(PSD). There are no accepted standard methods for dispersing SCM particles prior ..... needed to convert light scattering data to particle size distribution. ...... expressed as the two-sided 95% confidence interval, is computed by the bootstrap.
Materials and Structures Characterization of Particle Size, Surface Area, and Shape of Supplementary Cementitious Materials --Manuscript Draft-Manuscript Number: Full Title:
Characterization of Particle Size, Surface Area, and Shape of Supplementary Cementitious Materials
Article Type:
Original Research
Keywords:
Supplementary cementitious materials; particle size measurement; laser diffraction; Blaine; BET; image analysis
Corresponding Author:
Nele De Belie BELGIUM
Corresponding Author Secondary Information: Corresponding Author's Institution: Corresponding Author's Secondary Institution: First Author:
Eleni C. Arvaniti
First Author Secondary Information: Order of Authors:
Eleni C. Arvaniti Maria C.G. Juenger Susan A. Bernal Josée Duchesne Luc Courard Sophie Leroy John L. Provis Agnieszka Klemm Nele De Belie
Order of Authors Secondary Information: Abstract:
The physical characterization of supplementary cementitious materials (SCMs) is of great importance in optimizing the use of these materials in concrete in order to minimize cost and maximize performance. Techniques that are currently used for the determination of particle size, specific surface area and shape of cementitious materials are described and critically evaluated in this paper. Recommendations for testing using air permeability, sieving, laser diffraction, BET, image analysis and MIP are also provided, representing an output from the work of the RILEM Technical Committee on Hydration and Microstructure of Concrete with Supplementary Cementitious Materials (TC-238-SCM).
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Manuscript Click here to download Manuscript: paper_RILEM_TC_SCM_WG1_final.docx Click here to view linked References
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1
Characterization of Particle Size, Surface
2
Area, and Shape of Supplementary
3
Cementitious Materials
4
Eleni C. Arvaniti1, Maria C.G. Juenger2, Susan A. Bernal3, Josée Duchesne4, Luc
5
Courard5, Sophie Leroy5, John L. Provis3, Agnieszka Klemm6, Nele De Belie1
6 7 8
1
9 10 11
2
12 13
3
14 15 16
4
17 18
5
19 20 21
6
Magnel Laboratory for Concrete Research, Department of Structural Engineering, Faculty of Engineering and Architecture, Ghent University, Technologiepark Zwijnaarde 904, B-9052 Ghent, Belgium University of Texas at Austin, Department of Civil, Architectural and Environmental Engineering, 301 E. Dean Keeton St. C 1748, Austin, Texas 78712, USA Department of Materials Science and Engineering, University of Sheffield, Sir Robert Hadfield Building, Mappin St, Sheffield S1 3JD, United Kingdom Département de géologie et de génie géologique, Université Laval, Pavillon Adrien-Pouliot, local 4507, 1065, ave de la Médecine Québec, Qc, Canada, G1V 0A6 GeMMe research group, ArGEnCo Department,University of Liege, Liege, Belgium Department of Construction and Surveying / School of Engineering and Built Environment, Glasgow Caledonian University, Cowcaddens Road, Glasgow, G4 0BA, UK
22 23
Abstract
24
The physical characterization of supplementary cementitious materials (SCMs) is
25
of great importance in optimizing the use of these materials in concrete in order to
26
minimize cost and maximize performance. Techniques that are currently used for
27
the determination of particle size, specific surface area and shape of cementitious
28
materials are described and critically evaluated in this paper. Recommendations
29
for testing using air permeability, sieving, laser diffraction, BET, image analysis
30
and MIP are also provided, representing an output from the work of the RILEM
31
Technical Committee on Hydration and Microstructure of Concrete with
32
Supplementary Cementitious Materials (TC-238-SCM).
33
Keywords: Supplementary cementitious materials, particle size measurement,
34
laser diffraction, Blaine, BET, image analysis
1
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35
1 Introduction
36
The use of supplementary cementitious materials (SCMs) in the production of
37
concrete has increased worldwide over the past few decades [1,2]. These materials
38
can enhance the mechanical and durability properties of concrete, and contribute
39
to mitigation of the environmental impact associated with the construction
40
industry. SCMs are used as a partial replacement for Portland cement in concrete
41
reducing the fraction of Portland cement required to produce concrete with desired
42
performance. SCMs are mostly by-products of industrial processes such as fly
43
ashes derived from the coal-burning processes, blast furnace slags from the iron-
44
making industry, and silica fume from ferro-silicon industries [3]. However, in
45
recent years, greater attention has been given to natural materials with pozzolanic
46
activity such as calcined shales and clays along with metakaolin. Calcined clays
47
and shales are used as cement replacements, while metakaolin is more often used
48
as an additive to the cement.
49
The performance of SCMs in concrete is strongly dependent on their physical and
50
chemical characteristics, which vary depending on the nature and source of the
51
SCM. In general, the fineness is one of the most important physical properties
52
controlling the reactivity of SCMs and the subsequent strength development of
53
blended binders [4]. Reducing the average particle size increases the rate of
54
dissolution of the SCM, raising the pozzolanic activity and thus the development
55
of more strength-giving hydration products that enhance the long-term
56
performance of the concrete. Small particles can also facilitate nucleation and
57
growth of cement hydration products on the SCM surfaces, speeding up the early
58
cement hydration and therefore the strength development. However, reducing the
59
particle size of SCMs beyond an optimal value usually leads to an increased water
60
demand of the concrete mixtures to achieve a desired workability, which can
61
negatively affect both strength and its durability [5]. Further, if particle size is
62
decreased by grinding, this requires additional energy costs.
63
For most industrial control purposes, the primary characteristics measured in
64
powders are specific surface area, particle size distribution, particle shape, and
65
density. The specific surface area (defined on a mass basis) is the most common
66
property used to describe the fineness of Portland cement [6]. This surface area is
67
an integral parameter and gives no information about details of the actual particle 2
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68
size distribution, which is probably of greater importance in defining concrete
69
performance. The description of particle shape encompasses information about the
70
sphericity and angularity, which affect workability and also the physical
71
phenomena utilized for particle-size measurement [7].
72
Even though SCMs are widely used by the construction industry, their physical
73
characterization is challenging. As the most used SCMs are industrial by-
74
products, in most cases the quality of these materials cannot be controlled during
75
their production, resulting in materials with varied characteristics [8]. There are
76
standard methods used to determine particle characteristics for cement that may
77
not be as accurate when applied to SCMs. For instance, the air permeability test
78
for specific surface area (Blaine), which is widely used for characterizing Portland
79
cements [9], is based on the principle of resistance to air flow through a partially
80
compacted sample of cement. This method relies on the assumptions that there is
81
a relatively limited range of particle sizes in the material, with consistent inter-
82
particle interactions, and that there are available and internationally accepted
83
reference powders with properties similar to the material of interest. These
84
conditions may not apply for all SCMs.
85
Deviations from expected results in physical characterization of powders are
86
associated with instrument limitations, improper sample preparation procedures
87
(e.g. inadequate dispersion), operator errors (e.g. improper instrument set-up or
88
poor calibration), or incorrect sampling [10]. Although numerous techniques for
89
the measurement of the physical characteristics of powders have been developed,
90
most of the techniques are unsatisfactory in some respect, and there is no general
91
method that may be applied with a reasonable confidence to a wide range of
92
materials spanning several orders of magnitude in particle size, and with diverse
93
particle shapes.
94
The key consideration for the proper and accurate determination of physical
95
properties of SCMs lies in the selection of the adequate instruments and methods.
96
This paper presents a critical overview of the techniques that are currently used
97
for the determination of the particle size, specific surface area and shape of
98
cementitious materials. The aim is to systematize the existing knowledge on this
99
subject and to identify the most suitable techniques and methods that can be
100
applied to characterize SCMs. The most important criteria that should be 3
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101
considered as a starting point for method validation are also outlined. This paper
102
first discusses the methods of sample preparation prior to characterization, such as
103
sampling and dispersion, and then describes the standard methods for testing
104
specific surface area, particle size distribution, and particle shape, as well as tests
105
for properties such as
106
supporting information for the other tests. Finally, selected SCMs are
107
characterized with these methods in order to identify the factors that induce
108
variations in the results obtained from different techniques.
109
2 Methods for Sample Preparation
110
2.1 Sampling
111
Sampling is a very important step in the characterization of any material, as the
112
specimen selected has to be representative a large batch of material and provide
113
sufficient and accurate information to enable decisions on handling and use.
114
Sampling is one of the factors which can introduce the largest errors in particle
115
size, shape, and density measurements of a powder [11]. Whenever a powder is
116
analyzed, whether for physical or chemical assay, the quality of the measurement
117
depends on how representative the sample is of the bulk from which it is drawn.
118
Taking a sample of a few milligrams from a bulk of many tons, the chances of
119
measuring a non-representative sample are increased considerably. The
120
International Standard ISO 14488 [12], the American standards ASTM C 183-08
121
[13] and ASTM C311/C311M-13 [14] provide useful information on the
122
requirements for sampling of particulate materials.
123
Two types of sampling errors are possible [10]. First, statistical errors arising from
124
sample heterogeneity cannot be prevented, but can rather be estimated beforehand
125
and reduced by increasing the sample size. Even for an ideal random mixture, the
126
quantitative particle distribution in samples of a given magnitude is not constant
127
but is subject to random fluctuations. Second, there are errors that occur due to the
128
segregation of the bulk and depend on the previous history of the powder. Dry
129
powders tend to separate if they are stored for some time or they are vibrated
130
during storage. The larger particles tend to rise to the top and the smaller particles
131
collect at the bottom of the container. If the sample is taken from the top of the
132
container it will not contain the smaller particles, giving a biased measurement.
density and refractive index that are used to provide
4
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133
This error can be minimized by suitable mixing and building up a sample from a
134
large number of increments.
135
There are several different techniques of sampling that have been evaluated in
136
multiple studies (Table 1). The spinning riffle is the most reproducible method for
137
obtaining a representative sample for powdered materials when compared with
138
other techniques such as scoop sampling, table sampling, cone and quartering and
139
chute riffling [10].
140
Table 1 Methods of powder sampling and associated error (data from [10] and [15])
Method Cone & Quartering Scoop Sampling Table Sampling Chute Riffling Spin Riffling
Relative Standard Deviation (%) 6.81 5.14 2.09 1.01 0.125
Estimated maximum sample error (%) 22.70 17.10 7.00 3.40 0.42
141 142
2.2 Dispersion
143
The term ‘dispersion’ has a variety of meanings, but in this context it makes
144
reference to the process of separating solid particles from each other to measure
145
the physical characteristics of a given powder. For the characterization of SCMs,
146
dispersion is particularly important in accurate determination of particle size
147
distribution; however, if the natural, agglomerated state is of interest, this should
148
be taken into account during the sample preparation to avoid the break-up of
149
agglomerated particles. In either case, the dispersion medium, whether air or
150
liquid, should not cause irreversible changes to the particle size through processes
151
such as dissolution, grinding or aggregation.
152
The overall process of dispersion of a powder in liquid media comprises three
153
main stages: (1) wetting of the powder, (2) breakdown of particle clusters and (3)
154
flocculation of the dispersed particles [16]. The wetting of the particles depends
155
on different factors including the nature of the liquid phase, the character of the
156
surface, and the dimensions of the interstices in the clusters. The wetting
157
effectiveness is influenced by the existing forces between individual particles in
158
the clusters. The major difficulty during the dispersion process is achieving the
159
breakup of agglomerates to finer particles after the powder has been wetted, as 5
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160
particles tend to adhere together by weak forces unless the wetting is very strong
161
(i.e. contact angle is very low). In such cases, the penetration of liquid into the
162
particles can generate sufficient pressure to promote the dispersion.
163
Dispersibility is then defined as the ease with which a dry powder can be
164
dispersed in a particular liquid medium, which is essentially a measure of the
165
effectiveness of the first two stages of the dispersion process. The dispersability is
166
dependent on lyophilicity, particle size, specific gravity and ionic charges on the
167
surface (zeta-potential) of the material [17]. Dispersability is especially important
168
when characterizing SCMs because there are situations (e.g. silica fume) in which
169
the particles are highly agglomerated in the dry state, and therefore must be
170
properly dispersed in order to determine the “true” particle size distribution
171
(PSD). There are no accepted standard methods for dispersing SCM particles prior
172
to analysis, and therefore the degree of dispersion will vary depending on the
173
method that is used. This could potentially introduce a large source of variation at
174
the sample preparation stage [18].
175
2.3 Outgassing
176
Outgassing involves the heating of the powder at a given temperature in helium or
177
nitrogen flow. Outgassing strongly influences the measurement of specific surface
178
area; testing partially moist particles covered with molecules of previously
179
adsorbed gases or vapor, can lead to reduced or variable specific surface values
180
[19]. There are no established outgassing conditions to assure accurate
181
measurements of specific surface of powders. Most laboratories use their own
182
standard protocol at an established temperature, gas pressure and time of
183
outgassing, independent of the chemistry and structure of the material to test.
184
The ideal practice for determining the outgassing conditions should involve the
185
study of the potential impact of different outgassing conditions on the physical
186
and chemical properties of the tested material, to make sure that the original
187
surface of the particles evaluated is preserved after this treatment. For most
188
purposes, the outgassing temperature can be selected within the range where the
189
thermogravimetric trace of the tested powder exhibits a minimum slope [20].
190
Outgassing can be conducted at room temperature (20 - 25C) when the powder is
191
treated with a combined purge of a non-reactive, dry gas flow under vacuum, or 6
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192
when the specimens are subjected to desorption-adsorption cycles. These methods
193
of outgassing are strongly recommended when analyzing materials that can suffer
194
structural changes when exposed to elevated temperatures.
195
The effect of the outgassing conditions on the specific surface measurements of
196
the minerals goethite, quartz, calcite and kaolinite has been evaluated by Clausen
197
and Fabricius [19], where it was observed in goethite that increased outgassing
198
temperatures promoted a rise in the specific surface area, reaching a maximum
199
value at temperatures between 150C and 250C. This is associated with the phase
200
changes from a ferrihydrite to disordered hematite. Conversely for quartz, calcite
201
and kaolinite after dry heating above 100C the BET values are close to stable.
202
BET values calculated in these mineral by heating the specimens between 20C
203
and 250C do not promote significant changes in the values obtained. This
204
indicates that outgassing at room temperature of materials containing oxide
205
minerals, such as SCMs, can enable measurement of reliable specific surface
206
areas, as long as the outgassing time is prolonged (2h).
207
3 Methods for Particle Size Characterization of
208
SCMs
209
The classical techniques for determining fineness and particle size distribution in
210
cementitious materials include sieving, air permeability testing (Blaine), gas
211
adsorption (BET), laser light scattering, and image analysis. Mercury intrusion
212
porosimetry (MIP) for particle size analysis is also considered in this study, even
213
though it is not a widely used technique.
214
3.1 Sieving analysis
215
The simplest means of assessing the fineness of SCMs is through a sieve analysis
216
since it does not require the specialized instrumentation used in other methods.
217
However, the information obtained from sieve analysis of a fine powder is more
218
limited than that obtained through more sophisticated methods, as the most
219
commonly used sieve analysis procedures for powders utilize only one sieve size.
220
For example, ASTM C618 [21] specifies a maximum of 34% by mass retained on
221
the no. 325 sieve (45 μm opening size) for fly ash and natural pozzolans when
222
wet-sieved. Like density testing, the standard method used is one for portland 7
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223
cement, ASTM C430 “Standard Test Method for Fineness of Hydraulic Cement
224
by the 45-μm (No. 325) Sieve” [22]. The test standardizes the material mass to be
225
tested, the water pressure and nozzle type, and sieve calibration procedures. As
226
long as the material is in contact with water does not react. Sources of error in this
227
test can arise if the pozzolans are not adequately dispersed, as in densified silica
228
fume for example; agglomerated particles will not pass the sieve opening under
229
the low water-pressure specified.
230
An alternative to the wet sieving process is to use a dry, forced-air process to
231
sieve SCMs as described in EN196-6. This process can be more rapid than a wet
232
process since the sample does not need to be dried after testing. For example,
233
Hooton and Buckingham [23] demonstrated that an air-jet sieve using forced air
234
from a pressure-controlled vacuum measured the percent fly ash retained on the
235
no. 325 sieve in approximately 2 minutes. The values obtained are necessarily
236
slightly different than those obtained using the wet-sieve process, tending to be
237
slightly lower [33], but can be corrected using empirically-determined calibration
238
factors.
239
3.2 Air permeability test (Blaine)
240
Air permeability methods measure the resistance of flow of air through a packed
241
bed of cement of known dimensions and porosity. The time taken for a fixed
242
quantity of air to flow through a compacted material bed of specified dimension
243
and porosity is measured. Under standardized conditions, the specific surface of
244
the material, commonly referred to as the Blaine fineness, is proportional to t,
245
where t is the time for a given quantity of air to flow through the compacted bed.
246
The number and size range of individual pores in the specified bed are determined
247
by the particle size distribution, which also influences the time for the specified
248
air flow.
249
In 1939, Lea and Nurse introduced the constant flow-rate method that forms the
250
basis of British Standard BS 4550 [24]. A simpler, constant volume method that is
251
widely used in USA, UK and many other countries was developed by Niesel [25].
252
The apparatus (Fig. 1) consists of a U-tube manometer, a plunger, a permeability
253
cell and a perforated disc. It is calibrated according to the Lea and Nurse method
254
and the results are analyzed using the Carman-Kozeny equation [26] for viscous
255
flow through a bed, which involves knowledge of the density of the cement (or of 8
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256
the SCM). However, this ensures that the bed is uniform (which is very difficult to
257
achieve for platy-shaped particles such as those in most metakaolins), and that
258
none of the particles are very highly irregular in shape (which is violated for fly
259
ashes with punctured cenospheres and/or unburnt coal residues, or rice husk ashes
260
retaining some of the geometry of the original plant material).
261 Standard taper – female coupling to fit bottom of cell Valve or clamp
Glass tube
262 263
Fig. 1 Blaine air permeability apparatus
264 265
Today, two updated standards are in widespread use for the analysis of cement by
266
this technique, the American standard ASTM C204-07 [27] and the European
267
Standard EN 196-6 [28]. The bed of the material is prepared in a special
268
permeability cell to porosity e=0.500±0.005. The weight of the sample (m1) is
269
calculated from Equation 1:
270
[1]
271
where ρ is the density of the cement [g/cm3], and V is the volume of the bed [cm3].
272
The specific surface area, S, is expressed as:
273
[2]
274
where K is the apparatus constant, e the porosity of the bed, t the measured time
275
[s], ρ the density of the sample [g/cm3], and η is the viscosity of air at the test
276
temperature. 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
277
The apparatus constant is determined by measuring the permeability of the
278
reference material of a known specific surface area. Fine materials other than
279
cement may prove difficult to form into a compacted bed of porosity e = 0.500 as
280
described in this method. The reason for this may lie in the fact that thumb
281
pressure on the plunger cap may fail to bring it in contact with the top of the cell
282
or, after making contact and removing the pressure, the plunger may move
283
upwards as the bed restores semi-elastically to a larger volume. The porosity of e
284
= 0.500 is therefore likely to be unattainable for some materials, and this issue
285
will be revisited in section 4.2.
286
For such cases, the porosity required for a well-compacted bed needs to be
287
determined experimentally. The mass of the material to make the bed (m) then
288
becomes, in grams:
289
[3]
290
The specific surface area, S, is determined by Equation 4.
291
[4]
292
where e0 is the porosity of the bed of the reference material, S0 is the specific
293
surface of the reference material [cm2/g], t0 is the mean of the three flow times
294
measured on the reference material [s], ρ0 is the density of the reference material
295
[g/cm3], and η0 is the air viscosity at the mean of the three temperatures at which
296
the three triplicate measurements for the reference material were collected [Pa·s].
297
The air permeability test is a simple and rapid method that is used in the cement
298
industry [29]. However, air permeability is an indirect method and suffers from a
299
number of weaknesses, including an inability to account for variable particle
300
shape and bed tortuosity. The bed porosity is assumed to be close to 0.500, which
301
can lead to serious errors with some non-cement materials [30]. A significant
302
amount of the surface area of pores and cracks do not contribute to the flow
303
resistance, and so a lower result than expected may be obtained.
304
The method is comparative rather than absolute and, therefore, a reference sample
305
of known specific surface is required for calibration of the apparatus. The
306
reference material must have similar shape, particle size distribution, and surface 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
307
properties to the material of interest or it cannot be a valid comparison. In
308
addition, the test is designed for cement, so it becomes extremely unreliable at
309
surface areas greater than 500 m2/kg [29]. Its application to fly ash was suggested
310
to be of debatable value because of the unknown extent of influence of the
311
internal surface of unburned carbon particles present. Kiattikomol et al. [31] came
312
to the conclusion that Blaine fineness may not be sufficient to indicate the
313
fineness of fly ash, especially for fly ash with spongy phases. The full form of the
314
Carman-Kozeny equation includes an explicit sphericity term, which is
315
incorporated into the apparatus constant K in the Blaine method, and so it is
316
essential that the reference material is of a similar particle shape to the sample to
317
be analyzed.
318
3.3 Brunauer, Emmett and Teller (BET) Surface Area Analysis
319
In contrast to air permeability, the BET technique is a fundamental measurement
320
of specific surface area because it makes no assumption about the shape of the
321
particles. The BET method is based on the adsorption of a gas on the surface of
322
the solid, including any surface pores and cracks that the gas molecules can
323
access, and calculating the amount of adsorbed gas corresponding to a
324
monomolecular layer on the surface. Nitrogen is the most commonly used gas, but
325
any other inert gas can in principle be used. The physical adsorption of the gas
326
results from Van der Waals forces between the gas molecules and the adsorbent
327
surface area of the powder. The measurements are conducted at low temperature
328
(often the boiling point (-196 °C) of liquid nitrogen at atmospheric pressure, when
329
N2 is the probe molecule) and the amount of gas adsorbed can be measured by a
330
volumetric or continuous flow procedure.
331
Prior to BET analysis it is necessary to remove the gases and vapors that can be
332
physically adsorbed on the surface of the particles. This procedure is known as
333
outgassing (Section 2.3). It is important to bear in mind that BET analysis has
334
some limitations, as the possibilities of micropore filling or penetration into
335
cavities of molecular size are not considered in the measurement, which can
336
generate false results. When characterizing a material it is recommended to
337
measure at least three, but preferably five or more points, in the adequate pressure
338
range on the N2 sorption isotherm, to obtain reliable results. The conditions of
11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
339
outgassing, the temperature of the measurements and the range of linearity of the
340
BET plot should be reported along with the BET values [20].
341
3.4 Laser diffraction
342
Laser diffraction (LD) is rapidly becoming a more popular method for particle
343
size determination [18]. Technology and instrument characteristics have rapidly
344
developed in the last decades, and now LD is considered to be one of the quicker,
345
easier and more reproducible methods of characterizing particle size, because it
346
provides a complete picture of the full size distribution [32]. However, in laser
347
diffraction the mathematical models used assume that the material is isotropic and
348
consists of particles which can be approximated as spheres, meaning that the size
349
of the particle is determined as the diameter of a spherical particle with an
350
equivalent volume. These assumptions do not always hold for cements and SCMs,
351
as will be discussed in more detail below.
352
The International Standard ISO 13320 [33] on Particle Size Analysis for Laser
353
Diffraction Measurements is an introduction to laser diffraction particle sizing
354
systems giving information on theory, guidance on both dispersion and sampling,
355
and a methodology for proper quality control. However, the process by which a
356
method can be validated is not clear from this document.
357
It should be made clear that laser diffraction instruments do not measure particle
358
size distributions (PSD). What is measured is the light scattered by the particles.
359
To relate this to the particle size distribution, critical assumptions are made about
360
the optical properties of the material under analysis. A mathematical model is
361
needed to convert light scattering data to particle size distribution. Two optical
362
models are commonly used to calculate PSD, the Fraunhofer diffraction model
363
and the Mie theory.
364
The Fraunhofer approximation assumes that: (1) the particle being measured is
365
much larger than the wavelength of the light employed (ISO13320 defines this as
366
being greater than 40λ, i.e. 25μm when a He-Ne laser is used), (2) all sizes of
367
particles scatter with equal efficiencies, and (3) the particles are opaque,
368
transmitting no light. The Fraunhofer model does not make use of any knowledge
369
of the optical properties of the sample, and only scattering at the contour of the
370
particles (i.e. diffracted light) is considered to calculate the projected area of a 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
371
sample. It is important to note that diffraction is independent of the composition
372
of the particles [34], unlike the reflection and refraction that are not considered in
373
this model.
374
Mie theory [35], on the other hand, is a more accepted theory used in LD
375
measurements. The latest laser diffraction instruments use the full Mie theory,
376
which completely solves the equations for interaction of light with matter
377
(including diffraction, reflection and refraction of light). This can provide accurate
378
results over a large size range (typically 0.02 – 2000μm), as long as the optical
379
properties (refractive and absorption indices) of both the material and medium are
380
known. The Mie theory determines the volume of the particle, as opposed to
381
Fraunhofer model which predicts size based on a projected area. Whereas the
382
Fraunhofer approximation is not suitable for samples that are transparent or
383
semitransparent, and for small particles (i.e. less than 50 μm), Mie theory can
384
apply under these conditions [33].
385
Optical parameters
386
In order to apply the Mie theory, the optical parameters of the tested particles are
387
required. The optical properties determine how light interacts with a material, and
388
are defined by the complex index of refraction, ñ: ñ=n - ik
389
[5]
390
where i =
and n and k are the real and the imaginary parts of the complex
391
index of refraction. The real part, n, is called the refractive index while k is the
392
absorption (or extinction) coefficient. Both coefficients are dependent on the
393
frequency of light and standard refractive index measurements (n) are often
394
tabulated for wavelengths emitted by a sodium flame or a sodium vapor lamp
395
(589.3 nm) designated “D” [36]. The absorption coefficient ‘k’ is 0 or very close
396
to 0 for transparent or translucent material, and becomes important for opaque
397
media. In thin sections under the microscope a material will look opaque if its k-
398
value (the absorption coefficient), is greater than 0.01 [37].
399
The real part of the refractive index of a liquid or a gas is easily measured using a
400
suitable refractometer. However, the refractive index of a solid material in the
401
form of a fine powder is more difficult to measure, due mainly to the fact that the
402
material is often composed of more than one phase, which differ in their optical 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
403
properties. In fact, only a limited number of materials have a single, isotopic
404
refractive index: crystals belonging to the cubic crystal system, glasses and
405
amorphous substances. Minerals in other crystallographic systems are anisotropic,
406
with different refractive indices depending on crystal alignment with 2 or 3 main
407
values described as α, β and γ in tabulations of reference data [36,38]. The real
408
part of the complex index of refraction can be determined under an optical
409
microscope using the immersion method, in which the index of a solid is
410
compared with that of a liquid of known index [39]. A material grain which is
411
immersed in a liquid of matching refractive index as itself disappears from view.
412
However, if the liquid is of a different refractive index the grain stands out,
413
surrounded at the interface between the grain and the liquid by a thin band of light
414
known as the Becke line [39]. The greater the difference in the refractive indices
415
between the fragment and immersion, the greater is the intensity of the interface.
416
By using a series of liquids of varying refractive indices, the refractive index of
417
the material grain can be determined [39].
418
Direct measurement of the fundamental optical properties (refractive index n and
419
extinction coefficient k) can also be constructed using spectroscopic ellipsometry,
420
which is an optical measurement technique that characterizes light polarization
421
after reflection (or transmission) from a sample over a wide spectral range [40].
422
The use of correct input values for the optical parameters is very important for
423
particle size determination of smaller particles. When particles are large and have
424
a high refractive index difference compared to the suspension medium (e.g. air),
425
and if the absorption is low [41], the errors resulting from incorrect input of these
426
parameters are much smaller. Zhang and Xu [42] reported results on the effect of
427
particle refractive index on size measurement and noted that ‘it is well known
428
from Mie theory that the scattered light differs for particles with different
429
refractive indices, although the size or the distribution of the particles may be the
430
same’. Their conclusion was that if an incorrect refractive index is assumed when
431
the particle size distribution is computed from a measured scattered energy
432
distribution, a 10% error will be involved under most circumstances, but greater
433
errors may occur if the assumed refractive index is much less or greater than the
434
actual one.
14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
435
In the case of Portland cement, the refractive index is not a single value since
436
cement is a multiphase powder. Mean values are often calculated based on the
437
known optical properties for each constituent pure phase [43]. According to
438
Hackley et al. [41] for cementitious powders, absorption becomes important for
439
the fine fraction, below about 1 μm in diameter, where it can have a large impact
440
on the particle size distribution. For n ≥ 1.6 (fairly refractive materials), the model
441
is not very sensitive to the choice of n for weakly absorbing or transparent
442
materials (i.e., k < 0.1). It is only moderately sensitive at k = 0.1. The magnitude
443
of the calculated submicron fraction depends on the choice of k, with the
444
dependence being stronger as n becomes smaller [41].
445
Table 2 presents refractive indices n values for phases often present in Portland
446
cement and SCMs.
447
Table 2 Typical refractive index values (n) for phases often present in cements and SCMs
Phase
n
ref
Phase
n
ref
Pure C3S C4AF Arcanite Gypsum γ-CaSO4 MgO Akermanite Hydrogarnet Mirabilite Ettringite Thaumasite Calcite Magnetite Hematite Rutile
1.7139-1.07238 1.96-2.04 1.4935-1.4973 1.5205-1.5296 1.505-1.548 1.736 1.632-1.64 1.6041.734 1.394-1.398 1.462-1.466 1.468-1.504 1.486-1.658 2.42 2.87-3.22 2.605-2.908
[44] [44] [44] [44] [44] [38] [38] [38] [38] [38] [38] [38] [45] [45] [45]
β-C2S γ-C2S Ca(OH)2 Hemihydrate Syngénite Gehlenite C-S-H Merwinite Thenardite Monosulfate Quartz Mullite Maghemite Cristobalite Anatase
1.717-1.735 1.642-1.654 1.545-1.573 1.559-1.5836 1.5011-1.5176 1.658-1.655 1.49-1.530 1.708-1.724 1.464-1.485 1.488-1.504 1.544-1.553 1.642-1.654 2.54 1.485-1.487 2.488-2.561
[44] [44] [44] [44] [44] [38] [38] [38] [38] [38] [38] [38] [45] [45] [45]
448
Note – range of values for anisotropic substances
449
Values for the absorption coefficient k are less frequently reported. For cements
450
the imaginary parts k of the complex refractive index are reported within the very
451
wide interval of k = 0.003 to 1.0 [46]. A mean value of 0.1 was used by Hooton
452
and Buckingham [24] for ordinary Portland cement and fly ash and 0.001 for
453
silica fume. Gupta and Wall [47] presented a range for k from 0.005 to 0.01 for
454
char-free ash from subbituminous coal, while values between 0.005 and 0.05 have 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
455
also been reported [48,49]. However, those authors (working on the radiative
456
properties of fly ashes) concluded that it is not acceptable to ignore the
457
wavelength-dependence of fly ash refractive index and that previous studies
458
employing n = 1.5 and k ranging from 0.005 to 0.05 seem to overestimate the
459
Plank mean absorption coefficient of fly ash particles. Liu and Swithenbank [49]
460
mentioned that the average value of the imaginary part of the fly ash complex
461
refractive index k = 0.012 estimated by Gupta and Wall [50] is definitely too high.
462
Reported values in the literature for the refractive index and the absorption
463
coefficient of ordinary Portland cement and SCMs are shown in Table 3.
464 465 466
Table 3 Typical refractive index values (real) and absorption index values (imaginary) of cement and cementitious materials. OPC – Ordinary Portland Cement; BFS – Blast furnace slag; GFS – Gasification slag
Material OPC Fly ash Fly ash, Class F Fly ash, Class C BFS, GFS Silica fume
Refractive Index, n 1.73 1.73 1.50 1.56 1.65 1.62 1.53
Absorption coefficient, k 0.1 0.1 0.005 – 0.05 1.0 0.1 1.0 0.001
Reference [51] [51] [49] [52] [52] [52] [51]
467 468
Obscuration level and specific surface area
469
Another factor that affects the results in the laser light scattering method is the
470
obscuration, which is related to the sample concentration. Practically, it is the
471
fraction of light that is lost from the main beam when the sample is introduced. It
472
gives a visual indication of how much sample is added. Further, the measurement
473
is affected by the dispersant that is used for the de-agglomeration of the sample
474
and the measurement time. The optimum measurement time depends on the size
475
of the sample and particle size distribution. Normally a measurement time of
476
10sec is used, with 3 replicates.
477
The specific surface area (SSA) is then calculated from the particle size
478
distribution by Eq. 6, assuming that the particles are spherical and non-porous:
479
[6] 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
480
where Vi is the relative volume in class i with mean class diameter of di, ρ is the
481
particle density, g/cm3 and D[3,2] is the surface weighted mean diameter (μm).
482
3.5 Particle size analysis with microscopy image analysis
483
Image-based, particle size analysis relies on the principle developed by Medalia
484
(1970) [53]. Modern image analysis uses scientific cameras to provide low
485
distortion digital images that are instantaneously processed to extract particle size
486
and shape.
487
The imaging setups have to be calibrated in terms of illumination and spatial
488
resolution. Illumination is usually adjusted through trial and error procedures to
489
optimize the contrast between the background and the objects to be measured. A
490
blank image consisting in the imaging of the single background is usually
491
acquired to allow spatial correction of the illumination of the field of view.
492
The illumination intensity also needs to fit to the camera sensitivity to guarantee
493
the shorter exposure time possible. Camera saturation should however always be
494
avoided, as it can cause some blurring effect and compromise accurate
495
measurement. Various illumination geometries can be envisaged. However, the
496
highest resolution is achieved with an axial back-lighting of the particles [54,55].
497
Once the illumination setup is fixed, the spatial resolution in the field of view has
498
to be calibrated. This is usually performed thanks to the imaging of a reference
499
grate which size is well-known.
500
Overall imaging setups are commonly classified into two main categories:
501
dynamic or static type. In dynamic image analysis setups, particles are moving or
502
free-falling in the field of view of the camera which induces some uncertainties
503
related to the particle position and orientation. The impact on the measurement is
504
particularly sensible in the case of elongated particles. In the static setups,
505
particles are at rest in a plan thus the probability to measure the particle longest
506
dimensions is statistically high. The more controlled static setups should be
507
preferred for accurate measurements [56].
17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
508
3.6 Mercury Intrusion Porosimetry (MIP) for Particle Size Distribution
509
Mercury Intrusion Porosimetry (MIP) has formed the basis for a number of
510
internationally recognised standard analyses; however it seems, as observed by
511
León [57], that the full extent of its capabilities remains underexploited.
512
Generally MIP is used to study the volume, distribution and interconnectivity of
513
the voids (pores) within porous solid and fine-grained samples, relying on the
514
Washburn equation to build a picture of the microstructure. On the premise that
515
for a given pore radius, a certain pressure is required to intrude a non-wetting
516
fluid (mercury) and by recording the volume intruded for each pressure increment,
517
an intrusion curve may be derived. It can be represented by the Washburn
518
formula:
519
P = -2γcos(θ)/r
[7]
520
Where P is the pressure, γ is the surface tension of the fluid, θ is the contact angle
521
between the fluid and the material’s surface, and r is the pore radius [57,58].
522
The Washburn theorem assumes a model of cylindrical pores; the MIP technique
523
further assumes that these cylinders get progressively smaller towards the inside
524
of the sample; as pressures increase for further intrusion, it is assumed that this is
525
due to progressively smaller pore radii [59]. Naturally, these assumptions are
526
seldom representative of a porous material used in practice, however the data
527
produced when compared to data from other materials also assessed under MIP,
528
can be valuable for depicting trends and interrelationships.
529
There is little information in the literature about particle size distribution
530
determined via MIP [57,60,61]. Particle size distribution (PSD) by MIP is derived
531
from Mayer and Stowe’s [62] relationship established between particle size and
532
breakthrough pressure required to fill the interstitial voids between a packed bed
533
of spheres. Following the development of PSD by MIP, Mayer and Stowe
534
presented the benefits of the spherical model for characterising certain types of
535
porous solids, over that of the cylindrical model [63].
536
Employing the same principle of interfacial tensions giving resistant force to an
537
intruding, non-wetting liquid, a curve of intrusion vs. applied pressure is
538
produced. PSD by MIP relies on the premise that this curve contains structural
539
information about the studied material. 18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
540
MIP uses a model of cylinders for ‘typical’ pore analyses and a model of spheres
541
for particle size analyses. The particle size distribution as analysed by the MIP
542
curve is perhaps better termed the “Equivalent Spherical Size Distribution”, as the
543
calculated PSD derives from the modelled set of spheres which best represents the
544
logged experimental data [64].
545
The question of how representative these results are is therefore dependent on
546
how similar the particle geometry is to that of a set of spheres. Plate-like or very
547
angular particles conform less well to the mathematical model than mono-sized
548
well-rounded particles.
549
This application of the MIP technique is subject to some criticism arising from,
550
amongst other aspects, the set of inherent assumptions it relies on. Particle size
551
distribution is an extension of many of these assumptions, including its own
552
additional ones, and as such must be undertaken using a considered approach. The
553
results of the technique display an approximation of the particle size distribution,
554
rather than a measurement; it provides a ‘feel’ for the characteristics of the
555
particles, used along with complementary techniques and viewed in an objective
556
context.
557
Whilst Huggett et al. [60] considered the assumptions of Mayer-Stowe PSD by
558
MIP to be “gross”, seeking to refine the method and presenting their modified
559
alternative approach, they did indeed find that the Mayer-Stowe technique
560
presented “a good approximation” of PSD for certain types of samples.
561
Practically speaking, however crude the mathematical model may be when
562
compared to the true sample, careful management of certain variables can hold
563
significant benefit to the overall representivity of the analysis. One such
564
consideration is that of fine pressure increments as a pragmatic way of increasing
565
accuracy. Another is the contact angle assumed for analysis; setting a control
566
contact angle (e.g. [65]), if perhaps a little crude, remains useful for comparing
567
data from physically and chemically similar materials analyzed under the same
568
technique [57].
19
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
569
4 Materials and Methods for Demonstration Testing
570
4.1 Materials
571
Two batches of fly ash (FA1, FA2), two ground granulated blast furnace slags
572
(BFS1, BFS2), and a densified silica fume (SF), were used to demonstrate the
573
methods and techniques discussed in this paper. The chemical compositions of the
574
materials are presented in Table 4. Scanning electron micrographs providing a
575
qualitative indication of the shape and morphology of the materials under
576
investigation are shown in Figure 2. The fly ash and silica fume particles are
577
generally spherical, whereas the BFS particles are angular and irregularly shaped.
578 579
Table 4 Chemical composition of the materials used in this study, determined via X-ray fluorescence. Loss on ignition (LOI) was determined at 1000C
wt.% SiO2 Al2O3 Fe2O3 CaO MgO Na2O K2O P2O5 SO3 ClReactive SiO2 Free CaO Na-equivalent LOI
FA1 54.19 23.5 7.92 3.02 1.92 1.08 3.38 0.27 0.94 0.003 41.86 0.1 3.31 1.84
FA2 51.37 28.71 5.10 3.56 1.01 0.29 1.77 0.64 1.11 0.001 37.48 25µm
939
Differences between PSD and SIA results are usually attributed to insufficient
940
dispersion of the fine particles in the case of SIA, or inaccuracies in the optical
941
model in the case of laser diffraction [73]. In this study, different optical models
942
were used when analyzing the particle size of the slag via laser diffraction, and the
943
results derived from this technique are three times smaller than the ones obtained
944
applying SIA.
945
5.6 Particle Size Distribution determined using MIP
946
Limitations of the MIP technique are evident where considering a substance
947
where inter- and intra-particle voids are of a similar size, and distinction between
948
the volume of mercury intruded into the pores of the particle, and into the spaces
949
between the particles cannot practically be made. However, for the majority of
950
powder samples, it may be expected that while their inter-particle voids may be
951
high (spaces between particles), their intra-particle voids (spaces within particles)
952
are typically small; and hence, the distinction tends to be simple.
953
Mercury intrusion does not measure particle sizes in the way that techniques such
954
as laser diffraction and image analysis do. In MIP technique it is assumed that
955
particles have the same shape, spherical, and that they are evenly packed. The
956
mean particle size is estimated by the pressure it takes to fill the interstitial
957
volume with mercury. In other words, the particle size distribution derived from
958
this method is the size distribution of spheres that, when applied to the
36
959
mathematical model, most closely reproduce the experimental penetration data.
960
The size unit is ‘equivalent spherical size’.
961
Results obtained from MIP analysis of the fly ash, blast furnace slag and silica
962
fume are shown in Figure 14. The PSD graphs indicate a predominant particle size
963
around the 5-10µm range for FA1(Figure 14a), FA2 (Figure 14b), BFS1 (Figure
964
14c) and BFS2 (Figure 14d) samples. The silica fume PSD indicates a
965
predominant particle size centring around the 100-200 nm (Fig. 14e). Comparing
966
the results for SF from LD (Figure 12) and MIP (Figure 14) can be seen that in the
967
first method a bimodal distribution was found and measured particles have a
968
predominant size of 10 μm, whereas in the second method smaller particles of 0.1
969
μm are measured. In all the samples analyzed, the PSD peaks were sharply
970
defined, suggestive of a rather monosized (relative to the size spectrum) particle
971
arrangement.
972 Intrusion Volume (mL/g)
1.20
a
1.00 0.80 0.60 0.40 0.20 0.00 1
10 100 1000 10000 100000 Particle Equivalent Spherical Size Dia.(nm)
973 Intrusion Volume (mL/g)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
1.20
b
1.00 0.80 0.60 0.40 0.20 0.00 1
974
1000000
10 100 1000 10000 100000 Particle Equivalent Spherical Size Dia.(nm)
1000000
37
Intrusion Volume (mL/g)
0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
c
1
Intrusion Volume (mL/g)
975
10
100 1000 10000 100000 Particle Equivalent Spherical Size Dia.(nm)
1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00
1000000
d
1
976 Intrusion Volume (mL/g)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
10 100 1000 10000 100000 Particle Equivalent Spherical Size Dia.(nm)
1000000
2.50
e
2.00 1.50 1.00 0.50 0.00 1
977
10 100 1000 10000 100000 Particle Equivalent Spherical Size Dia.(nm)
1000000
978 979
Fig. 14 Particle size distribution of (a) BFS1, (b) BFS2 and (c) FA1, (d) FA2 and (e) SF samples
980
6 Conclusions
981
The use of SCMs has become widespread in the concrete and cement industry.
982
The shape and size peculiarities of SCMs differentiate them from cement, and
983
therefore the techniques that are currently used for the physical characterization of
984
cement may not be directly applicable to SCMs. Considering particle size
985
distribution as one of the most important parameters for the optimization of SCM
986
utilization, several techniques that are used for the determination of PSD have
987
been investigated in this study. Some of them are more widely used in cement (i.e.
using MIP.
38
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
988
air permeability test, sieving, laser diffraction, BET, image analysis) while MIP is
989
not generally applied to measure particle size distributions, but seems to be a
990
promising technique for the PSD determination of SCMs. However, it must be
991
realized that particle size analysis is not an objective in itself but is a means to
992
correlate powder properties with some process of manufacture, usage or
993
preparation.
994
Samples of fly ash, blast furnace slag and silica fume were measured using the
995
techniques presented in this study and the following conclusions are drawn:
996
Materials should be adequately dispersed before testing.
997
When applying an air permeability method to the SCMs, problems occur
998
during the procedure related to the difficulty to form a good compacted bed of
999
specific porosity.
1000 1001
For particles that are porous, or have a rough surface structure, the BET surface area is found to be greater than the Blaine surface area.
1002
Wet sieving overestimated the results because agglomerated particles remained
1003
on the sieve. The wet sieving method could not be used for silica fume since
1004
the criteria established for this method are only valid for fly ash and natural
1005
pozzolans.
1006
For the wet LD technique a method was developed for the measurement of
1007
SCMs. The optimized parameters for the sample of blast furnace slag are
1008
demonstrated in this study. The analysis presented here indicated that results
1009
obtained by LD method are strongly influenced by the optical parameters of the
1010
material that is measured.
1011 1012
Analysis of microscope images of blast furnace slag gave particle sizes three times larger than the ones obtained by laser diffraction.
1013
MIP is also presented as a method for the determination of particle size
1014
distribution of SCMs giving quite satisfactory results. The particle size
1015
distribution derived from this method is the size distribution of spheres that,
1016
when applied to the mathematical model, most closely reproduce the
1017
experimental penetration data.
39
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
1018
Accuracy can be difficult to define for size analysis of non-spherical particles;
1019
all sizing techniques give different answers. For irregularly shaped particles,
1020
characterization of particle size must include information on particle shape.
1021 1022 1023
References
1024 1025
[1] Lothenbach B, Scrivener K, Hooton RD (2011) Supplementary cementitious materials. Cement and Concrete Research 41 (3):217-229.
1026 1027
[2] Snellings R, Mertens G, Elsen J (2012) Supplementary Cementitious Materials. Reviews in Mineralogy & Geochemistry 74:211-278.
1028
[3] Siddique R, Khan MI (2011) Supplementary Cementing Materials. Springer.
1029 1030
[4] Celik IB (2009) The effects of particle size distribution and surface area upon cement strength development. Powder Technol 188 (3):272-276.
1031 1032
[5] Scrivener KL, Kirkpatrick RJ (2008) Innovation in use and research on cementitious material. Cement and Concrete Research 38 (2):128-136.
1033 1034 1035 1036
[6] Ursula Stark AM Particle size distribution of cements and mineral admixtures - Standard and sophisticated measurements. In: Owens DGGaG (ed) 11th International Congress on the Chemistry of Cement (ICCC), Durban, South Africa, 11-16 May 2003 2003.
1037 1038 1039
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