Interparticle Forces and Rheology of Cement
Based Suspensions
D. Lowke1
Abstract. Rheological properties of cement based suspensions are affected by
the surface properties of the particles, the properties of the solvent and the adsorbed polymers. To understand the interaction between these parameters and
the rheology of cement based suspensions the surface forces of the colloidal
powder particles were considered. Three surface forces are taken into consideration – the attractive van der Waals forces, the repulsive double layer forces and
the polymer induced steric forces. A theoretical basis for the evaluation of these
forces in cement based suspension is given. Within the experimental program
the superplasticizer adsorption was determined for cement and ground limestone
suspensions. Rheological measurements were performed with these suspensions
to determine yield stress and thixotropy. The results indicate a strong correlation
between polymer adsorption, rheological properties of the suspensions and
evaluated forces.
1 Introduction
Fresh properties of High Performance Concretes (SCC, UHPC) like flowability,
segregation resistance and formwork pressure are determined by viscosity, yield
stress and thixotropy. Thus the control of rheological properties is the key to successful application of these concretes. The rheological properties are affected by
the surface properties of the particles, the properties of the solvent and the adsorbed superplasticizer polymers. In particular, the use of superplasticizers to adjust rheological properties of fresh modern high performance concrete has gained
in importance during recent years. To understand the interaction between properties of the raw materials and the rheology of cement based suspensions the surface
forces of the colloidal powder particles have to be considered. This paper focuses
D. Lowke
Technische Universität München, Centre for Building Materials (cbm)
e-mail: [email protected]
www.cbm.bv.tum.de
296
D. Lowke
on the effect of superplasticizer adsorption on yield stress and thixotropy explained by the interparticle potential energy.
2 Materials and Methods
Portland cement and ground limestone were used as powder materials in the investigations. The density determined by helium pycnometry, the mineralogical composition determined by X-ray diffraction, the surface area determined by nitrogen
adsorption and the mean Particle diameter of the powder materials determined by
laser diffraction are shown in Table 1. Quartz sand with a 0/2 mm grading and a
density of 2.6 g/cm³ was used as aggregate. The mixes were prepared with a polycarboxylate ether superplasticizer (SP) with 35% solids in aqueous solution and a
mean molecular mass of 44,500 g/mol. The mean hydrodynamic Rh,avg was determined at 9.5 nm.
Table 1 Characteristics of the powder materials
Alite
Belite
C3A
C4AF
ρ
As
d50
[wt.%]
[wt.%]
[wt.%]
[wt.%]
[g/cm³]
[m²/cm³]
[µm]
Cement
62.3
10.5
8.0
6.7
3.2
6.38
15.1
Ground Limestone
-
-
-
-
2.8
3.39
7.0
Five Mortar mixes consisting of 150 L/m³ cement, 150 L/m³ limestone,
400 L/m³ sand and 315 L/m³ water were used in the investigations. The volumetric fraction of water and powder Vw/Vp was 1.06. For the reference mix the dosage
of superplasticizer was adjusted to 0.51 wt.% with respect to cement to yield a
slump flow of 260 ± 10 mm. To investigate the effect of superplasticizer content
on yield stress and thixotropy four mortars with varying amounts of superplasticizer were prepared. The amount of superplasticizer was changed by up
to ± 0.05 wt.%, Table 2. The rheological measurements for the determination of
yield stress and thixotropy were performed 10 min after water addition using a
rheometer with a rotating ball with a radius r of 10 mm. Before commencing the
measurements, the mortar was subjected to shear stress for 30 s in order to break
up agglomerates enabling the subsequent observation of structure formation. The
force of resistance Fmax needed to move the ball through the mortar suspension was
measured after waiting periods of 5, 30, 90 and 120 s during which the mix was at
-4
rest. Each measurement was performed at the very low rotational speed of 5·10
-1
m/s ( γ& ≈ 0.05 s ). Owing to the low shear rates in the investigations, the
measured resistance force Fmax is mainly due to the yield stress of the mortar.
Neglecting the shear force due to the rotation motion, static yield stress τmax was
calculated from the results of the rheological investigations using τ =YG F/(2πr²),
Interparticle Forces and Rheology of Cement Based Suspensions
297
YG = 0.14334, according to [1]. The first derivative of the yield stress as a function
of time (between 5 and 120 s) is a measure of the thixotropy T120.
Furthermore, three pastes with the same composition of cement, limestone and
water as the mortars and varying superplasticizer contents of 0.37, 0.51 and
0.95 wt.% were prepared to determine the superplasticizer adsorption. Pore Solution was extracted of the pastes 15 min after water addition. The total organic
carbon (TOC) content of the pore solution and the superplasticizer solution was
determined by high-temperature oxidation of the organic ingredients. The amount
of adsorbed superplasticizer was calculated as the difference between the TOC of
the added superplasticizer solution and the pore solution of the mortar.
3 Results
The superplasticizer adsorption of the pastes with superplasticizer contents of
0.37, 0.51 and 0.95 wt.% are shown in table 2. There was a strong linear relationship between the amount of added superplasticizer and the adsorbed superplasticizer. Thus the adsorption for the pastes with a superplasticizer content of 0.46,
0.50, 0.52 and 0.57 were calculated by a linear regression.
The effect of superplasticizer on the development of yield stress and thixotropy
of mortar is shown in Fig 1. It is apparent that larger amounts of superplasticizer
lower the yield stress as well as the thixotropy significantly. An increased SPcontent of 0.05 wt.% from the reference mix leads to an reduction of the initial
yield stress τmax,5 after 5s from 14 to 6 Pa and a reduction of thixotropy T120 from
0.16 to 0.09 Pa/s.
300
2.0
1.8
0.46
200
1.6
0.51
1.4
Thixotropy T120 [Pa/s]
Yield stress
0.50
0.52
max
[Pa]
250
0.56
150
100
1.2
1.0
0.8
0.6
0.4
50
0.2
0.0
0
0
a)
30
60
Time at rest tp [s]
90
0.0
120
b)
0.2
0.4
0.6
0.8
SP-Content [wt.% CEM]
Fig. 1 Yield stress as a function of time at rest at varying superplasticizer contents (a) and
effect of superplasticizer content on thixotropy (b)
298
D. Lowke
4 Discussion - Interparticle Forces, Yield Stress and Thixotropy
The effect of superplasticizer in fresh mortar may be understood in terms of the effect of polymer adsorption on the interaction forces between the individual particles of the powder suspension which may be divided into attractive van der Waals
forces, electrostatic forces and repulsive steric forces. In the case of cementitious
suspensions and its usual surface potential the electrostatic forces are thought to be
negligible compared with the van der Waals forces and polymer induced forces
[2]. According to [3], the van der Waals interparticle potential energy Gvdw between two spheres of radius a, separated by a distance h (between their surfaces
along the axis through the centre points) is given by
Gvdw = −
H
6
⎛
⎛ (h / a + 2)² − 4 ⎞ ⎞
2
2
⎜
⎟
⎜ (h / a + 2)² − 4 + (h / a + 2)² + ln⎜⎜ (h / a + 2)² ⎟⎟ ⎟
⎝
⎠⎠
⎝
(1)
where H is the Hamaker constant for the interaction. According to [4], the interaction energy Gster between adsorbed polymer layers can be calculated as follows.
Gster = πa
NA ⎛ Γ
⎜
υ3 ⎜⎝ ρδ
2
⎞
⎛1
⎞
⎟⎟ k BT ⎜ − χ1 ⎟(2δ − h )2 , h < 2δ
⎝2
⎠
⎠
(2)
Here NA is Avogadro’s number, ν3 the molar volume of the solvent, Γ the specific mass of the adsorbed polymer, ρ the density of the polymer, χ the polymer
segment interaction parameter and δ the thickness of the polymer layer. The
combination of the repulsive steric interaction with the attractive van der Waals
interaction yielding in the total interaction energy Gtot between the particles is
shown in Fig. 3a as a function of particle separation. As the particles approach,
the van der Waals attraction increases rapidly until the adsorbed polymer layers
on the particles meet (h = 2δ) and the steric repulsion superimposes on the van
der Waals energy, e.g. point C in Fig. 3a. For polymer concentrations encountered in flowable concretes, the polymer layer is effectively a wall by inducing a
very steep repulsion and prevents a further approach when h ≤ 2δ. In this case
the exact size of ν3, Γ, ρ and χ has little effect on the interaction so that the
thickness of the polymer layer is the paramount. Thin polymer layers mean that
the particles can approach to smaller distances and the interparticle attraction is
stronger, point A in Fig. 3a.
The thickness of the polymer layer was determined on the basis of absorptiometry, molecular weight and size. Assuming a spherical conformation of the
polymer in solution (compare [5]), the volume of a polymer molecule was estimated with the experimentally determined hydrodynamic radius (Fig. 2).
In a good solvent the side chains are stretched well in all directions around
the backbone which is situated in the centre of the polymer bundle. Due to the
Interparticle Forces and Rheology of Cement Based Suspensions
299
Fig. 2 Polymer conformation in solution and adsorbed on a surface and effect of adsorbed
polymer concentration on polymer layer thickness
negative charged carboxyl groups of the backbone, polycarboxylate ether adsorbs
with the backbone directly onto the surface. Thus the volume of the adsorbed
polymer bundle is about half the volume of the free polymer in the solvent. The
mean layer thickness δm is determined by the available surface area for the adsorbed polymer. This means that, the higher the amount of adsorbed polymer the
higher is the thickness of the polymer layer (Fig. 2). The calculated mean polymer
layer thicknesses δm of the mortars with varying superplasticizer contents are in a
range of 7.2 to 8.2 nm, see Table 2. They are in good agreement with values experimentally determined by [6, 7] using AFM.
Table 2 Variation of superplasticizer content, superplasticizer adsorption, calculated mean
thickness of the polymer layer and minimum of total interparticle energy
SP content [wt.%CEM]
0.37 0.46
0.50
0.51
0.52
0.57
0.95
Variation in SP [wt.%]
-0.14 -0.05 -0.01 ±0.00 +0.01 +0.05 +0.44
SP adsorption [mg/m²Solid]
0.409 0.461 0.484 0.490 0.496 0.522 0.728
Calc. mean polymer layer thickness δm [nm]
-
1
Minimum total interparticle energy Gmin/kT [-] 1
7.2
1
7.7
1
7.8
7.9
1
8.2
-
-58.1 -53.8 -52.8 -52.3 -50.0 -
Interpolated
The total interparticle potential energies between two particles with a radius
of 1 µm and different superplasticizer contents are shown in Fig. 3a. The depth of
the minimum in the total energy curves Gmin (Table 1) define the maximum attraction between the particles and determines the rheological properties of the mortars
at static conditions, like yield stress and thixotropy. The minimum depends on the
thickness of the polymer layer. With a decreasing layer thickness the minimum
decreases (Fig 3). According to [8] particles coagulate when the minimum energy
becomes smaller than -5kT. This causes a structure formation and thus yield stress
and thixotropy. A strong correlation between the minimum of the total interparticle potential energy Gmin, yield stress τmax,5 and thixotropy T120 was found for the investigated mortars, see Fig 3b. The lower Gmin the higher are yield stress τmax,5 and
thixotropy T120.
300
D. Lowke
250
-50
2δA
A
B
a = 1 μm
C
200
1.2
150
0.9
100
0.6
50
0.3
Thixotropy T120 [Pa/s]
-25
τmax,5 [Pa]
0
A 0.46
B 0.51
C 0.56
Gmin,C / kT
0
1.5
Yield stress
Thixotropy
Initial yield stress after 5s
Attraction Repulsion
Total interpaticle potential energy G tot /kT [-]
25
van der Waals attraction
-75
0
0
a)
5
10
15
20
Particle distance h [nm]
25
30
b)
0.0
45
50
55
60
Minimum total interparticle energy -Gmin/kT [-]
Fig. 3 Total interparticle potential energy (a) and correlation between minimum of total interparticle potential, yield stress and thixotropy (b)
5 Conclusion
The experimental investigations focused on the effect of superplasticizer content
on yield stress and thixotropy of fresh mortar. An increase in superplasticizer content led to a reduction in yield stress and thixotropy. The effect of superplasticizer
content on rheological properties can be understood in terms of the effect of
polymer adsorption on the interaction energy between the individual particles of
the powder. An increase in superplasticizer content results in a thicker adsorbed
polymer layer and consequently weaker van der Waals attraction between the particles so that less forces is needed to disperse the particles – yield stress and
thixotropy decreases.
It was shown that thixotropy and yield stress of the investigated mortars can be
explained by the interactions between the powder particles. The lower the minimum of the total interparticle potential energy Gmin, this means the higher the attraction between the particles, the higher are yield stress and thixotropy.
Owing to the complex nature of the interactions (e.g. heterogeneous composition of clinker particles, irregular particle shape, hydration reactions) the calculation of the interparticle interactions contain many assumptions and simplifications
so their accuracy is limited. However, this approach may be used to improve the
understanding of the mechanisms responsible for the rheological behaviour of
fresh mortar and concrete suspensions.
Acknowledgments. The author would like to thank the German Research Foundation
(DFG) for the financial support.
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301
References
1. Beris, A.N., Tsamopoulos, J.A., Armstrong, R.C., Brown, R.A.: Creeping motion of a
sphere through a Bingham plastic. J. Fluid Mech. 158, 219–244 (1985)
2. Kjeldsen, A.M., Geiker, M.: Modelling inter-particle forces and resulting agglomerate
sizes in cement-based materials. In: SCC 2005, pp. 105–111 (2005) ISBN 0-924659-64-5
3. Yoshioka, K., Sakai, E., Daimon, M., Kitahara, A.: Role of steric hindrance in the performance of superplasticizers for concrete. J. Am. Ceram. Soc. 80, 2667–2671 (1997)
4. Flatt, J.R.: Interparticle forces and superplasticizers in cement suspensions. Dissertation.
Lausanne (1999)
5. Gay, C., Raphaël, E.: Comb-like polymers inside nanoscale pores. Adv. Colloid Interf. 94, 229–236 (2001)
6. Kauppi, A., Andersson, M., Bergström, L.: Probing the effect of superplasticizer adsorption on the surface forces using the colloidal probe AFM technique. Cem. Con.
Res. 35, 133–140 (2005)
7. Laaraz, E., Kauppi, A., Andersson, K., Kjeldsen, A.M., Bergström, L.: Dispersing
multi-component and unstable powders in aqueous media using Comb-type anionic
polymers. J. Am. Ceram. Soc. 89, 1847–1852 (2006)
8. Hesselink, F.T., Vrik, A., Overbeek, J.T.G.: On the theory of the stabilization of dispersions by adsorbed macromolecules. J. Phys. Chem. 75, 2094–2103 (1971)