Properties of microfiltration membranes: The surface electrochemistry of anodic film membranes

Properties of Microfiltration Membranes: The Surface Electrochemistry of Anodic Film Membranes W. RICHARD BOWEN l AND DIANA T. H U G H E S Colloid and Interface Group, Department of Chemical Engineering, University of Wales, Swansea, SA2 8PP, United Kingdom

ReceivedJune 4, 1990;acceptedOctober 4, 1990 The surface electrochemical properties of capillary pore inorganic microfiltration membranes have been characterized by means of computerized measurements of rates of electroosmosis as a function of pH (reported as ~"potentials) and computerized surface pH titration. The membranes have modest values of ~"potential and high titratable surface charge. The incorporation of anions during the membrane manufacturing process has a substantial effect on their surface electrochemical properties. The electrokinetic and titration data have been quantitatively analyzed for a range of pH in 0.01 M NaC1 solution using models based on electrical double-layer theory and accounting for the nature of the charge-determining groups. Membranes produced in phosphoric acid and membranes produced in oxalic acid have been studied. A description of the membrane surface in terms of a two-dimensional array of aluminum oxide and phosphate or oxalate groups, a site dissociation-site binding model, gave estimates of the ratio (q) of aluminum oxide/incorporated anion groups at the membrane surface and of the p K values of these groups. However, such a model gave a reasonable match of calculated and experimental surface charge density/pH profiles only if physically unreasonable values for the thickness or dielectric constant of the inner part of the double layer were used. A much more satisfactory approach was to describe the membrane surface as a three-dimensional array (gel) of charged groups and consider that both protons and counterions could penetrate this gel region. Such a gel model allowed the a priori prediction of both surface charge density/pH and ~-potential/pH profiles and gave a good description of the membrane surface for both types of membrane. The model allowed estimation of the thickness of the gel layer, the specific adsorption energy of the counterions, the ratio q, and the p K values of charge-determining groups. © 1991Academic Press,Inc. 1. INTRODUCTION

The separation of dispersed materials in the size range 0.1-10 /~m by means of porous polymeric or inorganic barriers (membranes) is termed micr@ltration. The large-scale use of microfiltration membranes shows considerable potential (1). The prediction of the process properties of such membranes depends on the development of effective methods for their characterization. A range of methods is available for assessing the physical properties of membranes, such as porosity, pore size distribution, and pore structure (2). However, microporous membranes cannot be under1 TO whom correspondence should be addressed.

stood simply as sieves. Other properties also affect their separation abilities. In particular, the electrochemical properties of the membrane surfaces can have a significant influence on the nature and magnitude of the interactions between the membrane and the substances to be processed (3). Particle-particle and particle-surface interactions may often be quantified in terms of the ~ potentials of the interfaces (4). To give a relevant example, the adsorption of proteins on microfiltration membranes has been shown to be dependent on the ~" potential of the membrane surface (5, 6). Hence, a knowledge of membrane ~"potential is important in the prediction of membrane permeation rates and membrane rejection during processing. The ~"

252 0021-9797/91 $3.00 Copyright© 1991 by AcademicPress,Inc. All rightsof reproductionin any formreserved.

Journal of Colloid and Interface Science, Vol. 143,No. 1, April 1991

MEMBRANE

SURFACE

potential of microporous membranes may be determined by means of the measurement of the rate of electroosmosis through the membrane. We have previously described such measurements on polymeric membranes (7, 8). However, a detailed knowledge of the membrane/solution interface also requires a knowledge of the surface charge density. This can be determined by means of surface pH titration. One of the main purposes of the present paper is to combine such electrokinetic and titration measurements to provide a detailed assessment of the nature of the surface properties of an innovative type of membrane. From a process point of view, it can be advantageous if membranes have high porosity, a narrow pore size distribution, and pores of well-defined geometry. Such features also facilitate the characterization of surface electrochemical properties. The microporous membranes studied in the present paper were produced from anodized aluminum (9). When aluminum is made the anode in an electrolytic cell with an electrolyte such as phosphoric or oxalic acid a porous oxide surface film is formed. This film has a configuration consisting of a nonporous barrier layer adjacent to the aluminum anode contiguous with a porous layer that contains an approximately closepacked hexagonal array of cells, each cell containing a cylindrical pore. The anodizing voltage controls the pore size and pore density, while the thickness is determined by the amount of charge passed. If these films are to be used as membranes they need to be detached from the aluminum metal and the nonporous barrier layer removed. This may be achieved by a voltage reduction sequence conducted while the metal is still immersed in the anodizing electrolyte (9). The reduction in voltage causes the creation of pores in the barrier layer, a final acid treatment causing the oxide film to detach from the metal. Membranes produced in this way may have pore sizes in the range 10 n m to 0.25 um, pore densities in the range 1012 m 10 Is m -2, and film thicknesses of up to 100 #m. An important feature o f the membranes is that the anion

ELECTROCHEMISTRY

253

of the anodizing electrolyte becomes chemically bonded within the matrix of the membrane material ( 10, 11 ) (see Section 4). The distribution of the incorporated anions is not uniform throughout the material (12). Their presence has an important influence on the physical properties of the membranes and can be expected to profoundly influence their surface electrochemical properties. The present paper aims to quantify the latter effects. New approaches to membrane characterization are used followed by interpretation of the data in terms of G o u y - C h a p m a n - S t e r n - G r a h a m e site dissociation-site binding models (13) and Lyklema gel models (14) of the m e m b r a n e / solution interface. 2. M A T E R I A L S A N D M E T H O D S

The electrokinetic properties of the membranes, reported as ~" potentials, were determined by means of measurements of the rate of electroosmosis across the membranes. The membrane to be studied was held at the end of a tube, a "dipped cell" (7). Application of a constant current between an electrode positioned behind the membrane and a counter electrode outside the tube induced electroosmotic flow of electrolyte into the tube. A small peristaltic pump transferred these extracts to an electronic balance. These measurements were carried out under microcomputer control (8). Precision syringes allow the dosing of acid or base to the cell so that the pH dependence of the ~"potential may be automatically determined. Surface pH titration was also carried out in a computer-controlled apparatus. The test electrolyte was continuously circulated from a small-volume thermostated cell and through the membrane by means of a peristaltic pump. Two precision syringes could dose into the cell, each syringe volume being dispensed in up to 5760 steps (DBSS). The pH in the cell was determined by a pH probe connected to a "pH board" (Fylde Scientific) plugged directly into the microcomputer, giving a resolution o f 0.001 p H unit. Titrations reported in the presJournal of Colloid and Interface Science, ",Zol.143, No. ~ April 1991

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BOWEN AND HUGHES

ent paper were carried out using standardized 0.1 M HC1. The membranes used were supplied by A1can International Limited. Most of the data reported are for membranes produced in phosphoric acid electrolyte (type B, pore diameter 0.2 gm) or in oxalic acid electrolyte (type F, pore diameter 0.1 ~m). Similar membranes are available commercially from Anotec Separations Limited. Surface areas of membranes were determined by multipoint BET with nitrogen as the adsorbing gas. Solutions were prepared with water produced by reverse osmosis, ion exchange, carbon adsorption, and then microfiltration. Membranes were rinsed with such water for 1 h before characterization. High-purity aluminum oxide powders were obtained from Johnson-Matthey. All other chemicals were Analar grade. Electroosmosis experiments were carried out in NaC1 solutions at 10 -2 and 10 -3 M. Surface pH titration was carried out on 10-2 M NaC1 solutions. 3. RESULTS

3.1. Electroosmotic Measurements

Typical data showing the amount of electrolyte transported as a function of time for a type B membrane are shown in Fig. 1. The data show excellent linearity. Reproducibility was also generally excellent.

3.00

2iS0

I

I

I

I

I

t

30

40

50

60

--

200" -~ 1.50 :~ 1.00 •

Q

0.50

O,OC 10

20

'70

Time / s

FIG. 1. Etectroosmotic flow at type B aluminum oxide membrane. 10 -3 M NaC1, pH 9.0. Journal of Colloid arid Interface Science, Vol. 143,No. 1, April 1991

Under the limiting conditions of large pore size and high electrolyte strength the electrolyte flow through the pores may be related to membrane ~"potential by means of an equation due to Smoluchowski (4), V = Ie~/~lXo

[1]

where Vis the flow r a t e , / t h e applied current, the electrolyte permittivity, ~"the ~"potential, ~/ the electrolyte viscosity, and X0 the bulk electrolyte conductivity. That is, the ~'potential may be calculated from the slope of plots such as Fig. 1. ~"potentials calculated using Eq. [ 1] will be given the symbol ~'s. This limiting expression applies relatively well in 10-2 M solutions and somewhat less well in 10 -3 M solutions. A more thorough theoretical analysis of flow in fine cylindrical capillaries has been presented (15). This analysis assumed steady low Reynolds number flow in a circular tube with walls of uniform potential. The Poisson-Boltzmann equation describing the potential distribution normal to the pore walls was solved using an approximate analytical procedure. Assuming an uni-univalent electrolyte with cations and anions of equal mobility an equation of the form V = (IE~/nXo)F

[2]

was derived, where F is the factor which must be applied to Smoluchowski's result. F is a function of ~ and Kr, where K is the Debye parameter and r is the pore radius. In the analysis of the present data we have used this approach, but with a numerical solution of the Poisson-Boltzmann equation that allows for ions of differing mobility (A. E. James and D. J. A. Williams, to be published). ~"potentials calculated using Eq. [ 2 ] will be given the symbol ft. The pH dependence of the ~"potential of a type B membrane is shown in Fig. 2 at two ionic strengths, both ~s and fi being shown. The overall pattern of a negative ~-potential at high pH falling and becoming positive as the pH is lowered is consistent with proton equilibria at the membrane surface. The values of ~'sand ~'lare very similar in 10-z Msolution

MEMBRANE SURFACE ELECTROCHEMISTRY 80

J

;

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40 -

> 0

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6.0

70

I

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pH 200

I

I

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•

i (b)

1000I -100

-%

~o_ m -200 N -300 I -q00/ 2,0

Fig. 4. The reproducibility of the titrations was good. The curves have been corrected by subtraction of the acid required for the titration of the supporting electrolyte. The most striking feature of the curve is that it shows inflection points in the region of pH 7.0 and also in the region of pH 4.0. This is made clear in the differential plot also shown in the figure. Such sharp inflection points are unusual for solid surfaces; however, further titration of the supporting electrolyte in the absence of the membrane after the surface titration showed that the initial data were indeed a property of the surface alone. A typical surface titration curve for the type F membranes is shown in Fig. 5. The titratable surface charge is lower than is the case for the type B membranes. Also the clear inflection point in the region of pH 7.0 is no longer ap-

80

I

I

3.0

4-.0

[ 5.0

[

r

6.0

70

I B.0

255

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pH

FIG. 2. p H d e p e n d e n c e of ~-p o t e n t i a l for t y p e B m e m brane. (a) 10 -2 M NaC1. (b) 10 -3 M NaCI. (©) gs. (rq)

ft.

>E 40 -20 -& m N

but differ appreciably in 10-3 M solution. The magnitude of the ~"potential is substantially greater than that which we have previously found for polymeric membranes (7, 8). The is©electric point (pHiep), that is, the pH at which the membrane had a ~"potential of zero, was at pH 4.51 in 10 2 M s o l u t i o n and at pH 4.03 in 10-3 M solution. The pH dependence of the ~"potential of a type F membrane is shown in Fig. 3 at two ionic strengths. The overall pattern is similar to that for the type B membranes, though the magnitude of the ~ potential is appreciably lower. For this membrane in 1 0 - 2 M solution pHiep = 3.05 and in 10 3 M s o l u t i o n P H i e p = 3.75.

20 2 40

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3.2. Surface pH Titration A typical surface titration curve for the type B membranes in 10-2 M solution is shown in

[ 20

-40

FIG. 3. pH dependence of ~ p o t e n t i a l for type F m e m brane. ( a ) 10 -2 M NaCI. (b) 10 z3 M NaC1. (©) ~'~. (~q) ~1.

Journal of Colloid and Interface Science, Vol. 143, No. I, April 1991

256

BOWEN

1

I

I

AND

I

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100

(a)

5 ~_ 8O

N 60 x: u -g -'~ l,o i2

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J 70

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HUGHES

tratable surface charge over the whole pH range studied, superimposed on which were broad inflection points in the pH region 7.06.5 for the a-oxide and 4.5-4.0 for both oxides. On the basis of this comparison it is possible to provide a preliminary identification for the type B membrane suggesting that the inflection point at pH 7.0 is due primarily to phosphate incorporated within the matrix of the membrane (there is no free phosphate in solution during these measurements) with some contribution from aluminum oxide surface groups and that the inflection point at pH 4.0 is due to aluminum oxide surface groups. For the type F membrane a preliminary identification suggests that the inflection point at pH 6.5 is due to aluminum oxide surface groups and the inflection point at pH 4.0 is due to both aluminum oxide surface groups and incorporated oxalate groups. 20

I 9.0

I

10.0

FIG. 4. pH surface titration of type B membrane. 10 -2 N a C 1 . ( a ) Titration curve, (b) Differential titration curve. The curves contain 97 experimental data points.

I la)

_16 E u 12

M

~ 8

parent, though there is an inflection point in the region of pH 6.5 and a sharp inflection point in the region of pH 4.0. The type B membranes were manufactured in phosphoric acid electrolyte and the type F membranes were manufactured in oxalic acid electrolyte. As mentioned previously, it is known that the acid anions become incorporated into the porous structure during manufacture. Phosphoric acid has three ionizable protons with pKj = 2.15-2.23, pK2 = 7.17.21, and pK3 = t2.3-12.4; oxalic acid has two ionizable protons with pK1 = 1.25 and pK2 = 4.23-4.28 (16). Titration of these acids was used as a test of the automated titration system, good agreement with these values being obtained. We have also carried out surface pH titrations on a- and 7-aluminum oxide powder dispersions. Both materials had tiJour~ctl of Colloid and Interface Science, Vol. 143, No. 1, April 1991

30

E &,O

i m S.D

6.~

70

80

]

t

I

90

pH

I

I

(b)

01-------~--

r

]

-:2 <

-~ 3.~0

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I ,60

I 70

i ~0

9.0

pH F I G . 5. pH surface ~tration of type 'F membrane. 10 -2 M N a C I . ( a ) Titration curve. ~(b) Differential titration

e u ~ e . The curves ,contain 4:2 experimental data points.

MEMBRANE SURFACE ELECTROCHEMISTRY 4. DISCUSSION

The morphology of these aluminum oxide porous films can be observed by electron microscopy and the composition determined by various analytical procedures. The alumina ceils of the films (and hence membranes) are arranged in approximately hexagonal packing, with a pore located at the center of each cell. An important feature of such films is that polyvalent anions from the electrolyte solution become chemically bonded within the matrix of the film ( 11 ). When anodizing, oxide forms at both the metal/oxide and oxide/solution interfaces corresponding to the field-assisted transport of O 2- and A13+ through the film. The A13+ ions reaching the oxide/solution interface react with polyvalent anions from the electrolyte solution (PO 43-, (COO) 22-) as well as O 2- ions to form the outer phosphate or oxalate incorporating part of the film (10). Magic angle spinning N M R studies have shown that the aluminum in films formed in phosphoric acid has pentacoordination, while the aluminum in films formed in oxalic acid has tetra-, penta-, and hexacoordination ( 17 ). The average bulk level of anion incorporation has been found to be 7.6% PO43- for films formed in phosphoric acid and 2.4% (COO) ~- for films formed in oxalic acid ( 11 ). However, the incorporated phosphate level varies both through the depth of the film and from the bulk to the pore surface. Thus, it has been found by chemical sectioning combined with X-ray and solution analysis that the P / A1 ratio was almost 0.1 at the face of an anodic film that faced the solution during manufacture, decreasing steeply to about 0.03 at a depth of approximately 5 nm; the ratio then remained constant to a depth of nearly 50 nm (10). Using XPS data the composition of the outer part of films formed at 50 V, for example, has been represented as A120292( O H )0.48 ( P 0 4 )0.056 o r A1202.92 ( P O 4 )0.056 ° 0.26 H20. The composition is electric field dependent, increase in electric field strength enhancing deprotonation of H2PO4 and HPO 2- to form PO43- which has a higher co-

257

ordinating ability toward A13+ ions (10). Luminescence and ESR studies of films produced by anodization in oxalic acid solutions, which have a yellow coloration, have been interpreted in terms of intramolecular charge transfer between a l u m i n u m ions and oxalato ligands within complexes of the type Al[Al(C204)3] • n H 2 0 (18). It has been found by scanning transmission electron microscopy with energy-dispersive Xray analysis ( S T E M / E D A X , probe diameter 25 nm) (12) that the P/A1 ratio changes from 0.093 at a distance of ~ 18 nm from a pore wall to 0.014 at a distance of ~ 120 nm from the wall. Films formed in oxalic acid have been less well studied. Further, there has been no published information on the composition of the solid phase at distances of 1-2 nm from the pore wall/solution interface, which is the region responsible for the surface chemistry. Hence, the purpose of this section is to use the electroosmosis and pH titration data to provide a detailed description of the surface electrochemistry of the membranes. The analysis will be applied to the data obtained for 10 -2 M solution, an ionic strength readily amenable to both types of measurement and where the double-layer thickness is sufficiently small compared to the pore diameter for the pH of electrolyte in the bulk of the pores to be essentially the same as that of the solution outside the membrane. At this ionic strength, ~'s and ~'~are very similar, so there is no ambiguity in the value of the ~"potential. Also this is an ionic strength of practical interest as it is typical of that occurring in industrial processing of biological materials. Two approaches will be adopted. First, a site dissociation model is used in conjunction with a triple-layer model of the interface. It is shown that such an approach gives only a reasonable fit to experimental data for physically unreasonable values of the capacitance of the inner region of the solution part of the electrical double layer. Second, a site dissociation model is incorporated into a gel model of the solid side of the interface. This gives good prediction of both the surface charge density and ~'-potential data. Journal of Colloid and Interface Science,

Vol. 143,No. l, April 1991

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BOWEN AND HUGHES

4.1. Site Dissociation-Site Binding Model (Triple-Layer Model) The simplest models of the electrolyte/pore wall interface would describe the electrical double layer in terms of a charged plane at the solid surface with a diffuse layer of counterions in the solution, the distribution of which is given by the Poisson-Boltzmann equation. This is known as the G o u y - C h a p m a n model (4), and treats the ions as being point charges. The finite size of the real ions will, however, limit the inner boundary of the diffuse part of the double layer since the center of a hydrated ion can approach the surface only to within its hydrated radius. Thus, a refinement is to divide the double layer into two parts separated by a plane, the Stern plane, located about a hydrated radius from the surface. A further refinement is to distinguish between the Stern plane, also called the outer Helmholtz plane, and an inner Helmholtz plane (IHP). The ions in the inner Helmholtz. plane are considered to be dehydrated, at least in the direction of the surface, and are said to be specifically adsorbed. This is known as the G o u y C h a p m a n - S t e r n - G r a h a m e (GCSG) or triplelayer model. Figure 6 is a diagrammatic representation of this model where ~b0, ~¢, and

6,

%

~d

~bd are the potentials at the surface, IHP and O H P respectively; a0 and cr~ are the charge densities at the surface and IHP, and ~d is the charge density of the diffuse double layer. The analysis of the origin of surface charge to be used initially is the site dissociation model (19, 20). This treats the surface as a two-dimensional array of acid-base sites. When used with an appropriate model of the double layer, in the present case the triple-layer model, this can provide an interpretation of both pH titration and electrokinetic data. Such description of experimental data, rather than the gaining of physical insight into the nature of the electrical double layer, is the primary goal of the present work. It has been shown that a number of models for the double layer based on two-dimensional arrays of acid-base sites, and the adjustable parameters associated with each model, can all represent data for oxide/solution interfaces equally well (21). Further, a range of parameter values can in each case yield optimal fit (21, 22). This has to be borne in mind when attributing physical significance to the parameters. Compared to simpler models of the double layer, the triplelayer model has the important advantage of providing values of ~bd which can be used as estimates of the electrokinetic potential. The aluminum oxide surface consists of amphoteric sites which can become either positively or negatively charged depending on the pH. Such equilibria can be represented by (23), K1 H+ MOH ~ ~ MOH + K2 M O H ~ M O - + H +.

Surface IHP

OHP

,

.

FIG. 6. Schematicrepresentationofdouble-layer structure used in site dissociation-sitebinding model. Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991

[3 ] [4]

It will be assumed that the membrane pore surface is homogeneous. (An alternative possible representation of the charging mechanism for such surfaces is the one-pK model (24) with a single equilibrium, M O H 1/2+ = MOHI/2 - + H+). F o r the type B membranes over the pH range t o be considered, ionization of a singly charged phosphate site to give a doubly charged phosphate site needs to be considered:

MEMBRANE SURFACE ELECTROCHEMISTRY PH

K~ ~- p2- + H +.

[5]

For the type F membranes over the pH range to be considered ionization o f a carboxyl type group needs to be considered, K~ x

C O O H ~ C O O - + H +.

[6]

It is assumed that if the oxalate retains its integrity in the membrane structure, the second carboxyl group takes part in binding to aluminum oxide groups. There is an extensive literature on the adsorption of polyvalent anions, especially phosphate, on inorganic oxide surfaces (25-27). This includes spectroscopic studies aimed at identifying the chemical nature of the complexes formed on adsorption (27). However, as previously discussed, the phosphate in the present work is already incorporated into the three-dimensional matrix of the membranes. The concentration of protons in the surface plane [H]s is related to bulk concentration [H ]b by the Boltzmann distribution [Hls = [H]bexp(--~o)

[7]

where ~}0is the reduced potential at the surface (e~o / k T ) . Equilibria at the surface are written in the normal way, for example, KI = [ M O H ] [ H l s / [ M O H ~ - ] .

[81

The total number of ionizable sites at the surface (N~) is the sum of the ionizable oxide sites (Nmo) and the ionizable phosphate (Np) or oxalate sites (Nox): Ns=Nmo+Nv

or

[91

N,=Nmo+No×.

Further, the ratio of metal oxide to phosphate sites is denoted by q, using the appropriate form q = Nmo/Np

or

q = Nmo/Nox.

[10]

It may then be shown that for the type B membranes the total surface charge (a0) at any pH is given by (To = - e N ~ ( A + 2 B - qC + q D ) / ( q + 1)

259

charge is given by ~0 = - e N S ( B - q C + q D ) / ( q +

1)

[12]

where A = 1/(1 + (K3/[H]s)), B = 1/(1 + ([HIs/K3)), C = 1/(1 + K I / [ H ] s + KIK2/ [H]2), D = 1/(1 + [H]2s/KIK2 + [H]s/K2), and e is the electron charge. Simple calculations show that a G o u y Chapman description of the double layer is inadequate for surfaces with the high charge densities measured for these membranes. The double layer then needs to be considered using the GCSG model, taking into account the interaction of cations and anions with the surface groups. This leads to the site dissociation-site binding model (13). In this model the total titratable surface charge is still given by Eqs. [11] and [12], but the anions and cations are considered to form ion pairs with surface groups of opposite sign of charge, the locus of the centers of such ions being at the inner Hetmholtz plane. A series of equilibria at the inner Helmholtz plane are then define as K4 M O H ~ + C1- ~ MOH2C1 [ 13 ] M O - + Na + ~ MONa; for the type B membrane K6 P H - + Na + ~ PHNa K7 p2- + Na + ~ PNa-;

[141

[ 15 ] [16]

and for the type F membrane K8

C O O - + Na + ~- COONa.

[ 17 ]

The identities on the right-hand side represent interfacial ion pairs. The concentrations of counterions at the IHP are given by [Na+]~ = [ N a + ] b e x p ( - - ~ ) [C1-]~ = [C1-]bexp(+~}e)

[18]

where the terms subscripted with b refer to bulk concentrations and the terms subscripted with/3 refer to the IHP. Equilibria at the IHP are then written in the normal way, for example,

[111 /£4 = [MOH2C1]/[MOH~] [C1-]exp(+~}e). and for the type F membranes the total surface

[19] Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991

260

BOWEN AND HUGHES

Development of this analysis gives explicit expressions for the concentrations of ions at the IHP for given values of Ns, q, @0, ~Pm,and the relevant equilibrium constants 1£1-[<28. The charge at the IHP can then be written as a m = e ( [ M O N a ] - [MOH2C1] + [PHNa] + [PNa-])

[20]

for the type B membranes, and o-m= e ( [ M O N a ] - [MOH2C1] + [COONa])

[21]

for the type F membranes. Further, electroneutrality requires or0 + a m+ o-d = 0

[22]

and the charge in the diffuse double layer is given by (4) aa = -11.74C1/2sinh(19.46z~a)

[23]

where C is the bulk electrolyte concentration (mole liter -~) and ~d is the potential at the outer Hetmholtz plane. The potential and charge relationships in the compact double layer are given by (4) ~o = ~m + ~o/K~

[24]

tPm = ~Pd -- ~rd/K2

[251

and,

where K ~and K 2 a r e the integral capacitances of the inner and outer regions of the compact layer, respectively. Use of this approach for the interpretation of the experimental electrokinetic and surface pH titration data requires some preliminary consideration. First, the ~"potential as determined by electroosmosis is the potential at the plane of shear between the moving and stationary phases. The location of the plane of shear is not known exactly, but the ~"potential cannot correspond to a potential nearer the solid surface than ~pj, since ffd is the potential at the plane of closest approach of fully hydrated counterions. There is strong evidence that the assumption ~" = ffa, which will be made in the present work (using ~'l), provides Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991

a viable interpretation of a wide range of experimental data (4). Second, a knowledge of the pH at which the surface has zero net charge, pHpzc, is required to convert the titratable charge values found by hydrogen ion titration to absolute surface charge values. The identification of the pHpzc requires hydrogen ion titration data at different ionic strengths in an inert electrolyte, that is, an electrolyte that is not specifically adsorbed. This is a very difficult exercise (4). If there is no specific adsorption, then pHpzc = p H i e p , where p H i e p is the pH at which the surface has a ~"potential of zero, and is readily determined. It is known from the experimental data that pHiep depends on the ionic strength, suggesting that specific adsorption has occurred. At infinite dilution there could be no specific adsorption, but such measurements are not experimentally accessible. Hence, in the analysis of the data for 1 0 - 2 M solution it will be assumed that the pHpzc is equal to the pHiep measured in 10 -3 M solution, the lowest ionic strength studied, and where the occurrence of specific adsorption will be decreased. Third, capacitance values for the inner ( K 1) and outer ( K 2) regions of the compact double layer are required. The capacitance for unit area with units of uF cm -2 is given by K = 0.8854D/d

[26]

where D (dimensionless) is the dielectric constant of the region and d (nm) is the distance between the relevant planes ( d 1 or d2). Due to the high electric field gradients, considerable dipole orientation is expected to occur in these regions. The region between the wall and the IHP is usually thinner and the field strength higher than the region between the IHP and the OHP. Values o f d I = 0.15 nm, d 2 = 0.6 nm, D 1 = 6, and D 2 = 20 have been considered reasonable (4). This value of D ~ corresponds to measurements in bulk water at high frequency where the contribution of the rotation of the water molecules is negligible (28). Values o f D 2 much closer to the value for bulk water at low frequency (D = 79) have also been used (29). The Pauling ionic radii of

MEMBRANE SURFACE ELECTROCHEMISTRY chloride and sodium ions are 0.181 and 0.098 nm, respectively (30). Hence, approximating average values of these radii and considering values used by previous workers, in the present work it has been assumed that d~ = 0.15 n m and d 2 = 0.5 n m ( = 2 . ionic radius + diameter of water molecule). Initial values of the dielectric constants used were D 1 = 10-40 and D 2 = 39.5 or 79. This results in values for the capacitances o f K 1 = 60-240 ~F cm -2 and K 2 = 70-140 #F cm -2. Initial calculations showed that this variation o f K 2 had little effect on the overall analysis, so the higher value was used. Having established these values, o-d was calculated from Eq. [23] for various values of ~', corresponding values of ~# from Eq. [ 25 ], and values of ~o from Eq. [ 24 ]. For this last calculation a value of o'0 was determined at the p H value corresponding to each value of f by interpolation of the titration curves. Nonlinear parameter estimation (Micromath Scientific Software) was then used to determine Ns, q, KI, K2, and K3 using Eq. [ 11 ] or [ 12 ] and the experimental profiles of ~0 versus pH. Initial values of these parameters were based on the preliminary interpretation of the experimental titration data (Section 3). The optimized values obtained were then used to calculate ~# as a function of p H using Eq. [ 20 ] or [ 21 ], with values of K4-K8 in the range 0.1-1000, Eq. [22] being used as a criterion of a successful fit of the data. It was not possible to provide a satisfactory fit of the data using values of K I in the range 60-240 uF cm -2 as negative values of Ns (the total number ofionizable sites) were obtained. For the type B m e m b r a n e s positive values of Ns were obtained only for K l > 760/sF cm 2, and for the type F membranes, for K ~ > 400 #zF cm -2. The fit to the experimental data improved as K ~ was increased, though after K 1 = 5000 uF cm -2 the i m p r o v e m e n t was small. Such fitted data are shown in Fig. 7 for the type B m e m b r a n e and in Fig. 8 for the type F membrane, in both cases for a value of K ~ which just allows fitting to physically meaningful values and for the m a x i m u m value used. The best-fit values of the parameters are

261

z~O

i

I

I

20 =L 0

%

=~ -20 -z+O - -60 -80 I 3.0

I 40

50

I

I

I

60

70

80

90

pH

FIG. 7. Experimental and calculated surface charge density values for type B membrane. Site dissociationsite binding model. (O) Experimental.(zX)Calculatedwith K 1 = 800 #F cm-2. (r-l) Calculated with K ~ = 5000 p~F cm

2.

given in Table I, values ofK4-K8 = 100 being used. The values of Ns are physically reasonable, the m a x i m u m theoretical packing density of oxide sites on a surface being of the order of 5 X 1014 cm -2 (14). The values o f q show that there are about 1.6 times more incorporated phosphate sites than oxalate sites at the surface of the respective membranes. This compares to the analysis of the bulk anion content of anodic films where it was found that the corresponding ratio was 3.2 ( 11 ). The present data show that the phosphate content at the surface of the membranes is substantially greater than in the bulk of such porous films. Thus, S T E M / E D A X analysis of films gave values o f q of 71 at an average distance of 120 nm from a pore wall and a value of 10.8 at an average distance of 18 n m (12). Although all the values shown in Table I are physically reasonable, the earlier comments regarding the difficulty of using numerical methods to obtain a unique set of parameters should be borne in mind (21, 22). This approach gives valuable insights into the nature of the m e m b r a n e / s o l u t i o n interface. One weakness of the approach is the failure to allow reasonable fitting of the experimental a 0 / p H profiles at low pH. This is probably due primarily to irregularities in the calculation of the surface p H when Eq. [ 7 ] is Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991

262

BOWEN AND HUGHES

used at high values of~o. This simple equation does not allow for the fact that the proton is in an environment of low D at the interface. More importantly, very high values o f K l are required. For K 1 = 5000 #F cm -2, the effective distance between the surface and IHP ( d 1) is 0.0011 nm or 0.014 n m for the m i n i m u m and maximum likely values of D ~ of 6 and 79, respectively. These distances are much smaller than the ionic radii of the electrolyte ions. A possible physical interpretation is that the ions may have penetrated the surface. A formal description of this possibility may be provided by the gel model.

4.2. Gel Model (Incorporating Site Dissociation) The characteristic feature of the gel model (Fig. 9) is the postulation that surface groups are present not only in a two-dimensional array at the solid/electrolyte interface, but also in a volume phase of finite thickness extending from the surface into the interior of the solid (14). Counterions are also allowed to penetrate the solid phase. The interface region is then described in terms of such a gel layer and the diffuse layer in the solution. The model presented here will be a modification of Lyklema's original treatment that allows for the change in the degree of ionization of the 80

I

I

i

TABLE I Parameters Calculated from the Site Dissociation-Site Binding Model

Parameter

Type B membrane

Type F membrane

N, (sites cm -2) q pKl pK2 pK3

4.8 X 1014 1.6 4.1 6.2 6.9

2.0 X 1014 2.6 4.0 7.0 4.0

charge-determining groups with pH. That is, a three-dimensional array of acid-base sites with equilibria described by Eqs. [ 3 ] - [ 6 ] will be treated. The model will initially be written for a negative membrane surface and positive counterions. It is assumed that the penetration depth is small compared to the radius of curvature of the surface and that the total number of sites per square centimeter at any plane in the gel layer [Ns(x)] depends only on the distance from the surface (x) in an exponential manner, Ns(x) = Ns(O)e -ax

[27]

where Ns(0) is the number of sites at the interface. The penetration depth is then represented by a -l , the distance over which the

I I

i

60

I

~ ~o

Yo = (-e~/kT)

~ o ~ -2o -L,O

I 2.0

3.0

I z~.O

I

I

1

I

5.0

6.0

70

8.0

9.0

pH

FIG. 8. Experimental and calculated surface charge density values for type F membrane. Site dissociation-site binding model. ( 0 ) Experimental. (A) Calculated with K l = 500 ttF cm -2. (El) Calculated with K ~ = 5000 #F cm -2" Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991

o'd

%-0 m

Diffuse [ayer

[ayer

Sotufion

Gel

Sotid

(gel)

FIG. 9. Schematic representation of gel model.

MEMBRANE SURFACE ELECTROCHEMISTRY number of groups decays to 1/e times the number at the interface. Integration gives, Ns =

N s ( x ) d x = Ns(O)/a.

[281

From the previous analysis it is possible to write for the type B and type F membranes, respectively, Q=(A Q = (B-

+ 2B-

qC + q D ) / ( q + 1)

dimensionless quantities, y and u. The important difference from the original Lyklema model here is that Q is a function ofy. Further, it may be shown that the charge per square centimeter is given by ~ro = - e N s

O" m

O(x) = I Z l n m ( x ) / Q N d x )

[29]

where nm(X) is the number ofcounterions per square centimeter and z is their valency. The distribution ofcounterions is assumed to obey a Langmuir-type equation where there exists equilibrium between counterions in the bulk and those in a thin layer of thickness dx at a distance x from the surface. Then, 0/(1 - 0 ) = ( C/55.5 ) e x p ( - z e ~ p / k T ) e x p ( 4 ~ / k T ) = B exp(y)

[30]

where C is the electrolyte concentration, y = - ~ , and ~ is the specific adsorption energy. The relationship between the potential and space charge density, p, is given by Poisson's equation which in the present analysis becomes the Poisson-Langmuir equation, d2y / du 2 = p/c = ( e Z z / & T a 2 ) ( N d O ) e - U Q - NdO)e-UQO) = (e2zNs(O)Q/ckTa 2) (e-U~(1 + BEY))

[31]

where u = ax and ~ is the gel permittivity. This gives the potential distribution in terms of two

e "Qdu

[321

again a function of y, and that the charge per unit area due to counterions is given by

qC + q D ) / ( q + 1)

where Q is the fraction of available charge in the ionized state, from Eqs. [ 11 ] and [ 12 ], and where the present analysis starts to differ from Lyklema's original model. The fraction (0) of the negative charge that is compensated by the counterions is given by

263

----

zeNs

BeY-"Q

/

(1 + BeY)du.

[33]

The equations to be solved are [ 31 ], [ 32 ], and [ 33 ]. For a positively charged surface the righthand side of [ 31 ] becomes negative, and the right-hand side of [ 32 ] becomes positive. The right-hand side of [33] changes sign with z. The equations were solved numerically, using NAG subroutines DO2BBF and D O I G A F as a basis, with initial conditions corresponding to the interior of the gel of u = 20, y = 0, dy/ du = 0. Following Lyklema (14) a value of D g = 15 was used for the dielectric constant of the gel. Initial values of the variables in Q were selected using the optimized values from the site binding-site dissociation model. They were subsequently varied systematically, together with the new parameters of a and B, to give the best fit to both the a0/pH and ~'/ pH profiles. The best-fit numerically calculated values of y0 and o-0are compared to the corresponding experimentally determined parameters, -~" and a0, at various pH values in Table II for both type B and type F membranes. It should be noted that this approach gives an a priori prediction of both parameters. The overall agreement between predicted and experimental values is good, especially for the type B membranes and at the higher pH values. The values of the best-fit parameters are given in Table III. The values of a -1 are a measure of the thickness of the gel layer on the membrane pore walls. The values of B correspond to q~/ k T = 13. The values of both a -l and B are physically reasonable. The fit is quite sensitive to both of these variables, changes in a -1 of Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991

264

BOWEN AND HUGHES TABLE lI Experimental Values of Y0 (= - e ~ / k T ) and a0 Compared with Best-Fit Values from Numerical Analysis of Gel Model .Vo

pH

o-o(uC cm-2) Numerical analysis

Experimental

Experimental

Numerical analysis

~rm(#C cm-2)

ad (#C cm-2)

-70.1 -53 -36.9 -28.3 - 19.4 -9.6 -0.06 6.32

69.1 52.1 36.2 27.7 18.9 9.3 0.06 -6.1

0.98 0.85 0.69 0.58 0.45 0.26 0 -0.25

-16.0 -15.9 - 14.6 - 12.4 -9.0 -3.85 1.32 5.93 .

15.6 15.4 14.2 12.1 8.7 3.7 - 1.3 -5.7

0.42 0.42 0.39 0.34 0.26 0.12 -0.04 -0.22

(a) Type B membrane 7.98 7.03 5.99 5,45 4,99 4,51 3,99 3,52

3.14 3.1 2.34 2.11 1.18 0 - 1.22 -2.3

3.17 2.74 2.21 1.88 1.45 0.84 0.01 -0.8

-71.6 -46.5 -30.4 -28.1 -24.4 -20.1 3.3 22.6 (b) Type F membrane

7.98 6,98 5.98 5,49 5.04 4.52 4.03 3.54 3.05

0.94 0.44 0.69 0.69 0.56 0.84 0.64 0.69 0

0.87 0.86 0.81 0.71 0.53 0.25 -0.09 -0.45 -0.72

-13.8 -13.6 - 11.1 - 10.7 - 10.2 -9.0 -4.2 6.2 .

_+0.1 nm or changes in 4~/kTof +1 giving a significantly worse match to the experimental data. The values of N~ are lower than those obtained with the site dissociation-site binding model (see Table I). The values of pK~ and p/£3 are comparable for both models. The two models give significant differences in the values of pK2. The value of q for the gel model apTABLE III Parameters Calculated from the Gel Model

Parameter

Type B membrane

Type F membrane

a -1 (m) B Ns (sites cm -2) q pKI pK2 pK3

1.1 x 10-9 29.32 2.5 X 1014 2.0 4.1 5.0 6.9

0.7 × 10-9 29.32 1.0 × 10 TM 2.6 4.0 5.0 3.6

Journal of Colloid and Interface Science, Vol. 143,No. 1, April 1991

.

.

plied to the type B membranes indicates a somewhat lesser incorporation of phosphate than did the site dissociation-site binding model. For the gel model, most of the titratable surface charge is compensated by the presence of counterions in the gel layer. 5. CONCLUSIONS

The aluminum oxide membranes studied in the present work have modest values of ~" potential and high titratable surface charge. A satisfactory description of the membrane / solution interface should account for both of these properties. The incorporation of anions during the manufacturing process has a substantial effect on the surface electrochemical properties of the membranes. Models describing the membrane surface in terms of a twodimensional array of aluminum oxide and phosphate or oxalate groups can give only a reasonable fit to the experimental surface

MEMBRANE SURFACE ELECTROCHEMISTRY charge d e n s i t y / p H profiles if physically u n reasonable values for the thickness or dielectric c o n s t a n t of the i n n e r part of the double layer in the s o l u t i o n are used. Nevertheless, such models provide insights into the ratio of alum i n u m o x i d e / i n c o r p o r a t e d a n i o n groups at the m e m b r a n e surface a n d i n t o the p K values of these groups. However, a m o r e satisfactory approach is to describe the m e m b r a n e surface as c o m p r i s i n g a t h r e e - d i m e n s i o n a l array (gel) of charged groups a n d considering that both porous a n d c o u n t e r i o n s m a y penetrate this gel region. This a p p r o a c h allows the a priori prediction o f both surface charge d e n s i t y / p H a n d ~"p o t e n t i a l / p H profiles. This allows estimation of the thickness o f the gel layer, the specific a d s o r p t i o n energy o f c o u n t e r i o n s , the ratio of a l u m i n u m o x i d e / i n c o r p o r a t e d a n i o n groups, a n d the p K values of charge d e t e r m i n i n g groups. All o f the estimated parameters are physically reasonable. This gel model provides a good description of the m e m b r a n e surface. ACKNOWLEDGMENTS This work was supported by Alcan International Ltd., including provision of a Research Assistantship for Dr. Diana Hughes. We thank Dr. Robin Furneaux for many valuablediscussionsand much encouragement. We thank Dr. Hoze Sabuni for collaboration in the implementation of computer solutions. REFERENCES l. Bowen, W. R, I. Chem. E Syrup. Ser. 105, 37-46 (1987). 2. Cheryan, M., "Ultrafiltration Handbook," p. 53. Techomic Publishing Co. Inc., 1986. 3. Bungay, P. M., in "Synthetic Membranes: Science, Engineering and Applications" (P. M. Bungay, H. K. Lonsdale,and M. N. de Pinho, Eds.), NATO ASI Series C, Vol. 181, p. 109. Reidel, Dordrecht, 1986. 4. Hunter, R. J., "Zeta-Potential in Colloid Science," Academic Press, New York, 1981. 5. Bowen, W. R., and Hughes, D. T., in "Proceedings of the First International Conference on Inorganic Membranes," MontpeUier, 1989, pp. 147-152. 6. Bowen, W. R., and Hughes, D. T., Z Mere. Sci. 51, 189-200. 7. Bowen, W. R., and Clarke, R. A., J. Colloid Interface Sck 97, 401-409 (1984).

265

8. Bowen, W. R., and Cooke, R. J., J. Colloid Interface Sci. 141, 280-287 (1991). 9. Furneaux, R. C., Rigby, W. R., and Davidson, A. P., Nature (London) 337, 147-149 (1989). 10. Takahashi, M., Fujimoto, K., Konno, H., and Nagayama, M., J. Electrochem. Soc. 131, 1856-1861 (1984). 1I. Alvey, C. E., Wood, G. C., and Thompson, G. E., Proc. Interfinish 80, 275-280 (1980). 12. Thompson, G. E., Furneaux, R. C., Wood, G. C., and Hutchings, R , J. Electrochem. Soc. 125, 14801482 (1978). 13. Yates, D. E., Levine, S., and Healy, T. W., J. Chem. Soc. Faraday Trans. 1 70, 1807-1818 (1974). 14. Lyklema, J., J. Electroanal. Chem. 18, 341-348 (1968). 15. Levine, S., Marriot, J. R., Neale, G., and Epstein, N., J. Colloid Interface Sci. 52, 136-149 (1975). 16. Butler, J. N., "Ionic Equilibrium. A Mathematical Approach," p. 208. Addison-Wesley, Reading, MA, 1964. 17. Farnan, I., Dupree, R., Forty, A. J., Jeong, Y. S., Thompson, G. E., and Wood, G. C., Phil. Mag. Lett. 59, 189-195 (1989). 18. Shimura, M., J. Chem. Soc. Faraday Trans. 1 72, 2248-2256 ( 1975). 19. Healy, T. W., and White, L. R., Adv. Colloid Interface Sci. 9, 303-345 (1978). 20. Davis,J. A., James, R. O, and Leckie,J. O., J. Colloid Interface Sei. 63, 480-499 (1978). 21. Westall, J., and Hohl, H., Adv. Colloid Interface Sci. 12, 265-294 (1980). 22. Koopal, L. K., Van Riemsdijk, W. H., and Roffey, M. G., J. Colloid Interface Sci. 118, 117-135 (1987). 23. Huang, C.-P., and Stumm, W., J. Colloid Interface Sci. 43, 409-420 (1973). 24. Hiemstra, T., Van Riemsdijk, W. H., and Bruggenwert, G. M., Neth. J. Agric. Sci. 35, 281-293 (1987). 25. Chen, Y. R., Butler, J. N., and Stumm, W , J. Colloid Interface Sci. 43, 421-436 ( 1973). 26. Van Riemsdijk, W. H., and Lyklema, J., J. Colloid Interface Sci. 76, 55-66 (1980). 27. Tejedor-Tejedor, M. I., and Anderson, M. A., Langmuir 6, 602-611 (1990). 28. Gileadi, E., Kirowa-Eisner, E., and Peciner, J., "Interfacial Electrochemistry," p. 15. Addison-Wesley, Reading, MA, 1975. 29. Weise,G. R., James, R. O., Yates, D. T., and Healy, T. W., in "International Review of Science. Electrochemistry: Physical Chemistry," Series 2, Vol. 6, pp. 53-102. Butterworths, London, 1976. 30. Cotton, F. A., and Wilkinson, G., "Advanced Inorganic Chemistry," 3rd ed., p. 52. Interscience,New York, 1972.

Journal of Colloid and Interface Science, Vol. 143, No. 1, April 1991