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H. Manzano, A. N. Enyashin, J. S. Dolado, A. Ayuela,* J. Frenzel, and G. Seifert Recent developments in the chemical and mechanical performance of cement-based materials have been mainly in relation to the fine tuning of their nanostructure, which consists mainly of layered Portlandite (Calcium Hydroxide) and the CalciumSilicate-Hydrate (C-S-H) gel, as seen in Figure 1.[1–3] Tailoring the nanostructure may imply the cement reinforcement with Carbon Nanotubes (CNT),[4] in order to bring about the required improvement, as in nanocomposites, for example.[5–7] However, progress in research on cement-based materials is largely hampered by the intrinsically hydrophobic nature of CNTs and their chemical incompatibility with cement hydrates.[6,8] We herein present an interesting alternative to CNTs in the use of inorganic nanotubes (IN)[9] as reinforcement for cementitious materials. We report on calculations from first principles that predict the existence and stability of two new varieties of INs with two of the most important cement hydrates, namely Portlandite and the C-S-H gel.[10] The inherent compatibility of calcium hydroxide and CSH nanotubes with the cement matrix, together with their high stiffness and strength, means that they have the potential for widespread use as ultimate fibers for the reinforcement of concrete at the nanoscale. Cement-based materials, e.g. concrete, are second only to water in terms of the materials that are most commonly used by mankind. Though they are normally resistant to compression, they exhibit brittle behavior under tension. In order to address this weakness, concrete is traditionally reinforced, either by long continuous metallic bars that are uniformly distributed
Dr. A. Ayuela Departamento de Física de Materiales Facultad de Químicas Centro de Física de Materiales CSIC-UPV/EHU and Donostia Internacional Physics Center.20018. San Sebastián/Donostia, Spain E-mail:
[email protected] Dr. H. Manzano Molecular Spectroscopy Laboratory Department of Physical Chemistry University of the Basque Country UPV/EHU Apartado 644, 48080- BILBAO, Spain Dr. A. N. Enyashin, Prof. G. Seifert Technische Universität Dresden Physikalische Chemie D-01062 Dresden, Germany Dr. J. S. Dolado TECNALIA Research & Innovation Parque Tecnológico de Bizkaia Edificio 700, 48160, Derio, Spain Dr. J. Frenzel Lehrstuhl für Theoretische Chemie Ruhr-Universität Bochum D-44780 Bochum, Germany
DOI: 10.1002/adma.201103704
Adv. Mater. 2012, 24, 3239–3245
throughout the matrix, or by randomly oriented steel, glass or synthetic fibers.[11] While the primary aim of the metallic bars is to avoid macro-cracking that could lead to structural failure or collapse, the addition of microfibers is particularly intended to minimize the microcracks that occur during the early stages of hydration caused by autogenous and drying-related shrinkage.[7] However, the traditional approaches to the design of reinforced concrete relates to scales that are too large to have much effect on the chemical and mechanical damage that begins at the nanoscale. The fine-tuning of the cementitious nanostructure is one particular challenge, and represents the next source of improvement to the design of cement-based materials.[12] Cementitious Nanostructure: On the addition of water to grains of cement, tens of chemical reactions take place that give rise to the formation of a rigid cementitious matrix called cement paste. The matrix itself is a multi-phase, porous material that consists of calcium hydroxide (portlandite), aluminates and unhydrated clinker embedded into an amorphous nanostructured product of hydration, otherwise known as the so-called Calcium-Silicate Hydrate (C-S-H) gel, as shown in Figure 1. Considerable efforts have been made in recent years to develop nanoscale techniques of characterization,[1,2,13,14] in order to obtain insights of the cementitious nanostructure of C-S-H. The formation of C-S-H gel has been explained in terms of the aggregation of small bricks of C-S-H (∼5 nm in size). A number of authors have demonstrated that it is the motion and viscous response of the small C-S-H bricks that is the cause of creep and shrinkage,[15–18] and that depending on the packing factor, Low-density (LD), High-density (HD) or Ultra-High-density (UHD) varieties of C-S-H may be formed.[14,19] Recently, experiments on nano-indentation have shown that the LD, HD and UHD varieties exhibit rather dissimilar bearing capacities and even more pronounced differences in terms of their resistance to osteoporosis-like degradation.[16,20] In all cases these bricks contain a layered short-range ordering that is similar to that of layered minerals such as tobermorite (Figure 2).[3,21] Tailoring the Cementitious Nanostructure using Reinforcement: A number of different technological pathways have been proposed to improve the characteristics of existing cementitious nanostructures. The first involves intervention at the scale of the small bricks of C-S-H. This is the case for various attempts that have entailed the additions of colloidal silicate nanoparticles, because these are responsible for the formation of longer silicate chains and a reduction in Ca leaching, compared with normal C-S-H gels.[22,23] In a second approach, the formation of stiffer varieties of C-S-H is encouraged by adjusting the way in which the aggregation of the C-S-H bricks takes places. The relative abundance of LD, HD and UHD C-S-H varieties is known to be sensitive to the water-cement ratio and curing temperature, for example.[19] A third promising possibility lies in the search for new nano-fibers to address the nano-flaws that occur, for example, during the early stages of hydration as result of the
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Do Cement Nanotubes exist?
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Figure 1. Cement microstructure. SEM image of cement paste with portlandite precipitates within calcium-silicate-hydrated C-S-H gel.
changes in volume involved in autogenous and drying-related shrinkage.[8] It has been suggested that the ideal reinforcing material for use in concrete could be Carbon nanotubes (CNT),[4] as a result of their unique physical properties, including their exceptionally high strength, their modulus of elasticity, their elastic behavior and their aspect ratio.[24,25] While composites of carbon nanotubes with ceramic materials have been studied
relatively thoroughly,[26,27] composites with cementitious materials are still under development. A number of studies on the mechanical properties of nanotube-cement systems have shown inconsistent results; in comparison with purely cementitious samples, some authors have reported a slight improvement, and others have noted a clear deterioration.[5–8] The uncertainties found in the different CNT-cement composites are ascribed to the highly hydrophobic nature of CNTs and the differences in their chemical characteristics before mixing with cement paste, which allow them to become anchored to the silicate-calcium structures. Although there are a number of possible avenues of enquiry in the development of CNT-cement composites, it is the hydrophobic nature of CNTs that asks for research on different nano-reinforcement fibers that are fully compatible with the chemistry of water. Following the discovery of CNTs, new tubular structures[28] have been developed using layered inorganic compounds. Indeed, a number of families of inorganic nanotubes have been investigated in recent years, including metal dichalcogenides (sulphides, selenides and tellurides), halides (chlorides, bromides and iodides), as well as various ternary or quaternary compounds, oxides and hydroxides.[9] Having Young moduli (Y) that were only a few times lower than those of carbon nanotubes,[29–32] these inorganic nanotubes have also been considered as good fillers in organic polymer composites.[33,34] In comparison with CNTs, all these inorganic nanotubes could be used to improve the properties of cements thanks to their high hydrophilicity, and also their particular ability to be mass produced. To increase the strength of cement at the nanoscale, we can use, in particular, either other synthesized oxide nanotubes, H2Ti3O7, TiO2,[35] VOx,[36] Mg(OH)2,[37] or nanotubes of aluminosilicates found in nature, such as imogolite[38] or halloysite.[39] Although such oxide and aluminosilicate nanotubes
Figure 2. Construction of cement-based nanotubes. The layered structure of portlandite (a) and tobermorite (b) is shown in the left-hand panels, and the top view of the nanotubes is shown in the right-hand panels. Ca ions are shown as spheres in orange, oxygen in red, hydrogen in grey, and SiO4−4 tetrahedral units in purple. The axes of the primitive lattice of the layer are shown as a1 and a2. The nanotubes are formed by rolling along the following directions: armchair (n,n) and ziz-zag (n,0) for portlandite, and (n,0) and (0,n) for tobermorite.
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Energy (eV/atom)
are promising as fillers of cements, we go one step further because we notice that inorganic nanotubes made of the main components of cement paste, namely portlandite and tobermorite, show even more promise to reinforce cements. Cementitious Nanotubes - A New Technological Possibility: Within concrete, the most important hydrated components, namely, portlandite and C-S-H gel occur in layered compounds at the nanoscale (see Figure 1). Portlandite is a layered mineral that is formed by the octahedral coordination of calcium ions to hydroxyl groups, which alternate upwards and downwards from the central plane of the layer, as seen in Figure 2a.[40] The layers of tobermorite 14 Å (Ca4Si6O14(OH)4), the mineral analogue of C-S-H gel, consist of a calcium oxide sheet ribbed with silicate chains on both sides. These silicate chains follow a wollastonite-like or Dreierketten arrangement, in that the structure is repeated every third silicate tetrahedron (Figure 2b).[41] The aim of the study described herein was to “roll up” these layers into nanotubular structures, a possibility that has some appeal. Using simulations from first principles, we aim to demonstrate the existence of calcium hydroxide and C-S-H nanotubes, and to show that these nanotubes could represent an ideal type of nano-fibres for use in cements. In order to “fabricate” our cementitious nanotubes, it was first necessary to isolate individual layers from the bulk portlandite and tobermorite crystals and allow their relaxation to occur. Our calculations were performed using a tight-binding density functional theory (DFTB) code that was well suited to the study of these calcium silicate systems,[42] with some points also being checked using alternative density functional theory methods[43] (see Methods section). Molecular Dynamics simulations (NVT) at 300 K for a duration of 15 ps showed that isolated layers of both portlandite and tobermorite remain stable under these ambient conditions. The cementitious nanotubes were then fabricated by rolling these stable monolayers into cylindrical forms. For the Ca(OH)2 layer, the hexagonal arrangement of the hydroxyl groups allowed us to define nanotubes that were analogous in form to those of the carbon (CNT), boron-nitride (BN) or metal-chalcogenide nanotubes[29,30,44] as shown in Figure 2a. We therefore fabricated prototype zig-zag and armchair Ca(OH)2 nanotubes that had chiral indexes of (n,0) and (n,n) respectively (Figure 2a). For the tobermorite group, the monolayer does not have hexagonal symmetry, and in a similar manner to TiO2 lepridocite or γ-AlO(OH) nanotubes,[45,46] we define a two-dimensional rectangular primitive lattice, as shown in Figure 2b. One of the primitive lattice vectors runs parallel to the axis of the tube, with the other one being perpendicular. One index is therefore zero and originate (n,0) and (0,n) chiralities, with the silicate chains running parallel and perpendicular to the tube direction, respectively. Stability: The constructed portlandite and tobermorite nanotubes form stable structures after their geometries have been optimized. Such a condition is necessary, but is not sufficient to assess the stability of the nanotubes. For this reason, we also carried out MD simulations using the canonical ensemble at room temperature. In order to check the potential effects of the initial configuration, we began the simulations using several chiralities and starting geometries. Figure 3 shows some examples of the total energies of the portlandite and tobermorite nanotubes during our simulation.
(10,0) Ca(OH) 2
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-62.51
-62.55 (0,9) Tobermorite -62.57
-62.59 (9,0) Tobermorite -62.61 0
2
4
6
8
10
12
14
16
Time (ps) Figure 3. Stability of the cementitious nanotubes. Energy per atom against time for some examples of C-S-H and portlandite nanotubes using a molecular dynamics (MD) simulation at room temperature. Note the stability of (n,0) C-S-H and portlandite nanotubes at room temperature, as evidenced by the convergence towards an equilibrium value.
The energy of the Ca(OH)2 nanotubes in Figure 3 converges after a period of equilibration of about 1 ps. In fact, the energies of the nanotubes fluctuate around their average values, fluctuations that are attributed to the radial breathing mode of the nanotubes, in a similar manner to CNT.[47] Although for clarity not all the nanotubes are shown in the figure, this behavior is independent of their chirality, (n,0) or (n,n), and of their starting geometry. It is interesting to note that these energy convergences are clear signs of the stability of portlandite nanotubes at room temperature. In contrast, the stability of tobermorite nanotubes does depend on their chirality. In Figure 3, the energy of the (n,0) tobermorite nanotubes converges after the expected time of equilibration, while for the (0,n) nanotubes it continues to decrease even after 15 ps. These different energy convergences at later times indicate that the stability of the tobermorite nanotubes depends on the orientation of the silicate chains inside the nanotube. When the silicate chains run perpendicular to the axis of the tube (0,n), the energy does not converge, as the structural strain caused by the curvature of the tube induces a high stress. In order to assess the effect of such deformation, we analyzed some snapshots obtained from the MD simulation (Figure 3). At later time in the curve of energy versus time, we observed condensation reactions that took place between silicate groups in the bridging positions of the silicate chains inside the nanotubes. As a result of these reactions, the energy of the (0,n) nanotube does not reach a stable value. However,
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Strain energy (eV/atom)
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(5,0)
0.12
(n,0) portlandite (n,0) C-S-H
0.1 0.08 (5,0)
0.06 0.04
(5,5)
0.02 0 0
5
10
15
20
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nanotube radius (Å) Figure 4. Strain energy of the stable cementitious nanotubes. Strain energy per atom against radius. The portlandite tubes collapse to the same curve according to their radius, while the tobermorite tubes change to larger radii due the rolling of a thicker layer. The values of strain energy of the cementitious tubes are similar to those for existing carbon and inorganic nanotubes.
when the silicate chains are equiaxial to the nanotube, the energy converges towards the constant values shown in Figure 3 for tobermorite tubes. In such cases, the topology of the nanotube is maintained during the simulation, because the chains are subjected to a lower stress as a result of the curvature of the tubes, and the condensation reactions do not take place. We here consider only (n,0) tobermorite-like nanotubes, i.e. those structurally unmodified with silicate chains in a direction parallel to the axis of the nanotube. Strain Energy: Having established the stability of our cementbased nanotubes, we then turn our attention to the study of their strain energies. The strain energy of a nanotube is defined as the difference in energy between it and its corresponding planar monolayer. For most of the nanotubes reported[29,30,44,46] the strain energy is positive, and decreases inversely proportionally to the square of the radius of the nanotube, and represents the contribution of energy required to roll the layer into cylinders. Figure 4 shows the strain energy of the portlandite Ca(OH)2 nanotubes with the orange and green circles representing the armchair and zigzag chiralities, respectively. The energies decrease as the nanotube diameters increase, and they converge to the value of the planar layer in proportion to 1/R2, which is a similar trend to that of most types of inorganic nanotubes. The values of strain energy lie in the same range as those of CNT, BN, and Al(OH)3,[45,48] which indicates that they might be energetically accessible, and therefore synthesizable. In Figure 4, we show the same energetic trends for the (n,0) tobermorite nanotubes, in which the strain energy decreases monotonically and in proportion to 1/R2, and the values of energy per atom are also in a range that is comparable to that of other nanotubes.
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However, the curve of strain energy for the tobermorite nanotubes is shifted to larger radii due to the thicker two-dimensional unit cell required to describe their structure. Mechanical Properties: We begin by investigating the elastic properties of the cement-based nanotubes. The elastic properties of these nanotubes are of particular interest because they may be expected to be an excellent means of reinforcement of cementitious materials, both by improving the mechanical properties and by reducing the undesirable effects of creep and shrinkage. We calculated the reduced Young moduli and Poisson ratio of the portlandite and tobermorite nanotubes using the standard relationships described in the methods section. The reduced Young modulus,[48] Ys, is a quantity that takes into account the area of the nanotube wall rather than its volume, and is defined to avoid the controversial selection of a wall thickness originally for CNT. However, we also included estimates of the absolute values of the Young moduli, with the selection of the thickness of the nanotube walls being obtained with regard to the respective bulk crystals. The computed Young moduli and Poisson ratios are given in Table 1. For both the portlandite and tobermorite nanotubes, the YS values increase slightly with radius. This trend, which has already been observed for other nanotubes, may be explained by the high stress of the chemical bonds at large curvatures. As the nanotube diameter increases, the Young moduli approach those of the respective bulk crystals along their layers. The Young modulus of portlandite parallel to the layers is calculated to be 93.7 GPa using a force-field method[49] and 99.3 GPa using calculations from first-principles[50] both of which are slightly higher than the experimental value of 71.4 GPa.[51] The values obtained are close to the convergence limit Y ∼ 83 GPa of our portlandite nanotubes. To date, the elastic properties of tobermorite have not been measured experimentally, and the only data available in the literature relate to atomistic studies. The Young modulus of tobermorite 11 Å in the direction parallel to the silicate chains has been determined to be 87.7 and 94.3 GPa using force-field[49] and ab-initio[52] calculations, respectively. Our limit for the nanotube is Y ∼ 76 GPa, which is in good agreement with the theoretical predictions using the Table 1. Elastic properties of portlandite and C-S-H nanotubes. Values of reduced Young modulus and Poisson ratio versus tube radius. The estimated values of Young moduli accounting for layer thickness are also shown and are in the range 75-80 GPa, three times larger than the values for CSH gel under compression. Nanotube indexes Portlandite
C-S-H
Radius Reduced Young Estimated Young Poisson [Å] modulus [GPa·nm] modulus [GPa] ratio
(10,0)
6.17
(13,0)
7.89
36.5
73.7
0.23
(16,0)
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37.0
74.7
0.23
(10,10)
10.43
41.3
83.4
0.25
(13,13)
13.46
41.4
83.6
0.25
(16,16)
16.56
41.2
83.2
0.25
(9,0)
20.2
72.4
65.8
0.39
(12,0)
25.4
82.0
75.6
0.40
(14,0)
29.0
84.3
76.6
0.39
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71.3
0.23
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Experimental Section Due to the large number of simulations performed and the size of the nanotubes studied (up to 1000 atoms for the larger C-S-H nanotubes), traditional calculations using DFT were deemed to be unpractical. We therefore adopted a semiempirical tight-binding DFT (DFTB) method for the present study. In this approach, the energy of a system may be approximated by the sum of the occupied Kohn-Sham singleparticle energies and a repulsive energy, which are obtained using DFT calculations in properly chosen systems of reference.[42] The suitability of this method has already been proved for studies in material science in general, and for nanotubes in particular.[31,55] All the calculations were performed using periodic boundary conditions, by verifying the convergence of the k-points in the direction of the nanotube, and by setting the dimensions of the cell in a direction parallel to the tube axis that were large enough to avoid interactions between adjacent cells. The strain energy, elastic properties, and tensile strength were calculated using the DFTB+ code,[56] together with the conjugate gradient method to relax the atomic positions. The reduced Young moduli were calculated from the changes in the energy-strain relationship, by applying different degrees of axial strain to the nanotubes, both negative (contraction) and positive (expansion), following the equation:
9.0
tensile energy (eV/atom)
We can also use this relationship to estimate the ultimate tensile strength of tobermorite nanotubes to be about 7.5 GPa. These values of ∼8 GPa greatly exceed the tensile strengths of cement pastes and are at least an order of magnitude higher than those of typical reinforcing materials such as structural steels (∼500 MPa).[54] Conclusions and Future Perspectives: In summary, we have opened up a new area of research by proposing inorganic oxide nanotubes as natural means of reinforcements of cement pastes, in view of their chemically compatibility with the cement-water system. We here focus on cement-based nanotubes fabricated from calcium silicate hydrate gel and calcium hydroxide precipitates. We demonstrate the feasibility of these cementitious nanotubes in view of their stability at room temperature, with strain energies in agreement with values previously obtained for other nanotubes compounds. In addition, the high Young moduli and ultimate tensile strengths of cementitious nanotubes point to their convenience for use as reinforcement for cement pastes. A successful synthesis of portlandite and tobermorite C-S-H based inorganic nanotubes has yet to be devised by inorganic chemists. It is important to note that Mg-based nanotubes have been synthesized and even found to occur naturally. Although Mg(OH)2 and Ca(OH)2 are chemically very similar, there is no reported evidence of the existence of Ca-based nanotubes, despite their analogous electronic configuration. It therefore seem reasonable to propose that Ca(OH)2 nanotubes could be synthesized using a method that attempts to improve on the route previously reported to synthesize Mg(OH)2 brucite nanotubes.[37]
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bulk structure, given the uncertainty in our choice of nanotube thickness. The Young moduli of the cementitious nanotubes are considerably lower than those of carbon nanotubes (∼1 TPa), and of the same order of magnitude as those of other inorganic nanotubes, such as imogolite (∼250 GPa), MoS2 (∼230 GPa), GaS (∼270 GPa), and chrysotile nanotubes (∼159 GPa).[29–32] In fact, the Young moduli of portlandite and tobermorite nanotubes are slightly softer than those of inorganic nanotubes. Nevertheless, the nanotubes described here are particularly well suited to the reinforcement of concrete because (i) their chemical characteristics are fully compatible and (ii) they have a Young modulus that is three times higher than that of C-S-H gel (Y∼15 to 30 GPa), as measured by nanoindentation,[14] which is mainly responsible for the mechanical performance of cement paste. Finally, it is worth considering how these new nanotubes can improve the intrinsically low tensile strength of cementbased materials. A high Young’s modulus implies that a greater tensile force is required to elongate the nanotube by the same given amount. Since the values of Young’s modulus are much greater than that of cements, these nanotubes can certainly be used as reinforcements where stretching is applied. In addition, the critical stress-strain parameters, especially the stress prior to failure, i.e. the so-called ultimate tensile strength (UTS), are of particular interest for the range of potential applications of cements. It should be noted that these strengths for cements are in the range of 1–10 MPa.[10] To investigate this point, we focus on the tensile stress-strain profile under static deformation of portlandite nanotubes, as shown in Figure 5. The stress increases almost linearly up to a strain of 27%, at which point failure occurs in the nanotube. The corresponding critical stress is 8.4 GPa, which is about 10% of the Young’s modulus. This relationship UTS ∼ Y/10 is in excellent agreement with previous calculations for other inorganic types of nanotubes.[9,53]
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0
5
10
15
20
25
30
35
tensile strain % Figure 5. Tensile stress of a (9,9) portlandite nanotube as a function of strain. The nanotube fails after a strain of 27% when it is under a maximum stress of 8.4 GPa.
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YS =
1 S0
∂ 2 E ∂ε 2 ε = 0
(1)
where Ys is the reduced Young modulus, E is the nanotube energy, ε is the strain, and S0 is the optimized surface of the nanotube. The ordinary Young moduli were calculated by simply dividing Ys by the thickness of the nanotube wall. For portlandite, a reasonable choice for the laminar thickness is the lattice parameter c. In the case of tobermorite, after
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www.MaterialsViews.com analyzing a number of members of the tobermorite family that had different interlaminar spaces, we selected a thickness of 11 Å. Using the same axial deformations, we also calculated the Poisson ratio, which is a measure of the change in the mean diameter of the tube under stretching, and is defined as:
R − R0 =−σ·ε R0
(2)
where R is the radius, R0 the equilibrium radius, and σ the Poisson’s coefficient. The tensile stresses were computed by performing static deformations in steps of 2%, and relaxing the atomic positions at each strain step. For the MD simulations we use the DFTB implementation on the DeMon code,[57] and a supercell that consisted for each case in the numbers of unit cells required to reach at least 1 nm in the direction of the tube axis. A Berendsen thermostat was used, with a time constant of 0.5 ps. The MD time step was 0.5 fs. In order to ensure the validity of our calculations, some checks were made using standard DFT methods with the SIESTA code.[43] The details of the simulations are the same as in previous studies,[58,59] with the only difference being that single zeta polarized (SZP) basis sets were used, due to the size of the systems concerned.
Acknowledgements This study was supported by funding from the Basque Government through the NANO-IKER project (Grant No. IE11-304) under the ETORTEK Program, the Spanish Ministerio de Ciencia y Tecnologia of Spain (Grant Nos. TEC2007-68065-C03-03 and FIS2010-19609-C02-02), and the University of the Basque Country (Grant No. IT-366-07). H.M. acknowledges a postdoctoral fellowship from the Basque Country Department of Education, Research and Universities. The computing resources of the Donostia International Physics Center (DIPC), the HPC at ZIH Dresden, CESGA and the SGIker (UPV/EHU) are gratefully acknowledged. Thanks are due to T. Heine for the DFTB implementation in the DeMon code. Received: September 27, 2011 Revised: February 27, 2012 Published online: May 16, 2012
[1] L. B. Skinner, S. R. Chae, C. J. Benmore, H. R. Wenk, P. J. M. Monteiro, Phys. Rev. Lett. 2010, 104, 195502. [2] A. J. Allen, J. J. Thomas, H. M. Jennings, Nat. Mater. 2007, 6, 311. [3] I. G. Richardson, Cem. Concr. Res. 2004, 34, 1733. [4] S. Iijima, T. Ichihashi, Nature 1993, 364, 737. [5] S. Musso, J.-M. Tulliani, G. Ferro, A. Tagliaferro, Composites Science and Technology 2009, 69, 1985. [6] Y. Saéz de Ibarra, J. J. Gaitero, E. Erkizia, I. Campillo, Phys. Status Solidi A-Appl. Mat. 2006, 203, 1076. [7] M. S. Konsta-Gdoutos, Z. S. Metaxa, S. P. Shah, Cem. Concr. Res. 2010, 40, 1052. [8] M. S. Konsta-Gdoutos, Z. S. Metaxa, S. P. Shah, Cem. Concre. Compos. 2010, 32, 110. [9] R. Tenne, G. Seifert, Annual Review of Materials Research 2009, 39, 387. [10] H. F. Taylor, Cement Chemistry, Thomas Telford Publishing, London 1997. [11] J. P. Romualdy, G. B. Batson, in Selected landmark papers in concrete materials research, Vol. 249 (Eds: R. Detwiler, K. Folliard, J. Olek, J. S. Popovics, L. Snell), ACI Publications, Farmington Hills, USA 2008, p.251. [12] R. J. M. Pellenq, H. Van Damme, MRS Bulletin 2004, 29, 319.
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