J. Phys. Chem. 1993,97, 3824-3828
Electrochemical Characterization of a Hemodialysis Membrane Feng Yan, Philippe Mjardin,' and Adrien Schmitt Institut Charles Sadron (CRM-EAHP), CNRS- ULP Strasbourg 6, rue Boussingault, 67083 Strasbourg Cedex, France
Christian Pusinerit HOSPAL-R & D Int,, BP21, F-69881 Meyzieu Cedex, France Received: December 30, 1992
Transport parameters characterizing a commercial hemodialysis membrane (AN69, Hospal), with and without pretreatment with an adsorbed albumin layer, were determined as a function of the external sodium chloride equilibrium concentration. Measurements included membrane potential, streaming potential, and electroosmosis data. Transference numbers of cations and water were directly calculated from these data and were characteristic of high permselectivity a t low ionic strength. Model-dependent parameters of the charged membrane, such as potential and fixed charge density, were also calculated.
Introduction The performances of hemodialysis membranes are usually characterized by their ability to sieve or reject solutes during diffusive and ultrafiltration processes involving mass transport. However, little attention is generally paid to their electrochemical Wendt et a1.2 have shown that sieving properties of a Cuprophan membrane were well correlated by the KedemSpiegler equation, while those of AN69 were not, and the behavior of the latter was difficult to describe by any usual transport equation valid for a neutral membrane. While determining frictional coefficients, Collins and Ramirez3 showed that the membrane/solute frictional interactions were more pronounced with the AN69 than with thecuprophan membrane. Specifically, very high interactions between the strongly polar molecule sulfobromophthalein (BSP) and AN69 were observed. Bloch4 performed membrane potential and electroosmosis measurements with these two membranes and concluded that AN69 behaved as a cation-exchange membrane, whereas Cuprophan appeared to be neutral. These experimental results suggest that the transport properties and good clinical performanceSof the AN69 hemodialysis membrane are probably linked to its negative fixed charge density. Recent work has also shown that this charge could be useful in the adsorption of slightly positively charged copolymers aimed to passivate the membrane with respect to fibrinogen adsorption or platelet accumulation.6 The purpose of the present study was to evalute the effective fixed charge density and other electrochemical parameters such as transference number, permselectivity with respect to ions, and (potential of the AN69 membrane in order to provide an insight into its transport properties for solutes and hence its interactions with blood constituents.
Materials and Methods Membranes. Commercial AN69 hemodialysis membranes manufactured from a copolymer of acrylonitrile and sodium methallyl sulfonate were supplied by HOSPAL (Meyzieu, France). Some physicochemical properties of this membrane are given in ref 3 (Tables IV, IX, and X) and compared with those of the Cuprophan membrane. It is to be noted that the membrane resistance, defined as the reciprocal of the permeability coefficient, is much lower for AN69 than for Cuprophan for
nearly all solutes and that the AN69 membrane permeability is significantly reduced by protein adsorption. Beforeuse, membraneswere washed abundantly with deionized water (Super-Q, MILLIPORE) to remove free electrolyte and glycerine, which is added after manufacture to optimize conservation. Experiments were carried out at 25 f 0.2 "C in a thermostated chamber, using NaCl (99.5% pure) aqueous solutions at different concentrations. AN69-protein membranes (subsequently noted AN69-P) were obtained by adsorption from a solution of bovine albumin (0.35% w/w) in Tris buffer (0.05 M) containing NaCl (0.15 M) and NaN3 (10-3 M), pH 7.35, at 25 OC over a period of 16 h. Measurements of Membrane Potential. The device employed for membrane potential measurements was similar to that previously described.' Briefly, the membrane holder was clamped between two plexiglass half-cells, the membrane area exposed to flow being 0.5 cm2. Each compartment of approximate volume 60 cm3 was equipped with a silver/silver chloride electrode and integrated into a flow circuit including pump, flow meter, and reservoir havinga capacity of 2 dm3. The half-cells wereconnected to a U-manometer, and flow was adjusted so that the meniscus in each branch was at the same level, in order to ensure equal pressure in the two compartments. Cell potential was measured with a voltmeter (Keithley 197) and recorded as a function of time by a microcomputer, the concentrations C Iand Cl on either side of the membrane being chosen so that the ratio C,/C2 remained constant at a value of 2. Asymmetry between the two electrodes was generally negligible, in the presence or absence of a membrane. Measurements of Streaming Potential and Hydraulic Permeation. Thesamecell was used todetermine thestreamingpotential and hydraulic permeation in the absence of an electrical current. Hydrostatic pressure across the membrane was fixed by adjusting the levels of the solution reservoirs, and stirring was carried out by recirculating the same solution in the two compartments but was stopped immediately before measurements. To determine hydraulic permeation in the absence of current, the volume flow was calculated from the meniscus displacement in a capillary attached to the cell, under conditions of constant steady-state potential difference and hydrostatic pressure difference across the membrane.
Results and Discussion
* To whom correspondence should be addressed.
' Present address: Departement Silicones, RhBne-Poulenc Chimie. I8 Avenue d'Alsace, 92097 Paris-la-Defense Cedex 29, France. 0022-365419312097-3824%04.00/0
Phenomenological Flux Equations. Before presenting the experimental results, let us write down the linear flux equations 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3825
Characterization of a Hemodialysis Membrane necessary to describe the processes under study. We use the formalism introduced by Kedem and Katchalsky8 and further developed by Krtimer and me are^.^ If J I ,J,, and I are the cation, volume, and electric current fluxes, it may be shown that the appropriate conjugated forces are respectively AII/C,, (AP An) and AE where An and AP are the osmotic pressure and hydrostatic pressure differences between the outer solutions and AE is the potential difference measured with electrodesreversible to the anions. C, is the mean salt concentration defined by C, = An/[RTG(ln a,)] where as is the salt activity.
(1)
ow I
------\
-2
?
'
-
1
-10
-121
I '
'
'
'
20
0
.
'
'
60
40
'
I
100
80
I20
A h (cm water)
I = LE,AII/C, + LEp(AZ'- A n ) + LEAE
(2~)
In the absence of electric current, the relationship between J, and J I is given by
J, =
V,J, + VwJ,
lo-'
= FJ, / I = FL,E/ LE
(4)
1
1
t
10-(01
lo-'
T,
= FJ,/I = F(J, - V s J l ) / V w l
= LPE/LE &PILE = - ( u / W A , , , = o
(6)
The ratio L,E/LEmay be evaluated from the membrane potential AE,,,, since for I = 0 and AP = 0, eq 2c becomes
L E ~ I L= E G(LEP/LE - M / A n ) = &/LE Finally, the transference numbers from eqs 4-7: T+
T+
and
T,
(7) can be rewritten
= FC,[(&p/L,) - ( u / A n ) / . , p = o I
o
AN69
'
' " . ' " '
'
10-5
, ".''.'
,
,
, ,
Jv/l
i
, , . '
10-2
lo-'
100
IO'
C*(mol L-')
(5) = F(LpE/LE - VsLIE/LE)/Vw The term can be determined from electroosmotic flow data through the ratio J V / I(AP= 0, An = 0) or from streaming potential measurementsthrough M/AP( A n = 0, I = 0), provided the Onsager reciprocal relation holds for the membrane: (JJOAp,m=o
x dE/dP
AN69 AN69-P
t dE/dP 10-6
(3)
where J , and V, are the molar flux and partial molar volume of water and V, the partial molar volume of the salt. The transference numbers T+ of the cation and T , of water are easily expressed as a functionof the phenomenologicalcoefficients LnPfrom eq 2. In fact, when A l l = 0 and AP = 0, denoting by F the Faraday constant, T+
Figure 1. Streaming potential as a function of pressure difference at various salt concentrations for the albumin pretreated membrane. C,.,aCl (M) X 10' = 0.5, I , 2,4,8, and 16 (alternating open and closed symbols from bottom to top).
(8)
with
StreamingPotential and Hydraulic Permeation. Figure 1 shows the streaming potential difference AE,measured across the AN69 and AN69-P membranes as a function of the applied pressure difference AP expressed by the corresponding water height. At higher salt concentrations where the amplitude of LE, was small, it was necessary to take into account the asymmetry of the electrodes. The linear variation observed for both membranes, with or without adsorbed albumin, allowed us to use in subsequent calculations the experimental slope aE/aP as suggested by Broz and Epstein.10 Dependence of the streaming potential on the concentration of electrolyte was similar to that observed in electroosmosis studies4 at high concentrations for the same membrane (Figure 2), which confirms thevalidity of the Onsager
Figure 2. Streaming coefficient (&5/dP)llI=o.,.a for the untreated membrane (+) and the membrane pretreated with albumin (X)and (0) P =(from o ref 4) for the AN69 electroosmotic coefficient ( J , / ~ ) J ~ ~ = o , A membrane as a function of sodium chloride concentration. Linear regression lines for the untreated membrane (full line) and the albumin pretreated membrane (dotted line).
reciprocal relation expressed by eq 6. There was nevertheless a slight discrepancy below 10-I M. We used in our calculations linear fitting of the double logarithmic representation of aE/BP versus C,, Le., L E ~ / L=E (2.19 X 10-9)C,486for the AN69 membrane and (3.25 X 10-9)Cs479 for the AN69-P membrane. Hydraulic permeabilities Lpat zero current were calculated in the range of low applied pressure difference, where a linear relation was observed between volume flow and pressure difference, AP. Within experimental error, we found similar values of L p for the two membranes with a slightly lower figure for AN69-P: 0.9 X 1O-Ioas compared to 1.1 X m s-I Pa-' for AN69. This might be the result of increased hydrodynamic friction at the surface of the protein-coated membrane where the adsorbed layer may act as an interfacial barrier and within the larger pores where protein molecules may partially penetrate and be adsorbed. Membrane Potential. Cell potential, AEc, normalized to a maximum value of twice the Nernst potential, AEN, and membrane potential, AE,, across the AN69 and AN69-P membranes in contact with NaCl solutions at concentrations C, and Cz, with CI/C2= 2, are represented in Figure 3. The three potentials are connected via the relations:
AEN may be calculated using the co-ion (Cl-) activities a, ( i = 1, 2), equal to the mean ionic activities, as estimated from
Yan et al.
3826 The Journal of Physical Chemistry, Vol. 97, No. 15, 1993
4
+
20
I 6
i
I
t 0.01
l o L
io
0 2 1
'
'
"
'
'
"
10-2
" "
"""'
'
'
1 -10
1 00
10-1
C1 (mol/l)
Figure 3. Upper curves (left scale): Cell potential relative to twice the Nernst potential for the AN69 (open symbols, full line) and AN69-P (closed symbols, dotted line) membranes versus salt concentration C1 with CI/C2 = 2. Bottom curves (right scale): Corresponding membrane potentials versus salt concentration CI.
'50
a, = 2ckTKsinh(z+eS/2kT) z+e where k is the Boltman constant, Tthe temperature,e thesolution permittivity (equal to toe,, e, being the relative permittivity), z+ the valency of the couterions, and K the reciprocal of the electrical double-layer thickness. At 25 OC, for a 1-1 electrolyte with a, expressed in pC cm-2, [ in V, and C, in mol L-I, this relation becomesI3
100
us = 11.7C,'/z sinh(l9.5S)
. s - i E
Robinson and St0kes.l' We assumed vw= 18 mL/mol. To calculate the coefficient b appearing in the expression for T, ( q s 9 and lo), we used for the molar volume of NaCl the relation V, (cm3 mol-\) = 16.5 2.03C>S, with C,in mol L-l.I2 Results are summarized in Table I. The concentration dependence of T+ for the two membranes (Figure 5 ) is in good agreement with the variation of the permselectivity P,(Figure 6) as defined by Kamo et al.17 Evaluation of Fixed Charge Densities. We evaluated the fixed charge density first from streaming potential measurements and then from membrane potential data. (i) Fixed Charge Density from Streaming Potential. The surface charge density us within the pores of a membrane may be related to the [ potential through the Gouy-Chapman q u a tionl
Y"
50
(17) The [potential is evaluated from streaming potential measurements according to the Smoluchowski-Helmholtz equation"
-
t 01 0
20
KO
40
no
1
100
-bIl ( a h )
Figure 4. Composite curve of the cell electromotive force AEc (mV) as a function of osmotic pressure difference -An (atm) across the untreated AN69 membrane. The cumulative differences AE and AII are defined by e q s 13 and 14, respectively.
semiempirical relations given by Robinson and Stokes." We observed that the membrane potentials of AN69-P were systematically slightly higher than those of AN69, which would suggest that the adsorbed protein layer increases the overall negative charge at the interfaces, a possibility in accordance with the net negative charge of albumin at pH values higher than its isoelectric point pHi = 4.9. At lower ionic strength the cell potential reaches its maximum value ~ A E Nrepresenting , the behavior of an ideally permselective membrane through which negligible co-ion transport takes place. This permselectivity decreases with increasing mean external ionic strength. Transference Numbers of Cation and Water. To evaluate the transference numbers through eqs 8 and 9, we need to determine the ratio AE/AII and to estimate dAE/dAII. The latter may be derived from the cumulative curve7v9 obtained by plotting U ( C p c k ) against osmotic pressure difference AII(Cl+Ck) (Figure 4), defined by k- 1
hE(cl*ck) = caE(ci+cj(13) +l) i=l
and k- 1
-AII(C,-C,)
= C-AII(Cj-Cj+,)
(14)
i= I
The additivity rule expressed by eq 13has been verified by Bloch4 for the AN69 membrane, while the osmotic pressure II may be calculated from
II (atm) = -(RT/Vw) In (I,
(15) where aw is the water activity interpolated from the table of
X and being the conductivity and viscosity of the solution. This potential is an apparent value which depends on the salt concentration and the membrane pore radius R,since the model of Smoluchowski-Helmholtz is valid only for a pore radius much larger than the Debye screening length (KR>> l).10J5When this condition is no longer satisfied, to obtain the effective {potential from the apparent [a, Rice and WhiteheadI3 have proposed the following relation to take into account the size of the pore radius relative to the Debye screening length IC-I:
F(KR,B) is a modified Bessel function of the first kind and a parameter function of tj?/gX. Since F(KR,B)tends toward unity at high KR,[can be evaluated from the asymptotic {a at high KR and fixed salt concentration. To determinethevaluesof KR (Table 11),we assumed R = 3 nm 4 and calculated K from the simplified relation for a 1-1 aqueous electrolyte solution at 25 "C [Hunter p 3321: (nm-I) = 3.29Cs'/2 (20) with salt concentration C, in mol L-I. For such a small radius, KRbecomes larger than unity above l e 2M NaCl. Moreover, eq 18 cannot be applied to a charged membrane without caution, as Donnan exclusion leads to a X value in solution different from that inside the membrane pores. When the electrolyte concentration is sufficiently high, the Donnan effect however becomes negligible, and we may then assume the conductivity X to be the same in the internal and external phases. Using X and q data for NaCl solutions at 25 O C , 1 4 the apparent {potentials and surface charge densities were calculated from eqs 19 and 17 for both types of membrane (Table 11). As anticipated, there was an important concentration dependence of fa and us but without a large difference between the two membranes. Applying eq 17 leads to surface charge densities a, of 2.0 and 2.2 pC/cmz (0.125 and 0.138 e-/nmz) at the physiological K
The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3827
Characterization of a Hemodialysis Membrane
TABLE I: Transference Numbers of Cation and Water, Defmed br Eas 8 and 9. as a Function of Salt Concentrationa _
~
AN69
CI, mol/L
FC,(LEPILE)
0.004 0.008 0.016 0.032 0.064 0.128 0.256 0.512 1.024 a
~
T+
TW
0.927 0.878 0.805 0.723 0.645 0.557 0.484 0.386 0.237
1.02 0.98 0.91 0.84 0.78 0.70 0.64 0.56 0.43
1230 680 374 206 113 62 34 19 10
F G WEPILE)
-FG(aE/W
Tt
TW
0.098 0.114 0.132 0.152 0.176 0.204 0.236 0.272 0.3 15
0.970 0.924 0.872 0.779 0.670 0.595 0.543 0.461
1.07 1.04 1.oo 0.93 0.85 0.80 0.78 0.73
1370 790 456 264 152 88 51 29
aE/an was estimated at CIfrom the slope of the line joining the two closest points near C,. I
'
10-
.
'
1600
""'
1 200
08 -
06
+
_
AN69-P
-FC,(aE/an)
0.089 0.098 0.108 0.1 19 0.131 0.144 0.159 0.175 0.193
_
-
a00
c
c
t
01400
02 -
I
001 10-2
0
1 0'
10-1
C,(moi I-')
Figure 5. Transference numbers of cation (upper curves, left scale) and water (bottom curves, right scale) as a function of sodium chloride concentration for the AN69 (open circles, full line) and AN69-P (closed circles, dotted line) membranes.
0.6
E
p of 1.16 g ~ m and - ~bears a negative charge 2, of 600 mequiv/ kg, leading to the theoreticalvalue us= ( N ~ 2 ~ p=)0.57 ~ / e-/nm2 ~ where N A is the Avogadro number. Taking into account membrane swelling (s = 70% water) in an aqueous medium, we propose the value 0.57 (1 - s)2/3= 0.25 e-/nm2. However, we probably underestimate the real surface charge density in such a calculation, as ESCA studies have shown that the membrane surface is enriched in sulfonate groups with respect to the volume by a factor of 5.16 Therefore the streaming potential data at 0.154 M NaCl correspond to only about one-tenth "free" sulfonate groups, the others forming ion pairs with counterions. Let us note that even at the highest salt concentrations, the value of KR is not very large (Table 11). Thus the surface charge could be underestimated, while high concentrations of the solutions could induce modifications by adsorption of ions. Moreover, usseems not toattain a limitingvalueevenat the highest salt concentrations. The charge density (pXperunit of porous volume in the membrane is 2u,/R for a model of cylindrical pores with uniform radius R, giving (pX(AN69) N 13 C/cm3 and (pX(AN69-P) H 14.5 C/cm3 at physiological NaCl concentration. (ii) Fixed Charge Density from Membrane Potential. Kamo et a1.I' defined an apparent transference number of the negatively according to the following expression for the charged co-ion membrane potential AE,,,:
FAEJRT = (1 - 27-app)ln(C,/C2) i
Figure 6. Permselectivity P, from the model of Kamo et al." for the AN69 (open circles, full line) and AN69-P (closed circles, dotted line) membranes. Horizontal dashedlinerepresents P,= 1/5'/*, which crosses the permselectivity curve at about C = cpX = 0.1 M.
TABLE 11: Values of A arent { Potential and Surface Cbarge Density for AN68pI) and AN69-P(II) Membranes, Calculated from 4 s 19 and 17, as a Function of Salt Concentration C, -la
C,(mol/L)
KR
0.0005 0.001 0.002 0.004
0.22 0.31 0.44 0.62
0.008
0.88
0.016 0.064 0.154 0.3
1.25 2.50 3.87 5.41
I 9.21 15.5 16.6 18.3 15.1 22.6 21.3 22.3
(mV)
I1 8.33 11.4 15.8 17.7 19.6 25.0 25.5 23.9
us (rC/cm2)
I
I1
0.047 0.113 0.172 0.270 0.313 0.653
0.043 0.083 0.164 0.260 0.410 0.750 1.53 2.21
1.96 2.87
concentration0.154 M NaCl for AN69 and AN69-Pmembraneq respectively. If we assume the same average distance 6 between charged groups on the membrane surface and in the bulk volume, The copolymer has a volumic mass then uv= 6-3 while us =
Using empirical rules from polyelectrolytesolutions studies, they proposed an expression for the ratios of the counterion activity y and mobility u in the membrane (symbols with bar) and in solution (without bar):
e-
is the concentration of the anion and the concentration of fixed charges in the porous volume of the membrane. Activity and mobility of the co-ion are assumed to be the same inside and outside the membrane while (pXrepresents the effective charge density within the membrane. Assuming a Donnan equilibrium for small ions at the membrane/solution interface, these authors derived a theoretical relation for the co-ion transference number T-. Comparison between theoretical and experimental data showed the difference to be less than 2%in a given range of salt concentrations. Therefore, substituting ~-~Ppfor in their model, they proposed an expression for the permselectivityP,as a function of
r-app:
P =
1 - T-app - a!
-
1
(23)
where a is the transference number of the cation in free solution defined as u+/(u+ + u-) and & the reduced concentration C/(pX, C being the average concentration (C, + C2)/2. This equation implies that if the transference number of the co-ion r a p p is zero,
3828 The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 the membrane is perfectly selective and the permselectivity P,is unity, while if r - a p p has its free solution value (1 - a ) ,then P, is zero. Taking a = 0.41 for Na+ at 25 OC,’ we calculated the values of P, for our data from eq 23. When the results are plotted against log C(Figure6), theconcentration Cat which P, becomes 1/51/2 (& = C/pX = 1) gives the effective fixed charge density as required by the right hand of eq 23. For the two membranes we obtained a value close to 0.1 eq/ 1 or 10 C cm-I, in reasonable agreement with the figures of 13 and 14.5 C cm-’ deduced from streaming potential measurements at 0.1 54 M NaCl. Although Kamo et al. stress that this thermodynamically effective charge density should be distinguished from the hydrodynamically effective chargedensity at theorigin of the streaming potential,’* since the surface and volume charge densities are in both cases evaluated from somewhat crude models, only orders of magnitude should be expected.
Conclusions Streaming and membrane potentials show that the AN69 membrane behaves as a negatively charged cation-exchange membrane which demonstrates close to ideal permselectivity at low external ionic strength. Preadsorbed albumin slightly increases the membrane charge, with a corresponding small decrease in its hydraulic permeability. Evaluation of surface and volume charge densities, when compared to values calculated from the chemical structure of the polymer, shows that only a fraction of the ionizable groups contribute to the electrochemical properties of the membrane.
Yan et al.
References and Notes ( I ) Jonsson, G.In Dialysis inSyntheticmembranes: Science,Engineering and Applications; Bungay, P. M., Lonsdale, H. K., de Pinho, M.N., Eds.; D. Reidel Publishing Co.: Holland, 1986; p 625. (2) Wendt, R. P.; Klein, E.; Bresler, E. H.; Holland, F. F.; Seriro, R. M.; Villa, H. J . Membrane Sei. 1979, 5, 23. (3) Collins, M. C.; Ramirez, W. F. J . Phys. Chem. 1979, 83, 2294. (4) Bloch, G.;Man, N. K. Life Support Systems 1986, 4, 310-312 (Proceedings XI11 Annual Meeting ESAO, Avignon, France, Sept 1986). (5) Lonsdale, H . K. J . Membrane Sei. 1982, 10, 81. (6) Yan, F.; Dkjardin, Ph.; Mulvihill, J. N.; Catenave, J.-P.; Crost, T.; Thomas, M.; Pusineri, C. J . Biomater. Sci.: Polymer Ed. 1992,3, 389-402. (7) Schmitt. A.; Pusineri, C.; Khedr, G.; Pefferkorn, E. J . Membrane Sci. 1983, 16, 159. (8) Kedem, 0.; Katchalsky, A. Trans. Faraday Soc. 1963,59, 1918. (9) Kramer, H.; Meares, P. Biophys. J . 1969, 9, 1006. (IO) Broz, Z.; Epstein, N. J . Colloid Interface Sei. 1976, 56, 605. (1 1) Robinson, L. A.; Stokes, R. H. Electrolyte Solutions; Academic Press: New York, 1955. (12) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions; Reinhold: New York, 1967; pp 396-397. (1 3) Hunter, R. J. In Foundations of Colloid Science; Clarendon Press: Oxford, 1991: Vol. I . (14) Chapman, Th. W. Ph.D. Thesis, University of California, Berkeley, 1967. (15) Rice, C. L.; Whitehead, R. J . Phys. Chem. 1965, 69, 4017. ( I 6) Brun, C. (Rhane-Poulenc). Personnal communication. (17) Kamo, N.; Oikawa, M.; Kobatake, Y. J . Phys. Chem. 1973,77.9295. (18) Kamo, N.; Toyoshima, Y.; Kobatake, Y. Kolloid-Z. u; Z . Polymere 1971, 249, 1061-1068. (19) Klein, E., Ed. Evaluationof HemodialysersanddialysisMembranes: DHEW publication No. (NIH) 77-1294, National Institutes of Health, Bethesda, M D 20014, 1977.
