Dynamic surface tensions and dynamic surface potentials of aqueous solutions of a cationic surface active electrolyte

COLLOIDS AND ELS EV IER

Colloids and Surfaces A: Physicochemicaland Engineering Aspects 95 (1995) 281-291

A

SURFACES

Dynamic surface tensions and dynamic surface potentials of aqueous solutions of a cationic surface active electrolyte G. Geeraerts *, P. Joos, F. Vill6 Department of Chemistry, UIA, University of Antwerp, Universiteitsplein I, B-2610 Wilrijk, Belgium Received 20 June 1994; accepted 5 September 1994

Abstract

In this paper, dynamic surface tensions and dynamic surface potentials are compared for an ionic surfactant, myristyl trimethyl ammonium bromide (MTAB). This surfactant is cationic and therefore the potential due to the adsorbed dipoles adds to the double layer contribution. Moreover, for long chain ammonium salts, such as MTAB, the double layer potential can be effectively described by the Gouy-Chapman theory (the Stern potential may be neglected). The results indicate, in agreement with the non-ionics, that a transition exists from diffusion, through mixed, towards transfer controlled adsorption kinetics. Concerning the surface potential measurements again, a dipole relaxation is interfering with the adsorption process. In addition, for some concentrations a relaxation also appears in the double layer.

Keywords: Dynamic surface tension, cationics; Dynamic surface potentials, cationics

1. Introduction In a previous paper [ 1 ] we compared dynamic surface tension and dynamic surface potential data of non-ionic surfactants. Since the surface tension and the surface potential depend on the adsorption of the surfactant, it was expected that both experimental techniques should give the same conclusion with respect to the kinetics of the adsorption process. Indeed, for some systems both techniques yielded comparable results, but for other systems they did not. We explained this by the relaxation of the apparent dipole moments in the surface, In this paper we present results of similar experiments, giving the variation in surface tension and surface potential with time for an ionic surfactant, myristyl trimethyl ammonium bromide (MTAB). * Corresponding author,

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For non-ionic systems, at least at equilibrium, the surface tension and surface potential depend on the adsorbed amount. For ionic systems, however, the potential also depends on the potential in the double layer VDL [2]. Hence, the surface potential V is given by

V= VD-~- VDL where VD is the contribution of the dipoles to the surface potential. Obviously, for non-ionics VDL= O. The potential due to the dipoles is expressed by [2] VD =

#FNA/eeo

where # = the apparent dipole moment, F = the adsorption, NA = Avogadro's number, e = the permittivity of the solution and eo = the permittivity of the vacuum. Following the arguments of other

282

G. Geeraerts et al./Colloids Surfaces A: Physicochem. Eng. Aspects 95 (1995) 281-291

investigators [2] we take e = l. Expressing this equation in the following - - /~ in Debye, F in tool cm-2 and V in volts - - we have

are related through some surface equation of state. For the present system this relation is [5]

VD= 2.27 × 109/tF

F = F ~ a + C~t[1 + (C~/C~)] 1/2

The potential in the double layer is built up by two effects: the contribution due to the Gouy Chapman double layer V~ and the contribution of the Stern layer Vs: VDL= V~ + V~

where F ~ = the saturation adsorption, a = the Langmuir-von Szyskowski coefficient and C~ = the concentration of K + ions added to the systern. Since the K ÷ ion is not surface active, its concentration is uniform over the whole system and equal to the bulk concentration, C~. If the adsorption process is diffusion controlled, the adsorption as a function of time is obtained numerically from Eqs.(1) and (2). When the adsorption is diffusion controlled, the equation of Ward and Tordai can be simplified by restricting ourselves to small times (small time approximation) or to large times (large time approximation). For the small time approximation, the subsurface concentration in the equation of Ward and Tordai is nearly zero, and Eq. (1) approximates to [6]

C~[1 + (CfJC~)] '/2

For anionic surfactants, VD and VDL are opposite in sign; therefore we confined our studies to cationic surfactant systems. Moreover, it was shown [2] from equilibrium measurements that the contribution of the Stern layer may be neglected for cationic surfactants. This is a second argument for the choice of a cationic surface active electrolyte, The purpose of this work is now to compare dynamic surface tensions with dynamic surface potentials,

(3)

F = 2C~ (Ot/g) 1/2

2. Theory Let us signify the cationic surfactant MTAB by RX where R represents the myristyl trimethyl ammonium cation and X is Br-. The adsorption of this component with time is given by the equation of Ward and Tordai [3]: tl/2

f F = 2C~ (Dt/~z) 1/2 -- 2 ( D / x ) 1/2

C ~ ( t - z)dz 1/2

0 (1)

(2)

The relation between the surface pressure H and the adsorption for the present system is given by [5] ( 1 I = - 2 R T F ~ in

~_~) 1-

(4)

Substitution of Eq. (3) into Eq. (4) gives the dependence of the surface tension on time. For large times we notice that C~ is nearly equal to its equilibrium value and can be considered as a constant; hence Eq. (1) approximates to

where t = time, C~ = the bulk concentration of the R + ion, D = its diffusion coefficient, F = its adsorption and C~ = its concentration in the subsurface.

F = 2(Dt/x)l/2(C~ - C~)

As previously argued [4], the contribution due to the electric potential is not considered. The equation of Ward and Tordai, as it stands, is insufficient to predict the adsorption with time, because we have only one equation and two unknown quantities F and C~. Therefore this equation must be supplemented by some other equation. If there is a local equilibrium between the surface and the subsurface, both parameters

- d a = RT(FR d In CR + Fx d In Cx)

(5)

The Gibbs equation is now introduced into Eq. (5): (6)

where a is the surface tension, Ca and Cx are the concentrations of R + and X - ions respectively, and Fa and Fx are the adsorptions of the R + and X - i o n s respectively. Since the surface is electrically neutral, Fa = Fx = F applies. In combination with the condition of electroneutrality in the solution, Cx = CR + C~:,

G. Geeraerts et al./Colloids Surfaces A: Physicochem. Eng. Aspects 95 (1995) 281 291

the Gibbs equation yields ( Cao~ dC R

-da = RTF 1 + CzJ CR

the potential in volts, the contribution of the dipoles is (7)

and this combined with Eq. (5) gives

/ ~7 = Ge .-~- ~[RTF2 Cff \

1

+

C~ ~(n/4Dt)l/2 C~ +C~]

VD =

2.27 × 109/"#

2RT

(8)

where o-e is the equilibrium surface tension and, since we are close to equilibrium, and F is replaced by its equilibrium value F~ and the concentration of the R + ion by its equilibrium concentration C~ [7]. Eq. (8) applied to a solution for a nonionic surfactant differs from that of Hansen [8], only by a numerical factor. For some systems the decrease in surface tension with time is less than that predicted from Eqs. ( 1) and (2), and therefore the condition of local equilibrium between the surface and the subsurface is not met [6,9,10]. Hence the equilibrium equation (Eq. 2) is replaced by a kinetics equation. For non-ionic systems showing ideal surface behaviour, this equilibrium relation is well known: the Langmuir-Hinselwood equation [11]. In general, the requirement is that the kinetic equation must result in the equilibrium equation for t ~ ~ , where dF/dt = O. Recently, we have shown [18] that for the present system this kinetic equation is (9)

where kl and k2 are the rate constants for adsorption and desorption respectively. It is verified that Eq. (9) for dF/dt = 0 results in Eq. (2) with a = kz/k I

(11)

The contribution of the Gouy-Chapman potential is [2,13] Vc =

dF ( /__~)( CI(~ 1/2 F dt -kx 1 C~ 1 + C--~RJ --k2F~

283

(10)

It was found previously [ 10] that the rate constant for adsorption kl depends on the nature of the surfactant, and the desorption rate constant k 2 is nearly independent of the surfactant system and is of the order of magnitude of 10-8-5 x 10 8 mol cm-2 s-1. As already mentioned the dipole moment depends on contributions from the dipoles and from the Gouy Chapman layer, since for these systems the contribution of the Stern layer may be neglected, If we expresss F in mol cm-2, # in Debye and

FF l(8RT~x%e) m f

FIn

V + I_1 +

FF -]1/2~ (8RT-~xxeoe)l/2] j

(12)

where F = Faraday's number. If V is expressed in volts, F i n mol cm -2 and Cx in mol cm -3, Eq. (12) becomes [-2.6 x 108F Vo = 0.0504 In [ C~/2 N/ +

(2.6x10SF,~2] 1+

(13)

C~J ] whence the surface potential is V= 2.27 × 109F# + 0.05041nF 2"6 × 108F [_ C~/2 X/ +

1+

( 2"6-x10sF']2] C~2 j ]

(14)

The following can now be made. (i) The concentration of the X- ions at the subsurface has to be accounted for in Eq.(14), because the thickness of the double layer x-1 is much smaller than the diffusion penetration depth (~D:

~C- 1 ~.~ ( ¢ E o R T / 2 C x F 2 ) I / 2 (~D =

(nDt)~/2

(15)

After 10 .3 s, bt, ~ 10 .4 cm whereas ~c-1 ~ 10 .6 cm or less. (ii) The Gouy-Chapman equation is obtained from the Boltzman distribution law: C + = C ~_exp - (F(b/RT) (16) where C~_ is the undisturbed concentration when the potential ~bbecomes zero. Here C ; is a function of the distance z, and the question arises as to the

G. Geeraertset al./Colloids Surfaces A: Physicochem.Eng. Aspects95 (1995) 281 291

284

implications of this on the Gouy potential. At present this does not matter since, as argued, sub (i) x - 1 >>60 and the concentration profile due to the diffusion process is essentially flat in the scale of the double layer, and C~ can be considered as a constant. (iii) Since the concentration is not uniform, the subsurface is different from the bulk concentration, giving rise to a diffusion potential ~bd. This diffusion potential is obtained as follows. The flux of the R + ion is JR, that of the X ion is Jx and that of the K + ion is JK, where dCR FDR d~b

JR = --DR ~ -z -- CR R T dz

values in Eq.(19)). Since the accuracy of our experiments is within the same accuracy, the effect of the diffusion potential is neglected. In the present treatment the effect of the double layer is neglected during the adsorption process. According to several authors [14], once an ionic surfactant molecule is adsorbed an electric double layer is built up which makes it difficult for the following molecules to enter the surface. In other words, an electrical adsorption barrier is always present and the adsorption kinetics should never be determined by a simple diffusion process. It will follow from our experiments that the effect of this electrical adsorption barrier may be neglected (see Section 4.2.1).

where DR, Dx and DK are the diffusion coefficients for the R, X and K ions respectively. For the flux of K + ions, the diffusion flux is omitted since the concentration of this ion is C~, being constant over the whole system. In view of the electroneutrality conditions:

The basis of all dynamic studies on adsorption is the knowledge of the equilibrium adsorption isotherm. As argued by Lucassen-Reynders et al. [15], dynamic surface properties are much more sensitive to the surface equation of state than equilibrium ones. The reason for this is that for the equilibrium surface tension concentration curve the adsorption F is obtained. However, the dynamic surface properties, i.e. the Gibbs elasticity eo = - F & r / d F and the diffusion relaxation time rD, being for a diffusion controlled adsorption process require a second derivation. At present we

JK + JR = Jx

have

CI~ -11-C R = C X

eo'[~ 2 = RTF2/Co DUe

it follows that

requiring only one derivation to obtain /2. Since the equilibrium surface tensions are well described by the von Szyskowski equation, the adsorptions must be reasonably well expressed by a Langmuir

Jx = -Ox

dCx - C x FDx dd~b z

dCK JK=-DK~-z-CK

(17)

FDK dq~ R T d~

d(~ _ R T D x - DR dCR (18) dz F C R ( D x q- OR) q-- C~(Dx + DK) dz which upon integration between the limits z = 0, CR = C~, ~b= ~bs and z = ~ , CR = C~, ~ = ~bo,yields DK + Dx o R T Dx DR C~ q- DR q- D~ CK ~bd = ~bs- ~bo - F Dx + DR in DK + Dx -

c~ + -

-

DR + Dx

isotherm. Further, as seen from Table 3 the Gouy potential does not depend significantly on the concentration (in the concentration range considered) and the double layer potentials are proportional to it. Hence we believe the estimation of the total potential to be very reasonable.

c~

(19) It is clear that by the addition of a non-surface active electrolyte the diffusion potential is suppressed, but even when no indifferent electrolyte is added to the system this diffusion potential is only a few millivolts (this is verified by putting numerical

3. Experimental Dynamic surface tensions were measured using the oscillating jet and inclined plate techniques as described previously [6,9,16,17]. The time window of the oscillating jet is between 2 and 20 ms, and

G. Geeraertset al./ColloidsSurfaces A: Physicochem. Eng. Aspects 95 (1995) 281-291 t h a t of the inclined plate between 50 ms a n d 2 s. D y n a m i c surface p o t e n t i a l s were m e a s u r e d as d e s c r i b e d p r e v i o u s l y [ 1], the time w i n d o w being between 3 a n d 150 ms. All e x p e r i m e n t s were perf o r m e d at r o o m t e m p e r a t u r e . F o r the ionic surfact a n t we chose M T A B b e c a u s e (i) the c o n t r i b u t i o n s of the dipoles a n d the d o u b l e layer are of the same sign, (ii) the effect of the Stern layer for the d o u b l e layer p o t e n t i a l can be neglected [ 2 ] a n d (iii) it is expected t h a t this c o m p o u n d a d s o r b s in the time range c o r r e s p o n d i n g to t h a t of the surface p o t e n t i a l m e a s u r e m e n t s (and also to the oscillating jet o r inclined plate). E q u i l i b r i u m surface tensions were m e a s u r e d b y the W i l h e l m y plate technique using a C a h n electrobalance. T h e results are well described by the von S z y s k o w s k i e q u a t i o n [ 5 ] :

[ C~(1+(C~/C~)) 1/2] 17 = 2 R T F °~ In 1 +

285

Table 1 Equilibrium surface potentials (plateau values) and resulting apparent equilibrium dipole moments (#e) C~,TA~ (mol cm -3)

CKB~ V (mol cm -3) (V)

2 x 10 .6 10.6 7 x 10.7 5 x 10 -v 1.95 x 10_6 10-~ 1.56 x 10 -6 10 -6

~lmNm-'l 75

70 ~

(20)

i

0.470 0.452 0.440 0.395 0.460 0.440

i

F (mol cm-2)

VG (V)

~o (D)

2.37 x 2,06x 1.85 x 1.63 x 2.37 x 2.37 x

0.225 0.236 0.239 0.241 0.225 0.219

0"455 0.462 0.479 0.416 0.437 0.411

i

10-l° 10-1° 10 -l° 10 -1° 10-w 10-l°

i

"

• --m

a

It s h o u l d be r e m e m b e r e d t h a t the validity of this e q u a t i o n also requires the validity of Eqs. (2) a n d (4). The following p a r a m e t e r s are obtained: F °~ = 2.8 x 10 -x° m o l cm -2, a = 3.6 x 10 -7 m o l cm -3.

4. Results and discussion

4,1. Equilibrium surface potentials If we l o o k at the d y n a m i c surface potentials, we see t h a t at high c o n c e n t r a t i o n s a n e a r - s a t u r a t i o n value is reached for l o n g times. We expect these p l a t e a u values to c o r r e s p o n d with the e q u i l i b r i u m values. U s i n g the e q u i l i b r i u m a d s o r p t i o n from Eq. (2) a n d calculating the G o u y p o t e n t i a l using E q . ( 1 3 ) we can calculate the a p p a r e n t d i p o l e m o m e n t s at equilibrium. T h e results are given in Table 1. T h e m e a n value (/~e) = 0.443 D, which c o r r e s p o n d s very well with the result given by Davies a n d Rideal [-2] for alkyl t r i m e t h y l a m m o n i u m b r o m i d e (p~ = 0.45 D). T h e l a t t e r value will be used in subsequent calculations,

4.2. MTAB without KBr 4.2.1. Dynamic surface tensions D y n a m i c surface tensions of M T A B solutions at different c o n c e n t r a t i o n s are given in Figs. 1-3. T h e

i

-,2J

65

,

0,050

,

qlo0

,

0,150

,

0,200

,

0250 r(s)

Fig. 1. The dynamic surface tension a as a function of time for an aqueous MTAB solution at different concentrations. The symbol • refers to inclined plate data, whereas the symbols ©, x, [] represent oscillating jet data. Curve 1: CO= 10-~ mol cm-3; the solid line is calculated by Eqs.(1) and (2) (exact fit), and the broken line represents the theoretical line calculated according to the Sutherland equation with rD= 0.045 s (diffusion controlled kinetics). Curve 2: Co= 2 x 10 7 tool cm a; the solid line is calculated using Eqs. (1) and (2), and the broken line is calculated numerically from Eqs.(1) and (9) with k2=10-Smolcm-2s i (mixed controlled

kinetics).

results for the lowest c o n c e n t r a t i o n s (C~ = 1 0 - 7 tool cm -3) are well described by the S u t h e r l a n d equation [17]: t a = ae + da o exp - - erfc(t/ZD) 1/2 (21) rD where d a o = the initial j u m p in surface tension = ao - ae (ae being the surface tension of the solvent: a o = 7 2 . 5 m N m -1) a n d z D = t h e diffusion relaxa t i o n time. The S u t h e r l a n d e q u a t i o n is, in fact, an a p p r o x i m a t i o n to the W a r d a n d T o r d a i e q u a t i o n for a diffusion c o n t r o l l e d process when the initial j u m p in surface tension is small. The diffusion r e l a x a t i o n time ZD = 4.5 X 10 -2 S a n d c o r r e s p o n d s very well to the value o b t a i n e d from the surface

G. Geeraerts et al./Colloids Surfaces A." Physicochem. Eng. Aspects 95 (1995) 281-291

286

~lmNm'l

__ '--'

'

~

__ 1 ]

'

70

6c ~ !i so

~

~

................. OOSO

:. . . . . . . . . . . . . . . . . . . . , 0150

O.'rlO0

~ 0200

r _ 0250 f{s)

Fig. 2. The dynamic surface tension a as a function of time

for an aqueous MTAB solution at concentration Co= 2 × 10 6mol cm 3. The symbols ×, • , [] represent the oscillating jet data, and the symbol © displays the inclined plate data. The broken line is drawn using Eqs. (4) and (9) with k = 177 s L (transfer controlled kinetics), and the solid line is calculated according to a mixed model [Eqs. (1) and (9)] with k2 = 1.5 × 10 8 tool cm -2 s 1 (mixed controlled kinetics).

.

oCmNm-'l

.

.

.

.

(24)

where

(25)

Substitution of Eq. (24) into Eq. (4) gives the surface tension as a function of time: •

6s ]

I

a050

0,100

~

0,1s0

C

a=ao+2RTF°~lnIl-~G(1-exp(--kt))] I

o,2o0

Fig. 3. The dynamic surface tension a as a function of time 3 x 10 7 mol cm -3. The symbols (3, x, [], A represent the oscillating jet data, and the symbol • displays the inclined plate data. The solid line is calculated according to mixed controlled adsorption kinetics using Eqs. (1) and (9) with k 2 = 10 8 m o l c m - 2 s 1. The broken line refers to diffusion controlled adsorption kinetics with D = 5 x 10-6cm2s -1, calculated from Eqs. (1) and (2).

equation of state using a diffusion coefficient D = 5 X 10 - 6 cm 2 s - l :

1 (dF~ 2

-CD=~\dC//

(22)

where dF/dC is obtained from Eq. (2): F~ -

1 (

a

C)2

(26)

I

0,2s0

for an aqueous MTAB solution at concentration Co =

dC

giving F = F~(1 - e x p ~-kt))

k = kl C~ + k2/F ~ = Fo o 1 +

70

dF

centration C~ = 2 x 10 -v mol cm -3 corresponds to a diffusion controlled process using Eqs. (1) and (2). The data for the higher concentrations (C~ = 3 x 10 - 7 , 5 × 10 -7, 7 × 10 -7 and 10 - 6 m o l c m -3) are described for mixed adsorption kinetics using Eqs.(1) and (9) with a diffusion c o e f f i c i e n t D = 5 x 10 - 6 c m 2 s i, k 2 = 10 -8 m o l cm 2 s - 1 and k I =kz/a=2.78 x 1 0 - 2 s -1. The highest concentrations (2 X 10 - 6 and 4 × 10 - 6 mol cm -3) are compatible with a transfer controlled process. Here diffusion equilibrium between bulk and subsurface is established and Eq.(9) (with C ~ = C~ and C~ = 0 ) i s integrated,

(23)

1+

giving a value of zo = 4.54 x 10 2 s. The next con-

The

results

are

described

with

F~ = 2.37 x

10- lo mol cm -z (obtained from Eq. (2)) and a value of k = 177 s -1. Using Eq.(25) this corresponds to a desorption rate coefficient of k2 = 7.5 x 10 - 9 m o l c m - 2 s -1.

This system of MTAB, in c o m p a r i s o n with the alcohols, demonstrates a nice transition of pure diffusion controlled adsorption kinetics for the l o w e s t concentrations, through mixed adsorption kinetics, to a transfer controlled adsorption process for the highest concentrations. This behaviour is in agreement with the results obtained for other systems [10]. Also, the desorption rate constant is of the same order as found previously (k2 ~ 1 0 - 8 - 5 × 10 -8 mol cm -2 s a) [9,10]. We k n o w that initially the transfer step dominates the adsorption process, and as time increases the diffusion step becomes m o r e important. Therefore we have plotted the dynamic surface tension as a function of t - ~/2 (long time a p p r o x i m a tion) according to Eq. (8) (with C~ = 0). The results are shown in Fig. 4 and from the slope we obtain

G. Geeraerts et al./Colloids Surfaces A." Physicochem. Eng. Aspects 95 (1995) 281-291

~mNm,~ - -

I

r

q

r

70 6s

~

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

60 I

I

2

I

~

~ t-,,21s,~l

Fig. 4. T h e d y n a m i c surface t e n s i o n cr p l o t t e d as a f u n c t i o n of the inverse s q u a r e r o o t o f t i m e t -t/2 for a n a q u e o u s M T A B s o l u t i o n at c o n c e n t r a t i o n Co = 3 × 10 -7 m o l c m -3. T h e solid

line

is c a l c u l a t e d

according

to

Eq. (8)

(long

time

approximation), theadsorption(usingD=5 × 10-6cmZs-1)which must be compared with that obtained from Eq. (2). The results are given in Table 2. For the lowest concentration there is good agreement between both sets of data; for the highest concentrations the data from the dynamic experiments are systematically higher than those corresponding to the Langmuir data (expressed by F/F2),indicating that the transfer process is still of some importance even at these long times, If an electrical adsorption barrier is important, the effect should be most evident for the system without an indifferent electrolyte. As already mentioned, the adsorption kinetics are diffusion controlled at the lowest concentrations (C = 10 -7 and C = 2 x 1 0 - 7 tool cm-3). This means that the effect of the electrical adsorption barrier is of minor importance and may be neglected since, as will Table 2 A d s o r p t i o n s F f r o m t h e l o n g t i m e a p p r o x i m a t i o n u s i n g Eq. (8), c o m p a r e d w i t h t h o s e o b t a i n e d f r o m the L a n g m u i r e q u a t i o n (Fc) CMTAB (molcm 10 2 3 5 7 10 2

3)

7 x 10 7 x 10 7 x 10 -7 x 10 7 6 x 10 - 6

da/dt 1/2

F

FL

(mNm-ls~/2)

(molcm-2)

(molcm-2)

0.725 1.05 1.075 1.22 1.12 1.17 0.70

0.61 1.03 1.28 1.75 1.99 2.44 2.66

x x x x x x x

10 - 1 ° 0.61 x 10 lo 10 -1° 1.00 x 10 - 1 ° 10 lo 1.27 x 10 -1° 10 - 1 ° 1.63 x 10 lo 10 -1° 1.85 x 10 -1° 10 - 1 ° 2.06 x 10 1o 10 lO 2.37 x 10 - 1 °

287

become apparent, this effect must be present even at such low concentrations. At higher concentrations the adsorption kinetics are due to diffusion with a barrier, and finally at the highest ones ( C = 2 x 1 0 - 6 and 4 × 10 6 mol cm -3) we have only barrier controlled kinetics. The nature of this barrier is due to the hydrophobic effect as argued previously [ 10] and not to an electric barrier. In Table 3 we have calculated the double layer potential and the double layer thickness as a function of the concentration. It follows that the double layer potential d o e s n o t depend much o n the concentration; hence it is difficult t o s e e why the electrical adsorption barrier should be operative at a concentration of C = 4 × 1 0 - 6 tool cm -3 and not at the lowest one ( C = 10-7 m o l c m - 3 ) . From this Table it is seen that the double layer thickness decreases with increasing concentration; hence if the electrical adsorption barrier should be due to the double layer thickness it should be more operative at the lowest concentration and less so at the highest one. The reverse is found experimentally. From this we can conclude that the adsorption barrier is not of an electrical nature, but merely due to the hydrophobic effect as argued previously [ 10]. Some theoretical evidence about the non-occurrence of this electrical adsorption barrier was given previously [4] where the electrodiffusion equations are considered. It is found that the effect of the double layer may be neglected if the diffusion penetration depth 6, given by 6 = x/HDt is much larger than the double layer thickness. For the

Table 3 E q u i l i b r i u m d o u b l e l a y e r p o t e n t i a l ~b~ a n d d o u b l e l a y e r t h i c k n e s s ~c 1 as a f u n c t i o n of the c o n c e n t r a t i o n for the s y s t e m MTAB without KBr

F / FL

CMTAB (mol c m s)

~b~ (V)

K-1 (cm)

1 1.03 1.01 1.07 1.08 1.18 1.12

10 -7 2 x 3 x 5 x 7 x 10 - 6 2 x 4 x

0.232 0.240 0.242 0.241 0.239 0.236 0.225 0.212

307.7 217.6 177.6 137.6 116.3 97.3 68.8 48.7

10 _7 10 _7 10 _7 10 -7 10 -6 10 - 6

x x x x x x x x

10 8 10 8 10 -8 10 -8 10 -8 10 -8 10 8 10 -8

G. Geeraertset al./ColloidsSurfaces' A: Physicochem.Eng. Aspects 95 (1995) 281-291

288

present experiments the smallest time is 10 -3 s, giving 5 = 1.25 × 10 -4 cm, always being much higher than the double layer thickness as seen from Table 3.

4.2.2. Dynamic surface potentials We can describe the dynamic surface tensions using Eq. (1), and Eqs. (2), (9) or (26), with Eq. (4), depending on whether the adsorption process is diffusion controlled, we have mixed adsorption kinetics or the process is transfer controlled. The computer results give us the adsorptions and the subsurface concentrations as a function of time. With these data we can calculate the surface potential with time using Eq. (13) (here Cx = C]), and these data are compared with the experimental dynamic surface potentials. The results are given in Fig. 5. It is seen that for the lower concentrations the calculated dynamic surface potentials are considerably higher than the experimental ones. For a concentration of 7 x 10 .7 mol cm -3 both results are comparable, whereas for the highest concentrations the experimental data are higher than the calculated ones especially for short times, and this behaviour is similar to that observed for non-ionic

(vott-0250 ~ / _--

.___,__,_L---v=~,%p ~

'

.........

surfactants [1]. ation process is the experimental ones at lower question.

It is likely that the dipole relaxoperating here. The reason why data are lower than the calculated concentrations is still an open

4.3. M T A B with KBr Here we performed measurements with MTAB solutions where KBr is added to the system. Solutions were prepared so that for all the systems the equilibrium adsorption remains the same. In view of Eq.(2) this means that C~ (1 + C~/C~ )1/2 = constant = 2 x 1 0 - 6 mol cm -3, corresponding to an equilibrium surface tension ae =46.3 m N m -1.

4.3.1. Dynamic surfact tensions o f M T A B + KBr Results for the dynamic surface tensions are given in Figs. 6 and 7. The dynamic surface tensions of the lowest concentrations are diffusion controlled. For the low concentrations (C~ = 4 x 10 .8 mol cm -3, CI~ = 10 -4 mol cm-3), the data can also be analyzed using the short time approximation. The results are given in Fig. 8, and from the slope we can obtain the diffusion coefficient D = 13.4x 1 0 - 6 c m 2 s -1, a value which is somewhat too high. Previously [16], analyzing a similar system for the short time approximation we

q)G

0200

o x~X

,

°x ×

V

~

,

,

~voIt)

o:~x~

/5x O.t,OC

0150

oX ox x

0100

~

o

k'°×

0.30C

x&

f

J 0050

0.200L/"

~Oip

.........

I 0,100

Fig. 5. The d y n a m i c surface p o t e n t i a l

I 0150 t(s) l/plotted

as a f u n c t i o n

of time for concentration Co = 10-7 mol cm -3. The symbols @, x represent two different runs. The solid line represents the theoretical line calculated according to Eq. (14). The broken lines represent the different contributions ~bd and @c.

-

x

~ _ _ V=LPdip+q) 6

................

0050

i × ×

~P6

~Pdip

..'~ .......

0,100

I

50

I

100

I

150 f(msl

Fig. 6. As Fig. 5, but for concentration Co = 7 x mol cm 3.

10 -7

G. Geeraerts et al./Colloids Surfaces A. Physicochem. Eng. Aspects 95 (1995) 281-291

v (volt± ' o~o~>e_~ . . . . .

Again we have a transition from diffusion controlled, through mixed, towards transfer controlled kinetics. In Fig. 9 we presented the long time approximation and from the slopes the adsorption is obtained. These adsorptions are compared with that according to the Langmuir equation (FL = 2.37 x 10-xo mol cm -2) giving excellent agreement (see Table 4).

' v=%+%,p

/

0400 0300

0.200 "

/f

-........

%*

4.3.2. D y n a m i c surface p o t e n t i a l s

Following the same procedure as outlined in Section 4.2.2 we calculated the dynamic surface potential (here C ) = C ~ + C~), and these values are compared with the experimental results (see

//

/'

0100-/ I 50

I 100

I 150 t(ms)

(~(rnNm I)

Fig. 7. As Fig. 5, but for c o n c e n t r a t i o n Co = 10 -6 tool c m -3.

°-(mNm~

289

,

---

,

i

,

,

I

I

I

I

0,050

0,100

0,150

i

70

l

60

•

50

(

o,05o

i 0300

, 0,150

. 0,200

fts)

Fig. 8. The d y n a m i c surface tension cr as a function of time for a m i x t u r e of M T A B a n d indifferent electrolyte K B r at different concentrations. The symbols x , O represent the oscillating jet data, a n d the s y m b o l • displays the inclined plate data. C u r v e 1: C~ = 4 x 10 - s m o l cm -3 and C~ = 10 4 tool cm a. Curve 2: C~=8x10 8 m o l c m -3 and C~=5x 10 5 tool cm -3. C u r v e 3: C~ = 2 x 10 . 7 tool cm -3 a n d C~ = 1.98 x 10 5 m o l c m 3. C u r v e 4: C ~ = 3 . 8 5 x 1 0 - T m o l c m -a a n d C~ = 10 .5 mol cm 3. The solid line is c a l c u l a t e d by Eqs. (1) a n d (2) using a diffusion coefficient D = 5 x 10 -6 mol cm -3.

obtained a coefficient.

similar

result

for

the

diffusion

For the higher concentrations, i.e. C~ = 1.56 x 10 -5 mol c m - 3 , C~: = 1 0 . 6 m o l c m - 3 and C~ = 1.95 x 1 0 - 6 mol c m - 3 , C ~ = 1 0 - 7 mol c m - 3 , w e have mixed adsorption kinetics ( k 2 = 2 x 10 -8 m o l c m - Z s - X ) . Finally, for the system without KBr (C~ = 2 x 1 0 - 6 mol c m - 3 ) , as already discussed, we have transfer controlled kinetics.

I

0,200

0,250 ils)

Fig. 9. The d y n a m i c surface tension a p l o t t e d as a f u n c t i o n of time for a m i x t u r e of M T A B and indifferent electrolyte K B r at c o n c e n t r a t i o n C~ = 1.56 x 10 -6 mol cm -3 a n d C~ = 10 -6

tool cm 3. The symbols ©, x , [] illustrate the oscillating jet data, a n d the s y m b o l • represent the inclined p l a t e data. The solid line depicts m i x e d c o n t r o l l e d a d s o r p t i o n kinetics using Eqs. (1) a n d (9) with k 2 = 2 x 10 - s mol cm -2 s 1. The b r o k e n line is c a l c u l a t e d a c c o r d i n g to diffusion c o n t r o l l e d kinetics using Eqs. (1) and (2) with a diffusion coeffÉcient D = 5 x 1 0 6 c m 2 s 1.

Table 4 M T A B + KBr: a d s o r p t i o n s from the d y n a m i c surface tensions using Eq. (8)

c~

c~,

(mol cm -3)

(mol cm -3)

da/dt- ~/2 ( m N m 1 sl/2)

4 x 10 8

10-4

8x

10 8

2 x 10 -7

F (tool cm -2)

13.95

2.33 x 10 - l °

5 x 10 -5

6.72

2.33 x 10 -1°

1.98 x 10 -5

2.75

2.35 x 10 lo

3 . 8 5 x 1 0 -7

10 -5

1.45

2 . 3 4 x 1 0 -x°

1.56x10 6 1.95 x 10 -6 2 x 10 -6

10 6 10 -7 0

0.575

2.38x10 -x°

0.688 0.70

2.36 x 10 1o 2.66 x 10 lo

G. Geeraerts et al./Colloids Surfaces A." Physicochem. Eng. Aspects 95 (1995) 281-291

290

Ol ort eower o n c e t t o n there is agreement between the experimental and calculated data, for the next concentrations the experimental data are lower than the calculated ones, whereas for the highest concentrations the experimental data are higher than the calculated ones, especially at low times. This behaviour is in agreement with that found in Section 4.2.2, except that for the lowest concentrations agreement is achieved. At these low concentrations the adsorption rate is slow, and the relaxation of the dipoles F'(mo[

cm 2 )

,

,

,

............ o4o0

,5, ~"

o~oo~ L ~ *

~

~

i/~ //~ ~ ~ ~ 0~/~///~ ~ II/~lt~/°°~ ~ , 2 , ]~g¢ ~ . ~. . ~ S~ °

oioo~ ~

- -

210-~ °

o o o °

o o

151040

o

50

oO

110~

0510~

°

~

i

05

~

100

150 Urns

o

l

~5 ~ ( s '~z)

Fig. 10. The dynamic adsorption F is plotted as a function of the square root of time d/2 for a mixture of MTAB and indifferent electrolyte KBr at the respective concentrations C~=4xl0-Smolcm -3 and C~.=10 4 m o l c m - 3 . The solid line is drawn according to Eq. (3) using a diffusion coefficient D = 13.4 cm 2 s -~ (short time approximation).

Fig. 12. The dynamic surface potential V plotted as a function of time for a mixture of MTAB and indifferent electrolyte KBr at different concentrations. The symbols © and x represent two different runs. Curve 1: C ~ = 4 x l 0 - S m o l c m -3 and C~ = 10 -4 mol cm 3; the solid line represents the theoretical line calculated by Eq.(14) with # = 0 . 4 5 D and a diffusion controlled adsorption. Curve 2: C~ = 8 x 10 -8 mol cm 3 with C~: = 5 x 10 -s mol cm-3; the solid line is calculated according to Eq. (14) with IL = 0.45 D and a diffusion controlled adsorption. Curve 3: C ~ = 2 x l 0 - V m o l c m -3 and C ~ = 1 . 9 8 x 10 5 mol cm 3; the solid line depicts the theoretical line calculated,according to Eq.(14) with / t = 0 . 4 5 D and a diffusion controlled adsorption. Curve 4: C~ = 3.85 × 10 7 mol cm 3 with C~ = 10 -5 mol cm 3; the solid line is plotted according to Eq. (14) with ~ = 0.45 D and a diffusion controlled adsorption. Curve 5: C ~ = l . 9 5 x 1 0 - 6 m o l c m 3 and CI~= 10 ~ m o l c m 3; the solid line represents the theoretical line calculated according to Eq. (14) with/z = 0.45 D and a mixed controlled adsorption.

~mNm I ) d

~

,

i

i

and relaxation in the double layer must be fast in order that they do not interfere. Again, the type of relaxation in the double layer is unknown.

6~ ~

5.

Conclusion

tic

1'

2'

3'

-

'

~-

fW(s 'vz )

Fig. 11. The dynamic surface tension a as a function of the inverse square root of time (t ,/2) for a mixture of MTAB + KBr at concentration C ~ = 2 x l 0 7 m o l c m 3 and C ~ = 1 . 9 8 × 1 0 - S m o l c m -3 (©, inclined plate data). The solid line is plotted to Eq. (8) (long time approximation),

(i) Dynamic surface tensions of the MTAB system with or without KBr are well understood. For the lowest concentrations the adsorption process is diffusion controlled, for intermediate ones w e have mixed adsorption kinetics, and for high concentrations the adsorption process is merely ruled by the transfer process. This behaviour is in agreement with our previous results [ 10].

G. Geeraerts et al./Colloids Surfaces A." Physicochem. Eng. Aspects 95 (1995) 281-291

(ii) Dynamic surface potentials are in general agreement with predicted ones. For the highest concentrations the experimental results are higher than the predicted ones, especially at small adsorption times. For higher times equilibrium values are obtained which are in good agreement with the results of Davies and Rideal [2]. This behaviour for the highest concentrations is in agreement with the dipole relaxation process observed for nonionic surfactants. For lower concentrations, the calculated surface potentials are higher than the experimental ones. It seems unlikely this could be due to dipole relaxation (therefore we should

expect the experimental data to be above the calculated curve); the reason for this is probably a relaxation in the double layer itself. The identity of this relaxation is still an open question. For the system MTAB + KBr at very low concentrations of MTAB, the experimental dynamic surface potenrials are in agreement with the calculated ones. Obviously the adsorption process is so slow that dipole relaxation and relaxation in the double layer do not interfere.

References El] G. Geeraerts, P. Joos and F. Viii6, Colloids and Surfaces, 75 (1993) 243-256. [2] J. Davies and E.K. Rideal, Interfacial Phenomena, Academic Press, London, 1963.

291

[3] A.F.G. Ward and L. Tordai, J. Chem. Phys., 14 (1946) 453. [4] P. Joos, J. Van Hunsel and G. Bleys, J. Phys. Chem., 90 (1986) 3386. [53 E.H. Lucassen-Reynders, J. Phys. Chem., 70 (1966) 1777. [6] R. Delay and G. P6tr6, Surf. Colloid Sci., 3 (1871) 27. [7] G. Serrien and P. Joos, J. Colloid Interface Sci., 127 (1989) 97. [8] R.S. Hansen, J. Phys. Chem., 64 (1960) 637; J. Colloid Sci., 16 (1961) 549. [9] P. Joos, G. Bleys and G. P6tr6, J. Chim. Phys., 79 (1982) 387. [10] G. Bleys and P. Joos, J. Phys. Chem., 89 (1985) 1027. [11] C.H. Chang and E.I. Franses, Colloids and Surfaces, 69 (1992) 189-201. [12] P. Delahay, Double Layer and Electrode Kinetics, WileyInterscience, New York, 1966. [13] R. Defay and J. Hommelen, J. Colloid Sci., 13 (1958) 553; J. Colloid Sci., 14 (1959) 401-411. [14] R.P. Borwankar and D.T. Wasan, Chem. Eng. Sci., 38 (1983) 1027. S.S. Dukhin, R. Miller and G. Kretzschmar, Colloid Polym. Sci, 261 (1983) 335. V.B. Fainerman, KolL Zh., 36 (1974) 1112 (in Russian). v.B. Fainerman, Koll. Zh., 40 (1978) 924 (in Russian). s.s. Dukhin, Ju.M. Glasman and V.N. Michailovskij, Koll. Zh., 35 (1973) 1013 (in Russian). Ju.M. Glasman, V.N. Michailovskij and S.S. Dukhin, Koll. Zh., 36 (1976) 226 (in Russian). V.N. Michailovskij, S.S. Dukhin and Ju.M. Glasman, Koll. Zh., 36 (1974) 579 (in Russian). S.S. Dukhin, E.S. Malkin and V.N. Michailovskij, Koll. Zh., 38 (1976) 37. [ 15 ] E.H. Lucassen-Reynders, J. Lucassen, P. Garreth, D. Giles and F. Hollway, Adv. Chem. Sci., 144 (1975) 2726. [16] R. Van den Bogaert and P. Joos, J. Phys. Chem., 83 (1979) 2244. [17] K. Sutherland, Aust. J. Sci. Res., A5 11952) 683. [ 18] P. Joos, J. Colloid Interface Sci, in press.