(12) Denton, J. J American Cyanamid Co., Research division, Bound Brook, N. J., private communication, 1965. (13) Ferraro, J. R., Peppard, D. F., J . Phys. Chem. 67, 2639 (1963). (14) Forman, E. J., Hume, D. N., Talanta 11, 129 (1964). (15) Hantzsch, A., Chem. Ber. 55, 953 (1922). (16) Hantzsch, A,, Burawoy, A., Ibid., 63, 1760 (1930). (17) Heidenhain, LL, ilrch. Ges. Physiol. 100, 217 (1903). (18) Kehrmann, F., Grillet, E., Borgeaud, P., Helv. Chim. Acta 9, 866 (1926). (19) Kolthoff, I. AI., Rosenblum, C., “Acid-Base Indicatori,” Llacmillan, New York, 1937. (20) Lewis, G. E., Tetrahedron 10, 129 (1960). (21) hIcRae, E. G., J . Phys. Chem. 61,562 (1957).
(22) Mohlau, R., Uhlmann, K., Ann. Chem. 289, 90 (1896). (23) Paabo, M.,Robinson, R. A., Bates, R. G., J . Am. Chem. SOC.87, 415 (1965). (24) Powers, J. C., Jr., Heller, W. R., Kumamoto, J., Donath, W. D., Ibid., 86, 1004 (1964). (25) Pries, C., Bottcher, C. J. F., Anal. Chim. Acta 31, 293 (1964). (26) Reichardt, C., Angew. Chem. Intern. Ed. Engl. 4, 29 (1965). (27) Reimer, AI., J . Am. Chem. Sot. 64, 2510 (1942). (28) Schafer, W., “The Chemistry of the Phenoxazones,” in “Progress in Organic Chemistry, T’ol. 6 (Sir J. Cook, W. Carruthers, edj.), Butterm-orths, Washington, 1964. (29) Thorpe, J. F., J. Chem. SOC.91, 324 (1907). (30) 1-enkatsraman, K., “The Chemistry
of Synthetic Dyes,” 1-01. 11, Academic Pres., Xew York, 1052. (31) Yittum, P. IV., Weisaberger, A., J . Phot. Sci. 2, 81 (1954). (32) Zollinaer, H., “Azo and Diazo Chemistfir:. Ahhatic and Aromatic Compou .uch identification imply recommendation or indorsement by the Xational Bureau of Standards, nor does it imply that the material or instrument identified is necessarily the best available.
Voltammetric Membrane Electrode Study of the lon-Exc ha nge Properties of Cel Iop ha ne Memb ra nes RICHARD C. BOWERS and ROYCE W. MURRAY2 Department of Chemistry, Northwestern University, Evanston, 111.
b The diffusion properties of hydrogen ion and aquo-cadmium ion in cellophane, as characterized by their behavior at a voltammetric membrane electrode, have been investigated. It is found that ordinary cellophane has within its structure a number of fixed anion sites which are believed to be derived from carboxylic acid functional groups. The resultant ionexchange characteristics of the membrane give rise to cation partition coefficients between the membrane and aqueous phases that are greater than unity. Two phenomena, a Donnan partition and an association of the electroactive cation with the anion sites of the membrane, are considered to contribute to the overall partition coefficient. A marked decrease in the apparent diffusion coefficients of both the hydrogen ion and the aquocadmium ion is observed with increasing adsorption (association with the fixed sites in the membrane) of these ions. Steady state currents are influenced very little, if at all, by the association phenomenon but increase with increasing Donnan partition.
P
work in this laboratory ( I , 2 ) has shown that the diffusion behavior of thallous ion and tetraamine cadmium(I1) ion in cellophane agree well with simple theory. Aquocadmium ion, however, exhibits an abnormal behavior when present at low REVIOUS
concentrations. This was attributed to an adsorption of cadmium within the membrane. Subsequent experiments indicate that the behavior of hydrogen ion a t a cellophane membrane electrode is similar to that of the aquo-cadmium ion. The work reported in this paper was carried out in a n attempt to understand the adsorption properties of cellophane for cadmium and hydrogen ion and to study the effect of this adsorption on the diffusion characteristics of these ions in cellophane. The results obtained in this work have a bearing both on the practical use of the voltammetric membrane electrode as an analytical tool and on an understanding of the general phenomena of transport across membranes and related phenomena. These latter topics have been given considerable attention in the past few years (6, 7 , 9 ) . EXPERIMENTAL
Reagents. Supporting electrolyte solutions of potassium nitrate and tetramethyl ammonium chloride and stock solutions of thallous nitrate were prepared from t h e recrystallized salts. Standard cadmium solutions mere prepared from cadmium chloride dihydrate and standardized with (ethylenedinitri1o)tetraacetic acid using the method of Reilley (14). Mercury, which had been treated with a 10% nitric acid solution and then distilled a t reduced pressure, was employed in all experiments.
Electrode. T h e electrode employed was constructed in t h e manner described previously ( 2 ) . Two types of cellophane were used. Cellophane having the type number 600 PD was obtained through the courtesy of E. I. du Pont de Nemours and Co. Cellophane prepared by hydrolysis of Eastman Kodak cellulose triacetate film in 1M KOH methanol solution was also used. The latter was considerably purer and stronger than ordinary cellophane. Apparatus. T h e electrolysis cell and t h e instrumentation used were the same as previously described ( 2 ) . The general purpose electroanalytical instrument (5) also served as the coulometer in experiments in which integration of current-time curves was carried out. TREATMENT OF DATA
Evaluation of Diffusion and Partition Coefficients from Voltammetric Data. I n previous papers in this series ( 1 , 2 ) , equations applicable t o voltammetry at a membrane electrode have been given. However, these equations are based on the assumption of equal concentrations of electroactive species in the membrane and aqueous phases (unit partition coefficients). Present address, College of Liberal Arts and Sciences, Northern Illiiiois University, DeKalb, Ill. Present address, Department of Chemistry, University of North Carolina, Chapel Hill, N. C. VOL. 38, NO. 3, MARCH 1966
8
461
Table 1. Apparent Diffusion and Partition Coefficients of Hydrogen Ion in Cellophane Supporting Electrolyte: O.lOOM(CH3)JVCl A. 600 PD cellophane CH+,'(mM in
aqueous phase) 0.167 0.250 0.333 0.416 0.498 0.581 0.667 0.832 0.914
I, X
lo6 20.8 33.0 24.1 24.6 25.0 24.5 25.2 24.5 24.5
It X
lo3 29.1 25.6 24.0 21.8 20.4 18.2 16.9 14.6 13.6
D. X
lo6 0.510 0.805 1.00 1.27 1.51 1.81 2.22 2.82 3.22
Pa 40.8 28.6 24.1 19.4 16.5 13.5 11.4 8.69 7.60
B. Hydrolyzed cellulose triacetate 0.344 0.687 . .. 1.358 2.02
13.3 10.3 15.3 8.95 1 6 . 3 7.11 16.1 6.45
1.67 2.92 5.24 6.22
7.96 5.25 3.11 2.59
If the partition coefficient of the electroactive species between the membrane and aqueous phase is not unity, these equations must be modified by replacing C" by PC,". Thus:
i,
. . tt/a,
=
nFAPC,"D,/L
(1)
=
d;= nFAPC,"
d x / 2 i a
(4)
where P is the partition coefficient of the electroactive species between the membrane and aqueous phase, C", its concentration in the aqueous phase, D, its diffusion coefficient in the membrane phase, and d and 1 the cross sectional area through which diffusion occurs and the thickness of the membrane, respectively. The terms i,, it,i,, and 7 represent the steady state current, instantaneous current, applied current, and transition time, respectively. Equations 1-3 are applicable for constant potential voltammetry and Equation 4 for chronopotentiometry. Equations 3 and 4 are based on the assumption of infinite diffusion conditions and are valid only when t < 0.19P/Dm (2) or T < 1.6Dm ( l ) ,respectively. I n principle, diffusion coefficients can be evaluated from voltammetric data either by making use of Equation 2 or by combining Equations 1 and 3 or 1 and 4-i.e., from 1 and 3:
e/-
(5) or from 1 and 4:
If it is assumed that the cross sectional area through which diffusion occurs is 462
0
ANALYTICAL CHEMISTRY
equal to the total area of the membrane, then partition coefficients can be evaluated by making use of any of the equations, 1, 3, or 4,and the previously calculated diffusion coefficient. Since it has already been demonstrated ( 2 ) that cellophane, under conditions where unit partition coefficients are eupected, is homogeneous with regard to diffusion, this assumption is quite realistic. I n the writing of the above equations, it is tacitly assumed that the electroactive substance exists as a single species in the membrane phase or, if not, that D , is some mean or apparent diffusion Coefficient. Partition coefficients calculated using such apparent diffusion coefficients would, of course, be of dubious validity. Evaluation of Partition Coefficients from Coulometric Measurements. This method involves integration of the current-time curves obtained a t the voltammetric membrane electrode. Two integrations are necessary, one of the current-time curve obtained when the electroactive substance is present in the membrane prior to application of a potential sufficient to cause its reduction (equilibrium experiment or case A of reference 2). The other integration is of the current-time curve obtained when a small amount of solution containing the electroactive substance is injected into the aqueous phase after application of a potential sufficient to cause its reduction (injection experiment of case B of reference 2 ) . The total concentration of all forms of the electroactive substance in the membrane phase in equilibrium with the particular concentration of electroactive species in the aqueous phase is given by:
where QE and Q I represent the number of coulombs obtained by integration, over equal periods of time, of the equilibrium and injection current-time curves, respectively. Equation 7 is derived from a consideration of the origin of the electroactive substance being reduced in the two different experiments and is valid even if the absolute values of the current depend upon the rates of interconversion of the various forms of the electroactive substance as well as upon their rates of diffusion. Evaluation of Partition Coefficients from Equilibrium Studies. I n these measurements, a large sheet of the basic form of cellophane was immersed in a deaerated solution which was 0 . 1 X in tetramethyl ammonium chloride. After addition of various amounts of electroactive substance, t h e concentration of the electroactive substance in solution was measured using a previously
calibrated voltammetric membrane electrode. The total amount of electroactive species taken up by the membrane could thus be calculated. RESULTS AND DISCUSSION
Behavior of Hydrogen Ion. Current-time curves for the reduction of hydrogen ion a t electrodes employing 600 P D cellophane and hydrolyzed cellulose triacetate were obtained over a range of concentrations. rlnalysis of these d a t a to obtain diffusion coefficients was carried out by utilizing both Equations 2 and 5 . Excellent agreement between diffusion coefficients calculated using two different equations was obt ained--i .e., with 0.581m J I hydrogen ion one obtains apparent diffusion coefficients of 1.8 X 10-6 and 1.81 X cm.*/second from Equations 2 and 5 , respectively. Table I lists experimental values of the steady state current constant ( I , = i,L/FAC,"), the transient current constant ( I t = itd / n t l F S C , " ) , and calculated (Equation 5) values of the apparent diffusion and partition coefficients. The steady state current constants are essentially independent of the hydrogen ion concentration in the body of the solution whereas the transient current constants and the apparent diffusion coefficients are markedly dependent upon the hydrogen ion concentration. These data are consistent with the supposition that the membrane contains weakly basic anionic sites and that the hydrogen in the membrane exists in two forms, hydrogen ion which is free to diffuse and hydrogen associated with fixed sites in the membrane. Extensive evidence for the presence of residual carboxylic acid functional groups in cellulosic material has been cited in the literature (8, 10-13, 15). Ion Exchange Capacity of Cellophane. The concentration of weak acid sites in the membrane (e) was measured both by a direct titration of the acid form and a n indirect titration of the basic form of a large sheet of the cellophane. I n addition, measurements of the overall partition coefficient, P T , of hydrogen ion between the cellophane membrane and the aqueous phase were made as described above (coulometric and equilibrium measurements). The partition coefficients obtained using these two techniques agreed with one another but did not agree with those obtained from the voltammetric data (Table I). This substantiates the supposition that hydrogen exists in two forms in the membrane phase and indicates that the simple voltammetric equations given above are not strictly valid. The partition coefficients obtained from the coulometric and equilibrium studies were used to calculate both the
0.1
0.2
0.3
0.4
Ob
C\ (mM1
Figure 1 . Plot of ~ / P T- 1 vs. C," for hydrogen in 600 PD cellophane
capacity of the weak acid sites in the membrane and their pK, value. The capacity obtained from the titrations was such (0.022 meq./ml.) that in 0.1JP tetramethyl ammonium chloride one expects a Donnan partition coefficient close to unity. If this is true, essentially all of the extra hydrogen in the membrane is associated with the anion sites. Under such a circumstance it can be shown t h a t :
where Cxo is the concentration of hydrogen ion in the aqueous phase. Plots of ~ / P -T1us. CX"yielded straight lines (Figure 1) and values of e and K , were obtained from the slopes and intercepts of these plots. A summary of the values obtained for these quantities by the various methods is given in Table 11. The magnitude of pK, supports the assumption that the acidic groups in the cellophane are carboxylic acid functional groups and is in essential agreement with the value reported by Hirsch (8). A t the steady state, the hydrogen present as carboxylic acid would not be expected to contribute to the current. The steady state current constant is therefore a measure of the diffusion coefficient of unassociated hydrogen ion. If, as before, one assumes unit Donnan partition coefficient, a value of 2.45 X 10-5 cm.*/second is indicated for the actual diffusion coefficient of hydrogen ion in 600 PD cellophane. Behavior of Cadmium Ion. Current-time curves for aquo-cadmium in various supporting electrolytes were determined and apparent diffusion a n d partition coefficients calculated. T h e pertinent d a t a are given in Table I11 along with overall partition co-
efficients determined from coulometric measurements ( P T ) . As in the case of hydrogen ion, the partition coefficient calculated from the voltammetric data does not agree with those from the coulometric experiments except perhaps in supporting electrolyte A where the membrane is expected to be uncharged. Also, the apparent diffusion coefficient is dependent upon both supporting electrolyte concentration and cadmium ion concentration when the membrane is in the potassium form. The steady state current constant, I,, is also dependent upon the supporting electrolyte concentration as would be expected if some Donnan partition of cadmium occurs. Thus it appears that both a Donnan partition and a specific adsorption of cadmium ion occurs. I n 1.20M potassium nitrate or in 0.1OOM potassium nitrate plus 0.01051 nitric acid supporting electrolyte sohtions (A and B of Table 111) a Donnan partition coefficient of near unity is expected. An average value of 0.86 X cm.*/second for-the diffusion coefficient of aquo-cadmium ion in 600 P D celloDhane is obtained from the steadv stat; current constants in these t w i supporting electrolyte solutions. By
Table 111.
Table II.
Experimentally Determined Values of 0 and K,
e Method (meq./ml.) PK, Partition measurements Coulometric 0.022 3.69 Equilibrium 0.025 3.70 Equilibrium 0,0068" 3.67" Titrations Direct 0.022 . . Indirect 0.021 ... a Hydrolyzed cellulose triacetate (all others 600 P D cellophane).
making use of the steady state current constants, the above value for the diffusion coefficient of hydrogen ion and the overall partition coefficients obtained from coulometric measurements, it is posaible to calculate values for the concentration of unassociated and associated cadmium ion in the membrane phase. Assuming a reaction such as: CdR
Cdf2
+R
(1)
R represents adsorption sites in the membrane, it folloTvs that: 1 Kd 1 __=(9) [CdR] e[Cd+*] +
Apparent Diffusion and Partition Coefficients of Aquo-Cadmium Ion in 600 PD Cellophane
Cadmium nitrate concn. (mM)
I , X lo6 I I X lo3 D , X lo6 P, PT A. Supporting electrolyte:a 0.lOOM KKOa and 0.01M "03 1.16 1.08 0.730 0.213 1.70 1.99 1.13 1.10 0.764 0.418 1.73 1.98 1.12 1.10 0,771 0.902 1.73 1.97 B. Supporting electrolyte: 1.20.V KSOa 1.83 2.00 0.426 0.0660 1.56 2.39 1.66 1.93 0.507 0.1304 1.68 2.36 1.53 1.81 0.564 0.236 1.72 2.29 1.43 1.64 0.600 0.442 1.72 2.22 1.26 1.47 0.832 1.73 2.09 0.685 C. Supporting electrolyte: 0.10OM KTu'O3 3.02 5.35 0.338 0.0331 2.04 3.51 3.06 5.09 0.0660 2.00 0.327 3.50 2.85 3.80 0.236 2.16 3.51 0.379 2.32 3.72 0.442 2.16 3.17 0.465 2.23 3.05 0.832 2.16 0.485 3.10 D. Supporting electrolyte: 0,0107M KNO3 0.0223 11.2 20.4 41.4 21.4 0.274 0.0445 11.4 20.5 18.4 36.0 0,310 0.0666 11.3 20.6 0.301 18.8 32.8 0,1099 10.9 19.8 29.8 20.8 0.275 I n supporting electrolyte A above, the membrane was in the acid form whereas in all other cases (B, C, and D), the membrane mas put into the potassium salt, form and the
supporting electrolyte solution was essentially neutral.
Table IV.
Values of 0 and
Supporting electrolyte 1.203f KNOa 0.1OOM KKo3 0 . 010714f KN03
K d
Obtained from Plots of 1 /[CdR] vs. 1 /[Cd]
e( M 0.72 2.22 4.08
x x x
10-3 10-3 10-3
Kd 6 4 X 6 3 X lo-' 6.2 X l o +
VOL. 38, NO. 3, MARCH 1966
463
I
/
Figure 2. Plots of l / [ C d R ] vs. 1/[Cd+*Im in 600 PD cellophane Supporting electrolyte: 0.01 07M KNO3 Supporting electrolyte: 1.20M KN03
I. 11.
In this equation, 0 is the number of adsorption sites originally available to the cadmium and K d is the dissociation constant for Reaction 1. Plots of 1/ [CdR] us. l / [ C d + * ] yield straight lines (Figure 2) thereby allowing evaluations of 0 and K d . The values of 0 and K d so obtained are given in Table IV. The agreement between values obtained for Kd in the different supporting electrolyte concentrations is striking. However, the values obtained for e are much smaller than the value of this quantity obtained from the hydrogen ion studies and they decrease with increasing supporting electrolyte concentration. This may indicate that our treatment of the data, in this case, is incorrect. On the other hand, it may be that potassium ion blocks certain sites which might otherwise act as adsorption sites for cadmium. Since a larger concentration of potassium might be expected to result in more effective blocking] this could account for the dependence of e on supporting electrolyte concentration. Also it is reasonable to
Table V.
expect that not all of the anion sites are equivalent as far as cadmium ion adsorption is concerned and only those which have favorable geometry (with respect to other anion sites or hydroxyl groups) for chelate formation act as effective adsorption sites. Behavior of Thallous Ion. AIthough Bowers and Wilson (2) found that the diffusion characteristics of thallous ion in cellophane conform to simple theory, their experiments were carried out in 1M potassium nitrate supporting electrolyte. Some experiments with thallous ion were performed, therefore, to ascertain whether a t lower supporting electrolyte concentrations, some adsorption of this ion takes place. Values of the steady state current constant, the transient current constant and the diffusion and partition coefficients evaluated from these constants are given in Table V. The data in Table V clearly indicate that only a t very high supporting electrolyte concentrations does thallous ion behave ideally in cellophane.
Diffusion and Partition Coefficients of Thallous Ion in Cellophane
A. Hydrolyzed cellulose triacetate
Supporting electrolyte concn. (KXO3,M )
Thallous nitrate concn., mM
2.06 0,100 0.045 0.045 0.045
0.118 0.0599 0.0496 0,0988 0,195
I , X lo6
B.
Q
0.599 0.100 0.496 0.045 0.988 0.045 1.95 0.045 From integration experiments.
464
ANALYTICAL CHEMISTRY
It X lo3 2.84 1.67 2.71 4.35 4.66 7.05 4.74 7.12 4.71 7.20 600 PD cellophane 2.52 4.02 4.95 5.76 4.85 5.99 4.82 6.10
D, X los
P,
2.90 2.58 2.28 2.26 2.34
0.98 1.69 3.09(3.11)" 3.15(3.22)" 3.0S(3.01)"
2.54 1.36 1.52 1.60
1.72 4.24 3.94 3.81
Figure 3. Plot of apparent diffusion coefficient of hydrogen ion in 600 PD cellophane vs. C X " ( ~4- C H ' / ~ K , ) X
103
Furthermore, as in the case of cadmium ion, the steady state current constant increases with decreasing supporting electrolyte concentrations, indicating a Donnan partition. A small but definite decrease in the apparent diffusion coefficient with decreasing supporting electrolyte concentration is noted. From this, one concludes that some specific adsorption of thallous ion occurs; however the extent of this is small enough so that the apparent partition coefficient agrees quite well with the overall partition coefficient obtained by coulometric means. Interpretation of Apparent Diffusion Coefficients. Retardation of ions in an ion-exchange matrix has long been recognized ('7) and the electrostatic attraction of counter ions by the fixed ionic groups has been cited as the most likely explanation. Specific chemical interaction can also give rise to a lower mobility of the species as discussed by Spiegler and Wyllie (16). I n our experiments, it is apparent that when association of a diffusing ion with fixed sites in the membrane occurs, attainment of the steady state current will be slower, thus causing an increased transient current constant. On the other hand, since the adsorbed ions do not diffuse after the steady state is attained, the steady state current constant will not be influenced by this association. Combination of the steady state current constant with the transient current constants gives rise to an apparent diffusion coefficient which is smaller than the actual diffusion coefficient of the unassociated ion. Dwing the attainment of the steady state, some of the adsorbed ions become desorbed (dissociate) from the fixed sites of the membrane :
MR
kf
F!
-11
kb
+R
(2)
or if not: Table VI. Comparison of Experimental and Calculated Values of the Apparent Diffusion Coefficient of Hydrogen Ion in Hydrolyzed Cellulose Triacetate
Since the adsorbed ions cannot diffuse without first dissociating (diffusion coefficient of MR equal to zero), one has the following set of equations: I n the case of hydrogen ion diffusion in 600 PD cellophane, (Kd CM)' is negligible with respect to eKd and Equation 16 might be expected to apply. Using a value of 2.0 X for Kd, apparent diffusion coefficients for hydrogen ion (Table I) were plotted us. CH"( 1 f C H 0 / 3 K d )(Figure 3 ) . Although the validity of Equation 16 is open to question, the use of it to obtain a n extrapolated value of the apparent diffusion coefficient as C H o 0 is reasonable. The plot in Figure 3 indicates a value of 3.0 X lo-' cm.2/second for this quantity which is in fairly good agreement with the value of 2.3 X cm.2/second predicted from the relationship, D,(C.M 0) = DKd/(Q K d )(Equation 14),using values of 0.022, 2.0 X lom4,and 2.45 X IO-5 for 8, K,, and D , respectively. With hydrolyzed cellulose triacetate as the membrane material, (Kd -k c.~)' is not negligible with respect to OKd and Equation 17 must be used to predict values of the apparent diffusion coefficient. Using values of 6.8 X 2.1 X and 1.6 X 10-5 for e, K d , and D , respectively, values of the apparent diffusion coefficient were calculated. These are compared to the experimental values in Table VI. The agreement between the experimental and calculated values is quite good. The results of a similar treatment for the diffusion of cadmium ion in 600 P D cellophane are given in Table VII. K i t h cadmium ion the agreement between the experimental and the calculated values for the apparent diffusion coefficient is not very good. This is not surpriring in view of the uncertainty of the details of adsorption of cadmium ion in the membrane and therefore of the significance of the values used for 0 and Kd in the calculations.
+
T o the authors' knowledge, an explicit solution of the boundary value problem described by Equations 10 and 11 has not been given. If it is assumed that Reaction 2 is very rapid with respect t o the rate of diffusion of AI, the concentrations of AIR can be derived from the equilibrium expression for Reaction 2 (3). Thus
and
b2CM - bCMR ' Aw= D at at bX2
(13)
differentiation of Equation 12 and substitution into 13 yields:
ac.w --
-
at
The apparent diffusion coefficient resulting from the above assumption is seen t o be a function of the concentration of the species and a n explicit solution of the above equation cannot be obtained by conventional means. However, Equation 14 predicts a limiting value of D K d / Q Kd for the apparent diffusion coefficient as C.woapproaches zero. Crank and Henry (4)have pointed out that in systems where diffusion coefficients are dependent upon concentration, a n experimental determination of the diffusion coefficient yields some mean value and that this mean value is approximately given by the integrated average of the true diffusion coefficient over the extreme limits of concentrations in the diffusion layer. I n our case then:
+
-
+
ACKNOWLEDGMENT
The authors are indebted to D. D . DeFord for his help in instrumentation and for valuable discussions. LITERATURE CITED
D, =
( 1 ) Bowers, R. C., Ward, G., Wilson, C. M., DeFord, D. D., J . Phys. Chem.
If (Kd yields D.
-
+ C M ) 2
