Application of rotating disk electrodes to the study of electrode-initiated reactions of p-phenylenediamines

ELECTROANXLYTXCAL

APPLICATION

CHEMISTRY

OF

ROTATING

ELECTRODE-INITIATED

L.. K. J.

TONG.

Reseavclz

Labouafories.

(Received

KAI

INTERFACIAL

DISK

LIANG

AND

W_ R.

Kodak

OF

TO

245

THE

STUDY

OF

$-PHENYIJENEDLAMINES

RUB-Y

Cosnfiamy,

x965,; revised

ELECTROCHEMISTRY

ELECTRODES

REACTIONS

Easfmmz

6th December,

AND

RocJaester.

February,

~3rd

N. Y.

14650

(U-S-A

_)

1966)

INTRODUCTION This paper describes the use of rotating disk electrodes (RDE) for studying the rapid and irreversible reactions of oxidized N,N-dialkyl+phenylenedia_mines (PPD) with hydro,xide, and with phenolates or naphthoates, which are referred to

as couplers_ The former reaction leads to deamination of the substituted amine+. The latter reaction leads to indoanihne dyesa. The kinetics of these reactions have been described by TOKGL and TONG AND GLESMAWS~. In the experiments described, the reactions wereinitiated by oxidation at au inert platinum electrode followed by irreversiblereactions occnrring, as the resnltswillshow, exclnsivelyinthe diffusion Iayer of the solution_ The current-potential (voltammetric) curves were obtained for PPD under steady-state conditions in the presence or absence of other substances. Systems the kinetics of which have been accurately detetined by the flow methodI=2 were used for testing the validity of the model. TEEORETICAL

The behavior of the RDE thoroughlyaudlyzedby LEVICH out

by

VON

K~TAX~

and

nnder 3,

COCHRAN~.

conditions of convective diffusion has been

who based

The

his work

RDF

on the hydrodynamics

has several

advantages

worked over

other

types of electrodes: (r).The effective diffusionlayerthickness can be easily calculated and controlled experimentally. (2) The concentration of reactants is uniformly available over the entire surface of the electrodee &eady state can be attained rapidly, of the order of a fraction of a second.(3) Th (4) The electro d eisn?&confinedto onemetal, as in polarography_m Since~thesol~tionadjacenttotheelectrodesurface,convectionispractically nil,thecnrrentis detennin edbythehmitingdiffusionalflnxatthispointandisnot i.nfluence$by the fact that the gradientis not constant in the entire diffusion layer. Ifwe~furtherassumethattbeNemstequationisvalid,thenthepotentialisdeterm~ed simply by-the concentrations of the oxidized-&d reduced species adjkent to the eledtrode.These concentrations are obtainable fromthetransport equations and=the choice ofthethicluress oftheboundaryla+er_ 1:

ELz=cf~oamd__ iThem__

13

(1967)

2&s-262

I_. K.

246

J_ TONG,

-K.

LIAXG,

W.

R_ RUBY

diffusion-layer, The concept of using equivalent KhicL~ess for the Kemst 6orB~,calcuIatedforcaseswithconvection alone,orwithconvection plusirreversible reactions, has been described in detail by LEVICH~ and VON KARMIA~~. To gain insight into this method and justify the assumption further, we have calculated, by means of an analog computer (model DYSTAC 5Soo by Computer Systelns Incorporated) the concentration contours of asubstanceproduced on the electrode_ This substance subsequently undergoes mass transfer in the solution by convection and diffusion, and simultaneously is removed by an irreversible reaction. In later sections of this paper, models with a non-convective Nemst diffusion layer having appropriate 6's will be applied to describe current-potential relations and to show how the results can be used co study relatively fast reactions_

species satisfiesthe differential

The concentration, C, ofthereacting 'under the steady-state condition: =d"C ~&I?

equation

(1)

v x--kC=o, dC dx

where x=distance from the electrode, D =diffusion coefficient, Vv,= velocity componenttithedirectionperpendiculartothe surface of the electrode, and k= the reaction rate constant for the removal of the diffusing substance in the solution. For convenience, x was transformed to a dimensionless vaxiable;

where ibis a positive constant and B is a thickness defined by eqn_ (4)_ Aftertransformation, eqn. (I) becomes

For V,, we started with COCHRAX'S~ V,=(1,0)1,2[-00-5TO(~)~2

+

0.0127

(

Y>

0

equation, f o_333(g3'323

5/z

- o ro3(+4

Y _%z=+___ 1, 3

c-J+

+

0.002s3

0 ()

(3)

viscosity. where w = rotational speed of the electrode (rad./sec) and u =kinematic After substitution of eqn. (4), \ve obtain eqn. (5) which was used for computation in the azialog computer_ -

v9

= _t_‘5rn~X~D 6

[--O-510

+ 0-0127 S3X3

+

t_ O-333 sx

0_00283 Sax*

+

O.IC3 9X” _ _ -3,

where S~~r_6r~m(D/v)1/3_ Equation-(4) was defived by LEVICH mation, Using 0nIy the~first term 0% Commxrfs expansion.

as

a-first

(5) appro-d-

eqn. (2) was solved by using the outer boundary at In the computations, X = I (or x = ~2) as an approximation for 03, and the inner boundary at X = o, a point in th e solution nearest the electrode_ After setting the -2mer boundary conf or a even k/~, so that C = o at X = I_ The dition C = CO, we deterruined (dC/d%).

process

of

determining

the

initial

slope

was

carried

out

automatically_

Tables

of

for various values of k/D. Concentration profiles CO 71s. (dC/d.X) 0 were compiled from X = o to I were obtained from the computer displayA few of these are reproduced in Fig_ I to show the slope of the concentration profile and to show that ati decreases as k/D increases. For a given k/D, the fact that eqn. (z) is a linear differential dC

0

dxo

This

was

equation

6k is independent

and

from

the

of CO from

definition

of

6,,

co

_-

verified

we see that

z-

on

the

computer

by

various

choosing

values of CO.

I

0

0

0.2

O-4

0.6

08

IO

1'2

14

16

I-6

20

Fig. I. The talc. concn. profile of an electrode-generated and irreveslble reaction in the soln. Values of mSof diffusion layer is indicated by intercepts of tangents

reactant

undergoing

convective

diffusion thicbess

Fig. 3. The equiv. thickness of the Nemst diffusion layer_ Solid line, talc. by analog for convective diffusion; circles, talc by eqn. (II) for non-convective diffusion_

computer

(I), o; (2) I _o; (3). 1.5. Equiv. on abscissa_

The curves in Fig. I were obtained with yx+z = 2, since prelitinary calculations using WZ-= 3 produced essentially the same results_ For other values of k/D, the results a.re shown graphically as a solid line in the plot of &k/c? ‘us_ &ZJ in Fig_ 2_ -The prints

were obtained for comparison in a later section.

by a simplified

A$plicatio~~ to the stztdy of oxidized PPD

method

of calculation

to be described

reactions

The method given above using an equivalent thickness, 6, calculated for convective diffusion (eqn. (4)) for the- non-convective Nernst layer model has been applied in the stud+ of some- electrode-tiduced reactions involving oxidize-d PPD. It _is well-known2 that tae formation of indoaniline dyesby oxidative coupling between oxidized PPD Snd Com&ations arise becanke

a coupler is ustia.lly of theldeamination

can5ed out of oxidized

-mman alkaline medium_ PPD, which is Sapid in

L.

248

K_ J_ TONG.

K_ LIANG,

W_

R-

RUBY

high-pa solutions. This reaction must be taken into account when analyzing the result of the measurements of both redox potentials and coupling rates. We shall discuss first the effects of deamination of oxidized PPD on the halfwave potential, and then the effects on the coupling rates. (A) U~i&z~iozz poz%eszZiaZs. The electrode-induced reactions can be represented schematically as follows : -!?e

T

RW

T-%P

at _z = 0

(a)

in the solution,

(b)

where NH,

‘I Q

R-

(P=v

R 1y-R_

9

NH (oxidized

PPD*)

NH iI

II

P-

(quinone monoimine)

IrJl

b ad-k1

is a function The

of (OH-) _ relation. The

czrrrent+otentiaZ

differential

equations

for the reactions just

g-&m are

d2 (RI

DR~=O

(T;l

d’

DT ~ with

dxa

boundary (i)

=

-

(7)

kx(T)=o,

conditions

(R)o,

(T)

=

(T)o

at x=-o

9 -?-here are; ti &x5ral~~ m&e species. but fhe pr40 lainantspecies this

paper

is the

-q uinone

d&nine

shown-

IW for

osddized

PPD

used

in

REX~TIOFIS

OF+PHJZNYI.ENEDIAMINES

AT R.D.E.

249

and

(R) = (R)b (thebulk

(T)=o, Also,

conservation of fluxes at x=0

the

D

concentration), atx=

T-

(d(T) )

6.

gives

d(R) ( > R =o=O-

+D

dx0

Equations

(6) and

(R) =(R)o

+ ;I(R)a -

(8b)

(7) can be solved easily in closed forms:

(R)olx

(9)

and (T) =

(T),

(cash

Thederivative

h

coth ifa-sir& iz DYZ

x) .

(10)

of (IO) atx=ois

(- ) = -(T)o d t-U ax

x -

1%

cl

e

T

coth g

T

6 _

Therefore, for a fixed value of lk1/Dr a, dti, defined as the intercept on the abscissa z 0, is a constant fraction of 6, so that (TM-(d(T)P 1

__ The values of dr/6 were calculated as a function of I/kl/Dr 6 by means of eqn_ (II) and plotted as pointsin Fig. 2. The close agreement with the continuous curve calculated by an analog computer for the convective diffusion, justifiesthe use of the simplified model as an approximation for convective diffusion. To obtain the current-potential relationship, we assume further, that the Nemstequationatx=ois

E=E,+-&n-

RT

(T)o (R)o

(14

and the current

where Eh is defined as the appliedpotential_atwhich(T)o=(R)~, F=the Faraday (96,500 C/g-equiv_), and A = area of the electrode_ Note that+ this PapertheEuropean convekionis usedthroughouk-Proper eombination of eqy. (S),_-(g), (IO), (12) and (13) lead to the following- equations:

where

L. K. J_ TOSG,

Equation half-wave

(14) describes potential

El/s = Eh The

a-l -

the

reversible

condition reaction 1s

s atpH of high pH,

d&nine being the principal The redox potential for this

in eqn.

(12)

Eh=Eo If redox thenthe

is

-

S hasbeen semiquinone

showntobe was found

essentially to be neg-

HzO,

product. reaction

is

therefore R72F

h

(OH-1

-

equilibrium is assumed to hold in the solution nearest half-wave potential accordingto eqn. (r7) is

Ells=

a

NH I' +

En

having

(i7)

NH2

quinone

volt arumetricwaves

iV_ R_ RUBY

/I-

o_xidationofN,NdialkylPPD'

z-equivalent7_-Under this ligibles. Thus, the main

z-equivalent

K. LLAXG,-

the electrode surface,

Eh_~l_~~-_EO-~~(OH-)-al--B-

Fromeqn.(~S),~ifpropercorrectionsaremadef~raL~and~,Eocanbecalculated forthe system_ The term #?,the correctionfor unequal diffusion coefficients defined by eqn, (16). has been evaluated for the three PPD's used in this paper (Table I). These-compounds were selected_from the cl+, the members-of which have onIy on& predomiuant ionic species betwen pH 8 and pII12,~for both R-and T. This conditionjusIifiestheassumptionthat~othD~zandDrareindependentofpH,and Di

at the lower pH li&t where-T is sufficiently stable. -_ cc~rrectiori ml, owing to_ the 3ristability of T, c+n be calculated from

can be measured _~

The

eqneqn. (7)is due to the dearnination reaction_ It has (IZ)‘_ This m_s t ability reflectedby been sh&n Irh&for l3G.cla.ss pf PPD. tl+pseudu-first+kder rate constant, kl, is p%opotiggaX to -(OH-) be_twken pH_ 8 and pH xz?.‘Th~efore

REACTIOKS

TABLE

~FP-P~NYEXEDIA~~INES

AT

251

R.D.E_

1

STRUCXUPES

OF

REACTANTS

USED

IN

THIS

PAPER

agents

Developing

NH? I

X-H=

I’

,’

0

CHs

3 b

CH3

H N-

I

C&&f-QH4-

I

in (r8)

(OH-)

,

(19)

kl’ is a pH-independent, and, Em

III

II

k1 = kl’ where

SOdXCi

in turn,

eqns.

second-order

(IS)

rate

constant_

Substitution

of eqn.

(19)

and (16) in (18) gives D-r +ln-_tln It

= Eo -

“‘(OH) DT

6 . coth

kz’(OH-) Dr

6

>I .

(20) Note that eqn. (20) has the following At low pH values El/z

E Eo +

29-5 (14 -

pH)

-

limiting

29-5

cases:

log -

(2Iaj

DR

and

at high

pH

values

El/z g Eo +

44-3 (14 -

pH)

- 29-5 log r

B

-

29-5 1%

(=b),

which require the slope of E T/Z ZJS.pH plot to change from - 29.5 to -44-3 mV/pHunit-as the pH is increased_ (B) Ca-z$Eing ra.tes. In the presence of coupler, in addition to reactions (a) schematically by and (b). we have the coupling reactions (c) and (d), represented the following equations :

T

.+

C -L

kz (in the solution)

fast T-i-L where

--y+Q+R

/

,

(4

I..

XC_ JT- TONG,

IL

LL%NG,

W_

R_

RUES

(coupler anion)

klis a function of (OH-) (C) is the coupler-ion concentration used in excess so that it undergoes littlechange during the reaction. differentialequations are kz = kz’ (C) , where

The

d'(T)

~ &"

-

AZ(T)

= o

de(R) C %$(T)=o, iLx" where

RI and

kz are the pseudo-first-order rate constants

for de amiuation and coupling, respectively, as defined above. ,4s before, the boundary conditions are specified i.n thesetofconditionsineqn_ (S),thepotentialofelectrodeaudthecurrent~eexpressediu eqns. (12) and (13),respectively. Thesolution of eqn. (ma) is

(T) Wheu

=(T)o(coshAlx

- cothitlc? -sinh

(T)issubstitutedineqn_ boundary conditions (S) gives

(‘22b).

AIX) .

(23)

doubIeiutegrationwithrespecttox>he

(24)

The

derivative of (R) with respect to z at x=

(cg)o = (2?)‘lp

(;116cothl16-1I)

o

is

+ $((R),J -

(R)o) _

(x5)

Combining eqns. (23). (24). and (25) with (12) and (13).we have the currentpoteutial relationship: z’=&

I

[

-

exp

(

I

$$(E--E~+~x.~+P)+I

,I’

(261

where

and Ek aud~bearthesamesignificauce asin eqns. (Tz) and (16)~ Equation (26) represents a reversible voltammetric wave with the ha-wave potential EIJZ = Eh - a1.z - fi . (29) The term, alv2, is duetoirreversible reactions in the solution:de aminationandcoupling. Like al in eqns. (IS) and (17).al._ -is defined relative to the half-wave potential obtainedinthe absence of any irreversiblereactions. It is of interest to point out some limiting conditions of eqns_ (27) and (28): (-4) If kz =o, i.e.,no coupler is present, the equations degenerate to those of the earliercase, eqns. (14) and (IS)_ (B) If kT+cr, and k1 is finite,i-e..either the coupler is very reactive or its concentration

is very

high,

orboth,

then

This predicts that the-diffusion current should have the upper limit of twice that for kT=o bnt that the half-wave potential changes without limit (in principle)(Cl If kp is finite and RI + 00 then AI = vkl/DT and

This predicts that-if the-coupling rate is kept cqnstant, and the decomposition rate (not nec&.saAly the de ;rmination rate) isticreased, the lir&ing current. decreases_ coupling andthus This is understandable sine for large kl,the fraction df Tvsedfor also for oxidation of theleuco dye, decreases owing to the increase in competitive decompoGtjon.

L. K. J. TONG,

254

K.LIAKG,

W. R. RUBY

Thepointsbroughtoutbytheaboveconditionsnggestthatboththevariation of i, and aI,3 as responses to the variation of (OH-) and coupler-ion concentration maybe utilized to study the rates of deamination and couphng reactions. EXPCRIJIENTAL

amodification of that The rotating disk electrode (RIDE) usedinthisworkis described by AZIZ xx~ RIDDIFORD~_ The I_o3-cm-diam. platinum disk is attached to a r/4-in.-diam- stainless-steelshaft, precision ground_ The disk and shaft are press-fittedinto abell-ShapedTefloninsulating sleeve,having amaximnm diameter of 2.5 cm_ The platinum disk and subsequently the Teflon sleeve are accurately machined by using the ground shaft to fix the axis of rotation_ The eccentricity is 0.001 in_ The electrode face is finished on a metallurgical polisher by using Rayvel cloth* andGeociencelevigated alumin aabrasivespray(o.o5y)**-. Asimilarelectrode with a silver -l&k has also been constructed. A soft-rubber wiper blade mounted in the cellcanbe swung into position to remove electrolysisproductsbetween readings_ Theelectrodeis drivenbyaHeDermotorandan electroniccontroUer_Therotational speed is measured 3~ a tachometer generator and meter calibrated against a standardized photoelectric tachometer (Hewlett Packard Model 505B)_ Rotational speeds can-be varied from 0-70 rev_/sec. The three-electrode cell consists of the RDE as a working electrode, a large platinum disk as an auxiliary electrode, and a saturated KNOs-agar bridge to a SCE as a reference-The platinum auxiliary electrode has a diameter of 2.5 cm andis positioned about 2 cmbelow and paraleltotheface ofthe RDE_ The tip oftheSCE bridge is positioned outside and slightly below the RIDE_ A water-jacketed Ioo-ml glass beaker with a Teflon top serves as a cell body and maintains the solution at 25 _+o_I". A Nn-,W inlet through a sintered-glass bubbler is used for degassingthe solution_ The potentiostat is a modification of that described by ALDEN, CHAXBERS AND ADAIMS~O. The function generator is replaced by a multi-turn potentiometer adjustable to a fixed potential or connected to a constant-speed motor for a slow sweep cf poter,tiaI range at 500 mV/min_ The cllrrent-potentid or current-time relationship was plotted on a Model 3 Moseley X-Y Recorder operating either continuously or intermittently_

For convenience,the PPD's uedesignatedinthis articlebyroman numerals, and couplers by letters, as given in Table r. The preparation and purification of all reactants used in the experiments have been describ.edl-"c.

AUb~ersandthedistilledwaterusedinthereactionmixtureswerede-aerated with 142 for 15-20 & beforetransferenceto the cell to reduce the error due to air * Bediler.

*I

Ltd..~ E v%nston.

Geoscience

Instruments

ILL Carp_, Kew

York,

N-Y_

~ZE-KTI~NS

~F~-PI~ENYLENEDIAMINE~

oxidation.

The

buffers,

AT

prepared

by

255

R.D.E.

mixing

the

appropriate

volumes

of

KHZPOJ,

K?HPOd, and KaPOa solutions, gave a constant final ionic strength of 0.375 in the reaction mixture. The coupler was dissolved in the buffer, and the PPD separately in the water. The latter is essential since accidental oxidation of PPD at high pH causes rapid de amiuation_ The final composition of the solution (PPD, I - IO-~ M an& coupler 4 - IO-~ 5 . 10-3 M) was attained by pipetting pre-detetined volumes of component solutions into the electrode cell previously filled with NZ and continuously purged by this gas. Care was taken to raise the e_xit of the NT-delivery tube to a height above the liquid level so that bubbles were not formed on the electrode during the measurements. Two to three minutes were allowed for the solution to attain thermal equilibrium, with the water at 25 + o. IO circulating m the jacket. Prelimmary experiments showed that the current decreased slowly when the potential was maintained anodic. It was subsequently found to be due to accumulation of reaction products on the electrode_ It is knowu that there are further followingreactions which produce insoluble materials at slower rates than those considered in this paper_ The initial current was found to be restored after a sizeable downward drift by wiping the electrode with a rubber squeegee while the former was rotating. A squeegee that could be swung aside during the measurement was installed and the procedure of wiping the electrode just before taking the reading was adopted_ It has been estimated that less than I set is required to restore the steady state after a disturbance at the speed of rotation used. Blank runs using buffer, and buffer plus coupler were made in the same manner for corrections. The voltarnmetric curves for pure PPD. and for PPD plus coupler were obtained over a wide range of potentials, about IOO mY on both sides of El/z. The

diffusion

coefficient

of

the

o_zdized

PPD

A pH S-buffer andPPDweretransferredtothecellasaheadydescribed_With the electrode in rotation and a pre_deternGned potential set, a ferricyanide just

sufficient

to o_xidize the PPD

to the cell with

Pi-D

I II

III

DR.

105

a syringe_

DT

diffusion

current

to quinone

diirnine,

for the reduction

was

solution

quickly

of the oxidized

added PPD

- IO=

[cm”lsec)

(cmzlsec)

0537 O-483 0.67s

o-537 O-585 o-567

= European

The

completely

con%-ention. vs. standard

+:: -2 calomel

-

I22

93 63 6$

--II9

-

97 56 5s

cell.

measured at the shortest time interval after oxidation, which was usually I-Z set_ This interval was found to be long enough to attain the steady state at the regular rotational speed of the Electrode and sufficiently short -that decomposition of the oxidized PPD at thispH could be ignored_ The diffusion coefficients for R and T are listed in Table 2. was

J. EZeciroamzE.

Chm.,

13 (1967) 245-262

256

J_

I- K_

TONG,

R.

LL4NG.

XV_ R.

RUBY

ThecelEwasfilledtotheproperlevelwithasolution of PPDatpHS. With the potentIaZsetneartheEl/~andtheelectrodeinrotation.oneequivalentofferricvaTllde/ mole of PPD WLXS added for the purpose of half*,xidizing the PPD, z’.e_, to make (R)o = (T)o_ A short section of the i-E curve was produced on the reccrding paper and

Eh

was

at the intersection

found

with

the i=o

line. With

several

trials, the

set) after o_xidation. was used. IncidaEh-value obtained attheshortesttime (-2 taUy,oxXationof PPD at pH S would produce some semiquinone, according to the equation R + T+z S, where S represents semiquinone. However, by starting with (R) be

=

(T),

used

Rate TONGS_

th e reaction

up

in the

wilI

same

constantsfw

not

deamination

Therate constants The rateconstants

equality

since

components

both

wouid

and

cou$ing

described

weretaken detetined by

TONG

from an earlierpublicationby recentlybythe steady-state

AND

GLESMAXX~C

These

values

3

SECOND-ORDER XEXRIC_.LY

I II III

the

fordeamination for couplingwere

flow method in the apparatus are listed in Table 3TXBLE

destroy

amount.

BY

RXTE FLO=-

3-22 3-78 4-40

DISCUSSION To

CONSTAKTS METHOD)

5_r1 5-M 6-83

FOR

DEAJIIWATION

AND

COUPLIETG

(OBTAINED

SPECTROPHOTO-

3-85 5-45

OF RESULTS show

_(< 0.2 mA/cm") hi,-her current linear current

that

the

electrode

process

is diffusion-controlled, densities, by increasing density

(G/A)

3s. ~m/2n

at the

current

densities normally

used

we carried out some experiments at much the concentrations_ Figure 3 shows that a

relationship was

observed

for each of the

concentrations of III use&as

high as 25tirm.3 the normal concentration_ Theslopes of these lines zre proportionalto the concentration within this range. Furthermore, replacement of Ag for he Pt electrode produced deviation only at current densities much higher than diffusion-controlled

the density normally used here, showing forbothelectrodes below this limit_

that

Further, the shapes of the normal$ed voltammetric waves used are in fair agreement with the theoretical curves calculated case (eqn. (z6))_ Thk is illustratedin Fig. 4_

the

current

is

for all the PPD's for the reversible

To evaluate the parameters, ]&/DT~, and v(kl + akz)/D~ 6, in eqns_ (15) available- Since 6 and
REXGTIONS

3.5

OF $-PHENYLESEDIAMINIZS

AT

R-D-E.

257

-

3-o -

2.5 -

2.0 -aI9 1.5 -

LO -

0.5 -

Fig.

3_ The

agent

III

(&am.

=

hmiting current density US_ the square root of the electrode speed for the developing at pH II and different COIX~LS.I ( o), Pt electrode (diam. = r-03 cm); (e), Ag electrode r.zg

cm)_

Fig- + The normalized voltammetric curves_ theoretical : (--1, z-eleczlxon ch~ges; {---) , r-election change. Observed; ( 0). PPD I ; ( A), PPD II ; ( u), PPD Irr ; ( *), PpD 1 with coupler (a) at 3 - IO-= A!!. Ml measurements at pH II, speed 7_7rev./se~, and PPD CONCH. = I - x0-! M_

I,. X_

W_

R. RUBY

(for water at;zsO, Y = o_Sgg - IO-~

cmz/sec

258 Thus, errors was

in

DT

as

well

as

in

Y

J_ TONG,

IL

I_IAN_G,

used) do not produce serious errors in the parameters. For c~cula~ons,

DT = = -

determined

10-5cm*/secw;~~used,~uhichisinreasonableagreement~vlththerecently values of 0_5+o_7 x IO-~ cm~/sec. Thus, &/~DT= ~_o/co~‘“_

The pH-dependence of El/z was analyzed by the use of eqn- (zo)The last term, defined as a1 in eqn. (15),is completely determined by &‘(OH-) _ Since k1’ has been independently determiuedl, ?he relation of _E~,zto pH can be calculated with the proper choice of (Eo + p)_ The results of this c+culation. with the verlica_l displacementzthe only degree of freedominthefitting,havebeen plottedin Fig. 5 and compared with experimental observations_ -5oo-

I

-80

-

-60

-

I

I

I

I

t

I

I

k

/I

0

0

/

-40

W ”

t -20

c

, , . , , I 85

9.0

9.5

IO-0

II.0

Ia5

11-5

12.0

12.5

PH

for oxidation 5_ El,? t’s_ pH PPD I; (a). PPD II; ( c), En - equilibrium measurements Fig. (0).

of PPD’s. Theoretical PPD III, all at 10-a M_ at I - 10-3 _ii_

I solid (A).

line, PPP

talc_ by- eqn. (20) _ Observed I II at Io-3 M: (+). (A), (9).

The expekirnents contain four sets of data with a concentration of IO-~ M for each of I, II, and III, and of IO-~ M for II. The agreement in each case with respect to ~limiting slopes and positions of divergknce is reasonable. The correction; p. was calcukt-ed from Dr and D =, obtained directly as described in the experimental se&km_ This correction is~usually insignificant. We now -have sufficient information to calculate the standard potential, 2%; owing to the method use& EO so -from .voltammebic measuYrements_ However, Calcnlated~Iscir;ly a constant having the dkqension of a potential and & independent of pH and & &e diffusion kdficienfs of X? and T_ TO identi~ & a2 the -standard

OFT-PHENYLENEDIANINES

Fuz~crIo~s

“0 -

AT

259

R-D-E.

O-6

IO

4 1 +1OCl

I

I +!io E

I

I

0

-50

(mV)

vs.

I

-lOG

-I50

SCE

Fig. 6. Observed voltammetric curves for oxidation of PPD I (I - IO-~ M) in the presence of &r); (3). couplers. pH. 11.20; speed, 7-7 rev_/sec. (I), no coupler; (1). coupler (b) (2.5 x 10-X coupler (a) (_t- xo-.1 1cT); (+). coupler (a) (I - Io-3 M); (5). coupler (a) (3 - Io-3 iW)_

I

IO 20

I

I

I

40

60

00

I

100

I

129

I

140

0

Fig. 7_ Effectofcouplingrates ontheltitingcurrentfor the brddationofmPPD's_ Curves talc. for values of RI indicated as parameter, pH = ir.mPPDmI (& = 3_r6): (0). with coupler (b); _ (+), with coupler (a)_ PE'D II& = 10-7):(A); with coupler (S)_ PPD III (Kx = 40]:m(oj, with coupler (a); ( 0); with cOupler (b)_= J- EZectu&d-Cliem.,

13 (xg67)m3-45-26z

La K. J_ 701*TG, K. LIANG.

260

W.

R. RUBI-

potential, wEch was defined in terms of the electrode eq~b~~ with R and T, we must have independent experimental verification. For&nnately, this can be obtained at lower pH where the half-oxidized system is stable enough to allow equilibrium measurements. The values of EO measured by kinetics and by eqnilibrium methods are compared in the last colnmn of Table 2.

When a coupler is added to a PPD, the voltarnmetric wave is expected to vary acccording to equs, (z6]-(~8). The diffusion current increases aud, simultaneously, the half-wave po,tential becomes more negative (European canvention) _ However, the shape of the wave remains practically the same (Fig. 4)_ This effect has been verified (Fig, 61, by using PPI3 I alone, and with added couplers_ Quantitative compzisons between theory and observations are illustrated by .Figs. 7 and 8.

0

I lil

20

30

do

I

Ha 7’0

50 qy

I

1

I

I

1

I

I

eo

so

too

110

120

130

140

8=k,6

I

150

-

8.. Effect of coupling rates on Eli-_ for oxidation of PPD”s_ (----), c&c. for kz = a and varymg irk; (--I. talc. for const_ k~ and rar_ving ktr_Observed B;t pfT = zx and speed 7-7 rc%-.fsec. unless otherx+se specified. PPD.1 (kr = 3.16): [+->, \vith coupler -(a); [o) x%-it& coupler (b). PPD II (RI = 10.7): ( a). with coupler (a). PPD III (R, 4.0) (0). +\-it6 couplei (a); {c)) 114th coupler (b) (speed 30.8 recjscc) ; ( z). xx-ith coupler (b). Fig-

Figure 7 shows the ratio of Emitin, w current with and without coupler, i&,e, as a of the variable bf(& + z&)/J& fi = 2~ 6, where RI and KZar.e the rate constants and Dr is the thickness of the diffusion layer_ The curves were caldnlated from eqr~ (227), by using kl = o, 3.~6, 10.7, and 40~ the deamination rat&for I, II, and III, respectively_ The’ intersection with the abstiissa is- t/AQDr 6, which is different, in is comxnon to alL coup&x-genera& for each PPIX 22x2-k curve w5th RX as a p meter PPD combinations, as long as the o_xi&ed PPD has the same K.-valne, For small values of Al, data are ~&ilable for only one PPD in this group. (I),because of the %mPosed rest~Sction thak the coupler concerrtxation must be s&ic~entIy Iarge so that: function

m3crIoxs

~F~-PHENYLENEDI~~IINES

its concentration where

is not

significantly

kz’ is the specific

rate

261

_4T R-D-E.

lowered

constant

in the reaction

-of coupling

and

region.

(C) is the

Since

KZ = ,%3’(C),

coupler-ion

concen-

tration, the lower Limit of KS is set by the practical lower limit of (C) when ks’ is large, asisthe case for II and III. The upperlimitof 2.0 foridlid.0 hasbeen demonstrated with the more reactive couplers. The agreement of the results with theory is quite satisfactory, especially for I at lower values of A_ This is a test for the accuracy of 6 as well

as for

that

of Kz, since

the

variable

for

the

abscissa

is the

product,

AiS.

Experimentally, the half-wave potential was measured at constant pH and This is equivalent to varying ionic strength but at varying coupler concentrations. RI =o and kz but keeping& constant_Sinceml andocl._3 were definedwithreferenceto k2=o, an ideal condition, and experimentally we canonly observe the displacement relative to no coupler present, 0~1 from eqn (IS) must be added to this to obtain LYE.?_ the

The curves displacement

of 0~i.s vs. I/& as a function

+ zkz)/DT6 of k,, with

(Fig. 8 andeqn (2s)) actuallyrepresent as a parameter_ The curves begin at

RI

k-, = o, shown

in Fig_ 8 as the dotted line representing 011 as a function of k1 (eqn. (IS))_ The experimental points are more scattered than those for limiting current, but the general characteristics arein aseementwith the theory_ In Table 4, the coupling rate constants, obtained by the electrochemical method with eqn_ (27) or Fig. 7, are compared with those obtained by the spectrophotometric method for systems having slower coupling rates. The agreement is satisfactory. For more reactive systems, the id/id.o-values approach asymptotically to 2-0, and hence for these systems, the error in the determination of ko from the current is espectedto be large.

T_XBLE

4

CO?.lPAKISON BY

(C)

THE

OF FLOW

- 70-.x

COUPLITSG

RATE

M

BY

AX

ELECTROCHESIIC.9L.

LIMITING

PPDI--(b) EZ~CttrOdW?7ZiGd

PPDI-ia) EZechochenricaZ

ks

ks

ka’ - 10-1

(set-I)

(Zfsec-mole)

kn, - 10-3 (Zlsec-mole)

(see-1) 4-o

TO.0

36.2

3.2

8.0

9-5

9-5 5-6 4-7 -47.. y-o+

Z=j-0

14.0

50.0

23.6

We

COKST_%NTS

CURRENT

AND

hIETHOD

may

conclude

that

I-3 (vs. 7_0+

the

model,

S-g (us. 13 fromthe

0.2 Zrom

the

formulated

flow

by

flow

method)

method)

using

6 gas obtained

for

convective diffusion for the. thickness of a non-convective diffusion layer, is satisfactory for describing the diffusion process of a rotating disk electrqde.accompanied by irreversible reactions_ This model offers a convenientand simple method. for studyingthe reactions of 6,xidized PPD. Although.this method is less accurate than thefloru'method,itisgenerallytiork convonientand espediallyvaluab1e~th~stu.d~ of systems-

sy St ems) _

where

spectrophotometic

me+mements~carinot

be

made-

(e.g.,- opaque

262

L_

K_ J- TOYG.

K_ LIA&IG,

W_

R_ RUBY

A theory has been formulated to relate the oxidation current and potential of a rotating diskelectrode for the o,tidation of+-phenylenediamines in the presence ofothersubst~cesthatreactirreversiblywiththeoxldationproducts. Suchreactants include the OHion and coupler ions. The rates of these reactions influence the current--potential relationship in such a manner that variations in the latter can be usedtomeasuretheratesinwhichweareiuterested. Correctionsforerrorinpotentials, duetoinstabilityofo,uldizeddevelopingag~~,werededuced_Afterthesecorrections were applied to the measured half-wave potentials, the equilibrium standard potentials of these developing agents were obt-&ed_ Using compounds by flow-machine methods, we have found the electrode method

studied previously to be reliable, by

comp&on_

REFERENCES I__ K_ J_ TOXG. I_ Phys. Chetn.. 58 (rggA&) rogo. (a) H. KOECHLISE _.XD 0. N. WILT, Ckr. Pat15.915 (1881) ; (b) P. w_ VI~~IJM AKD -4. WEISSBERGER. J_ Phot. Set.. 2 (1954) SI: (c) L_ K_ J_ TOSG AND 31. C. GLEShL4lr‘N, J_ Am. climn_ SOL, 79 (‘9571 5s3V. G_ -VICH. Physicoc,~zmical Hydrodynamics. Prentice-Hall. Englewood Cliffs. New Jersey. rg6z_ 2. A~~zgew. &IaZh. &Tech_. I (1931) z44_ 4 T_ VOX nRMXh_, W_ F_-Cocrr~zx. Proc. Canzbridge P&Z. SOG-, 30 (19x4) 365_ T K- J_ ToNG.MC. GLESMANN AWD R. L. BENT.]. Ant_ Chem_ Soc..fk (1960) 1988. -. et al.. /_ Am. C?zenr. Sot.. 73 (195x) 3100: H_ Y. LEE AND R. BTU'. _~DABIS. AxraZ_ 7 R. L_ BENT Cher/a_, 34 (1962) 1587_ S I- K_ J_ TONG AND ST. C. GLESNAYX, Phob. SC& ENS_. 8 (1964) 319. -4. C. RIDDIFORD. -4 naZ. Chem.. 34 (1962) 1023. 9 S. -4z1z AKD J_ Q_ CHAMBERS AND R K_ _%DXMS,]. EZecttreanaZ_ Chem.. =j (1963) 152. IO J_ R. _~LDEX,

2