Dielectric Dispersion in the Frequency Range 1 MHz–1 GHz of Concentrated Suspensions in Relation to Rheology

Dielectric Dispersion in the Frequency Range 1 MHz–1 GHz of Concentrated Suspensions in Relation to Rheology

A. Assifaoui, ∗ R. Moussa, ∗ and P. Blanchart †

∗Facult´e des Sciences A¨ın Chock, Universit´e Hassan II, B.P. 5366, Ma ˆarif, Casablanca, Morocco; and†GEMH, Ecole Nationale Sup´erieure de C´eramique Industrielle, 87065 Limoges Cedex, France

Received March 18, 2001; accepted August 4, 2001; published online October 24, 2001

Dielectric measurements were performed on concentrated sus- pensions of TiO

(50 vol%) and clay (40 vol%) in the frequency range 1 MHz–1 GHz. The suspension rheology was modified by various Tiron or sodium tripolyphosphate additions. Using a spe- cific procedure for data interpretation, it was shown that the global dielectric relaxation phenomenon, in the intermediate frequency range, is composed of three or four more-or-less separate dielectric relaxations. The peak positions and intensities vary with the dis- persant quantity and the suspension rheology. A correlation was found between the aspect of dielectric spectrums and the suspen- sion consistency when the dispersant quantity varied. The dielec- tric spectrum aspects were also related to the existence of active surface sites on particles, which were subject to physical adsorption or chemical binding for cations and anions from the dispersant.

°C2001 Academic Press

Key Words: dielectric dispersion; suspension, clay.

INTRODUCTION

Concentrated suspensions of oxides or minerals are exten- sively used in mineral selection or treatment and in ceramic material processing. A high concentration of powder, up to 55 vol%, is often used to ensure process efficiency.

Rheology and stability are very useful characteristics of con- centrated suspensions, which must be accurately controlled.

They are macroscopic characterizations of the fluid flow under various stresses. At the microscopic scale, particle-surface be- havior changes the interparticle forces and the state of dispersion or linkage. These phenomena are highly related to suspension rheology.

A common tool for the surface characterization of particles is electrokinetic potential measurement by electrophoresis (1).

This method is restricted in its applicability by the very low particle concentration required for the measurement compared to that of real suspensions.

A more recent method is based on the measurement of the electrokinetic sonic amplitude generated by small particles in

1To whom correspondence should be addressed. E-mail: p.blanchart

@ensci.fr.

an alternating electric fluid (2). In that case, the mathematical description (3) connecting mobility and ζ potential is mainly valid for dilute suspensions ( ∼ 10 vol%).

At high particle concentrations, the dielectric response of the suspension provides information about the particle-surface behavior. The theoretical calculation of this effect does not in- volve any assumption that the suspension is dilute, particularly in the case of phenomena in the high frequency range (i.e., 1–

500 MHz) (4). In general, it is considered that the large dielectric phenomenon, which is measured, is associated with the charge redistribution over the whole particle surface. It theoretically supposes the existence of a global surface conductance from an overall flow of the surface charge (4).

Nevertheless, the surface charge of a solid particle in an aque- ous electrolyte is associated with local interactions of ions from the solution with various surface sites of the material. Oxide and mineral surfaces are in fact more complex. The interface results from the local accumulation of species, but also from chemical reactions at particular surface sites. Therefore, electrical mea- surements should be more related to various and local charge motion on surfaces.

The objective of this study is to analyze the dielectric disper- sion in the range 1 MHz–1 GHz for one oxide (TiO

) and two clay raw materials in concentrated suspensions (40–50 vol%), in relation to the rheology of these suspensions. Powders were selected by taking into account the increasingly complex char- acter of surfaces from the TiO

oxide to clay surfaces. This paper details the phenomenon in terms of relaxation frequency distribution. Experiments were carried out with a view toward showing the relationship between the relaxation frequency dis- tribution and the rheology of concentrated suspensions against the dispersant role on surfaces.

MATERIALS AND METHODS

The TiO

(rutile phase,

/ m = 0 . 6 µ m) was used in con- centrated suspensions of 20–50 vol% (5), dispersed with a poly- mer (6) (Tiron: 4,5-dihydroxy-1,3-benzenedisulfonate acid, dis- odium salt monohydrate). In this study, variable Tiron quantities (0.1–0.7 wt% of dry powder) were added at a constant powder content (50 vol%).

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TABLE 1

Chemical Analyses of C4 and R40 Clays

Wt % R40 C4

SiO2 48 49.7

Al2O3 34.5 20.7

Fe2O3 1.9 9.7

TiO2 1.9 1.4

CaO 0.44 0.9

MgO 0.18 1.6

Na2O 0.04 2.9

K2O 0.04 2.6

Loss on ignition 13 10.5

The clay raw materials used were an almost pure kaolinitic clay, as reference material (R40, Charentes, France), containing 92% medium crystallized kaolinite and 8% quartz, and a more complex common clay containing 65% kaolinite, 26% illite, and 9% quartz (C4), which comes from the Casablanca region, Morocco, and is used in floor-tile manufacturing. For these clays, the quartz content is low enough to influence the whole material properties very weakly.

X-ray diffraction analysis indicated a close crystallinity degree between the two kaolinite minerals contained in R40 and C4. The illite phase of C4 was identified as a true illite phase without interstratification. The clay chemical analyses, given in Table 1, point to the relative high purity of the R40 clay. For C4, the presence of iron and alkaline earth is due to minor quantities of goethite and dolomite phases, respectively.

All suspensions were prepared by ball milling the dry powders in water, in which the dispersant was preliminarily soluted. For clays, the volume ratio was maintained at 40 ± 0.5%, close to the maximum value that is possible when such clays are used. To change the suspension rheology at a constant density, we used dilute solutions of sodium tripolyphosphate (Na

P

O

, named Tpp), which is widely used for dispersing concentrated suspen- sions of common clays. Besides the common interaction of such dispersants with the mineral surface, phosphate anions are ef- fective in precipitating soluble, highly charged cations from the electrolyte.

The rheologies of suspensions were characterized using a variable-speed concentric cylinder viscometer (Rheo, VT500).

In general, our fluids exhibited typical pseudoplastic behavior and the rheology description used the general equation (7)

τ = τ

+ K · g

, [1]

where τ and τ

represent the shear strain of the fluid and the shear limiting value, respectively, g is the shear stress, n indicates the nonlinearity behavior of the fluid, and K is the consistency, which should represent the intrinsic fluid viscosity.

In this study, electrical measurements were carried out between 1 MHz and 1.8 GHz using the 4291A Hewlett–Packard apparatus. The complex admittance was calculated from the

reflection coefficient of an electromagnetic wave at the mea- surement port, equipped with a specific coaxial flat cell, which ends inside the suspension. Cell dimension and shape as well as the suspension volume were adapted to prevent any distur- bances of wave propagation into the medium. The suspension was agitated slowly and continuously.

For an alternating field, the complex permittivity ε

of the suspension is given by

ε

= ε

− i ε

= ε

· ( ε

− i ε

) , [2]

where ε

is the permittivity of vacuum and ε

(respectively ε

) and ε

(respectively ε

) are the real and imaginary parts of the permittivity (respectively relative permittivity). The dielectric dispersion is calculated using ε

, the typical variation of which is known (8). From the experimental complex admittance, Y

, we have

Y

= Y

+ i Y

[3]

and

ε

= − Y

ω L( ω ) , [4]

where L( ω ) is the geometrical factor from dielectric water–

dioxane mixtures measurements (9).

The calibration procedure of the apparatus, the compensation of the measurement cell, and the reduction of the electrode effect at the low-frequency end and of the evanescent modes of wave propagation at the high-frequency end were performed using methods recently described in Ref. (5).

All measurements and calibrations were performed at 25

± 0 . 1

C. The result reproducibility was ensured by successive data acquisitions.

RESULTS

Two examples of permittivity characteristics for R40 and C4 are presented against frequency in Fig. 1, using an intermediate Tpp quantity (0.35% by weight of clay). Curvatures of both char- acteristics are slightly modified in the intermediate-frequency range, indicating the existence of a particular phenomenon re- lated to the solid-phase surface.

A classical way to fit the experimental data is to consider a limited distribution of relaxation times around central values, using K. S. Col and R. H. Cole’s model; a recent attempt is in Ref. (10). Such an approach has been often applied, giving a good fit to experimental data. Nevertheless, the major drawback of this method is the necessity of arbitrarily defining the preliminary distribution. Furthermore, there is a large mathematical difficulty in finding an accurate solution.

A more tempting approach is not to make any assumption

about the distribution of relaxation time s( τ ), as proposed by

Provencher (11). On the basis that the observed data are linear

FIG. 1. Relative permittivity against frequency of R40 (dashed line) and C4 (solid line) clay suspensions (40 vol%) containing 0.35% by weigh sodium tripolyphosphate.

integral transforms of the quantities to be estimated, Provencher proposes to use a constrained regularization method to find the simplest (most parsimonious) solution that is consistent with experimental data. In this approach, ε

can be expressed as

ε

= ε

− i σ

ω + Z

0

s( τ ) d( τ )

1 + i ωτ , [5]

where σ

and ε

are the material conductivity and permittivity at lower and higher frequencies, respectively.

From Eq. [4], the real part of the permittivity, ε

, can be derived as

ε

= ε

+ Z

0

s( τ ) d( τ )

1 + ω

τ

, [6]

FIG. 2. Relative permittivity of R40 clay suspension (data points) and fit from CONTIN (solid line).

FIG. 3. Distribution of relaxation times versus frequency for TiO2against Tiron content.

where s( τ ) , σ

, and ε

can be deduced from a specific proce- dure, CONTIN (11), involving a least-squares approximation of the data with an added quadratic form, to ensure that the cal- culated values are the most representative of the system being tested.

By applying Provencher’s approach, it is possible to obtain a very good fit to our data points. An example of such a fit is presented in Fig. 2 for an R40 clay suspension containing 0.35%

Tpp. The calculated distributions of relaxation times versus fre- quency are given in Figs. 3–5 for TiO

, R40, and C4 clays, respectively. In general, three or four peaks are observed, which can overlap when the dispersant quantity varies.

The TiO

spectra, which are composed of three reduced peaks at lower Tiron content (Fig. 3), become progressively more dif- fuse but accentuated under the addition of dispersant. For R40, the spectrum is composed of three distinct peaks (Fig. 4). When the Tpp quantity increases, the peak positions are shifted to

FIG. 4. Distribution of relaxation times versus frequency for R40 clay against Tpp content.

FIG. 5. Distribution of relaxation times versus frequency for C4 clay versus Tpp content.

higher frequencies. For C4 (Fig. 5), a series of three peak po- sitions is observed, in frequency ranges similar to R40 curves.

Under the Tpp addition, the lower frequency peak is slightly shifted and the highest frequency peak is significantly moved to the highest frequency, while s( τ ) becomes more narrow and accentuated. For the central frequency region, a large small peak is progressively changed into two more accentuated peaks.

The TiO

rheology is changed by the Tiron addition. In Fig. 6, the consistency (K ) presents a minimum value at 0.4% of Tiron.

For R40 clay (Fig. 7), K values decrease with Tpp addition, and for C4 suspensions (Fig. 7), K presents a minimum value for 0.75% of Tpp.

Chemical analyses of suspension supernatants for TiO

(Fig. 8) show a constant increase in Tiron adsorption, up to 0.7%

of Tiron added. For C4 clay (Fig. 9), the variation of sodium and phosphate adsorbed on surfaces against the Tpp added is accen- tuated above 0.75% of Tpp.

FIG. 6. Consistency (K ) parameter against the Tiron content for TiO2.

FIG. 7. Consistency (K ) parameter against the Tpp content for R40 (circles) and C4 (squares).

FIG. 8. Tiron quantity adsorbed on TiO2surface versus Tiron added.

FIG. 9. Sodium (squares) and phosphorus (circles) quantities adsorbed on clay surfaces versus the Tpp added.

DISCUSSION

A large global dielectric relaxation process was recently ob- served with colloid (12) and clay (13) suspensions, in the range 1–500 MHz. For clays, a pH influence was also pointed out (13).

In this study, in the same frequency range, we instead observed a group of individual phenomena which should correspond to more detailed contributions of the global relaxation process.

In the case of the TiO

oxide, it appears that dielectric spec- tra are combined with rheological results, shown in Fig. 3 and Fig. 6, respectively. This oxide is pure rutile phase, with the most well-known and simplest surface compared to clay surfaces.

Correspondingly, the s( τ ) distribution is composed of a large and diffuse spectrum. It is related to the surface of TiO

, which presents different crystal surface types exposed to the aqueous solution (14), where only two active site types, ≡≡ TiOH

and

≡ ≡OH

, were proposed (15), the former type being subject to chemisorption.

At lower Tiron quantities (0.1%) the very small and almost individual peaks of s( τ ) correspond to partial active site oc- cupancy. Above that dispersant quantity, the adsorbed Tiron in- creases linearly (Fig. 8), which means a progressive surface cov- erage. At 0.4% Tiron, s( τ ) peaks overlap and the consistency is at its minimum value. For higher Tiron contents (0.7%), the sur- face coverage is high and s( τ ) peaks become more continuous and accentuated. Simultaneously, the characteristic frequency increases with the suspension consistency, which means a high binding level of surface species. At higher Tiron quantities, a contribution to the suspension structuring should not be avoided.

TiO

has a rather simple surface compared to natural min- erals, the surface of which is often more complex. R40 clay is composed of kaolinite with one site group, ≡≡SOH, identified as A1–OH at particle edges (16), where phosphate anions from Tpp are most probably bounded. Na cations are physically ad- sorbed in association with water molecules on ≡≡XH surface sites, which can be assimilated to the edge of silica layers, (17) and on basal surfaces (18). This surface characteristic favors a specific s( τ ) distribution with three distinct peaks (Fig. 4).

The increase in the dispersant quantity shifts the position of the intermediate and higher frequency peaks toward the higher frequencies, and their intensities increase. Correspondingly, the suspension consistency decreases (Fig. 7).

The more complex surface of C4 clay, containing kaolinite and illite minerals, is due to some specific surface sites. The 2 : 1 layer-type clay minerals (illite) add to the active site types of kaolinite an additional surface hydroxyl group, ≡ ≡ TOH (19, 20).

Otherwise, to take into account the heterogeneous surface of il- lite, two kinds of surface sites, ≡≡S

OH and ≡ ≡S

OH, with differ- ent surface acidic constants were also suggested (17). This more complex surface results in a multiple s( τ ) spectrum (Fig. 5), with a significant change in the peak intensity and position of inter- mediate and higher frequencies under the dispersant addition. A connection with the consistency (Fig. 7) is made considering

that the minimum value (for 0.75% Tpp) corresponds to the observation of four well-separated and accentuated peaks.

For C4, a correlation is also found on Fig. 9, since the ad- sorption rates of phosphate and sodium ions increase with about 0.75% Tpp added. This means that phosphate anions, which form inner-sphere complexes, SOM

, at ≡ ≡SOH or ≡≡TOH sites on the edges of alumina layers, and sodium cations, attracted on basal surfaces and ≡≡XH groups at edges of silica layers, reduce the apparent charge of particles, increasing the global structural linkage of the suspension.

CONCLUSION

The global dielectric relaxation process from clay concen- trated suspensions, in the range 1–200 MHz, is composed of three to four particular phenomena. The aspects of dielectric spectra are related to the rheology of the suspension and there- fore to adsorbed species quantities at specific surface sites on surfaces. Information at the microscopic scale from the dielec- tric dispersion appears to be connected to macroscopic behavior, the rheology of concentrated suspensions.

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