A study of ion transfer across the interface of two immiscible electrolyte solutions by chronopotentiometry with cyclic linear current-scanning

J. Electroanal. Chern., 189 (1985) 35-49

35

Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

A STUDY OF ION TRANSFER ACROSS THE INTERFACE OF lWO IMMISCIBLE ELECTROLYTE SOLUTIONS BY CHRONOPOTENTIOMETRY WITH CYCLIC LINEAR CURRENT·SCANNING PART III. lWO·COMPONENT SYSTEM

WANG ERKANG • and PANG ZHICHENG Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130021 (People's Republic of China)

(Received 28th November 1984)

ABSTRACT In this paper we study the transfer of two ions across the aqueous/organic phase interface by means of chronopotentiometry with cyclic linear current-scanning. The relationships of the interfacial potential difference with time and current, the expressions for transition time and limiting diffusion current at both positive and negative current-scanning stages have been derived. The experimental results are coincident wi th the theoretical expressions.

INTRODUCTION

In Part I [1] and Part II [2] we discussed the transfer of a single ion across the aqueous/organic phase interface. In this paper we discuss the behaviour of the system containing two ions which can transfer across the interface in the process of cyclic linear current-scanning. The discussion of a two-component system is of importance, because in many systems it often happens that two ions transfer across the interface one after another. The transfer of two ions across the aqueous/organic phase interface may take place in two ways: either the two ions transfer at close interfacial potentials and in this case the two waves on the chronopotentiogram will overlap; or the two ions transfer at considerably different potentials and in this case the two waves on the chronopotentiogram will be distinctly apart. Here we only consider the latter case. THEORY

Supposing that there are two ions, MZ, and NZl, in the aqueous phase, their standard transfer potentials (tl~rp? and tl~rpJ) differ considerably from each other.

*

To whom correspondence should be addressed.

0022-0728/85/$03.30

(i)

1985 Elsevier Sequoia S.A.

36

At the positive current-scanning stage, M =, first transfers across the interface into the organic phase. After a period of time (transition time 7;) the concentration of M Z, at the surface of the aqueous phase decreases to zero. The interfacial potential difference carries out a positive jump. Then the N=, ion begins to transfer into the organic phase. Again after a period of time (transition time 1j) the concentration of NZl at the surface of the aqueous phase also decreases to zero. The interfacial potential difference carries out a new positive jump. At the stage of negative current-scanning, the two ions transfer back into the aqueous phase in reverse sequence. The NZ, ion first transfers back into the aqueous phase. After a period of transition time its concentration at the surface of the organic phase decreases to zero. The interfacial potential difference carries out a negative jump. Then the M =, ion begins to transfer back into the aqueous phase. Again after a period of transition time 7/, its concentration at the surface of the organic phase also decreases to zero.

7;,

rjllA 80

60

40

20

0

E/mv

-20

-40

-60

-80

Fig. 1. The chronopotentiogram for the transfer of Cs+ ion and TEA + ion. Water phase: 0.01 M LiCl. 6 x10- 4 M CsCl. 6x10- 4 M TEACI. Nitrobenzene phase: 0.01 M TBATPB. P =1 p.A S-l.

37

The interfacial potential difference will carry out a new negative jump. Figure 1 shows the chronopotentiogram of a two-component system containing Cs+ ion and TEA + ion in the aqueous phase. The positive current-scanning stage

M=' and N=, transfer from the aqueous phase into the organic phase one after another, as shown in Fig. 2. According to the analysis above, we know that at t = 0, the MZ, ion begins to transfer into the organic phase; at t = 'T j , the concentration of M z, at the surface of the aqueous phase decreases to zero and at the same time the NZ, ion begins to transfer into the organic phase; at t = 'T; + ~, the concentration of NZ, at the surface of the aqueous phase also decreases to zero. We can write the diffusion equation for the transfer of M Z ' and NZ,: ac(X t)

, '+

at

acj(x, t)

at

=D I

a 2c(x t) a 2cj (x, t) +D--"---ax 2 j ax 2 I

'

(1)

with initial conditions

(2)

t=o and boundary conditions

(3) (4) where subscripts i and j denote M=' and NZ" respectively. Other symbols have their usual meaning. We solve the equation step by step. At < t ~ 'T;, only the MZ, ion transfers across the interface. So the scanning current in this period of time should be equal to the diffusion current (/;) of the MZ, ion. Thus we can write the diffusion equation for

°

Interface

w

o

--------''-------x x:o I

= vt

Fig. 2. Transfer process of ions M Z , and N Z , across the interface at the stage of positive current-scanning.

38

the transfer of M

Z

in this period of time as

,

aci(x, t) a2dx, t) ---'--':---'---'-- = D --'--'---~ at ax2

(5)

I

with initial conditions t=0

Ci(x, t)=c?

(6)

and boundary conditions

x=o x=

(7)

dx, t)=c?

-00

(8)

Solving it, we get

ci(x,t)=c?-

l x 4pt ! ![(1+4xD2 )exp(-4 D2) 3zFAD77T' J J I

I

7T~

3 x 2 ) ( --x) erfc ( - -x + ( -+--)

2

4DJ

2Dl t~

2Dl t~

1

(9)

The concentration of MZ, at the surface of the aqueous phase is

4pt l 3ziFADl7T2 From this we can get the transition time 'Ti for the transfer of the MZ, ion: o

ci(x, t)lx=o=ci(O, t)=c i -

1

1

(10)

(11) At t = 'Ti , the distribution of concentration of M z, in the aqueous phase is

e;(x, t )1,-.,

~ ,? - c? [( 1 + 4~:T,)

exp ( -

7T~X)

4~:T')

+ ( -+-3 X2)( - - - erfc ( - -X)] 2

4Di'Ti

2D: 'Tl

2Dl'Tt

(12)

and the concentration of MZ, at the surface of the aqueous phase is

ci(O, t)lt=T, =

°

°

(13)

In a similar way we can get the distribution of concentration of M z, in the prganic phase at < t ~ 'Ti :

4ptl [( 1 + 4-D X2) exp ( (A x, t) = 3zFAD77T' J !!

I

I

7T~X)

X2) 4-D it

- ( -+~ 3 X2) ( - - erfc-(x)] 2 4DJ 2Dtt~ 2Dlt~

(14)

39

Its concentration at the surface of the organic phase is

4vt l _" 3z;FAD;'7T'

Z\(x, t}lx=o = (';(0, t}=

(IS)

At t = 1';, it becomes

(16)

(';(0, t}I,=T, =c?D:/D}

After t = T;, the concentration of M=' at the surface of the aqueous phase is always zero. The diffusion current of M=' decreases gradually. Now let us find the diffusion current I; of the M=' ion at 1', < t:( 1'; + 1'j • From the diffusion equation for M =, in the aqueous phase

i)c;(x, t}/at=D;a 2C;(x, t}/ax 2

(17)

with initial conditions

t ~',

c,(x,

th? - C?[ (1+ 4~;'}XP(

3 X2)( -7T~X) + ( -+---

2

4D;1';

2D: 1'}

-4~;',)

x)]

erfc ( - - -

(18)

2D} 1'/

and boundary conditions

x=O x

C;(x, t}=O

(19)

C;(x, t}=c?

=-00

(20)

we can get

aC;(x,t}1 =_ v [7T~t' " 2T:(t-1';)~ a " x x=O z;FAD!7T 2 D/ 7T2D/

2t 7T DJ

- -,i -, arctg

(t-1")~] , 1'/

(21)

So we can get the diffusion current I; at the interface I; = -z;FAD;

=v t-

[

ac;(x, t}

a

x=O

x

21'l(t-1'J~ 7T

I 2t 7T

- - arctg

(t-1';);] , 1'/

(22)

It can be seen from this expression that the diffusion current decreases with the time (see Table 1). During this period of time, the NZ, ion also takes part in the transfer process, and its diffusion current I) increases with time: 1)=1-1;

=v

2t + [ 21'l(t-1'J~ 7T 7T

-arctg

(t-1';);] , 1'/

(23)

40 TABLE 1

Relationship between the diffusion current of M:, ion and time at

T,

< t .;;

Tj

+ Tj

t;lTj 1.0 1.1 1.5 1.9 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 00 Ij/PTj 1.000 0.684 0.462 0.378 0.363 0.310 0.275 0.231 0.203 0.183 0.168 0.156 0.146 0.139 0

Thus, at as

1'i


~ 1'i

+ ~, the diffusion equation for the transfer of N=, can be written

ac/x, t) a\(x, t) ----=--- = D--'---at J ax2

(24)

with initial conditions

(25)

c/x, t)=cJ and boundary conditions

x

=

°

Ij

v

=

[

21'f(t-1';)i 7T

2t

+ - arctg 7T

(t-1'i)ij I

1'1

(26) x= -00

(27)

c/x, t)=cJ

Solving this equation, we can get the concentration of N Z , at the surface of the aqueous phase at 1";';;; t .;;; 1"i + Tj:

ciO, t) =

o

Cj

4v(t L

-

Tn I

I

3zj FADJ7T 2

(28)

From this we can find the transition time for the transfer of the NZ, ion

(29) We define

t/ =

1'i

+~)

as the total transition time for the two components, i and

j. From eqns. (12) and (13), we get

(30) Thus, we have

3. = ~

(ziDl c?+ ZjDjcJ)~ -(ziDlc?)~

(31)

41

(32)

T,

+ T,

at

Similarly we can get the concentration of NZ, at the surface of the organic phase Ti < t ,;;; Ti + Ti

t,

_

c,(O, t) = .

4p( tl-

Tn

_I

(33)

1

3zFAD''1T' J ,

At the total transition time, ti = (T, + Ti ), the concentrations of N=, at the surfaces of the aqueous and organic phases are

(34) (35) Now we can obtain the relationships for potential difference with respect to time and current. At 0 < t,;;; Ti , the transfer of the MZ' ion is the controlling process and the interfacial potential difference may be written as ,\w

,\w

°

I.l.()rp = I.l.orpi

RT I Yi

+F Zi

RT I <:;(0, t) n ( ) ci 0, t

+F Yi Zi

n -

4pt~ ,\w

°+-F RT In -+-F Yi RT In

=I.l.()rpi

Yi

Zi

3zFA-m'1T~ I I

z,

(36)

4pt~ co - - - - -

3z.FAD~ 7T~ I I

I

Substituting eqn. (11) into eqn. (36), we get ,\w

,\w

°

I.l.orp = I.l.orpi

At t

=

RT

+F Z,

'Ii In -

Y,

RT

Di

RT

+ 2F In D + F z,

i

Z,

t;

In -,--, Tl - t,

(37)

0.63Ti , the last term is equal to zero. Thus we have

,\w

I.l.()rpi 063T ,. ,

=

°+ -F RT I Y RT n - +2 F

,\w

I.l.orpi

i

Zi

Yi

Zi

Di

In =Di

(38)

Then we can write the relationship for potential difference-time: /).W

orp =

/).W

orpi,O.63T,

RT I

+F Zi

t~

n ~

Tl - t'

(39)

and the relationship for potential difference-current: '\W!l.w I.l.orp l.l. oCf>i,O.63T

=

,

RT I

[, + -F n -,--,

'Zi

[~ -

[,

(40)

42

where IT, is the limiting diffusion current of M=' denoting the current at t = 'T;: !

1

2

2

2

1

1

02

IT =p'T.=(9/16)'p'z'F'A''fT'D'c' ,' I

I

I

(41)

At 'T j < t ~ 'T; + ~ = ti , the diffusion of the N=, ion is the controlling process. The interfacial potential difference may be written as W

ti.ofP

cia, t)

Yj RT

woRT

= ti.ofPj + -F In - + -F In Zj

Yj

( ) cj 0, t

Zj

(42)

Substituting eqns. (11) and (29) into this equation, we get

(43) At t=0.63[('Ti+~)~+'TN=0.63(tj+t})~, the last term is equal to zero. We can write the interfacial potential difference at this time as w

ti. o fPj.O.63T,.

)

woRT Yj RT Dj = ti.ofPj + -F In - + 2 F In -D Zj Yj Zj j

where t; = 'T;, tj = 'T; difference and time:

+~.

(44)

Then we can write the relationship between potential

(45) and the relationship between potential difference and current:

,

AW AW urn-urn oT oTj,O.63T,.)

,

RT I J2 - 12I, +z.F - n~ - -~ J

I'I) - I'

(46)

where

(47) (48) (49)

43

The negative current-scanning stage As in the case of single ion transfer [1], we assume that the initial condition of the two components, i and j, at the beginning of negative current-scanning is aqueous phase

organic phase

ci(x, t )11~T/2 = 0

ci(x, t)II~T/2=C?D}ID}

cj(x, t)II~T/2

cj(x, t )11~T/2 = cJD} II5}

=

0

When the negative current-scanning begins, the N°, and M O' ions will transfer from the organic phase back into the aqueous phase, one after another. This can be expressed as in Fig. 3. We can write the equation for diffusion of ions in the organic phase as

acj(x, t) at

'-:-'-:--- +

ac(x t) ' , at

=

_ a2cj (x, t) _ a2c(x, t) D + D _..:...'-'----'j ax 2 'ax2

(SO)

with initial conditions

t=O

D!

D!

DJ

Df

j + Ci0 =-;c-j( x, t ) +c-i( X, t ) =cj0 =-;I

(Sl)

and boundary conditions

x=O

(S2)

x=

(S3)

00

We solve this equation step by step as we did for the positive current-scanning Interface

W

0

z·

z·

N )(w)

N )(0)

.. i1i=i-v(t-f)1

------~----~

x=o

Fig. 3. Transfer process of ions M z, and N

X

Z}

across the interface at the stage of negative current-scanning.

44

stage. The results can be written as follows: At T/2
(54)

where 7"

J

=

.!

2

2

2

2

t

1

2

i D'Ci (9/16)'p-'zlF'A''1T J J J

At

1-

w ti. of{Jj.O.63T' J

(55)

~ = O.631j', the interfacial potential difference can be written as woRT

RT

Yj

= ti.of{Jj + -F In - + 2 F In Zj "Ij Zj

Dj

-D

j

(56)

Thus, we have

(57)

and

,

RT (-IJ>-(-I» tl:f{J = tl:f{Jj.O.63T' + -F In J , Zj ( - I)"

,

(58)

J

where I T; =

-117"= - ( J

!

02

9/16 ) 'p'ziF'A''1T'DiC' J J J I

2

2

2

,

I

(59)

where 7'. I

,

1 ~3 31T'FA

1

1 0 " j 1] 0 '

0

= (+ ZD1C.) -(Z.D1C.) 4p ) [(ZD1C. J J J J J J I

I

I

(61)

When

Ij = 1j'

t; = Tj + T/

(62) (63)

45

we get 1

,

, , , (37T 2 FA)'( Z,DjC, '0 + z,Dlc; ! 0): t; = 7j + T; = ~

(64)

At t - T/2 = 0.63(t'} + d)l, the interfacial potential difference may be written as RT I

0

Y;

RT I

I.lcp =I.lcp +zF - ny.- +2zF -o ;.0.63,;., 0; AW

AW

I

I

D;

n~

D

I

(65)

I

Thus, we have

AW 1.l 0

CP =

AW

l.l o

CP;.0.63,;.,

+

RT I zF n I

(t;)'l - ( t-

2T)l

(t- 2T)l -(t;)'

(66)

3

and 3

3

( - IJ 2 - ( - I) i AW AW RT I I.lCP-I.lCP + n o 0 ;.0.63,;., zF (_I)l_( -II,)l

(67)

I

I

where II; = -vt; = -v(

T; + T;')

(68)

II; = - vt; = - v7j'

(69)

= t'i + t'l ~

(70)

T' . j.1

3

(

j

3 )

I

EXPERIMENTAL

The instrumentation and electrolytic cell are the same as before [1]. Chemicals

All chemicals were analytical grade except TBATPB presented by the J. Heyrovsky Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences. LiCI was used as the base electrolyte of the aqueous phase and TBATPB was used as the base electrolyte of the organic phase. Twice-distilled water was used to prepare the aqueous electrolyte solutions. All the measurements were made at 20 ± 1°C. RESULTS AND DISCUSSION

Because the standard potential difference of the TEA + ion is less than that of the Cs+ ion, TEA + in the aqueous phase first transfers across the water/nitrobenzene

46 r/ILA

-80

Fig. 4. Influence of change of concentration of TEA + ion on the chronopotentiograms. Water phase: 0.01

M LiCl, 6X10- 4 M CsCl, concentration of TEACl: (1) 0; (2) 2XlO- 4 ; (3) 4X10- 4 ; (4) 6x10- 4 M. Nitrobenzene phase: 0.01 M TBATPB. If = 1 /LA S -1.

interface into the organic phase. Then Cs + in the aqueous phase transfers across the interface into the organic phase at the positive current-scanning stage. At the negative current-scanning stage, Cs + first transfers from the organic phase back into the aqueous phase. Then TEA + transfers back into the aqueous phase. This process is shown in Fig. 1. Experiments varying the concentrations of TEA + and Cs + ions have been made to observe the change of wave heights in chronopotentiograms. Figures 4 and 5 show the influence of concentration on the wave heights. Figure 6a is a plot of the transition time against the concentration of TEA +. It can be seen that the transition time for the transfer of the TEA + ion is directly proportional to the 2/3rd power of the concentration of TEA +. For the ion which transfers first across the interface in a two-component system,

47

lilA

100

80

60

40

20

-20

-40

-60

-80

Fig. 5. Influence of change of concentration of Cs + ion on the chronopotentiograms. Water phase: 0.01 M LiCI, 8 x 10- 4 M TEACI, concentration of CsCI: (1) 2 x 10- 4 ; (2) 4 x 10- 4 ; (3) 6 x 10- 4 ; (4) 8 x 10- 4

M. Nitrobenzene phase: 0.01 M TBATPB.

P

= 1 /LA

S -I.

the transition time is directly proportional to the 2/3rd power of its concentration, but for the ion which transfers second across the interface, the transition time is not directly proportional to the 2/3rd power of its concentration. Figure 6b shows that the total transition time (Ij) for the two ions to the power 3/2 is directly proportional to the concentration of the Cs + ion. IC the standard transfer potentials of two ions which transfer across the interface are similar, they will transfer across the interface at similar potentials and the two corresponding waves on the chronopotentiogram will overlap. According to the discussion of the single component system [1], we know that the potential range for

48

1r

tjjs2 900

800

300,

700

200

600

100

/ o

500

/

I 2

4

6

8

0

4

10 C'TEA+/ M

(a)

I

I 2

(b)

4

6

8 4

1Q CC:/M

Fig. 6. (a) Relationship between the transition time and concentration of TEA +. Water phase: 0.01 M LiCI, concentration of TEACI: variable. Nitrobenzene phase: 0.01 M TBATPB. 11=1 /LA S-I. (b) Relationship between the total transition time, Ii' and concentration of CsC\. Water phase: 0.01 M LiCI, 8 X 10- 4 M TEACI, concentration of CsCI: variable. Nitrobenzene phase: 0.01 M TBATPB. 11=1 /LA S-I.

the wave caused by single ion transfer is relatively wide. The potential range from the potential value corresponding to one-tenth of the wave-height to the potential value corresponding to nine-tenths of the wave-height is about 135 mY. Thus, we can consider approximately that the potential range for a wave of ion transfer is about 135 mY. Therefore if the difference of the standard transfer potentials of two ions is less than 135 mV, we consider that the two waves cannot be separated distinctly. It can be seen from expression (30) for the total transition time of two ions, that if the charge numbers of the two ions are the same and the diffusion coefficients are also the same, i.e. Z; = Zj and D; = Dj , the expression for the total transition time can be written as t·J

!

~

= 'T. + 'T.J = (9/16)'p-'F>A'?T'Zi Di (CO + CO), J I

2

2

2

I

2

1

I

I

I

(71)

Then the total transition time is directly proportional to the sum of the concentrations of the two ions, MZi and NZJ, and therefore we may consider the two ions as a single component and calculate the total transition time from the expression for the transition time of a single component.

49

ACKNOWLEDGEMENTS

Gratitude is expressed to Dr. Guo Du for helpful discussions and for the gift of TBATPB from the J. Heyrovsky Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences. REFERENCES 1 Wang Erkang and Pang Zhicheng, J. Electroanal. Chern., 189 (1985) 1. 2 Wang Erkang and Pang Zhicheng, J. Electroanal. Chern., 189 (1985) 21.