RI-IOSIC POTENTI-%LS .%CROSS POROVTS hIEhIBR.%RES. I
1211
(31) PRECKSHOT, G. W.,DELISLE,S . G . , COTTRELL, C . E., A S D K A T Z ,D. L . : Petroleum Techno]. 5, S o . 5, Techn. Publ. Xo. 1514 (1942). (32) ROMBERG, J . X . , A X D T R A X L E RR, . S . :J. Colloid Sei. 2, 33 (1947). (33) S a . 4 ~ : R . S. J . , BAAS,P. W.,ASD HEUKELOlf, P . W.:J. Chem. Phys. 43, 235 (1916). (34) S ~ A L R ,. S . J.. ASD L - ~ B O CJ. T ,W.A , : J. Phys. Chem. 44, 149 (1940). (35) SACHASES, A . S . :Petroleum Z.21, 1441 (1925). (36) S.ICH.~SES, -4.S.: T h e Chemical C o n s t i t u t i o n of Petroleicm. Reinhold Putdishing Corporation, Sen- T o r k (1945). (37) SACK,H . -4.; A S D TRILLAT, J. J.: Compt. rend. 224, 1502 (194T). (38) STRIETER, 0. G . : J. Research S a t l . Bur. Standards 26, 415 (1941). (39) S n - ~ s s o sJ. . 11.:J. Phys. Chem. 46, 141 (1942). (40) T R A X L E RR, . S . :J. Colloid Sei. 2, 39 (1947). (41) T R A X L E RR, . S . ,ASD Coouss, C . E.: Proc. -1m. Soc. Testing Materials 37, 549 (1937). (42) TRAXLER, R . s., A S D CoolfBs, c. E . : Ind. E n g . Chem. 30, 440 (1938). (13) TRISLER,R . S.,A S D SCHWEYER, H . E , : Proc. -1m. Soc. Testing Xaterials 36, 511 (1936).
THE OKIGIS O F BI-IOSIC POTESTL4LS ACROSS POROUS lfElIBR-4SES O F HIGH IOSIC SELECTIT‘ITY. I’ THE BI-IOSICPOTESTLIL ISD THE ~ Z E C H A X I S M OF ITS ORIGIS; THE T-ARIOIX FACTORS TYHICH DETER~IISE THE SIGA-.IYD THE >I.~GSITL-DE OF THE BI-IOSIC POTESTI.IL : THE SIMPLEST CHAISS IS WHICHBI-IOSICPOTESTLILS AIUSI.:: STSTEMS TJ-ITH CRITIC-IL I O S S O F THE S.1JIE S I Z E . I S D O F D I F F E R E l - T , ~ D S O R l i ABILITY
KARL SOLLSER Laboratory of P h y s i c a l Biology, E x p e r i m e n t a l Biologg a n d Medicine I n s t i t u t e , .l-cctiotinl Insfitictes of Health? Bethesda l 4 >M a r y l a n d Receiced Janitarg 6, 1949
I The present paper deals with the mechanism of the origin of the hi-ionic potentials ( 5 ) across membranes of porous character which show a high and in limiting cases an ideal degree of ionic selectivity. The hi-ionic potential (B.I.P.) has been defined as the dynamic membrane potential which arises across a membrane separating the solutions of two electrolytes at the same concentration with different “critical” ions, which are able t o exchange across the membrane, and the same “non-critical” ion species for which the membrane is impermeable (5). The critical ions in the case of electronegative membranes, such as collodion membranes, are the cations; conversely, in the case of‘ electropositive membranes the critical ions are the anions. I Presented in abstract a t the Harry B. Weiser Testimonial Symposium of the Division of Colloid Chemistry a t the 110th Meeting of the American Chemical Society at Chicago, Illinois, September 10, 1946.
1212
I L I H L >OLLXElZ
Accordingly, the general scheme of a chain in which a B.1.I’. arises across an electronegative membrane clan he represented in the folloJving manner: Solution 1
I
~
Solution 2
I
Elec tronegative Electrolyte B+ CI membrane I (‘1 I n this scheme -1-and I3+ represent univalent cations which are able t o eschange freely across the membrane, and C- an anion ivhich is unable t o penetrate through it. The sign and the magnitude of the B.I.P., as was pointed out by Michaelis (14), are determined by the relative ease with which the tlyo critical ions penetrate the membrane: if in the given scheme the cations dt of solution 1 penetrate the membrane with greater ease than do the cations B+ of solution 2, then solution 2 will be charged positive; if the (sonverse holds true, solution 2 will be negative. Ri-ionic potentials, as the scheme indicates, arise by dehnition in systems which undergo a continual degradation consisting of the eschange of the t\yo critical species of ions. Severtheless, it is easily possible t o make accurate and reproducible measurements of R.I.P.’b n-hich correspond t o the well-defined condition of minimum degradation of the measured systems ( 3 ) . ? A corollary of the essentially dynamic nature of the B.I.P. is the fact that it is not possible t o predict a priori either the sign or the magnitude of the B.I.P. of a given chain, since nothing can be foretold in an a priori manner concerning the relative ease with which different critical ions may penetrate a membrane. Though the idealized conditions n-hich should prevail in ideal B.I.P. systems are realized esperimentally only in rare instances, many experimental systems can be studied readily in which these conditions are approached so closely that they may be utilized as the basis of the present investigation. From a wider point of view R.I.P. chains represent one particularly simple case of a membrane diffusion chain ivhich in\ olves more than trvo species of ions, -the t\vo electromotively acti\ e “c.ritica1” ions and the common, electromotively indifferent counter ion. -1thorough iiiidcrstanding of the-e more complex chains will of necessity he h s e d on the thcory of the simpler R.I.P. bystems. Complex situations of this general nature esist regularly in living organisms: membranes of various degrees of ionic selectix-ity separate solutions which contain several species of electromotively active ions of the same &n. d n y basic physicochemical information which can he deduced from relatively simple systems Trill thus contribute ultimately to the better understanding of many intricate problems of cellular and general phyiology, w c h a i muscle and ncrve wxitahility, action potentials, :tiid kindred que‘stion‘s of Iiioelectrical and elcctrophysioloffical interest. Electrolyte -1-(’“1
2 The value of the 13.1 1’ acres a given menlbrane specimen may be reproduced readily within a few millivolts for a n y given electrolytc combination. With the proper technique, and if considerable rarc IS taken, reproducibility within a few tenths of a millivolt may be obtained in most instances (5).
1213
BI-IOKIC POTENTIALS ACROSS POROUS MEMBRAKES. I
I1 The most extensive, and therefore the most useful, measurements of bi-ionic potentials n-ere reported by Michaelis and Fujita (15) for chains with electronegative collodion membranes of high ionic selectivity, and by Mond and TIoffmann (16) and Hober ( 7 ) for analogous electropositive Rhodamine 13 wllodion membranes. They are reproduced in tables 1 and 2.3Other data on 13.1.1'. chains 11-liich can bc found in the litcrnturc (1.3 ) are too limited in scopc to l)c of murh value in the clucidation of the mechanism of the origin of the R.T.1'. The prohlpm of the oriqin of the I3.T.I'. lins bwn dealt with in thc litclatruc primnrily by Afichndi. ( 1 i3 I.; I . hy AIond and Hoffmmu (l(i'8, :inti 1)y I T o 1 ) c ~
HCI HC1 IICl IICI
+87 +93 +I10 +165
( 7 ) . 11-ill)randt 124) 11n- i-cccmtly pnitl qome attention t o thi, question, h u t from a different point of viciv.
Ilhrshall (10) hac discussed the origin of the I3.T.P. ncrohs clay memhrunei which are concidtli ed t o he non-porous in character. T h u i their c.oniideiation i h A comparison of the riuniericul values of the potentials obtained with the same 1)nirs of critical ions by Mond and Hoffmann and by Hober (ser tahle 2) clearly shotvs thr qunrit i t a t ive differences between chairis with membranes prepared under different conditions. These data a t t h e s:me time drnionstrate thc coiisistent qualitative likeness of the results: the same ionic sequence is obtainpd throughout by different invcstigators iiritl undrr varying conditions.
1214
K h R L SOLLXER
outside the scope of the present paper, which is concerned exclusively with membranes of porous character.4 llichaelis (14) suggested that the B.I.P. he interpreted as heing due to differences in the “mobilities” n-ithin the membrane of the two critical species of ions. The various critical ions have different sizes in the hydrated state, as is evident from the differences in their electrolytic mobilities in free solution. On-ing t o the heteroporosity of the membranes there are many more pathn-ays available to the smaller ions than to the larger ones. I n this way the steric-geometric theory explains-formally at least-n-hy the sequence of the “mobilities” of the alkali ThRIL 2 The hi-aonzc potenfzul OCI’OSS elect7oposatz~eRhodanwne B collodzon membranes of hzgk zontc sel ec f z 1 z t i l (;liter Mond and Hoffmann (16) and Ilober ( 7 ) ) -
____
SOLCTIOK 1
(0.1
_ _ __-
SOLK-TlOS
1
2
10.1 sj
si
’ ~
.
~
.-
.~..~ ~
I
SaSCS
SaC1 SaCl SaCl SaCl SaCl SaCl
sasoj S:iI Sa131 SaCl CII ,COOS
i
1 3
BI-IOSIC POTESTIAL (B.1.P.) (TEE S I C S REFERS TO SOLUTIOY
3lond and Hoffmann
____
,
I
I
C sEI4iOW)COOSa CsH,COOSa C6HjS03Sa CIIaCH2COOSa CHaCHOHCOOSa
~~.~
mu.
~
1
+144 f90 +83 +53
+7* -18
I
+
I
SaCl XaC1 SnCl SaCl KaC1
Hober :T = 2j.O’C.)
- .__.-
mc.
+60 +51 +33 +20 0 -8
2)
I
65 +33 +lo - 16
I
-41
I
I I
I
__
SaCl SaCl SaCl
(COOSa)? S a a citrate Sa?SO1
-50 -51 I
-38
-7 3
.~
“This value should be zero as i n the case of the nieasurements by N o n d and Hoffmann; i t must be attributed to a sunimation of ehperiniental errors.
cations within the membrane is the same as that of their electrolytic mobilities or diffusion Velocities in free solutions. I t also accounts qualitatively for the fact that the relative differences in hbmobility”of the various cations are greatly increased Tvithin the membrane. I n order to obtain quantitative information concerning the relative ionic “mobilities” of the two critical ions in the (negative) membranes, Michaelis (14) The basic most valuable membranes of in the present
therniod) naniic consideration of Xarshall, x i t h o u t any doubt, will piove in the evolvement of a complete thermodynamic theorj- of the B.I.P. across porous character. L o ntteiiipt, honever, at this latter subject nil1 be tried paper, IThich is confined t o the phenomenological aspects of the problem.
I31-IOXIC POTENTIALS ACROSS POROUS MEJIBRASES. I
1215
employs-not ivithout misgiyings-the formula usually applied t o the liquidjunction potential arising between the solutions of two electrolytes of equal concentration having tn-0 different ions of the same sign of charge and a common counter ion. For a pair of uni-univalent electrolytes with two different cations and a common anion this equation reads
n-here E is the experimentally determined B.I.P., u:’ and u y ’ are the “mobilities” of the tn-o cations in the membrane, and ZL is the “mobility” of the common anion in t h r membrane, which Michaelis assumes t o be zero. Michaelis’ basic trend of thought concerning the quantitative interpretation of the B.I.P. i t a s recently taken up by Gregor and Sollner ( 5 ) . T o avoid a variety of conceptual tlifficulties which are connected with the idea of ionic mobilities within memhraneq of porous character, it was suggested that the quantitative evaluation of the B.I.P. be based on the more basic and more general concept of the transference numbers.j I n order t o evaluate quantitatively from the magnitude of the B.I.P. the true relative rontributions of the different ions t o the virtual transportation of current arross the membrane, it is necessary only t o substitute transference numbers for ionic mobilities in the above equation 1. For the case of a system cwnsisting of an clecatronegative membrane n-hich separates the solutions (of the same concentration) of tn-o different cations, this modified equation reads
in \\-hich E’ represents tile B.I.P., and T ? ) , T:), and r?’” the transference numbers within the membrane6 of the two species of cations and of the common anions, respectively. The three transference numbers are linked by definition together by the equation (1) (2) ‘+ ‘f ‘F2) = 1 (3)
+
+
For electronegative membranes of ideal ionic selectivity, i.e., for membranes across n-hich no anions are transferred, equation 3 is reduced t o the expression ‘+(1)
+
7:2) =
1
(3a)
The concept of ionic “mobilities” in t h e membrane if understood in analogy n-ith t h e concept of ionic mobilities in free solution embodies of necessity several rather specific assumptions which are not likely t o be adequate for the particular situation \Tithin t h e membrane. T h e magnitude of a B.I.P. quite obviously is a function of t h e relative contributions of t h e different species of ions in the system toward the (virtual) transportation of current across the nienihrane. Thus. t h e concept of transference numbers permits the quantitative interpretation of the experimental B.I.P. values in terms of niolecular (ionic) processes with n minimum of hypothetical assumptions. To distinguish the transference numbers n.ithin the membrane from transference numbers in free solution, a small Greek t a u ( 7 ) will lie used for the former.
1216
KARL SOLLSER
and equation 2 becomes the expression
Equation 4 can he used to calculate the tranhf~rence numbers 7:) antl T: of a pair of critical ions from the magnitude of thr c.oi-i*espondingB.I.P.7 For electropositivr membranes (of i d e d ionic. selectivity) rimentul sc,riw in each of x h i c h the caritid ion in solution 1 \vas the sarw, xhilc t l w (ariticd ion in solution 2 \vas 1-aried. Thc ratios 7:’ T+( 1 and r-( 2 ) T-( 1 .lor thc swics of c4h:iins with negatil-e anti positi1.e memhranes, respec.ti\-dy?:ire t h u s c:ilculatcd from equations 4 and h,antl arc arranged according to their nxignitudc in ti caation :dt m :inion series. Tlir rational explanation of these scqucnc of the electromoti\-e cfficwy in 13.1.1’. systems of the Txrioiis ions aiisrs :is thc targc,t of the present inrestigation. The problcm consists in correlat ing t lie tliff‘rrcntinl heha\.ior of the various ions in 13.1.1’. sywtcnw \vith thc more fiinthment:il 1)hysic.al propertics of these ions. in taldes 3 and 4, \vhich iii’c 1)ased on t h c data of tat)lcs 1 antl 2 , i*espectively, tlic first column gives the v r i t i d ions in solution 2 ; thc seceontl column shons the ratios of the tranxferencc \-dues T?’ ~ $ :tnd 1 7?’ 7&’lY7 respcctildy, I-sisinto such component factors :IS “relativc abundance,” “apparent concentration,” ,‘~l~7~iiI:i~)ility,’’ and “mean t rur mobility.” For this purpose, however, it would be necessary t o define these or similar magnitudrs in a manner which woultl lit. fitting t o t h e peculiar situatioii within the mcnihrnnr, and t o have available experimental methods for their determination. 8 The possible influence of a significant deviation of the esperiniental chains from the ideal behavior which is assumed here \ d l he discussed in P a r t I1 of this paper.
1217
I%I-IOSIc' POTESTI.%LS ACROSS POROTR 1IE1IBR.ISES. I
If \\e confine our attention to the inorganic cations the t\vo sets of data appear to he in satisfactory sequential agreement, as predicted by the steric-geometric TABLE 3
T h e ratzos of the transference ni(inbers T ? ) / r $ of i a r t o i i s critzcal cations calculated f r o m t h e data oj' table 1 , a n d f h e i e l a t t z e Tales oj d i f f u s i o n of the sanie ? o m 7n f r e e solution (DK-
=
100)
( T = 200°C)
~ _ - _ _ _ _
~
CRITIC\L I O S I S SOLTTIOI
2
H'
40.0 1.-I 1.3
Itb"
",& K+
0.36 0.25 0.20 0.15 0.15 0,053
Pilocarpine Strychnine .Itropine Quinine Sa'
L1'
* Estimated on t h e basis
-
RELITIVI: R \TE O F DIFFUSIOS I N FREE SOLUTIOS
5.2 1.04 1.oo
1.oo 0.43* 0.34 0.3T" 0.35 0.65 0.48
of the Riecke-Euler equation, .1LD2 = const.
T.IRI,L: 1 12
(1
T h e iatios of the traiisi'erence nuinbers T- / T C ~ -o J t a i i o i t r irniictlent ~ ) . 7 t ~ e u ~ a n z o i z s c a l ~ i r l a f e d jronz the data o j table 2 , a n d the ,elafiiv rates of dzffits?on of the s a m e i o n s in free soltition (Dci- = 1 0 0 ) (7- = 250°C.) -
-
-
TK2) ~~
"3 33 25 13 7 .9 3.6 1..5
0.54 0.50 0.20
-
-__
REL.kTIVE RATE OF DIFFUSION I N F R E E SOLCTIOS
0.87 0.93 1.01 0.41 1.02 0.44 0.49 1.oo 0.49 0.53 0.54
theory. But even in this rebtricted range the agreement between the predictions of this theory and the experimental facts is unsatisfactory from a quantitative
1218
KARL SOLLSER
point of vielv-. The theory nould lead to the conclusion that many pores n-hich are not available for the I
