Jan., 1959
IONICMIGRATION IN ION-EXCHANGE MEMBRANES
55
IONIC MIGRATION IN ION-EXCHANGE MEMBRANES BY W. T. GRUBB General Electric Research Laboratory, Seknectady, New York Received April 16, 1068
The resistivities of some ion-exchange membranes have been measured at a frequency of 1000 c cles per second using a Shedlovsky conductivity bridge. The resistivities of three commercial types of membranes have geen compared a t 25’ I n addition, one type of sulfonated phenol-formaldehyde ion-exchange membrane has been further investigated under variety of conditions. The effects of the size of the mobile ion, the temperature and the level of water activity in this membrane upon its resistivity have been measured. It has been observed that the resistivity of the membrane is a linear function of the Stokes law radius of the mobile ion for a series of alkali metal ions. For membranes saturated with water the temperature coefficient of the specific conductance indicates an activation energy for ionic migration of about 3 kcal. per mole. When the activity of water in phenolic membranes in the hydrogen ion form is varied, it has been observed that the logarithm of the specific conductivity is a linear function of the activity of water. These results were obtained by equilibrating these membranes in solutions in water in ethylene glycol of varying composition. The implications of these results with regard to the mechanism of ionic migration in ion-exchange polymers are discussed.
a
Introduction The electrolytic properties of ion-exchange membranes have been studied t o a relatively slight extent compared t o other properties of these materials. This is true despite the convenience of making such measurements and the close relation of ionic conductivity t o the self-diffusion constant for the ion in question.‘ Although the relatively new class of materials comprising the ion-exchange membranes have found only a few applications notably in the purification of saline waters by electrodialysis,2 other uses would seem to be inevitable for the very special properties of these polymeric solid electrolytes. An excellent review of general properties of ion-exchange membranes recently has been published. Their application as solid state battery electrolytes4 has been reported. It is the purpose of this paper t o describe a method of obtaining the volume resistivity of ionexchange membranes under well defined conditions and to report the results of a study of the effect of some variables upon the volume resistivity. Many determinations of electrolytic properties of ion-exchange membranes have been carried out by the method of compartmented cells in which the conductivity of the membrane is determined by difference between the cell containing a membrane separator and the cell containing only the aqueous ele~trolyte.~-’ If the conductivity of the membrane containing no leachable electrolyte (i.e., in equilibrium with pure water) is desired, this may be found by extrapolation of the results of compartment cell measurements a t increasingly lower concentrations of electrolyte. Ion-exchange membranes can also be measured by a direct method consisting of clamping a sheet of the membrane directly in contact with inert metal electrodes and employing a conductivity bridge
in the usual way. I n this manner, Spiegler and Coryelll have investigated a phenol sulfonate formaldehyde membrane in its sodium, zinc and calcium forms near room temperature. They have also measured self diffusion rates of the cations using radioactive ions and have found that the Einstein* relation is approximately correct in describing the relation between electrolytic conductivity and self diffusion. Since the direct method for conductivity measurements on ion-exchange membranes gives results of greatest interest in considering their solid state properties, it has been refined and extended to the measurement of membranes under a variety of conditions. The characteristics of three types of cation-exchange membranes have been determined for the acid form and one type of membrane has been investigated under a variety of conditions to determine the effects upon its electrolytic conductivity of varying the ionic form, the temperature and the solvation of the membrane. I n the latter instance water-ethylene glycol solutions of various compositions have been employed. Experimental
The conductivity cell used to clamp the membrane in place between electrodes was constructed of Teflon. With a membrane in place, the electrolyte conductance was obtained directly at the terminals of the cell. However, since the contact resistance of the electrode-membrane interface might not be negligible, the cell was designed to eliminate this error by providing a number of fixed positions of the electrodes on the membrane such that a series of measurements at different cell constants was made. The plot of resistance versus cell constant (in the form of cell length divided by the product of membrane width by membrane thickness) was linear, and from its slope was obtained the volume resistivity of the membrane. The physical dimensions of the membranes were obtained by measurements with a micrometer caliper. The length in each measurement was determined by measuring the distance between the leading edges of the cell electrodes using a travelling microscope. Any errors in this arbitrary choice of reference points also cancel out when the method of variable cell (1) K.S.Spiegler and C. D. Coryell, THISJOURNAL,67, 687 (1953). constants is employed. The method of variable cell constants has been employed by Hills, et al.? in the measurement (2) C. B. Ellis, “Fresh Water from the Ocean,” The Ronald Press, of resistivities of some polyelectrolyte gels and found to New York, N. Y.,1954. (3) K.S. Spiegler, Chapter 6 of “Ion Exchange Technology,” ed. b y be satisfactory. The electrical measuring equipment consisted of a ShedF. C. Nachod and J. Schubert, Academic Press, New York, N . Y., lovsky conductivity bridge. A Wagner earthing circuit was 1956. employed to balance out unsymmetrical capacity paths to (4) W.T. Grubb, J . Electrochem. Soc., in press.
( 5 ) Ann. Rev. P h g e . Chem., 8 , 126 (1052). (6) G. Manecke and E. Otto-Laupenmtihlen, 2. phyeik. Chem. N . F . , 2, 336 (1954). (7) A. G. Winger, G. W. Bodamer and R . Kunin, J . Electrochem. Soc., 100, 178 (1953).
( 8 ) W. E. Garner, “Chemistry of the Solid State,” Butterworth’s Scientific Publications, London, 1955,p. 27. (9) G. J. Hills, J. A. Kitchener qnd P. J. Ovenden, Trqne. Fqradoy Soc., 61, 719 (1955),
W. T. GRUBB
56
ground. The detector was a pair of sensitive headphones behind a 2-stage amplifier. I n many of the ion-exchange membrane samples, the capacity compensation component is large, and to obtain a completely silent minimum, the capacitor of the bridge included a General Radio Co. Decade capacitor, which permitted capacity readings up to 1.2 microfarads. The conductivity cell was kept a t constant temperature in a heavy copper box immersed in a water thermostat. This box served the purposes of providing shielding, distributing any thermal gradients and confining the cell and membrane sample in a known atmosphere. Used in this manner, the copper box is a n air thermostat, and if electrically grounded, the usual objectionlo to the use of water thermostats in conductivity measurements is avoided. The atmosphere inside the copper box usually was kept a t 100% relative humidity by the presence of a small beaker of water with a wick immersed in it. Measurements in the present report have been confined to membranes in their leached states. Three commercid ion-exchange membranes of different type and manufacture have been employed. The procedures of Juda, et al.," were employed to ensure complete conversion into one ionic state and removal of counter electrolyte. The effect of the electrode surface upon the measurements was investigated. The resistance is a linear function of the variable cell constant for the same membrane whether bright platinum electrodes or platinized platinum electrodes are employed. Platinizing has mainly the effept of reducing the apparent contact resistance and does not markedly influence the slope. This means that the condition of the electrodes is not too critical in determining resistivities. Platinized platinum electrodes have been employed in all the experiments described. Cation membranes from three commercial suppliers have been compared in their hydrogen ion forms. These membranes are known under these trade names: "Amberplex C-1" manufactured by the Rohm & Haas Co., Philadel hia, Pa., "Zerolit 315" manufactured by the Permutit Co. Etd., London, England, and "Nepton CR-51" manufactured by Ionics, Inc., Cambridge, Mass. Their resistivities at 25.00 f 0.03' and 1000 cycles/sec. are, respectively, 38.2, 16.7 and 9.6 ohm cm. Unless otherwise indicated all resistivity data in this paper refer to 25' and 1000 cycles/sec. Various samples of membranes from a given manufacturer vary in resistivity from one sample to the next somewhat more than experimental errors could explain. Nine separate pieces of Ne ton CR-51 were measured and the results are shown in Tatle I.
TABLE I Sample no. 1 2 3 4 5 6 7 8 9 Av. 9.59 10.0 9.54 9.37 9.66 9.50 9.73 9.42 9.78 9.62 Resistivity (ohm om.)
The conductivities of ion-exchange membranes are affected not only by the membrane type but also by the ionic form of the membrane, the temperature and the solvating liquid. The effects of these !her factors have been determined for "Nepton CR-51, a condensation product of phenol-sulfonic acid and formaldehydelZ (hereafter called the phenolic membrane). Selected pieces with conductivity close to the average value of 104 milliohm cm. (see above) have been employed, and conclusions of the present work are based only upon the relative values of conductivity as a function of varying conditions, thus avoiding the variability indicated in Table I above. The phenolic ion-exchange membrane is characterized by its capacity in terms of amount of exchangeable ions per unit volume and its relative degree of cross-linking as indicated by the amount of swelling in water. These properties have been determined for a membrane of typical conductivity value and compared with previous values in the literature .I1 Measured dimensions of leached H + and N a + membranes indicate approximately 1% linear shrinkage in the conver(10) G. Jones and R. C. Josephs, J . Am. Chem. Soc., 60, 1065 (1928). (11) W. Juda, N. W. Rosenberg, J. A. Marinsky and A. A. Kasper. ibid., 74, 3736 (1952). (12) W.Jud8 et d.,U. S. Patent 2,636,851,
Vol. 63 TABLE I1 Present work (H+form)
Water content, % Wet density Capacity
0
*
Lit.11 (Na+ form)
*
54 1" 55.3 1" 1 . 2 i 0.1" . 1.33 i 0.01" 1 . 2 f0.1 1.26 f 0.02 meq./ml." meq ./ml." 1.01 meq./g. 0.94 meq./g." 2 . 2 meq./dry g. 2.1 meq./dry g. Based on leached aqueous sample wiped dry.
sion from H + to N a + for Nepton CR-51. The data of Table I indicate that the present samples of Nepton CR-51 are very similar to materials of the same manufacturer that have been characterized previously.ll
Results and Discussion Electrical Conductivity as a Function of Ionic Type.-A single strip of the phenolic ion-exchange membrane was measured in a series of ionic states through the cycle H+, Na+, Li+, K+, H+. The results are presented in Table 111. TABLE I11 RESISTIVITYOF PHENOLIC ION-EXCHANGE MEMBRANE IN UNIVALENT IONIC FORMS AT 25" Ionic form
H+ K+ Na + Li +
H+
Specific resistance, ohm cm.
Specific conductanre, millimho cm.-l
9.6 50.8 71 93.8 9.7
104 19.9 14.1 10.7 103
The final measurement of the H+ membrane shows a variation of about 1% from its initial value. The relative values of ionic conductance have therefore about this limit of accuracy. The conductivity values in the present work are somewhat higher than those previously reported by Rosenberg,Ia who has not published this work in detail. It is probable that only the relative values of conductivity have real significance at the present time since the absolute values depend upon frequency, variations of the membrane, contact resistances and also upon the method of measurement. It was pointed out14 that absolute resistivities are very sensitive to details of preparation of the membrane. The resistivities are found t o be linear with the hydrated ionic radii ( R i ) as calculated by Remy.16 The values of R i were computed by Remy from Stokes law and the mobilities of the ions (at infinite dilution). This particularly simple relation of p to Ri does not extend to ions of different valence or heavy metal ions. This is illustrated by measurements on zinc and copper presented in Table IV which includes a measurement upon the H+ state of the same membrane sample (differing from that of Table 111). Effect of Temperature upon Conductance of Phenolic Membranes.-The conductivity of aqueous solutions of electrolytes at varying temperatures frequently obeys Walden's rule in that (13) Ann. Rev. Phya. Chem., 4, 389 (1953) (referense to a Gordon Conference Presentation on Ion Exchange, July, 1951). (14) K. Sollner, Ann. N. Y. Acad. Sci., 57, 192 (1953). (15) H.Remy, Z.physik. Cham., 89, 467 (1915).
IONIC MTGRATION IN ION-EXCHANGE MEMBRANES
Jan., 1959
57
ylene glycol-water was selected somewhat arbitrarily for this part of the investigation. Leached H+ membranes were equilibrated for at least 150 hours in the selected solution of H20 in ethylene S ecific Specifio contuctance, glycol. While the membranes swell approximately Ionic resistance. millimho form ohm om. om.-' 100% in water alone, the swelling in ethylene glycol Zn++ 210 4.8 is about 14% greater than this, and intermediate swellings are observed for the solutions. Because CU++ 176 6.7 the swelling is so nearly constant the effect of the 9.1 110 Hf polymer network itself upon conductance is the increased conductance with rising temperature expected t o remain roughly constant over the range is proportional t o the decrease in viscosity of the of solvate composition. solvent. At 25" for example the viscosity of water Actual analysis for H20 in the polymer phase was decreases 2.2% per degree.l6 Since no measurable not obtained in this work. However, the activity viscosity exists in a polyelectrolyte gel swelled with of HzO was calculated from the water analysis water, interest attaches t o the measurement of ionic (Karl Fischer titration) in the solution, published conductivity as a function of temperature. A vapor pressure data,17 and density data of Curme single strip of the phenolic ion exchange membrane and Johnston'* for the water-ethylene glycol was measured at a series of temperatures between system. The H20 activity in the solution phase 0 and 41'. is, of course, equal t o that in the membrane. The following table presents the conductivity of TABLEV H+ membranes as a function of the solvate the RESISTIVITY OF PHENOLIC ION-EXCHANGE MEMBRANES IN composition expressed in various ways. THE H + FORM AT VARIOUS TEMPERATURES
TABLEIV OF PHENOLIC ION-EXCHANGE MEMBRANE IN RESISTIVITY DIVALENT IONICFORMS AT 25"
Temp. (0, OC.
25.00 0.1 12.6 20.0 40.6
10a/T
Specific resistance. ohm om.
S ecific cond'uctance, millimho om.
3.356 3.661 3.502 3.413 3.190
9.7 16.2 12.3 lo., 7.9
103 61.7 81.4 96.1 126.7
These data fall approximately upon a straight line when plotted as log K vs 10a/T. A least squares calculation (minimizing the squares of the log K residuals) shows the equation of the line to be log
K
= 9.79
or In K = 22.6
- 1.54 X 10*/T
(1)
- 3.54 X
(2)
10S/T
where T = temperature in degrees Kelvin K
= conductance in millimho cm.-'
This equation yields a temperature coefficient of 2y0 per degree centigrade near 25". Equation 2 may also be interpreted in terms of an enthalpy of activation for ionic migration. The calculated value of AH* for ionic migration is 3.0 kcal./mole. This conductivity-temperature relation confirms the generally accepted view of nearly complete ionization of the sulfonated polymeric ion exchangers, otherwise, a temperature dependent ionization constant would lead to a higher apparent value of AH* for ionic migration. The identity of the AK/At coefficient of the membrane with that of aqueous solutions also indicates that in H f migration the polymer network is not activated when the ion migrates. Effect of Solvation upon the Electrical Conductivity of Phenolic Ion-exchange Membranes.-The mechanism of ionic conduction of the H+ form of phenolic ion-exchange membranes is further elucidated by their conductive properties in equilibrium partially non-aqueous solutions. The system eth(16) "Handbook," 80th Edition, Chemical Rubber Co., Cleveland, Ohio, 1948, p. 1729.
TABLEVI OF H + PHENOLIC ION-EXCHANQE MEMBRANES RESISTIVITY AS A FUNCTION OF SOLVATION AT 25' USING THE SOLVATE SYSTEM H 2 0 - E GLYCOL ~ ~ ~ ~ ~ ~ ~ Cornnosition of solvatine soh. Activity -% Mole Concn. HtO HsO HIO,' fraction mg./ml. by wt. HnO (OHIO)
-
98 8.9 0.252 0.24 200 19.2 .434 .37p 310 28.5 .516 .579 395 36.6 .59s .665 997 100 1.000 1.00 From Karl Fiacher titration.
Resistivitv of m e k brane, ohm om.
335 150 89.2 58.5 9.6
Conductivity
of mem-
brane millimho
om.-#
2.98 6.7 11.2 17.1 104
The conductivity K of the membranes is a strong function of the activity of water in the solvate solution and therefore also in the membrane. The logarithm of K is very nearly linear with U H ~ O . This is true over the range of water activity from 0.2 t o 1.0. The best linear relation has been calculated by the method of least squares (minimum of squares of log K residuals). This line is expressed by the equations log K = 0.0899 In K = 0.207
+ 1.920~ano
+4
. 4 2 ~ ~ ~
(3) (4)
The actual reason for this linearity of log K with is not obvious. It means that the free energy of activation of ionic migration decreases linearly with rising water activity. Further work at varying temperatures is needed to establish whether this is the effect of solvation upon AH* or AS* or both. However, if it is assumed that AS* is constant, then it might be postulated that AH* would be inversely proportional t o the dielectric constant of the solvate since the migration of ions from the vicinity of one site to another in the polymer network requires separation of charges in a diUH*O
(17) H. M . Trimble and W. Potta, Znd. Ene. Chehem., 27, 66 (1936). (18) G. 0. Curme, Jr., and F. Johnston, "Glycols," Reinhold Pub]. Corp., New York, N. Y., 1952.
58
T. M. REED111 ASD T. E. TAYLOR
electric medium and the well known rule of electrostatic forces would apply. Equation 4 yields a t UH*O = 0 (pure glycol) the value In K = 0.207 and AH* = 5.4 kcal./mole. This predicts the dielectric constant of ethylene glycol a t 25" t o be 43 using the above assumption while the measured value is 37.7. Such agreement as this is satisfactory in view of the crudeness of the assumptions. Further investigation t o determine the actual polymer phase composition (in terms of water content) and measurements of K a t varying temperatures t o separate out entropy effects are needed t o determine whether AH* actually inversely proportional t o dielectric constant. If the linearity of log K with UH*O observed is general t o other solvating solutions, e.g., water
Vol. 63
plus alcohols, this simple rule will permit data on the diffusion of ions in ion-exchange polymersin partially non-aqueous media t o be extended with a minimum of experimental effort. The present approach to the conductivity of a partially hydrated ion-exchange polymer may differ only formally from that of ion pair formation employed by GregorIQand that of hydrat,ion shells employed by Glueckauf. 2o Acknowledgment.-The author thanks Dr. G. L. Gaines of this Laboratory for several helpful discussions in connection with this work. (19) H. P. Gregor, D. Nobel and M. H. Gottlieb, THISJOURNAL, 69, 10 (1956). (20) E. Glueckauf and G. P. Kitt, Proc. Roy. SOC.(London), A228, 322 (1955).
VISCOSITIES OF LIQUID MIXTURES BY T. M. REED111AND T. E. TAYLOR Department of Chemical Engineering, University of Florida, Gainesville, Florida Received April 24, 1968
The viscosities of ten binary liquid systems have been determined as a function of composition and of temperature in the range 25 to 45'. The thermodynamics of these systems range from the ideal solution to partially miscible liquids. The free energy of mixing alone is insufficient thermodynamic information in attempting to correlate the thermodynamic behavior with the viscosity behavior of solutions. The volume change on mixing and the entropy of mixing each are related to separate viscosity effects. Based upon the absolute reaction rate theory of Eyring these systems have been divided into three classes which differ in the dependence of the temperature coefficient of viscosity on temperature. It is found that as the temperature is decreased t o approach the two liquid phase region of a mixture, the viscosity as a function of composition displays an abnormally high value. This effect is found a t 22' above the critical unmixing temperature for the system composed of isooctane and perfluoroheptane. This analysis shows that the enthalpy of activation for all solutions may be considered as essentially independent of temperature even though the temperature coefficient of viscosity varies with temperature.
listed in Table I1 describe fairly accurately the activity coefficientsin systems 1,2, 3 , 4 . Experimental
Viscosities of liquid mixtures have been discussed by various authors.l-a A familiar approach is the hypothesis that there is a direct correlation between the viscosity and the thermodynamic behavior of the s ~ l u t i o n . In ~ this work it has been found that no simple relationship, such as that proposed by Grunberg3 and others14 exists. It has been found to be insufficient to limit the thermodynamic considerations to the free energy of mixing (activity coefficients). The entropy of mixing is related to viscosity effects. The ten binary systems studied in this work are listed in Table I in the order of increasing positive deviation from ideal behavior (positive free energies of mixing). The values B in this table are those which appear in Hildebrand's theory6 ( B equals zero for an ideal solution and increases with larger deviations from the thermodynamic ideal solution behavior). Solutions of hydrocarbons with fluorocarbons require special treatment.6J It has been shown7 that the B-values
Densities were measured in calibrated pycnometers .a Precisions of ~k0.00005and &0.0002 g. per milliliter were obtained for the ten- and one-milliliter pycnometers, respectively. Viscosity.-Cannon-Fenske9 viscometers were calibrated with a National Bureau of Standards oil and with pure toluene (properties identical to those in the literature'o), a t each temperature. Ubbelohde suspended level viscometersg calibrated by the Cannon Instrument Company were used for about 60% of the measurements and reproduced the data obtained with the other viscometers. Temperatures were read from thermometers or thermocouples calibrated with a National Bureau of Standards calibrated thermocouple having an accuracy of f.0.01'. Va or pressures were determined by boiling the liquid in a 8ottrell apparatus under air pressure. Gas-liquid chromatography was used for determinations of purity. The stationary media were those reported by Reed." Materials. Perfluoroheptane ( C,Fle) .-A fluorocarbon material (Minnesota Mining and Manufacturing Co. mat8erialF M 3130) was distilled in a 60-plate column.1a The
(1) D. B. Macleod, T r a m . Faraday Soa., 20, 348 (1924). (2) F.W. Lima, J . Chem. Phys., 19, 127 (1951). (3) L. Grunberg, Trans. Faraday SOC.,60, 1293 (1954). (4) S. Glasstone, I
