271 1
Communications to the Editor TABLE I: Difference between Observed and Corrected Volume Flows in Electroosmosis Experiments on Anion Exchange, Cation Exchange, and Charge-Mosaic Membranesa Membrane Solution (Active area, c m z ) concn, (Current l . mA/cm2) M
J,, c m i s e c
Jvobsd,c m i s e c
-12.4
x 10-7 x 10-7 x 10-7
-10.1 x 10-7 -10.7 x 10-7
0.1
+io.8
x 10-7
+i2.5 x 1 0 - 7
(1.05)
0.01 0,001
$13.7 X f14.7 X
Mosaic
0.1
f1.3
(0.092)
0.01
+i.5
(1.08)
0.001
+2.8
Anion exchange
0.1
(0.094) (1.06)
0.01
-11.8
0.001
Cation exchange (0.095)
a
-9.7
-8.0 x
f15.4 X f16.3 X
x 10-7 x 10-7 x 10-7
$3.0 +3.3 f4.6
x x x
lop7
10-~ 10-7 1 0 - ~
From the data of Weinstein, et
PE ((Ap - Ar)/E)j\,,Apsc= - ( I / J v > ~ p , ~ , s (15) the observed volume flow must be corrected.? Ion exchange membranes of relatively loose structure will tend to have high values of p, and consequently the correction will generally be negligible, but for tight membranes it may be significant. The correction will be especially important in the study of charge-mosa.ic membranes, which consist of alternating anion and cation exchange regions. For such membranes /3 may be nearly zero since the electroosmotic flows through the two types of region are oppositely directed and tend to cancel. Table I contains data from experiments described by Weinstein, et aL,* on the electroosmotic coefficients of homogeneous and charge-mosaic membranes. Note that J , is roughly double Jvobsd in the case of the mosaics. Acknou-ledgments. This study was supported by the Office of Saline Water (Contract No. 14-30-3145) and the U. S. Public Health Service (Grant No. HL 14322 to the Harvard-MIT Program in Health Sciences and Technology). References and Notes
@' = JVobsd(Ap-
Sir: The correction given by Weinstein and Caplan is clearly justified and I would like to add a small reformulation. The dissipation function for discontinuous systems is derived by calculation of the entropy changes in the compartments separated by the membrane. In the absence of an electric current, the flows JLare given by the change of the amount of each species in the compartments, =kdrz,/ dt. In order to pass an electric current, electrodes have to be introduced and their entropy changes must be included in the calculation; for the derivation of entropy production in the membrane the electrodes are assumed to be reversible. Mazur and Overbeekl emphasized that this leads to the simple form of the dissipation function generally used (eq 1 in Weinstein and Caplan,2 and eq 1 in ref 1 therein), with the flows explicitly referring to the number of moles passing through the membrane and not necessarily to the changes of n, in the solution compartments. Thus our statement that upon introduction of electrodes reversible to ion 2 we may identify the flow of ion 1 with the salt flow is inexact. It should have read J i / u l is equal to the flow of salt in the absence of electric current, and gives the composition changes in the solutions if current is passed through electrodes reversible to ion 2. In this case
-dn,'ldt = dn,"/dt = A J l / u l (A-membrane area) Following the inexact definition, we wrote for the volume flow
J\.
AT) + JsAfisc+ / E '
- Vl(Ap - A x ) / z 2 F .
(6) D. Mackay and P. Meares, Trans. Faraday Soc.. 55, 1221 (1959). ( 7 ) Three of the Kedem-Katchaisky coefficients ( K , P E , i l ) may be measured by the passage of current under conditions of zero voiume flow. In practice such determinations are invariably carried out with Jlobsd = 0 though the rigorously correct condition is Jv = 0. (8) J. N . Weinstein, B. M. Misra, D. Kalif, and S. R. Caplan, Desalination, 12, 1 (1973).
Stanford University Medica/ Center Palo Alto, California Biophysical Laboratory Harvard Medical School Boston, Massachusetts 021 15 Received February 72, 1973
John
N. Weinstein
S. Roy Caplan*
=
J,v,
+ J,v,
J , = Jl/u,
(14)
instead of the correct expression
J,
=
J,v,
+ Jlvl+ J , v ,
(14.cor)
counting the total volume of the species passing the membrane. The corrected expression for J\ gives (with dilute solutions) for the transformed dissipation function =
0. Kedem and A. Katchaisky, Trans. FaradaySoc., 59, 1918 (1963). 0. Kedem and A. Katchaisky, Trans. Faraday Soc., 59, 1931 (1963). 0. Kedem and A. Katchalsky. Trans. FaradaySoc., 59: 1941 (1963). V1 and V Z are subject to the same thermodynamic questions of definition as AGl and A L P . (5) Alternativeiy, the dissipation function could be written in terms of JVobsd. From eq 4 ana 10 (1) (2) (3) (4)
where E' = E
Comments on the Paper by Weinstein and Caplan on the Definition of Volume Flow in the Kedem-Katchalsky Formulism of Electroosmosis
(J,, - Iv,/z$')(A.p
- An) + J,Ap,'
+ IE (16, cor)
As pointed out by Weinstein and Caplan,2 with the other forces as defined here, J , - I V Z / Z ~ Fand , not J,, is the flow conjugate to ( A p - A T ) . The correction is small in most cases, but may be very important in some systems. I would recommend leaving the notation J , for the total in ref 2. Jv according to eq 14, cor volume flow (Jvobsd here) in accord with the literature and introduce, if necessary, another abbreviation for J , - I V ~ J Z ~ F . References and Notes. (1) P. Mazur and J. T. G. Overbeek, Red. Trav. Chim. Pays-Bas, 70, 83 (1951). (2) J. N. Weinstein and S. R. Caplan, J. Phys. Chem.. 77,2710 (1973).
Polymer Department The Weizmann lnstitute of Science Rehovot, lsrael
0. Kedem
Receivea March 5, 1973
The Journal of Physical Chemistry, Vol. 77, No. 22, 1973
