599
POROUS GLASSAS AN IONIC MEMBRANE
Porous Glass as an Ionic Membrane by Inci Altug and Michael L. Hair Research Laboratories, Corning Glass Works, Corning, New York
(Received July 24, 1967)
Porous glass has been shown to behave as an ionic membrane in electrolyte solutions. For solutions in which cation and anion mobilities are approximately equal, the membrane behavior closely approximates that predicted by Teorell and Meyer and Sievers, except with very dilute solutions and in instances involving solutions of low pH. Use of this model enables estimates of the fixed ion concentration to be made. Some deviations from the model are discussed, and it is shown that the measured membrane performance is dependent upon the way in which the porous glass is prepared.
to synthetic ion-exchange resin membranes, l v 2 collodionbased and ~ e o l i t eor ’ ~clay ~ membranes.’~~ All of these systems suffer from experimental disadvantages. The collodion membranes, although they can be prepared in a stable form, are very sensitive to deterioration; the synthetic resins are subject to hydration and consequent changes in electrochemical properties due to differing volumes of water contained in the membrane; and the clay and zeolite membranes suffer from the disadvantage that the individual crystallites must be either embedded in a plastic matrix or sintered to uniform porosity. It has recently been shown that porous glass can be successfully used as a membrane electrode which is sensitive to changes in divalent-ion concentration in aqueous solution6 and whose behavior can be described in terms of Teorell’s fixed-charge theory.? The porous glass may be prepared in uniform sheets of desired thickness, and its practical utility as an artificial membrane is thus suggested. The surface properties of the porous glass (after dehydration a t 500”) have been studied8-l0 and reviewed.” The material has a welldefined porous structure, and the surface area, pore size, and pore-size distribution of the dry material can be determined. On contacting with water. the silica is virtually insoluble, and this suggests that all effects, Other than that Of the surface On the pore liquid, can be ignored. A well-characterized membrane is thus obtained, In aqueous solution, the surface of the porous glass behaves as a weak dibasic acid’’2 due to hydration can be considered negligible, and the relatively inert character of this inorganic material reduces deY
2. Ionic Membranes According to the early fixed-charge theories, an ionic membrane is assumed to have fixed charges distributed uniformly throughout its porous structure. These charges are presumably due to the dissociation of surface sites and give rise to ion exchange. In the model, these sites are assumed to be strongly dissociated, and therefore the degree of dissociation remains constant under a certain set of conditions. Thus, the membrane is regarded as having a constant charge per unit volume or a fixed ion concentration. This value is also known as the charge density of the membrane. No further assumptions are made concerning the nature of these charges, and a monophase membrane model is discussed. In the case of a porous glass, however, with its well(1) G. J. Hills in “Reference Electrodes,” D. J. G. Ives and G. J. Janz, Ed., Academic Press, New York, N. Y., 1961, pp 411-432. (2) N. W. Rosenberg, J. H. B. George, and W. D. Potter, J . Electrochem. Soc., 104, 111 (1957). (3) H. P. Gregor and K. Sollner, J. Phys. Chem., 58, 409 (1954). (4) M. R. J. Wyllie and H. W. Patnode, ibid., 54, 204 (1950). (5) C. E. Marshall, ibid., 52, 1284 (1948). (6) N . C. Hebert and I. Altug, Second International Biophysics Conference, Vienna, Sept 1966. (7) T. Teorell in “Progress in Biophysics,” Val. 3, J. Butler and J. Randall, Ed., Academic Press, New York, N. Y., 1953, pp 305-309. (8) M, La Hair and 1. D, Chapman, J . Am. Ceram, Sot., 49, 651 (1966). . . (9) N. W. Cant and L. H. Little, Can. J . Chem., 42, 802 (1964). (10) M. J. D . Low and N. Ramasubramanian, J . Phys. Chem., 70, 2740 (1966). (11) M. L. Hair, “Infrared ~ p e c ~ r o s ~ oin p ySurface Chemistry,?? Marcel Dekker, Inc., New York, N. Y., 1967. (12) I. Altug and M. L. Hair, J . Phys. Chem., in press.
Volume 72, Number 8 February 1968
600
INCI ALTUGAND MICHAEL L. HAIR
defined, open porous structure, the charge density must be related to both the pore radius and the nature of the surface charge. If we have a charged pore of radius R, containing charges per unit area of surface, this charge must give rise to a potential ?Ilo a t the pore wall, which falls off as a function of distance until it reaches a minimum at the center of the pore. If W X is the theoretical fixed-ion concentration (where X represents the number of ionized sites per unit volume and w = f1, depending on the nature of the dissociated sites), then WXrepresents the average charge which is affecting ion movement and is physically represented by some function of 2n/R. The membrane properties of such a truly porous membrane were realized by Schmidla in his derivation of equations for electrokinetic quantities. Schmid did, however, treat his membrane as a quasihomogeneous electrolyte. It is the purpose of this work to show that the electrochemical potentials produced across a small-pore (40 A) glass membrane can be successfully accounted for using the extended fixed-charge theory of Teorell. The tacit assumption, therefore, is that the liquid in a true pore functions in much the same way aou water sorbed into more conventional, but structurally less well-defined, organic membranes. According to the Teorell model, the behavior of a charged membrane in an electrolyte solution can be characterized in terms of ionic mobilities, concentrations, and the fixed charge in the membrane. The membrane potential, E , is defined as the electrochemical potential difference between two electrolytes separated by a charged membrane. It is the sum of the two phase boundary potentials (nl m) and diffusion potential (#Q- cpl) within the membrane
+
E = (n1
+ rz) + (42 - 41)
(1)
Because of the membrane charge, an unequal distribution of ions at the interface is obtained, and this gives rise to opposing-phase boundary potentials n1 and nz, expressed as rl=
RT -In r1
r2 =
RT - In r2 F
F
(2)
where rl and r2 are the Donnan distribution ratios at the two interfaces. These ratios are given by the equation12
where a is the external solution concentration and c is the concentration in the membrane phase. The use of concentrations, rather than activities, is an assumption based on the practical difficulty of measuring ion activities in a membrane phase. I n membranes with low The Journal of Phgsical Chemistry
fixed ion concentrations (such as the porous glass under discussion), the activity coefficients of the ions in the membrane phase are probably not much different from those in solution and allow the use of the concentration term in eq 3. The diffusion potential (42 - $1) has been derived by Teorell, but its determination introduces a series of cumbersome calculations. However, the algebraic evaluation of (42 - 41) is simplified for a special case. When the membrane separates solutions of a single univalent electrolyte in different concentrations, (4z - 41) takes the following form12
u and v being the cation and anion mobilities in the membrane. In the present calculation, these are assumed to be the same as in pore solution. Subscripts 1 and 2 refer to the solutions on each side of the membrane. By substituting the suitable expressions in eq 1, the total membrane potential becomes Etotsi
=
ul(r1u u - uRT -- In u 4- v F az(r,u
+ v/rl) + RT r2 - In + v / r z ) F rl
(5)
If the principles of ionic membrane theory are valid for a porous glass membrane, then it should be possible to predict the membrane potentials when the fixed ion concentration, wX,is known. In the case where w X is not known, then membrane potentials measured in various single univalent electrolytes over a given concentration range should yield the same w X values. A graphical representation of eq 5 can then be used in order to determine wx,using a best-fit approach to previously determined curves.
3. Experimental Section The porous glass membranes used in these experiments were prepared in the conventional manner by the acid leaching of a phase-separated borosilicate g l a s ~ . ' ~ J ~ The final composition of the glass was approximately SiO2, 95%; Bz03,4%; and NazO, 1%. The surface area and pore-size distribution of the glass were determined by standard nitrogen adsorption techniques and application of the BET equation.16 The surface area of the glass was 110 m2/g and the average pore diameter was 32 A. The glass exhibited a narrow pore-size distribution, 96% of the pores being within + 3 A of the average value. The glass was used in the form of a closed tube about 14 cm in length and 6 mm i.d. Wall thickness was (13) G. Schmid, 2. Elektrochem., 54, 424 (1950). (14) M.E. Nordberg, J . Am. Ceram. SOC.,27, 299 (1944). (15) W.Haller, J. Chem. Phgs., 42, 686 (1965). (16) S. Brunauer, P.H. Emmett, and E. Teller, J. Am. Chem. SOC., 59, 1653 (1937).
POROUS GLASSAS
AN
IONIC MEMBRANE
601
approximately 1 mm. The resistance of this membrane in solution was essentially the same as that of the free solution. The membrane potentials were measured by means of the cell Ag, AgC11 solution 11 membrane 1 solution 2 1 satd KC1 I HgC12, Hg An sce with a salt bridge (saturated KCI) was used as reference electrode. The emf change of this electrode due to the concentration changes was assumed to be negligible. The leads of the standard calomel and silver-silver chloride electrodes were connected to a Corning Model 12 pH meter, used as a potentiometer. (The silver-silver chloride electrode placed in the internal solution 1 was used primarily to prevent any effects due to diffusion of KC1 from a calomel electrode into the small amount of solution 1. Experimentally, the volume available inside the porous glass tube did not permit insertion of an sce.) The total membrane potentials reported in this work are the difference in potentials measured between the cell
CONCENTRATIONS
Irqll 1
Figure 1. Total membrane potentials across a porous glass membrane in KC1 solutions of varying concentrations: solid lines, calculated values for various fixed ion concentrations; circles, observed values.
Ag, AgCl 1 solution 1 I membrane I solution 1I satd KC1 I HgClz, Hg and the one described above. Testing electrolytes were KCl, NaCl, HCl, and NHlNO3 of varying concentrations from 1.0 to N . The ratio of the solution concentrations in the cell remained 10: 1, solution 1 always having the higher concentration. The external solution was stirred during the measurement of the membrane potential, although it was found that this stirring did not have any effect on the emf except in solutions of low concentration N). to 4.
Results and Discussion
Values of w X can be obtained from eq 5 and 3, using the measured membrane potential. This procedure, however, is complicated, and an indirect method was used to interpret the results. A value for w X was assumed, and the rl and r2 distribution ratios were calculated according to eq 3 for the given electrolyte concentrations, a1 and u2. The theoretical total membrane potential was then determined from eq 5 for the 1.0N concentration range. The free solution values of u and v used in this calculation are taken from ref 17. By following this algebraic procedure, a series of theoretical curves can be obtained, one of which matches the experimental curve determined over the same concentration range (Figure 1). The fixed ion concentration of the membrane is the same as that of the theoretical curve which overlaps the experimental potential curve. The results for KC1 and other salt solutions are shown in Figures 1-4. In Figure 1, the measured and calculated membrane
""1, B
ol 1.0 a2 10-1
I
-,
CALCULATED FOR wP n0.06 I N I
10-1
10-2
143
IO-* 10-3 10-4 CONCENTRATIONS (rq/ I )
164
14s
Figure 2. Total membrane potentials across a porous glass membrane in NHaNOs solutions of varying concentrations: dotted line, observed values; solid line, calculated values assuming u.? = 0.00 N .
potentials are plotted as a function of KC1 concentrations. When a fixed ion concentration, w f z = 0.06 N , is assumed, it is seen that the agreement between the calculated and experimental points is good, and therefore this membrane is assigned a fixed ion concentration of 0.06 N . Figures 2 and 3 show similar plots for "*NO8 and NaCl solutions. In these cases, the experimental values agree with the calculated values for WX= 0.06 N in the lo-' and N concentration range. However, calculated membrane potentials deviate from the observed potentials in HC1 solutions (Figure 4) and a t low concentrations. The low potentials in dilute solution might be ascribed to leakage of electrolyte across the membrane. However, changes in the dissociation of the surface hydroxyl groups at low con(17) W. J. Moore, "Physical Chemistry," 3rd ed, Prentice-Hall Inc., Englewood Cliffs, N. J., 1963, p 337.
Vohrne 72, Number 2 February 1068
602
INCI ALTUGAND MICHAELL. HAIR
a1 1.0 a
IQI
i0-I IC2 iU3 W4 10-2 tcrj 10-4 I@ CONCENTRATION (op! I)
Figure 3. Total membrane potentials across a porous glass membrane in NaCl solutions of varying concentrations: dotted line, observed values; solid line, calculated values assuming UT = 0.06 N .
Z
Y
I
-CALC.LATED FOR wx ~ 0 . 0N 6
aI 1.0 a2 i d
la3 10-3 10-4 CONCENTRATION (rqll)
' 0 1
10-2
10-5
Figure 4. Total membrane potentials across a porous glass membrane in HCl solutions of varying concentrations: dotted line, observed values; solid line, calculated values assuming UT= 0.06 N .
centrations cannot be ignored, and it is possible that eq 3 does not hold at these low concentrations. Examination of eq 4 reveals that, for electrolytes having nearly equal cation and anion mobilities, the diffusion potential is reduced to small values. Thus, the membrane potential becomes almost independent of ion mobilities. For both KC1 and NH4N03, the cation and anion mobilities in free solution are almost identical, and good agreement is found between experimental and theoretical curves. In the case of NaCl and HC1, the cation and anion mobilities are considerably different, and eq 4 makes a significant contribution to the total membrane potential. Good agreement with theory is obtained for the NaC1, but not for the HC1. It should be noted that the cation and anion mobilities used in the present calculations are those of the free ions in solution.17 Diffusion data in the literature, however, indicate that the ion mobilities go through a considerable change in a charged phase.18 The good The Journal of Physical Chemistry
agreement between observed and calculated curves in the cases of the salt solutions indicates that the poroas glass membrane is behaving in a manner closely allied to that predicted by Teorell? and Meyer and Sievers,l8 and that the cation: anion mobility ratio is little affected by the charged membrane pore. In the case of the HC1 solution, even a negligible charge density will not account for the low emf which is observed. In this case the cation :anion mobility ratio may be considerably altered by the charged pore, the mobility of the cation being decreased relative to that of the anion. An assumption made in the Teorell model is that the sites in the porous structure do not have preference for any specific ion in the solution. However, experimental data suggest that the sites on the porous glass surface prefer H + over other cations a t certain concentrations.'2 The difference between the calculated and observed membrane potentials a t 10-L10-6 N concentration range is possibly due to this effect. In the case of the NH4NO3 solutions (Figure 2), a deviation between predicted and measured potential is observed for the 1.0-lo-' N range. Although this is not the only explanation, this deviation might also be due to a pH effect, the pH of the 1.0 and lo-' N NH4N03solutions being 4.6 and 5.2, respectively. The pH is also of some consequence in its effects on the number of exchangeable sites present on the glass surface. Previous work12 has shown that porous glass of the type used in these experiments behaves as a weak dibasic acid with surface pK, values of about 5 and 8. In view of this, the number of exchanged cations is considerably dependent on the pH of the surrounding solution. This is more clearly seen from some results in which the charge density of a single membrane was determined in KCl solutions of pH 5.0 and 8.5. The charge-density values a t these pH levels were 0.04 and 0.06 N, respectively. Thus, the charge density of the same membrane is higher when determined with solutions of higher pH. Titration data reported previously show that the K + uptake from KC1 solutions at pH 5.0 and 8.5 is about 4 x and 1 X lo-' mequiv/g, respectively. Thus, the number of exchanged sites also rises with pH. From the gas adsorption data and with the assumption of cylindrical pores, the pore volume of the glass is calculated to be 0.087 ml/g. At pH 5.0, the density of exchanged sites is calculated to be 0.045 N, which is in fair agreement with the observed electrochemical value of 0.06 N. This agreement, however, is probably fortuitous, since gross deviations are observed at higher pH's. From the preceding discussion, it seems inevitable that the fixed ion concentration in a porous glass mem(18) D. MacKay and P. Meares, Trans. Faraday SOC., 5 5 , 1221
(1955). (19) K. H.Meyer and J. F. Sievers, Helv. Chim. Acta, 19, 649,987 (1936).
603
THERMODYNAMICS OF HICH-TEMPERATURE HIGH-PRESSURE SOLUTIONS brane is dependent both on the radius of the pores and the surface charge on the pore wall. It is known that the geometry of the pores in the porous glass can be altered by the heat-treatment schedule to which the glass is subjected prior to leaching; lower temperatures give rise to smaller pores.16 In view of this, the base glass used in these experiments was subjected to heat treatment at 580" rather than 620". Subsequent leaching conditions were made identical. The resultant porous glass was then made into a membrane and the membrane potentials measured in KCI solution. Calculation of the fixed ion concentration of this membrane was found to have been increased to 0.15 N in accord with the prediction. These results show that porous glasses function satisfactorily a,s model ionic membranes. The low
fixed ion concentration precludes large concentration jumps a t the phase boundaries, and the results suggest that the Donnan equilibrium at the membrane-solution interface is close to that predicted. The low ion selectivity which is observed between K+, Na+, and Li+ ions during adsorption on the porous glassI2 is a further fulfillment of the Teorell assumption that the porous membrane does not have a preference for any specific ion in the solution. The possibility of altering both surface charge and pore size in these glass membranes provides an opportunity for further study.
Acknowledgment, The authors wish to express their thanks to Dr. G. Eisenman (University of Chicago) and Dr. L. Hersh (Corning Glass Works) for their helpful comments during the course of this work.
Thermodynamics of High-Temperature High-pressure Solutions. Argon in Molten Sodium Nitrate' by James L. Copeland and Lawrence Seibles Deprtment of Chemistry, Kansas State University, Manhattan, Kansas 66602
(Received July 24, 1967)
The solubility of Ar in molten NaN03 has been determined over a temperature range from 356 to 441" at pressures from 151 to 395 atm. Henry's law constants, Kh, and distribution coefficients, K O ,were found for the resulting six solubility-pressure isotherms. A plot of log K hus. 1/T yielded a value for the enthalpy of solution, AH, of - 1.69 f 0.21 kcal mole-'. The standard entropy of solution, corresponding to a standard state of 1 M concentrations of gas in both the liquid and gaseous states, AS,", resulted as -4.97 f 0.32 eu from the intercept of a plot of log K, us. 1/T. The results are compared to similar work in this laboratory involving Nz in fused NaNOa, where AH = -2.73 f 0.09 kcal mol-' and AS," = -6.78 i 0.18 eu, and with low pressure work in molten fluoride systems performed in other laboratories where AH values were endothermic. Calculations of AH'S of solution for both the Ar and Nz work using approximate fugacities rather than pressures did not change the values appreciably, yielding -1.84 f 0.21 kcal mol-' for Ar in NaT\'Os and -2.69 f 0.08 kcal mol-' for NZ in NaNOs. Conclusions are drawn which compare the relative contributions of exothermic solvation effects and endothermic molecular cavity creation work in the liquid to the over-all heat of solution. It is seen that predictions based on such a simple model conceived for the Np work are, for the most part, reasonably confirmed in the present investigation.
Introduction In a previous paper the authors reported the results of a study of t'he temperature and high-pressure dependences of the solubility of Nz in fused NaNOa.Z The system was found to possess an exothermic heat
of solution and a rather high negative entropy of solution. A tentative simple model was advanced which (1) This work was presented in part at the Third Midwest Regional Meeting of the American Chemical Society, Columbia, Mo., Nov 1867.
Volume 72, Number 2 February 1068
