fadadaic rectification and electrode processes

Review of Polarography (Japan) ポーラログラフイー

Vol. 10 1962 No. 5/6

Fadadaic Rectification and Electrode Processes

•\ Experimental Review•\

By

Hideo IMAM

1. Relaxation Methods

The potentiostatic methods (voltage-step method), galvanostatic methods, coulostatic

methods (charge-pulse method), faradaic impedance methods, and faradaic rectification

methods have been developed in these fifteen years for the study of fast electrode kinetics. Indirect methods such as photo-electric current by a flash light or a voltammetry using

vigorous mechanical stirring possibly be used for this purpose.

These relaxation methods are based on measurement of the reaction rate under high

rate of mass transfer, which is achieved by diffusion with steep concentration gradient or

by vigorous stirring. So far as diffusion is the sole mode of mass transfer, the average

flux of reducing species diffusing toward a plane electrode is given by 2C•K(Dhrt), where C•K

is the bulk concentration of the reducing species, D its diffusion coefficient, and t the time

elasped since the biginning of electrolysis. In a process with mixed control by mass and

charge transfer, this conclusion is qualitatively valid, and diffusion is no longer rate-deter-

mining in a measurement at a sufficiently short time interval.

An overall electrode reaction is schematically given by a diagram as shown in Fig.

1. In relaxation methods, it is expected that chemical reactions, specific adsorption of the

reactant or/and product, or the charge transfer process will be rate-determining, provided

the the time of measurement is sufficiently short. It is noteworthy that the datum obtain-

ed at a time interval has to be analysed

in relation to a corresponding rate-deter-

mining step.

Fig, 1. Relation of standard free energy to dis-

tance in consecutive processes of an electrode

reaction. 1, 5•\Mass transfer of O and R ;

2, 4•\Coupled chemical reactions of O and

R ; 3•\Charge transfer.

In pluse techniques mentioned

above, measurement at a short time in-

terval has restriction from charging of

the double layer capacity, transient of

the pulse from the net-work composing

the cell circuit, and the rise-time of a

pulse and detector used. The double-

pulse galvanostatic method enables

measurement at a very short time inter-

val up to about few microsec. by using

an ingeneous method of compensating

double layer charging. A cathode ray

* Laboratory of Chemistry, Department of General Education, Hiroshima University, Hiroshima.

210

oscilloscope usually used in these method is accompanied by meager precision and accu-

racy. The faradaic impedance method seems to be the most accurate one, while the upper

limit of the frequency is about 20 kc which corresponds to the time interval of 5•~10-5 sec.

The faradaic rectification method is promising at very high frequencies up to 50 or

possibly to 100 me (10-8 sec.), being unaffected by transients and double layer charging by

using the double-pulse method or null method. The apparent cxchange current density

evaluated by this method was 10 amp./cm2 in the electrode process of Hg(I) in 1.1 M

HClO4, which corresponds to an apparent standard rate constant of ka•K =100 cm./sec. for

an electrode process involving both soluble oxidant and reluctant of equal concentration

of C•K = 5•~104 M (n=2, Do = DR =10-5 cm2/sec.) or to ka•K =1000 cm./sec. for C•K =5•~10-5 M.

The theory of the faradaic rectification has been developed by Barker1 and Matsuda-

Delahay, and more extensively studied by Delahay-Senda-Weis. This review will

cover rather an experimental point of view including the method of analysis and experi-

mental techniques.

2. Types of Control

In the faradaic rectification method, the sinusoidal current or potential is applied to

the cell, where the oxidant and reductant are in an equilibrium (under a given potential

in the case of generation of a reactant in situ). Control of the component is more involved than the usual case, and one has to consider two types of control, (a) control of alternating

component of the current density (IA) or potential (VA) and (b) control of mean component

of the current density (I) or potential (E).

a. Control of Alternating Component :•\The a-c current flowing throngh the cell is given

by IA= U0/Z0, Ua being the a-c voltage applied to the cell, and Zo the total cell impedance

including the capillary, double layer, solution, and lead wire. The amplitude of a-c vol-

tage yielded across the double layer (VA) is determined by the product, IA•~Zl, Zl being the

double layer impedance. This ralation tacity indicates identity of IA and VA control.

Zl is given by a parallel equivalent circuit of the dif-

ferential capacity (C1) and the faradaic impedance (Zf) as

shown in Fig. 2, Zf being composed of the series Warburg

impedance of the oxidant and reductant (rw and Cw) and

charge transfer resistance (rat). At a rather low frequency,

ZfCl/wCl and VA =IAxZf, IA flowing mostly through Zf.

Since the value of VA is necessary in order to analyse the

data by the method (cf. sections 4 and 5), this condition is unfavorable, and the frequency has to be high enough as

1/WCl•áZf and VA=IA/w Cl or Uo/ZowCl (1)

Note that evaluation of Zo and accordingly VA is rather

complicated at very high frequencies owing to the induc-

tance and stray capacity of the cell circuit. So far as

enough out-put voltage of the signal oscillator to give VA

•¬5 mV. is available at the desired frequency, the greater

radius of the mercury drop and the concentrated support-

Fig. 2. Equivalent circuit

of a cell and double layer

impedance. Z1- Capil-

lary and lead wire im-

pedance, Cl-Differential

capacity, rw, Cw; -Warburg

impedance, rat- Charge

transfer resistance, rs -

Solution resistance.

ing electrolyte are preferable in order to avoid influence of the stray capacity (The solu-

tion resistance is approximated by 1/4ƒÎrkej r being the radius of the mercury drop and ke

the specific conductivity of the solution.). In the case of a miniature DME, the surface

211

Fig. 3. RF bridge for the cell impedance measurement. O -RF pulse generator , B-RF bridge, H-Hammer, C-Cell,

P1, P2-Binding post, R-Re- ceiver (National Model HRO- 50T1), CR0-Tektronix Type 531 CR0 with Type D plug- in amplifier.

area A=5•`10•~10-3 cm.2 and the maximum value of

Z0 tolerable up to 10 me is 100-150 ohms. A miniature

cell is designed to minimize the stray capacity and

to fit the binding post (5 cm. apart) of a conventional

bridge (General Radio Type 1606A or 916AL RF

bridge). As to the hanging mercury drop electrode,

the orifice of the platinum tip has to be less than 0.05

mm. in order to avoid deformation of the sphere of

a small size drop which is often required from the

meager out-put voltage of a signal oscillator at the

frequency higher than mc. It is recommended to seal

a platinum of a needle point in a glass tubing and

grind the tip very carefully.

Za is measured by a synchronized oscillator, a RF bridge, and a detector as shown in Fig. 3 (As to

synchronization cf. Fig. 7.). Uo is directly measured by using a probe (cf. Fig. 7).

Conditions for control of the a-c voltage across

the electrode impedance by the double layer capa-

city is determined from the slope of the plot of log

(|‡™E•‡| /IA2) versus log w, ‡™E•‡ being the rectification

voltage (cf. equation 4.) When Zf•t1/wCl, VA=

IA/wCl and |‡™E•‡|/IA2 is inversely proportional to w2

for pure charge transfer control or inversely propor-

tional to w5i2 in the range of frequencies in which 4 varies linearly with w-y. Converse-

ly, when Zf•s 1/wCl, VA =IAZf and |‡™E•‡|/IA2 is inversely proportional to w at frequencies

at which 4 varies linearly with w--1/2.

b. Control of Mean Component :-Two types of control are proposed, i.e., control of mean

current density at zero and control of mean potential at a given equilibrium potential.

When there is a-c control and I=0, the variations of E with time are given by the sum

Fig. 4. Qualitative representation of the

nonlinear I-E relationship and recti-

fication voltage. I=O, IA control, E-Ee

=‡™E•‡.

Fig. 5. Schematic representation of cir- cuits for two types of control of mean component. F-Low-pass filter, C- Cell, R-External resistor, (A) I=O,

(B) E-Ee.

212

of a pure sinusoidal function at the frequency f as the current and a periodic component

at the frequency 2f. The latter component of 2f frequency results from non-linearity of

I-E relation about Ee. Assuming the limiting case of the infinite frequency (Note that

at finite frequencies the effect of mass transfer must be taken into account for I-E rela-

tion.), it is easily understood from Fig. 4 that shift of the mean potential E with respect to

Ee is observed as the rectification voltage. Since I=0, there is neither net chemical change

nor mass transfer polarization for the mean component of the concentrations. According-

ly, mean rectification voltage is time-independent provided double layer charging is com-

pensated (double pulse method). Measurement under this controlling condition is em-

bodied by a cell circuit with a very high series resistance (>l Mƒ¶) as shown in Fig. 5A,

where a-c current flow is not restricted, but the d-c current flow is practically equal to

zero (Note that the in-put resistance :of Tektronix Type E plug-in amplifier is 10 Mƒ¶.).

As mentioned previously, the rectification voltage is the same whether there is a-c or a-v

control because of their reciprocity rela-

tionship.

Rectification for E=Ee and a-c control

results in an alternating component of

potential at the frequency 2f, which will be compensated by an equivalent shift of

potential with constant amplitude and op-

posit direction. Compensation results in a rectification current accompanied by the net chemical change, and the current

gradually decays until the potential about which I-E relation is linear, the mode of

decay of the current being similar to that

of the potentiostatic voltage-step current.

The d-c current flow is no longer restrict-

ed in Fig. 5B, and the ohmic drop across

the series resistor R gives the current signal to the detector.

Fig. 6. Influence of external resistance (R of

Fig. 5) for the discharge of 0.63 mM Hg (I)

in 1.1 M HC1O4 on Hg at 1 me and 30•K.

A 0.0041 cm2, Circuit resistance except R

1209, Uu (peak to peak) 1.6 v. The shift

of E is negative.

The controlling condition for the mean component changes from I=0 to E=Ee cor-

responding to the change of the series resistor as shown in Fig. 6.

3. Analysis of Datas

Let us consider reaction for a simple charge transfer process without corlplications

due to adsorption, coupled chemical reactions, etc. The rectification voltage for a reaction

O + ne = R involving two soluble species is such that', when n•s RT/anF,

•¬(2)

where ctn ƒÆ = wRsGs,ƒÆ being the phase angle between current and voltage, RS and 1/wCs

the series resistance and capatitance of the faradaic impedance respectively, and n, F, R,

T, a, G's, D's are as usual. ‡™E•‡ is expressed for t•¨•‡ to allow for charging of the double

layer.

At sufficiently high frequency, ctn ƒÆ•t 1, and

213

•¬

where Ia•K is the apparent exchange current density.

Equations 2 and 3 lead;

•¬ In equation 4,•¬ is linearly proportional to w-1/2 (VA is computed from equa-

tion 1.). The intercept of this plot extrapolated at w-1/2 =0 or w•¨•‡ gives the value of a

and the slope gives the value of L. The apparent standard rate constant is given by,

•¬(5)

In order to evaluate C1 a conventional impedance bridge measurement in the support-

ing electrolyte solution is usually used. However, when there is specific adsorption of the

reactant or/and product or in the case of the electrode process of Hg(I) on Hg, evaluation

of Cl by this method is difficult. In these cases, the following method is recommended.Combining equations 2, 3, 4, and 5, one obtains,

•¬(6)

When one put

•¬(7)

the ratio of the slope of •¬ versus w-1/2 plot at two concentrations of O-R couple

•¬(8)

•¬(9)

The intersection of two plot, log•¬versus a and (1-a) •¬ versus

•¬ a gives the value of a. Then, C2 is obtained from the intercept of the plot, and ka is com-

puted from equation 6. Assumption is made that Cl is constant in the range of potentials corresponding to the variation in C and C2 is frequency independent (no frequency dis-

persion in the double layer, cf. section 9.). When Co•sCR (for example, the case of Hg(I)•¨Hg), one leads more simple relation

and

•¬(10)

a is directly evaluted from the ratio of the slope li obtained at two concentrations. When

one uses the foot of the polarographic wave, Co•tCR and the equation can also be simpli-

fied.8

The mean rectification current is given by equation 11 as followsh;

•¬

with

•¬(11)

where r is the total resistance in the cell circuit.

214

•¬

one has Ir=‡™E•‡/r. If the resistance of the cell circuit is much smaller than R in Fig. 5,

the ohmic drop across R is for all practical purpose equal to ‡™E•‡. For the compensation

method by the potentiostatic voltage-step current refer section 5.

4. Direct Measurement of Rectification Voltage and Double Pulse Method

The equipment consists of a synchronization device, radio-frequency pulse generator,

cell circuit, and a detector of the mean component with a low-pass filter. The assembly

is given in Fig. 7.

Fig. 7. Circuit for direct measurement of ‡™E•‡. D-Rotating drum

(18 rpm.) for synchronization, c-c' 2-3 sec., W-Wave form

generator ; s, negative-going saw-tooth out, g, gate out, A-

Amplifier for hammer, P1-Pulse generator (duration 5-40

msec., 50 v.), R-Mercury wetted contact relay, T-Trans-

mitter, k, key circuit, Fh-High-pass filter to remove 60 cps.

hum, B-Bias control, O-Signal generator, m, external

moduration, P2-Pulse generator for charging pulse (dura-

tion 10-30 usec. •}50 v.), r-1-10 Mƒ¶, c-0.02 ƒÊF, Fl-Low-

pass filter, L-0.5 mH., H-Hammer, P-Probe (tektronix P-

80), C-Cell, CRO1-Tektronix Type 531 CR0 with Type

E plug-in amplifier, CR02-Tektronix Type 585 CRO with

Type 80 plug-in amplifier, t-Trigger for CRO 1 and 2.

Synchronization is achieved by a drum with contacts rotating at constant speed (with

a 12 or 18 rpm synchronous motor). The contact gives 45 V. pulse which triggers the amp-

lifier (single stage with 6J5) for a magnetic hammer (Glare 39EC magnetic relay with a

rod) to fit the DME. The life-time as controlled by the hummer is 5 or 3.33 sec. The drum

also provides the second pulse to trigger a wave form generator (Tektronix Type 162) 2-3

sec. after the application of the hammer. The gate-out of the wave form generator trig-

gers cathode ray oscilloscopes to measure the amplitude of the RF pulse (Tektronic Type

585 CR0 with P-80 probe and Type 80 plug-in amp.) and the mean component (rectification

voltage) (Tektronix Type 531 CR0 with Type E plug-in amp.). The connection of the

gate-out of the wave form generator to the external triggering of Type 531 CRO requires

100 ƒ¶ resistor or 0.1,uF capacitor in series in order to avoid undisrable hum which often

interferes the measurement at a high sensitivity (50-200 ,ƒÊV./cm.). The saw-tooth out of

215

the wave form generator triggers two pulse generators (Tektronix Type 161), one of which

provides 100% external moduraton for a signal generator (Hewlett-Packard Model 606A) after a suitable bias control, or to enerigize the solenoid of the mercury wetted contact relay (Clare HC 1001) which gives contact of the key circut for conventional transmitters

(Apache Model TXl for 3.5, 7, 14, 21, 28 mc, or Seneca VHF-1 for 50, 144 mc), the other

pulse generator provides charging of the double layer (double pulse method). The syn-chronization of the RF pulse and charging pulse is achieved by the manual control of the

delay circuit. A miniature cell with the minimum resistance, inductance, and stray capacity is used

in the high frequency rneasurement

Fig. 8. Voltage-time curves for

the double pulse method for

the discharge of 0.12 mM Hg

(I) on Hg in 1.1 M HC1O4 at

0.5 me and 30•K A 0.0051 cm2,

Cell resistance 819, Uo (peak

to peak) 1.2 v. Duration of

charging square wave pulse 30

sec., Amplitude of the current

square wave is indicated in

vamp. on each. The shift of

E is negative.

The low-pass filter consists of 12 stages of the L-

C network, the first three being composed of series 3

shielded sections of 2.5 mH coil and 0.05 aF capacitor

and the rest 9 shielded sections of 6 turn coil of gauge

•”i8 wire with 22 mm. diameter and 3 mm. spacing

and 1001 F capacitor. The latter filter network is

necessary to avoid the spurious effect which occurs at

very high frequencies by the stray capacity of a con-

ventional choke coil. The cut-off frequency is about

130 kc. For lower frequencies another filter network

consisting of 2 sections of 5 mH coil and 0.2 ,uF capa-

citor is required (cut-of frequency 40 kc). Condi-

tions for critical damping is rather difficult to design,

so the net-work is rather in oscillatory condition.

Since the input-resistance of the Type E amp. is

as high as 10 Mƒ¶, the d-c current flowing through the

cell is practically equal to zero. Strictly speaking,

there is possible current flow through the faradaic

impedance to charge up the double layer. This has

Fig. 9. Effect of double layer and double pulse on the oscillographic

pattern. CHg(I) 0.12 mM, Ciiclo4 0.1 M, IA 1.11•~10-2 cm2, avert.

0.5 mv./div., hon. 1 msec./div. C, D-same as above except for

RF 14 mc, IA 30 amp./cm2, A, C-double layer effect, B, D-

double pulse method.

216

a fairly large time constant corresponding to increasing Z at the lower concentration of

the depolarizer, and the observation of ‡™E•‡ is eventually impossible in a rather short

duration of the RF pulse (5-50 cosec.). Note that application of the RF pulse in a long

duration hinders the observation by heating of the electrolyte . This difficulty is elirninat-

ed by the double pulse method, a square wave pulse being adjusted to charge up by trial

and error (cf. Fig. 8.). However, adjustment of the charging pulse is extremely difficult

at very high frequencies because of distortion of the rectification voltage pattern by heat-

ing of the electrolyte (cf. Fig. 9.D).

The temperature raise during the RF pulse is aproxi-

mately given by

•¬(12)

where ke is the specific conductance of the electrolyte, Ca

its specific heat, and d its density. In Fig. 10, the varia-

tion o' the potential is as much as 0.8 mV. at the current

density of 31 amp./cm2, and 7 cosec. after application of

the the RF pulse (14 mc) in 0.1 M HC102. The tempera-

ture dependence of the Hg(I)-Hg electrode potential mea-

sured is -0.045 mV./deg. and the potential change of 0.8

mV. corresponds to the temperature change of 18•K. This

gives a fairly good agreement with the value computed

by equation 12.

As the conclusion, the heating effect is the majorr dis-advantage of this method, being coupled with the impos-sibility of generating reactants in situ by an external poten-tiometer circus.

5. Compensation Method for Rectification Current

The necessary experimental condition for the rectifica-

tion current measurement is achieved provided the mean rectification current is exactly compensated by a synchro-

nized current of opposit direction from an external voltage

stept so that E2 remains unchanged. In general, complete

compensation throughout the RF pulse can not be achiev-

ed for approximately 100 ,sec., because the transient cha-

racteristic of the compensation circuit is not the same as

for the rectification process, especially the charging cur-rent of the voltage step is quite different from the non-

faradaic rectification current (cf. section 9.) as shown in

Fig. 11.

Fig. 12 shows the circuit diagram for this method .

The voltage step yielded across 19 resistor r1 by energiz-

ing the solenoid of a mercury wetted contact relay by a

pulse generator triggered by a wave form generator is ap-

plied to the cell circuit. The wave form generator also

Fig. 10. Effect of heating of electrolyte on the oscillo-

patten. CHg(I) 0.47 mM, CGCIO4 0.1 M, RF 14 mc,

IA 31 amp./cm2, vert. 0.5 mnv./div., hon. 2 msec./div.

Fig. 11. Oscillographic pattern

of compensation of the fara-

daic rectification current by

a voltage-step current. A-

Faradaic rectification cur-

rent, B-Voltage-step cur-

rent, C-Compensation, 0.5

M NaCI at -1.95 v. res.

pool, RF 2 mc, Uo 4.52 v.,

In 3.74 amp./cm2, ‡™V -1

mv., vert. 0.4 scamp./div.,

hon. 0.4 msec./div.

triggers another pulse generator used for the external modulation of a signal generator .

Synchronization is thus achieved, and the ohmic drop across a series resistor R observed

217

Fig. 12. Circuit for compensation method, c-c' 50 msec., c'-c" 2-3 sec.,

P3-Pulse generator (duration 300 msec.), P2-Pulse generator

(duration 5-40 msec.) MR-Mercury wetted contact relay, B-

1.5 v. battery, r2-10 kƒ¶ decade box, r1-1ƒ¶, Po-potentiometer,

M, mercury wetted contact relay, C2-1 OF, For the rest cf. Fig. 7.

by a detector CRO1 with Type E plug-in amplifier. The rectification voltage is directly

evaluated from the relation, ‡™E•‡=‡™V, ‡™V being the compensating voltage step which can

be measured on the screen of CRO2 by connecting point G to the ground.

Generation in situ can be widely used in this method as the circuit is shown in Fig.

12. The undersirable capillary response is eliminated by using synchronized potentio-

meter circuit.

6. Zero Rectification Current

This extremely simple method is based on the fact that ‡™E•‡ = 0 under a certain con-

dition of a. Eejyand w. The first term in the right hand side of equation 2 or 4 is positive

or negative according to a•¬0.5 and the second term is negative or positive depending on

the value of a•¬0.5 and Ee (or concentration).

When ‡™E•‡ = 0, equations 4 and 5 lead

•¬(13)

where fp is the frequency at which AR =0 for the value of p which is given by equation 7.

•¬(14)

The parameter a is determined from the intersection of the curves representing the

left-hand and right-hand members of equation 14, respectively, as functions of a. ka•K is

then calculated from equation 13 (for the value of p for generation in situ cf. section 7).

The above procedure can be simplified when the frequency for which ‡™E•‡=0 is

measured at half-wave potential (Co=CR) when one can assume Do = DR (In most redox

systems this assumption safely holds.). One then has

•¬(15)

In order to evoluate a one has to obtain the data for ‡™E•‡ = 0 at an applied potential (E•‚

E1/2) and, one uses equation 13 for the calcuration.

In this method the circuit in Fig. 12 is used, CRO1 being used as the null detector.

Measurement of Uo, Zo or C1 is unnecessary. Criterion of a-c control by Zf or by 1/wCl is

needless. Even Wthe possible fluctuation of the DME characteristics during the measure-

ment is allowed so far as the condition i n•sRT/anF is satisfied. It is noteworthy that a

postulation, ctn ƒÆ•t 1 is made in the derivation of equation 13.

218

7. Generation of Reactants in situ

So far as the cell circuit is composed of rather low resistance net-works, generation of

reductant in situ has the merit of maintaining the concentration at the intereface constant

(Note that the reductant or amalgam in most cases are usually unstable.)When R is generated in situ by polarography,

•¬

(16)and

•¬(17)

where C•K's are the bulk concentration, i the polarograghic current and id, the diffusion

current.

When one uses the relation in equation 7,

P=(i/id) / (1- i/id) (18)

Since there is no postulation about the mode of mass transfer in equation 17, one can

evaluate Co and Cx from equations 16 and 17 by evaluating is from Ilkovic's equation even

in the case of the polarographic reduction with no supporting electrolyte.

The undesirable capillary response, which often takes place in a rather concentrated

solution of the depolarizer and at the reduction potential apart from the potential of the

electrocapillary maximum, is avoided by setting the potential at E=Emax, during a short

time interval of dropping of the DME. The circuit for this purpose is shown in Fig. 12.

8. Double Layer Correction for Kinetic Parameters

It has been pointed out that an apparent rate constant or exchange current density is

different from the net one owing to the potential distribution at the vicinity of an electrode

surface. According to Fru.mkin,

•¬(19)

and

•¬(20)

where z is the ionic valence of the discharge species and 4cp the diliterence of potential

across the diffuse double layer from the plane of the closest approach to solution. Equa-

tion 19 is the correction for the potential as the activation energy of the electrode reaction,

and equation 20 is that for the distribution of the discharge species in the diffuse double

layer due to potential difference 4. p. Equations 19 and 20 result in the following expres-

sion

•¬(21)

where I•K (k•K) and Ia•K (ka•K) are the net and apparent exchange current density (standard rate

constant) respectively.

Acs is evalutated from the Gouy-Chapman theory or by the modified form of this

theory by Brodowsky and Strehlow who has taken into account the effect of electric field

on dielectric constant.

The method of calculation of 4cp from the experimental value of the surface charge

density q evaluated by graphic integration of Cz versus E curve from Emax to E is as follows

According to the Gouy-Chapman theory ;

•¬(22)

219

or, at 25•K

q(ƒÊ coulomb/cm2) =•}5.87•¬[exp (- 38.92z‡™ƒÕ)-1 ] (23)

or for 1:1 electrolyte

q

(ƒÊcoulomb/cm.2= -11.72•¬sinh 19.46z‡™ƒÕ (24)

where Ci is the concentration of ions in M, and dcp is given in V.

Evaluation of ‡™ƒÕ by Brodowsky and Strehlow's theory is more involved. Relation

between a and K (insensity of the electric field) is given by

•¬(25)

where L(x) is a Langevin function and L(x) = ctnh x-1/x, and

•¬(26)•¬

(27)

where ,u is the dipole moment, and n. the refractive index. From eqations 25, 26 and 27,

one can obtain a plot of q versus 1E0, and j9E0 is obtained graphically from the experi-

mental value of q. Relation between ƒÀEo and ‡™ƒÕ is given by the equations, i.e.,

•¬(28)

with

•¬(29)

•¬(30)

when n is the concentration in mole/cm8, v the molar volume and ro the radius of hydrated

ions (For radii of solvated ions, see E. Wicke and M. Eigen, Z. Elektrochem., 56, 551

(1952). Further, the depression of dielectric constant of water ƒÃv by electrolyte is given

by

•¬(31)

where C is the concentration in M and o the constant (cf. J.B. Hasted, D.M. Ritson and C.H. Collie, J. Chem. Whys,, 16, 1 (1948).). Note that Brodowsky-Strehlow's correction is more significant when r0 n, and q have rather greater values.

Repulsion or attraction of reactant or/and product in the diffuse double layer is the

further problem of the above mentioned Frumkin correction, and is more prevailing when

ƒÂ•s 1/k, ƒÂ being the thickness of the diffusion layer and 1/ic the thickness of the diffuse

double layer. The equations derived by Matsuda are Delahay are as follows :

•¬(32)

•¬(33)

•¬(34)

where and z are the valency of the reducing species and the supporting electrolyte re-

spectively and CS the concentration of the supporting electrolyte.

In the equivalent circuit of the faradaic impedance in Fig. 2, the repulsion resistance

rrep is in series with the charge transfer resistance.

Further problems in the analysis of the kinetic parameters by relaxation methods

may involve complication due to coupled chemical reactions, the adsorption of reactant

220

or/and product etc. Theoretical elucidation is given by Senda on these problems .

9. Nonfaradaic Rectification

The nonfaradaic rectification is the rectification due to the double layer, and it results

from the nonlinearity of nonfaradaic current versus potential relationship . According to

Parker the rectification voltage is given by

•¬(35)

when the mean rectification current is equal to zero. Equation 35 leads,

•¬(36)

Equations 35 and 36 mean that the shift of mean

potential or the change of the surface charge density results from application of sinusoidal waves to the

electrode, being correspondent to the variation of the

differential capacity with potential (cf. Fig. 13.).

This provides a method of studying surface phe-

nomena at the electrode-solution interface at very

high frequencies. For instance, the frequency dis-

persion of the double layer or adsorption kinetics1

will be the primary purpose of this method. An ex-

perimental technique developed in our laboratory

will be described bricfly.

Fig. 13. Nonfaradaic rectification

versus potential curve. DME

in 1.1 M HC104, 0.5 mc, A

3.1•~10-3 cm.2

Fig. 14. Circuit for nonfaradaic rectification. CRO3•\Tektronix

Type 535 CR0 with Type G plug-in amplifier. For the

rest cf. Fig. 7.

As is shown in Fig. 14, an external pulse generator provides a constant charge to the

double layer through a high resistance. The RF voltage is adjusted to compensate the

charge previously given. Actually, compensation is achived after 100 ƒÊsec. by using 2-30

kƒ¶ resistor (R) in series (Note that achievement of condition I-0 is practically impossible

because of fluctuation of the mean component displayed on the screen of CROl.).

Acknowlegdement

The author withes to express his hearty gratitude to Professor Paul Delahay for his

interest.

2211) G.C. Barker, "Transactions of the Symposium on Electrode Processes, Philadelphia, 1959," E. Yeager editor, John Wiley and Sons, New York, 1861, pp. 325-365. See reference 4 for bibliography .

2) H. Matsuda P. Delahay, J. Am. Chem. Soc. 82, 1547 (1960).

3) P. Delahay, M. Senda and C.H. Weis, J. Am. Chem. Soc., 83, 312 (1961).4) For a review, cf. P. Delahay in "Advance in Electrochemistry and Electrochemical Engineering," vol.

1, P. Delahay editor, Interscience Division, John Wiley and Sons, New York, 1961, pp. 279-300.

5) P. Delahay, "New Instrumental Methods in Electrochemistry," Interscience , New York, 1954, p. 148.6) H. Imai and P. Delahay, J. Phys. Chem., 66, 1108 (1962).

7) M. Senda, H. Imai and P. Delahay, ibid., 65, 1253 (1961).

8) H. Imai and P. Delahay, ibid., 66, 1683 (1962).9) H. Imai, ibid., 66, 1744 (1962).

10) cf. reference 5, p. 54.

11) For a review, see A.N. Frumkin, Z. Elektrochem., 59, 807 (1955), also for a extensive review

see R. Parsons, in referent 4, pp. 1-64.12) For a review see D.C. Grahame, Chem. Rev., 41, 441 (1947) .13) H. Prodowky and H. Strehlow, Z. Elektrochem., 63, 262 (1959), 64 , 891 (1960).14) H. Matsuda and P. Delahay, J. Phys. Chem., 64, 332 (1960).

15) M. Senda and P. Delahay, J. Phys. Chem., 65, 1580 (1961).16) M. Senda and P. Delahay, J. Am. Chem. Soc., 83, 3764 (1961).

電解整流効果と電極反応

今井日出夫

　第1節に高周波を用いる電解整流の迅速な電極反応

速度解析法としての有用性について論じる.第2節は

この方法における交直両電位電流成分の規定条件とそ

の実際的意義を解説し,第3節にDelahay-千田理論

による整流電圧測定値の一般的解析法,微分容量値が

未知であるときの別法,整流電流測定法の基礎的概念

について述べる.高周波パルス(50MC迄)による整

流電圧測定法,voltage-stepを用いて整流電流を補償

する方式の測定技術について第4,5節に述べ,第6

節にはゼロ整流電流を与える周波数,濃度関係より

kinetic parametersを解析する簡便法の理論とその実

験法について述べる。第7節には整流電流測定法に併

用される還元体内部生成法(gcneration in situ)につ

いて述べる.第8節にはこのようにして評価せられた

kinetic parametersの電気2重層構造にもとづく補正

について述べる.すなわち拡散2重層における電位差

⊿ψの見かけの加電圧および復極剤濃度分布に対する

Frumkin補正,⊿ ψ値評価に対するGouy-Chapnlan

式とBrodowsky-Strehlowの修正式,更にLevicnh,

松田-Delahayにより論ぜられている⊿ ψ による復極

剤の静電的吸引または反撥の効果である.第9節に高

周波による電気2重層の分散効果や電極溶液界面にお

ける吸着現象の研究に有望な電気2重層そのものによ

る整流効果non-faradic rectificationの理論式と実験

方法について概説する.

fadadaic rectification and electrode processes

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