, frequently, repre- which are bathed by different NaCI aqueous solutions sented by an array of equal cylindrical microcapillary at 298 K. Once the membranes are characterized from pores whose walls are uniformly charged and sur- the structural point of view, by using a liquid-displa- rounded by a diffuse electrical layer, with an effective cement method, and the streaming potentials are thickness which is given by the Debye's length [8-12]. measured, a function is obtained giving the surface Then, the equations of transport (Nernst-Planck, charge density at the shear surface versus the chloride Navier-Stokes, Poisson, and charge and mass con- molar fraction. servation laws) can be numerically solved, with the Given that only diluted solutions are used [14,15], adequate limit conditions, and the electrokinetic coef- the adsorption isotherms can follow or an heteroge- ficients calculated. Once anyone among them, the neous or an homogeneous adsorption pattern. If the streaming potential or the membrane conductance complete range of analyzed concentrations are taken per surface unit, for example, has been measured, into account, an homogeneous mechanism seems to we can obtain the surface charge density at the shear act. While for low concentrations an heterogeneous surface, according to the so-called microcapillary adsorption mechanism can be assumed with a rela- model for the transport, tively narrow and sharp distribution of adsorption free

In any case, an unimodal and narrow porous struc- energies that can be calculated from the phenomen- ture should allow to use the average pore size to ological adsorption isotherm. The proper charge of the analyze experimental data. In effect, the use of a well membrane can be fitted too. In our case, a negligible characterized membrane with an ideally regular pot- proper charge will be obtained, with low values of both ous structure is helpful when fundamental transport the adsorption free energy and the maximal number of studies are envisaged. Nevertheless, this easiest model accessible sites. will be here made more realistic, by accepting that the pores have unequal sizes which are statistically distributed. 2. Theory

Most membrane manufacturers characterize their products by a single pore size or molecular weight cut- 2.1. Equal capillaries model off value. These values are usually obtained by mea- suring the rejection of various macromolecules or When an electrolytic aqueous solution passes particles of increasing hydrodynamic diameter or throughout a microporous membrane whose walls molecular weight. It is understood that this single wear a proper charge per square meter ~0, some of value is not an adequate measure of the membrane the ions are so strongly bound to the pore surfaces that pores; however, it is useful for preliminary selection, they can be considered as fixed on it. In such a way Nevertheless, for microporous membranes, the pores that, only a fraction of cr 0 is effective in relation with have to be assumed as size-distributed, even for the resulting electrokinetic phenomena. membranes with relatively uniform pore sizes as the When a pressure gradient acts through the mere- track-etched or anodically deposited membranes, brane the solution close to the solid surface keeps

R. Pastor et al./Journal of Membrane Science 137 ~1997) 109 119 III

immobile while the rest of the solution filling the (c) a diffuse layer including the adjacent solution pore moves along it. This movement leads to the whose distribution of ions is determined by the need of appearance of an electric potential drop from one to an overall electric neutrality leading to a total charge the other side of the membrane, AV, which corre- E~ and an electric potential ~,~,~ at the border of the sponds to a dynamical contribution to the total electric diffuse layer. In between the static and mobile portions potential profile. In stationary conditions, both the of solution there is an edge which is the shear surface contributions to the total potential inside the pore and whose potential is called zeta-potential, and is can be written as given by (. In the Stern model, the Stern-surface, the

RT shear surface and the edge of the diffuse layer are 0(r. = ) - z ~ ~i,(r)+ V(z) (1) taken as coincident at some distance from tile real

solid surface, ~', usually taken as a counterion radius, where r is the radial coordinate while z is the long- leading to itudinal one. The ratio of the z-dependent potential drop over the applied pressure difference, in zero ~,!:(rp) c,~ ~,'d ( (4) current conditions, is called streaming potential. It Here we assume that the microporous structure is well can be ewfluated from the phenomenological equa- represented b> a mean cylindrical pore. Therefore. the

tions Stern surface is a tube of radius rp while the pore wall Jv LIIAp + L12AV. 1 LIzAp 4- L22 /XV , (2) itself is a concentric microcapillary of radius rp÷a.

where Ap and AV are the pressure and electric According to the Stern model, the electroneutrality condition leads to

potential drops through the membrane, Jv is the volume flow and I the electric current, both per unit ~() + Vs + E,~ - 0 (5) of total membrane area. The L 0 are the phenomenological coefficients and the Onsager reciprocity but the Stern surface and the microcapillary have the la,a has been used. The streaming potential can be same length Az, thus written as

rp + h - - - - o r ( > + crs =: cr d (6)

I~p \ - - kP / t o L22 (3) where cr o and crs are the surface charge densities on the

and evaluated from the Nernst-Planck, Navier-Stokes solid surface and the Stern layer, respectively. While and Poisson-Boltzmann equations corresponding c7 d is the surface charge density that should be neces- to the solution actually moving through the pore, sary in the Stern layer i f it had to balance the diffuse which is treated as consisting of point charges accord- charge by itself. ing to the Gouy-Chapman picture. Here we wil l As mentioned before, the streaming potential or consider [16,17] that the counterions are tightly held any other combination of the phenomenological on the pore surface as a result of the action of the drop coefficients can be calculated [16,17] as a [unction of the static electric potential referred to the bulk of the solution viscosity, /&, the dielectric constant, solution along with the specific forces that bound ~, both the ionic diffusivities, D~ and D , the ratio them to the solid surface. The centres of these immo- between the mean hydrodynamic radius and the bile ions are supposed to define what is called the Debye's length, rp/A, and the surface charge Stern-surface. According to this model [14,16,17], the density, cr d, which determines the ~,(r) profile static solid-l iquid interface is considered as simply through the Poisson-Boltzmann equation. In effect consisting of: [g-12.1g]. l, r can be calculated according to Eq. (3)

(a) the pore surface with a total charge and at an using electric potential level over the bulk solution given by ~() and ~/'o, respectively: (-)eRT ~ '

(b) the Stern surface with a charge ~s and an L I 2 - ( - ~ ~:,(r)rdr (71 electric potential ~/'s:


and far as the total fluxes should be the sum of all the F rp partial fluxes through each pore in the parallel bunch,

2F2c0 F 2 -v(r' the coefficients given by Eq. (7) and Eq. (8) should a,sobeadd t, ea d so

2cRTO ~i"-I L12 (i) + u z2D_e z ~,(r)/z+} rdr V p -

rpZ+ AZ ~i'-1 L22 (i) t l 9 , . ,

rp. ~ i : 1 (7r /am)rp(O(L,2( t ) / (~( ' ) ) j ~ - - t7 ~ , , . . x {u+z+e -':'(r) + u z_e- : ~:'(r)/:+} ~ i : 1 (TV/Am)r~(t)(L22(t)/O(t)) (10)

0 where Am is the membrane area. In this equation,

x {~" - z)(r) } r drJ (8) L~ 2(i)/e)(i) and L22(i)/O(i) can be calculated according

where ui is the stoichiometric coefficient, O is the to Eqs. (7) and (8), respectively, once the potential membrane porosity for pores of radius rp (the fraction profile (i.e. ad) is known. Here we assume, as seems of the surface occupied by these pores) and c is the reasonable, that the adsorbed charge density is equal concentration. It is worth to mention here that neither for all the pores of different sizes as far as it is a O nor Az are needed in order to calculate Up as far as material-solution interaction parameter. Thus factors factor O/Az should cancel out. 7r/(AZAm) cancel out and are not needed in order to

The streaming potential is not given by an analytical obtain the streaming potential. In the same way that, as function because the solution of the Poisson-Boltz- already mentioned, the factor (-)(i)/Az should disap- mann equation is needed to determine the ~(r)profile pear when the Up for each pore in the bunch is and it can only be obtained in general by numerical evaluated. methods [8-12,18,19].

If the bulk solution values are taken for q~, ~, D~ 2.3. Adsorption isotherms and D , we can obtain ad for each bulk concentration by fitting the experimental results on the chosen If an homogeneous mechanism of adsorption of electrokinetic parameter. At the same time the anions is assumed, the resulting immobile or adsorbed corresponding profile of the radial part of the charge per unit surface should follow [14,15], the so- electric potential, and concretely the ~-potential, is called Langmuir isotherm, i.e.

calculated, z-eNsx exp( - AGads/RT) as = (1 1)

1 + )~_exp(-AGads/RT) 2.2. Size distributed capillaries model

where e is the elemental charge, N~ the total number of In an actual membrane there is always a distribution sites of adsorption accessible to the anions, X- the

of pore sizes around a mean one. Thus in order to molar fraction of anions in the bulk solution and simulate a real membrane, the model should be AG~d~ the molar Gibbs tree energy of adsorption. improved by allowing the pore radii to be distributed On the other hand, a Freundlich dependency, i.e., a according to a more or less broad Gaussian. What can power dependence like: be done is to assume a bunch ofn parallel pores whose a;yt ' radii are assigned according to as (~ ) = (12)

rp(i) = ( r p ) + a -2x f i2~cos (27 rB) , i = l . . . . ,n should correspond to an exponentially decreasing molar free energy of adsorption distribution [20]. In (9) this case, the maximum number of occupiable sites

where A, B _< 1 are random numbers, rp(i) is mean should be: radius of the ith pore among the n assumed array and (rp} is the mean one around which actual radii are a sin(Trb)

Ns -- (13) normally distributed with an standard deviation a. As z e (Trb)

R. Pastor et al./Journal of Membrane Science 137 (1997J 109 119 II 3

and the average adsorption free energy: 3.2. P o r o m e t r v

R T (AG~d~> b (14) An extension of the bubble point is used to obtain

the pore size distr ibution by means of a Coulter ~'

Porometer II. This apparatus uses a liquid displace- 3. E x p e r i m e n t a l ment technique. The sample is first thoroughly wetted

with l iquid of low surface tension and low vapour 3.1. M a t e r i a l s pressure (Coulter '~ Porofil) such that all the pores

have been filled with the liquid. The wetted sample is Two porous polyethersulphone membranes subjected to increasing pressure, applied by a com-

(Supor" ), treated to make them hydrophil l ic , with pressed air source al lowing air flows of 100 l/rain at 14

nomina l pore diameters of 0.2 btm ($20) and 0.45 bun bar. All data are sent to a computer where they are ($45) were obtained from Ge lman 'i~ . Some nomina l treated and plotted.

characterist ics of these filters as given by the manu- This technique is based on the fact that when facturers are shown in Table 1. The m e m b r a n e thick- increasing applied pressure it reaches a point where

nesses have been measured by micrometry and are it overcomes the surface tension of the liquid in the shown in Table 2. Note that they result to be signifi- largest pores and push the liquid out. Increasing the

catively different f rom the nomina l ones. pressure still further allows the air to flow through The membranes were soaked in the solut ion or smal ler pores, according to Washburn equation:

solvent to be used in each exper iment for 12 h prior 2q, cos0 to any measure in order to assure that a good equili- A p ~ ¢15) br ium is reached. All exper iments were done at 298 K. rp

All sohttions were prepared from degassified, bidis- rp being the pore radius, ~. the surface tension of the

tilled and deionized (Mi l l i -Q! ' treated) water and liquid and 0 the wett ing angle with the solid matrix of puriss NaC1 in concentra t ions ranging from 0.01 to the membrane I",. cos 0 is called the Wi lhe lmy surface 1 tool/in ~. tension).

Table I Nominal data on Supor membranes

dp (/.tin) Az (lam) Lll ( lf l s m/s Pat Lii ( 10 s m/s Pat Bubble point (water at 25 C) (air at 25 C) presstire 1105 Pa)

$20 0.2 3.7 500 3.2 152.4

$45 0.45 7.3 830 2. I

Other manufacturer data for these filters are: density 4.10 io kg nl : and refraction index 1.640. Here dp is the nominal pore diameter.

Table 2 Membrane thicknesses and porometric data of Supor membranes

A: (gin) (rp) (pin) o- (~um) Ell ( 1 0 s m/s Pa) Np I I0 i2 m ') (water at 25 (7)

$20 I OOze I 0.1582:0.003 0.009±0.003 3.10i0.19 14. I ±0.7 $45 120± I 0.318±0.002 0.017 ±0.001 15.4i0.2 3.58i0.09

(re' ,> is Ihe mean pore size, N n is the total number of pores while Lll is the corresponding calculated permeability.


. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . able to the nominal water bubble points. In effect by

2.0 ~$20 taking into account Eq. (15) a water-polyetersul- phone contact angle of 56.8 for $20 and 54.9 for $45 are obtained which seems reasonable [22], mainly if it is taken into account that they are pre-treated to make them hydrophillic.

rm/g oa

Streaming potentials measurements were per- ,.. . . . . ,~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . formed using a simple membrane holder and cell,

0.05 o.lo 0.15 oao 0.25 0.3o 0.35 0.4o 0.45 which is shown elsewhere [23]. A pressure difference

rp (m") is applied by a constant height column of solution in vertical capillaries by means of a Mariotte flask, while

Fig. 1. Pore size distributions for $20 and $45 membranes. two chloride selective electrodes are used to measure the resulting potential by means of a high impedance

By monitoring the applied pressure and the gas flow voltmeter. through the sample, a wet run was obtained, followed by a dry run performed with the dry sample (with no liquid in the pores that has already been expulsed by 4. Results air). The measurement of the flux for wet and dry runs, combined with a model for gas transport through the 4.1. Streaming and zeta potentials pores, allows to obtain the pore size distribution (it has been assumed that, according to the operation condi- The measured streaming potential for all concen- tions, the transport is of the Knudsen diffusion type for trations and both the membranes are shown in Fig. 2. pores until 0.96 ~tm, while for wider pores there would To calculate the adsorbed surface charge density cro, appear viscous or Hagen-Poiseuille flow). The pore the real pore size distribution has been used by size distribution is fitted to a normal law in order to assuming equally adsorbing pore walls for all sizes, evaluate the mean pore diameter and the correspond- i.e. a given ~r,l independently of rp. The resulting ing standard deviation. Other related parameters may overall streaming potential has been compared with also be computed: total number of pores and the the experimental result and cr d modified until the corresponding calculated water permeability, for experimental result is reproduced. The finally example. This extended bubble-point method was described and analyzed in details in a previous work [21].

Fig. 1 shows the corresponding differential pore - , - - - , ~ _. number distributions. Some of the so obtained para- " - ~ o S 4 5

meters are shown in Table 2. Note that the average ~ t0-~

diameters, 0.32-/-0.02 ~tm for $20 and 0.64±0.04 ~tm for $45 as seen in Table 2, are clearly over the nominal ones. In relation with calculated permeabilities, only the $20 agrees with the nominal one while for $45 it roughly doubles the manufacturer's datum. In any case t0~

both the calculated values fairly agree with experi- . . . . . . . . . . . . . . . . . . . . . . mental ones. 1o-~ t~, 1o.

On the other hand, it is worth to mention that the c Cmot/nd)

Porofil bubble point diameters result to be 0.45 and Fig. 2. Streaming potential versus concentration for the $20 and

0.80 for $20 and $45, respectively, which are compar- $45 membranes.

R. Pastor et al./Journal of Membrane Science 137 (1997) 109-119 115

~%"i ° 9.0 9S

y f - - ~ 1 7 ~ 2.0 no~ s $20 I v

¢ = 0,1 mol/m 3 • I i ' o

/ $20 4 " , n.S

.;' ~ 1.0 ~_

1~, .:~ ~ 2 Freundlich

:i: Langmuir o.5 I

lO~10" . . . . . . . . . . 10 ~ 10 ~ . ¢ ~ 0 [ \ O '

Z - (dimensionless) 0 0.0 0.14 0.16 0.18

Fig. 3. A d s o r b e d surface c h a r g e d e n s i t y versus the m o l e fract ion o f rp (l~n)

a n i o n s for both the m e m b r a n e s $ 2 0 and $ 4 5 . T h e best L a n g m u i r

( for the w h o l e range ) and Freundl i ch ( for the l o w c o n c e n t r a t i o n s Fig . 5. Pore s i z e distr ibut ion c o m p a r e d with the c o r r e s p o n d i n g

range ) f i tted curves are a l so s h o w n , s t r e a m i n g potent ia l d is tr ibut ion for $ 2 0 and a c o n c e n t r a t i o n of

0.1 m o l f m 3.

25 . . . . . - - 2.0 ~ - - -

$45[ . . . . . . . . $45 c -O.OI mol/m 3 ¢ ~0 .2 mol/m 3

20 ' ¢ ~ 0.1 mol/m 3

: 1.5

[ c = O.l moi/m 3 c ~ t mol/m 3

i II ~ i ..~ 1.o , ~

~ ' c = 0,2 mol/m 3 - - [

0,5 5 [ c = 0.01 mol/m 3

c - I loUm 3 . . . . . . . . i

0 i - - 0.0 . . . . . . . .

0.20 0.32 0.36 0.20 0.32 0.36

rp (Itm) rp (Itm )

Fig. 4. S t r e a m i n g potent ia l for the pore d i a m e t e r s present in the Fig . 6. Z e t a potent ia l for the pore d i a m e t e r s present in the s i z e

s i z e distr ibut ion for $45 and several concentra t ions , d is tr ibut ion for $45 and several concentra t ions .

obtained surface charge densities are shown in Fig. 3. In Figs. 2 and 8, it is seen that streaming potential On the other hand, the streaming potential correspond- decreases steeply with electrolyte concentration as ing to each pore in the distribution has been also known while zeta potentials substantially increase calculated giving the streaming potential distribution, with concentration up to a maximum above which The u v versus rp dependence has been shown in Fig. 4 it decreases very s lowly in increasing concentration. for several concentrations and both streaming potential and pore radii distributions for a given concentra- 4.2. Adsorption isotherms tion are compared in Fig. 5. The corresponding zeta potentials are also shown in Figs. 6 and 7. The mean It is seen that best results are obtained if a Langmuir zeta potential is shown versus concentration in Fig. 8. homogeneous adsorption mechanism is assumed for


-((dimensionless) with the presence of difl%rently adsorbing sites that, 0.97 0.98 0.99

] , . . . . . . . T ~ 0 for concentrations over a certain threshold one, should F be saturated leaving substantially equally adsorbing

, , ~ , sites (homogeneous) and leading to a Langmuir 4~ • " _ o -6 adsorption mechanism. In Fig. 3 the low concentra-

. ~ tions fitted Freundlich isotherm is also shown. This ~ could be correlated with the presence of maxima in

~" i / ~ zeta potential versus concentration plots [23]. In any 2 ~ • * ] case, the proper charge should be better represented by .: /

. , / / • | ~ 2 the Freundlich result while the number of sites and ! / •

. . . o , . adsorption parameters relevant for the membrane . . . , . ~ [ S 2 0 , ,• * i ,-o.,..~.~ behavior under operative conditions should be char-

0 L . . . . . . . . . 0 acterized better by the high concentration ones, i.e. by 0.18 0.16 0.14

rp(u,,,) the Langmuir homogeneous adsorption mechanism. The obtained values for the adsorption parameters are

Fig. 7. Pore size distribution compared with the corresponding zeta shown in Table 3. The calculated values of the proper potential distribution for $20 and a concentration of 0.1 mol/m 3. charge clearly show that in fact it could be assumed as

nonexistent; i.e. that, from the point of view of the . . . . . . . . . ~ _ experimental results, the membrane can be taken as

neutral. / - - * , , ,

1.5 ; " " - - - . . . . ~ S 4 5

5 . D i s c u s s i o n a n d c o n c l u s i o n s

• 3 1.0 - -

~ ' ~ : ~ The structural parameters of the Supor membranes, -" ----- S 2 0

~ ' as obtained from bubble point porometry, are shown in ~' 0.5 _ Table 2. The pore size distributions, both from the

point of view of the volume flow and pore density are i almost Gaussian and very narrow when compared

with other commonly obtained distributions [24]. It 0.0 ~ ' ~ ' J '

0.0 0.2 0.4 0.6 0.8 1.0 is worth noting that the mean sizes are over the e~'mound) nominal corresponding values; in fact, the nominal

Fig. 8. Zeta potential versus concentration for the $20 and $45 sizes equal the obtained smallest pores for each membranes, membrane.

It has been shown how to evaluate surface charge all the concentration range. This fitted Langmuir curve densities from measurements of streaming potential is shown in Fig. 3. In fact a Freundlich (i.e. hetero- when the membranes are heteroporous [25]. Demon- geneous) adsorption mechanism could not be rejected strating that the presence of a Gaussian distribution of for low concentrations as far as this could be related pore sizes has a little but certain influence on the cr,~

Table 3 Adsorption parameters on SUPOR membranes

o% ( 1 0 5 C / m 2) N s (1016 s i t e s / m "~) AGaj~ (kJ/mol) (AGads ) ( k J / m o l )

$20 Langmuir 34-5 1.0+0.8 30+2 Freundlich 85-9 23005-500 -3.34-0.3

$45 Langmuir 64-7 2.84-0.7 -294-3 Freundlich 84-8 40004-600 3.1 +0.4

R. Pastor et al./Journal of Membrane Science 137 (1997) 109 119 117

that, equally distributed on the walls of all the pores, alumina ones, [16,20]. From the obtained values )or should explain the experimental results. Streaming adsorption parameters, the following conclusions can potentials slightly greater (more negative) than those be raised: corresponding to the mean pore in the distribution are 1. The number of sites of adsorption accessible to always obtained. The obtained zeta potential (surface anions is quite similar for the two analyzed charge density) is always less negative than the cor- membranes, according to dependence of adsorp- responding to the mean pore size. Nevertheless these tion on the solid-solution interactions that should differences are around a 1%. be equal for both the membranes.

If the cumulative flow pore distributions, as 2. The negative sign of the molar Gibbs free energies given by the air-liquid displacement method, are of adsorption for both the concentration ranges, used, prior to be converted to pore number distribu- implies an spontaneous process of adsorption of the tions; a mean flow pore size, rMW can be defined C1 ions. as corresponding to the pore size below which 3. Any chemical reaction should be discarded given half the flow is passing. In this case, as shown in the low values of AGads and {L-~Gads). Fig. 5, an almost total coincidence is seen between As far as the proper charge is concerned, the method the experimental streaming potential and the result shows low sensibility on the proper charges leading to that should be obtained if all the membranes were very small positive charges, with so high error ranges assumed to have equal pores with size rMFV, This than zero proper charges should be entirely compa- should allow to use mean pores or better mean flow tible with results. pores to get surface charge densities from streaming potentials without taking care of the actual size distribution. 6. List of symbols

The charge versus concentration dependence seems to be well explained in terms of an heterogeneous a 1st Freundlich's constant (C/m-') adsorption mechanism for low concentration ranges; A Random number to generate Gaussian while, for high concentrations, chloride ions seem to distributions adsorb on equally adsorbent sites according to a Am Membrane transversal area (m 2) Langmuir pattern. When a low concentration baths b 2nd Freundlich's constant (dimensionless) the membrane, the anions adsorb on a high number of B Random number to generate Gaussian sites which are partly also relatively well adsorbent but distributions leading to an average free molar energy of adsorption c Electrolyte concentration (mol/m 3) ((AGads)) relatively small. When increasing concen- D i Diffusion coefficient of the ith ion, i : -+.

trations, most of the highly adsorbent sites have (m2/s) already been covered by chloride ions while the huge e Elemental charge (C) number of less adsorbent sites are screened and F The Faraday number (C) adsorption should be determined mainly by the I Electric currentthroughthemembrane (A) remaining low number of middle adsorbent sites. Jv Volume flow (m3/s) The concentration at which this change in the adsorp- Lij Phenomenological coefficient, i. j - l . 2. tion mechanism appears coincides with the maximum (m3/s Pa for Lil, m3/s V or A/Pa for in zeta potential (see Fig. 8). LI2:L21 and A/V for L22)

The calculated adsorption parameters, Ns, /kGads tT Assumed total number of parallel pores and (z--~Gads}, are relatively small according with the (dimensionless) hydrophillic character of these membranes. They are Np Total number of pores per surface unit also very similar to those obtained for other micro- (m 2) porous substantially neutral membranes. Nevertheless Nr Number of pores with pore radius rp N~ seems to be lower than for neutral polycarbonate (dimensionless) membranes [23], higher than for polysulphonic mere- Ns Maximum number of accessible sites for branes [17], but only slightly higher than for Nylon or adsorption per surface unit (m -')

118 R. Pastor et al. /Journal of Membrane Science 137 (1997) 109-119

N,, Number of pores with streaming potential X- Mole fraction of anions (dimensionless) Up (dimensionless) ~ Normalized static electric potential (di-

N( Number of pores with zeta potential ~ mensionless) (dimensionless) ~o Normalized radial potential on the pore

r Radial coordinate in the pore (m) wall (dimensionless) rp Pore radius (m) ~d Normalized radial potential in the edge of rMFP Pore radius below which a 50% of the the diffuse layer (dimensionless)

volume flow is passing (m) ~/~'s Normalized radial potential in the Stem {rp} Mean pore radius (m) layer (dimensionless) R Gas constant (J/mol K) T Temperature (K) V Dynamic electric potential (V) Acknowledgemen t s z Longitudinal coordinate in the pore (m) zi Charge number (dimensionless) Thanks are due to projects QU196-0767 from the

Spanish PN I + D and VA-10496 from the Junta de 6.1. G r e e k letters" Castilla-Ledn.

7 Surface tension (Pa m) 6 Distance form the pore wall to the Stern References

layer (m)

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tool) [2] K. Kamide, Thermodynamics of Polymer Solutions. Phase A p Appl ied pressure (Pa) Equilibria and Critical Phenomena, Polymer Science Library, A V Electric Potential through the membrane Vol. 9, A.D. Jenkins (Ed.), Elsevier, Amsterdam, 1990.

(V) [3] B. Rasneur, Porosimetry (Characterization of porous membranes), Summer School on Membrane Sci. and Tech.,

AZ Membrane thickness (m) Cadarache, France, 1984. Dielectric constant (F/m) 141 s, Lowell, J.E. Shields, Powder Surface Area and Porosity,

~- Zeta potential (dimensionless) Powder Technology Series, B. Scarlett (Ed.), Wiley, New

7]~ Viscosity of the solution (Pa s) York, 1984. 0 Wetting angle (dimensionless) [51 M. Mulder, Basic Principles of Membrane Technology,

Kluwer, Dordrecht, 1991. O Membrane porosity (dimensionless) [61 K. Persson, C. Andersson, V. Gekas, Nondeterministic models A Debye ' s length (m) of the hydraulic permeability of fouled and unfouled UF ui Stoichiometric coefficient of the ith ion membranes, in: A. Hernfindez (Ed.), Membranes, Processes

i = + -- (dimensionless) and Applications, SPU VALL, Valladolid, Spain, 1993. /Jp Streaming potential (V/Pa) 171 T, Courtois. Etude de la formation de la couche de

polarisation de concentration en microfiltration tangentielle, c~ Standar deviation (m) Ph.D. Thesis, Toulouse, France, 1992. C~o Surface charge density on the pore walls [81 C.L. Rice, R. Whitehead, Electrokinetic flow in a narrow

(C/m 2) cylindrical capillary, J. Phys. Chem 69 (1965) 4017. ~d Surface charge density in the edge of the [9] s. Levine, J.R. Marriot, G. Neale, N. Epstein, Theory of

diffuse layer (C/m 2) electrokinetic flow in fine cylindrical capillaries at high zeta- potentials, J. Colloid Interface Sci. 52(I) (1975) 136.

~S Surface charge density in the Stern layer [101 W. Olivares, T. Croxton, D. McQuarrie, Electrokinetic flow in (C/m 2) a narrow cylindrical capillary, J. Phys. Chem. 84 (1980) 867.

~0 Total charge on the pore wall (C) [11] G.B. Westerman-Clark, L. Anderson, Experimental verifica- ~d Total charge in the edge of the diffuse tion of the space-charge model for electrokinetics in charged

microporous membranes, J. Electrochem. Soc. 130 (1983) 839. layer (C) [12] E. Donath, A. Voigt, Streaming current and streaming

ZS Total charge in the Stern layer (C) potential on structured surfaces, J. Colloid Interface Sci. 0 Total electric potential (V) 109(1) (1986) 122.

R. Pastor et al./Journal of Membrane Sciem'e 137 (1997) 109-119 II 9

113] F.R Cuperus, Characterization of ultrafiltration membranes, [20] A. Hermlndez, F. Martfnez, A. Martin. R Prfidanos, Porous Ph.D. Thesis, Univ. Twente, The Netherlands, 1990. structure and surface charge density on the walls of

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J15] A.W. Adamson, Physical Chemistry of Surfaces, Wiley, New [21] A. Hemfindez, J.l. Calvo, R Prfidanos, F. Tejerina, Pore size York, 1982. distributions m microporous membranes. A critical analysis

[16J A. Hernimdez, L. Man/nez, M.V. Gdmez, Concentration of the bubble point extended method, J. Membrane Sci. 112 dependence of the adsorbed charges and the zeta potential on 11996) I. the walls of neutral and charged microporous membranes, J. [22] R.E. Kesting. Synthetic Polymeric Membranes, Wiley, Ncw Colloid Interface Sci. 158 (1993) 429. "~k)rk. 1985.

[171 J. Benavente. A. Hern;indez, G. Jonsson, Proper and adsorbed [23] J. l Calvo, A. Hernfi.ndez, R Prfidanos, F. Tejerina, Charge charges on the surfaces of the polysulfonic support of a adsorption and zeta potential in Cycloporc membranes. J. composite membrane from electrokinetic phenomena, J. Colloid Interface Sci. 181 (1996) 399. Membrane Sci. 80 (1993) 285. [24] Y.X. Wang, S.C. Wang, K.T. Yu, A statistical model o! pore

[181 L. Martfnez, M.A. Gigosos, A. Hernfindez, E Tejerina, Study size distributions in membranes. J. Membrane Sci 72 ( It)92/ of some electrokinetic phenomena in charged microcapillury 13, porous membranes. J. Membrane Sci. 35 (1987) 1. [25] R. L6pez. J.l. Calvo, A. Hermindez, Electrokinetic phenom-

[19] L. Martfnez. A. Hern,:indez, A. Gonzdlez, E Tejerina, Use of ena for a microporous network membrane. Effec! of the pore variational methods to establish and increase the ranges of size distribution, Electrokinetic Phenomena'93. Theory and application of analytical approximate solutions of the Applications. Granada, Spain, 19t)3. Poisson-Boltzmann equation tot a charged microcapillary. J. Colloid Interface Sci. 152 (1992) 325.

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Surface charges and zeta potentials on polyethersulphone heteroporous membranes