Along the S‐Curve – How Superplasticizers Affect the Yield Stress of Cement Paste

In cementitious systems, superplasticizers have two core purposes. On the one hand, they are used to lower the yield stress of a cement paste without changing the water to cement (w/c) ratio. On the other hand, they can reduce the w/c ratio without changing the yield stress. The relationship between slump flow and dosage of a superplasticizer containing cement paste can be described as an S‐curve. Below a critical dosage, the superplasticizer does not increase the flow. Above this dosage, the flow increases linearly until the saturation dosage is reached. Further addition of polymer will therefore not increase the fluidity of the cement paste. The minimum dosage which corresponds to an onset of increased flow compared to a dispersant free paste is referred to as the critical dosage.

There are three stages of surface coverage of a cement particle if an adsorbing superplasticizer is added in increasing amounts: zero coverage, partial coverage and full coverage with polymer.At zero coverage, only interparticle forces of the bare cement particles occur [4].At full surface coverage, only interactions of the polymer covered particles are expected.In cementitious materials, most of the time, a fully covered surface is not required or experimentally desirable.Superplasticizers are often used at a dosage below full surface coverage.An excessive dosage can result in sedimentation, also known as bleeding, which results in unacceptable concrete quality.Even if a sufficient dosage for complete adsorption is applied, incomplete surface coverage can occur due to the competition of another species (like sulfates or retarders) which also can adsorb on the surface.A second mechanism is connected to polymer loss due to adsorption on newly formed hydration products [5].A statistical distribution is usually assumed at partial polymer surface coverage.Adsorption measurements at incomplete surface coverage show a linear relation between the amount of adsorbed polymer and the amount of polymer dosed [6].This linearity is also observed in the increase of fluidity between zero and full surface coverage.There are two regions which deviate from this linearity: the region around and below the critical dosage and the region around and above the saturation dosage.
This study focusses on analysing the data obtained at the different regions of the dosage curves of three different superplasticizers.We chose a melamine formaldehyde sulfonate polymer (MFS), a polycarboxylate ether (PCE) and a polyphosphate ether (PPE) superplasticizer.The dosage curves were measured at two different w/c ratios for each superplasticizer using slump flow tests.The critical dosage and saturation dosage were calculated by using linear regression.To measure the region at ultra-low dosages, additional experiments were conducted using a rotational rheometer and MFS as dispersant.Based on the obtained data, it is shown that the definitions of the critical dosage and saturation dosage need to be extended.

2
Materials and methods

Cement
A Portland Cement CEM I 42.5 R was used for all measurements.Selected parameters are shown in Table 1.

Monomer Synthesis
To synthesize the phosphate bearing monomer 2-(methacryloyloxy) ethyl phosphate (monoheme phosphate, MHP), 48.65 mL (52.05 g) HEMA were placed in a threeneck flask at 0 °C.20.29 mL (41.79 g) polyphosphoric acid were placed in a dropping funnel and heated to 100 °C with a heat gun until they were fluid enough to be added dropwise.After the addition, the reaction mixture was stirred at 0 °C for 2 h.Subsequently, the sample was stored at 4 °C.

Polymer Synthesis
The polycarboxylate and polyphosphate superplasticizer were both polymerized by free radical polymerization.In the following, the polymerization is described, the amounts of the chemicals can be seen in Table 2.The monomer and MPEG 5005 MA were placed in a flask, the amount of water needed to achieve a solids content of 20 % was added and the mixture was preheated to 80 °C.After the temperature was reached, 3-MPA was added.NaPS solution was added and the reaction mixture is stirred for 1 h at 80 °C.When the solution has cooled down, the pH value is adjusted to pH 7 with sodium hydroxide solution.The schematic polymerization reaction can be seen in Figure 2, the structure of all polymers is shown in Figure 3.

Cement paste preparation
The preparation and mixing protocol which was used for all rheological measurements is shown in Table 3.The upper diameter was 7 cm, the lower diameter was 8 cm, and its height was 4 cm.The cement paste was prepared as described above.The measurement start was lifting the cone.The slump flow diameter was measured two times in perpendicular directions and then averaged.

Rotational rheometer measurements
The rheometer measurements were carried out using a MCR 502 rheometer (Anton Paar) equipped with a vane in cup geometry.The vane diameter was 2 cm, the cup diameter was 7 cm, and its depth was 6 cm.The cement paste was prepared as described above.The measurement start was a 90 s pre-shearing phase, afterwards 15 steps, lasting 6 s, respectively, the torque was measured with decreasing shear rates from 80 s −1 to 0.02 s −1 .Each step contained 60 data points, i.e., one data point each 0.1 sec.
The yield stress  0 and viscosity µ for each flow curve was calculated by using the Reiner-Riwlin equation [7] for a Bingham yield stress fluid.

3
Results and discussion

Overview of slump flow tests
In this study, three different superplasticizers were analysed by slump flow measurements.PCE and PPE are comb polymers and provide steric hindrance to avoid agglomeration of the cement particles.They differ in the nature of the anionic functionality, which is a carboxylate group for PCE and a phosphate group for PPE.In contrast, the mode of action of MFS is based on electrostatic stabilization.For the first time, these three polymers were directly compared in the same experimental setup by using slump flow measurements (see Figure 4).
The two comb shaped polymers PCE and PPE have comparable dosing curves, whereas the curve of melamine is shifted further towards higher dosages and noticeably flatter.This demonstrates the strong dependence of the dosing efficiency of a superplasticizer on the mode of stabilization.

Below the critical dosage
Below a critical dosage, the superplasticizer has no effect on the properties of the cement paste.The surface coverage of the cement particles by the superplasticizer is too low to prevent agglomeration.Beyond this critical dosage, the flow behavior improves with increasing dosage until saturation of the superplasticizer on the surfaces is achieved [9].However, even at ultra-low dosages, the addition of superplasticizer affects the interparticle forces.In a solution containing charged particles and superplasticizer, three types of interparticle interactions that can occur: the interactions between two bare particles (B-B), the interaction between a bare particle and a particle which is covered with superplasticizer (B-P) and the interactions between two covered particles (P-P).In absence of any superplasticizer, only B-B interactions can occur and at a full covered particle surface, only P-P interactions take place.Kjeldsen et al. [4]   The rotational rheometer measurements can also be used to determine the Bingham viscosity of the cement paste, which is shown in Figure 6.In contrast to the yield stress, the viscosity captures the energy dissipation of the material during deformation.This curve can be divided into four different regions.Region 1 between 0.00 and 0.06 %bwoc corresponds to the region below the calculated critical dosage.The linear relation between the decrease of the viscosity and the polymer content can be interpreted as an increasing share of B-P interactions between particles.Region 2 between 0.06 and 0.14 %bwoc is characterized by incomplete surface coverage and mostly B-P interactions.The slope in this region is larger than for region 1 due to a larger fraction of B-P and some additional P-P interactions.Region 3, between 0.14 and 0.20 %bwoc, shows a decrease in viscosity due to the decrease of B-P interactions, i.e.P-P starts to dominate.Region 4 is between 0.20 and 0.32 %bwoc, where saturation with polymer is reached.A similar regime of 4 distinctive regions is found for the adsorption of ionic surfactants, such as alkenesulfonates, onto adsorbents with strongly charged sites, like alumina, in aqueous solution [8].A linear relationship between interparticle forces at very low surface coverage could be possible based on the same observations made by Rosen in adsorption behaviour.However, further measurements are needed to confirm this.
In addition to the initial detection of a change in rheology, the critical dosage is associated with the beginning of a linear relation between the dosage and the effect on rheology.Linear regions can be observed in region 1 in both the dosage curve for Bingham viscosity and the dosage curve for Bingham yield stress.However, the linear region that represents the linear relationship between dosage and effect only begins in region 2. Therefore, a more accurate definition for the critical dosage would be the dosage at which linearity between dosage and effect with a uniform slope can be observed.

The saturation dosage
By comparing the dosage curves of PCE at two different w/c ratios, it is found that the saturation dosage decreases with an increase of the w/c ratio (see figure 6).The ratio of the superplasticizer amount to the cement surface is the same in both cases because the polymer dosage is normalized with regard to the cement weight (note that the polymer dosage is always adjusted "by weight of cement" which implies a fixed ratio of polymer mass per cement mass).At the saturation dosage, the surface is completely covered, and the yield stress reaches a minimum value [9].If this definition would be strictly valid, the saturation dosage should not depend on the w/c ratio.The w/c ratio is related to the solid volume fraction Φ of a cement suspension (a decrease in w/c ratio leads to an increase in Φ).
The relation between the volume fraction of a cement paste and its yield stress has been formulated by Flatt [10] in the so-called YODEL model and can under certain conditions be simplified to: Where  is the yield stress, Fmax is the maximum interparticle force, Φ0 is the percolation threshold and Φmax is the maximum packing fraction.According to equation (1) a higher solid volume fraction Φ will result in a higher yield stress.Because the yield stress is linked to the slump flow (vide infra) an increased yield stress will result in a lower slump flow.Therefore, a lower w/c ratio will result in a lower slump flow at fixed polymer dosage which corresponds to the data presented here.If the same yield stress is to be achieved at different solid volume fractions, the interparticle forces must change accordingly.An increase in volume fraction must be compensated by a decrease in interparticle forces if the yield stress is to stay constant.In the context of cement pastes containing superplasticizers, this implies the amount of adsorbed superplasticizer needs to increase if the same yield stress is to be obtained at decreased w/c values.As can be seen in Figure X, the flow values of cement pastes without superplasticizers differ at various w/c ratios due to differences in the densities of the pastes.Therefore, it is not possible to compare the dosages of the superplasticizers at a certain flow value.However, slump flow values can be transformed into the yield stress of the cement paste via an equation first reported by Roussel.This equation has been modified later by different authors [11,12].We chose to use the simplest form of this approach.

𝜏 = (2)
Where ρ is the density of the cement paste, V is the volume of the cone and R is the radius of the slump flow.
As reference, the slump flow at a w/c ratio of 0.30 and a dosage of 0.06 %bwoc was used.The slump flow was converted into the yield stress using Equation ( 2).Then, the corresponding flow value for a w/c of 0.34 was calculated using this yield stress.Since the dosage curve was only measured at certain dosages, there is not a corresponding dosage for every slump flow value.Therefore, using the regression line, the dosage at which the calculated flow value must occur was determined (marked in orange in Figure 7).The relation between superplasticizer dosage and interparticle forces becomes more obvious when comparing superplasticizers with different modes of action.While PPE and PCE have similar architectures and primarily impact the interparticle forces through steric interaction, MFS acts through increased electrostatic repulsion.To compare the three superplasticizers, the slump flow of PCE at a w/c ratio of 0.34 was chosen as the reference again.Subsequently, the dosages for the same slump flow were determines on the regression lines of the two superplasticizers.A conversion to yield stress was not necessary since the same w/c ratio was used.Table 4 shows the calculated data.Comparing the dosages required to achieve a slump flow of 22.5 cm at a w/c ratio of 0.3, it can be observed that the saturation dosages of PPE and PCE are similar (0.06 and 0.08%), while MFS requires a dosage of 0.49 % bwoc, which corresponds to a factor of 8 and 6 for PCE and PPE respectively.This observation supports the expectation that sterically stabilizing superplasticizers have a significantly higher dosage efficiency.
These data demonstrate that the saturation dosage is independent of the particle surface coverage.A more accurate definition would be the dosage at which further addition of superplasticizer does not cause any changes in interparticle forces and therefore changes in rheology.

Above the saturation dosage
As mentioned earlier, MFS is a less dosage efficient superplasticizer and is therefore more suitable to capture small changes in the properties of cement paste (the sampling density is limited and comb polymers have a much larger slope in the dosage curves).By measuring the slump flow of MFS at different polymer dosages, two different regions are observed in the resulting curves (as shown in Figure 8), regardless of the measured w/c ratio.Region 1 has a lower slope than the linear region before it, forming nearly a plateau that represents the maximum slump flow of cement paste, which is needed to calculate the saturation dosage.In region 2, an increase in slope can be observed, resulting in a higher spread diameter which is caused by bleeding of the cement paste.
PCE and PPE, being much more dosage efficient superplasticizers, did not reveal the first region in their dosage curves (compare Figure 6).This is because the slopes of the dosage curves of these superplasticizers are significantly steeper and the intervals at which the superplasticizers can be dosed are limited by the accuracy in weighing.As the maximum slump flow is needed to calculate the saturation dosage, the last measurable datapoint before bleeding occurred was used.

The linear region
As demonstrated earlier, the critical dosage refers to the point where a strong change in the rheological parameters occurs, while the saturation dosage is the point at which the addition of further superplasticizer has no effect on the rheological properties or causes bleeding.The linear regime between the critical and the saturation dosage represents the effective working range of a superplasticizer.The critical and saturation dosage can be calculated from the dosage curve (see Figure 9).The blue line represents the dosage curve and the linear regression calculated at the linear region is shown by the orange line.The slump flow of the cement paste without any superplasticizer represents the minimum slump flow which is possible and is therefore taken as the lower boundary (grey line).The upper boundary is the maximum slump flow measured, which varies depending on the superplasticizer (green line).The intersection of the regression line with the lower boundary represents the critical dosage (marked with light blue).Similarly, the intersection of the regression line with the upper boundary represents the saturation dosage (marked with black).The slope of the regression line can be interpreted as the dosage efficiency of the superplasticizer.The obtained values for each superplasticizer at every w/c ratio are shown in table 5.The comb copolymers PCE and PPE exhibit much larger slopes than MFS.Additionally, the slope is steeper at higher w/c ratios.For instance, the slope of MSF is approximately ten times smaller than that of PCE, reflecting the different dosage ratios required to achieve the saturation dosages.The two comb shaped superplasticizers have comparable slopes and critical and saturation dosages, attributed to their similar architecture and mode of stabilization through steric repulsion (compare Figure 4).These observations are consistent with those made in 3.2.
(compare Table 4) and demonstrate that the values calculated from the dosage curve are appropriate for comparing different superplasticizers.

Conclusion
The focus of this study was on the typical S-curve obtained when plotting a dosage curve of a superplasticizer against cement paste.Therefore, the points defined in the S-curve were thoroughly examined, and it was shown that a modified definition of these points is reasonable.The revised definitions have no impact on the calculated values, but rather on the understanding of these points.It has been demonstrated that linear regions may be measured depending on the measurement method used.Thus, the critical dosage needs to be revised from being based on the initial onset of an (linear) effect on the rheological properties to the measurement of a region with a linear relationship and consistent slope.With regards to the saturation dosage, it has been conventionally assumed that it is the dosage at which the particle surface is fully covered, and therefore, any further dosage of superplasticizer would not affect the rheological properties.However, it has been shown that at the saturation dosage, further addition of polymer does not affect rheology because there are no further changes in the interparticle forces, rather than because the particle surface is completely covered.

Figure 1
Figure 1 Typical flow curve which is obtained by plotting the dosage against the slump flow (adapted from [3])

Figure 2
Figure 2 Schematic polymerization reaction of PCE.C represents the amount of charged monomer, E represents the amount of side chains.For MPEG 5005 MA n is 113

Figure 3
Figure 3 Schematic structure of the polymers PCE, PPE and MFS

Figure 4
Figure 4 Dosing curves of PCE (blue), PPE (orange) and MFS (green) at a w/c ratio of 0.30.The data was obtained from slump flow tests demonstrated a linear correlation between the change in interparticle forces and increasing surface coverage with polymer.Therefore, below the critical dosage, only B-B and B-P interactions occur due to the ultra-low dosage of the superplasticizer.MFS is well suited to study the transition between the regimes due to its low dosage efficiency compared to steric dispersants.The slump flow test was used to determine the dosage curve.To measure the region below the critical dosage obtained from slump flow tests, a rotational rheometer was used.The yield stress and plastic viscosity was calculated by using the Bingham model (see Methods).The Bingham yield stress represents the force required to maintain movement of the cement paste.The yield stress for increasing MFS dosages is shown in Figure5.Overall, the dosage of the rheometer measurements is similar to the dosage curve of the slump flow test (they look like a reversed S due to the reciprocal relation between slump flow and yield stress).The yield stress decreases with increasing MFS amounts.Here, three different regions can be identified.In region 1, minor changes in the flow can be noticed.In region 2, a linear correlation of the dosage and the changes in yield stress can be observed.In region 3, the saturation dosage is reached and a further addition of superplasticizer provides no changes in yield stress.Referring back to Kjeldsen's study, these three regions can be attributed to the different occurrences of interparticle forces.In region 1, only B-B or B-B and B-P interactions take place, in region 2 all three interactions occur, and in region 3 only B-P and P-P, or P-P interactions occur.

Figure 5
Figure 5 Dosage curve for the Bingham yield stress of cement pastes containing different amounts of MFS.The data was obtained from rotational rheometer experiments

Figure 6
Figure 6 Dosage curve for the Bingham viscosity of cement pastes containing different amounts of MFS.The data was obtained from rotational rheometer experiments

Figure 7
Figure 7 Dosage curves of PCE at a w/c ratio of 0.34 (blue line) and 0.30 (black line).The slump flow of cement paste without PCE is drawn as a dashed line for the w/c ratio of 0.34 (light blue) and 0.30 (grey).The calculated dosage of PCE at a yield stress of 6.38 Pa is marked orange

Figure 8
Figure 8 Dosage curve of MFS at a w/c ratio of 0.34 (blue) and 0.30 (orange)

Figure 9
Figure 9 Determination of the critical dosage (light blue marker) and the saturation dosage (black marker) through linear regression (orange line) at the dosage curve (blue line) The upper boundary is the maximum slump flow (green line), the lower boundary is the slump flow of cement paste without superplasticizer (grey line)

Table 1
Mixing protocol

Table 2
Amount of chemicals which were used in the polymerizations

Table 4
Dosage required of each superplasticizer to obtain a slump flow of 22.5 cm

Table 5
Calculated values by using linear regression of the dosing curve measured by slump-tests of the different superplasticizers