It has been shown that it is possible to compatibilize hydrophobic silica aerogels particles with water-based mineral binders to form highly insulating composites by using a surfactant to modify the aerogel’s interaction with water. In view of understanding the factors that control the performance of the resulting composites, a systematic study was performed using two different dosages of surfactant and several different aerogel contents.
Water accessible porosity
The surfactant modifies the aerogel surface generating a hydrophilic coating around the hydrophobic core. Depending on the amount of surfactant added, the amount of water that penetrates into the aerogel granules varies; however, there is a minimum surfactant dosage needed to change the aerogel’s hydrophobic behavior and to allow the formation of a slurry. For the surfactant used in this study, this amount has been found at a 0.1 % wt. addition with respect to water. To notice that the interaction of the aerogel particles with water changes suddenly at the mentioned surfactant amount, thus lowering the surfactant addition does not provide the compatibility needed to form slurries. This results into a fixed amount of water and a fixed amount of surfactant related to the aerogel addition, to which the water needed by the mineral binder to form a slurry must be added. The relationship between the surfactant and the water suggests that the surface tension of the solution should be decreased enough to be able to form the slurries.
An interesting result is that although more water is needed as the aerogel content is increased, this amount is roughly constant with respect to the mass of aerogel particles and this regardless of the surfactant dosage. This suggests that a constant amount of water is absorbed in the aerogels. Further increase of the amount of surfactant will increase the aerogel’s water absorption (up to 3.7 grams of water per aerogel gram, for a 5 % wt. surfactant addition in respect to water).
Engineering properties of composites
Mechanical behavior of composites
The final distribution by volume of the components within the mixtures in the fresh state, set (both dry and water saturated) is presented in Fig. 8. These values are calculated using the skeletal density of the aerogel particles, the particle density, the water absorbed by the aerogel particles and the surfactant adsorbed by the mineral binder. The gypsum formation of each sample, in the dry state, is calculated by the DOH measured by XRD. They provide a basis for more detailed consideration of the water distribution in these samples.
In particular, they highlight the fact that during sample preparation, the aerogel particles are capable of absorbing not only a very high amount of water, but also of surfactant. This value is obtained by considering that in the sample preparation the surfactant solution first reaches an equilibrium with the mineral binder, so the surfactant concentration decreases in relation to the data presented in Fig. 1. Using the reduced concentration and the amount of liquid invading the aerogel we can calculate the amount of surfactant that can be considered to have been absorbed into this material. This provides a lower bound for the amount of surfactant absorbed in the aerogel, assuming that the surfactant does not get displaced from the mineral binder to the aerogel owing to a higher adsorption energy on the latter.
Moreover, as observed in Fig. 4, the addition of aerogel and surfactant together increase the air content within the mixtures, by a constant of 0.7 m3 and 0.6 m3 of air per m3 of aerogel for the low and high surfactant content respectively (Fig. 5).This unexpected behavior generates an air volume of around 40 %, which decreases the volume fraction of aerogel and the gypsum, compromising both thermal conductivity and strength.
Also, as shown before in Fig. 2, the surfactant causes an increase in the air content in absence of aerogel particles, forming air bubbles. This is explained by the fact that the surfactant molecules tend to minimize unfavorable interactions between the liquid phase and the surfactant lipophilic tail, aligning to form a monolayer at the interface between the liquid phase and the compressed air. The air bubbles are stabilized in the slurry by the electrostatic and steric repulsions of the surfactants; the interfacial properties at the air bubble surfaces are determined by its physical and chemical properties given by the nature and concentration of the surfactants [19]. This surfactant foaming ability has been well established and studied by other authors [19, 46, 49, 70, 73]. Nevertheless, in presence of aerogel particles, no stabilized air bubbles within the composites were detected; although, an important amount of air entrained is measured.
The inclusion of aerogel increases the total porosity as expected (Fig. 6). However, as observed in Fig. 4, only part of the total porosity can be assigned to the aerogel structure, while another important part is located within the gypsum matrix. Interestingly, the water accessible porosity of these composites is lower than the volume of air entrained within the gypsum matrix, which suggests that in the set composites, water does not partially invade the aerogel, unlike as in the fresh state. Nevertheless, the water accessible porosity between the A and B series (with different surfactant ratio) is quite different (Fig. 6). The highest surfactant ratio leads to an increased water uptake (B series), as can be expected for the modified aerogel’s hydrophobic to hydrophilic behavior. However, the samples with the lowest surfactant ratio (A series) show a decreasing water accessible porosity with increasing aerogel content. Here the primary hydrophobic nature of the aerogels themselves and the lower surfactant dosage can be argued to account for this behavior.
Therefore, depending on the surfactant and aerogel concentration, it can be achieved different water absorption capacities within the composites.
The crucial and most important side effect of the air entrained by the aerogel granules is observed within the gypsum in the composites, decreasing the bulk density of the matrix from 1354 kg/m3 down to 233 kg/m3 as the aerogel content is increased (Fig. 7).
The schematic illustrations in Fig. 7 explain the changes in mechanical properties of the composites. As the aerogel content is increased, more water is needed in the mix and more air is entrained, so that the binder density decreases (shown by using lighter color). Moreover, the cross-section of the matrix, which bears the load, decreases. Both changes negatively affect the strength. Very interestingly they also combine to give a direct dependence of compressive strength on the volume fraction of gypsum in the mix as can be observed in Fig. 8.
A possible second order effect could be an impact of the admixture on the hydration kinetics of the anhydrite binder, either in terms of dissolution, nucleation or growth. This would however mainly affect the amount of gypsum formed and therefore strength. It would therefore be a kinetic factor hidden behind the relation revealed in Fig. 8. Apart from this, a modification of gypsum morphology may also modify intercrystalline bonding (Fig. 3c), as already proposed elsewhere [62]. However, the impact of hydrate morphology on strength is beyond the scope of this paper, and while probably of second order important, it is nevertheless something that we hope to investigate in the future.
Thermal conductivity of composites
The thermal conductivity of our composites depend on the volume fractions and thermal conductivities of gypsum, aerogel and air. In what follows we propose a way to estimate this on the basis of the proportions of these three phases. In particular, it is proposed to handle this in a two stage process. We emphasize here that the assumption of a fixed w/b in the matrix only affects the composition listed for the fresh state in Fig. 4, but not the dry state ones, which are those used in the model.
First we calculate the thermal conductivity of the matrix, considered as a mixture of air (phase A) and gypsum (phase B). In a second step, calculate the conductivity of the composite, considered as mixture of the aerogel (phase A*) and of the matrix (Phase B*) determined in the first step. In both steps we use the same mixing rules to calculate the composite conductivity based on [33]. This relies on calculating upper (k
U) and lower (k
L) bounds of the thermal conductivity using the following equations:
$${\text{Model A}} ({{\text{Upper}}\;{\text{bound}}}){:}\,k_{\text{U}} = k_{\text{B}} + \emptyset_{\text{A}} / \left( {\frac{1}{{k_{\text{A}} - k_{\text{B}} }} + \frac{{1 - \emptyset_{\text{A}} }}{{3k_{\text{B}} }}} \right)$$
(1)
$${\text{Model B}} ( {{\text{Lower}}\;{\text{bound}}}){:} k_{\text{L}} = k_{\text{A}} + (1 - \emptyset_{\text{A}} ) / \left( {\frac{1}{{k_{\text{B}} - k_{\text{A}} }} + \frac{{\emptyset_{\text{A}} }}{{3k_{\text{A}} }}} \right)$$
(2)
\(\emptyset_{\text{A}}\) = Phase A volume fraction, k
A = Phase A k, k
B = Phase B k.
The authors of this model initially proposed to use the arithmetic mean of the k
U and k
L to evaluate the thermal conductivity of the composite material. However, we found that for our composites, the geometric mean provides results in much better agreement with our experimental data. Therefore in both steps we calculate the composite thermal conductivities as:
$${\text{Model C:}}\,k = \sqrt {k_{\text{U}} k_{\text{L}} }$$
(3)
Numerical applications were done using the following thermal conductivity values for the phases: k
Aerogel = 0.013 W/m × K, k
Binder = 1.25 W/m × K (Gypsum solid phase) from [33] and k
Air = 0.026 W/m × K, while the volume fractions of the phases come from our measurements reported in Fig. 4.
The model predicts extremely well all our measurements without the inclusion of any fitting parameter, as shown in Fig. 9. We can therefore conclude that this model can reliably be used to estimate thermal conductivities having compositions in the range of those reported in this work. It does however have some limitations, in particular the link between scales. Indeed, including a phase in one or another level of the homogenization procedure does not lead to the same result. The definition of the phases to be included at each stage of the homogenization is therefore crucial. In our samples, taking air and gypsum as first level, leads to good results. However, this should not obscure the risk misinterpretations that may result in applying the same model to other systems.
Towards an optimization of aerogel composites
In practical terms, the optimization of these composites will involve a compromise between reducing thermal conductivity and losing strength when the aerogel content is increased. From this perspective, it is useful to plot compressive strength versus thermal conductivity as in Fig. 10. This reveals a relation between both properties, highlighting the difficulty of substantially increasing strength at a defined thermal conductivity.
In practical terms significant strength improvements, may not be easily noticeable in Fig. 10 because of the logarithmic scale. For this reason, we included the two discontinuous lines representing respectively an improvement and a worsening of strength by a factor 5. Achieving such a strength increase without changing the thermal conductivity would already be very interesting in practice. Such effects are within the “scatter” of the data reported in Fig. 10, suggesting that second order effects can play an important effect in this optimization process.
These changes may relate to modifications of the microstructure. Although of second order with respect to the main factor of gypsum content, they probably offer useful avenues to exploit for optimization. For example only may consider trying to eliminate the air entrained during the preparation of these materials as it does not contribute to strength and has a higher thermal conductivity that the aerogel granules (entrained air is about 40 % by volume as shown in Fig. 4). This would probably worsen the fluidity of the paste, which would then possibly have to be adjusted by the inclusion of chemical admixtures such as superplasticizers [23, 29].
This optimization of component proportions would include two main options. The first is to replace the volume of entrained air with aerogel to reduce the overall thermal conductivity. This would not change the volume fraction of gypsum and should consequently leave the strength unchanged in accordance with Fig. 8. The second option consists in increasing strength without changing the thermal conductivity. For this, the right proportion of gypsum and aerogel must be determined for replacing the air. Changes in strength would be best estimated using the exponential fit of the A(10) to A(100) samples presented as the continuous line in Fig. 8.
The thermal conductivity can be estimated using our model. Because of the previously mentioned issue of homogenization, the same two step procedure would be used. Here however, in the first step the air volume would be replaced by a mixture of gypsum and inclusions having the same thermal conductivity as the aerogel. Following this procedure, we find that the changes proposed would provide substantial improvements as can be observed in Fig. 11.
Replacing the volume of entrained air by aerogel would improve the overall thermal insulation of the composites, as shown in Fig. 11. Fixing the volume of gypsum, and thereby the strength would decrease the thermal conductivity of the samples by about 20 %, providing a very interesting ultralow thermal conductivity of 23 mW/m × K for our A′(100) and 63 mW/m × K for A′(10). Moreover, modifying the volume of gypsum and fixing the thermal conductivity value would improve the strength significantly: 82.5 % (0.024 MPa) and 227.4 % (2.57 MPa) respectively for A″(100) and A″(10). Figure 11 also shows what would happen if all the aerogel were replaced by air, without changing the content of gypsum. The thermal conductivity would increase by 57 % for A″(10) and by 72 % for A″(100) compared to the corresponding samples A′(10) and A′(100) respectively. This clearly illustrated the benefit of using aerogel to enhance the thermal insulation capacity of these composites.
Finally, we can also mention that changes in morphologies of hydrates may be beneficial, for example by enhancing the intercrystalline bonding in the matrix and/or the bonding between the granules and the matrix. Our results show that such changes take place, but a detailed discussion of how to exploit this in an optimization procedure is beyond the scope of this article.