Cement and Concrete Research 83 (2016) 152–163
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Microstructure of lime and lime-pozzolana pastes with nanosilica Cristiana Nunes a,⁎, Zuzana Slížková a, Maria Stefanidou b, Jiří Němeček c a b c
Institute of Theoretical and Applied Mechanics, Prosecká 809/76, 190 00 Prague, Czech Republic School of Civil Engineering, Aristotle University of Thessaloniki, Building E10, University Campus, 54124 Thessaloniki, Greece Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 16629 Prague, Czech Republic
a r t i c l e
i n f o
Article history: Received 14 May 2015 Accepted 9 February 2016 Available online xxxx Keywords: Nanosilica Pozzolana (D) Surface area (B) Elastic moduli (C) Microstructure (B)
a b s t r a c t Nanosilica particles (nS) were added to lime (L) and lime-pozzolana (LP) pastes to study the effect of nS as a pozzolanic admixture in L and to synergistically improve the pozzolanic reactivity of LP. Relationships between microstructure and mechanical properties of the pastes were examined. The macroporosity of both pastes decreased, and the compressive strength increased. SEM and X-ray μ-CT analysis accounted for explaining the inconsistent results between the porosity obtained by MIP and density by He-pycnometry. The strong pozzolanic reaction in LPnS explained the high consumption of mixing water, increment of density, and pores assigned to CSH. The SEM analysis also showed that BET and BJH can give erroneous results regarding the adsorption/desorption isotherms, thus affecting the values of the specific surface area and nanoporosity. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction While nanotechnology in cement and concrete is maturing [1–3], to date, limited attention has been paid to lime-based systems containing reactive nanoparticles that can significantly improve the performance of lime mortars to be used in the repair of the built heritage [4–6]. Much of the work to date with nanoparticles to improve the properties of cementitious composites has been with nanosilica (nS) [7–10]. Nanosilica particles have much higher pozzolanic reactivity than that of silica fume products that are commonly used as ultrafine pozzolanas for producing cementitious materials with advanced properties [11]. By using colloidal silica, it is assumed that the mono-dispersed nanoparticles can act as fillers and seeds much more effectively than the agglomerates of silica particles generated from powders or slurries [12]. Particles of nS can act as nuclei for hydraulic phases due to their high chemical reactivity, which is partly assigned to their high surface-area-to-volume ratio [11]. The accelerating effect of nanosilica on cement hydration has been assigned to a rapid depletion of calcium ions by nS, which can keep the paste at low undersaturation of calcium ions, thus enabling a higher dissolution rate of calcium ions from clinker particles, and hence helping to shorten the induction period [13]. Investigation on the use of nS on the performance of cementitious composites has shown several positive outcomes, e.g., reduction of capillary pores leading to lower water absorption and sorptivity, improvement of the interfacial transition zone between the aggregates and binder [10], porosity reduction and increment of the early mechanical ⁎ Corresponding author. Tel.: +420 774854391. E-mail addresses:
[email protected] (C. Nunes),
[email protected] (Z. Slížková),
[email protected] (M. Stefanidou),
[email protected] (J. Němeček).
http://dx.doi.org/10.1016/j.cemconres.2016.02.004 0008-8846/© 2016 Elsevier Ltd. All rights reserved.
strength [10,14], improvement of the salt [15,16], and frost resistance [17]. The main drawbacks pointed out about the effect of nS particles on the properties of cementitious composites are the reduction of consistency and workability [10,18], lower hydration degree at later ages [19], and agglomeration of the nS particles leading to an increase of the void space [13,20]. Few research groups have recently started to study the effect of nS on the properties of lime-based systems; the main results are summarised as follows: • The water/binder ratio increases with increasing amount of nS, whereas the workability and setting time decreases with the incorporation of nS [21,22]. Superplasticisers have been added successfully to tackle this problem [22,23]. • The mechanical strength increases with increasing percentage of nS at early ages (from 3 up to 28 days) in lime-pozzolana pastes [21] and until later ages in lime mortars (with 180 days [6] and from 7 up to 365 days [4]). • The total porosity increases with increasing amount of nS in limepozzolana pastes [21] but decreases in lime mortars [4]. Stefanidou [21] assigned the porosity increment to the higher water/binder ratio of pastes with nS addition. • Lime-pozzolana pastes with nS showed higher crystal size and sharp needle-like crystals [21] whereas lime mortars showed a denser matrix and honeycomb-shaped CSH structures [4]. • The progressive increase of nS shifts the mean pore size diameter towards lower diameters regardless of the curing time (from 7 up to 182 days) [4]. • The durability of lime mortars assessed by climatic chamber (cycles of temperature, relative humidity, rain and UV light), freeze-thaw cycles
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Table 1 Chemical composition of the natural pozzolana used in the preparation of LP and LPnS specimens.
Amount (wt. %) a
Na2O
K2O
CaO
MgO
Fe2O3
Al2O3
SiO2
L.I.a
Cl−
NO-3
SO2− 4
2.78
4.05
15.25
8.22
1.89
9.79
49.57
8.45
0.34
0.0
0.23
L.I. = loss on ignition
and magnesium sulphate attack was improved for the mortars with large amounts of nS (20 wt. %) [4] and the resistance to sodium sulphate was considerably higher for lime mortars with 1 wt.% [5] and 3 wt. % [6]. The results on the effect of nS particles on lime-based systems are promising and, given the limited published data, the present study aims at contributing for a better understanding of the effect of nanosilica on the micro-textural properties of lime-based pastes. The knowledge of the main physicochemical characteristics of the pastes, such as morphology and texture, are important parameters for the design, and for the prediction of the durability of mortar mixes. The objective of the present study is to determine the main micro-textural characteristics and micromechanical properties of lime and lime-pozzolana pastes with the addition of nS particles. A natural pozzolana of volcanic origin composed mainly of silica, calcium oxide, and alumina was used. Tests have been performed on pure aerial lime pastes and combination of lime and natural pozzolana pastes (1:1 wt.) with 1 year of age. The time parameter is important as these binders develop their properties slowly and the mechanism of carbonation and/or hydration, which is responsible for the strength increase, act competitively with deterioration actions such as cracking [24]. 2. Experimental part 2.1. Materials and sample preparation The analysis of the materials used for the production of the pastes was performed before the specimen preparation. Hydrated lime (type N according to ASTM C206) and natural pozzolana from the island of Nisyros (Greece) were used to prepare the specimens. The chemical composition of the pozzolana is given in Table 1. The nanosilica (nS) used was supplied by Sigma–Aldrich and, according to the provider, it is produced by pyrolysis and has a primary particle size of 14 nm. The grain size of lime and pozzolana was determined with a particle analyser (Mastersizer 2000 Malvern). The pozzolanicity index of the natural pozzolana was determined according to the international standard ASTM C311-13. The properties of the raw materials are presented in Table 2. Additional tests with X-ray powder diffraction, scanning electron microscopy, and transition electron microscopy were performed in the nS grains and can be found in [14]. Nanosilica was added in 1.5 wt. % of the binder weight, following the results obtained by Stefanidou and Papayianni [14] who mentioned an optimum amount between 1 and 2% wt. (with the same type of nS) for both the microstructure and mechanical strength. The most significant issue for all nanoparticles is that of effective dispersion. Aggregation of the nanoparticles reduces the benefits of their small size by creating unreacted pockets leading to a potential for concentration of stresses in the material [1]. Therefore, 6 g of nS was firstly mixed with
Table 2 Properties of the materials used for the preparation of the pastes. Material
Code Density Mean (g/cm3) particle size (μm)
Lime L Pozzolana P Nanosilica nS
2.47 2.40 2.20
10.8 11.6 0.014
Specific surface area (m2/g)
Pozzolanicity Ca(OH)2 content index (wt. %) (MPa)
2.25 1.82 200
– 10.5 –
75 – –
200 ml of water and subsequently, the solution of nS was subjected to ultrasound treatment (using a HYDRO 2000MU Mastersizer 2000 system) for 60 min to avoid agglomeration and promote a good dispersion of nS in the binder matrix. Agglomerates of nS could be observed by naked eye before the ultrasound treatment; these disappeared afterwards. A pre-determined amount of additional water was added to each mixture to obtain a consistency of 6 ± 1 mm in all pastes with the Vicat method (EN196-3:1994). The water content of the colloidal nS was considered as a part of the mixing water. The paste prisms were prepared in casts of 25 × 25 × 100 mm and cured in high humidity conditions: 90% RH (20 °C) for the first 28 days and afterwards at 60% (20 °C) until the testing date. The samples were tested at 2 months of age for mechanical strength and nanoindentation, and at 1 year of age for the other tests. Before the nanoindentation test, small slices (25 × 25 × 5 mm) were cut from the specimens with a diamond saw and subsequently they were polished with a series of grinding papers (grit sizes nos. 2000 and 4000). The specimens were then washed with alcohol in an ultrasonic bath to obtain the required flat and smooth surface to perform the analysis. Table 3 presents the composition of each specimen. The water/ binder ratio (w/b) increased significantly for the pastes with nS incorporation, particularly for the paste with pozzolana (increment of 12%), which is in line with the results reported in the literature concerning the addition of nS to lime-pozzolana pastes [21], to Portland cement pastes [14,19], to lime mortars [4,23,25] and to cement mortars [12, 26]. The reduction of workability of the fresh mixtures, reflected on the higher amount of water necessary to achieve the same consistency as the reference mixes, has been assigned to the high water adsorption by nS due to its large specific surface and high nanoscale porosity [13]. Thus, the free water available for lubricating the granular system is reduced. 2.2. Testing equipment 2.2.1. Microstructure Cross-sections of the prismatic specimens (25 × 25 mm) were prepared by impregnating them with an epoxy resin followed by drying at 60 °C and then polishing. Afterwards, the specimens were sputtercoated with a thin layer of carbon and analysed with the scanning electron microscope (SEM) MIRA II LMU (Tescan, Czech Republic) equipped with energy dispersive X-ray detector (EDX) from Bruker Corporation (Germany). Images of the fresh fracture of each paste were collected with SEM to study the influence of nS addition on the morphology. Before the analysis, the specimens were dried at 60 °C, then broken to have a freshly fractured surface, which was then coated with gold and observed under the SEM. The images were collected under high voltage (15 kV) Table 3 Paste identification code, composition by weight and water/binder ratio. Paste code
Composition
nSa (wt. %)
w/bb
L LnS LP LPnS
L L + nS L : P (1 : 1) L : P (1 : 1) + nS
– 1.5 – 1.5
0.78 0.82 0.66 0.75
a
Values are expressed in wt.% of nS with respect to the weight of binder. w/b: water/binder ratio, i.e., water/hydrated lime and/or water/hydrated lime + pozzolana ratio. b
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the displacement of gas to measure the material's volume accurately. The specimens were first dried and degassed at 105 °C for 24 h. Helium was used as the displacement medium. Ten purges of the system were performed to ensure the equilibrium and to degas the samples completely. This was followed by ten consecutive volume measurements, which were then used to obtain the values of the average density. Table 4 presents the average of the results obtained for each specimen at 1 year of age.
Fig. 1. Pore size distribution curves of the studied pastes.
at a working distance of 15 mm and under high vacuum regime using SE detector. X-ray microtomography (μ-CT) was also used to study the microstructure of the pastes. The specimens were cut and drilled to obtain cylindrical cores of 2 mm diameter. The cores were scanned using a Perkin Elmer device with a flat panel XRD 1622 AP 14 detector. The scans were made with a transmission type X-ray tube working at 70 kV and 9.1 W. The magnification (source-detector distance/source-object distance ratio) was 60 and the voxel size was 3.28 μm. 2.2.2. Pore size distribution The pore size distribution was performed with a mercury intrusion porosimeter (MIP) Quantachrome Poremaster® PM 60 13 with one specimen of each paste type at 1 year of age. Two equivalent penetrometers were used with a 5 cm3 bulb and a total intrusion capacity of 0.500 cm3. Low-pressure testing ranged from 6894.7 Pa (1 Psi) to 344,737 Pa (50 Psi) and high-pressure analysis from 275,790.3 Pa (40 Psi) to 172,368,925 Pa (30,000 Psi). Equilibration times were 15 s for low pressure and 30 s for high pressure. The following mercury parameters were used: advancing and receding contact angle = 140°, surface tension = 0.485 N/m, and density = 13.5487 g/cm3. Differential pore radius distributions are shown in Fig. 1 and Table 4 shows the values of intruded porosity. 2.2.3. Specific surface area and pore size distribution by N2 physisorption analysis Gas sorption (both adsorption and desorption) is the most common method for determining the surface area of powders as well as the pore size distribution of porous materials [27]. An ASAPTM 2020 from Micromeretics equipment using N2 was used for the gas physisorption analysis. The specific surface area of the samples at 1 year of age was calculated according to the Brunauer–Emmett–Teller procedure [28]. The pore size distribution was determined by the Barrett–Joyner–Halenda (BJH) method [29]. Before the analysis the specimens were degassed for 150 min at 35 °C. 2.2.4. Density by helium pycnometry The density, here defined as the ratio of the mass of the solid material to the sum of the volume including closed pores, was measured on a helium pycnometer AccuPyc ® II 1340 from Micromeretics. Gas pycnometry is a commonly used analytical technique that is based on Table 4 Main physical properties of the paste specimens. Paste
Specific surface area BET (m2/g)
Density He-pycn. (g/cm3)
Bulk density MIP (g/cm3)
Porosity MIP (%)
Main radius MIP (μm)
L LnS LP LPnS
6.09 7.53 24.22 23.46
2.39 2.41 2.27 2.43
1.17 1.33 1.17 1.17
51.00 44.20 43.72 44.40
1.03 0.56 0.06 0.06
2.2.5. Macro and micromechanical analysis Flexural and compressive strengths were determined with three specimens of each paste at 2 months of age using a universal traction machine. The flexural strength was evaluated from three-point bending tests (according to ASTM C191-81). The specimens were broken in flexure into halves and each half was tested for strength in compression. The dynamic elastic modulus (Ed) was computed according to ASTM C597-71 by measuring the pulse velocity of longitudinal ultrasound waves in 25 × 25 × 100 mm specimens (Pundit instrument by Proceq). Specimens of L and LnS were prepared for nanoindentation and tested in a Nanohardness tester (CSM Instruments, Switzerland) equipped with Berkovich tip (three-sided diamond pyramid). Nanoindentation is a high-resolution technique that allows to analyse separately distinct material phases at low indentation depths or measure compound properties within the material volume affected by the probe at larger depths. The principle of nanoindentation consists of bringing a sharp probe of known geometry into contact with the deformable surface of the microvolume to be investigated. The load and penetration depth are the main parameters that are recorded through the loading cycle, which includes several stages (loading, holding, and unloading phase). Intrinsic material constants are deduced from the measured loaddisplacement curves for the given material microvolume. Since lime pastes are microstructurally highly heterogeneous materials with high levels of porosity, the surface preparation does not allow proper interpretation of low depth measurements. Therefore, indentation on larger volumes (≈ 1–5 μm3) leading to average mechanical properties of the matrix phase were in focus. The static modulus (Es) was evaluated with the Oliver and Pharr method [30]. The testing region was selected to be free of large pores and a grid containing 6 × 6 indents (with 20 μm mutual indents' spacing) was drawn. Four indentation cycles (maximum loads 2–25 mN) were prescribed for each indent in the grid with a constant loading and unloading rate of 24 mN/min. Each cycle also contained a holding period of 15 s included to minimise creep effects on the elastic unloading [31]. The cyclic indentation was introduced to quantify the influence of the underlying porosity included in the indentation volume (Fig. 1) because the majority of pores in limebased pastes are situated between 0.1 and 1 μm [32]. The evaluation was performed with a Poisson's ratio of 0.2. 3. Results and discussion 3.1. Porous structure, density, and specific surface area Table 4 summarises the main physical properties of the pastes. The porosity decrease (ca. 13%) between L and LnS can be assigned to the densification of the binder matrix by the nS particles. Thus, we can assume that the nanofiller effect overcomes the influence of the higher w/b ratio used in LnS (ca. 5% increment). Regarding the pastes with pozzolana, the w/b ratio is considerably higher for LPnS in contrast with LP (ca. 12%). However, the porosity of LPnS was only slightly higher (0.7% increment), which can be assigned to the consumption of water by the strong pozzolanic reactions derived from the combination of pozzolana with nS. On the other hand, the addition of pozzolana to lime induces a decrease in the w/b ratio and, therefore, the porosity is reduced. The reduction of the w/b ratio can be assigned to the higher particle size and lower specific surface area of the pozzolana, but the
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pozzolanic reaction occurring during the hardening process leads to a higher specific surface area of the paste. The pore size distribution curves (Fig. 1) show that all pastes have a predominantly unimodal distribution. The addition of pozzolana to lime paste had a significant effect on the pore size distribution: the pore volume in the region between 0.1 and 1 μm (79% of the total porosity) was shifted to 0.01–0.1 μm (82% of the total porosity). These results indicate that the pozzolana particles may tend to fill up the larger pores present in L. The addition of nS to L paste shifted the main pore volume maxima from ca. 1 μm to 0.6 μm. Other authors [4,23] also reported a shift of the mean pore size towards lower diameters in lime mortars and assigned the phenomenon to both the filling effect of nS and the formation of CSH. Regarding LPnS, the pore size dispersion was maintained and only the pore volume maxima, located at ca. 0.06 μm, increased. Since MIP only detects interconnected pores, the volume increment of pores of the same size indicates that the interconnection of these pores increased. Kong et al. [13] state that the influence of nS addition on the rheological behaviour of the paste is mainly dependent on whether the agglomerates can act as fillers. Therefore, if some nS particles flocculate and are not well dispersed during the mixing process, the resulting paste can develop clusters unable to act as fillers because they push away the binder particles around them, causing an increase of the void space. Iler [33] (as quoted by [19]) reported that the adsorption of Ca2+ by only ca. 0.6% of the weight of a nanosilica sol with a surface area of 200 m2/g leads to a significant aggregation of the nanosilica particles. Therefore, the observed increment of the pore volume maxima on LPnS could be explained by the nS aggregation phenomena, which leads to the increment of kneading water because the agglomerates developed, unable to act as fillers, will consume some free water that originally contributes to fluidity. On the other hand, the increment of pores within this pore size range corresponds to sorption pores, according with the IUPAC pore size classification [34]. Thus, given that sorption pores are associated with CSH (calcium silicate hydrate) gel [35] the increment of the pores within this size range can be attributable to the pozzolanic reaction between nS and LP. The peaks located in the macropore region completely disappeared with the addition of nS to LP, indicating that the capillarity pores were blocked in accordance to Stefanidou [21]. In contrast, LnS showed some small peaks within the macropore region, which could be assigned to shrinkage due to the higher w/b ratio or to agglomeration of some nS particles. Given that the addition of nS to LP promoted a significantly higher increment of the w/b ratio, the results could be assigned to the fact that the pozzolanic reactions are enhanced in the presence of both nS and pozzolana. Therefore, a much higher amount of the free water available is consumed in the pozzolanic reaction, thus not contributing to shrinkage. Figs. 2 and 3 illustrate adsorption/desorption isotherms and pore size distributions obtained for the different pastes using BET and BJH determination methods, respectively. The volume of the nitrogen adsorbed obtained from the adsorption and desorption isotherms varied, depending mostly on the presence of pozzolana. Pastes LP and LPnS adsorbed more nitrogen than L and LnS due to their considerably larger surface area (Table 4). The four pastes show a physisorption isotherm shape of type IV (porous materials) and a hysteresis loop of type H1, according with the IUPAC nomenclature [36]. The hysteresis loop is associated with capillary condensation taking place in mesopores (type IV isotherm). The presence of a hysteresis loop in desorption isotherm shows that the samples are macroporous (pores larger than 50 nm). According to Quercia et al. [12], the macroporosity is mainly produced by the packing effects of primary particles of a spherical shape and a probable contribution of mesoporosity (2–50 nm). The pore size distribution determined by the BJH method (Fig. 3) does not agree with the MIP results (Fig. 1), particularly in the case of LP and LPnS pastes. LP showed a slight decrease in the pore volume
155
Fig. 2. Nitrogen adsorption/desorption isotherm of the pastes: a) L and LnS; b) LP and LPnS.
between 0.01 and 0.1 μm with the BJH method, in contrast with the MIP results. Considering that the BJH method is more accurate for the detection of pores within this size range, the increment of the pore volume detected by MIP could also be assigned to inhomogeneities in the specimens. In this case, the decrease of pore volume in LPnS could be attributed to the nS filling effect. On the other hand, nS had the opposite effect on L, which can be assigned to the formation of CSH gel. The density of LnS was only slightly higher than that of L (Table 4). A greater increase in the density of LnS was expected given the porosity reduction. In the case of LPnS, the density is considerably higher than that of LP, despite the fact that the porosity is only slightly lower. The results of the microstructural analysis presented in the next section can account for explaining this inconsistency. The specific surface area (Table 4) increases remarkably (221%) with pozzolana addition to L but it is slightly reduced with nS addition to LP.
Fig. 3. Comparative pore size distribution curves (BJH method) for the pastes.
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Table 5 Pore volume (cm3/g) as determined by BJH and MIP. Name
Pore radius
L
LnS
LP
LPnS
Meso gel pores Micro/meso capillary pores Macro-capillary pores
~1.0–25 nm ~25–50 nm ~50 nm–1 μm ˂1 μm ˂5 μm
0.77 0.06 35.04 8.59 0.23
0.85 0.07 14.71 1.31 1.07
3.86 0.40 22.84 1.06 1.02
0.03 0.07 20.32 0.41 0.39
The specific area, in this case, is mainly related to the shape, porosity, and texture of the particles and, to a lesser extent, to their particle size, which is only slightly higher for lime in respect to pozzolana (Table 2). In contrast, nS addition to L increased the specific surface area. Other authors also reported a higher surface area for the lime mortars with the incorporation of nS [25]. The fact that the surface area of LPnS is lower than that of LP can be explained based on the study by Odler [37]: in the initial stage of hydration, the network of the formed hydrates is rather open. Thus, nitrogen can penetrate into the entire pore space; the surface area value increases proportionally to the amount of hydrates formed. As the hydration progresses and free water is consumed, the overall pore space becomes smaller, and the network of hydrates becomes more interwoven. Under these conditions, an increasing number of regions develops, which are separated from the rest of the pore system by narrow openings that are either totally or partially impermeable to N2 molecules. At this stage, a linear proportionality between the amount of hydrates formed and the resultant surface area value ceases to exist, as part of the surface will not be covered by the adsorbed N2 molecules anymore. After reaching a critical point, the fraction of the pore system inaccessible to nitrogen may increase so fast, that even the overall surface area of the paste declines, even
though additional hydrates are formed. Furthermore, the sample preparation, in particular, the removal of free water from the pore system, causes irreversible alterations in the microtexture of hydrated materials, which affect the magnitude of the resultant BET surface area and BJH pore size distribution [25,38]. Table 5 shows the pore volume of the pastes according to the classification proposed by Espinosa et al. [39], which sets a boundary between gel and capillary pores at 25 nm. The values of meso gel pores and micro and meso capillary pores were calculated by the BJH method (Fig. 3), and the macro-capillary pores were determined by MIP (Fig. 1). The aim of grouping the pores according to the classification proposed by Espinosa et al. is to identify the presence of CSH phases and compare its amount between the different pastes. The results indicate that LPnS has a lower amount of CSH phases compared to LP, expressed as a lower amount of pores between 1 and 25 nm and between 25 and 50 nm. The apparently contradictory results can be explained taking into account that a significant fraction of the overall pore space in specimens containing CSH as a product of hydration appears inaccessible to nitrogen even at a partial pressure of p/ps = 1.00. Consequently, one can assume that these pores will be inaccessible to nitrogen even at p/ps b 0.35, which is the range of partial pressures used in BET determinations [37]. Furthermore, the recent study by Alvarez et al. [25], about the influence of different drying conditions on the micro and mesoporous structure of lime-based mortars with nS, indicated that pores under 10 nm (assigned to the presence of a certain amount of CSH phases) are slightly affected by drying in oven at 60 °C. Snoeck et al. [40] reported similar conclusions: when using oven drying, the amount of removed water is higher but the surface area is smaller. This can be interpreted as a possible pore collapse or pore alteration. As more water is removed, finer pores are accessed, but some gel pores cannot be accessed due to pore collapse.
Fig. 4. SEM photomicrographs of L (a–c) and LnS (d–f) pastes.
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The pore collapse will cause a decrease of the smallest pores present as capillary pressure increases with decreasing pore size. The pore size distribution shown in Table 5 can partially explain the denser structure observed in the nano-modified samples. In the case of pure lime pastes, the increase of meso gel pores may be considered as an indication of the reaction of lime with nS particles and the formation of CSH phases. The results suggest a better influence of pozzolana addition to lime pastes compared to the addition of nS. However, as mentioned earlier, the addition of nS to LP eliminated the macro-capillary pores, although the w/b ratio was significantly higher for LPnS, compared to LnS. This could be assigned to the fact that the pozzolanic reactions are enhanced in the presence of both nS and pozzolana, therefore consuming a much higher amount of the free water available. Thus, the porosity increment as determined by MIP (Table 4) could be interpreted as rather related to the increment of pores assigned to CSH formation, which BJH analysis can have been unsuccessful in detecting as mentioned earlier (e.g. due to the drying method used). 3.2. Microstructure observations by SEM and X-ray μ-CT Fig. 4 is a representative set of SEM views of freshly fractured surfaces of the pastes. Paste L shows a finer grained structure with generally equant crystals and some plate-like crystals (Fig. 4.b,c) whereas LnS shows slightly larger crystals (Fig. 4.e). Needle-like crystals were detected mainly inside pores or cracks (Fig. 4.f); these have also been reported in other studies [21] and have been assigned to CSH phases [4,25]. The SEM observation of LP and LPnS (Fig. 5) enabled detecting generalised cracking (with ca. 1 μm width) in both pastes. These cracks are probably due to carbonation shrinkage (e.g. by decalcification) induced by the long-term curing at 60% RH. The removal of interlayer calcium
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ions from the CSH can create an excess negative charge, which is most readily balanced with protonation and subsequent formation of the Si–OH groups. It has been suggested that at least some of these siloxane bonds form bridges between neighbouring surfaces or regions, thus pulling them closer together and causing shrinkage [41]. A higher magnification (Fig. 5.f) showed that LPnS presents well-defined honeycomb structures, probably corresponding to CSH phases; these have also been observed in lime mortars with nS [4]. Paste LPnS also shows large compact crystals resembling pieces of obsidian with conchoidal features surrounded by amorphous CSH (Fig. 5.e). The images depicted in Fig. 5.c) and f) indicate that LPnS presents higher porosity at the submicrometer level and that LP shows higher porosity at the micrometer level. Therefore, the latter confirms the pore size results obtained (Fig. 3 and Table 5). The previous interpretation of the BJH results, based on the formation of CSH phases with pores inaccessible to N2 [37], is supported by the SEM observations because the pores observed at the submicrometer level were not detected by the BJH method. Fig. 6 presents SEM-BSE images of the lime pastes' microstructure. L images (Fig. 6.a and b) illustrate lime grains having a size of 10–50 μm, which are the most frequently occurring in the sampled area. Finer particles of size under 10 μm fill the space between the larger lime grains. The investigated grain size distribution is in agreement with the results of particle size analysis (Table 2). The CaCO3 grain shown in Fig. 6.b) presents an interesting shrinkage-induced pattern of curved cracks. Fig. 6.c) shows grains exhibiting a white area surrounded by a grey rim, the largest detected being almost 50 μm in size, the smallest less than 5 μm. In cement pastes, the brighter areas are usually assigned to residual unhydrated cement grains and most of these remnants are surrounded by, and are in close contact with, smooth-textured
Fig. 5. SEM photomicrographs of LP (a–c) and LPnS (d–f) pastes.
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Fig. 6. SEM-BSE photomicrographs of L pastes: the red arrows in a) and b) indicate lime grains; the green arrow in b) indicates a lime grain with shrinkage-induced patterns and the red arrow in c) indicates a grey rim. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
uniformly grey hydration product shells of varying thickness [42]. The EDX analysis showed a strong peak assigned to Si, having a higher intensity in the grey rim, whereas the brighter area showed a stronger peak assigned to Ca. Therefore, these grains are probably resulting from the reaction of calcium hydroxide grains with nS particles; although initially the access to nS particles is available, with the progress of the reaction mechanism, a hydrate layer is formed on the surface of the portlandite crystals, gradually limiting access to their interior [19]. However, the majority of the grey grains are composed of fully hydrated products (smooth-textured and uniform grey colour), which are intermingled with pore spaces. The bright grains showing cross-hatched appearance are characteristic of partially hydrated 2CaOSiO2 [42]. These grains also show a hydration rim with similar content of Si and Ca, as the previously described grain but with lower density. According to Diamond [42], the differences in grey level may represent differences in internal porosity (the brighter zone being less porous) or it may under certain circumstances reflect differences in composition. Fig. 7 shows the distribution of Si obtained by EDX elemental mapping: Si is generally homogeneously distributed within the groundmass but also concentrated in clusters, corresponding to the residual and fully hydrated grains (uniform grey colour). The image shown in Fig. 7 also indicates the presence of big lime grains that did not react with nS particles (irregularly textured grey-coloured grains). The groundmass of both L and LnS also contains many individually recognisable pores (darker areas), which seem to have higher representation in L paste, confirming the MIP results.
Fig. 8.b) and 8.d) indicate that nS addition to LP paste did not induce significant detectable alterations on the microtexture of the paste as seen by SEM. However, the composition of the groundmass of LPnS is richer in Si, as Fig. 9 shows. Both pastes show lime unreacted grains, up to 50 μm in size, and smaller grains (generally lower than 10 μm) corresponding to aluminosilicates as determined by EDX (grey smooth-textured grains) well dispersed within the sample matrix; these are assigned to alumina present in the pozzolana (Table 1). In paste LPnS, no residual unreacted grains were observed like in LnS and LP, therefore indicating that nS addition to LP has synergistically improved the pozzolanic reaction. To unveil the inconsistent results of density and porosity, we have further analysed the pastes with X-ray microtomography (μ-CT) (Fig. 10). The pastes L and LP showed some large pores (dark areas) with diameters around 200 μm, which MIP is not adapted to determine, and between 100 and 150 μm, respectively. The intrudable porosity as analysed in MIP is not a measure of the total porosity of the system, and some completely isolated pores that are entirely sealed against intrusion may be present [43]. Therefore, the total porosity can be underestimated. The μ-CT scans of the pastes with nS showed lower porosity than the respective reference, the widest pores having diameters lower than 100 μm that MIP can detect. Thus, the porosity of the pastes with nS can be, in reality, lower than the porosity of the reference pastes. These results can account for explaining the significant increase in the density of LPnS in respect to LP, which is probably assigned to the reduction of the macroporosity. As previously mentioned, the higher
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Fig. 7. SEM-BSE image showing the distribution of Si in LnS cross-section.
density of LPnS in respect to LP can also be assigned to the improvement of the hydraulic reactions, producing CSH phases, whose structural disorder is considered partially responsible for its high atomic packing density [44]. On the other hand, other phases that are not consumed in the hydraulic reactions may also be intercalated within CSH on a nanoscale, e.g. portlandite (2.25 g/cm3) [45], thus affecting the density of LP negatively.
In μ-CT, the image contrast mechanism stems from differences in X-ray adsorption induced by differences in the density of the volume elements (voxels) imaged. The effect is somewhat similar to the contrast mechanism in SEM-BSE, which results from differences in the backscatter electron coefficient among the different pixels, since the backscatter electron coefficient also correlates well with density [46]. As seen in Fig. 10, all pastes show brighter areas, which could be assigned to lime
Fig. 8. SEM-BSE photomicrographs of the LP pastes.
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Fig. 9. SEM-BSE image showing the distribution of Si on LP (top) and LPnS (bottom) cross-sections.
Fig. 10. Sections of images of the pastes obtained by μ-CT: a) L; b) LnS; c) LP; d) LPnS.
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unreacted grains, as in the SEM-BSE images. Accordingly, the μ-CT images show that the paste with higher density is LPnS, confirming the results by SEM-BSE. However, the μ-CT results still cannot explain the density differences between L and LnS and between L and LP, as a much higher increase in density was expected for LnS and LP, in respect to L. Therefore, we can only assign the density results obtained by Hepycnometry to an experimental error or inhomogeneities in the specimens, probably in L specimen. 3.3. Macro and micromechanical analysis The amelioration of the nanoscale stiffness and strength properties should ultimately result in the improvement of the same properties at the macroscale. This is partly confirmed by the mechanical strength measurements performed at the macroscale (Table 6). Paste LnS showed a significant increment of the compressive strength (16%) but no effect on the flexural strength. In contrast, the compressive strength of LPnS was improved to a lesser extent (ca. 5%) and the flexural strength was rather enhanced (16% increment). The different effect of nS addition on the mechanical properties of L and LP can be possibly explained by the differences in porosity and pore structure: the porosity reduction in LnS could have contributed to a higher increment of the compressive strength, but the slight increment of the pores within the macropore region as determined by MIP (which can be assigned to a crack type of void) could have had a higher impact on the flexural strength. Otherwise, in the case of LPnS, the reduction of the macrocapillary pores promotes an increment of both the compressive and flexural strength. The dynamic and static elastic moduli of the pastes, determined according to ASTM C191-81 and nanoindentation, respectively, differ significantly from each other. Several experiments on different types of materials have reported that the dynamic moduli (Ed) are higher than the static moduli (Es) [47–49]. The discrepancies between Es and Ed have been widely attributed to microcracks [50]; nevertheless, several studies have demonstrated a correlation, expressed by an analytical function, between the static and dynamic modulus of elasticity of rocks [48,51], soils [52], and cement-stabilised materials [53]. A correlation between static and dynamic elastic modulus for lime-based materials has not been found in the published literature. The Ed and Es of LnS are contradictory in this regard, which can either be related to heterogeneity of the specimens (heterogeneous dispersion of nS in the sample) or experimental errors. The dynamic modulus of elasticity was significantly reduced with nS addition to L (54% reduction), and to a lesser extent to LP (19% reduction). The results agree with those obtained by Stefanidou et al. [14], who reported a decrease of 26% of the Ed for lime-pozzolana grouts with 1 wt. % nS with the same materials used in the current study, but with the addition of a superplasticiser. The contradictory reduction of Ed, which should increase with the densification of the matrix, can be again attributed to experimental errors assigned to the ultrasound technique used. On the other hand, LnS shows higher Es than L (26% increment), which was the result expected as the densification of the matrix by nanosilica particles should lead to higher stiffness.
Fig. 11. Typical cyclic load-penetration depth curve obtained by nanoindentation on L (a) and LnS (b) specimens.
The relatively low stiffness of the lime specimens and their wide pore distribution required the nanoindentation measurements to be performed with high indentation volumes (penetration depths of the indents in four cycles ranging from ca. 200 to 2000 nm, Fig. 11) to derive the influence of porosity on the measurement of the stiffness. As expected, shallow indents (depth b1 μm) were less influenced by the porosity and exhibited higher stiffness, which progressively decreased with increasing penetration depth, as more pores were involved in the indentation volume (Fig. 12). The elastic modulus stabilised at depths larger than 1 μm, suggesting that the significantly high matrix porosity was already included in the indentation volume. Such values can be considered as effective elastic moduli of the matrices including all underlying microporosity, i.e. pores less than 1 μm (Fig. 12). The elastic modulus of L and LnS matrices measured with nanoindentation approached the mean values of 10.5 ± 1.6 GPa and 13 ± 4.5 GPa, respectively. It is important to outline that on the one hand, such a high stiffness value of the matrix compared to the macroscopic values measured on large samples (e.g. by ultrasound) is natural since samples also contain a large volume of macroscopic porosity. On the other hand, the large capillary and entrapped air macroporosity (ca. 10–200 μm) reaches values of about 50%. Taking this effect into account, the stiffness of the entire sample can be calculated based on micromechanical
Table 6 Main mechanical properties of the lime paste specimens. Paste
Flexural strength (MPa)
Compressive strength (MPa)
Dynamic modulus of elasticity (GPa)a
Static modulus of elasticity (GPa)b
L LnS LP LPnS
1.33 1.33 2.11 2.45
2.64 3.06 4.20 4.41
6.69 3.08 6.48 5.26
3.41 4.60 n.d. n.d.
n.d. = not determined a Determined according to ASTM C191-81. b Determined by nanoindentation and elastic homogenisation.
Fig. 12. Evolution of the elastic modulus received from nanoindentation at increasing depths on L and LnS specimens.
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principles (e.g. the Mori-Tanaka method, [54]), which can be successfully applied also to heterogeneous structural materials [55]. Assuming a two-phase composite consisting of the matrix phase (EL,matrix = 10.5 and ELnS,matrix = 13 GPa) and spherical air inclusions (Eair = 0 GPa) in the specific volume fractions, the homogenised composite elastic modulus is predicted by the Mori-Tanaka method as EL = 3.41 and ELnS = 4.6 GPa (Table. 6). 4. Conclusions The addition of 1.5 wt. % of a colloidal suspension of nanosilica particles with 200 m2/g specific surface area to lime and lime with pozzolana attributed distinct properties to both pastes. LnS porosity as studied by MIP was significantly reduced, but the density was only slightly higher than the reference; in contrast, LPnS porosity as determined by MIP was slightly higher but the density was substantially greater than the reference. The X-ray μ-CT analysis helped in unveiling the inconsistent results of porosity obtained by MIP and density determined by Hepycnometry. The X-ray μ-CT scans showed larger porosity in the structure of L and LP specimens, which MIP did not detect; consequently, the porosity was probably underestimated with MIP. Thus, the obtained contradictory differences can be assigned to the different pore types developed in the pastes and to the inaccuracy of the MIP technique. The increase in the density of LPnS can be also attributed to the enhanced pozzolanic reaction promoted by the combination of pozzolana and nS. The increment of the w/b ratio was significantly higher for LP-LPnS in comparison to L-LnS, probably thanks to the strong pozzolanic reaction leading to the increase of pores assigned to CSH phases and the disappearance of macro-capillary pores. The early mechanical strength was improved for both pastes and the different increment values obtained between the two pastes with nS can be attributed to the different pore structure and mineralogical composition. SEM analysis showed that both L and LP pastes with nS had a denser structure. The results obtained by this method also showed that BET and BJH can give erroneous results regarding the adsorption/desorption isotherms thus affecting the values of the specific surface area and nanoporosity as also suggested by other authors. The analysis performed by SEM-EDX showed that LPnS had no remaining lime unreacted grains in contrast to LP, indicating that nS addition to LP synergistically improved the pozzolanic reactions. The results obtained agree well with the published studies about the effect of nS in lime-based systems listed in the introductory section, except the ones concerning the influence of nS on the durability of mortars, which were not addressed in the current study. For future work, further analysis should be performed at earlier ages, especially regarding the phases formed over time (with e.g. TG/DTA, FTIR, XRD) and the modification of properties such as the mechanical strength and specific surface area. Acknowledgements This work was generously supported by the project P105/12/G059 from the Czech Science Foundation. The authors are grateful to MSc. Dita Machová and MSc. Veronika Petráňová, and Dr. Ivan Jandejsek for performing the porosity, SEM, and μ-CT analysis, respectively. Two anonymous reviewers provided enlightening suggestions to improve the paper. References [1] F. Sanchez, K. Sobolev, Nanotechnology in concrete – A review, Constr. Build. Mater. 24 (2010) 2060–2071. [2] M. Schmidt, K. Amrhein, T. Braun, C. Glotzbach, S. Kamaruddin, R. Tänzer, Nanotechnological improvement of structural materials – impact on material performance and structural design, Cem. Concr. Compos. 36 (2013) 3–7.
[3] L.P. Singh, S.R. Karade, S.K. Bhattacharyya, M.M. Yousuf, S. Ahalawat, Beneficial role of nanosilica in cement based materials – a review, Constr. Build. Mater. 47 (2013) 1069–1077. [4] A. Duran, I. Navarro-Blasco, J.M. Fernández, J.I. Alvarez, Long-term mechanical resistance and durability of air lime mortars with large additions of nanosilica, Constr. Build. Mater. 58 (2014) 147–158. [5] M. Stefanidou, The role of nanoparticles to salt decay of mortars, Proc. 8th Int. Symp. on the Conservation of Monuments in the Mediterranean Basin, Petra, 2010. [6] M. Theodoridou, L. Kyriakou, I. Ioannou, Salt crystallization resistance of nanomodified repair lime mortars, in: H. de Clerq (Ed.), Proc. 3rd Int. Conf. on Salt Weathering of Building and Stone Sculptures, 2014. [7] M. Berra, F. Carassiti, T. Mangialardi, A.E. Paolini, M. Sebastiani, Effects of nanosilica addition on workability and compressive strength of Portland cement pastes, Constr. Build. Mater. 35 (2012) 666–675. [8] D. Kong, X. Dua, S. Wei, H. Zhang, Y. Yanga, S.P. Shah, Influence of nano-silica agglomeration on microstructure and properties of the hardened cement-based materials, Constr. Build. Mater. 37 (2012) 707–715. [9] J.J. Kim, M.K. Rahman, A.A. Al-Majed, M.M. Al-Zahrani, M.M. Reda Taha, Nanosilica effects on composition and silicate polymerization in hardened cement paste cured under high temperature and pressure, Cem. Concr. Compos. 43 (2013) 78–85. [10] E. Ghafari, H. Costa, E. Júlio, A. Portugal, L. Durães, The effect of nanosilica addition on flowability, strength and transport properties of ultra high performance concrete, Mater. Des. 59 (2014) 1–9. [11] A. Korpa, T. Kowald, R. Trettin, Hydration behaviour, structure and morphology of hydration phases in advanced cement-based systems containing micro and nanoscale pozzolanic additives, Cem. Concr. Res. 38 (2008) 955–962. [12] G. Quercia, A. Lazaro, J.W. Geus, H.J.H. Brouwers, Characterization of morphology and texture of several amorphous nano-silica particles used in concrete, Cem. Concr. Compos. 44 (2013) 77–92. [13] D. Kong, Y. Su, X. Du, Y. Yang, S. Wei, S.P. Shah, Influence of nano-silica agglomeration on fresh properties of cement pastes, Constr. Build. Mater. 43 (2013) 557–562. [14] M. Stefanidou, I. Papayianni, Influence of nano-SiO2 on the Portland cement pastes, Compos. Part B 43 (2012) 2706–2710. [15] H. Madani, A. Bagheri, T. Parhizkar, A. Raisghasemi, Chloride penetration and electrical resistivity of concretes containing nanosilica hydrosols with different specific surface areas, Cem. Concr. Compos. 53 (2014) 18–24. [16] J. Setina, A. Gabrene, I. Juhnevica, Effect of pozzolanic additives on structure and chemical durability of concrete, Procedia Eng. 57 (2013) 1005–1012. [17] K. Behfarnia, N. Salemi, The effects of nano-silica and nano-alumina in frost resistance of normal concrete, Constr. Build. Mater. 48 (2013) 580–584. [18] Y. Qing, Z. Zenan, K. Deyu, C. Rongshen, Influence of nano-SiO2 addition on properties of hardened cement paste as compared with silica fume, Constr. Build. Mater. 21 (2007) 539–545. [19] H. Madani, A. Bagheri, T. Parhizkar, The pozzolanic reactivity of monodispersed nanosilica hydrosols and their influence on the hydration characteristics of Portland cement, Cem. Concr. Res. 42 (2012) 1563–1570. [20] H. Li, H.G. Xiao, J. Yuan, J. Ou, Microstructure of cement mortar with nanoparticles, Compos. B Eng. 35 (2004) 185–189. [21] M. Stefanidou, Nano-modified lime-pozzolana pastes, Rom. J. Mater. 43 (2) (2013) 223–226. [22] I. Papayianni, V. Pachta, M. Stefanidou, Experimental study of nano-modified limebased grouts, World J. Eng. 9 (6) (2012) 501–508. [23] J.M. Fernández, A. Duran, I. Navarro-Blasco, J. Lanas, R. Sirera, J.I. Alvarez, Influence of nanosilica and a polycarboxylate ether superplasticizer on the performance of lime mortars, Cem. Concr. Res. 43 (2013) 12–24. [24] I. Papayianni, M. Stefanidou, The evolution of porosity in lime-based mortars, Proc. 8th Euroseminar on Microscopy Applied to Building Materials, Athens 2001, pp. 451–458. [25] J.I. Alvarez, J.M. Fernández, I. Navarro-Blasco, A. Duran, R. Sirera, Microstructural consequences of nanosilica addition on aerial lime binding materials: influence of different drying conditions, Mater. Charact. 80 (2013) 36–49. [26] B.B. Mukharjee, S.V. Barai, Assessment of the influence of nano-silica on the behavior of mortar using factorial design of experiments, Constr. Build. Mater. 68 (2014) 416–442. [27] R. Xu, Particle Characterization: Light Scattering Methods, Kluwer Academic Publishers, New York, 2002. [28] S. Brunauer, P.H. Emmett, E. Teller, Adsorption of gases in multimolecular layers, J. Am. Chem. Soc. 60 (1938) 309–319. [29] E.P. Barret, L.G. Joyner, P.P. Halenda, The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms, J. Am. Chem. Soc. 73 (1951) 373–380. [30] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (6) (1992) 1564–1583. [31] J. Němeček, Creep effects in nanoindentation of hydrated phases of cement pastes, Mater. Charact. 60 (9) (2009) 1028–1034. [32] M. Arandigoyen, J.L. Perez Bernal, M.A. Bello Lopez, J.I. Alvarez, Lime-pastes with different kneading water: pore structure and capillary porosity, Appl. Surf. Sci. 252 (2005) 1449–1459. [33] K.R. Iler, Coagulation of colloidal silica by calcium ions, mechanism and effect of particle size, J. Colloid Interface Sci. 53 (1975) 476–488. [34] IUPAC, Manual of symbols and terminology, Appendix 2, Pt. 1, Colloids Surf. Chem. Pure Appl. Chem. 31 (1972) 578. [35] P.F.G. Banfill, A.M. Forster, A relationship between hydraulicity and permeability of hydraulic lime, in: P. Bartos Paislez, C. Groot, J. Hughes (Eds.), Proc. Int. RILEM
C. Nunes et al. / Cement and Concrete Research 83 (2016) 152–163
[36]
[37] [38]
[39]
[40]
[41] [42] [43]
[44]
Workshop on Historic Mortars: Characteristics and Tests, RILEM Publications, Cachan 2000, pp. 173–183. International Union of Pure and Applied Chemistry IUPAC, Reporting data for gas/ solid systems with special reference to the determination of surface area and porosity, Pure Appl. Chem. 57 (4) (1985) 603–619. I. Odler, The BET-specific surface area of hydrated Portland cement and related materials, Cem. Concr. Res. 33 (2003) 2049–2056. N.C. Collier, J.H. Sharp, N.B. Milestone, J. Hill, I.H. Godfrey, The influence of water removal techniques on the composition and microstructure of hardened cement pastes, Cem. Concr. Res. 38 (2008) 737–744. R.M. Espinosa, L. Franke, Influence of the age and drying process on pore structure and sorption isotherms of hardened cement paste, Cem. Concr. Res. 36 (2006) 1969–1984. D. Snoeck, L.F. Velasco, A. Mignon, S. Van Vlierberghe, P. Dubruel, P. Lodewyckx, N. De Belie, The influence of different drying techniques on the water sorption properties of cement-based materials, Cem. Concr. Res. 64 (2014) 54–62. J.J. Chen, J.J. Thomas, H.M. Jennings, Decalcification shrinkage of cement paste, Cem. Concr. Res. 36 (2006) 801–809. S. Diamond, The microstructure of cement paste and concrete – a visual primer, Cem. Concr. Compos. 26 (2004) 919–933. S. Diamond, Mercury porosimetry: an inappropriate method for the measurement of pore size distributions in cement-based materials, Cem. Concr. Res. 30 (2000) (2000) 1517–1525. J.J. Thomas, H.M. Jennings, A.J. Allen, Relationships between composition and density of Tobermorite, Jennite, and Nanoscale CaO-SiO2-H2O, J. Phys. Chem. C 114 (2010) 7594–7601.
163
[45] M. Balonis, F.P. Glasser, The Density of Cement Phases, 2009, http://www.nanocem. org/MC-RTN/. [46] S. Diamond, E. Landis, Microstructural features of a mortar as seen by computed microtomography, Mater. Struct. 40 (2007) 989–993. [47] E.I. Mashinsky, Differences between static and dynamic elastic moduli of rocks: physical causes, Russ. Geol. Geophys. 44 (2003) 953–959. [48] A. Mockovčiaková, B. Pandula, Study of the relation between the static and dynamic moduli of rocks, Metalurgija 42 (2003) 37–39. [49] V.M. Malhotra, V. Sivasundaram, Resonant frequency methods, in: V.M. Malhotra, N.J. Carino (Eds.), Handbook of Nondestructive Testing of Concrete, second ed.CRC Press, 2006. [50] D.F. Howarth, Apparatus to determine static and dynamic elastic moduli, Rock Mech. Rock. Eng. 14 (1984) 255–264. [51] J. Martínez-Martínez, D. Benavente, M.A. García-del-Cura, Comparison of static and dynamic elastic modulus in carbonate rocks, Bull. Eng. Geol. Environ. 71 (2012) 263–268. [52] A.H. Hammam, M. Eliwa, Comparison between results of dynamic & static moduli of soil determined by different methods, HBRC J. 9 (2013) 144–149. [53] S. Kolias, R.I.T. Williams, Relationships between the static and the dynamic moduli of elasticity in cement stabilised materials, Mater. Struct. 13 (1980) 99–107. [54] A. Zaoui, Continuum micromechanics: survey, J. Eng. Mech. 128 (2002) 808–816. [55] J. Němeček, J. Vondřejc, V. Králík, Micromechanical analysis of heterogeneous structural materials, Cem. Concr. Compos. 36 (2013) 85–92.