330
KARL SOLLNER AND HARRY P . GREGOR
(8) SOLLNER, K., AND GREGOR, H. P . : J. Phys. Chem. 60, 4iO (1946). (9) SOLLNER, K., A N D GREGOR, H. P . : J. Phys. & Colloid Chem. 61, 299 (1947). K . , A N D GREQOR, H. P.: J. Phys. & Colloid Chem. 64, 330 (19.50). (10) SOLLNER,
T H E ELECTROCHEMISTRY OF PERMSELECTIVE PROTAMISE COLLODION MEMBRASES. I1 EXPERIMEXTAL STUDIES ON THE CONCENTRATION POTENTI.4L ACROSS VARIOUS TYPESOF PERMSELECTIVE PROTAMINE COLLODIOX MEMBRAXES TTITH SOLUTIOKS OF SEVERAL ELECTROLYTES KARL SOLLNER’
AND
HARRY P. GREGOR2
Department of Physiology, University of Minnesota, ikfinneapolis 14, Minnesota, and the Laboratory of Physical Biology, Ezperimental Biology and Medicine Institute, National Institutes of Health, Bethesda 14,Maryland Received April 11,
lQ4Q
I The preceding paper (19) presents data concerning the rates at which final, stable concentration potentials with various electrolytes are established across several types of permselective protamine collodion membranes. The present paper is a further contribution to the systematic investigation of the permselective membranes and presents an experimental study of the final, stable concentration potentials established by various electrolytes a t different concentrations across several types of permselective protamine collodion membranes. Not only are such studies necessary to enhance an understanding of the fundamental physical chemistry of membranes of porous character, but they are also desirable in view of the usefulness of these membranes in such investigations as, e.g., the study of Gibbs-Donnan membrane equilibria (5, 13, 14, 16) and in the electrometric determination of ion activities (3, 5, 12). The present investigation is parallel in plan, theoretical background, and technique t o an earlier study on the concentration potentials arising across (electronegative) permselective collodion membranes (18). Certain details which are treated briefly here are describkd in greater length in this previous paper. I1 The physical meaning of experimental concentration potentials measured across ion-selective membranes can be visualized best by reference to the t,heoretical limits of the possible electromotive properties of real membranes. With membranes of high ionic selectivity the more important of these limits are the 1 Present address: Laboratory of Physical Biology, Experimental Biology and Medicine Institute, Kational Institutes of Health, Bethesda 14, Maryland. 2 Present address: Polytechnic Institute of Brooklyn, Brooklyn 2, New York.
PERMSELECTIVE PROTAMIXE COLLODIOK MEMBRASES. I1
33 1
(calculated) potentials, E,,,, which would arise if the membrane would permit the reversible transfer of a single, the “critical,” ion species, thus acting as reversible “membrane electrode” ( 3 , 5 , 12). The “critical” ion in the case of electropositive membranes, such as protamine collodion membranes, is the anion. The other, lower, limit of the possible electromotive properties of real membranes is the potential which would arise across a membrane which does not show any ion selectivity of its own; it is identical with the liquid junction potential El xhich arises on free diffusion in solution. The theoretically possible maximum values of the concentration potential, E,,,, across a positive membrane in the chain: saturated calomel electrode 1 solution 1 i membrane 1 solution 2 i saturated calomel electrode, is defined by the general equation
where t- is the valency of the critical anion (considered as a positive quantity) and ai“ and ai2’ are its activities ci“ . y i i ) and ci” .yi*’in the two solution^.^ The majority of the numerical values necessary for these and the subsequent 3lacInnes calculations were taken preferentially from Harned and Owen (i), (9), and the International Critical Tables ( S ) , intermediate data being interpolated graphically. The probable errors in the calculated E,,, values are probably small compared nith the accuracy and reproducibility of our experimental data. The potential arising from diffusion in free solution, that is, the liquid-junction potential cz/cI, was calculated from the equation
where Ei(calc) is the liquid-junction potential, and where t and a refer to transference numbers and single ion activities in the respective ~ o l u t i o n With . ~ electrolytes other than potassium chloride, systematic errors of at least 0.10 mv. may occur in the calculated values of E l ( c e ~ c ) .
I11 The technique used for the measurement, of the concentration potential across the membranes was the same as that described in the preceding paper: saturated calomel electrode 1 saturated potassium chloride 1 saturated potassium chloridea I n the case of uni-univalent electrolytes, mean activities (a- = a,) were used. With the bi-univalent electrolyte magnesium chloride the activity coefficient for the critical ion, the chloride ion, is calculated assuming t h a t the activity coefficient of a given ion is a function only of the ionic strength of the solution. Then the activity coefficient y c i - i n a solution of magnesium chloride is the same as y c i - in a potassium chloride solution having the same ionic strength, assuming that y c i - = YK- in a solution of potassium chloride alone, 4 In a previous paper (18) the transference numbers were referred t o as being “\Tithin the membrane” (J. Phys. & Colloid Chem. 61, 300 (1947), line 7 from the bottom) when their values in free solution were meant, and referred t o as such further below in the t e s t .
332
KARL SOLLKER AKD HARRY P. GREGOR
agar bridge 1 electrolyte c? 1 membrane 1 electrolyte c1 1 saturated potassium chloride-agar bridge 1 saturated potassium chloride 1 saturated calomel electrode. In all instances the final, stable concentration potentials e were determined with all the precautions discussed in preceding papers (17, 18, 19). The electrolytes used mere potassium chloride, potassium iodate, lithium chloride, and magnesium chloride. The concentrat,ions investigated ranged from 0.002 si0.001 s to 0.4 ~ ; / 0 . 2K. Three types of membranes, Hum 20-Shr 20, Hum 58-Shr 58, and Hum 58, were studied. All measurements reported in table 1 for one type of membrane viere performed successively with a single membrane specimen. The reproducibiiity of the measurements is, in most cases, approximately =!=0.10mv.; in some instances the error may be twice as large, particularly with the most concentrated and the most dilute solutions. The liquid-junction potential of the membrane-free chains: saturated calomel electrode 1 saturated potassium chloride I saturated potassium chlorideagar bridge j electrolyte CP electrolyte c1 1 saturated potassium chloride-agar bridge 1 saturated potassium chloride saturated calomel electrode were measured in a simple W-shaped tube (18). At medium and higher concentrations the measurements were reproducible within about 0.10 mv.; at the lorvest, concentrations the probable error is greater than 0.10 mv. in some instances. Table 1 gives the values of the liquid-junction potential, El(exp)*, as measured, together with the corresponding calculated values, E i ( c a ~and c ) , their differences, A. The difference A is a correction xhich must be applied t o the concentration potentials as measured in the experimental membrane chains in order to arrive at the true values of the concentration potential as it was discussed in a preceding paper (18). Values of A which are positive have to be deducted from the (negative) experimentally determined value of the concentration potential ; negative A-values have to be added. The values of the concentration potentials e given in table 1 are all corrected in this manner. Table 1 gives the experimental and calculated data at the temperature 25.00"C. 0.05' for four different electrolytes. Column 1 gives the concentrations, CP and cl, of the electrolyte solutions used in equivalents per liter; column 2 gives the theoretically possible, maximum value of the concentration potential E,,, calculated as out,lined in the preceding section; columns 3, 4, and 5 present the concentration potentials e across three different membranes corrected as outlined above; column 6a gives the calculated liquid-junction potential Eiceaie, in free solution, computed as indicated before; column 6b gives the liquid-junction potential E L ( e x pas) measured; column Gc gives A, the difference between 6a and 6b, xhich has been applied to the values given in columns 3, 4, and 5 . Figure 1 presents these data in the form of graphs to facilitate their visualization and evaluationP Following an established convention the concentration c1 *See p. 333. 5 I n many instances the experimental concentration potentials obtained with different membranes and the same electrolyte coincide. In order t o make the graphic representation of these points feasible, the expedient has been chosen in figure 1 of not plotting some of the points in their proper positions b u t of arranging them outside the curves and indicating their proper positions by arrows.
333
PERMSELECTIVE PROTAMINE COLLODION MEMBRASES. I1
TABLE 1 Concentration potentials ( C , : C I = 2:1) of seueral electrolytes across various permselective protamine collodion membranes (1)
1
(2)
rpuis.lliler
'1
mo.
0.002/0.001 0.004/0.002 0.01/0.005
0.02/0.01 0.04/0.02 0.1/0,05 0.2/0.1 0.4/0.2
~
'
i ,
,
17.5 117.3 -17.1 -16.9 -16.6 -16.3 -16.1 -16.0
(4)
(3)
(5)
mc.
mlr.
-16.4 -16.5 -16.2 -16.2 -15.9 -15.2 -14.5 -13.2
ma.
-16.4 -16.5 -16.3 -16.0 -15.5 -14.3 -12.9 -11.0
-16.5 -16.5 -16.2 -16.1 -15.9 -15.3 -14.5 -13.0
i
(6a!
mu.
i
(6b)
mt
'
(6c)
mt
5i1 511
-0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3
511 511
511 511 511 511
B. Potassium iodate 0.002/0001 0.004/0.002 0.01/0.005 0.02/0.01 0.04/0.02 0.1/0.05 0.2/0.1 0.4/0.2
~
-17.5 -17.3 -16.9 -16.7 -16.1 -15.1
-16 2 -16 2 -16 1 -16.0 -11.9 -12.4 -10.2
-16.2 -16.1 -16.0 -16.0 -14.9 -12.6 -10.2
-15.9 -15.8 -15 4 -15.0 -13.5 -10.2
~
-6.9
1-5.5
+5.0
+0.5
+5.5
+5.0
+5.4 +5.3 +5.2
+5.0
+0.5 +0.4
f5.0 f4.8
+4.9
-5.8 -5.8 -5,s -5 8
-5.7
+5.1 +5.0
+4.7
f0.2 +0.2 +O. 1 4-0.1
~
C . Lithium chloride n.002/n.001
0.004/0.0OZ
0.01/0.005 0.02/0.01 0.04/0.02 0,1/0.05 0.2/0.1 0 . 4/0. 2
II
-17.~5 ' -17.3 i -17.1 -16.9 -16.7 -16.5 -17.0 -16.0
-16 6
-16.5 -16.6 -16.4 -16.3 -16.2 -16.2 -16.1
i1 ~
i
-16 -
8
-16.5 -16.6 -16.4 -16.4
-16.1 -16.0 -16.1
i1
1
.
-16.8 -
16.6 116.5 -16.1 -16.0 -15.3 -15.0 -14.2
-5.9 -6.0 -6.3
-5.7 -5.6 -5.6 -5.5
-5.1 -5.1
-0.1 -0.1 -0.2 -0.2 -0.4
-6.5
-4.7
-0.6 -1.2 -1.8
-7.2 -7.1 -7.1 -7.1 -7.1 -7.2 -7.2 -7.0
-6.5
-0.5
D . Mal ssium chloride 0.002/0,001 0.004/0.002 0.01/0.005 0.02/0,01 0.04/0,02 0.1/0.05 0.2/0.1 0.4l0.2
-17.4 -17.1 -16.9 -16.7 -16.4 -16.1 -15.9 -15.8
-17.5 -17.3 -16.7 -16.4 -16.2 -16.0 -16.0 -16.0
-17.3 -17.2 -16.7 -16.3 -16.1 -16.0 -16.0 -16.0 --
-17.1 -16.9 -16.5 -16.0 -15.8 -15.1 -15.3 -15.0
-6.5
-0.6
-6.7 -6.8 -6.8 -6.7
-0.4
-6.4
-5.3
-0.3 -0.3 -0.5
-0.8 -1.7
334
KARL SOLLXER AND HARRY P. GREQOR
Log c,
-2
-I
1
o: ;
I
~
-3
T I
-15
0 Hum 20- Shr 20 .Hum 5 8 - S h r 5 8 @Hum 58 --Theoretical maximum, Emax -0----Free diffusion, E Q ~ ~ & ~ , )
-5
1-01-
-5
-5-
I .------- ..-.___
--.I--...---.-.--
oa
CI
-2
-I
Fig. I
Concentration potentials C,:CI=2:I across various permselective protamine collodion membranes.
PERMSELECTIVE PROTAMINE COLLODION MEMBRANES. I1
335
indicated in the graph refers to the more dilute solution; plotted in this manner the data become easily comparable to analogous data on permselective collodion membranes and numerous other data published in this literature.
IV The data of table 1 and figure 1 show the same high degree of regularity and consistency that was previously observed in the case of the permselective collodion membrane (18). As in the former case me shall evaluate these data here merely in the conventional qualitative and semiquantitative manner, postponing to a later date the attempt a t their quantitative evaluation from a more theoretical viewpoint. The criterion for the evaluation of the data on membrane concentration potentials is the difference between the calculated theoretically possible maximum values, E,, and the corresponding experimental concentration potential, t . The smaller the difference between two corresponding such values, the higher is the “ionic‘selectivity” of a membrane under the particular conditions. In comparing the different types of membranes, it is obvious that the membrane Hum 20-Shr 20 and the membrane Hum 58-Shr 58 used in the present study behaved in the concentration chains virtually the same ; no significant differences between the two membrane specimens are evident (6). Membrane Hum 58 is of decidedly lower ionic selectivity as compared with the two other membranes (5, 6). This lower selectivity of the less dense membranes is conspicuous particularly at the higher concentrations, as is the case with the collodion membranes (18). In the comparison of the concentration potentials which are observed with the solutions of various electrolytes it is necessary to keep in mind the limits of the accuracy of the calculated as well as of the experimental data. Any conclusions which are drawn with respect to the differences of behavior of different electrolytes should be based primarily on the trend of the curves over wide concentration ranges and on the data obtained with higher concentrations (18). From table 1 and figure 1 it is immediately evident that the agreement between the calculated and the experimental concentration potentials is best with magnesium chloride; the ionic selectivity of the membranes is highest in this case. With magnesium chloride ideal ionic selectivity is approached closely in the case of the two denser, more highly dried membranes. Sone of the membranes referred to in table 1 and figure 1 s h o w an ideal degree of ionic selectivity with uni-univalent electrolytes, or nearly so. Even a t the lowest concentrations there exists a considerable difference between the measured and the theoretically possible maximum concentration potentials, in full agreement with previously published, less extensive data (1, 2, 5). With the uni-univalent electrolytes the membrane selectivity is highest with lithium chloride, less with potassium chloride, and still less, to a very considerable extent, with potassium iodate. The results are in full agreement with the concept put forward by Michaelis (10) that electrical and steric pore blocking account for the characteristic ionic
336
KARL SOLLKER AND HARRY P. GREGOR
selectivity of membranes of porous character, as exhibited in concentration chains. The electrical and the steric blocking reinforce one another in the case of the magnesium chloride: the magnesium ion is prevented from penetrating the membrane both on account of its large size and on account of the electric repuls'on which arises betwen the fixed positive groups at the pore ~i-allsand it,s two positive charges. On account of its double charge alone the magnesium ion would be screened out much more effectively than ions xvhich carry single charges only, such as the potassium ion. With pot,assium chloride the steric factor does not play an important role, since potassium and chloride ions have very nearly the same size; here, essentially the elect'ric factor of pore blocking alone is operative. In the case of lithium chloride the steric factor of pore blocking comes prominently into play on account of the great size of the hydrated lithium ion. Certain pathways across the membrane on a purely steric basis are inaccessible to the noncritical (lithium) ion.e The opposite situation prevails in the case of the potassium iodate; here the critical ion, the iodate ion, is considerably larger than the noncritical (potassium) ion'; the latter has a relatiaely better chance to penetrate the membrane than in the case of potassium chloride, the result being the observed, somewhat smaller, ionic selectivity in the case of the potassium iodate. The fact that the permselective protamine collodion membranes even in fairly dilute solutions do not shoiv a virt,ually ideal degree of ionic selectivity (except in cases of extreme steric hindrance of unusually large or polyvalent cations), as is found with their (electronegative) collodion counterparts, may be explained by the presence in the protamine molecule of at least one acidic (anionic) group. Accordingly, acidic groups must occupy some critical spots in the pore system of the protaminized membranes. These membranes, therefore, represent mosaics of numerous selectively anion-permeable pores and a few selectively cationpermeable pores, an electrochemical structure, which, according to all available information (15) could not result in an ideal degree (of purely electrical) ionic selectivity. The relative leak of noncritical ions can, of course, be calculat'ed readily from the ratio of the values of the experimental concentration potential and its theoretically possible maximum (4); it is approximately 3 per cent even in dilute solutions. It might be added here that the concentration range of usefully high ionic selectivity of these membranes, as was also the case with the permselective collodion membranes, can be expanded an appreciable extent beyoncl that indicated in table 1 and figure 1 by keeping the concentration at the one side of the membrane fairly low, e.g., ten or one hundred times lower than that' of the more concentrated solution. With this precaution the membrane selectivity as determined by potential measurements can be fully satisfacfory, e.g., for electrometric ion activity determinations (3, 5 , 12) at electrolyte concentrations considerably higher than those indicated by the experimental data which, employ a 2 : 1 concentration ratio. X probable explanation of this effect \vas discussed previously (18). 6 The relative diffusion coefficients of the potassium, chloride, lithium, and iodate ions in solution are in the ratio of approximately 1:1:0.5:0.5.
PERMSELECTIVE PROTAJIIXE C O L L O D I O S MEJIBR.iKES.
I1
337
Although the inherent shortcomings of the permselective protamine collodion membrane available at present have not prevented their successful use as physicochemical and analytical tools (3,5 , 12, 13, 14, 16) and in certain model studies (11, 20), their usefulness is such as to emphasize the desirability of further improvements in the degree of ionic selectivity of these membranes. Certain efforts in this direction are under lyay at present.
1. Concentration potentials of potassium chloride, potassium iodate, lithium chloride, and magnesium chloride solutions across several types of permselective protamine collodion membranes were measured at several concentration levels between 0.001 N and 0.4 x, the concentration ratio being 2:l. 2. The experimentally obtained concentration potentials are compared with the calculated values of the concentration potentials which would arise with membranes of ideal ionic selectivity, in other words, with the potentials which would originate if the membrane Lyould act as ideal reversible membrane electrodes for the critical anion. 3. Ideal ionic selectivity is not observed n-ith uni-univalent electrolytes. An appreciable leak of noncritical ion occurs in all instances,-approximately 3 per cent, even in the most dilute solutions. With magnesium chloride, an electrolyte with a very large and bivalent noncritical ion, ideal ionic selectivity is approached closely over a wide concentration range. The correlation between the selectivity of the membranes and the nature of the electrolytes is that expected on the basis of theoretical considerations. The membrane selectivity decreases in the series magnesium chloride, lithium chloride, potassium chloride, and potassium iodate. 4. The desirability of further improvements in the ionic selectivity of the permselective protamine membranes is stressed. REFERESCES (1) ABRAMS, I . , AND SOLLSER,K . : J. Gen. Physiol. 26, 369 (1943). (2) CARR, CH. GREGOR, H. P . , A S D S O L L S E R , I < . :J. Gen. Physiol. 28, 179 (1945). W. F., A N D KOLTHOFF, I. 11.: J. Phys. & Colloid Chem. (3) CARR,CH. W . , JOHSSOS, 61, 636 (1947). (4) CARR,CH. W., AND SOLLNER, K . : J. Gen. Physiol. 28, 119 (1944). ( 5 ) GREGOR, H . P . : P h . D. Thesis, University of Minnesota, 1945, (6) GREGOR, H . P . , ASD SOLLSER,K . : J. Phys. Chem. 60,88 (1946). (7) HARSED,H . S., ASD OWES,B . : T h e Physical Chemistry of Electrolyte Solutions. Reinhold Publishing Corporation, S e r York (1943). ( 8 ) International Critical Tables, Vol. VI. LIcGraw-Hill Book Company, Inc., S e w York (1929). (9) X ~ C I S S E SD. , A . : T h e Principles of Electroche7nistry. Reinhold Publishing Corporation, Sew York (1943). (10) XICHAELIS, L.: Bull. S a t l . Research Council, No. 69, 119 (1929); Kolloid-2. 62, 2 (1933). (11) SEIHOF, R E X :P h . D. Thesis, University of Minnesota, 1950 (in preparation). (12) SOLLSER, K . : J. .4m. Chem. SOC. 66, 2260 (1943). K . : J. Phys. Chem. 49, 265 (1945). (13) SOLLSER, K.: J . Am. Chem. Soc. 68, 156 (1946). (14) SOLLSER, K . , .4SD CARR,CH.W . : J. Gen. Physiol. 26,309 (1943). (15) SOLLJER,
w.,
338
J. 0. THOMPSON
(16) SOLLNER, K.,A K D GREGOR,H. P.: J. Am. Chem. SOC.87,346 (1945). K , A N D GREGOR,H. P . : J . Phys. Chem. 60,170 (1946). (17) SOLLNER, (18) SOLLNER, K.,A N D GREGOR,H. P.: J. Phys. & Colloid Chem. 61, 299 (1947). K., A N D GREGOR,H . P . : J. Phys. & Colloid Chem. 64, 325 (1950). (19) SOLLNER, (20) SOLLNER,K.,A N D XEIHOF,R. A , : J. Phys. & Colloid Chem. 64, 157 (1950).
SEDIMENTATIOS EQUILIBRIA OF POLYDISPERSE S O S I D E A L SOLUTES. I11 THE DEGR.4DATION
OF
POLYSTYRENE
IN
SOLUTIOS’
J. 0. THOMPSON 8 Department of Chemistry, University of Wisconsin, Madison, Wisconsin Received March 88, 184.9 I. IKTRODUCTIOK
The molecular size distribution existing in polymeric systems at equilibrium may be derived by statistical thermodynamics. This has been done for vinyltype systems by Tobolsky (12), who assumes that simultaneous polymerization and degradation may exist under certain conditions. Flory’s derivation (3), specifically for condensation systems, yields a similar result, but with reference to this result he states: “Vinyl type polymerizations could be included, although these processes generally are not reversible in the thermodynamic sense.” The attainment of thermodynamic equilibrium in vinyl systems under various conditions of heat, light, and catalyst has been suggested (6, 7, 9, 11). The dcpolymerization reaction was assumed to proceed by way of a radical chain mechanism and to compete with the polymerization reaction. On the basis of this simultaneous polymerization and depolymerization thermodynamics is introduced to determine the equilibrium distribution of molecular sizes. This equilibrium distribution turns out to be such that it may be regarded as being the result of a random scission process on an “infinite” linear polymer. For this size distribution the ratio of the -numbwaverage, weight-average, and z average molecular mights, approaches 1: 2 : 3 as the fraction of parent molecules decreases (4, 8, 10). It is the purpose of this paper to describe an investigation into the mechanism of attainment of this so-called equilibrium, and to show that the apparent approach t o a steady-state relative viscosity may not be construed as indicating an approach to equilibrium conditions. Some preliminary experiments (Section 111)
a,,:aw:Mz,
More complete details of this work are t o be found in the thesis submitted by J. 0. Thompson t o the Faculty of the Cniversity of Wisconsin in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June, 1948. This work was supported in part by a grant from the Wisconsin Alumni Research Foundstion. Present address: The Institute of Paper Chemistry, Appleton, Wisconsin.
