MASAOYAFUSOAND MICHAELE, GREEN
654 active in Figure sites6for (plot hydrolysis bl). It are may also bethe concluded acidic functional that the groups on the carbon surface, and the initiation step for hydrolysis is the same as that described in eq 4. Further substitution of NHs like eq 5 might be depressed in bhc present case, because the concentrated aqueous ammonia was used as a solvent. The hydroxide ion ahtacked the Co-0 bond rather than the Co-N bond, and the product, [Co(NH&(OH) 12+, was obtained IBS shown in the following equation.
~ + W W d 5 1 2 +
+
OH-
-t
6G(~H&(OH)]2* ( 6 )
Noise Spectra Associated with Hydrochloric Acid Transport through Some
Cation-Exchange Membranes1 by Masao Yafuso and Michael E. Green* The City College of The City University of New York, New York, New Yorlc 10031 (Received August 7, 1970) Publication costs assisted by The City College of the City Universitu of New York
The noise spectra and some other electrical phenomena associated with transport of hydrogen ion across a cation-exchange membrane have been studied a t currents great enough to cause the formation of a depletion layer. Under these conditions, one obtains noise spectra which show a frequency dependence of approximately u - ~a t low frequencies and a-4 a t high frequencies. Combined with data on voltage drops as a function of time and distance from a membrane, we find the principal noise source to be within 40 pm of the membrane surface. The frequency a t which the change in slope occurs was measured as a function of current, temperature, and concentration. The total current can be split into a diffusion contribution and a contribution from 8’ and OH- ions from dissociation of water. The corresponding electric field for dissociatioii is calculated from the Onsager equation. The frequency a t which the change of slope occurs, taken a t constant field, 1s B function of temperature, with an activation energy of 16.4 & 0.9 kcal/mol, and the dissociation flux is proportional to this frequency. Possible sources for the noise are considered.
Introduction I n a previous paper2 we reported some results on the noise spectra associated with the transport of various ions t h sough several cation- and anion-exchange membranes. ‘Et was not possible a t that time to give a mechanism for the generation of the noise, except to note that it was associated with the formation of the depletion 1a:yer (the layer formed in front of the membrane when the current exceeds the maximum current density which the ions in solution can maintair~).~ The critical current density has been measured by many authors, and from this the thickness of the diffusion layer h,as been estimated and descriptions of the associated phenomena given in terms of diffusional fluxes.* However, a microscopic model for these processes does not appear to be available a t the present The Journal of Physical Chemistry, Vol. Y 6 , No. 6,1971
time. Gregor and Miller5 did attempt t o estimate the field at which water dissociation occurs from a kinetic argument, but their model seems, at least, incomplete. By studying noise spectra, one can get kinetic data not limited to the slowest step of the overall process, and this has been applied in various systems of semi(1) Based upon a dissertation submitted to The City University of New York by M. Y. in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (2) (a) M. E. Green and M. Yafuso, J . Phys. Chem., 72,4072 (1968) ; (b) M. E. Green and M.Yafuso, ibid., 73, 1626 (1969). (3) F. Helferich, “Ion Exchange,” McGraw-Hill, New York, PI’. Y., 1962, p 399. (4) (a) A. M. Peers, Discuss. Faradau SOC.,21, 124 (1956); (b) K, S.Spiegler, U. S.Office Saline Water Res. Develop. Prog. Rep. 1968. (5) 1%. Gregor and I. F. Miller, J. Amer. Chem. Soc., 86, 5689 (1964).
BCE TRANSPO~RT THROUGH CATION-EXCHANGE MEMBRANES conductors.6 Applications to membrane studies have also been made by physiologists.’ I n this work, we have chosen a single system which gives well defined results, HC1 on either of two similar polystyrene sulfonake resin membranes. From the work reported earlier2 we hoped to find a single relaxation time which could be tied to a single process. Some tentative models have been investigated, none of which seems to be able to account for all the data.
Experimental ;Section The ion-exchangr membranes were the same ones described earliere2 Most of the studies were carried out with 31C 3235 cation exchange membrane. Some modifications were made on the measuring system. The noise cell was changed to a Plexiglas box 4.0 X 10.9 cm with a middle divider which had a flared hole in the middle. The membrane was taped onto the hole with black friction tape. A hole on the tape determined the exposed surface area. A cover for this cell had Eve holes over each compartment. Four holes held the 1 mro current carrying electrodes and the two amplifier electrodes. Two more holes over each compartioent were used to circulate heating oil through glass tubing that extended into the solution. The instrumental setup was similar to that used previously2 except for the use of the Tektronix 3L5 spectrum anal,pieer. The noise was picked up through the inner electrodes by a PS5AH Philbricli operational amplifier wired as EL follower with a gain of 100. A (3.5-puF capacitor in series uith the input blocked dc voltage. The amplified noise was amplified further when necessary with a Hetvlett-Pacliard 4668 amplifier, then passed to the 3L5 through the Kronheit Model 3100A band pass filter. (The Kronheit filter uee the total signal entering the 3L5 by cutting off the low-frequency signals. This was necessary since the 3L5 had approximately a 30-db dynamic raagt in power.) The output from the 3L5 was then fed into 1 Keithley 610C electrometer on which all readings were made. The fluctuating voltage was time averaged by means of a 3000-pF capacitor attached acrosh the electrometer input. The input electrodes were connected directly to another electrometer (Keithley 1610B) to read simultaneously the voltage dron acrosE the membrane. Measurements were made in fhe rnanual mode (point by point) as scanning the noise spectrum produced serious problems. The bandn-idths w e r e calibrated using a known noise source (General Radio Model 1340B). Data in Figure 5 are given a k power spectra (power per unit bandwidth). The spectrum analyzer did not have a linear dispersion as qpecified. In addition, calibration was complicated by an instability of the zero frequency position. Calibrations of the dispersion were made with sine uraw signals of known frequencies. Voltage us. distance from membrane and noise us.
655
distance measurements were made using a tapered tungsten microelectrode which was attached to an S. S. White Industrial Miniprobe Model 356-8245Y. This miniprobe had a 3.5-mm maximum movement corresponding to a 180” turn of an Allen wrench attachment. By attaching a stationary protractor on the movement and a pointer on the turn screw it was possible to divide the 3.5 mm total displacement into 180 parts or 1.9 X lo-* cm/deg. The microelectrode was prepared by passivating 10mil tungsten wire in saturated potassium nitrate solut i o m s The tapered wire was coated except for the very tip with nail polish (wax and dissolved Plexiglas were unsatisfactory) and slipped into a hypodermic needle which acted as a holder. The size of the exposed electrode tip was measured under the microscope with calibrations on the eyepiece and found to be cm (20 pm). about 2 X The microelectrode was connected to an electrometer (Keithley 61OB) for voltage measurement and to a P85AH Philbrick preamplifier for total noise measurements. I n this way total noise and membrane voltage were monitored simultaneously. The ground was attached to another tungsten wire at the opposite side of the membrane surface. The electrometer output was fed into a Tektronix Type 3A72 dual trace amplifier plug-in with a Type 564 storage oscilloscope. The voltage-time behavior was photographed with the C-27 oscilloscope camera. A family of voltage-time curves for various current densities was put on a single photograph by using a triggered sweep. The pulse caused by the switch that closed the circuit was used as the trigger. T o minimize pickup the first stage, including the electrometer] was put on the first shelf of a metal cart and covered on three sides with aluminum foil. The point of contact of the electrode with the membrane was determined by the bending of the electrode.
Results The family of voltage-time curves for lclG 3235 cation-exchange membranes at three different HCl concentrations can be seen in Figure 1. Similar curves have been reported by other^.^^^^ The time lag in the voltage change corresponds to the finite time required for the depletion of electrolytes from the membrane surface and the formation of a steady-state eoncentration gradient. The same time lag is observed before the onset of noise. This suggests strongly that cation ( 6 ) (a) K. M. van Vliet and 3. Blok, Physicu, 22, 231 (1956); (b) K. & van I.Vliet, J. Blok, C. Riis, and J. Stekette, ibid., 22, 525, 723 (1956). (7) (a) H. E. Derksen and A. A. Verween, Scieme, 151, 1388 (1965); (b) A. A. Verween and K. L. Schick, h’ature, 316, 688 (1967); (e) W. H. Calvin and C. F. Stevens, Science, 155, 842 (1967). (8) D. J. Ives and G. J. Jam, “Reference Electrodes,” Academic Press, New York, N. Y., 1961. (9) N. Lakshminarayanaiah, “Transport Phenomena in Membranes,’’ Academic Press, New York, N. Y., 1969, pp 230-231.
The Journal of Physical Chemistru, Vol. 76, No. 6,1971
MASAO YAFUSO AND MICHAEL E.GREEN
656
_ I I
" I -
Figure3. Voltnw-time eurvc with rriicroelectrode touching and possibly penetrating the membmne. \IC 3142, 11.025 df HCI, 1 sec/div, 0.050 V/div. From top to bottom, J in mA/cm': 33, 33,44, and .55. Note: The first run at 33 mA/cmZ triggered after the sweep was initiated.
,-,,,. - -mmm-n*IIp., Figure 1. Voltnge-time curves for IICl nnd \IC3235,5 rec/div, 0.225 Vfdiv: (a) 0.0X AI HCI. From top to bottom in mA/ em': 67,60, 42, 37, and 33; (b) 0.010 A[ HCI. From top to bottom in mA/cm': 67, 5433, 17, snd 12.
0.0
c
I
100
I
200
I
(membrane surface1
Dislance, s. arbitrary origin Figure 4. Membrane volts and noise us. distance for MC 3235, 0.025 M HCI, 83 mA/cm'. Figure 2. Voltncc-time curves :rt distnncrs, T, from membrane 1\IC 3142, 0.025 .I/ IICI, 44 inA/cm*, 2 see/div, 0.2 V/div. From top to hobtam, z in 10-4 pm: 0, 40, 200, ROO, and 1200.
exchange noise is intimately related to the formation of a depletion layer. The time lag for MC 3142 cationexchange membrane with sodium chloride and the absence of a time lag with the MA 3148 anion-exchange membrane were reported previously.2 Some secondary voltage changes can be seen in the The Jouml 01Ph#&l
Chcmiatry, Vol. 76, No. 6.1971
cation-exchange membrane curves a t low concentrations and high current densities (Figure lb). These changes were eliminated when the electrode was brought to within 40pm of the membrane surface on the depleted side. The voltage-time curves a t various distances from the membrane can be seen in Figure 2. Some voltage changes with time were observed with the electrode touching and possibly slightly penetrating the membrane. This can be seen in Figure 3.
HCl TRANSPORT THROUGH CATION-EXCHANGE MEMBRANES
I
11Y
ios
13"
Frequency, Hz Figure 5. Power spectra of 0.050 ill HC1 with hIC 3235 a t 30" obtained with tha 3L5 spectrum analyzer. From top TO bottom in nA/cm2: 76, 59, 50, 45, 35, and 31.
The relation of steady-state ir drop across the electrodes with distance from the membrane and the total noise with distance w r e also plotted. The membrane and the total noise with distance were also plotted. The results (Figure 4) show a sharp drop in voltage when the electrode contact with the membrane was accompanied by a simultaneous increase in noise. (Xote: The voltage inversion that was recorded may have been due to electrode asymmetry.) The sharpest changes in noise and voltage occurred within 40 pm of the inembrane surface. The power spectra obtained for 0.050 M HCl with MC3235 at 30' are shown in Figure 5. Similar curves were obtained at 19, 40, and 49" and for 0.025 M HC1 at the same temperatures. The feature of interest that was common to all was the intersecting straight lines. The point of intersection shifts to higher frequencies with increasing current density.
Discussion The electrical properties recorded in Figures 1-4 help to locate ihe noise source. The sharp change in voltage that occurs after a time lapse can be attributed to the drop in conductivity with electrolyte depletion at the membrane surface. This depletion is a consequence of the Donnan equilibrium between the menibrane and solution phases. The stable electrostatic potential at the interface opposes penetration of the
657
membrane by ions. As a result the counterion transport number in the membrane is larger than in the solution phase. This difference causes electrolyte depletion at the membrane surface, creating a concentration gradient of sufficient magnitude to maintain the flux. At the critical current density the diffusional flux has reached a maximum, and any further increase in the flux must come from water dissoci~ltion.~The voltage-time curves for currents exceeding the critical current density are characterized by a sharp voltage change; after a time lapse secondary- voltage changes following depletion can be attributed to the formation of a steady-state concentration profile. We reported earlier2 that for cation-exchange membranes, noise was not measurable until the critical current density was exceeded. In addition a time lag for the appearance of noise was observed. These observations suggested that the observed cation noise was dependent on the formation of a depletion layer. The time lag observed in the voltage-time curves makes the relation even more obvious. The voltage-time curves at different distances from the membrane (Figure 2 ) and the voltage and noise with distance curves (Figure 4) show that the region of interest lies within 40 pm of the membrane surface. The fact that some of the secondary voltage changes referred to previously are cut off at 40 pm suggests that the concentration gradient extends beyond this distance. The sharp drop in voltage from a distance of 40 pm to the membrane surface shows that most of the voltage drop measured is across the depleted region and not across the membrane itqelf. The behavior of noise with distance is interesting (Figure 4). The noise level rises sriarply when the electrode contacts the membrane. This may be the result of contact noise or the diminishing of an internal resistance that was causing power dissipation. The former should give a step function response at the point of contact, whereas the latter should give a eontinuous first derivative of the noise-distance curve. Our micromanipulator was not sensitive enough to make this distinction. The HC1 power spectra were of considerable interest. The two intersecting lines of approximately w - 2 and w - ~dependence resembled a normal relaxation spectrum passing through a low pass filter. When the point of intersection (obtained by extrapolation) was plotted against current density a linear relationship was obtained (Figure 6). J =
K j + P
(1)
where f is the frequency at the point of intersection, J is the current density, is the slope, and /3 is the intercept. Experimentally zf is not observable when the current falls below the critical current densitj.. This suggests that xf is the added flux due to water dissociation and The Journal of Physical Chemistru, Vol. 7 5 , Yo. 5 , 1971
65s
h/lASAO YAFUSO AND MICHAEL
E. GREEN
e
I
40
2.0
’I-
f , kHz
+
L-
@ (eq I), where f is frequency Figure 6. Plot of 9 = d where the power spectrum slope in Figure 6 changes: O, 0.050 M HCl, 30’; 0, 0.025 Ill HCl, 30”.
p is the flux due to the diffusion of HC1. Then p must be of the formlo
34
3.2
vi- io3 Figure 7. Plot of log @ v s . 1/T; here p is defined by eq 1: 0, 0.050 M HCl, MC 3235; e, 0.025 M HCl, MC 3235.
where D is the coefficient of diffusion given by ( p ~ + constant, and C is the concentralion. The values of the mobilities, p , for the temperatures of interest are given in Table I. p ~ ~ - ~ ~ ) /-t-( p i ul ~~ l +- )F~ is ~ ~Faraday’s
1_____1
Table I : h4obiIities Calculated from Diffusion Activation Energies Cited in Ref 1 2 in m2/V See
Y
0,
D = Do(IX+) = Do(OH-) = Do(C1-) =
D13exp( --E,/RT) 22.17 X 10-7 mz/sec 23.89 X 10-7 mz/sec 26.40 X 10-7 m2/sec
Temp,
MI5 +
ON.
( X 108)
292 303 313 322
3
33.58 39 56 45,33 61 - 5 4 I
E,(“) = 3.230 kcal EE,(OH-)= 3.610 kea1 E,(Cl-) = 4.220 kcal vc1-
I.IOH-
x
x
108
18.47 22.33 26 19 30.40 I
2
10s
6.978 9,728 10.61 12.68
3.2
3.4
I/T
io3.
Figure 8. Plot of In 7i( 2)s. 1 / T , where x is defined by eq 1: 0, 0.050 M HCl, MC 3235; 0, 0.025 M HC1, MC 3235.
The mobiljtics were calculated from the activation energies citled by Longswort h. l 2 Since pli + iF, about 5 times as large as pel- the term ( p H + p c i - ) / ( p ~ ~ ~pol-) can be approximated roughly by pcI-. The fl can be written in the form
+
@ == Po exp(-E,/RT)
(3) where E , is the activation energy of the mobility of the chloride ion. The plot In 21s.1/T is given in Figure 7. Value? for E , of 3.8 f 0.8 kcal were obtained which can be compared to 4.22 kcal reported in the literature. H has the dimensions of C/m2 which is a surface charge density term. The plot of In IL us. 1/T can be seen in Rg;ure 8 to be an approximate straight line The Journal ojpPhysical Chemistry, Vol. 76, N o . 6,1971
with slopes of 1.9 X 10* and 3.3 X 10a for 0.050 and 0.025 114 HCI, respectively. Since flux is the product of conductivity and the electric field, ,uf and /3 can be expressed in the following form Hf
P
+ POrr-lFE C c , - ( m + + MLCI-FE
= COH-(PH+ =
(4) (5)
(10) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” 3rd ed, Reinhold, New York, N. Y.,1958, p 118. (11) See ref 10, p 120. (12) b. G. Longsworth, “Electrochemistry in Biology and Medicine,” T. Shedlovsky, Ed., Wiley, New Yorlr, N. Y . , 1956, p 225.
Hc1 7:RANSPO
RT THllOUGIl
CATION-EXCHANGE MEMBRANES
where C’s are Ibe concentrations, p’s are the mobilities, F is Faraday’e constant, and E is the electric field in V/m. Values of x rind p are given in Table 11.
659
Table I11 : The Values for f for Various Temperatures and Concentrations of HC1 a t a Field of 3.16 x 10’ V/mu Temp,
~~~-~
Concn
OK
f, Hz
Table I1 : Values of x and p a t Various Temperatures and Concentrations
0.050 0. olio 0.050 0,050 0.026 0.025 0.026 0 025
292 303 313 322 292 303 313 322
689 2453 4133 8994 524 I219 3619 8020
Goncn, M
Temp, ON
x,
8,
C/ma
A/mz
0,050 0.050 0.050 0.050 0.025 0.025 0.025 0.025
2 92 303 313 322 292 303 313 322
0.096 0.062 0.073 0,054 0.153 0.177 0.099 0,072
230 290 310 430 168 118 176 227
~~-~
I
a
Values were obtained via eq 4-9.
By applying 0nsag;er’s equation for the field dissociation of weak electrolytes to water, the three variables COH-, C C i - , and E can be determined. Onsager’s equationlais given by K , = K,F(b) where KO is the dissociation constant in the absence of an external electric field. F(b) and b have the form
F(b) = 1
-+ h + b”/3 + b3/18 + b4/180 + . . .
(6)
where b
~
9.636 X 10-12E D T2
I _ -
D is the dielectric constant, T is the absolute temperature, and E is the electric field in V/m. The values ol“F(b) and therefore K , at various values of E were determined from eq 6. The flux due t o water dissociation corresponding to E was determined from K , and p
K,
== c H + G o I p =
(Cc1-
+ Coa-)Cow-
The values of E corresponding to the various values off can be determined by dividing J d l s s by K where J d i s s , the flux due to water dissociation, is given by ~ j == ’ COH-FE(pH+
4- p o H - )
(9)
The effect of E’ on ,f at various temperatures can be seen in Table 111. It was assumod carllier that f is a function of the rate constants of the process, The rate constant IC is given by E, - E e l RT
)
I 3.4
1 / T X 103.
Figure 9. Logf vs. l / T a t a constant electric field strength of 3.16 X 107 V/m. Equation 1 definesf. 0, 0.050 M HCl; e, 0.025 $1 HC1. See Table 111.
(7)
The OH- concmtration is given by
J d l s s ==
I 3.2
where E, is the activation energy and Eel is the energy due to the electric field. Assuming that the activation energy is field independent its value can be obtained by finding b In f / (b 1/T) a t a constant value of E . The linear plots for two different concentrations, 0.050 and 0.025 M HC1, can be seen in Figure 9 at a field of 3.16 X lo7V/m. Values of 15.5 and - 17.3 kcal were obtained for 0.050 and 0.025 M , respectively. Before any models can be proposed another factor must be considered. The power spectrum of a single relaxation process has the form14 G(w) =
T
1
+
d T 2
(13) L. Onsager, J . Ghem. Phys., 2, 599 (1934). (14) (a) K. M. van Vliet and J. R . Fasset, “Fluctuation Phenomena, in Solids,” R . E. Burgess, Ed., Academic Press, ?Jew Yorli, N. Y., 1965, p 267 ff; (h) M. Lax, Rev. Mod. Phys., 32, 25 (1960).
The Journal of Physical Chemistrg, lid. ‘76,YO. 6,1971
MASAOYAFUSOAND MICHAELE. GREEN
660
Table IV : Slopes of the HCl Spectra in Terms of d(1og power)/ d(logj) ( a and y are the First and Second Slopes of Figure 5, Respectively, arid Are Functionally Defined by Eq 11) C onon,
Temp,
M
OM
0,050 0.050 0.050 0 * 050 0.050 0 050 0.050 0.0,50 0.050 0,050 0.0
