A QUANTITATIVE ELECTROCHEMICAL THEORY OF T H E ELECTROLYTE PERMEABILITY OF MOSAIC MEMBRANES COMPOSED OF SELECTIVELY ANION-PERMEABLE AND SELECTIVELY CATIOX-PERMEABLE PARTS A S D ITS EXPERIMENTAL VERIFICATION. I’ AN OUTLINEOF
THE
THEORY AND ITS QUANTITATIVE TESTIN MODELSYSTEMS WITH AUXILIARY ELECTRODES REX NEIHOF’
AND KARL SOLLNERa
Department of Physiological Chemistry, The Medical School, University of Minnesota, Minneapolis 14, Minnesota; and Laboratory of Physical Biology, Ezperimental Biology and Medicine Institute, National Institutes of Health, Rethesda 14, Maryland Received August 88, I949
I The complex nature of the majority of the biologically important membranes is generally recognized today. Many of the involved in vivo functions of living membranes are attributed to the intricacies of their physicochemical structure (9). Thus, the elucidation of the fundamental physical chemistry of membranes of complex structure arises as a problem challenging to the physical chemist interested in biology. Complex membrane structures, aside from still more involved cases, might be either “layered” membranes composed of several layers of different properties, or the membranes may have a “mosaic” structure consisting of parts of different properties in juxtaposition. One special case of this latter nature will be investigated here. With membranes of porous character the simplest case of a mosaic-like structure consists of membrane heteroporosity. The characteristic permeability and osmotic properties of these membranes can be explained only on this basis (3, 8, 10, 11, 18, 19). Another possible mosaic structure among the membranes of porous character consists of a membrane which is composed of selectively anion-permeable and selectively cation-permeable parts. The simplest case of a mosaic membrane of this general type obviously consists of a membrane which is composed both of ideally anion-selective and ideally cation-selective parts. A quantitative theory of the electrolyte permeability of mosaic membranes of this latter type was outlined some time ago by one of the present writers (12). At that time it could not be tested experimentally, as suitable membranes were Presented a t the Twenty-third Xational Colloid Symposium, which waa held under the auspices of the Division of Colloid Chemistry of the American Chemical Society a t Minneapolis, Minnesota, June 6-8, 1949. Present address: Laboratory of Physical Biology, Experimental Biology and Medicine Institute, National Institutes of Health, Bethesda 14, Maryland. 157
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REX NEIHOF AKD KARL SOLLNER
lacking. Sow, however, this test has become an experimental possibility, owing to the availability of the recently developed permselective collodion and protamine collodion membranes (1, 2, 6, 7 , 14, 15, 16). This test is the main topic of the present investigation. The theory of the electrolyte permeability of mosaic membranes which are composed of ideally anion-permeable and of ideally cation-permeable parts is most easily developed by reference to a sequence of line drawings. Figure 1 illustrates schematically a system in which a mosaic membrane of this type separates a lower compartment (of invariable volume) from an upper compartment, the striated structure in the figure indicating the membrane itself. The electronegative, cation-permeable (anion-impermeable) parts of the membrane are indicated by minus signs, and the electropositive, anion-permeable (cation-impermeable) parts by plus signs. The lower compartment is assumed to be filled with 0.1 s potassium chloride solution and the upper compartment with 0.01 N solution of the same electrolyte.
FIG.1
FIG.2
Contrary to certain ideas which are reviewed in Hober’s book (9), quoted above, it was postulated that such membrar-ds must permit the penetration of electrolytes from the lower compartment to the upper one (12). Cations move through the electronegative parts of the membrane and anions through the electropositive parts, neutralizing each other electrically. Thus a continuous movement of the electrolyte occurs across the membrane which does not cease until equilibrium between the two compartments is established. In formulating this qualitative concept in a manner which is susceptible to a critical, preferentially to a quantitative, test it is necessary to consider a system in which the cation-permeable and anion-permeable parts are separated from each other. Figure 2 shows a U-tube containing in its left arm an electronegative (cation-permeable) and in its right arm an electropositive (anion-permeable) membrane, both membranes being assumed to be of an ideal degree of ionic selectivity. The lower part of the system (having an invariable volume) is filled with 0.1 N potassium chloride solution, while the two separate compartments :hove the membranes contain 0.01 K solution of the same electrolyte. The only
ELECTROLYTE PERMEABILITY O F MOSAIC YEMBR.4BES.
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processes, according to the premises, which can occur in this system consist of the establishment of static membrane potentials (concentration potentials) across the two membranes, and the establishment of a hydrostatic pressure in the lower compartment, due to the difference in water activity between the concentrated and the dilute solution. The magnitude of each of the two membrane potentials in the system of figure 2 is numerically defined by the Sernst equation:
where t is the electromotive force and aland a2 are t,he molar activities of the electromotively active ion. The direction of the two electromotive forces is obvious from the mechanism of their origin; it is indicated in figure 2 by brokenline arrows pointing a t a plus and a minus sign, respectively. The numerical value of c amounts to +55.l mv. and -55.1 mv. for the pair of solutions indicated in the figures. As is evident from figure 2, the dilute solution in the upper left-hand compartment, according to the premises, xi11 have a pokntial difference of +110.2 mv. against the solution in the upper right-hand compartment. In order to reestablish in figure 2 the essential features of the situation represented in figure 1, it would be necessary to connect the two compartments containing dilute solution by a liquid conduit filled with 0.01 s potassium chloride solution, as shown in figure 3. Figure 3 can be considered from t\vo different viewpoints. On the one hand, it represents in a slightly more elaborate manner the essential situation of figure 1: potassium ions mill migrate to the dilute solution through the cation-permeable membrane and chloride ions through the anion-permeable membrane, the brokenline arrows in figure 3 indicating the direction of the movement of the cations and anions, respectively. On the other hand, the system of figure 3 may also be considered as a “Fliissigkeitsring,” an “all-liquid electrical circuit” or, better, an “all-electrolytic electrical circuit” in the sense of Dolesalek and Kriiger (4),a a (positive) electric current flowing in a clockwise direction through the system, as is indicated by the solid arrows in figure 3. The total E.M.F. in the system, E , as stated above, is 110.2 mv. The strength of the current, I , is defined by Ohm’s law,
where R is the total resistance of the system. The current lvhich flows in a clockwise direction in the system of figure 3 is transported through the negative memDolezalek and Kriiger deduced from Nernst’s theory of the liquid-junction potential t h a t an electric current must of necessity flow in a closed ring filled with nothing but a sequence of electrolyte solutions, provided any asymmetry of an electrical nature arises in the system. They proved this point by demonstrating the deflection of a magnetic needle placed in the center of an all-electrolytic ring system made up of a sequence of properly selected elect,rolyte solutions (4).
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REX NEIHOF AND KARL SOLLNER
brane in the left arm of the system exclusively by cations which move clockwise, in the direction of the broken-line arrow; through the positive membrane in the right arm the electricity is transported exclusively by an equivalent quantity of anions which move in a counterclockwise direction, as indicated by a brokenline arrow. Accordingly, the quantity of electrolyte (in equivalents) which moves in a given time in the mosaic system of figure 3 from the concentrated to the dilute solution must be numerically identical with the number of electrochemical equivalents of current (faradays) which flow in the system during the same period.
n
i I
I
FIG.3
FIG.4
I1 The ultimate goal of the experimental test of the outlined theory of the electrolyte permeability of mosaic membranes obviously is its quantitative verification in model systems identical in all essential features with the all-electrolytic ring system of figure 3. The general approach toward this end-in principle, at least-is exceedingly simple. It aims at the comparison of the number of equivalents of electrolyte which traverse the membranes in a given time and the number of faradays which flow in the system during the same period, the theory predicting numerical identity of these two magnitudes. From the experimental point of view, however, the situation is not quite as favorable as might be supposed at first sight.
ELECTROLYTE PERMElBILITY O F MOSAIC MEMBR.iSES.
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While the quantity of electrolyte which moves in a given period from the more concentrated to the more dilute solution can readily be determined conductometrically or by chemical-analytical methods, a model system of the type shown in figure 3 does not lend itself readily to a quantitative determination of the strength of the electric current which flows in it. The deflection of a magnetic needle, e.g., as used by Doleaalek and Kriiger (4),under the most favorable conditions, can demonstrate the existence of an electric current in an all-electrolytic circuit, but an arrangement of this nature is not suitable for the quantitative determination of current intensities. The main difficulty one is confronted with, therefore, consists in the exact determination of the number of coulombs which flow in an all-electrolytic ring system during a measured period. The seemingly most straightforward may of circumventing this difficulty consists in calculating the number of coulombs flowing in the system during a given period from the readily measured E.M.F.of the system, its total ohmic resistance, and the duration of the experiment The E.H.F. of the system and its resistance, however, are not constant over any experimentally useful period. A system like that of figure 3 is nothing but a working and, thereby, degradating all-electrolytic galvanic cell. The unavoidable degradation of the system during the experimental period results in a decrease in its E.M.F.; likewise, the resistance of the system does not remain constant. The conductance of its component parts, of the solutions and of the membranes alike, varies as the electrolyte concentration of the solutions in the two compartments changes. In addition, membrane polarization might arise as a further complication, since concentration polarization occurs at membrane I solution interfaces in the same manner as at metallic electrodes. This effect cannot be ignored or ruled out a priori; it must be tested for in the working model systems. The exact calculation from E.M.F.,resistance, and time measurements of the number of coulombs which flow in an all-electrolytic circuit in a given time is, therefore, a problem which can be solved in a satisfactory manner, if at all, only after considerable exploratory work. Thus, it becomes necessary to look for some other exact method of current measurement. The obvious approach t o this problem consists in some alteration in the simple theoretical model of figure 3 which will permit the current in the system to flow through some measuring instrument. The practical way of doing this is to cut the system at some suitable point and attach to the two open ends of the interrupted circuit two symmetrical electrodes which can reversibly take the current from and return it to the system. The two electrodes in turn are connected to each other by some conventional currentmeasuring instrument and a closed circuit is thus reestablished. The electrodes must be chosen so that they do not bring about any significant change in the original system which would not occur on closed circuit in their absence. The system shown in figure 4 illustrates schematically one possible arrangement of this nature which makes use of silver 1 silver chloride electrodes in chloride
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R E X NEIHOF .4XD KARL SOLLEER
solution^.^ I t may be represented as a galvanic cell in the conventional way, double vertical lines representing the negative and the positive membranes, respectively : A g 1 AgCl I KCI c1 i 1 KCI CZ 11 KC1 c1 j AgCl1 Ag
+
€1
€2
(a
€4
c;
a;
I n this chain tjhe electromotive forces c1 and e;, and e2 and e;, are equal but opposite in direction; they cancel out and do not contribute to the total (effective) E.M.F. of the cell. The introduction of reversible and symmetrical electrodes in a mosaic model system makes it,, therefore, possible to determine directly and accurately the number of faradays which flow in it during the period for which the circuit is closed. Thus, by the use of systems involving auxiliary electrodes, one should be able tjo compare accurately in the modified mosaic system of figure 4 the number of faradays which flow and the number of equivalents of electrolyte which are found analytically as having been transferred during the same period. If the ratio of these two magnitudes is found to be 1:1, within the limits of the experimental error, the outlined theory of mosaic membranes would be proven to be correct, a t least for the type of model systems in which a pair of reversible electrodes has been introduced. This would mean that one is able for the first time t o calculate from purely electrical data the rate of electrolyte permeation in a complex membrane system.
I11 The experimental plan to be pursued towards this end must be introduced with some considerations of a general nature: The geometry of the experimental system, that is, the size and shape of its component parts, is inconsequential from the point of view of the theory, provided the essential electrical features of the model are not altered. Likewise, the electrolyte used, the resistance of the membranes, the absolute concentration of the t,wo electrolyte solutions, and also their concentration ratio may be freely selected as required by the experiment. Here, the only restricting condition is that the ionic selertivity of the membranes must be so high that the “leak” of noncritical ions does not, blur the essential features of the model system.6 ‘The electrode reaction on the right-hand side of figure 4 consists in the formation of solid silver chloride from the silver of the electrode and chloride ions identical in number with those which have traversed the positive membrane. The electrode reaction on the left-hand side of the system is the formation of metallic silver from the solid silver chloride of the electrode and the release into the solution of an equivalent number of chloride ions. The net process in the cell of figure 4 is thns the same 11s that in the model without electrodes of figure 3 : namely, the transfer of electrolyte. 6 The imperfection in the ionic selectivity of a membrane which results in the movement of ions of the “noncritical” species across it (of anions in the case of the negative membranes, and of cations in the case of the positive membranes) can be calculated conven-
E L E C T R O L I T E PERME.iBILITT
OF MOSAIC MEMBR.IXES. I
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This freedom in the choice of the experimental details of the model studies is of considerable importance in view of the fact that even the best available membranes, the permselective membranes, generally speaking are not of ideal ionic selectivity. With such nonideal membranes it is necessary to balance carefully the several variable factors of the system with one another in such a manner as to establish the approximate optimum conditions. It is advisable to reduce the experimental periods as much as practical (since the absolute “leak” of ions across a given membrane is proportionate to the duration of the experimental period) and to increase the current intensity in order that the effect of the “leak” may become small or, better still, insignificant. One of the most important steps in the direction of decreasing the resistance of the experimental model systems consists in the selection of a suitable geometric arrangement. It will be helpful t o increase the cross-sectional dimensions of all the component parts of the system and to make all dimensions in the direction of the flow of the current as small as possible. This is particularly true of the dilute solution. One also might increase the absolute concentration of the solutions in order t o decrease the resistance of the system. The full exploitation of this possibility is limited by the fact that the “leak” of the membranes increases considerably as the absolute concentration of the two solutions is raised (5, 6). Another possibility of increasing the current lies in the choice of a high concentration. ratio, which iyould result in an increase in the E.Y.F. of the system. The usefulness of this possibility is also limited. Too high a concentration of the concentrated solution increases the “leak,” and too low a concentration of the dilute solution unduly increases the resistance of the system. The resistance of the membranes can be varied ( 5 , G, i ) ,but it cannot be lowered too much without adversely affecting their ionic selectivity; this means without increasing the “leak” of noncritical ions. iently from membrane concentration potential and expressed in terms of per cent “leak” (1, 2 ) . The Sernst equation for the diffusion potential may be applied to the case on hand. For a uni-univalent electrolyte it assunies the following form:
E = +=?
+ r+ RT in a?
T-
(3)
where r- and rT are the relative contributions of anions and cations, respectively, to the virtual transport of electricity across a (poqtive) membrane, and a, and Q the activities of the electrolyte in the two solutions. The value of RT In al/at for 0.1 ~ / 0 . 0 1N potassium chloride solution, e.g., ie -55.1 mv. a t 25.0”C. If a concentration potential, E , of -53.0 mv. is measured for this case the leak of cations can be calculated as follows: -53.0 =
7+ -
7-
-T (-55.1) i- 7+
tlirreforr.
T+ =
2.1
r-
108.1
This corresponds to a cation leak of about 2 per cent.
(5)
164
HEX NEIHOF AND KARL SOLLSEIt
The choice of the electrolyte to be used does not represent any difficulty. Any readily available strong, neutral, uni-univalent electrolyte can be expected to he suitable with only minor differences between different) salts (15, 16). With other electrolytes, e.g., uni-bivalent salts, the membranes must be selected with special care; otherwise the “leak” may become a very disturbing factor. The nature of the electrodes to be used, in essence, is immaterial provided they are strictly reversible, not polarized too much by the current intensities likely t o be encountered, and of lo^ resistance, the two latter factors being influenced favorably by large cross-sectional dimensions. The problem of concentration polarization at the four membrane solution interfaces is not a serious one in models with auxiliary electrodes, since the number of coulombs flowing in the system is measured directly. Stirring vould be helpful in reducing any polarization which may arise in the systems on closed circuit. It will be helpful also in maintaining homogeneous the composition of the individual solutions and in keeping the full concentration difference active across the membrane itself. The possibility must also be considered of a disturbing osmotic movement of liquid across the membranes which might’ occur, owing t o the difference in the concentration of the two solutions. However, if permselective membranes are used there is no such difficulty, since the osmotic water movement which occurs across these membranes with concentration differences of a magnitude which is of interest here is insignificantly small, of the order of magnitude of 0.01 ml. per 100 cm.2per hour (1).
Iv This section describes the special geometrical arrangement of the actually constructed and studied model systems with auxiliary electrodes; the individual component, parts of these models; certain auxiliary procedures, including an appropriate method of correcting the raw experimental data for the “leak” of the membranes; and t,he calculation of t’heresults and the method of their evaluation. A suitable geometrical arrangement consists of two test tube-shaped membranes, the annular space between the two membranes being filled with the dilute solution. The smaller membrane throughout its length is provided with a concentric electrode and filled with concentrated solution. The larger membrane is surrounded by a cylindrical electrode, and is immersed in a container also filled with concentrated solution. The two electrodes are thus electrochemically symmetrical (though they are not identical in size or shape). This arrangement embodies large membrane (and electrode) areas with a short distance for the current to travel through the more dilute solution. I t has the additional practical advantage that it does not require a tight sealing of membranes between flanges, a likely source of experimental errors when flat membranes are used. Figure 5 shows the actual experimental model system of this type with specific (Ag I AgC1) electrodes. The elements of this system hear the same essential relationship t o one anot,her as in the corresponding theoretical model of figure 4.
ELECTROLYTE PERMEABILITY OF MOSAIC MEMBRANES. I
FIG.6
I OR
166
REX NEIHOF APiD KARL SOLLKEH
The singly existing, minor difference is that the dilute solution is contained in a single compartment, while the concentrated solution is separated into two part?. The analogous model system with nonspecific electrodes is shown in figure 6. In the models shown in figures 5 and 6, several precautions were taken to assure that the experimental conditions were maintained as closely as possible t o those assumed in the theoretical model. The concentrat,ion of the solution inside the positive membrane was maintained constant during the experiment by a stream of fresh solution (500 ml. per hour) coming under low pressure by gravity from a large storage bottle. Entering near t)he bottom of the membrane through a small glass tube, as shown in figures 5 and 6, the solution left through another tube at’the top of the membrane and mas discarded. This also provided an adequate intensit,y of stirring. The dilute solution was stirred by means of a current of air bubbles, about two per second, issuing from a small glass tube in the lower part of the space between the two membranes. It escaped from the system through a small groove in the stopper supporting the glass ring of the positive membrane. The concentrated solution outside the negative membrane was neither changed nor stirred, since preliminary experiments had shown that these precautions \rere without detectable influence. S o accurate control ofthe temperature is necessary in the study of model systems with auxiliary electrodes. Fluctuations in the temperature are entirely immaterial if the number of coulombs flowing in the system are measured directly. They are of minor significance only if an ammeter is used, provided an adequate number of readings are taken a t appropriate intervals. All experiments reported here were carried out at room temperature, the variation in temperature during any single experiment being rarely as much as 2.OoC. The membranes used in the model experiments mere permselective collodion and protamine collodion membranes prepared according to the method described by C,arr, Gregor, and Sollner (1, 5, 6, 7 ) . The inside (smaller) membranes were cast on 25 mm. glass mandrels; the outer (larger) membranes on similar 45 mm. test tubes which, for the rasting, were rotated at the same peripheral speed as the 25 mm. mandrels. The membranes were attached to glass rings, as previously described (1, 6, i ) .As a special precaution their top edges mere sealed t o the glass rings with paraffin to insure against any possible leakage by capillarity of the solutions between membrane and ring. The suitability of the various membranes for use in the model systems was appraised in a preliminary manner on the basis of their characteristic concentration potential (abbreviated C.Co.P.) and their ohmic resistance in 0.1 N potassium chloride, PO.] N KCI. The C.Co.P., that is, the potential of the concentration chain, 0.1 N KCI 1 membrane 0.01 ~
~i KC1
of the various membranes was measured with a probable error of f 0.1 mv. Bn experimental C.Co.P. less than the theoretically possible maximum (+55.1 and -55.1 mv., respectively) indicates a “leak” of the noncritical ion species which
ELECTROLYTE PERMEABILITY O F MOSAIC MEMBRANES. I
167
may be calculated as discussed in footnote 5 . Negative membranes with a C.Co.P. of less than $54.9 mv. were not considered potentially useful in the model system; positive membranes with a C.Co.P. more than 2.0 mv. below the maximum were not used.e The ohmic resistance of the positive membranes was measured by the method and with the equipment described by Gregor and Sollner (6). The resistance of the larger, negative membranes was obtained in a similar manner, but instead of platinum foil electrodes a platinized platinum wire cage about 60 mm. wide and 120 mm. high was used as the outside electrode and a helical coil 5 mm. in diameter and 80 mm. in length of platinized platinum wire wound round a glass rod as the inside electrode. The resistance data, recorded in the tables, are given in ohms per membrane, pa.1 K c 1 . 7 The electrolytes chosen for the experiments reported below were potassium chloride, lithium chloride, and potassium sulfate. The range of the absolute concentration of the two electrolyte solutions and the ratio of the concentrations of the concentrated and the dilute solutions were explored in a series of preliminary experiments; a fairly broad range of useful concentration was found to exist. Half of the final experiments mere carried out with pairs of solutions 0.05 ~/0.0015PI', other combinations used being 0.05 s,'0.005 x and 0.1 s / O . O l x . Two different types of electrode systems were employed, silver silver chloride electrodes as specific electrodes with chloride solutions, and Cu 1 CuSO4 1 agar bridge electrodes as nonspecific electrodes which may be used with any electrolyte solution. The larger one of the silver 1 silver chloride electrodes, which acts as the negative pole of the model system of figure 5, was a cylinder 125 mm. high and 61 mm. in diameter shaped from a piece of chemically pure sheet silver 0.25 mm. in thickness. The inside electrode was a spiral of chemically pure silver wire closely wound around a glass rod 10 mm. in diameter and about 80 mm. in length. These electrodes were covered electrolytically in the conventional manner with a layer of silver chloride. Whenever they became asymmetrical in use by more than 2 mv. they were renewed. The polarization of the electrodes on closed circuit seems to be small,-in the majority of instances not more than 2 or 3 mv. This is insignificant compared with the sum of the electromotive forces of the model systems used (110-160 mv. in the majority of instances). For nonspecific electrodes any reversible electrodes may be used which are ~
Some of the permselective protamine collodion membranes which were used in the experiments described later in this paper were prepared with protamine which had been modified by (partial) esterification of the free carboxyl groups which exist, probably aa end groups, in the native protamine molecule. The ionic selectivity of the improved membrane is significantly greater than that of the previously described protamine membranes, their C.Co.P. being increased up to -51.1 i.0.1 mv. against the heretofore reached optimum of about -53.2 h 0.1 mv. The membrane resistance p o . ] s mi does not give the resistance which the membranes show in the mosaic model, since membrane resistance is a function of the electrolyte used and of the concentration of the adjacent solutions ( 5 , 17).
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REX NEIHOF AND KARL SOLLNER
connected to the solutions by means of a sequence of suitable electrolyte solutions or electrolyte solutions immobilired in agar gels. A suitable arrangement with nonspecific electrode assemblies is shown in figure 6. It represents a chain, which in the conventional manner may be written as follows the double vertical lines representing the membranes:
-
cu
1
t
b a C c 1 b a ' CuSOh KNOa KCl KC11KC1 KCl KCI KCl KC1 KNOa c1 c2 c1 satd. satd. lsatd. cl c1 satd. satd. agar agar agar agar agar agar ~
The only nonsymmetrical and therefore active electromotive forces in this system are €6 and €7, the two membrane potentials.s The situation is identical with that arising in systems with specific electrodes. Four electrode assemblies connected in parallel were dipped into the outside solution and constituted the negative pole of the model systems; one assembly was used inside the positive membrane as the positive pole. The five electrode assemblies to be used simultaneously in one model system were prepared at the same time with the same solutions to assure electrode symmetry. The potential difference between the two poles of the model systems (when they were immersed in the same solution before the experiment) was never more than 2 mv. After an experimental run the asymmetry of the nonspecific electrodes usually had shifted somewhat from the initial value, but it never amounted to over 5 mv. The quantity of electricity JEowing in the model systems was measured directly with a semi-micro silver coulometer or calculated from the area under a currenttime curve. The maximum error in weight of the deposited silver waa about f0.00004 g. The quantity of electricity in faradays calculated from these coulometric data, Nooul, is
wc - wo
Nm"I = ____ 107.88
where WOand W t are the initial and final weights of t,he coulometer crucible in grams. The accuracy of the Noouldata reported later in this paper can be estimated to vary from 0.5 per cent up t o 2.0 per cent, according to the different weights of the silver deposited in the several experimental cases.
* The agar plugs, a, in this chain contain the same electrolyte a t the same concentration as the solutions in which they dip in order t o prevent any disturbing concentration changes in these solutions. The next agar plugs, b, are made of a saturated solution of the same electrolyte so as t o keep the resistance of the electrodes low, while increasing the distance between the plugs c and the solutions. This third set of agar plugs, c, which contact the copper sulfate compartments, are saturated with potassium nitrate. They serve to separate the agar plug saturated with the electrolyte used in the model from the copper sulfate solution, thus preventing possible reactions there which would adversely affect the electrodes.
ELECTROLYTE PERMEABILITY OF MOSAIC MEMBRANES. I
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For determining the number of coulombs moved from current-time curves two (factory new) Weston ammeters were available: one with an internal resistance of 55 ohms and a range of 0-500 microamp. and the other with an internal resistance of 5.7 ohms and a range of 0-5 milliamp. The probable error of the individual current readings was not more than 1 0 . 5 per cent of the full scale value. The time was measured with an electric timer. Since the intensity of the current diminished in the course of an experiment,, decreasing very considerably in some instances, an appropriate number of current-time readings were noted in each case. These data gave the ampere-minutes of current which had flowed in toto t,hrough the model system while the circuit was closed. The quantity of electricity moved. expressed i n faradays, as calculated from the ctirrcnt-time data. N,,,, is Ne,,
X ampere-minutes 96,494
X 60
(7)
The accuracy of the experimental X,,, values varies from less than 1 1 . 0 per cent t o f 2 . 0 per cent, according t o the strength of the current measured in the different experiments. The quantity of electrolyte which penetrates across the membranes from the concentrated to the dilute solution in a given time, either on open or on closed circuit, can be calculated from the known volume of the dilute solution and the increase of its concentration during the period under consideration. All concentration determinations were made conductonietrically ( T = 25.0OOC. f 0.05"). For the measurements the conductivity cell was rinsed at least three times with a solution of approximately the same concentrat,ion of the same electrolyte as the unknown. The last rinse solution was removed as completely as possible from the cell, with only an insignificant quantity of adhering solution remaining in it. About 5 ml. of the unknown solution was then transferred with a pipet from the model system to the conductivity cell, wit'hdrawn from it, and returned t o the model. Thereafter another ,5-ml. sample of the unknown was transferred to the conductivity cell for the actual resistance measurement after which the solution, as before, was returned to the model. These concentration determinations were accurate to about 0.2 per cent. The quantity of electrolyte moved on closed circuit in a mosair model system with nonideal, leaky membranes is obviously composed of three parts: the electrolyte, the movement of which is physically identical vith the flow of current; some electrolyte which might leak across the negative membrane; and some electrolyte Trhich leaks across the positive membrane. The translocation of electrolyte due to leak of the membranes, if of sufficient magnitude, would falsify the experimental results. Therefore, the leak of electrolyte of tjhe model systems, the sum of the two possible separate leaks, must be measured and appropriate corrections must be applied t o t,he raw experimental data. The obvious \ray of making these corrections consists in determining the rate
170
R E X NEIHOF AND KARL SOLLNER
of the leak on open circuit before and after the experiment and in applying a proportionate correction to the conductometrically determined quantity of electrolyte which on closed circuit is transferred to the dilute solution. Since the leak is small in comparison with the looked-for effect, the correction for the leak of electrolyte across the membranes, which corresponds to the closed-circuit period of each experiment, was made by straight-line extrapolation either graphically or by an equivalent calculati~n.~ The number of electrochemical equivalents of electrolyte moved on closed circuit corrected for leak, Naeono, was calculated from the equation
N
(Ct - Co - Amin X t)v A= ~ ~ ~ ~ 1000
In this equation Co and C, are the concentrations in equivalents per liter of the dilute solution in the middle compartment of the model system at the beginning and at the end of the closed circuit period; A,,, is the concentration change per minute of the dilute solution in equivalents per liter which is due to the leak of electrolyte (as determined on open circuit); t is the duration of the closed circuit period in minutes; and v is the volume of the dilute solution in milliliters. The data reported later can be estimated to vary from 1.5 accuracy of the NaeOne per cent to 2.5 per cent, depending on the magnitude of the relative increase in the concentration of the dilute solution. The evaluation of the experimental data consists in the comparison of the (corrected) number of electrochemical equivalents of electrolyte, N A ~ ~which , ~ , have moved into the compartment of the dilute solution and the number of faradays which have flowed in the systems, N,,,I or N.,,, as the case may be. The theory predicting identity of these two sets of figures, their per cent deviation from this prediction, A per cent, can be calculated readily, e.g., according to equations 9 and 9a, which define Naoono as the reference unit:
and
The deviation of A per cent from zero which results alone from the random combination of the above-discussed errors in N,,,I, N.,,, and N A can~be ex~ ~ pected to amount in the average to f 2 . 0 per cent or 2.5 per cent. In rare instances it might be up to about 5 per cent.
v This section presents a description of the experimental procedures employed in running the actual test experiments and representative experimental data. 9 In some instances it xas ascertained by separate tests that the membranes had a negligible leak of electrolyte under the conditions of the experiments. In such cases the described experimental procedure could be omitted when carrying out an actual experiment.
~
ELECTROLYTE PERMEABILITT OF MOSAIC MEMBR.PI\'ES.
I
I71
A typical experiment with a model with silver I silver chloride electrodes (figure 5) proceeded as follows: A positive and a negative membrane of the desired characteristics, mounted by means of their glass rings, were hung concentrically TABLE 1 Model ezperiment with specafie electrodes Segative membrane: C.Co.P. = f 5 5 0 my.; po I N K C I 2.0 SI Positive membrane: C.Co.P. = -54.0 mv.; ~ ~ I N X = C I 18.0 R Electrolyte: KCl Concentration of concentrated solution = 0 050 N Volume of dilute solution. u. = 70.0 ml.
-
I 1
DUXAIIONOF
INIXRVAL
1
CUPPENT
AVEaAGKI
IN INTERVAL
LL~TIIIcITy
O? DILUIE SOLUIION
amp. X 1 P
min.
-
0
600
m*
-
-
1.15
23.00
1.11
16.65
1.09
16.35
1.06
63.60
1.03
15.45
1.02
15.30
1.02
20.40
1.00
70.00
1.18 20 1.12
620 15 635
1.10 15 1.08
650 60
1.03
7 10
15 725
1.03 15 1.02
740 20
1.02
760 70
0.98
830 -
230
t
*
' CONCEYTPAIIOZ
LIOVED
1
0.00757
240.75
(800th to 830th) Circuit closed a t t = 800 min.
240.75 X lo-' x 60 = 149.7 X lo-' faradays 96,494 (0.00757 - 0.00543 - 0.00000025 X 230) X 70 - 145.6 X lo-' equivalents NAmm = loo0 149.7 X lo-' - 145.6 X lo-' A per cent = = +2.8 per cent 145.6 X lo-' Nsmp
=
~
in the middle of the rubber plate which also carried the large outside silver/ silver chloride electrode. The positive membrane was filled with the more concentrated solution and its glass ring was tightly closed with a rubber stopper
172
REX NEIHOF AND KARL SOLLNER
which carried the smaller of the above-described silver I silver chloride electrodes and the two glass tubes for flowing solution through the innermost compartment of the system. Next, a measured volume of dilute solution was pipetted into the space between the two membranes. The assembly prepared in this manner was lowered into the glass vessel containing a large volume (about 1000 ml.) of the concentrated solution and the level of this outside sqlution was adjusted to coincide approximately with that of the dilute solution between the membranes. The flow of solution through the innermost compartment and the stirring by air of the dilute solution were started. TABLE 2 Model experiment with nonspecijic electrodes Negative membrane: C.Co.P. = +51.9 mv.; @ . I N X C L = 115 0 Positive membrane: C.Co.P. = -53.5 mv.; @ . I N K C I = 50 0 Electrolyte: KCI Concentration of concentrated solution: 0.050 N Volume of dilute solution, u, = 80.0 ml. I
WEIOEI OF COOLOYETEE
~ramr
min.
16.84855 16.85150
0'
360
* Circuit
'
closed a t t
=
27.3 - 28.0 21.0
A per cent = -=
0.
-
~~T~~~~~~
cpuio./lilcr
~
0.001510 0.001860
LEAK PEP MlNU'lX
q&./lilw
Insignificant
_
_
-2.5 per cent
In this system the concentration of the dilute solution was measured repeatedly on open circuit during a period usually ranging from 2 t o 18 hr. Immediately after the last of these concentration measurements and without making any other changes in the system, the circuit was closed with the current flowing through the silver coulometer or one of the ammeters. When an ammeter was used a series of readings was made of the current intensity and of the time elapsed since the moment of closing the circuit. After the current had flowed for a period ranging from 1 to 6 hr. the circuit was interrupted and the h a 1 concentration of the dilute solution was determined. This concluded the experiment, except for some additional determinations of the leak which were added in many instances.1° The experimental procedure in the case of the model systems with nonspecific Cu I CuSO, I agar gel electrodes (figure 6 ) was essentially the same as with the 10 The leak after the closed-circuit period was found t o be practically the same a s initially; it, therefore, waa not measured in many of our later experiments.
~
ELECTROLYTE PERMEABILITY O F MOSAIC MEMBRAh'ES.
173
I
a
%-
M
d
0 0 0 0 0
~
P N I Od
9
539s-s
0 0 0 0 0
174
REX NEIHOR AND KARL SOLLNER
systems with silver 1 silver chloride electrodes. However, where an i n i a l run on open circuit of considerable length was indicated the electrodes were not inserted from the beginning but added later when the circuit was to be closed. This procedure prevented contamination of the solutions into which the electrodes dipped and, equally important, the electrodes could be prepared just prior to the critical, closed-circuit part of the experiments. Table 1 shows as an example the detailed experimental data pertaining to a model with specific auxiliary electrodes, silver 1 silver chloride in potassium chloride solutions, and membranes of fairly low resistance. The number of coulombs moved in this experiment is obtained from current and time readings. The quantity of electrolyte transferred is duly corrected for the “leak” of the system. Table 2 shows the analogous data for a system with non-specific electrodes and membranes of fairly high resistance, the “leak” of the membranes in this case being insignificantly small. The number of coulombs moved here is measured with a coulometer. Table 3 summarizes, in an abbreviated form, several more experiments with models in which the quantity of electricity transferred was determined coulometrically. Table 4 does the same for several systems in which current and time readings were taken.
T’I The experimental data summarized in tables 1 to 4 do not require extensive comment. The number of faradays moved, N,,,I and N.,,, and the number of equivalents of electrolyte transported, Naoona, agree satisfactorily. The per cent deviations of their ratios from the theoretically predicted 1:1 ratio, A per cent, given in the last column of the summarizing tables 3 and 4,are of the magnitude which must be expected in view of the previously discussed limits of the accuracy of the measurements, the mean deviation being less than &2.5 per cent. The theory of the electrolyte permeability of mosaic membranes outlined in this paper must, therefore, be considered to be verified by the experiment. One is now able to calcukte solely from the electrical characteristics of a mosaic system the quantity of electrolyte permeating to the dilute solution per unit of time. The verification of the theory of the electrolyte permeability of mosaic membranes in systems with auxiliary electrodes is conclusive and adequate from the strictly physicochemical point of view. The demonstration of the applicability of the theory in model systems without electrodes remains, however, desirable in order to show directly that all-electrolytic systems can not only be discussed adequately from the theoretical viewpoint, but can also be inirestigated quantitatively without any auxiliary devices. We expect to report shortly, in Part I1 of this paper, on the promising experiments which are currently being carried out on mosaic model systems without auxiliary electrodes.
ELECTROLYTE PERMEABILITY OF MOSAIC MEMBRANES. I
175
SUMMARY
1. The electrolyte permeability of mosaic membranes which are composed of ideally anion-selective parts and ideally cation-selective parts in juxtaposition is investigated theoretically by the consideration of model systems in which the anion-selective and the cation-selective parts of the membrane are separated from each other. A ring system is discussed quantitatively which consists of the cyclic arrangement of four component parts: 1 dilute solution I anion-selective membrane I concentrated solution I cation-selective membrane 1 . 2. In the ring systems described in paragraph 1 cations move from the concentrated to the dilute solution across the cation-selective membrane in the one arm of the model, and an equivalent number of anions through the anionpermeable membrane in the other arm, their electrical charges neutralizing each other. The system is also an “all-electrolytic electrical circuit” in the sense of Dolezalek and Kruger. The intensity of the current flowing in it at any given moment is determined by the total E.M.F. of the system, the sum of the two membrane potentials, and its total resistance. The movement of ions and the flow of current being only two different aspects of the same physical process, the number of electrochemical equivalents of electrolyte which penetrate across the membranes in a model system must be identical with the number of faradays which flow during the same period in it. 3. The general electrochemical considerations are presented which form the basis for an experimental test of the theory of the electrolyte permeability of mosaic membranes by means of model systems which involve the use of auxiliary electrodes. The limitations in the choice of the geometry of the model systems and in the conditions of their operation which stem from the lack of an ideal degree of ionic selectivity of the available membranes aTe evaluated. 4. Model systems are constructed consisting of a pair of coaxially arranged, test tube-shaped membranes (one being anion-selective and the other cationselective), and two auxiliary electrodes, either specific Ag I AgCl electrodes in chloride solutions or non-specific electrodes of the Cu I CuSO4 1 agar bridge type. The annular space between the two membranes is filled with a known volume of the dilute solution of some (preferentially) uni-univalent electrolyte. The inside of the smaller membrane is filled with a more concentrated solution of the same electrolyte, and the larger membrane is placed in a container filled with identical solution. Symmetrical electrodes are immersed in the latter two compartments. The number of faradays moved and the number of electrochemical equivalents of electrolyte translocated on closed circuit in such systems show a 1:1 ratio, with a mean deviation of less than f 2 . 5 per cent. The predictions of the theory, therefore, must be considered as proven quantitatively, well within the limits of the experimental error.
The thanks of the authors are due to Dr. Charles W. Carr for valuable suggestions and active help in the course of the experimental work presented here.
170
CHARLES W. CARR AND LEO TOPOL REFERENCES
(1) CARR,C. W.. AND SOLLNER, K . : J. Gen. Physiol. 26, 119 (1944). H . P., AND SOLLNER, K.: J. Gen. Physiol. 26,179 (1945). (2) CARR,C. W., GREQOR, (3) COLLANDER, R.:Kolloidchem. Beihefte 19, 72 (1924);500. Sci. Fennica, Commentationes Biol. 2, 6 (1926). (4)DOLEZALEK, F.,AND KRUGER,F.: Z. Elektrochem. 12.669 (19%). (5) GREGOR, H.P.: Ph. D.Thesis, University of Minnesota, 1945. (6) GREOOR,H . P., AND SOLLNER, K.: J. Phys. Chem. 60, 53 (1946). (7) GREGOR,H . P., AND SOLLNER, K.: J. Phys. Chem. 60, 88 (1946). (8) GROLLMAN, A., AND SOLLNER, K.: Trans. Electrochem. SOC.61, 487 (1932). (9) H ~ B E RRUDOLF: , Physical Chemistry of Cells and Tissues. The Blakiston Company, Philadelphia (1945). (10) MICHAELIS,L.:Bull. Natl. Research Council (U. 5.) No. 69, 119 (1929). (11) SOLLNER, K.:Z.Elektrochem. 98, 36,234 (1930);Kolloid-Z. 62,31 (1933). (12)SOLLNER, K.: Biochem. Z. 244, 370 (1932). (13) SOLLNER, K., AND GREQOR, H. P.: J . Am. Chem. 500. 67, 346 (1945). (14) SOLLNER, K., AND GREGOR, H. P.: J. Phys. Chem. 60,470 (1946). (15) SOLLNER, K., AND GREGOR, H . P.: J. Phys. Chem. 61, 299 (1947). (16) SOLLNER, K., AND GREGOR,H . P.: J. Phys. & Colloid Chem. 64 (March, 1950). (17)SOLLNER, K., AND GREGOR, H . P.: In preparation. (18) SOLLNER, K . , AND GROLLMAN, A.: Z. Elektrochem. 88, 274 (1932). L.: J. Gen. Physiol. 12, 55 (1928). (19) WEECH,A. A,, AND MICHAELIS,
T H E DETERMINATION OF SODIUM-ION AND CHLORIDE-ION ACTIVITIES IN PROTEIN SOLUTIONS BY MEANS OF PERMSELECTIVE MEMBRANES’ CHARLES W. CARR
Department of Physiological Chemistry, The Medical School, University of Minnesota, Minneapolis 14, Minnesota AND
LEO TOPOL Division of Physical Chemistry, School of Chemistry, Institute of Technology, University of Minnesota, Minneapolis 14, Minnesota Received August 8.9, 10.43
I The study of the interaction of various ions with proteins in solution has been of considerable interest for many years. It is now well known that the activity of many ionic substances is markedly influenced by the presence of proteins, the most familiar case being that of the binding of acids and bases. Through the use of various experimental techniques, it has also been shown that the activity of 1 Presented at the Twenty-third Kational Colloid Symposium, which was held under the auspices of the Division of Colloid Chemistry of the American Chemical Society at Minneapolis, Minnesota, June 6-8, 1949.
