particle size

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Particle Size Distribution Measurement fromMillimeters to Nanometers and from Rods toPlateletsP. BowenPublished online: 05 Feb 2007.

To cite this article: P. Bowen (2002) Particle Size Distribution Measurement from Millimeters to Nanometers and fromRods to Platelets, Journal of Dispersion Science and Technology, 23:5, 631-662, DOI: 10.1081/DIS-120015368

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Particle Size Distribution Measurementfrom Millimeters to Nanometers andfrom Rods to Platelets

P. Bowen

Powder Technology Laboratory, Materials Department, Swiss FederalInstitute of Technology Lausanne (EPFL), 1015 Lausanne, SwitzerlandE-mail: [email protected]

ABSTRACT

There are many instruments for particle size distribution (PSD) measurement, each

using a particular physical phenomenon to define the size (e.g., sedimentation, laser

diffraction). Particle size distribution measurement although important, most people

want it done as quickly as possible. This paper will compare rapid methods [ laser

diffraction and photon correlation spectroscopy (PCS)] with sedimentation

techniques and image analysis.

Nanometer powders (primary particles 1050 nm) have been studied using,

photocentrifuge, PCS, and x-ray disc centrifuge. The median diameters are very

consistent for all instruments for narrow size distributions at around 20 nm but

a divergence of results for the 50 nm range when distributions are broader.

Comparison with image analysis for a spherical silica (50 nm) illustrates the

accuracy possible in this domain.

In the 0.1 to 5 micron range examples showing how the width and size range of

the particle size distribution of typical commercial aluminas and calcites, can

influence greatly the reported values from different instruments will be presented.

The resolution and accuracy of PSD measurement for laser diffraction has been

investigated using spherical glass beads ranging from 70 to 400 mm, sieved into fivefractions. Particle size distributions measured by image analysis are compared with

the laser diffraction results.

The shape also has a profound effect on the interpretation of data provided by

commercial instruments which ordinarily assume a spherical shape. Results for

plate and rod like particles will be presented and the most appropriate method for

the shapes suggested.

631DOI: 10.1081/DIS-120015368 0193-2691 (Print); 1532-2270 (Online)Copyright # 2002 by Marcel Dekker, Inc. www.dekker.com

JOURNAL OF DISPERSION SCIENCE AND TECHNOLOGY

Vol. 23, No. 5, pp. 631662, 2002

2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.

MARCEL DEKKER, INC. 270 MADISON AVENUE NEW YORK, NY 10016

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INTRODUCTION

The aim of the current paper is not to be an exhaustive

review of all methods but to share the experience gained

in our laboratory over the past 1015 years which may

then help the reader in their choice of particle sizing

method for particles in the nm to mm range. Where other

work in the literature is relevant it has been cited in an

effort support our general findings and conclusions. We

shall also try and point out in which domains we have

found the methods used in our labs to be particularly well

adapted and where one must take great care in simply

interpreting the data provided by various commercial

instruments. We shall not restrict ourselves to particles

with spherical shapes but also approach the issue of

anisotropic particlesrods and platelets in particular.

We shall however restrict ourselves to inorganic particles,

and not include comparisons based on latex spheres, as

the world of organic based particulates bringing often

their own particular problems or simplifications quite

different to inorganic powders. There will be a short but

concise first section on the general definitions of

diameters and distributions which will allow people

new to the field to follow the more detailed discussions

without having to refer to basic texts for an introduction.

Why measure particle size distributions? In industrial

as well as everyday life materials are often found as

powdersfrom coffee granules, washing powder, house-

hold dust, drugs and cosmetics, to ceramic and metallic

powders. The powder properties are often influenced by

the particle size; raising questions such asdoes the

powder flow or how quickly does it dissolve? (sugar is a

good household example). In one of the best monographs

on particle size measurement,[1] Allen mentions a survey

made at Du Pont by Davies and Broughton on 3000

products where they found that 80% involved a powder at

some stage of the manufacture. This highlights the

importance of powder technology in the modern indus-

trial world. The study of powder technologya field in

its own rightis heavily dependent on our capability to

measure the powders particle size and its distribution.

The particle size distribution of a powder is a key

characteristic that influences its properties, handling and

domain of application. Some examples are; the covering

power and color quality of cosmetics and paints,[2] its

packing behavior,[3] reactivity or sinterability of ceramic

and metallic compacts.[46] If we take the example of

advanced ceramic materials, in order to increase reacti-

vity and minimize the final grain size, which consequently

influences the properties of the final products,[7] the

ceramic powders have more and more particles in the

sub-micron range. The particle size and distributions will

have an influence on which processing routes may be

suitableslip casting or dry pressingand how the

powder compacts during this process. On firing, the

shrinkage, final density and properties are all influenced

by the raw materials particle size and distribution. So,

the characterization of powder size is clearly important

but particle size and distribution (PSD) measurement on

its own is not enough and the results must be coupled

with other characterization techniques (such as

microscopy, x-ray powder diffraction, surface area

measurement, and chemical composition analysis) to

correctly interpret and use the measured PSD. Often a

PSD measurement is made with the aim of relating the

PSD to a particular property or behavior of a powder and

when choosing a method for the PSD measurement the

application should always be borne in mind.

Different methods for PSD measurement often have

limitations and when these are ignored, correlation with

a particular property of interest and the conclusions

drawn can be erroneous. The aim of this overview is to

familiarize the readers with some of the methods

currently available along with their limitations and to

what degree we can use these methods for absolute or

comparative particle size measurement. Particle shape is

one of the factors that often limits the use of certain

instrumentsalthough comparison of measurements

from instruments using different principles can also

provide information on particle shape. After a brief

introduction to some key definitions for particle

diameters, shapes, and distributions, a brief overview of

current methods will be given before moving onto more

detailed discussions of some specific instruments and

comparison between the instruments for particles from

nanometers to millimeters.

Diameters, Distributions and Shape

All too often when one reads the powder character-

ization section of scientific papers one finds the average

particle size was 2 micronswith no reference to the

method of measurement or distribution base. Figure 1

shows an example of the same distribution plotted as a

number or volume based distribution. The marked differ-

ence shows how important the precise definition of the

average particle size can become.

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Particle Size

There are many different ways of defining a particle

sizefor a sphere we have an unambiguous definition

of diameter and likewise the edge length of a cube.

Most particles we come across in everyday work and

life are unfortunately, rarely spherical or cubic and more

than one dimension may be necessary to describe the

particle. Table 1 lists a number of particle diameter

definitions and some of these are illustrated in Fig. 2.

The most widely used diameters are the equivalent

spherical diameters and particularly the equivalent

volume spherical diameter, dv, which is the diameter

of the sphere which has the same volume as the

particle. A cube of length 1 mm has an equivalentspherical diameter equal to 1.24 mm. Each measuringtechnique measures a certain diameter and for a sphe-

rical shape these sometimes give the same result. For

irregularly shaped particles there will however be an

influence on the assigned size and this should always be

taken into account when choosing the method of

analysis (again bearing in mind the application of

your PSD measurement). The sieve diameter for exam-

ple is the minimum size that can pass through the

square aperture and for irregularly shaped particles will

not necessarily be the same as the Stokes diameter

measured by a sedimentation technique. Irregular parti-

cles can have the same equivalent spherical diameter

but vastly different shapes. For regularly shaped parti-

cles we can also have a distribution in shapes or aspect

ratios (e.g., length to diameter ratio for a cylinder).[8]

Microscopy is a very popular method for shape analysis

as one can identify individual particles and quantify a

shape coefficient. A microscopic examination of a

powder should always be carried out even if the

shape and size are not going to be analyzed quantita-

tively by image analysis. An image of the particles

contained in your powder will very quickly tell you if

Figure 1. Example of the same PSD represented either as a

number or volume distribution.

Table 1

Different Definitions of Particle Diameters[1]

Diameter Symbol Definition

Stokes diameter dst Diameter of free falling sphere which would fall at the same rate as the particle

in a given fluid

Sieve diameter dT Minimum square aperture through which the particle will pass

Volume diameter dv Diameter of the sphere with the same volume as the particle

Surface diameter ds Diameter of the sphere that has the same surface area as the particle

Projected area diameter dA Diameter of the circle which has the same area as the projected area of the particle

Ferets diameter dF Distance between two parallel tangents which touch the outline of the particle

projection

Average Feret diameter dFav Average Feret diameter from diameters measured over all angles between 0

and 180

Maximum Feret diameter dFmax Maximum distance between two parallel tangents which touch the outline

of the particle projection

Minimum Feret diameter dFmin Minimum distance between two parallel tangents which touch the outline

of the particle projection

PSD Measurement from Millimeters to Nanometers 633



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the powder is homogeneous in shape e.g., disc-like or

rod-like or spherical. Irregularly shaped particles such

as the ground calcite shown in Fig. 2(b) is typical of a

ground ceramic powder and is often encountered in the

ceramic industry. With the improvement in the power of

computers over the last 10 years, image analysis

programs have become very powerful and quantitative

data can be obtained from microscopic observations.[8]

The limitations often being linked with sample

preparationoverlapping particlesand the 2D repre-

sentation of our 3D particle.

Shape Factors

There are many ways of describing shape depending

on the regularity of the shape itself.[8] Here we shall

describe two simple concepts, a particles sphericity and

an aspect ratio. For anisotropic particles with a relatively

regular morphology such as a rod or plate one can define

the aspect ratio as the ratio of the major to the minor axis.

For irregular particles, where a simple definition of major

and minor axes is not so clear the ratio between the

Maximum and Minimum Feret diameters (dFmax=dFmin)gives a very good indication of the elongation of a

particle.

Aspect ratio Major axisMinor axis

ordFmax

dFmin1

The shape most often assumed in particle size analysis is

the sphere and one can define how close a particle

approaches a sphere by the use of a sphericity shape

factor. This can be defined as

cw Surface area of a sphere having the

same volume as the particle

Surface area of the particle2

Equivalent Spherical Diameter

Most commercial instruments assume a spherical

shape for data analysis and the result is given as an

equivalent spherical diameter (ESD). The ESD is the

diameter of the sphere that would give the same result as

that observed for the real powder under observation. The

various physical phenomena used in particle size

measurement often show functional variations with

particle shape. Therefore, the ESD measured by sedi-

mentation will not be equivalent to that measured by laser

diffraction for non-spherical particles. The ESD which is

reported by most automatic PSD instruments currently

available will also vary as the aspect ratio of the particles

vary. Jennings and Parslow[9] have computed the varia-

tion of the ESD with the aspect ratio for oblate and

prolate spheroids for the different physical phenomena

used in several commercially available instruments. They

showed from the theoretical calculations that the ESD is

always smaller than the real major dimension of the

anisodiametric particle. There have been many attempts

to determine shape distributions mainly by comparison of

different techniques and when judiciously chosen an

Figure 2. (a) Examples of some diameters for a non-spherical particle (b) typical irregular particlea ground calcite.

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estimation of the aspect ratio and the particle minor

dimension can be made.[10,11]

Distributions and Average Diameters

The powders we deal with everyday are rarely single-

sized or monodispersed and are part of a distribution of

sizes which occur with different frequencies and we have

to choose how to represent this distribution in a concise

and accurate manner. The distribution can be represented

as either a cumulative distribution [Fig. 3(a)] or as a

density or frequency distribution [Fig. 3(b)]each

having its use depending on the information we want

from a graphical representation. The base to which the

distribution is normalized is of great importance and

certain measurement techniques give us directly a

number (microscopy) or weight (sieving) based distribu-

tion. The transformation between different distributions

is not always easy and care should be taken to verify with

what accuracy this can in fact be done.[1]

The average of a distribution is a measure of the central

tendency which is not greatly affected by a few extreme

values in the tails of the distributions. There are several

central tendencies which can represent a distribution and

some examples of these, the mode, median, and mean are

shown in Fig. 3(b). The mode is the value which occurs

most frequently in the distribution and will be the peak in

a frequency curve. The median is the middle value of a

distribution where the total frequency of values above and

below it are equal (i.e., the same total number or total

volume of particles below the median as above it)from

a cumulative distribution curve it can be read directly

[Fig. 3(a)]. The mean value has to be calculated and is the

point about which the moments of the distribution are

equalseveral examples of different mean diameters are

listed in Table 2. For a symmetrical distribution, such as a

normal distribution, the mode, mean, and median coin-

cide but for skewed distributions they differ [Fig. 3(b)].

The manner in which a continuous size distribution is

sampled to provide a frequency distribution has an

important consequences on the accuracy and form of

the frequency distribution.[1] For broad size distributions

a geometric progression should be used e.g., x,2

px, 2x,

2p

2 x, where x is the smallest size interval, du. For

narrower size distributions arithmetic progressions can be

used. The underlying rule is that the resolution of each

class interval should be similar, where the resolution is

defined as the width of the interval divided by the mean

class size. The cumulative distribution, FN(x), for a

number based distribution, is defined in Eq. (3) and can

be represented unambiguously on linear and logarithmic

axes for the particle size.

FN x numer of particles < du

Total number of particles3

where du is the upper particle size of the size interval.

The frequency or density distribution, fN, is defined as

the derivative of the cumulative distribution Eq. (4),

which usually discretized into different size classes, di,

as discussed above. The frequency

fN dFNddN

FN d2 FN d1d2 d1

DFNd2 d1

4Figure 3. Examples of (a) a cumulative distribution and(b) a frequency distribution.




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distribution however can give ambiguous representations

when using a log scale and for comparisons should be

plotted as size (linear scale) vs. the fraction of particles in

the interval, DFN , as recently re-iterated by Sommer.[12]

Many instrument manufacturers make the mistake of

providing frequency distributions as relative % frequen-

cies which can be very misleading when comparing

distributions which do not have the same size classes.

The easiest way to correctly represent and compare PSDs

is using the cumulative representation.

The average of a distribution indicates the central

tendency; the dispersion or width of the distribution is

described by its standard deviation, s the root meansquared deviation Eq. (5). Each standard deviation is

calculated with respect to the central tendency used in the

formula of Eq. (5); in this example, dw ,the mean weight

diameter.

sw fidi dw2

W

s5

where, fi is the frequency particles (as a weight) of that

diameter and W total weight for all of the diameter

intervals.

Distributions can often be represented by mathematical

expressions which describe the whole of the distribution

with the central tendency and the standard deviation.

For a detailed discussion of the normal, log-normal, and

RosinRammler distributions in particle size measure-

ment the reader is referred elsewhere.[1] If the particle size

distribution under investigation does follow a type of

distribution, comparison and transformation from number

to volume distributions are more easily calculated.

Having seen the sometimes frightening number of

possible particle sizes and distributions the question of

which diameter should one use is often asked. As a general

rule, most powder suppliers quote an equivalent sphere

median volume diameter. When dealing with powder

packing the volume distribution is a convenient base.

When we are dealing with agglomerating systems or

milling processes where population balances are often

used, the number distribution is usual. As mentioned in

the introduction the PSD measurement is usually made

with the aim of relating it to a particular property, either of

the powder, process or product. In this case the best base

must be chosen as a function of the correlation sought after.

For example, if you are dealing with a process sensitive to

fine particles, such as the flowability of flour the number

distribution is more sensitive. If it is the strength of

sintered ceramics then it is a small agglomerate population

that determines the critical flaw size and a volume based

distribution will be the most adequate.

CURRENT METHODSA BRIEF

OVERVIEW

There are a vast number of methods and suppliers of

equipment for particle size analysis and a few are listed

in Table 3. Other types of machines and analysis ranges

can be found in the literature.[13,14] Many groups have

made evaluation studies on the various commercial

instruments available,[1,1519] only a very brief descrip-

tion of some popular methods will be presented here.

Microscopy

Microscopy has obvious advantages in that you actu-

ally get information on the morphology of the particles at

the same time as a size distribution. The problems arise

when you consider the sampling and statistics. Sample

preparation is very important and overlapping particles

and sampling errors even on well prepared slides (e.g.

size segregation) are often problematic. These limitations

can be minimized by analyzing the whole area prepared

and not just a central area, as well as numerous slides to

Table 2

Some Examples of Different Mean Diametersand Their Mathematical Representation[1]

Diameter Definition

Number-length dnl ePn

i1 diNiPni1 Ni

Number-surface dns Pn

i1 di2NiPn

i1 Ni

2

s

Number-volume dnv Pn

i1 di3NiPn

i1 Ni

3

s

Length-surface dls Pn

i1 di2NiPn

i1 diNi

Surface-volume dsv Pn

i1 di3NiPn

i1 di2Ni

Volume-moment

(weight-moment)

dv Pn

i1 di4NiPn

i1 di3Ni

Specific surface area dBET 6SBETr (mm)

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minimize variations between specimens. With the possi-

bility of automating some of the analysis with the use of

image analysis packages the number of particles counted

can be put into the thousands and the statistics become

quite acceptable [for a sampling error of

using an analytical ultracentrifuge (AUC).[20] The main

assumption made here is the spherical shape of the particle

in the Stokes law calculation. The detection method can

also lead to limitations. Some instruments use light absor-

bance to detect the sedimentation of the particles and when

the size is similar to that of the wavelength of the light used,

scattering phenomena become important. The use of x-rays

alleviates this problem but one must have a material that

adsorbs enough x-rays at a dilution which avoids hindered

settling problems. So for materials with a low x-ray

absorption such as, organic polymers the use of x-rays

are not an ideal case. By using multiple speeds, centrifuga-

tion can access the whole colloidal range, and with the

AUC even in one experiment.

Single Particle Counters

Single particle counters such as the electrical sensing

zone technique,[1,15] is a well established technique and

works well down to about 0.5 mm. It is one of the fewtechniques that measures a mass and number distribution

directly. The particles are suspended in an electrolyte and

pass through an aperture between two electrodes. The

voltage pulse produced as the particles pass through this

aperture is proportional to the volume of the particle. One

of the draw backs with this method is that different sized

apertures must be used to cover the whole range of sizes

(albeit a very large size range 0.5 to 1000 mm). Care mustalso be taken to count enough particles in the largest size

category. The use of a mass balance is imperative to

check what quantity of material is outside the size range

of the aperture in use and how accurate a calibration has

been carried out. Also, care must be taken to ensure the

nominal values quoted for the sampling volumes are

correct.[15] More recently optical detectors have been

introduced where the passage of particles in a photo-

sensitive zone give rise to pulses which are proportional

to the particle diameter.

A method often used for dry powders, of particular

interest to the pharmaceutical industry is the aerosol time

of flight particle sizer which is another variation of a

single particle counter. Particles are fluidized and pass

through a detection zone via a nozzle, carried by

compressed air which accelerates the particles. The

time of flight between two laser beams is measured and

the size calculated. When using spherical particles the

results are directly comparable with other methods[21] but

care must be taken when dealing with bi-modal or

very broad size distributions.[17] For non-spherical or

irregularly shaped powders, the difficulty in relating the

aerodynamic diameter to other equivalent spherical

diameters has limited the use of such instruments. Irre-

gularly shaped particles can however align in the aerosol

flow conditions and measured PSDs therefore depend on

particle shapecomparison with other methods can lead

to information on the shape of the particle.[21]

Gas Permeability

The measurement of particle size using gas perme-

ability is frequently used for metallic powders and is

often quoted FSSSFischer sub-sieve sizerthe type of

instrument used. The particle size is deduced from a

measurement of the permeability of a gas through a

compact of the powder under investigation.[1] This

method does not give a distribution but the surface-

weight mean diameter and is not very suitable for sub-

micron powders where high resistance to the flow occurs

and the theoretical approach used is no longer valid.

Light Scattering

Light scattering particle size analyzers fall into two

main categories-the low angle laser light scattering

(LALLS) or laser diffraction group which measure from

3500 to around 0.05 mm and the dynamic light scattering(DLS) which measures from about 500 nm to around 2 nm.

Laser diffraction analyzers can be used with suspen-

sions and dry powders, where more recently, better

sampling systems have helped improve the dry powder

measurement.[17] Both diffraction and light scattering

theory are needed to cover the range of particles sizes

claimed by these instruments as discussed in more detail

below. The main limitations arise when non-spherical

particles need to be analyzed and when the optical proper-

ties necessary for the models are not available. These

methods are very quick and the results reproducible. More

recent instruments have added supplementary detector

arrays, light polarization and or different wavelengths to

try and access with more accuracy, the sub-100 nm range.

The dynamic light scattering (DLS) method is based on

the light scattered by particles (colloidal) which are under-

going random thermal motions. The light scattered fluc-

tuates with time and can be related to the particle diffusion

coefficient in a given suspending medium and conse-

quently a particle diameter. For sub 200 nm narrow size

distribution particles, DLS is a very good, quick, and

accurate technique. The main problems arise once the

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powder under investigation does not have a narrow or

single mode distributionthe method gives an idea of the

dispersion or polydispersity of the distribution but does not

give a particle size distribution only a mean diameter and a

polydispersity. The technique will be discussed in more

detail below. Borkovec and Sticher have shown the utility

of using both techniques in seriesLALLS and DLSto

cover the large size range often found in natural materials

such as soils.[22]

Gas Adsorption

Nitrogen adsorption can be used to measure the

specific surface area of a powder. If the powder is

assumed to be monodispersed and spherical, an average

particle diameter having the same surface in m2=g as thepowder under investigation can be calculated. This is

normally written as dBET after the adsorption model used

to describe the nitrogen adsorption isotherm (Brunauer,

Emmett, and Teller).[23] When compared with the median

diameter, dv50, from other methods the dv50=dBET ratiocan be defined as the agglomeration factor FAG indicative

of the state of agglomeration of the powder under

investigation.[24]

For all the methods described, particle size standards

can be used to get a more reliable quantitative number from

the analysis but, beware that your material to be analyzed is

similar to that of your standard used to calibrate the

instrument otherwise very erroneous results can ensue.

SPECIFIC METHODS

In this section we shall describe in more detail several

different methods used for PSD measurement and the

commercial instruments used in our laboratory to cover

the nm to mm range. We shall describe briefly their

physical basis and experimental set up. Then we shall

look at their performance and highlight certain limita-

tions pertaining to the particular method before moving

on to the final section where we shall compare results for

a series of different powders. The instruments used were,

laser diffraction in general a Malvern Mastersizer S

(MMS) [and some preliminary results with Micromeritics

Saturn DigiSizer (MSD)], cuvette photocentrifuge a

Horiba CAPA-700 (PC), Brookhaven X-ray Disc Centri-

fuge BI-XDC (XDC), and for photon correlation spectro-

scopy a Malvern ZetaSizer 4 (MZS4). The dispersion

concentrations used for PSD measurement were around

0.1 mg=mL for DLS, 0.5 mg=mL for PC, MMS and

MSD, and 100 mg=mL for the XDC. The percentagevolume of solids for the XDC was less than the 2% at

which hindered settling is expected to occur.[25] All

samples underwent an ultrasonic treatment (150 W,

10 min) prior to measurement.

SedimentationCentrifugation

Cuvette Photocentrifuge

A typical cuvette photocentrifuge used in our labora-

tory is the Horiba CAPA-700. It uses the principle of

liquid-phase sedimentation and light absorption to

measure a particle size distribution. A homogeneous

suspension of particles is prepared and as the particles

settle either by gravitation or centrifugation, the change

in concentration of the suspension is monitored by the

change in intensity of a light beam (Fig. 4). The sedi-

mentation velocity is calculated using Stokes law Eq. (6)

for sedimentation by gravity and Eq. (7) for centrifugal

sedimentation.

d

18Z0Hr r0g

s6

d 18Z0 ln x1=x2 r r0o2t

s7

where d is the particle diameter, Z0 the viscosity of thedispersion medium, H the sedimentation distance, r thesample density, r0 the dispersing liquid density, t thesedimentation time, x1 the distance between the center of

rotation and the sedimentation plane, x2 the distance

between the center of rotation and the measuring plane,

g the acceleration due to gravity, and o the rotationalangular velocity. The change in the optical transmission

during a certain time interval corresponds to a particular

size range. The relationship between the change in light

intensity, absorbance, the size and number of particles,

from the Beer-Lamberts law, is given by Eq. (8),

log I0 log Ii AXni1

KdiNidi2 8

where I0 is the intensity of the initial light beam, Ii is the

light intensity after passing through the sample, A is an

optical coefficient for the cell, di is the particle diameter,

Ni the number of particles, and K(di) the light extinction

efficiency or coefficient which is a complex function of




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size and the relative refractive index of the suspending

medium and particle.

When the particle diameter is comparable to the light

wavelength, light scattering becomes important and a

correction must be made using the Mie theory.[26] One of

the problems encountered in our laboratory when trying

to use the light scattering correction mode with the

Horiba CAPA-700 was the lack of resolution allowed

for in the light scattering extinction coefficients in the

small microprocessor which controls the apparatus.[27,28]

The fitting of a function which oscillates and varies

steeply with particle size using a polynomial function

was very unsatisfactory. Consequently a computer

program was written which takes the raw absorbance

data and corrects for light scattering using an extinction

coefficient calculated using a modified Mie theory.[27,28]

An example of the function K(di) for a calcite powder

with spherical particle morphology is shown in Fig. 5.

For a 50=50 wt.% mixture of two spherical silicapowders with nominal diameters of 0.25 mm and 0.6 mmthe differences with and without the extinction coefficient

correction is striking, as shown in Fig. 6. The small

Figure 4. Schematic representation of cuvette photocentrifuge (a) sample cell and detection geometry and (b) typical absorption

curves, illustrating the need for two plateaus as a good data criterion as discussed later in the text.

Figure 5. Calculated extinction coefficient K(di) vs. diameter

for a sphere (calcite in water).

Figure 6. Particle size distributions for a 50=50 wt.%. sphe-rical silica powder bi-modal mixture with and without the light

scattering correction.

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particle fraction is grossly underestimated if the correc-

tion is not used, indicating that our 50=50 mixture was infact 70=30 wt.% mixture of the 0.6=0.25 mm powders.The data corrected for light scattering indicates a

54.4=45.6 mixture. These results show the improvementin accuracy using the light scattering correction for this

ideal case of a mixture of two powders both with narrow

size distributions and spherical shape [Fig. 7(a)].

The PSD results for a commercial alumina powder

[Fig. 7(b)] are shown in Fig. 8. A large discrepancy is seen

between the uncorrected Horiba CAPA-700 data and the

suppliers x-ray sedimentometer data. The corrected data

shows a very good correspondence with the suppliers x-

ray sedimentometer data and gives a more complete PSD

analysis below the 0.2 mm size range. An important aspectof this result is the fact that the Horiba CAPA-700 data

had to be collected in two size ranges to give the data

quality necessary to apply the light scattering correction.

If the good data criterion is not satisfied, i.e., a plateau

of absorption at beginning and zero absorption at end

[Fig. 4(b)],[28] then the light scattering correction on poor

data [Fig. 4(b)] gives an erroneously fine distribution, as

for example, in one single measurement on the alumina

powder shown in Fig. 9. This is because the size of last

data point in the incomplete data is underestimated at 0.01

because of the simple averaging method used by the

Figure 7. Powders used to illustrate importance of the light scattering correction with the cuvette photocentrifuge (a) TEM of

0.25 mm model silica spheres (b) Commercial alumina powder BY2.

Figure 8. Particle size distributions for a commercial alumina

powder showing the suppliers data, the Horiba photocentrifuge

uncorrected data and the corrected data (light scattering and

radial dilution).

Figure 9. Example of the a commercial alumina powder

where the data collected did not fit the Good Data Criterion

for light scattering correction to be correctly applied when

using a photocentrifuge.




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software.[28] The percentage of particles smaller than

0.1 mm increases from 0.4% for the uncorrected data to22% for the corrected data (and is 11% for the data which

fits the good data criterion Fig. 9). This inconvenience, a

straight forward lack of versatility of data collection with

the Horiba CAPA-700, undermines the otherwise quick

and reliable data collection. For finer powders in the sub

100 nm range the light scattering correction and good data

criterion becomes even more critical as for a 40 nm

diameter alumina particle the extinction coefficient is

only 2.75105. For the gamma alumina powdersdiscussed later in the comparison of instruments section;

diameters can be overestimated by up to a factor of ten.[29]

The upper range of the Horiba is 300 mm and althoughLALLS is better suited to this size range, even with dense

powders such as atomized steel powders reproducible and

reliable results have been collected up to 150 mm.The PSD data for a European Community standard

quartz powder, BCR 66, is shown in Fig. 10. When

Horiba CAPA-700 data is corrected for light scattering a

much finer PSD than the standard data is seen. The two

major assumptions made in the light scattering correction

are the quartz refractive index and the spherical shape of

the quartz particles. The real part of the refractive index

was verified using the liquid immersion method to be

1.55 0.015 and the imaginary part was estimated tobe much less than 0.1.[28] The particle shape observed by

scanning electron microscopy is very irregular and

platelet-like, rod-like and equiaxed particles were

observed [Fig. 11(a)]. If the extinction coefficients for

an infinite cylinder are used instead of those for a sphere,

the quartz PSD is similar to the standard data distribution

(Fig. 10). This result suggests that for such very irregu-

larly shaped particles the simple spherical particle light

scattering correction is not applicable and the shape has

to be taken into account. In the case of the standard

quartz powder studied, the mixture of morphologies is

too complex to attempt a correction and the use of the

infinite cylinder extinction coefficients are used only to

illustrate the significant effects that shape can have on the

PSD when correcting for light scattering. In Fig. 10 the

standard data and Horiba uncorrected data show a very

good correspondence suggesting an averaging out of

the effects of light scattering. Some striking examples of

such averaging out of some of the fluctuations in the

light scattering coefficients for irregularly shaped quartz

particles can be found in the monograph of Bohren and

Huffman[26] again supporting the above interpretation

with respect to particle shape and the light scattering

correction.

Figure 10. Particle size distributions for the BCR 66 quartz

powder showing the standard data, the Horiba uncorrected data

and the corrected data.

Figure 11. SEM micrograph of irregular and anisotropic powers (a) the BCR 66 standard ground quartz powder illustrating the

irregular shape of the particles (b) glass fibers of constant diameter (c) copper oxalate rods of constant aspect ratio.

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In light of this sensitivity to shape and the importance

of anisotropic particles in practice further work has been

carried out on the PSD analysis of anisotropic particles

using the photocentrifuge.[3032] For cylindrical particles,

model glass fibers and precipitated copper oxalate

rods,[31,32] [Fig. 11(b) and (c)] the CAPA-700 has been

found to give a very good correlation with image analysis

as illustrated in Fig. 12. To compare the equivalent Stokes

spherical diameter that the photocentrifuge provides, with

the image analysis data the anisotropic particle must have

some regularity in its shape distribution.

One possibility is when the diameter of the rods is

constant [glass fibers, Fig. 11(b)] then a fiber length (or

spherical volume) can be calculated by equating the

spherical and cylindrical volumes. The fiber lengths are

consequently well predicted from the photocentifuge

ESD.[31] This approach assumes that the drag coeffi-

cients for the sphere and cylinder are the same and until

now no satisfactory hydrodynamic explanation as to

why this is the case has been found. This is discussed in

more detail elsewhere[31] and further investigations are

in progress.

A second approach is if the particles have a reasonably

constant aspect ratio then an equivalent spherical volume

can be computed from the cylinder volume for

comparison purposes [Fig. 11(c) copper oxalate]. A

very good correlation was also found[32] this time for

cylinder lengths in the micron range rather than the

600 mm of the glass fiber example discussed above. If apowder does not fit either of the above cases (constant

diameter, length or aspect ratio) then correlation between

image analysis datacylinder length and the Stokes

diameter cannot be made. For platelet like particles no

correlation was found[31] even when light scattering was

taken into account for thin (0.5 mm) platelets.The main conclusion to draw from this section is that,

in order to make accurate sub-micron particle size

measurements using a cuvet photocentrifuge by correct-

ing for light scattering, care must be taken to characterise

the powder under observation with respect to particle

shape. Particular care must also be taken with respect to

data quality and light scattering characteristics such as

the effects that impurities can have on the imaginary part

(absorption) of the refractive index. The cuvette photo-

centrifuge has been shown to give useful information on

cylindrically shaped particles, if there is some constant

factor in the geometry. If the particle shape is not

homogeneous or, cannot be approximated by a simple

geometric shape such as a sphere or cylinder then an

alternative method for accurate particle size measurement

should be sought. For such cases the x-ray centrifuge

could be a suitable alternative where the mass of the

sample in the x-ray beam is measured directly and no

scattering phenomena are encountered as discussed in the

next paragraph. One advantage of the cuvette photocen-

trifuge is measurements can be made with just a few mg

of samplex-ray sedimentometers often need up to 100

times more material.

X-ray Sedimentation

X-ray sedimentometers have been used for many years

and are particularly well adapted for inorganic powder

where the method of particle detectionabsorption of

x-rays is sufficiently high to allow detection. The most

celebrated instrument is the Micromeretics

SedigraphTM[33]which uses gravitation to separate

particles and measures an undersize mass PSD using

Stokes law and the x-ray absorption. For particles finer

than around 0.25 to 0.5 mm the gravitational force is notsufficient and is about the lower limit for the instrument.

Earlier instruments were also relatively slow for sub-

micron particle size measurementalthough by introdu-

cing a relative movement between sample cell and

detector this has been significantly improved in recent

years. The main advantage of such systems is that x-ray

absorbance is simpler than the use of light for particle

detection as seen above for the photocentrifuge,

where light extinction corrections can become veryFigure 12. Comparison of equivalent spherical diameter for

glass fibers from image analysis and photocentrifuge.




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complicated. The main limitation of this instrument is

that one must have a material that absorbs enough x-rays

at a concentration which avoids hindered settling

problems (less than 2% volume). So for organic polymers

x-rays are not an ideal case and for inorganic materials a

couple of grams of material is sometimes needed whereas

with the light based systems often 5 to 50 mg is enough

for several measurements. The advantage with the couple

of grams quantity is that it is normally a representative

sample of the distribution. Whereas with the 2050 mg

care must be taken and repetitions performed to ensure a

representative result especially when the powder has a

wide distribution of sizes. This can be achieved by using

sampling procedures such as spin-riffling to generate

sub-samples which are completely consumed.[1] The

gravitation based sedimentometer is widely used and

very reliable but to speed up analysis and extend the

finer end of the range an x-ray disc centrifuge has

become available.

The x-ray sedimentometer used in our laboratory is

the Brookhaven X-ray Disc Cenftrifuge (XDC). This

instrument was designed to analyze inorganic powders

quickly, accurately, and reproducibly using centrifugation

and x-rays for the particle detection. The sample cell is a

hollow x-ray transparent disc, into which a suspension

is injected and then spun to centrifuge the

particles (Fig. 13). The principle is then as described

above for the photocentrifuge using Eqs. (2) and (3) to

follow the sedimentation of the particles and the change

in x-ray intensity. The spherical assumption is again a

limitation for the hydrodynamic aspects of sedimentation

but no scattering phenomena are encountered within the

range of 100 to 0.05 (0.01) mm. Results from Allenswork on the BCR 66 quartz powder (discussed in the

previous section) show very good agreement with the

standard data.[34]

To illustrate the capabilities of the XDC for fine

particle analysis a commercial boehmite was dispersed

in nitric acid and its PSD measured assuming its theore-

tical density of 3.01 g=cm3. The specific surface area ofthis powder was measured to be 214 m2=g which gives adBET of 9.3 nm (assuming spherical primary particles).

The XDC gave a dv50 of 16 nm suggesting a certain

amount of agglomeration which is probable when look-

ing at the TEM photographs [Fig. 15(a)]. The micrograph

also shows the primary particles to be somewhat elon-

gated which can also modify the dBET although for

platelets often attributed to boehmite particles it would

decrease, increasing the apparent degree of agglomera-

tion. The data was collected in just under 2 hours using

Brookhavens recently upgraded 10,000 rpm disc and is

presented in Fig. 14. Comparison with other instruments

Figure 13. Schematic representation of an x-ray disc centrifuge and cuvette photocentrifugeillustrating the different geometries.

Figure 14. Illustration of fine particle analysis

gave very consistent results [photon correlation spectro-

scopy (PCS) and photocentrifuge] and is discussed in

more detail elsewhere[29] and later in the final section of

this paper.

To what degree the median diameter of 16 nm is

accurate is difficult to assess with these boehmite particles

because of their non-sphericity and difficulty in preparing

TEM specimens without touching particles [Fig. 15(a)].

Consequently a spherical silica was used which simplifies

the image analysis considerably. When using the standard

density of 2.2 for a precipitated silica a large discrepancy

between the XDC and image analysis was observed(Fig.

14). The silica powders were supplied as a dispersion and

diluted in 0.0025 M HCl for the analysis. A sample of this

dispersion was freeze dried and the porosity measured

using nitrogen adsorptiondesorption. If the density of the

silica is recalculated taking into account this porosity and

the thickness of the electrical double layer (assumed to

move with the particle) then a figure of 1.52 is found for

this effective hydrodynamic density. Re-analyzing the

XDC data with this shows a very good correspondence

between the XDC and image analysis data.[26] These

results imply that in order to have accurate PSD data in

this

alumina at both 2000 rpm and 600 rpm and the data

renormalized or merged as the manufacturer describes

it. This was carried out for four pairs of data and four of

the five percentiles have standard deviations less than 5%.

One of the disadvantages with the CAPA-700 photo-

centrifuge was its limited run time capacity which led to

collection of data in two or three separate runs to cover

broad size distributions. The XDC does not have this

limitation, but if we are dealing with a relatively broad

size distribution (e.g., 5 mm to 50 nm) then in order tocollect sufficient data points at the large size end of the

distribution excessively long runs, >8 hours, have to beperformed. One problem with running samples for

8 hours apart from the analysis time is that there is an

evaporation of the dispersion liquid which renders base-

line identification difficult. To remedy this the XDC

already has the tool for merging data collected at

different speeds to allow more rapid data collection for

such samples. An example for the commercial alumina

studied above for runs at 600, 2000, and 3000 rpm

in Fig. 17 shows the type of data that is typically

produced. The median diameters are really in very

good agreement but the tails differ greatlythe high

particle size being poorly sampled at the higher speeds

only four and three points before 0.5 mm for the runs at2000 and 3000 rpm respectively. The overlap with the

600 rpm run just below 0.3 mm is really very goodindeed. In fact the 600 rpm run only collects data to

0.23 mm with 38% of the distribution being finer thanthis value. The 2000 rpm data finds a 0% value at

0.12 mm. The data plotted in Fig. 16 for the dv5 anddv15 of runs at 600 rpm is the result of an extrapolation

and both show values lower than the 0% value found

for the 2000 rpm run, showing the extrapolation to be in

significant error. The raw data is available to check on

this possible over extraction of data and it should

always be consulted to avoid gross errors. This over

extraction of data has been corrected in more recent

software. The overlap of two measurements at different

speeds is not always as smooth as found in this example

Figure 16. Repeated PSD analysis with the XDCdifferent sample preparations showing good reproducibility from run to run.

Figure 17. Example of same alumina dispersion run at

different speeds using the XDC.

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and care must be taken with respect to the cross over

point used.

In conclusion the XDC has very good fine particle

capabilities (4 mm theoptical properties of the material and medium do not play

an important role and the resulting diffraction pattern can

be described by diffraction theory.[35] For a powder

suspended in air or a liquid this produces a series of

rings, the position and intensity of these diffraction rings

being dependent on the particle size Fig. 18. When the

particles are

shape. If the particle size distribution to be analyzed is

known to follow a particular distribution e.g., log-normal

or Rosin-Rammler the initial guess can use this informa-

tion to simplify the data analysis. There are a vast number

of LALLS instrument manufacturers and each has their

preferred algorithm for data reduction which can lead

to differences of up to 20% when using the same

dispersion.[37]

There have been many studies using this type of

instrument with various particles[15,36,37] and very good

results are found for particles >10mm. For sphericalpolystyrene particles[36] the results are very accurate and

very reproducible. For inorganic particles both spray dried

powders[37] and glass beads have been investigated[38]

using various laser diffraction instruments and compared

with image analysis. Figure 19 illustrates an example of a

narrow sieved fraction (160200mm) for glass beads wherelaser diffraction and image analysis show good agreement

(5%) for the dv50 with slightly more variation (10%) at the

tails (dv10 and dv90) of the distribution.[38] The results with a

standard quartz powder in the 1090mm range are a littleless accurate (1015% variation for median) as we move

away from the perfect spherical shape assumed in all data

reduction algorithms but still very reproducible.[15] The

method is also very quick, the analysis takes only a few

minutes so a high throughput can be achieved and auto-

matic samplers are also available.

When we move below 10 mm towards 1 mm then lightscattering becomes more important and the Mie theory has

to be applied. Further limitations of the instrument arise

when particles are non-spherical and when the relative

refractive index between solvent and powder is small or

optical constants of the powder unknown. Another limita-

tion is found when trying to use the method for on-line

analysis and suspensions are too concentrated leading to

multiple scattering problems.[36] When the refractive

indices of the medium and particle are similar (ratio of

real parts of the RI< 1.1), even for particles >5 mm, thenagain the Mie theory has to be used and the optical

constants input into the analysis routine if not assigned

diameters can be as much as 25% in error.[36]

When we have spherical particles and a narrow size

distribution (e.g. 0.5 to 2.0 mm) the results compared toimage analysis can be very good even in the micron

range. For example a spherical silica of nominal diameter

1 mm gave a median diameter of 1.04 mm from imageanalysis[39] and 1.032 mm (standard deviation 0.0083from five repetitions) when using a MMS with a refrac-

tive index of 1.412 (real) and 0.00 (imaginary) for

amorphous silica. When there is a significant fraction

of sub-micron particles present in the powder to be

analyzed, the optical model chosen in the set-up becomes

critical. The Mie theory requires knowledge of the

refractive indices of the particles and suspending

medium. A systematic study of laser diffraction instru-

ments with the BCR 66 standard quartz powder covering

the 3 to 0.3 mm range by Allen and Davies[15] stillshowed limitations in this range even when using the

Mie theory correction. This study was carried out some

years ago and current algorithms may have improved but

this effect, to a major extent, may be due to the irregular

shape of these particles as seen in the photocentrifuge

study described earlier.

There has been much discussion about the complex

part the refractive index of powders which corresponds to

the absorption of light where often there is no informa-

tion available and the value has to be estimated. One

method of arriving at a value is to adjust the value until

the best fit between the calculated and measured data is

found; though naturally care must be taken assure the

result for the imaginary part is reasonable for the material

under investigation. In the ISO 13320-1 Particle Size

Analysis by Laser Diffraction Methods the conclusion

was that small values of the imaginary part of the

refractive index (about 0.010.1) are applied to cope

with the surface roughness of the particles. The authors

personal opinion is that this correction has more to do

with shape than surface roughness as illustrated for the

Figure 19. Example of PSD comparison between image

analysis and laser diffraction (MMS) for sieved spherical

glass beads.

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light scattering correction with the photocentrifuge

previously discussed. The motivation behind this

approach may be understood from the results shown

in Fig. 20. Here the standard quartz powder BCR 66

data is compared to the laser diffraction PSDs using

absorption coefficients of 0.1 and 0.001. The results for

the 0.1 coefficient are closer to the standard data (for all

percentiles >40%) even though the coefficient for such arelatively pure quartz should be closer to 0.001. As

discussed above the reason for this discrepancy is

thought to be related to the non-spherical particle shape

of the BCR 66 and this effect of particle shape will now

be discussed in more detail. Before we do that, one last

point is that the BCR 66 was standardized by a sedi-

mentation method where perhaps the very irregular shape

has less influence. One of the favored ways of standar-

dizing a powder is to use image analysisseeing is

believing as they saybut using image analysis of an

irregular shaped particle to then produce an ESD for

comparison with diffraction or sedimentation is in itself

a difficult task.[8] This point for irregular particle

shapes will be further discussed in the comparison of

instruments section.

When the particles deviate significantly from a sphere

then all the spherical assumptions in the optical models

are obviously at fault. Azzopardi[36] quotes an example

from the work of Swithbank et al. where for cylinders

with lengths more than three times the diameter, the

diffraction method gave a particle size (volume

diameter) which was 12% smaller than the cylinder

diameter and not at all sensitive to the cylinder length.

Other studies have also shown that with aspect ratios

below three then the ESD from laser diffraction reason-

ably represents the real volume of the particle.[40] So

although there is the possibility of detecting changes in

shape using such methods[41] it is a detection and not a

PSD measurement. Gabas et al.[42] studied some model

non-spherical particles, namely cubes, flat rectangular

plates, and cylinders using laser diffraction. The parti-

cles were monodispersed with dimensions between 200

and 1000 mm and they saw that the minimum andmaximum dimensions were detected with a more or

less continuous size distribution between. This leads to

the conclusion that an aspect ratio could be calculated

reliably for these regular monosized anisotropic parti-

cles, but information on the size distribution was not

possible. Naito et al. have also looked at the effect of

particle shape on the response from five different types

of instruments[43] laser diffraction included, and also

concluded that an aspect ratio can be extracted for rod

like particles and orientation effects in the cell play a

significant role. More recently Matsuyama et al.[44] have

derived quantitative diffraction patternESD relation-

ships for laser diffraction illustrating the above effects.

They show that for aligned monosized ellipsoids a bi-

modal distribution will result from the diffraction data. If

the ellipsoids have a size distribution and are randomly

oriented the resulting distribution becomes monomodal.

The fact that the diffraction pattern for an ellipsoid is no

longer symmetric in the x-y plane [Fig. 18 (c)] means

that in order to derive shape information from the

diffraction pattern data has to be collected in this

plane and not just the y direction as for most

instruments. This has recently been developed with

the Micromeritics Saturn Digisizer but although shape

analysis is not yet available the potential for regular

shape investigation is becoming a reality.

Recent work at LTP has looked at the use of some

model anisotropic particles with regular cylindrical or

platelet morphologies,[32] as well as some more realistic

natural powders namely a commercial mica and some

precipitated copper oxalates rods.[32] Several methods as

well as laser diffraction data were compared with image

analysis to help interpret the results. The glass fibers

[regular cylinders, 10 mm diameter and lengths from10600 mm, Fig. 11(b)] showed no correspondencebetween laser diffraction and image analysis data in

agreement with the work of Gabas et al.[42] but contrary

to the photocentrifuge discussed above.[32]

Figure 20. Standard quartz powder BCR 66 data and the

measured laser diffraction PSDs using absorption coefficients

of 0.1 and 0.001.




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For the platelet morphology laser diffraction has

already been shown by Baudet et al.[45], with clay

samples and an estimated thickness, to give good

median diameter (d50) correlations. To compare data

collected, contrary to the Baudet et al. method which

needs a calibration sample, we chose to calculate rota-

tional volume diameters (Dvrot) from the image analysis

data (simply the spherical volume of a disc rotated 360

through the diametral axis). The orientation of the plate-

lets as they pass through the laser diffraction sample cell

was treated as being perfectly oriented perpendicular to

the laser beam (i.e., plane of disc normal to the incident

beam) or randomly oriented. The final assumption made

to allow a comparison of the Dvrot and Dv laser diffraction

data is that the diffraction pattern of a disc approximates

that of a spherefrom the results of Baudet et al.[45] this

assumption seems to be reasonable. The platelets studied

were alumina single crystals (Atochem, France) which

had a very regular morphology and a reasonably constant

thickness of 0.6 mm (Fig. 21(a)). Figure 22 shows thePSD results and we see a reasonable correlation between

the oriented image analysis Dvrot median (6.8 mm) and thelaser diffraction median (7.7 mm). This was by far thebest correlation between the image analysis and any of

the four PSD instruments studied.[31] The tails of the

distributions show a large divergencethis was also the

case with the study by Baudet et al.[45] The discrepancy

can be attributed both to the laser diffraction deconvolu-

tion algorithm and to some degree for the coarse fraction

the image analysis. As agglomerated platelets were

eliminated in the image analysisand some degree of

agglomeration seems very likely from the micrograph

shown in Fig. 21(a). So care should be taken when using

this approach, if the tails of the distribution are of

particular importance in an application but the laser

diffraction median is representative of the real platelet

median.

Further work on mica particles with aspect ratios

between 10 and 20 has confirmed this correlation

between laser diffraction and image analysis.[32] The

image analysis was carried out on several different size

ranges (010, 10250, 250400, and >400 mm) to mini-mize sampling errors.[32] The distribution is very broad

ranging from 10 mm to 1000 mm. The correspondencebetween image analysis and laser diffraction is reason-

ably good (Fig. 23). The discrepancies seen at the higher

particle sizes have been attributed to the sampling

Figure 21. Micrographs of (a) the model alumina platelets

and (b) the commercial mica.

Figure 22. Particle size distributions of alumina platelets

from laser diffraction and image analysis as a function of the

volume ESD.

Figure 23. Comparison of image analysis and laser diffraction

PSDs for a commercial mica.

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problems of image analysis despite the precautions of

analyzing four fractions. Even though 8000 particles in

total were counted by image analysis we sample less than

1 mg and to have a statistically representative sample for

the higher end of the distribution 2 g is needed[32]

(the laser diffraction was collected using 12 mg of

mica). To actually back calculate a disc particle size

distribution, rather than the rotational equivalent

compared in Fig. 23, an assumption of constant thickness

would be necessary this will depend on the production

route of the powder but is surprisingly often a reasonable

assumption.

In conclusion we have seen that despite the complica-

tions of the data reduction in laser diffraction methods

when a certain number of the basic assumptions are met,

very reliable data can be collected. The method is

particularly well suited to particle size measurement in

the 101000 mm range where comparison with imageanalysis gives dv50s within 5%. When dealing with

narrow size distributions of a spherical silica even at

around 1 mm dv50s better than 5% can be obtained. Thetails of the distributions seem to be in less agreement

with image analysisbut then image analysis is also

prone to sampling errors if the distribution is particularly

broad or there is a population of agglomerates difficult to

interpret in the image analysis. For very irregular shaped

particles such as ground quartz there is also the problem

of transforming the shape into an ESD for comparison

with laser diffraction. These aspects for a sub-micron

alumina will be discussed further in the comparison of

instruments section.

For anisotropic particles such as discs and plates a

very good correspondance can be found for discs

assuming alignment in the measuring cell and that the

data is put on the same equivalent volume basis. Many

authors have pointed out the possibility of gleaning an

average aspect ratio from rod like particles,40,42,43,45 but

information on the length or size distribution does not

seem possible. The non-symmetry of the diffraction

pattern for such ellipsoid particles does allow for further

development with new 2D detection systems which

could help improve this aspect. In general, when the

dispersions used are themselves reproducible, the laser

diffraction method gives very reliable results. Much

effort has been made very recently by the various

manufacturers to improve the sensitivity and accuracy

in the sub-micron and even sub-100 nm range by using

extra light sources, detector arrays, polarized light and

different wavelength light.[46,47] This along with more

rigorous improved algorithms and inversion techniques

due to improved computing power are helping push this

speedy and reliable method to its limits.

Photon Correlation Spectroscopy

The DLS method or PCS or quasi-elastic light scatter-

ing (QELS) as it was first termed is another method

which depends on the interaction of light with parti-

cles.[48] The earliest work on light scattering was carried

out by Rayleigh[49] and the assumptions used in his

approach limits the application to particles much smaller

than the wavelength of the incident radiation. Rayleigh

showed that the scattered intensity I (flux per unit area),

I I016p4R6n2 1n2 22

r2l410

Where I0 is the incident intensity, n n1=n0 the relativerefractive index of particle of refractive index n1 and

suspending medium n0, R is particle radius, l thewavelength of light in the medium, and r the distance

between the scattering particle and the detector. The Mie

theory,[26] as already mentioned, gives a complete solu-

tion for spherical particles of any size and refractive

index. The light scattered by colloidal particles in suspen-

sion, which undergo Brownian movement due to thermal

agitation, will fluctuate with time and can be related to the

diffusion coefficient, Dt of the particle.[48] The diffusion

coefficient can be related to a hydrodynamic diameter dhand for spherical morphology is given by the Stokes

Einstein equation

Dt kBT

3pZdh11

where T is the absolute temperature, Z is the suspendingliquid viscosity, and kB Boltzmans constant. This

hydrodynamic diameter is very similar to the geometric

diameter in most cases. The main exception being very

small (

the cumulant method. For a Rayleigh scatterer the results are

independent of the angle at which you make measurements

but once out of this region (n17n0)R=l 1 more completetheories have to be used.[48,50]

The PCS method is particularly well suited to the

measurement of narrow particle size distributions in the

range 1500 nm and very accurately as for the examples

of latex standards frequently cited and Weiner even

quotes an example where the standard was corrected

after some PCS measurements.[48] Photon correlation

spectroscopy is capable of measuring accurately down

to 1 or 2 nm as illustrated by the example on tetra-

propylammonium bromide[48] but not with a low inten-

sity laser and the preclusion of dust is imperative. The

dependence of the scattered intensity for Rayleigh

scattering was shown in Eq. (10) to be proportional to

the sixth power of the diameter. A particle only twice

the size will give 64 times the intensity so any dust

contamination will bias the results significantly. One

method often used to remove dust for very fine colloids

(

Zetasizer (MZS) manual) where several PSDs are shown

all of which fit the PCS data with similar accuracy. One

can derive acceptable particle size distributions from PCS

measurements but more complicated algorithms for the

data analysis must be used and more accurate and multi-

angle data collected.[53] However, as this method is

extremely quick, rapid analysis can be carried out and

if the resulting distribution is narrow and reproduceable,

the data is probably reliable. If a certain polydispersity is

registered then another method, such as microscopy or

sedimentation, should be used to discover which of the

various solutions (e.g. Fig. 24) gives the best agreement

with the other methods.

The upper size limit of the PCS method has been stated

as being around 500 nm. Wiener[48] has very clearly

described the reasons behind this which are related to

the number of particles per unit volume, sedimentation,

slower diffusion for larger particles. First sedimentation, if

the particles are too dense with respect to the suspending

liquid they may sediment during the course of the data

acquisition. Also the diffusion slows down as particles get

bigger and experiments take longer to collect the same

quality data as collected for smaller particles. Also one

must be careful to make sure that there are enough

particles per unit volume otherwise small fluctuations in

the baseline can have drastic effects on the data quality.

The difficulty in assuring that the volume fraction of

particles is sufficient is that at higher concentrations we

meet the onset of particleparticle interactions (around

102) and this is often difficult to achieve in the 0.5 to1 mm range where methods such as centrifugal sedimenta-tion are better suited.

So in summing up the PCS section, we can say that it

is very useful for rapid measurements of narrow size

distributions between 1 and 500 nm. Most of the results

on sub-100 nm particles collected at LTP over recent

years, have used PCS as a starting point or a back up

screening method. Most of the examples are best

described and discussed in comparison with other meth-

ods such as sedimentation and microscopy (linked with

image analysis) which leads on to the following and final

section of this paper.

COMPARISON BETWEEN

INSTRUMENTS

In this section we shall look at a series of powders

from 20 nm boehmites to 400 micron glass spheres and

101000 mm mica flakes and compare results from eitherdifferent methods or different instruments that use the

same basic principles. Before doing this one or two

statements about which methods and why different

methods should produce more reliable results for certain

powders than others. The main difference is between the

ensemble techniques; where we have a diffraction pattern

or light scattering signals that come from all of the

sample and the separating techniques, such as sedimenta-

tion or even microscopy, where the contribution from

different size ranges is separated to a certain degree. The

separation techniques are generally believed to give more

reliable representation of the size and distribution widths

whereas the ensemble techniques are very rapid. So the

separation techniques are slower and are to be preferred if

an accurate size and distribution are needed whereas the

ensemble techniques are well adapted to rapid screening

or comparison between samples for say quality control

techniques. Bearing in mind these points we shall now

look at the various powders from nm to mm.

Colloidal Boehmite (1040 nm)

A commercial boehmite, Disperal HP 14=2 (suppliedas a dry powder, Condea, Germany), has been analyzed

using, PCS, XDC, a photocentrifuge (CAPA), and gas

adsorption. The boehmite was dispersed in a 2% acetic

acid solution and treated for 10 min using an ultrasonic

probe (150 W, 20 kHz, 50 mL volumes). The samples

were diluted as necessary for the photocentrifuge and

PCS measurements. For the sedimentation methods the

theoretical density 3.01 g=cm3 was used because the verylow agglomeration factor after dispersion (see Ref. [29]

for more details). The specific surface area from nitrogen

adsorption was 214 m2=g which gives a spherical dBET of9.3 nm [Fig. 26(a) shows a somewhat elongated primary

particle shape]. The PSDs for the three other methods

are shown in Fig. 25 and show very good agreement with

each other showing a median diameter of 16 nm (1 nm,average from 23, PSDs for each instrument). The

photocentrifuge data is corrected for light scattering

after re-normalization and averaging of 69 separate

measurements (of between 1 to 3 hrs)the whole data

collection and data processing taking about 18 hrs i.e.,

nearly two working days. The XDC took less than 2 hrs

and has a much greater data resolutionthe photcentri-

fuge having only three data points in this interval. That

the photocentrifuge gives such a good correlation with

the other two methods when taking into account the lack




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of resolution and data correctionis quite remarkable.

The PCS with powder dispersion included took less than

20 minillustrating its great benefits when dealing with

narrow size distributions in the nm range. To what degree

the dv50 of 16 nm is accurate has been discussed to some

degree in the XDC section and also by Staiger et al.[29]

Commercial Gamma Alumina 30200 nm

The particle size distribution results for a commercial

gamma alumina powder Aluminiumoxid C (Deg C,

99.6% Al2O3, 2.8% alpha, Degussa, Switzerland) for

PCS, XDC, and the CAPA are shown in Fig. 27. Here

we see a much greater variation in the PSDs measured by

the various instrumentsvarious characteristic values are

given in Table 4. The specific surface was measured to be

92 m2=g leading to a spherical dBET of 19.2 nm indicatinga certain amount of agglomeration when compared to the

other instruments. For these sedimentation measurements

hydrodynamic densities were calculated using porosity

data from nitrogen adsorption measurements. These were

made on loose or freeze dried powders to avoid inter-

particle porosity that might be introduced from packed

powders.[29] For comparison of results the XDC has been

used as the yardstick. This choice was made as the x-ray

absorption is directly proportional to mass, no models for

light scattering needed, as for the two other methods.

Which method gives the most accurate absolute measure-

ment is not always easy to discern without image

analysiswhich is difficult to perform on such fine

powders.

For the photocentrifuge, bearing in mind the assump-

tion of spherical particle shape and a refractive index

estimated, assuming the porosity in the agglomerate was

filled with waterone can see that the light scattering

correction for Horiba data is really quite good. The

correction seems to slightly overcorrect, showing smaller

values for mean and median diameters but are within

20% of the XDC data. The results from PCS however

seem to significantly underestimate the sub-100 nm range

and consequently the fine tail of the distribution. This

gives a mean diameter of 134 nm and a median diameter

of 123 nm. This is a typical example of the sensitivity of

light scattering to a low population of agglomerates

discussed above. This can be seen in the XDC standard

Figure 25. Comparison of PCS, XDC and photocentrifuge

(CAPA) PSDs measured for a commercial boehmite.

Figure 26. TEM images of (a) the commercial boehmite and (b) gamma alumina investigated.

654 Bowen



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