Polarized electric light scattering study of interactions in α-FeOOH suspensions

Co&ids and Surfaces A: Physicochemical and Engineering Aspects. 14 (1993) 223-231 0927-7757/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved.

223

Polarized electric light scattering study of interactions in a-FeOOH suspensions V. Peikov, I. Petkanchin” Bulgarian Academy of Sciences, Institute of Physical Chemistry, Sojia 1040, Bulgaria (Received

21 April 1992; accepted

14 January

1993)

Abstract The changes of electro-optical behaviour with increase in particle concentration are followed by the electric light scattering method to study the effects of interactions (optical and electrical) in cI-FeOOH aqueous suspensions, Different polarizations of the initial and scattered light are used as well as light of two different wavelengths. The peculiarities of the electro-optical effects (the decrease and the negative values as well as a decreased particle relaxation time) observed at a high particle concentration are common for many other disperse systems. A comparison between different experimentally measured electro-optical quantities shows that the electro-optical behaviour observed with increase in particle concentration is connected with the effects of optical interactions in the suspensions, For the present system, the concentration limit below which the electro-optical effect is not influenced by existing effects of multiple light scattering is 0.01 g 1-r. Key words: Electrical

interactions;

r-FeOOH

suspensions;

Optical

interactions;

Polarized

electric light scattering

Introduction

particle interaction is also possible. In our previous investigation of two types of aqueous FeOOH

The electric light scattering (ELS) method is usually applied to follow changes in the electrical, optical and geometrical properties of colloid particles in very dilute disperse systems where neither optical nor electrical interparticle interactions exist

suspensions (the CI- and fl-modifications) [3], the following EO peculiarities were observed with the increase in particle concentration C by weight: a

[1,2].

frequency

As the real systems

are concentrated,

it is

interesting to follow the changes of the electrical and optical properties by electro-optics when the volume part of the disperse phase increases. In the concentration region of the transition from very dilute to concentrated systems, different electrooptical (EO) effects occur. In this region, the effects of multiple light scattering are observed, being manifested in a deviation from linear concentration dependence of the light intensity scattered from the suspension in the absence of an electric field. In addition, the appearance of an electrical inter*Corresponding

author.

decrease

in the values

of the electro-optical

(EOE) cx;the appearance (below

of a negative

effect

EOE of low

100 Hz) for a-FeOOH;

a change

in the sign of the EO response (for all frequencies) at concentrations above 2 g 1-i for !z-FeOOH and 0.5 g l- ’ for /?-FeOOH;

a considerable

the shape of the EO response

change

in

and in the relaxation

time of the EOE at full particle orientation coinciding with the transition from positive to negative EOE. Similar EO behaviour with the rise in particle concentration has been observed for many different disperse many

systems optical

suspensions

[449].

theories

In spite of the existence dealing

of submicron

still no EO theory

which

particles takes

of

with concentrated into

[lo]

there

account

is the

224

V. Peikm

and I. Petkanchin/Colloids

optical interactions in such systems. This hampers the interpretation of the experimental EO data at increased particle concentrations. Often authors give different, even contradictory, interpretations [4,8,9]. Generally, the following explanations of the observed peculiarities are possible: (1) interparticle interactions, which dominate the changes in the EO effect (appearing with increase in concentration) [S]; (2) the appearance of interactions induced by the applied electric field (electro-coagulation); (3) optical interactions in semi-dilute suspensions in which we include the near- and far-field expanding wavefront effects. The incoherent far-field effects are usually described by the term multiple scattering. Since the terminology is unsatisfactory, some authors use the term multiple scattering to include also the near-field effects [I 11. In the term optical interactions we exclude here the coherent optical effects such as Bragg diffraction, for instance, which are due to the spatial correlation and arrangement of the particles resulting from electrical interparticle interactions. One has to choose between the three possible explanations. For instance, the negative EO effects observed at low frequency are usually explained by the appearance of permanent dipole moments connected with electrical interparticle interactions [ 1,2]. The main problems concern which of the possible interactions optical or electrical dominates the changes in the EO behaviour of the disperse systems in the transition from the very dilute to the semi-dilute region, and up to which concentration one can neglect the optical interactions in the suspensions. The lack of theoretical EO criteria to distinguish optical and electrical interactions makes the solution of these problems very difficult. The present EO investigation of aqueous cc-FeOOH suspensions has been carried out over a wide concentration interval (up to 5 g lP ‘) using the polarized electric light scattering method to answer the above questions. The investigation involves measurements using different polarizations of the initial and scattered light as well as experiments with unpolarized light. The changes in the EO effect and in the particle electrophoretic mobility with the increase in particle concentration are followed.

Surjaces A: Physicochem.

Eng. Aspects

74 11993) 223-231

Method and apparatus The EO method used is electric light scattering [l]. The steady state EOE x is defined as XX_

I, - I,

where I, and I, are the scattered light intensities in the absence and in the presence of the electric field respectively. The intensity I, is measured when a steady state is established

in the suspension.

Intensities I, and IE are corrected for scattering from the pure solvent (triply distilled water), the electrodes, the EO cell and the walls of the apparatus. With the increase in electric field strength, the EOE increases owing to the increase in the degree of particle orientation. When a full particle orientation is established, the EOE proceeds to saturation and does not change with further increase in electric field strength. The value of the EOE 2 at full particle orientation is denoted 2,. The transient EO process after the switching off of the electric field (at time t=O) is described [2] by a(t) =

cc0

-I

exp (

51

where r(t) is the EOE at a time t after the switching off of the electric field, and T is the relaxation time due to Brownian rotational motion of the particles. In the present study, all values of rcr and T for different polarizations were measured at a constant field frequency of 1 kHz and 10 kHz respectively (in the plateau region of the frequency dependence of c(, Fig. 1). From the frequency dependence of c( at low particle concentration and constant electric field in the Kerr region (the region in which EOE 2 is proportional to the square of the electric field strength) we define kilohertz EOE as a+ and hertz EOE as C. The parameter a+ is the value of the EOE in the kilohertz frequency region and is connected with the polarization of the diffuse part of the electric double layer [ 1,2]. The parameter a - is the difference between r+ and the value of

V. Peikou und I. Petkanchin/Colloids

Surfaces

A: Physicochem.

Eng. Aspects 74 (1993) 223-231

225

3

2

1

b Fig. 2. Electron Fig. I. Dependence of EOE on the ax. field frequency at E= 18.75 kV m-l (cc-FeOOH particle concentration, 0.5 g I-‘), and the definition of the kilohertz s(+ and hertz OL- electro-optical effects.

the EOE in the hertz frequency region and could be connected with the so-called transverse interfacial “permanent” dipole moment or other polarization mechanisms with relaxation times near to the particle relaxation time [2,12] (Fig. 1). The apparatus for electric light scattering used by our group [ 133 was modified by placing a polarizer and an analyser (both Polaroids) in the initial and the scattered light beams respectively. All measurements were carried out at a constant angle of scattering, i.e. 90”. A digital oscilloscope is used, and the electrical signal of the EO response received from the photomultiplier is processed with a personal computer. The indices h, v, H, V and Uu used in the text denote the polarizations of the initial and scattered light and have the usual meaning: h and v, horizontal and vertical polarizations of the initial light with respect to the plane determined by the initial and scattered light beams; H and V, horizontal and vertical polarizations of the scattered light; Uu, scattered light measured without Polaroids in the initial and scattered light beams. Materials The materials used were a-FeOOH rod-like particles, strongly polydisperse and aggregated (Fig. 2)

microscopy

photograph

of a-FeOOH

particles.

obtained by the Atkinson method [ 141. The density of cr-FeOOH is 4.28 g cm 3. The average aggregate sizes measured from electron micrographs are as follows: average length a= 2533 A; average diameter 6= 1290 A; 162 aggregates counted. From the EOE at the full particle orientation CX~,measured at a low particle concentration (0.01 g I-‘), the average particle sizes are calculated using the EO theory in the Rayleigh-Debye-Gans (RDG) approximation for slightly elongated cylinders [ 151. The calculated sizes are ti = 2790-2910 A, 6=940-l 170 A, which are very close to the sizes of aggregates obtained by electron microscopy. With increase in concentration, the x-FeOOH suspensions exhibit all the peculiarities of the EOE mentioned above. The initial a-FeOOH suspension with a particle concentration C = 5 g l- ’ is prepared from the dry substance. All other suspensions intended for EO measurements are prepared by dilution of the base suspension with triply distilled water (conductivity K = 1.1 x 10m4 S m-l). Before each dilution the initial suspension is sonicated for 3 min at a frequency of 22 kHz. The cc-FeOOH suspensions are electrostatically stabilized and the particles are positively charged under the experimental conditions used (conductivity about 3 x 10e4 S m-r and pH 5.5) [16]. The concentrated suspensions are sedimentationally stable for the time of the experiments.

V. Peikoc

226

and I. PetkanchiniColloids

Surfaces

dences

Results and discussion Firstly, we follow the changes in the scattered light intensity in the absence of an electric field I,. Figure 3(a) shows the concentration dependences of I, for Vv, Uu and Hh polarizations.

The curves

A’ Phgsicochem.

of I,.

Figure

Eng. Aspects 74 (1993) 223-231

3(a) also

shows

that

the

concentration dependences of I, for Uu and Vv polarizations are similar, with a small difference in the exact position of the maximum. The concentration dependences of I, for Hh, Hv and Vh polarizations coincide within the limits of experi-

have a bell shape with a maximum in the region 0.5-0.75 g 1-l. Two concentration regions can be defined, i.e. below and above 0.75 g 1~ ‘, connected

mental error. That is why the curves for the last two polarizations are not given in Fig. 3(a). In Fig. 3(b) the concentration dependences below

with

0.01 g l- ’ of I, and EOE at full particle orientation x, are given for unpolarized light. Up to a concentration of 3 x 10m3 g l- ‘, I, is a linear function of C, and consequently there are no optical interactions in the suspension. Above a concentration of 3 x 10 3 g 1~ ‘, I, becomes a non-linear function of C, independent of the electrolyte concentration. This is not due to aggregation since CI, and the particle relaxation time t remain constant throughout the whole concentration region shown in Fig. 3(b). Consequently, the deviation from linearity of the concentration dependence of I, is an indication of the appearance of optical interaction. The relatively low concentration at which the

the maximum

of the concentration

depen-

20 t

> 0

_

10

0 01

(a)

0,

Conceniration,

1

g/l

I

10

‘.;

’ ‘,

(b) Fig. 3. (a) Concentration dependences of the scattered light intensity in the absence of the electric field I, at different light polarizations: curve 1, Vv polarization; curve 2, Uu polarization; curve 3, Hh polarization. (b) Concentration dependences, below 0.01 g I-‘, of I, (C, right ordinate) and EOE at full particle orientation z, (El, left ordinate; electric field frequency, 1 kHz) for unpolarized light.

optical effects appear could be due to the high value of the particle refractive index (2.2-2.6) and to the large (approximately half the wavelength) sizes of the aggregates. Thus the optics of an individual particle (aggregate) is very complicated and this could result in the appearance of optical effects at such concentrations. The construction of the EO cell is also quite important. The optical thickness (2 cm) and the angle of scattering (90”) must be taken into account when considering the exact value of the particle concentration at which the optical effects appear. Up to a concentration of 1 x lo-‘g lP’, EOE x, is constant because it is a ratio of the two quantities I, and I,, which at these low concentrations depend in the same way on the particle concentration. Consequently, at low concentrations (in the region of (3 x 10m3)(1 x IO-‘) g 1-l) the EOE is not influenced by the effects of the optical interactions existing in the suspension. Secondly, we follow the behaviour of the suspensions

changes in the EO with the increase in

V. Peikoc

and 1. PetkanchinlColloids

particle

concentration

Surfaces

A: Physicochem.

C. All measurements

Eng. Aspects 74 11993) 223-231

are

227

the concentration range studied, the average distance between particles increases from 2800 8, at a

carried out at constant pH (5.5). With the increase in particle concentration, the conductivity of the

concentration

suspensions increases slightly (above 3 x 10m4 S m-l) owing to the increase in the total amount of

In the most dilute suspensions (C = 1 x lo-3 g l- ‘), 6 = 4.8 pm. The values of 6 are determined assum-

dry cr-FeOOH in Ref. 3 that

ing that only individual exist in the suspensions.

in the suspension. We have shown the changes in the EO behaviour

of 5 g 1-l

to 5300 A at 0.75 g l- ‘.

particles (no aggregates) If there are some aggre-

observed with the increase in particle concentration are not due to an increase in electrolyte concen-

gates, the value of 6 should increase. The thickness of the electric double layer depends on the electro-

tration.

lyte concentration and is about 600 A under our experimental conditions (conductivity, 3 x 10e4 S mm’). The calculations show that even for the highest investigated concentration of 5 g 1~ ’ the overlapping of electric double layers is negligible. This is important evidence that the observed peculiarities of the EOE are not electrical in origin. The changes in the kilohertz EOE c(+ with increase in concentration are shown in Fig. 5. The measurements are carried out at a constant electric field E = 3 1.25 kV m ‘. At a concentration of 0.01 g 1-l the value of E=31.25 kV m-l used is in the Kerr region, i.e. the measurements are carried out at a low degree of particle orientation. For our material the Kerr region extends up to 40 kV m-l [3]. For all values of E below 40 kV mm ‘, EOE c1+ shows similar concentration dependences to those in Fig. 5. It can be seen that c(’ rapidly

The concentration

dependences

of c(, are

shown in Fig. 4. The x”,’ and LX”,”values are practically equal, with similar concentration dependences. At concentrations above 0.75 g l- ‘, LX”,’ and z”,” become negative. The concentration dependences for other polarizations are quite different and strongly depend on the type of polarization. One of the reasons for the observed peculiarities in the EOE could be the appearance of electrical interparticle interactions. It is well known that electrical interparticle interactions depend on two main factors: the average distance between particles (6) and the thickness of the electric double layers (the radius of Debye screening, K- ‘). The value of 6 could be calculated using the equation 6 = N - ‘I3 where N is the particle number concentration. In

001

01

Concentration,

1

10

g/l

Fig. 4. Concentration dependences of the EOE at full particle orientation c(,, at a constant electric field frequency of I kHz and for different light polarizations: curve 4, Hv polarization; curve 5, Vh polarization. Other curve designations are the same as in Fig. 3.

001

01

Concentration,

1

IC

g/l

Fig. 5. Concentration dependences of the kilohertz EOE r+, at a constant electric field strength E ~31.25 kV mm’ and for different light polarizations. The curve designations are the same as in Figs. 3 and 4.

V. Peikoc rwd I. PetkanchiniColloids

228

decreases with the increase in particle concentration for Uu, Vv and Hv light polarizations. For

Sur$&es

A: Physicochem.

Eng.

Aspects

74 11993)

223-231

6

Uu and Vv light polarizations at concentrations above 0.5 g ll’, X+ follows the trend in the corresponding component of I, as a function of C. At the same time, LX&,(curve 3) is practically constant over the whole concentration region investigated. The similarity

between

the concentration

depen-

dences of 2 ’ and I, (Vv and Uu polarizations) above 0.5 g lP 1 shows that in this concentration region the decrease in X+ is due to the effects of optical interactions which also cause the decrease in I,. In the region 0.01-0.75 g ll’, x:, and #Y& slowly decrease with the increase in concentration. At the same time, I, increases and reaches a maximum. The optical interactions in the region of maximum I, could be the reason for the observed decrease of @’ in this concentration region too. Consequently, the changes in the Uu, Vv, Hv and Vh polarization components are not connected with the appearance of electrical interparticle interactions and the change in the degree of particle orientation. The observed changes in the polarization components are connected with the optical interactions in the suspension manifested as multiple light scattering. The concentration dependences of the hertz EOE Y at different light polarizations are shown in Fig. 6. The measurements are carried out at a constant electric field E= 18.75 kV m- ‘, at a low degree of particle orientation. Here, as for cx’, EOE dependences for cr- shows similar concentration all values of E in the Kerr region (below 40 kV mm ‘). For Vv, Uu and Hh polarizations, c(depends slightly on the concentration in the region below 0.75-l g l- ‘. This supports our previous conclusion that CY is an individual effect connected with the existence of aggregates even in dilute xFeOOH suspensions [3]. For the other polarizations, (curves 4 and 5) Y decreases monotonically in this concentration range. At concentrations higher than 0.75 g l- ‘, drastic changes in ‘x- are observed; sl_ decreases for unpolarized light following the trend in the concentration depen-

‘I

Fig. 6. Concentration dependences of the hertz EOE Y, at constant electric field strength E= 18.75 kV mm’ and for different light polarizations. The curve designations are the same as in Figs. 3 and 4.

dence of I, (see Fig. 3(a)), but increases rapidly for Vv and Hh polarizations and passes through a minimum for Hv and Vh polarizations. The correlation between the concentration dependences of I, and Y for unpolarized light, as well as the drastic changes in rP at particle concentrations above 0.75 g 1-i (in the decreasing section of the concentration dependences of I,), suggests that in this concentration region the changes in the EOEs and the observed EO behaviour are determined by optical interactions in the system. Above a concentration of 0.75 g l- ’ these optical interactions are manifested as a drastic change in the value of x-, as a decrease

in the values

of CI+ and x,

for Uu

and Vv polarizations, and as a decrease in lo. In Fig. 7, the concentration dependences of the ratio I’x(-/~+/ are presented. For very dilute suspensions this ratio is equal to the ratio between the particle electrical properties in the hertz and kilohertz frequency regions. In the concentration region below 0.75 g l- ‘, the ratio (cI-/z+[ depends slightly on the particle concentration for all types of polarization. Again, drastic changes in the (x-/u+ ( ratio are observed above a concentration of 0.75 g I- ‘. The changes strongly depend on the type of optical

V. Peikou and I. PetkanchinlColloids

Surfaces

A: Physicochem. 9

1

25

Eng. Aspects 74

(1993J

223-231

229

as a possible explanation of the observed EO behaviour. The strong concentration dependence of the EOE manifests itself in drastic changes in the

I

relaxation

time of the EOE. The relaxation

times

measured at different light polarizations are shown in Fig. 8. In the concentration region 0.75-1.34 g lP ‘, TV” and 7Hh are almost constant, while T'" and z “” are changing considerably; tUu and rvV have similar concentration

Fig. 7. Concentration dependences of the ratio (Y ja+ 1, at constant electric field strength E=31.25 kV rn~’ and for different light polarizations. The curve designations are the same as in Fig. 3.

polarization. The region of the changes coincides with the concentration region in which c( is changing and in which the concentration dependence of I, decreases. This is the same region in which the EOE is determined by the optical interactions in the system. In the concentration region above 0.75 g 1~ ‘, the optical interactions depend more strongly on concentration than on particle electric polarization and determine the changes in the EO behaviour of the a-FeOOH suspensions. From our experimental results, one cannot reject the possibility of the existence of long-range interparticle electrical interactions

influencing

the electric

polarization

dependences.

The latter refers

to all EO quantities (a+, cy-, z,, 5) measured at these light polarizations. At low concentration, z”” and T”” are independent of C. Above 0.1 g l- ‘, ?” and t”” Increase . rapidly. With further increase in concentration, when LX”,”and Z: become zero, T”” and t”” could not be defined. When rot becomes negative, tUu and gvv are of the order of 0.5 ms and again show a slight increase with further increase in the particle concentration. The strongest changes of $” and tVv are around and above the maximum of I, as a function of C, where the sign of the EOE is changed. On the same figure, the concentration dependence of the particle electrophoretic mobility, which is independent of the optics of the system, is shown. In this way we

of the

particle and manifesting in a concentration dependence of the electric polarization of the particle. To check the possibility of electro-coagulation, the particle orientation time, defined as the time after the switching on of the electric field for which the EOE reaches 67% of its steady state value, was measured. If an electro-coagulation appears the time for particle orientation should increase. No experimental evidence for such an increase was observed. The particle orientation time (about 0.3 ms) was independent of the particle concentration. This is the reason for rejecting electro-coagulation

001

01

Concentration,

I

10

g/l

Fig. 8. Concentration dependences of the relaxation time of the EOE at full particle orientation r, at constant electric field frequency of 10 kHz and for different light polarizations. The curve designations are the same as in Figs. 3 and 4. The concentration dependence of the electrophoretic mobility U is also presented (see right-hand scale).

230

V. Peikoc

and I. Petkanchin!Collolds

eliminate the influence of the optics. In the concentration region of the strongest changes in all the measured EO quantities (i.e. in the region around and above the maximum of I, as a function of C) the particle electrophoretic mobility is constant. Consequently, the peculiarities in the EO behaviour are not connected with the changes in the particle electrokinetic potential. All this suggests that the changes in the concentration dependences of T" and T"' are not connected with the changes of particle rotation after the switching off of the electric field, but are due to the optical interactions, which are different for each polarization. The optical interactions modify the relaxation curves of the EO responses and in this way change the measured value of T. Similar effects due to the change in the optical properties of the individual particles have been calculated theoretically [ 171. The significance of the optical properties of the particles and the optical interactions for the EO behaviour with the increase in particle concentrations is demonstrated also from the concentration dependence of I0 (Fig. 3(a)). We emphasize that in the concentration region of the EO peculiarities (around and above 0.75 g 1~ ‘), I, for all light polarizations passes through a maximum and becomes a decreasing function of the particle concentration. Consequently, in this concentration region, optical interactions are clearly pronounced. This demonstrates once again the dominant role of the cooperative optical effects in this concentration region. To investigate the influence of optical properties on the EO behaviour we also carried out experiments using light of different wavelength. In dilute suspensions, the change in the wavelength of light used (from 546 to 435 nm) leads to only a 5% change in the value of z$‘. At a concentration of 5 g ll’ the same change in the wavelength leads to a 50% change in the 3: value. This is additional evidence for the domination of the optical effects in the semi-dilute FeOOH suspensions. Conclusions The EO behaviour of the dilute r-FeOOH suspensions

investigated semicould be charac-

Surfaces

A: Physicochem.

Eng. Aspects 74 (1993) 223-231

terized by the concentration of the maximum of the concentration dependences of I, (0.550.75 g l-i),

where the optical

sions

are clearly

interactions

pronounced.

can be used to characterize of the suspension. At concentrations (for this material,

much

in the suspen-

This concentration the optical

properties

lower than

0.75 g 1-i

below 0.01 g 1~ ‘), the EO behav-

iour of r-FeOOH suspensions is determined by the electrical and optical properties of the individual particles. Electrical interparticle interactions and electrical properties of the particles can be studied by means of ELS in this concentration region without considering the effects of optical interactions. The EO behaviour at concentrations above 0.01 g 1-l is determined by the optical interactions in the suspension. The ELS can be applied to the investigation of electrical properties and electrical interparticle interactions only after considering the effects of optical interactions in the suspensions. In addition, the ELS can be a useful method for investigating the optical interactions in the suspensions when the degree of particle orientation is changed, and would help in the creation of new models and EO theories of interacting systems. Acknowledgements This work has been supported by the national fund “Science Research” (no. X-44/91) of the Bulgarian

Ministry

of Education

and Science.

References S. Stoylov, V.N. Shilov, S.S. Dukhin, S. Sokerov and 1. Petkanchin, Electra-optics ofColloids, Naukova Dumka, Kiev, 1977. S.P. Stoylov, Colloid Electrooptics, Academic Press, New York, 1991. V. Peikov, LB. Petkanchin and S. Stoylov, Bulg. Acad. Sci., Commun. Dep. Chem., 24 (1991) 536. M.J. Shah, D.C. Thomson and C.M. Hart, J. Phys. Chem., 69 (1963) 1170. I. Petkanchin and T. Suong. Colloids Surfaces, 16 (1985) 127. C.T. O’Konski and B.H. Zimm, Science, I I1 (1950) 113. J. Errera, J.T. Overbeck and H. Sack, J. Chem. Phys., 32 (1935) 681.

V. Peikov and I. PetkanchinlColloids

Surfaces

A: Physicochem.

M. Stoimenova and Ts. Radeva, J. Colloid Interface Sci., 141 (1991) 433. H. Hoffmann, I-J. Kramer and H. Thurn, J. Phys. Chem., 94 (1990) 2027. A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. 1 and 2, Academic Press, New York, 1978. H.C. Van de Hulst, Multiple Light Scattering, Vols. 1 and 2, Academic Press, New York, 1980. G.H. Meeten, in G.H. Meeten (Ed.), Optical Properties of Polymers, Elsevier Applied Science, New York, 1986, pp. 3355392. I. Petkanchin, in H. Watanabe (Ed.), Dynamic Behaviour

Eng. Aspects 74 (1993)

231

223-231

of Macromolecules, Biological Systems Methods, Hirokawa,

Colloids, Liquid Crystals and by Optical and Electra-optical Tokyo, 1988, pp. 337-342.

13

S.P. Stoylov,

14

R.J. Atkinson, A.M. Posner Chem., 30 (1968) 2371.

Adv. Colloid

Interface

Sci., 3 (1971) 45.

and J.P. Quirk,

J. Inorg. Nucl.

15

M. Stoimenova,

16

R.J. Hunter, Zeta Potential Press, London, 198 1.

in Colloid

Science, Academic

17

N.G. Khlebtsov, Russian).

Spectrosc.,

50 (1989) 977 (in

J. Colloid

J. Prikl.

Interface

Sci., 53 (1975) 42.