COLLOIDS A AND

Colloids and Surfaces SURFACES ELSEVIER A: Physicochemical and Engineering Aspects 131 ( 19981 95 107

Low frequency dielectric dispersion in ethylcellulose latex. Effect of pH and ionic strength

A.V. Delgado a, F. Gonzfilez-Caballero a . , F.J. Arroyo a F. Carrique b S.S. Dukhin c I.A. Razilov ~

~ Department of Applied Physics, Faculty o/'Science, University of Granada, 18071 Granada, Spain b Department ~fApplied Physics, Faculty of Science, University qfMc'daga, 29071 Mfilaga, Spain

c Dumanskii hlstitute of Colloid and Water Chemistry. Ukrainian National ,4 cadem v ~?/Sciences, Pr. l~'rnadskogo 42. Kiev 252680, Ukraine

Received 13 June 1996: accepted 23 February 1997

Abstract

The study of the conductivity and dielectric response of colloidal suspensions in a.c. electric fields is an excellent probe of the particle double layer characteristics. In fact, the strong dielectric dispersion shown by such systems for frequencies of the field < 1 MHz, is intimately related to the polarization mechanisms of both the diffuse and internal parts of the electric double layer. In this work we present experimental determinations of the dielectric constant of latexes of spherical ethylcellulose particles (commercially available as Aquacoat R:). The effect of both the ionic strength 110 -4 10 3 M KC1) and pH (at constant KC1 concentration} is considered. It was found that the dielectric constant of the suspensions decreases with frequency, tending to the pure solution value for lYequencies ca 250 kHz. The increase in ionic strength gives rise to higher dielectric constants at any frequency: similar conclusions are valid for increased pH values of 5 8. The absolute value of the contribution of the dispersed phase to the dielectric permittivity was lbund to be very high. It exceeds several times the values predicted by theories developed for non- conducting particles even if very high surface charge density is assumed. It is proposed in this paper that this fact can be ascribed to the influence of adsorption oscillations of additional hydrogen counterions reversibly adsorbed in the Stern layer. ~c~> 1998 Elsevier Science B.V.

Keywor&v Ethylcellulose latex: Low frequency dielectric dispersion: Mutual enhancement of adsorption oscillations of ordinary and additional counterions

1. Introduction

When an alternating electric field, E = Eo exp (i~ot), is applied to a colloidal suspension, the polarizat ion generated in the different parts o f the electrical double layer ( E D L ) is in general out of phase with respect to the applied field. This

* Corresponding author. Fax: + 7 34-58-243214: e-mail: fgonzale@goliat.ugr.es

0927-7757/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII SII927-7757(97)00077-(I

phase difference results, in the frequency domain. in a frequency dependence o f both the real and imaginary parts o f the complex dielectric constant o f the suspension:

e* = e ~ - i e ' r' ( l l

All quantities in Eq. ( 1 ) depend on the frequency (,) of the applied field. It is interesting that the (o- dependence o f e* (that is, the characteristics of

96 A. I~ Delgado et al. / Colloids Surjaces A: Ph.vsicochem. Eng. Aspects 131 (1998) 95-107

the low frequency dielectric dispersion, or LFDD) of the system is intimately related to the properties of particles: size, shape, conductivity; to those of the medium: concentrations, valencies and mobili- ties of the ions present: and, most important, to the properties of the interface. The fact that LFDD is very sensitive to the surface characteristics is the reason for the increasing interest in this method of investigation.

In this work, our contribution deals with experimental measurements and theoretical inter- pretation of dielectric dispersion in suspensions of ethylcellulose latex (commercially available Aquacoat@ sample manufactured by the FMC Corp., Philadelphia, PA., U.S.A.) with different volume fractions, electrolyte concentrations and pH values. The surface properties of this latex have been described elsewhere [1].

A linear dependence will be assumed between the complex conductivity, K*, of the dilute suspen- sion, and its volume fraction, ~:

K*(~o) = K* (o~) + ~bAK*(~o) (2)

where K*(o~) is the complex conductivity of the electrolyte

K*(co) = K ~ +i~eoGa (3)

and ~AK*(o~)is the contribution of the particles to K*. In Eq. (3), K °~ is the d.c. conductivity of the electrolyte, eo is the permittivity of vacuum, and £rd is the dielectric constant of the solution. In terms of the complex dielectric constant of the suspension, one can write:

K*(c~) = K(~o) + ~oeoe~'(o~) + iCOeoe~(~o) (4)

where we have shown that K(~o) is in fact indepen- dent of m and has the meaning of d.c. conductivity of the suspension. The linearity between K* and ~b implies:

C r((O) = ~'rd + ~bA£ 'r(O~) ( 5 )

e~'=~bAe~' (6)

We will focus on the frequency dependence of e'r(e~), e~'(~) and the dielectric increments Ae~((o) and Ae"(co). Experimental data will be compared with predictions based on different theoretical models of LFDD.

There exist various theoretical approaches to the calculation of LFDD. These differ from one another mainly in: • the assumptions concerning the role played by

the polarization of different EDL parts: diffuse layer dominant polarization [2-7], Stern layer dominating mechanism [8,9] or comparable polarization of both EDL parts [10-15];

• the assumptions concerning the conditions of ion exchange between the diffuse and Stern layers: free exchange [11-14]; very hampered exchange [8-10];

• the restrictions imposed on numerical parameter values, among other aspects.

However, all the variety of theoretical models possess one common feature: the correct solution of the EDL polarization problem leads to the conclusion that for non-conducting particles dis- persed in a binary electrolyte solution, there is a limiting value of the dielectric increment, (AG) . . . . which corresponds to Ae~ when the surface charge ar approaches infinity. An approximate expression for this limiting value, valid for ~'a >> 1 is [2,3,10,11,15-17]:

Aer(~O ) < A£r(0) < (Aer)ma x

= (AG(0)) . . . . < 9 Gd(~a)2 (7)

Here Aer(0)=AG(o)-*0), K is the reciprocal EDL thickness, a is the particle radius. Grosse and Foster [16] obtained another expression for the maximum dielectric increment, assuming that only ions in the inner part of the double layer contribute to the polarization of the system, and neglecting any effect of the diffuse layer. Their expression for (Ae'r) . . . . considering also an infinite surface charge density is valid for any value of ~:a

( ) ( ' ) (Ae~)ma×= Aer(0 ) <9Gd(Ka)2 1 + _ _~f_ ~ 1 + ~'a

(8)

Finally, the theory developed by DeLacey and White [5], although yields only numerical results, can be used to predict approximate values of the

,4. I ~ De&a&~ et al. / Colloids Surfaces A: Physicochem. Eng. Aspects 131 1998) 95 107 97

maximum dielectric increment by setting the potential of the particles to a very high value.

In a number of cases, however, the inequalities [Eqs. (7) and (8)], as well as the predictions of Ref. [5] have been shown to be violated [18-23]. It will be demonstrated below that the dielectric increment of the suspension studied here also exceeds any estimation of (A£~)ma x significantly. Possible reasons for this fact will be considered in Section 4 below.

2. Experimental

The polymer dispersion used, Aquacoat~R, is a registered trade mark of FMC Corp., U.S.A., and was kindly supplied by Foret, U.S.A., Barcelona, Spain. In order to enhance the stability of the latex, the commercial formulation contains ca 1.3% sodium dodecyl sulphate (SDS) and 2.5% cetyl alcohol. A through characterization of the surface electric properties of the latex was carried out in Ref. [1 ].

It appeared necessary to better control the com- position of the dispersion medium of the latex by cleaning it and reducing it to a minimum its surfactant concentration. Hence the latex was repeatedly centrifuged at 27 000g (Kont ron T-124 high-speed centrifuge, Kontron Instruments, Milan, Italy) and redispersed in Milli-Q water. After this cleaning process, the surface charge was obtained by conductimetric titration; it was found that the polymer contains both strong and weak acid groups, with 2.2 ItC cm -2 corresponding to the former, and 5.9 ItC cm -2 to the latter. The origin of the strong groups is the polar (sulphate) heads of the SDS molecules remaining on the latex surface after the cleaning process described. Acid groups are likely carboxylic, as demonstrated by IR spectra of the desiccated polymer. The particle size of Aquacoat:R, was determined both from transmission electron microscopy pictures and by means of photon correlation spectroscopy (Malvern PCS 4700, Malvern Instruments, Malvern, U.K.). Fig. 1 shows the results: from the parameters of the logarithmic distribution the number average particle diameter can be estimated to be d = 110 _-4- 20 nm.

The suspensions to be analysed were prepared by serum replacement of the water with KC1

25

20

,--~ 15

o ¢ -

©

10

\

/ 100

dmTEM=94nm %:0,28

drnPCS=105nm %=0,50

0 0 400

[ [--7~ TEM ] Pcs I

U1,- ~ i , - ] - q , 200 300

diameter (nm)

Fig. 1. Diameter distribution of Aquacoatl{ particles, as obtained from transmission electron microscopy (TEM) pictures and photon correlation spectroscopy q PCS ).

solutions of the desired ionic strength in a stirred filtration cell: the process was continued for several days until the conductivity of the filtrate was equal to that of the KC1 solution. The concentrated dispersion was then diluted to the desired volume fraction using the same solution. Finally, the pH was adjusted if needed.

The electrophoretic mobility of the particles was measured, as a function of KCI concentration and pH, in a Malvern Zetasizer 2c apparatus at 25 C. The standard error in electrophoretic mobility was estimated from at least ten independent measurements.

A two-electrode cell with variable interelectrode distance, similar to that described by Springer [24], was used for dielectric dispersion measurements in Aquacoatq~ suspensions. It was calibrated with 10-3M KCI solution for a range of electrode distances. Our experiments were performed for seven distances (between 3.5 and 6.5 mm), and for each distance the complex admittance Y*=

98 A. V. Delgado et al. / Colloids Surfaces A:

Y' + i Y" was measured as a function of frequency for 60 logarithmically spaced values between 1 and 251 kHz. The method of Springer [24] was used to obtain the true sample admittance, and, from this, its complex conductivity, Eq.(4). A Hewlett-Packard HP-4192A impedance analyser was employed to perform the measurements (Hewlett-Packard, Hyogo, Japan).

According to Springer's calculations, the following linear relationships must hold:

y, - A + B 2 y,2 + ]1,,2

/ i t

= C + D 2 (9) ~o(y,2 + y,,2)

where 2 is the cell constant for each separation. Fig. 2 illustrates this behaviour with one of the systems.

3,6x10 3

3,2x10 3 g

==._ 2,8x10 3 >- +

~ 2,4x10 3

2,0×10 a

18

z, 100 kHz

20 22 24 26 28 30

(m -1)

1,6xl 0 4

" • 1,2x10 ~

%~ 8,0x10 -5 >- +

~ 4,0x10 -5

18

o lkHz ] o 3 kHz

100 kHzJ

O , , ~ O

20 22 24 26 28 30

;L (m -1 )

Fig. 2. Linear relationships [see Eq. (9)] for a 1% suspension of Aquacoat in 5 x 10 -4 M KC1 (pH 5).

Physicochenl. Eng. Aspects 131 (1998) 95 107

Table 1 Electrophoretic mobility and tea for Aquacoat@ suspensions of different KC1 concentrations and pHs

KCI conc. (M) pH po (p ms-1/Vcm 1) i,a

10 - 4 5.2 -3.02_+0.26 1.6 3 x 10 -4 5.2 -3.97_+0.08 2.8 6 x 10 -4 5.2 -4.69+_0.09 4.0 10 -3 5.2 -4.64_+0.07 5.2 5x10 4 5 -4.18_+0.04 4.08 5 x 10 -4 6 -4.85_+0.05 4.04 5 × 10 4 7 4.98_+0.04 4.04 5 x 10 -4 8 -4.93+_0.05 4.04

3. Results

3.1. Electrophoretic mobility of the particles

The LFDD of Aquacoat@ latexes was deter- mined, as already mentioned, both for different KC1 concentrations and various pH values. With the aim of carrying out the desired integrated characterization of the electrokinetics of these sys- tems, we measured the electrophoretic mobility for all the experimental conditions. The results are summarized in Table 1.

3.2. Dielectric dispersion of the suspensions

3.2.1. Effect of KCl concentration Fig. 3 shows the real part of the dielectric con-

stant of the latex for different volume fractions, and all the KC1 concentrations. The following features are worth noting in these plots: (1) The dielectric dispersion is clearly observed;

the values of e~ of the suspensions can be as high as 300 for low frequencies (<104rads-1), and tend to the electrolyte value for ~o~ 10 ° rad s 1.

(2) At constant volume fractions, the concen- tration of KCI does also affect e~ (both through the double layer thickness h--1 and other double layer parameters); we will con- sider these points below.

Finally, it must be mentioned that the linear relationship predicted by Eq. (6) is verified. Data in Fig. 4, for instance, show that Ae~ is in fact

,4. V. Delgado et al. / Colloids Surfaces A. Physicochem. Eng. Aspects 131 (1998) 95 107 99

240

220

200

18o

_ = 16o

140

120

lOO

8o lO 4

" 1 0 4 M K C I

-% o • ~=1,22%

~ - . ~ ' ° [ o d0=3,27% I

o o° O~oO

• oX

m m

105 106

( r a d / s )

280 t o 3x10-4M KCI

r'a,o I • i

120

80 . . . . . . . . I , ~ i I i , l l

104 105 106

~ ( r a d / s )

400

360

320

280

240

200

160

120

80

6xl 0-4M KCI

• ~ = 1 , 4 5 %

, . o ¢ = 3 , 8 0 % .

a m

J •

104 105 106

320

280

240

200

160

120

10"3M KCI

• 0 ~ = 0 , 9 9 %

o ~=2,21%

8O . . . . . . . . ~ . , , , , , ,

104 105 106

~o ( r a d / s ) ~,~ ( r a d / s )

Fig. 3. Real part of the dielectric constant of Aquacoat:I~, suspensions, plotted as a function of frequency, for the volume fractions and K('I concentrations indicated.

essentially independent of ~b for the relatively low volume fractions analysed.

The effect of KC1 concentration on the L F D D of the systems is clearly observed in Fig. 5. For the concentration range studied, Ae~ increases at all frequencies with [KC1], and only for o9> ca

2 x 10 5 rad s 1 do all curves coincide and tend to the pure electrolyte value, Ae'r=0. The absolute value of &e; will be shown to be anomalously high. This result is very significant it enables one to identify the EDL polarization model [17].

It is interesting to consider also the behaviour

100 A. F. Delgado et al. / Colloids Surfaces A." Physicochem. Eng. Aspects 131 (1998) 95 107

7000

6000 3x10"4M KCI • e=1,67%

• • o 4,=3,85% 5000

o

4000 ~ _

- c o <I 3000 .o.o, oo ~. •

2000 ~ ' ° " ~ % , %x ~

1000

0 . . . . . . . . I l I i i i i i i

10 4 105 106

(rad/s)

Fig. 4. Dielectric increment of Aquacoat@ latex plotted as a function of frequency for [ K C I ] = 3 x l 0 - 4 M , and two volume fractions.

of the imaginary part of the dielectric increment, A _ tt ~ , although it must be stressed that it is related through Kramers-Kr6nig relationships to Ae~, and hence it does not provide new physical insight into the dielectric behaviour of the systems. Ae~' was calculated from:

Sci (~o) Ae~'- - - (10)

(DE o

where Sci (co), the specific conductivity increment, is given by:

Re [K*(m)]- Re [K* (0)1 Sci (~o) = ( 11 )

Fig. 6 shows both Sci(~o) and Ae~'(o 0 for the different KC1 concentrations. Note that Sci is an increasing function of both the frequency and the electrolyte concentration. The latter effect is easy to understand, since an increase in ionic concen- tration in the system must lead to a correspond-

8000 Iv,',v • 10 4 M KCl o 3x104 M KCl • 6x10 " 4 M K c l

v 10 -3 M KCl v

6000 % , {

<~ •,,£o v

4000 . •. o o ' , v

• ° ~'o~°,2

mm •16o 2000 "4, ~, ,~

104 105 106 ~(rad/s)

Fig. 5. Dielectric increment of Aquacoat~g~ spheres as a function of frequency for the different KCI concentrations used.

ingly higher concentration in the double layer. As a consequence, each particle must have a more important contribution to the bulk conductivity, as observed. It must be mentioned, however, that if surface conductivity (non-zero lateral diffusion coefficients of ions in the Stern layer) is present, an increase in ionic strength brings about a decrease in the dimensionless number Rel (Rel = ~:~/K~a; ~'~ is the surface conductivity). This in turn should provoke a decrease in Sci; the resulting Sci-ionic strength dependence might be decreasing if the latter effect predominates over that of the increased ionic concentration in the diffuse double layer.

Concerning the effect of the frequency on Sci, it can be explained by considering that the higher the frequency, the lower the (slow) diffusion cur- rents which are directed in the opposite direction to the current due to electromigration of ions. Hence the smaller the hindering effect of the par- ticles and their double layers on the ionic motions.

The values of Ae~', also included in Fig. 6, have

A. I': Delgado et al. / Colloi& Surfaces A: Physicochem. Eng. Aspects 131 (1998) 95 107 10l

0,010

0,008

" " 0,006 E oo ._~ 0,004 O

0,002

0,000

10000

• 10-4M KCI / o 3x10-4M KCI ~ , ~ • 6xlO-4M KC, J

104 105 106

¢,~ (rad/s)

=~ <1

8000

6000

4000

2000

0

0 o° o ,2"~o • 10-4M KCI / - - % ^ o 3x10-4M KCI

7 ~ . " 6xl0"~M KCI ' " ~ o 10-3M KCI

% • • • A

• °o

i i L I t J I i i L I I [ I I I ] * * I I

104 105 106

~) (rad/s)

Fig. 6. Specific conductivity increment Sci (~)), and imaginary, part of the dielectric increment, Ae;'(o)}, for different KCI concentrations.

been obtained from the best fit to Sci(o)). The maximum in Ae£', expected from relaxation pro- cesses in the double layer, occurs at frequencies ~o~28-90 x 103 rad s q, depending of the concen- tration of potassium chloride in the medium. This is a very significant result, as we shall see. In fact, according to the classical theory of L F D D [5] the critical frequencies should range between 160 x 103 (for [KC1]= 10 _4 M) and 400 x 103 (for [KC1]=10 a M ) r ads 4 for our experimental conditions.

3.2.2. Effect of pH Since a noticeable effect of pH was observed in

both the electrophoretic mobility (Table 1) and the titratable surface charge density [1] of Aquacoat,l~., it seemed of interest to perform the LFD D analysis also as a function o fpH , maintain-

ing the ionic strength constant with 5 × 10-4M KC1.

The experiments were also carried out at two volume fractions (q~= 1 and 0.25%). The main features of the results above reported for suspen- sions of different KC1 concentrations (linearity with ~b, dependence with the cell constant, and so on) were also obtained in these cases. Hence only the final dielectric dispersion data will be considered.

Thus, Fig. 7 shows the dielectric constant of I% suspensions as a function of frequency for pH 5 8; the behaviour of g'r for a 5 x 10-a M KCI solution (pH 5.5t is included for comparison. Although the experimental difficulties involved yield somewhat noisy results, the effect of both the particles and the pH on e'r are clearly seen. The pH-dependence of e; is best analysed considering its increment,

280

240

200

160

120

80

o

"%q? ii • pH 5 1 o ~... i ,? pH 7 J

o \ o • 3 • ~o,o

i J i a I j 1 i i i i i i [ i i . . . . . . I ]

104 105 106

el (rad/s)

280

240

200

160

120

80

" • pH 6 "o " pH8 © \

• oO~,~ o KCI 5x10 -4 M

I • i n •m • • ~o°

o o ~ o

104 105 106

o~ (rad/s)

Fig. 7. Real part of the dielectric constant of Aquacoat P, sus- pensions of different pHs plotted as a function of frequency. Electrolyte values ( , : ) have been included l\~r comparison. Ionic strength: 5 × l0 4 M KC1.

102 A. K Delgado et al. / Colloids Surfaces A." Physicochem. Eng. Aspects 131 (1998) 95 107

14000

12000

10000

.8000

6000

4000

2000

0 104

i o

• pH 5 o pH 6 • pH 7 o pH 8 A

• N, o ~o

o'~ - . % o Q

i i i i i i

10 5 i i i i i I i i I

10 6

(rad/s)

Fig. 8. Real part of the dielectric increment of Aquacoa t@ latex for different pH values. Ionic strength: 5 x 10 -4 M KCI.

A6£, as shown in Fig. 8. Note that this quantity decreases with frequency (although frequencies well above l 0 6 S -1 seem to be needed to obtain the expected null value at high frequencies, mainly at the highest pHs studied). This is a distinct feature of these plots when compared to those in Fig. 5. The effect of pH on A6£ is straightforward to analyse; in any case, Aer increases, on the average, with pH, mainly at the frequencies of interest, where the dispersion is more intense. Even simply the increase observed in p~ upon raising the pH would lead us to expect this type of behaviour.

The increasing trend of Sci (co) with both pH and co is clearly observable in Fig. 9, where Ae~' is also included. The relaxation frequency can be clearly observed, and corresponds to o)~2.5x104s -1, a value quite close to that obtained for [KC1]=6 x 10 . 4 M , when the effect of [KC1] was considered in Fig. 6. Note that the relaxation frequency is rather independent of pH, if the ionic strength is kept approximately constant.

4. Discussion: EDL relaxation mechanisms in Aquacoat@

4.1. ~ potential

The suspensions studied here are characterized by the combination of anomalously high dielectric increment values, and low Ka values. Since no rigorous LFDD model is available to explain LFDD in such extreme conditions, it was not possible to obtain ~ potentials from dielectric meas- urements. Furthermore, the electrophoretic mobili- ties reported in Table 1 were shown to lie above the theoretical maximum [25,26]. We therefore restricted ourselves to the calculation of ( from Henry's theory [26]; the results are summarized in Table 2. It is worth to note here, however, that the electrophoretic mobility of Aquacoat® presents a maximum absolute value for a 6 x 10 . 4 M electro- lyte concentration. Such a p~-c trend--unexpected if only double layer compression exists due to the increase in ionic strength--has been repeatedly reported by authors working with different poly- mer colloids [1,27-30]. Although explanations for this behaviour have ranged from the existence of a rough surface of the particles [29] to co-ion adsorption in the inner part of the double layer [30], more recent models suggest that the fact that pC increases with the concentration of indifferent electrolytes (instead of showing a decrease due to double layer compression, only found for concen- trations 10-3M in most polymer colloids) is related to the existence of surface conductance (non-zero mobility of ions in the inner part of the double layer) of the particles. In fact, when models taking into account dynamics processes in the double layer are used [31], the maximum in disappears in some cases.

4.2. Anomalously high dielectric increment and its origins

The data concerning the ionic strength and pH effects on the characteristic frequency ((Dcr c o r r e -

s p o n d i n g to the maximum in Ac~') and the ratio

p - A£;(0)/(A¢ 'r)ma x

obtained using Eq. (8) are summarized in Table 3.

A. 1.'1 Delgado et al. ,; Colloids Surfaces A: Physicochem. Eng. Aspects 131 (1998) 95 ]07 103

0,006,

0,005 t

0,004 ~-

E o,oo3 O0 v

09 0,002

0,001

l pH 5 ,°1

L ° pH 7 ,,~ / ' 0

, 0 [

e ~ a f ~

. . . . . . . . K

10 6

~(rad/s)

0,000

104 . . . . . . . . . 105 "0'00104 . . . . . . . . . . . . . . . . . . 105 106

3,006 t ot o pH 6

o,oos I " pH 8 ,,_"|

0,004 ,"

~,,~ 0,003 ~" =

,J' o

0,002 . , : ~ 0,001 o,~e

°,.

0,000 ~ ~ d ~

e(rad/s)

3000

000000 2 5 0 0 . ? %o " - - pH 5

~AAAAAAAA 00%0 - - o - - p H 6 ooo ,, . . o^ _ . _ o . 7

" " - - : : ° ° °oo + - ;"8

, o o o °°°°°°~"";;;oo_-..o^_ -==~Oo '&%Yo

500 "-=-~OoS~£o^

0 10 4 10 5 10 6

o~ (rad/s)

Fig. 9. Specific conductivity increment and imaginary part of the dielectric increment of Aquacoat,~ dispersions as a function of frequency and pH. Ionic strength: 5 x 10 4 M KC1.

Significant violation of inequalities [Eqs. (7) and (8)] for Ae~(0) is evident.

Three reasons could be given for explaining the

violation of the inequality [Eqs. (7) and (8)] in the non-conducting particles suspensions: (1) since Eq. (7) is only valid for large ~a~ and

104 A. V. Delgado et al. /Colloids Surfaces A: Physicochem. Eng. Aspects 131 (1998) 95 107

Table 2 ( potential of Aquacoat:~J, as deduced from electrophoretic mobility using Henry's theory

KCl conc. (M) pH ~ (mV)

10 4 5.2 -55 .2 3 x 10 -4 5.2 -69 .8 6 x l O 4 5.2 -79 .5 lO 3 5.2 -76 .5 5 x 10 -4 5 -68 ,9 5 x 10 -4 6 -79 .9 5 x 10 -4 7 -82.1 5x10 4 8 -81 ,2

Table 3

A¢~(0)/(Ae'r)ma x [Eq. (8)] and (Ocr (see text) as a function of KCI concentration and pH

KCI conc. (M) pH O)cr (103S -1) Ae;(0)/(Ae;)~.x

10 -4 5.2 90 22 3 X 10 4 5.2 20" 10 6X 10 4 5.2 27 7.5 10 -3 5.2 18 8.2 5 X I 0 4 5 24 5.9 5 x 10 4 6 26 8.7 5 x l O 4 7 24 10 5 x l O 4 8 25 13

"This value can be somewhat in error, since the maximum could not be clearly detected in this case.

5000 --"-- 104M KCI --o-- 3xlff4M KCI

6xl O-4M KCI ~ KCI 10-3M

4000 ~ , . . . . . . ~ . . . . ~ * ~=-250 mV

- . \ 3000 * ' ~ , , ,

2000 ~ '~ ,~ ,~

10oo ~..~..._~

o . . . . - 7 _ - : ..... 104 105 106

o~ (rad/s)

Fig. 10. Theoretical (DeLacey and White's) values of Ae'r(e)) for Aquacoat~;~', suspensions in KC1 solutions of the molar con- centrations indicated (pH = 5.2 ). The values obtained under the assumption that ~ = - 2 5 0 m V , and ha=5.2 (10 3M KCI), have been included for comparison.

Eq. (8) can only be used under the assumption that only the inner ionic layer contributes to Aer, a theory based on the classical electroki- netic model, and valid for arbitrary xa values (like DeLacey and White's) must be used;

(2) the hypothesis of slight aggregation of par- ticles set forth in Ref. [32];

(3) in the framework of the model of the mutual enhancement of adsorption oscillations described in Ref. [15], even small amounts of added counterions (e.g. H + in our case) may give rise to a large increase in Ae£, as well as to changes in COcr. (These factors could also act simultaneously.)

In order to check the first hypothesis mentioned, we calculated the dielectric increment of our sus- pensions using the numerical method proposed by DeLacey and White [5]. The results are shown in Fig. 10, corresponding to the effect of KC1 concen-

tration on Ae£ of Aquacoat(gi: suspensions. Since the ~ potential data based on Henry's theory for the double layer thickness of the systems under study are little reliable, we have also included the predictions of the model for a very high ~ potential, - 2 5 0 mV. The comparison between these plots and the experimental results in Fig. 5 shows that the differences between (low frequency) theoretical and measured spectra amount to almost one order of magnitude, if ( values in Table 2 are used, and to a factor of ca 3 if ( = -250 mV. However, it must be mentioned that the qualitative features of the experimental data are indeed reproduced by the theory. Similar results have been reported by several authors working with a number of different systems [23, 33-36 ].

These results led us to explore the feasibility of the other two hypotheses (i.e. particle aggregation and adsorption oscillations effect) mentioned

A. I~ Delgado et aL/ Colloids Surfaces A." Physicochem. Eng. Aspects 131 (1998) 95 107 105

above for the justification of the high dielectric • increments found in our suspensions. In this analy- sis, we will take into account the features character- • istic of LFDD in the framework of each of the two hypotheses.

4.2.1. Characteristic features o/LFDD for slight particle aggregation

The hypothesis of slight particle aggregation has been mentioned in Ref. [32] to explain the experi- mental results of Springer et al. [20]. Those authors pointed out that even a slight coagulation of the latex studied in Ref. [20], and the subsequent presence in suspension of doublets, triplets or higher multiplets, would result in an increase of the effective particle size. This would in turn rise the value of the limiting dielectric increment [Eqs. (7) and (8)]; therefore, if the slight aggrega- tion hypothesis is applicable, the increase in Ae'r(0) observed experimentally could be justified. But, simultaneously, the characteristic frequency ¢O~r will decrease. By the same token, more stable suspensions should show lower P ratios, and corre- spondingly higher values of <O~r. It will be shown below that these features are not found in our experiments with Aquacoat,O,, and that the hypothesis of particle coagulation cannot be applied to the data presented in this paper.

4.2.2. (77aracteristic lk>atures ~( LFDD in the framework o f the mutual enhancement of adsorption oscillations model

It was shown in Ref. [15] that in real suspensions the role of the additional counterions adsorption oscillations can be significant. In the case consid- ered here, the added counterions can be H +, which are well adsorbed in the dense part of the Aquacoat'.r~ EDL. The mutual enhancement of K + and H + ions adsorption oscillations can lead to the violation of the inequalities [Eqs. (7) and ( 8 )] if several conditions formulated in Refs [ 15, 17] are satisfied simultaneously: • the exchange of counterions between the Stern

and diffuse layers is free enough (the mean residence time of ions in the adsorbed state is small or at least comparable to the period of the external field):

the adsorption of both K + and H + counterions is sufficiently high; the effectiveness of the tangential transfer of ordinary and added counterions along the EDL is significantly different, This can be due to different electro-osmotic tangential transfer efficiencies, and to the existence of lateral transfer of counterions adsorbed in the Stern layer.

In the framework of this theory, the violation of inequalities [Eqs. (7) and (8)] might be accom- panied by a significant change (increase or decrease) in ~')~r, but it can be shown [17] that the characteristic frequency will not change if some conditions regarding the surface potential and ionic mobilities prevail.

4.3. E/feet of KCl concentration and possible reasons Jor the extremeh' high dielectric increments

For fixed pH =5.2, both the P ratio, and ~Uc,. usually decrease with the increase in KC1 concen- tration (see Table 3). Let us consider here how this type of concentration influence corresponds to each of the possible reasons for the violation of inequality [Eq. (7)].

4.3.1. Effect ,!f KC1 concentratio, a,d slight aggregation

For constant Stern layer potential, particle aggregation will increase with electrolyte concen- tration, due to the growing screening of the surface charge. In the Aquacoat I~ suspension, however, the potential increases with KCI concentration (see Table2); as a consequence, the same (or even larger) increase in Stern potential is expected. Hence, the following casual relationship is possible: concentration increase~potential increase~ enhanced particle repulsion--,decrease of aggregate size and number--*decrease in P. This enables one to explain the nature of the KC1 concentration effect on P in the "slight coagulation" framework.

According to this hypothesis, however, the decrease of the quantity P has to be accompanied by an increase of ~o~. Nevertheless, a more complex (and sometimes directly opposite) dependence is observed (see Table 3).

106 A. I~ Delgado et al. / Colloids SurJaces A: Physicochem. Eng. Aspects 131 (1998) 95 107

4.3.2. Effect of KCl concentration and mutual enhancement of adsorption oscillations

With the increase in total electrolyte concen- tration, the influence of a given quantity of H + counterions (pH =const.) will decrease. Therefore, if the violation of inequalities [Eqs. (7) and (8)] were related to the influence of H + impurity counterions, then P should decrease with increas- ing KC1 concentration. Exactly this KC1 concen- tration effect was measured in all experiments except for the 10-3 M concentration case (Table 3).

It is thus impossible to reach any definite conclu- sions regarding the primary cause of the high dielectric increments observed, from the experi- mental results concerning the ionic strength effect. Some increase in P in the KC1 millimolar concen- tration range is most probably indicative of weak particle aggregation in this region. On the other hand, the information concerning ~o¢~ is against the conclusion that the main cause of the violation of [Eqs. (7) and (8)] is aggregation.

Similarly, the data concerning the KCI concen- tration effect on the LFDD for the concentration values < 10-3M can be completely explained in the framework of the mechanism proposed in Refs [15,17]. Here the problems arise, however, when the attempt is made to explain the increase in P when 10-3M concentration is considered.

To resolve this alternative, the effect of pH was analysed.

4.4. Effect of p H and the mechanism of violation of [Eqs. (7) and (8)]

P do not correlate with a decrease in o~cr: data in Table 3 shows that ~ocr remains constant between pH 5 and 8. This fact also contradicts the hypothe- sis of particle coagulation to explain LFDD results.

4.4.2. Effect of p H on LFDD in connection with the adsorption oscillations model

The decrease in H + concentration in the medium will provoke a decrease in the equilibrium adsorp- tion of these counterions in the Stern layer. It can be expected that the enhancing effect of adsorption oscillations on Ae~(0) should also decrease. Again, experimental results behave in the opposite way (Table 3). However, the theory offers the possi- bility of qualitatively explaining these results on the basis of the assumption of an increasing differ- ence between the effectiveness of the tangential fluxes of K + and H + as the pH is raised (cf. [15,17]). Since ~ is approximately constant between pH 6 and 8, such difference cannot be related to changes in electro-osmotic transport of the ions, but rather to variations in the lateral transfer of counterions along the Stern layer. In addition [17], there is also the possibility of explaining the constancy of ~oo: between pH 6 and 8, even though a simultaneous increase in Ae'r(0) is found.

These reasonings point to the conclusion that the main cause for the extremely high values of dielectric increment shown in Table 3 and in Figs. 5 and 8, is the mutual enhancement of K + and H + adsorption oscillations in the Stern layer of Aquacoat@.

4. 4.1. Effect of p H and the slight aggregation model

For fixed KC1 concentration (constant K), the increase in pH in the range 5-6 gives rise to an increase in surface electric potential (as measured by the ~ potential, Table 2). If the aggregation of particles were the predominant mechanism, the value of P should decrease with pH. This is contrary to experimental observation (Table 3), since the ratio increases with pH for the whole pH range studied, including the interval (6-8, see Table 2) in which both ~-a and ~ remain essentially constant. Furthermore, the significant increases in

5. Conclusions

Mutual enhancement of adsorption oscillations of ordinary and added counterions is a hypothesis which gives a satisfactory explanation of experi- mental results in Aquacoat@ suspensions. The pH influence on LFDD in the framework of this hypothesis can be explained only for non-zero lateral mobility of counterions adsorbed in the Stern layer. In the millimolar concentration range, slight aggregation of Aquacoat(~ particles cannot be excluded.

It must be noted, however, that the qualitative

A. K Delgado et al. Colloids Surfaces A. Phys'icochem. Et~. Aspects 131 (1998) 95 1(17 107

considerations presented in the Section 4 cannot be regarded to as rigorous proof. The dominant role of mutual enhancement of K + and H + ions adsorption oscillations in the LFDD of Aquacoat,g: suspension will be definitively estab- lished only through the comparison between exper- imental results and quantitative LFDD theory which accounts for adsorption oscillations and which, in contrast to Refs [15,17], is valid for small ~ca wdues.

Acknowledgment

Financial support for this work from DGICYT, Spain (Project No. PB94-0812-C02-1), and the International Association for the Promotion of Cooperation with Scientists from the New Independent States of the Former Soviet Union (INTAS) (Project No. 93-3372) is acknowledged. Thanks are also due to Professor V.N. Shilov, of the Ukrainian National Academy of Sciences in Kiev, for fruitful discussions, and to Mr G. Molina-Cuberos for his experimental assistance.

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