clay particle sizing by electrically- induced birefringence · clay particle sizing by...

Clay Minerals (1982) 17, 313-325

C L A Y P A R T I C L E S I Z I N G BY E L E C T R I C A L L Y - I N D U C E D B I R E F R I N G E N C E

D. M. O A K L E Y AND B. R. J E N N I N G S

Electro-Optics Group, Physics Department, Brunel University, Uxbridge, Middlesex UB8 3PH

(Received 1 November 1981; revised 28 January 1982)

A B S T R A C T: Under the influence of a pulsed field, dilute clay sols become birefringent as the particles undergo orientational order. The rate of decay of the birefringence on removal of the field is characteristic of the particle geometry. Measurement of the decay rates under two specific experimental conditions provides sufficient information from which the particle-size distribution can be evaluated in terms of a two-parameter function. Experimental data are reported and analysed in terms of a log-normal distribution of particle sizes for attapulgite (rods), kaolinite (discs) and halloysite (ellipsoids) sols and compared with success to electron microscopic data. The ability of the method to determine size distributions in terms of the major dimensions of the clay particles, rather than those of the often used equivalent sphere, is highlighted.

I N T R O D U C T I O N

Knowledge of the size and size distribution of clay particles in a sol is of extreme importance both in the commercial utilization of the minerals and during the preparat ion and segregation of fractions from the raw material. The ability to obtain such information with extreme rapidity and, if possible, within the processing environment, is doubly beneficial.

A method of rapid particle sizing has been developed in this research group which appears to have the aforementioned properties and to be especially suited to the sub-micron size range. Furthermore, if the predominant particle shape is known, the sizing can be expressed directly in terms of the major particle dimensions without the limitation of expressing dimensions in terms of equivalent spherical diameters, as is commonplace with techniques based on particle settling velocities. As the method has greater sensitivity with particles of increasingly anisodiametric form, it is especially suitable for the analysis of clay sols. In this paper, the principles of the method, the experimental procedures and representative data on rod-like, disc-like and ellipsoidal clay minerals are given.

The basis of the method comprises the recording of the transient changes in the optical birefringence induced in the clay sol when subjected to one or more short-duration electric pulses. Analysis of the rates of change leads directly to information on the size of the dispersed phase. Details are as follows. The majori ty of mineral particles have an anisotropic structure which is evidenced in varying optical and electrical polarizabilities along each of the particle major axes. In dilute suspension, the dispersed particles adopt a random array. The optical anisotropy of the individual particles is thus averaged over all orientations and the bulk dispersion appears isotropic. When some degree of orientational order is imposed on the particle array, the bulk sol partially exhibits the anisotropy of the individual particles. A sensitive indicator of optical anisotropy is the birefringence of the

�9 1982 The Mineralogical Society

314 D. M. Oakley and B. R. Jennings

suspension. This can be conveniently measured by placing the sample between a crossed pair of polarizers and measuring the intensity of light penetrating the system. Order is imposed by applying a short-duration, high-voltage electric pulse across the sample. This couples with any permanent or induced dipole moment in the clay particles. By applying the field as a pulse, a transient birefringence (Fig. 1) is induced in the sample resulting in a transient change in the transmitted light. Initiation of the pulse is accompanied by a gradual increase in detected light level up to a steady equilibrium condition in the field. Termination of the pulse results in particle disorientation under Browian disorienting forces, leading to a decay of the birefringence at a rate which is characteristic of the size and shape of the particles in their viscous medium. It is this decay rate which is utilized herein.

Two facets of the decay require highlighting for an appreciation of the method. First, for a monodisperse suspension, the birefringence decay is a single-component monoexponen- tial function, depending directly on the rotary diffusion coefficient (D) of the particles. Such a coefficient D can be related directly to the particle size for rods, discs, ellipsoids and spheres via Perrin's (1934) equations. With a polydisperse suspension, all composite particles contribute to the multiexponential decay which can be described by the equation (Benoit, 1951)

An = ~ (AnoieX p -- 6Dit ) (1)

where An is the birefringence at any time t after the termination of the pulse for which t = 0. The in-field birefringence at t = 0 is An o and the subscript i indicates the composite species of particle present. In principle, it ought to be possible to deconvolute the decay data and construct the complete distribution of particle sizes from such information. In practice, perfect experimental data would be required. Theoretically, one needs less than 1% noise in the data if even as few as three particle components of widely separated sizes are to be discriminated (Lanczos, 1957). This is an impractical limitation to overcome. The most accurate data in an experimental decay transient are those close to t = 0. Hence, the

FIG.

Induced Birefringence

An

Applied Field

E

PRE-FIELD REGION

ORIENTATION REGION

t = 0 time t

DECAY REGION

a

b t ime t

1. Idealized transient birefringence response of a mineral sol. (a) transient induced birefringence; (b) applied field.

Clay particle sizing 315

practice is to take the initial slope of a plot of the logarithm of the normalized birefringence with time. Such a slope (S) is related directly to - 6 (D), with (D) an average D detemined by the experimental conditions.

Secondly, the characteristics of the applied field pulse are important. Assuming that the pulse is of sufficient duration to allow all particles to align, then the field amplitude can be used to advantage. Smaller particles require a larger amplitude field to produce the same degree of orientation as their larger neighbours. This will be reflected in the ensuing decay. Hence, the experimental S and (D) will vary with the strength of the applied field. Furthermore, as the permanent and induced dipole moments involve different dependences on particle size (Fredericq & Houssier, 1973; Mandel, 1961) it is advantageous to isolate these two orientation mechanisms. This is readily performed by applying pulses of high- frequency sinusoidal field rather than d.c. bursts. In such cases, only induced polar mechanisms can contribute as particle dipolar orientation cannot follow the polarity changes in the high-frequency field (Debye, 1929).

For the majority of clay suspensions, a monomodal, two-parameter function is sufficient to describe most particle-size distributions. A log-normal function is commonly employed. To characterize this, only two elements of experimental data are required and these are obtained by recording S and hence (D) under two closely defined conditions. These are from birefringence data using (a) a single low-amplitude, high-frequency field burst, and (b) a single burst of high-amplitude saturating field. The terms 'low' and 'high' are delineated as follows. With increasing applied field, the steady birefringence amplitude increases linearly with E 2 at 'low' E (Fredericq & Houssier, 1973). It then gradually deviates from this quadratic behaviour by an ever increasing degree as the orientation tends towards complete parallel alignment of the particles in the bulk sol. This is the 'saturation' or 'high' field limit.

In this paper, data are presented for the three aqueous clay mineral sols, attapulgite, halloysite and kaolinite. These represent rigid particles of rod, prolate ellipsoid and disc-like shapes, respectively. Size distributions are evaluated for a log-normal spread of major dimensions and compared with electron microscopic data.

E X P E R I M E N T A L

Materials

The attapulgite, halloysite and kaolinite samples were obtained as washed powders of fine mesh size. They were dispersed in doubly-distilled, deionized water using a high-speed commercial blender. The resulting suspensions were left undisturbed for two days to allow the coarser material to settle. The turbid supernatant was then removed, diluted and introduced directly into the birefringence cell. Dilution was to the order of 10 -4 g m1-1. This was for convenience rather than for necessity, to indicate the sensitivity of the method. Simultaneously, samples were removed for evaluation in the electron microscope.

Apparatus

A schematic representation of the electric birefringence system is given in Fig. 2. A lowpower helium-neon laser is the source of a well-collimated beam of red light (633 nm wavelength) which passes through a high quality Glan-Thomson polarizing prism and enters the sample cell. This is 5 cm long and holds 3 ml of sample suspension in the 2.0 mm interspace between two electrodes mounted either side of the light path. The system is


Oscilloscope x/y Recorder

Microcomputer

-I Printer

Disk Unit

Transient recorder ,ow--q

, dtage I ulser i

H.V. pulse ] former

FIG. 2. Schematic representation of the apparatus. Optical components: 1 = low-power laser; p = polarizer; c = sample cell; q = quarter-wave plate; a = analyser; p.m. = photomultiplier. H.V. =

high voltage.

arranged with the inter-electrode field horizontal and the azimuth of the linearly polarized incident light at 45 ~ to this. When the sample is birefringent, elliptically polarized light leaves the cell, passes through a quarter-wave plate positioned in parallel azimuth to that of the initial polarizer, and is incident on a second polarizing prism. This is oriented to be 'crossed ' (or nearly so) with the initial polarizer. Any light penetrating this component is detected by a photomultiplier whose output can be related to the birefringence of the test sample.

Two pulsed voltages are applied successively to the cell electrodes. The first constitutes a low-voltage sinusoidal field of high frequency (i.e. f ~ c~). The second is a saturating field (i.e. E ~ ~) . With clay particles in the sub-micron size range, these fields are typically 100 V cm -1 at 10 kHz frequency and 6 kV c m - ' d.c. or a.c., respectively. In both cases, the pulse durations range between 3 ms and 1 s, depending upon the clay sample.

The photomultiplier output is fed directly to a transient recorder from whence it can be directed to an oscilloscope, chart recorder or microcomputer for visual inspection, hard copy or direct analysis, respectively. The last mentioned is essential for complet e , rapid size an~ysis . The appropriate software has been written so that the system evaluates the initial \ slopes for each of the two transients and calculates the corresponding experimental averages of the rotary diffusion coefficients. These may be referred to as ( D I ~ ) and

(De~) for the low-intensity a.c. field (subscript f ~ ) and saturating intensity field (subscript E ~ ) conditions respectively. The programme operates on a choice of particle shapes from ' rod ' , 'prolate ' or 'oblate ellipsoid', ' thin disc' or 'sphere ' . In the case of rods

Clay particle sizing 317 and ellipsoids an axial ratio must be given, although the ultimate size data are not too dependent on the value chosen (see later). The microcomputer then evaluates the two-parameters of the log-normal distribution which is displayed graphically by a printer. The calculation and display time is of the order of one minute.

T H E O R E T I C A L R E S U M E

The measured birefringence An is defined as the difference in refractive index parallel and perpendicular to the applied field direction (E) within the sample at any instant. When the polarizer and analyser are crossed, the intensity of light penetrating the optical system, and hence the photodetector output, is proportional to (An) 2 (Riddiford & Jerrard, 1970). A slight off-set of the analyser gives increased detection sensitivity, but involves a more complex analysis (Fredericq & Houssier, 1973) to evaluate An. In the following theoretical discussion it is assumed that the photomultiplier output is transposed into birefringence values (An) prior to subsequent analysis. This can be incorporated in the microcomputer software (see above). The decay of the birefringence transient has the form of equation (1) from which the initial slope S and hence ( D ) are obtained directly.

The size distribution is conveniently expressed in terms of the major particle axial dimension l. For a total number concentration N particles per unit volume, of which dN have major dimensions in the range I to (l + dl):

dN = Nf(/) dl.

For a log-normal distribution (see Hastings & Peacock, 1975):

1 1 e x p [ 1 { ln(I/m)} 2] f(0- ---'-g-- with

(2).

f o f(/) dl = 1 (3).

Here m and o are the positioning and breadth factors of the distribution, respectively. The first-mentioned is the median of the distribution if this is allowed to extend over the complete size range 0 < 1 < oo. In a series of theoretical papers (Morris et al., 1978a,b,c; Jennings & Oakley, 1982), expressions have been developed for the experimental (D ) in terms of m and tr (and the equivalent two parameters for the other distribution functions) for various rigid particles of discrete geometry. These expressions are summarized in Table 1. In each case, the factor K = kT/Trrl, where k is the Boltzmann constant. T the absolute temperature and r/the solvent viscosity. The function ~(r) depends upon the axial ratio r which is always taken as the ratio of the major-to-minor particle dimensions. The function ~(r) varies with the molecular model, but is constant for a chosen model and sample. It has been derived from Perrin's (1934) equations for rotary diffusion and has the following forms.

For a sphere,

For a rod,

~(r) = 1 (4).

318

For a disc,

For a prolate ellipsoid,

~(r) :

For an oblate ellipsoid

D. M. Oakley and B. R. Jennings

O(r) = 3 (In 2r --0.5) (5).

(r) = 3 ~r/4 (6).

2(r 4 - 1) r(r z - 1) vz (7).

3r 3 r4)" [ 2 - r 2 1) 1/2 --1] O(r) = 2(i----- [ �9 arc tan(r 2 -- (r 2 ~ ]~T/2 (8).

In the derivation of the expressions given in Table I, the rods are assumed to be of constant diameter, the discs of constant thickness and the ellipsoids of constant axial ratio.

For all models, it is seen that the ratio

(D)Eoo/(D)ioo = exp (6a 2) (9)

and this is the basis for the evaluation of o. Once determined, this value is used with either experimental value of (D) to get m.

TABLE 1. Experimental rotary diffusion coefficients expressed in terms of the log-normal distribution parameters for the major particle dimensions.

Model (D)/oo (D)e ~

Sphere m~ my exp )

Rod K~(r)m3 exp (-- V ) K~(r)~ exp ~-~-[302~]

Disc K~(r) exp ( - r n 3 1~ --~z ) K~(r)exp(-3a~2)m3 k

Kfk(r) ( _ ~ ) K~(r) exp (_ ~ ) Ellipsoid ~ exp m3

The experimental procedure is as follows. The sol is placed in the cell and a low-voltage pulse of sinusoidal voltage ~ 10 kHz frequency is applied to the electrodes. The transient photomultiplier response is captured in the transient recorder and observed on the oscilloscope as a check for regular behaviour. It is then passed in digitized form to the microcomputer where S and (D)io~ are determined. If need be, the voltage can be increased and a second low field applied to verify that the birefringence is in the region of quadratic dependence on E, thereby constituting a true 'low' field condition. To measure (D)eoo, a further pulse of much higher voltage is then applied. The transient response is visually inspected and passed to the computer. True 'saturating' field conditions can be verified by increasing the field strength until no further increase in birefringence amplitude is obtained, thereby indicating complete particle alignment. The initial slopes of the low-


and high-field transients are then evaluated in the microcomputer. On receipt of instruction regarding the model to be assumed and the axial ratio (where appropriate), the computer calculates the relevant m, tr and mean size whilst a printer displays the distribution directly.

R E P R E S E N T A T I V E D A T A

Halloysite--prolate ellipsoids

Halloysite is a mineral which is used commercially in the manufacture of fabrics, pharmaceuticals, pesticides, inks and cosmetics. The size of the particles is of importance in these applications. Halloysite particles usually occur as tubes, the length of which depends upon the extraction and handling procedures. The broken linear fragments are well represented as prolate ellipsoids. The two birefringence transients obtained under the low- and high-field conditions are shown in Fig. 3, from which the notably faster decay relaxation in response to the high field is evident. This is a result of the smaller particles achieving greater orientation in the more intense field and thus influencing the observed birefringence to a greater degree. F rom these two transients, ( D ) / ~ = 25 s -1 and (D)E~ = 160 S -1 were determined. Hence, the full-line distribution shown in Fig. 4 was generated via the evaluation of m = 222 nm and a = 0.55 for the major ellipsoid axis. The mean of the distribution, given by m (tr2/2), has the value 259 nm. For these calcu- lations r = 5 was assumed.

FIG. 3. Low- and high-field transients for a haUoysite sol. c = 2.5 x 10 -4 g m1-1. In (A) a low field of 150 V cm -1, 500 Hz, and 50 ms duration was used. The high field for (B) was 5 kV cm -1 and

1 ms duration.


z

60

50

40

30

20

10

�9 " . equivalent sphere

/ , / ,

1

l i /

I

i �9 I

: I

i l , : l : l

i / i

0.1 0 - 2

. , ~ at e ellipsoids

L I 0 . 3 0 . 4 0 . 5 0 . 6 0 7 0 . 8

Particle Size (~tm)

FIG. 4. Log-normal distribution for halloysite particles. Full and broken lines for prolate ellipsoids with r = 5 and r = 3 respectively. The dotted line indicates the equivalent sphere

distribution. The histogram was calculated from electron microscopic observations (see inset).

From Fig. 4 we note three points. First, there is good agreement between the electron microscope data (on 241 particles) and birefringence data in the ellipsoidal nature of the particles, and the breadth, position and type of the distribution. Such a comparison between the 'wet' birefringence data and the 'dry' electron microscope histogram is especially meaningful in this case as halloysite is a non-swelling clay. Second, the choice of axial ratio is not critical, as is shown for the broken line for which r = 3 was assumed. Whereas r = 5 provides the best fit, r -- 3 is quite acceptable. Third, had the shape of the particles been ignored and the data treated simply in terms of the 'equivalent sphere' of


equal volume, then spheres with a mean diameter of 148 nm would have been indicated. Although such a representation is common with commercially available sizing instruments, it is clearly an inadequate alternative with extended clay particles.

A ttapulgite--rods

Attapulgite particles occur as long thin needles or rods, which have narrow longitudinal channels in their interior and along their surface. The material is used commercially as an

100

80

60 E

40

20

equivalent sphere : . ~

~ gite rod

3 2 Particle Size (/~m)

FIG. 5. Distributions for attapulgite rods, with constant diameter of 50 nm. Dotted line indicates the equivalent sphere. The histogram was generated from electron microscopic data (inset).


industrial absorbent, catalyst carrier and molecular filtrant, for which the particle size is of importance.

The rod nature is confirmed in the electron micrograph inset in Fig. 5. This figure also shows the histogram of approximately 270 particle lengths alongside the log-normal distribution calculated from the transient birefringence data. A low-intensity field pulse of 100 V cm -~ at 103 Hz frequency and 1 s duration was used, from which (D)1o~ = 1-4 s -1 was determined. A sufficiently high-intensity pulse was of 4 kV cm -~ amplitude and 7 ms duration from which (D)Eo~ = 24.5 s -~ was evolved. With a rod diameter of 50 nm, the distribution with rn -- 1.10 pm, tr = 0.71 and the mean = 1.43 pm was evaluated. Here again, the agreement is most satisfactory.

With such highly extended rod-like particles, the use of an 'equivalent sphere' model is fatuous. The data correspond to the impractical situation of a distribution with a mean diameter of 223 nm (Fig. 5).

Kaolinite--discs

Kaolinite is a layer-silicate mineral which readily cleaves into flaky plate-like particles of ill defined geometry. The plates may be thin and approximate to discs when well separated. Alternatively, they may appear as thick discs, better represented by oblate ellipsoids. Such particle morphology owes its origin to the basic bilayer lattice structure of the mineral. Single sheets of silica tetrahedra overlap inverted sheets of alumina octahedra to form the bilayers which are naturally of infinite lateral extension (Gruner, 1932). During extraction, the material cleaves and cracks into the ill-defined disc-like particles. The mineral has had extensive commercial exploitation in the paper, paint, pottery and refractories industries where the particle sizes are of significance.

The thin-flake nature of the present sample is seen in the inset electron micrograph in Fig. 6, along with the histogram of particle maximum diameters on some 350 particles. For thin discs, no assumption need be made of the axial ratio to evaluate the size distribution from birefringence data. Experimentally, the low-field condition used was with pulses of 100 V cm -1 amplitude at 1.5 kHz modulated frequency and for a duration of 15 ms. A value of (D)io~ = 3.3 s -1 was obtained. A high field pulse of 3 ms duration at 11 kV cm - ' amplitude yielded (D)eo~ = 320 s -~. From these, the distribution of disc diameters shown in Fig. 6 was obtained. This corresponds to m = 183 nm, a = 0.52 and a mean diameter of 209 rim. The agreement between the electron microscope histogram and the birefringence log-normal size distribution is impressive. For comparison, the equivalent spherical diameter distribution is shown in Fig. 6.

C O N C L U S I O N S A N D C O M M E N T S

The aforementioned samples were chosen because they consisted of particles of well-defined morphology, representing the three major geometric shapes encountered in clay mineralogy. Although the data are not presented here, studies have been made of sepiolite, montmorillonite, imogolite and hectorite sols with the same degree of success. It would thus appear that analysis of the transient decay of electrically-induced birefringence in clay sols provides a promising means for particle-size distribution analysis. By analysing the decay characteristics under two specific experimental conditions, two-parameter distribution functions can be used to describe the particle size range. As a log-normal

Clay particle sizing 3 2 3

100

80

E 6 0 s

40

20

�9 . equivalent sphere

2

/

\

oi,c

I I 0.1 0.2

I I - - ] - ~ 0 . 3 0 . 4 0 . 5 0 . 6

Particle Size (#m)

FIG. 6. Size distributions for kaolinite particles, treated as thin discs. Alternative analysis in terms of a sphere model is shown by the dotted curve. Electron micrograph (inset) and related

histrogram also shown.

distribution is often used commercially, it has been used herein. The data on rod-, ellipsoid- and disc-like clays indicate the suitability of this distribution for experimental samples and the ability of the birefringence method to characterize monomodal size distributions in terms of it. The procedure is not limited to this distribution however. In principle, many arbitrary field conditions can be used to generate the points of a multiparameter, multimodal distribution. Future theoretical and experimental studies are aimed at this


objective. The success of the current determinations encourages our endeavours to this end.

Clay particles are generally highly anisodiametric. Long rods, laths, needles, flaky discs and ellipsoids are frequently encountered. Currently, many commercial particle sizes for use with colloids only provide information on an average particle size which, moreover, is that o f a sphere of equivalent particle volume, or hydrodynamic volume. This is inadequate for clay minerals. Transient electric birefringence size analysis allows the experimenter to use realistic models in the analysis and to give reliable size and size distribution data.

When it is appreciated that the rates of the birefringence changes rather than the absolute values of An are analysed, a further advantage of the method is apparent. A mixture of two or more minerals may be studied. Although particles of the same size (or rotary diffusion coefficient) may not give rise to the same birefringence amplitude, their contribution to the birefringence decay will be the important factor (of. equation (1)). Hence, they will be analysed by the apparatus and weighted into the distribution. If the various species are of different shape however, the 'equivalent sphere' model is best used. The method thus has potential not only for the analysis of well-beneficiated clays, but also for less pure materials. It is o f interest to note that this consideration is also applicable to sols containing flocs and aggregates which also contribute to the birefringence decay and can thus be detected.

Finally, the optical components of the system can be made in a compact form which can be used in factory and field applications. The use of the method for routine quality control is indicated. Current studies are considering the development of an apparatus for specific use with eluting columns of slurries and sols of different concentrations.

ACKNOWLEDGMENTS

D.M.O. thanks the S.E.R.C. for the award of a post-graduate studentship whilst both authors thank the Department of Physics for facilities provided and Mr D. Waterman for discussions and general help with the apparatus. The attapulgite was donated by Dr J. Chambers of Steetley Minerals Ltd., the halloysite by Dr BI Neumann of Laporte Industries and the kaolinite by Dr L. Gate of English China Clays Ltd.

REFERENCES

BENorr H. (1951)Ann. Phys. (Paris) 6, 561. DEBYE P. (1929) Polar Molecules. Reprinted in 1958 by Dover Publications, New York. FREDERICQ E. &; HOUSSIER, C. (1973) Electric Dichroism and Electric Birefringence. Clarendon Press,

Oxford. HASTINGS N.A.J. & PEACOCK J.B. (1975) Statistical Distributions. Butterworths, London. JE~rmNGS B.R. & OAKLEY D.M. (1962) Applied Optics 21, 1519. LANCZOS C. (1957)AppliedAnalysis. Pitman, London. MANDEL M. (1961) Mol. Phys. 4, 489. MORRIS V.J., FOWERAKER A.R. & JENNINGS B.R. (1978)Adv. Mol. Relxn. Int. Proc. 12, 65. MORRIS V.J., FOWERAKER A.R. & JENNINGS B.R. (1978)Adv. Mol. Relxn. Int. Proc. 12, 201. MORRIS V.J., FOWERAKER A.R. & JENNINGS B.R. (1978) Adv. Mol. Relxn. Int. Proc. 12, 211. PERRIN F. (1934) J. Phys. Radium 5,497. RIDDIFORD C.L. & JERRARD H.G. (1970) J. Phys. D. (Appl. Phys.) 3, 1314.

RESUME: Sous l'influence d'un champ 61ectrique pulse, des suspensions dilu6es d'argiles deviennent bir6fringentes au fur et it mesure que les particules s'orientent. La vitesse de diminution de la bir6fringence apr6s coupure du champ est caract6ristique de la g6om&rie de la

Clay particle sizing

particule. La mesure de ces vitesses sous deux conditions exp6rimentales sp6cifiques fournit suffisamment d'informations pour 6valuer la distribution de tailles des particules sous forme d'une fonction ~ deux param&res. Des valeurs exp6rimentales sont pr6sent6es et analys6es sous forme d'une distribution log-normale des tailles de particules pour des suspensions d'attapulgite (b~tonnets), de kaolinite (disques) et d'halloysite (611ipsoides); ces r6sultats sont eompar6s avec succ6s/t des mesures par microscopic 61eetronique. On insiste sur la possibilit6 de la m&hode de d&erminer des distributions de taille en tenant compte des dimensions majeures des partieules argileuses alors qu'usuellement on se contente du mod61e de la sph6re 6quivalente.

K U R Z R E F E R A T : Unter dem Einflul3 eines pulsierenden elektrisehen Feldes werden verd/innte Tonsuspensionen doppelbrechend, wenn sich die Teilchen orientieren. Aus der Geschwindigkeit der Abnhame dieser Doppelbrechung beim Abschalten des elektrischen Feldes bei zwei unterschiedlichen Versuchsbedingungen kann die Geometric der Teilchen bzw. die Teilchengr6~nverteilung als Funktion zweier Parameter abgeleitet werden. Die experimentellen Datan f'tir Sole yon Attapulgit (Leisten), Kaolinit (Scheiben) und Halloysit (Ellipsoide) werden mitgeteilt, auf der Basis einer log-normalen Korngr6Benverteilung ausgewertet und mit elektronenmikroskopischen Werten verglichen. Die F~ihigkeit der Methode, dir Korngr613enver- teilung auch bei von der Kugelgestaltabweichenden Teilchen zu bestimmen, wird hervorgehoben.

R E S U M E N : Bajo la influencia de un campo el6etrico pulsado las suspensiones diluidas de areiUas se hacen birrefringentes como consecueneia de la orientaci6n preferential de las partieulas. La velocidad de disminuci6n de la birrefringencia, cuando se elimina el campo el6ctrico, depende de la geometria de las particulas. A partir de medidas de estas velocidades para dos condieiones experimentales especifieas, es posible determinar la distribuci6n de tamafios de particula en t6rminos de una funci6n con des par/tmetros. Los resultados experimentales expresados en forma de distribuci6n logaritmica de tamafios de particula, para suspensiones de palygorskita (flbras), caolinita (discos) y haloisita (elipsoides), concuerdan con los obtenidos por microscopia electr6nica. El m&odo permite obtener distribuciones de tamafio en t6rminos de las dimensiones mayores de las particulas de arcillas, lo cual compara favorab- lemente este m6todo con los m/ts usuales en los que el tamafio de particula se obtiene eomo di~imetro de la esfera equivalente.

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