Tracing Polymerization in Calcium Silicate Hydrates Using Si Isotopic

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Tracing Polymerization in Calcium Silicate Hydrates Using Si Isotopic Fractionation Romain Dupuis, Jorge S. Dolado, José Surga, and Andres Ayuela J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00307 • Publication Date (Web): 20 Mar 2018 Downloaded from http://pubs.acs.org on March 23, 2018

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The Journal of Physical Chemistry

Tracing Polymerization in Calcium Silicate Hydrates using Si Isotopic Fractionation Romain Dupuis,† Jorge S. Dolado,‡ Jose Surga,¶ and Andrés Ayuela∗,§ †Paseo Manuel de Lardizabal, 4, 20018, San Sebastian, Spain. ‡Parque Cientifico y Tecnologico de Bizkaia, 48160 Elexalde Derio, Spain ¶Urb. Santa Rosa, Los Teques, 1201, Venezuela §Paseo Manuel de Lardizabal, 5, 20018, San Sebastian, Spain E-mail: [email protected]

Abstract Silicate-chains polymerization is a crucial process in calcium silicate hydrate minerals, with large relevance for improving the durability and reducing the environmental impact of cement-based materials. To better understand the evolutionary mechanisms underlying the polymerization of silicate-chains in layered calcium silicate hydrates, we herein propose to trace the evolution of the polymerization degree by using silicon isotopes. The method requires tabulating the isotopic fractionation of several basic chemico-physical mechanisms that we obtained by performing atomistic simulations. The calculations reveal that the highly polymerized structures have longer Si-O bonds and that the Ca2+ cations play a dual role in the stretching and bending modes properties of silicates, such as isotopic fractionation is able to discern not only between the polymerization order of calcium silicate hydrate minerals, but even between cement gels suffering calcium leaching. Silicon isotopic fractionation can, therefore, be used to quantify the different evolutions of calcium silicon hydrate phases in a sample of

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man-made gel cement in order to improve its sustainability along lifetime stages in the quest for green cement.

Introduction Silicon is one of the most common elements on Earth which makes silicon isotopes a preeminent tool to trace seafloor erosion, continental weathering, water fluxes, flora ecosystems, and other processes. 1–3 The growth of silica occurs through the polymerization of silicate groups Si(OH)4 , known as oligomerization. 4 More complex silicates form over time via reversible processes. Depending on the conditions, the oligomerization process can produce a well-ordered skeleton with double silicate-chains (such as a calcium silicate hydrate mineral, as shown in Fig. 1) or an amorphous glass. In nature, isotopes can be exchanged between different phases. Although the amounts involved might be tiny, the energies in the structures are altered by the swap of isotopes. Isotopic exchange will often reach an equilibrium after a while, and the ratio between two different isotopic phases can be measured by determining the isotopic fractionation factor. 5 The isotopic fractionation factor is an echo of all equilibration processes that have occurred. Measuring the isotopic signature at different times and places provides information on the evolution of the phases. This was first used to trace geological events 6–9 and then used later in other fields including planetary science, 10 medicine 11 and biology. 12 Stable isotope geochemistry may, in the near future, be of use in many fields, such as materials science. Isotopic fractionation involves processes over long periods of time and can be arduous to assess experimentally. However, recent methodological developments have made it possible to predict the isotopic properties of equilibria between minerals. 13–15 These equilibria can even implicate liquids, 14,16–19 for which evaluating the local vibrational properties is complex. Isotopic fractionation is useful because it is closely related to local changes in a structure. 18,20,21 Cement, which is the most-used material by mankind, is principally formed by calcium

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Figure 1: Illustration of different polymerization stages of silicates. The most complex system (on the right) is comparable to structures found in cementitious materials (calcium silicate hydrate mineral). silicate hydrate gels that bind the whole structure. In order to control the production of more sustainable cement, which is more ecological to produce or have more durability, 22 it is key to characterize the polymerization of these silicates. For the reasons outlined above, isotopic fractionation is a powerful tool for gathering information, step by step, on the polymerization of silicate tetrahedra to form chains. Calcium silicate hydrates include crystalline structures of interest in minerals science 23 and poorly ordered phases that are key in the cement industry. 24 The diverse phases of calcium silicate hydrates provide useful information to improve our understanding of the polymerization of silicates because they have different polymerization orders of between zero and four. The underlying processes of the cement chemistry are similar to natural chemical processes such as the formation or dissociation of silicate chains. Silicates are clearly tied to the presence of silicon atoms; hence, silicon isotopes can be valuable as markers. The measurement of precise silicon isotope concentration became possible few decades ago using mass spectrometers. As aforementioned, isotope geochemistry, has growing interdisciplinary interests and we propose to use it for tracing the chemical changes in concrete and of calcium silicate minerals. Two ongoing questions can be addressed by studying calcium silicate hydrates: the first one relates to the effect of Ca2+ cations essential to many minerals on the isotopic fractionation; the second one is what, if any, relationship there is between the polymerization order and isotopic properties. 21,25 Therefore, we have to investigate mainly the isotopic properties of silicon. Anyhow, we also

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report the values calculated for calcium isotopes. In the present study, we find that substantial fractionation of silicon and calcium isotopes occurs through equilibria between calcium silicate hydrates with temperature. We use density functional theory to compute the vibrational properties of involved calcium silicate hydrates and identify important changes in the vibrational properties that explain isotopic fractionation. We then interpret these results based on local structural differences. We find large isotopic fractionation factors, that can be experimentally measured to use them afterward as a new tool to measure the durability of cement-based materials.

Structures Among calcium silicate hydrates, we selected four phases having different polymerization orders and forming at different pressures and temperatures. In the following, structures are described using the abbreviations: C=CaO, S=SiO4 , and H=H2 O. The phases are displayed in Fig. 2 and are (i) α-dicalcium silicate (labeled C2SH), which is not polymerized, (ii) calcium silicate hydrate gel (labeled C-S-H gel), which has some Q1 silicate polymerization within silicates, and (iii) a tobermorite polymorph with Q2 polymerization order, and (iv) a tobermorite polymorph with Q2 and Q3 polymerization order. The two tobermorite mineral polymorphs can be distinguished by their basal peak distances which can be 11 or 14Å, respectively T11 and T14. The phases with different polymerization orders also correspond to distinct stages of a cement after hydration. The process is accompanied by mass transport, so that the density of the C-S-H gel increases, during which isotopes could be fractionated. 26 Adding water to cement clinker drives to the synthesis of C-S-H gel, which plays a major role in ensuring the cohesion 24 of the structure together and retaining water, 27 as shown in Fig. 2(b). Tobermorite is an inosilicate with silicate-chains along the CaO layers with a structure similar to the C-S-H gel 28 but with infinite chains. It is a highly ordered phase that exists under several polymorphs. At room temperature, T14, is formed (see Fig. 2

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Figure 2: Calcium silicate structures of minerals related to hydrated cement paste. (a) dicalcium silcate C2SH, (b) C-S-H gel, the structures of tobermorite with an inter-reticular distance of (c) 14Å (labeled T14) and (d) 11Å (T11) are shown. The Ca, O, and H atoms are indicated in light blue, red and white, respectively. Silicate groups SiO4+ 4 are presented by yellow tetrahedra. Hydrogen bonds are shown as dashed black lines. The main differences between the structures reside in the inter-reticular distance (11Å or 14Å) and the presence of cross-links in T11 caused by the interlayer space being small. (c)). Its structure was characterized by

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Si nuclear magnetic resonance which indicates

the binding configurations of the silicon tetrahedra. 29 Heating a C-S-H gel to about 55o C causes water molecules to be removed from the interlayers and the chains between the layers to start condensing as double chains. This is associated with the material shrinking in the c-axis and ends in a T11-like mineral being formed. At higher temperatures, above 100o C, these layered inosilicate calcium silicate hydrates are transformed into orthosilicates in the form of α-C2SH mineral, hereafter labeled C2SH, as shown in Fig. 2. 30 More details of the relaxed structures are given in Supplementary Information. It would be interesting to quantify experimentally 31 the loss of durability of cementitious 5



materials under heating. As the temperature increases, the silicate-chains in C-S-H gel break to form single SiO4− 4 tetrahedra and the C-S-H gel transforms into the C2SH phase. The shortening of silicate-chains is corresponding to a loss of strength of the concrete, solutions were proposed to increase the chain length such as nanoadditions, 32 in order to reinforce the structure at the nanoscale. The isotopic fractionation factor could yield information related not only to the bonds but also to the near environments of the silicon atoms. Most silicon atoms in Portland cement (the most common type) after hydration are part of the C-S-H gel that is formed. Other relevant cement phases are composed of other elements, such as oxygen, calcium, and hydrogen. For example, one of such phases is portlandite (Ca(OH)2 ) involved in alkali-carbonate reactions. 33 Note that other secondary phases, such as thaumasite, can contain silicon, but once these phases are formed they are not involved in the process causing loss of strength unless external sulphuric acid attacks the cement, 34 transforming it into ettringite. A loss of durability can then be traced by determining changes in the 30 Si and 28 Si isotopic composition. We also report the isotopic properties between stable calcium isotopes 44 Ca and 40

Ca, that provide valuable information for studying dissolution processes in geochemistry.

A cement structure will be stronger the longer the chains are, 32 so a correlation between isotopic fractionation and the degree of polymerization would allow gains or losses in cement durability to be experimentally determined. We use three structures to allow our method to be compared with previous calculations and experiments. These structures are (i) quartz, which is normally used as a reference, (ii) kaolinite, which is a layered phyllosilicate with Q3 polymerization order, and (iii) C-S-H gel, in which all the interlayer Ca2+ cations, that are located in a bridging position, in-between two silicate dimer, are replaced with two H+ . The H+ are replacing relevant Ca2+ cations in the interlayer space and their position was relaxed. This C-S-H gel has a low Ca/Si ratio compared with typical cement structures, which generally have a Ca/Si ratio of 1.7. 27 C-S-H gel herein denotes a system with interlayer Ca2+ if the presence of H+ is not specified.

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Methods Isotopic fractionation occurs because of a difference in the energy when isotopes exchange between two phases. 35 The energy change is slight and is caused by the isotopic shift in the energy levels in a quantum system. We first consider the β-factor, defined as the theoretical isotopic fractionation factor for a phase with respect to its gas. This factor is computed using the phonon frequencies 36 using the equation:

β 30 Simineral (T ) ≈

"N Y

#1/N β 30 Sii,mineral

i=1

=

3×N Yat i=3

−hν30,i 2kB T

−hν28,i 2kB T

(1)

1−e ν30,i e −hν28,i −hν30,i , ν28,i 2kB T e 1 − e 2kB T

where Nat is the total number of atoms, and ν30,i and ν28,i are the frequencies of the TO phonon modes, calculated at the Γ point of the Brillouin Zone, for the mineral with all sites occupied by 30 Si and 28 Si isotopes, respectively. The measured isotopic fractionation factor, called the α-factor, corresponds to the ratio between two β factors, one often being a reference system. The α-factor can also be measured in natural samples or on experimental samples. The calculations give the opportunity to predict the isotopic fractionation properties in conditions where it is difficult to investigate experimentally (e. g. low temperatures). We compute the isotopic fractionation properties following the approach described in Refs. 13,37 This approximation has been proved to be appropriate for studying minerals in the temperature range in which harmonic behavior occurs. 18,21 We first optimize the cell and atomic structure, then calculate the phonon properties to be used in Eq. (1).

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Figure 3: (a) Logarithms of the β-factors for T11, T14, C-S-H gel, and C2SH plotted against temperature. The inset is the plot magnified around room temperature. The dotted line relates to the quartz reference.

Results β-factors The fractionation β-factors are shown in Fig. 3. The isotopic fractionation factor tends to zero at high temperatures because the system becomes classical. The β-factor indicates the enrichment of the heavy isotope all other studied phases, and

30

30

Si. The C-S-H gel phase is less enriched in

30

Si than

Si enrichment increases in the following order: C2SH, T14,

quartz and T11 minerals. A table showing the dependence of the β-factor on temperature is provided in Supplementary Information.

Vibrational properties Differences in isotopic fractionation are caused by changes in the vibrational properties of the phases. The vibrational modes contribute more to the β-factor in Eq. 1 at higher

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Figure 4: Top panels: density of states for the phonons projected for the Si and O atoms in T11, T14, C-S-H gel, and α-C2SH. Bottom panels: the corresponding contributions to the beta factor for each mode. The arrows in the side structures show the normal vectors of the important vibrational modes. frequencies. The density of phonon states projected on to the modes involving Si and O motion is shown in Fig. 4. These modes contribute most to the Si β-factor. The effective contributions of the modes to the total β-factor are displayed in the bottom panels of the figure, two phases being considered in each panel. We determine the characteristic phonon frequency for Si-O stretching and anti-stretching modes of the silicates SiO4 to be around 900cm−1 for every phases. 38 The T11 system has other peaks with wavenumbers higher than 1000cm−1 , and these correspond to O-Si stretching in the silicate caused by two chains being bound together, a polymerization that occurs in silicates at Q3 sites. That explains the enrichment in heavy isotopes of T11 compared to T14 (see Fig. 3(a)). Other stretching modes associated with silicon in Q2 sites for T14 are mostly at the same frequencies as for T11. In the C-S-H gel, the silicon atoms are in Q1 sites and the stretching modes are at a lower frequencies. These modes are moreover shifted at lower frequency by the presence of interlayer Ca2+ in the direction of the Si-O 9



bond in the C-S-H gel compared to the C-S-H gel with H+ substitutions, in agreement with the results in the work of Méheut et al. 2014. More precisely, cations usually cause nearby Si-O bonds to be elongated with respect to other Si-O bonds in the system, and generally favors the presence of light isotopes. We next consider the silicate chain bending modes frequency, shown on the left of Fig. 4. The bending modes are found for the tobermorite minerals, as shown in panel (a). These modes are found at frequencies of about 600-700cm−1 . The modes make substantial contributions to isotopic fractionation, as shown by the arrow in the bottom panel of Fig. 4(a). We suggest that bending modes frequencies of the silicate-chains could be increased due to the presence of Ca2+ cations. In particular, the large ionic radius of Ca2+ (around 1.94Å) may be a factor in increasing the frequencies of these modes. Note that other interlayer cations (e.g. Al, Li, and others) could affect differently the frequencies compared to Ca2+ . From panel (c), it can be seen that the contribution of the silicate chain bending modes to the isotopic fractionation factor is mostly equal to the difference between the total β-factor for T14 and the C-S-H gel. This is relevant because T14 tobermorite is used to model the C-S-H gel. 39 The silicate SiO4 bending modes for C2SH are found centered on a peak at 700cm−1 , as shown in Fig. 4(b). These modes in pure silica SiO2 40 are normally in the range of 400-600cm−1 for symmetric bending (also called E-bending) and between 300 and 500cm−1 for asymmetric bending, for which the bending angles of two pairs of O-Si-O angles are different. Unlike for the Si-O stretching modes, the effects of Ca2+ ions drives the bending modes to higher frequencies (between 600-800cm−1 for T11, T14, and C2SH), which make the phases heavier than expected. This counterintuitive result stems from configurations where the Ca2+ cations retain oxygen atoms, as shown on top of the Fig. 4. Thus, the increase in the bending mode frequencies of C2SH could be linked to the loss of flexibility of the tetrahedra. In other words, the silicate groups are located in a cage of cations which could have a retention effect likewise for silicates in a liquid. Note that forsterite mineral, 21 that has a polymerization order of Q0 (isolated silicate tetrahedral) like the C2SH phase, is

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found to be heavier than expected. Enrichment in this mineral could be caused by changes in the bending modes caused by the presence of Mg2+ cations. In summary, the key modes that play roles in isotopic fractionation are closely related to the presence of Ca2+ in the phases. In particular, we have identified two cases in which the ions play different roles in the Si-O vibrational stretching modes in single tetrahedral and the O-Si-O bending modes in silicate-chains. These findings have implications for the classification and measurements of the aging of cement, discussed in the sections below.

Discussion General implications It is essential to understand the relationship between isotopic fractionation properties and local structure, to allow the properties of minerals to be understood. We compare our values with values for a reference mineral quartz, which is generally used when dealing with silicates. To our knowledge, there is not yet measurements of the isotopic composition of silicon on the systems we study. The isotopic fractionation factor α30 Simineral−quartz at 300K is plotted versus the mean distance d¯Si−O in the system in Fig. 5. The values are compared with values found from the literature for other equilibria involving silicates with silicon in a tetrahedral site. Values from the literature for phyllosilicates 21 and silicates dissolved in water 18 are also shown. We calculate a α30 SiKaolinite−Quartz value of -1.9% at 300K, which is comparable to other reported values in the range of -1.8 to -1.6%. 13,18,21 We also find that the isotopic fractionation factor for the C-S-H gel with H+ substitutions is linearly correlated with the mean distance d¯Si−O . For these three structures, in particular for quartz and kaolinite used for reference, we find that the heavy isotopes become enriched as the polymerization order increases. This was predicted in earlier isotopic studies, 25 but recently the roles of added cations have been questioned. 21 We also consider the T11, T14, and C2SH minerals that, as aforementioned, exhibit 11



Figure 5: Logarithm of the isotopic fractionation factor α30 Si for an equilibrium of minerals with quartz versus the variation of the mean distance d¯Si−O (see text). Kaolinite and C-S-H gel (H) phases follow the trend proposed for pure silicates 18 whereas other phases are enriched in heavy isotopes (T11, T14 or C2SH) or light isotopes (C-S-H gel (Ca)). Vibrational properties differ due to the rich-Ca environment around SiO4+ 4 silicates. Even though the 4+ SiO4 polyhedra have similar shape the two minerals can be differentiated by their isotopic composition. important bending modes of either the silicate group SiO4 or the silicate-chains. For these three minerals, plots of isotopic fractionation factor versus d¯Si−O follow similar trends. The values are, however, shifted relatively to one of the minerals that do not contain Ca2+ cations with an offset of ≈2%: the systems are enriched in

30

Si. This implies that the isotopic

properties are not related only to increased Si-O distances because of the presence of Ca2+ and highlights the importance of the bending modes. Fig. 4(a) shows that the bending modes around 700cm−1 account for the observed changes in the β-factor between T11 and T14. Nonetheless, the similar linear correlations between the isotopic fractionation factors for T11, T14 or C2SH and the mean distance d¯Si−O indicate that the variations in the isotopic properties for T11, T14, and C2SH mostly comes from the Si-O stretching modes at high 12


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frequency. The isotopic fractionation properties, due to silicate polymerization, is correlated with the Si-O bond-length which confirms the key role of the shape of the tetrahedron SiO4 in the isotopic fractionation properties of silicon in calcium silicate hydrates as in pure silicates. The calcium atoms that belong to the second layer of atoms in relation to silicon atoms are less likely to affect the vibrational properties. Note that the distance dSi−Ca decreases (3.26Å in C2SH, 3.24Å in T14, and 3.19Å in T11) as the isotopic fractionation increases. The isotopic fractionation of the C-S-H gel is shown in Fig. 5. The C-S-H gel is much lighter than any of the other minerals studied. The absence of chain-bending modes around 650cm−1 in C-S-H gel contributing to the β-factor (see Fig. 4 (c)) decreases the calcium’s effect in the isotopic fractionation properties of C-S-H gels. Furthermore, the Si-O...Ca angle present larger values in the case of C-S-H gels (145o C) than in T11, T14, and C2SH (about 130o C), a fact that is related to the effect of Ca2+ on the bending modes. It is noteworthy that interlayer cations play a role in the neighborhood of Si atoms. We compare the calculated values for the C-S-H gel with H+ cations and with Ca2+ cations as compensation charges. In C-S-H with Ca, the distance dCa−O (2.48Å ) in the interlayer is shorter than in the CaO layer (2.55Å ). We observe similar structures for the two compensation schemes with similar mean distance d¯Si−O . The isotopic fractionation factor α30 SiC−S−H(H)−quartz fits on the linear trend calculated for pure silicates such as phyllosilicates and also dissolved species. Although there are Ca2+ in the CaO layer, the isotopic fractionation properties are similar to the ones of pure silicate, because the bending modes around 700cm−1 does not contribute much to the β-factor. Moreover, there is no Ca2+ in the interlayer. Thus, the SiO4 polyhedron size is directly associated with the isotopic properties. As a result, the C-S-H gel (H) is enriched in

30

Si compared to the normal C-S-H gel with interlayer Ca2+ .

In summary, the role of Ca2+ is dual, depending on the conformation of the system it can either modify the bending mode frequency as in T11, T14, and C2SH or increase the stretching mode frequency as in the C-S-H gel with Ca2+ as compensation charges. The

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polymerization of the chain also plays an important role as longer chains have shorter d¯Si−O and higher stretching mode frequency. As it was shown previously, in silicates there is a correlation between the mean distance dSiO and the fractionation factors. The trend is mostly due to the stretching modes, in agreement with previous studies on pure silicates for minerals 21 or for dissolved species. 18 Therefore, the trends are similar (but shifted) between phyllosilicates and calcium silicate hydrates, so that the statement that Ca2+ ions are affecting similarly the bending modes is reinforced. We further explain that the CSH gel (Ca) deviates from this trend because there the Ca2+ ions in the interlayer space have a linear conformation that is different than in the T11, T14, and C2SH series, so that the vibrational modes are affected differently. The C-S-H gels have different isotopic properties with very different Si environments. Further implications of Fig. 3 suggest that secondary clay minerals and silica gels produced by silicate weathering could have similar Si isotopic signature to C-S-H gels. The value for the α30 SiH4SiO4−quartz between a dissolved species in pure water and quartz reported in 18 is -2.09 ± 0.13%. We can compare the value of α30 SiH4SiO4−quartz value to the value for C-S-H gel (Ca), which corresponds to the common structure in Portland cement, and find that the C-S-H gel is lighter than the dissolved species H4 SiO4 by about -2.3% at 300K. Furthermore, the β-factor for 44/40 Ca equilibrium depends on the phases. Figure 6 shows that C2SH is the most enriched in 44 Ca followed by T14, T11, and the C-S-H gel. The relation between C2SH, T14, and T11 is reversed when we compare to the Si isotopic fractionation. This is related to the distances Ca-O or Si-O. C2SH has the shortest average distance for the Ca-O bond (2.49 Å) but the longest Si-O distance. There is a correlation between the fractionation properties of Ca and the mean distance d¯Ca−O in the minerals and gels that are being here studied (see Fig. 6).

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Figure 6: (a) Logarithms of the calcium β-factors for T11, T14, C-S-H gel, and C2SH plotted against temperature. The inset is the plot magnified around room temperature. The dotted line relates to the quartz reference. (b) β-factors for T11, T14, C-S-H gel, and C2SH plotted against the mean distance d¯Ca−O at 300K.

Implications for cementitious materials Isotopic fractionation measurements could allow the limited number of phases involving silicon in cement to be investigated. Isotopic fractionation factors are calculated at equilibrium (i.e. when the exchange of isotopes between phases has equilibrated). Using isotopic fractionation factors to measure cement hydration or deterioration requires α-factors that are sufficiently large. The calculated α30 SiCSH−C2SH at 410K is -1.6 %. This is a large value compared with those that can be measured. 3,41 However, it is difficult to ascertain when fractionation occurs at (or near) equilibrium or for a kinetic process. On the one hand, the silicate-chains in cement grow much longer over long periods of time, of the order of months and years. On the other hand, the transformation of C-S-H gel into C2SH is initiated at about 110o C. Both processes are considered to be relatively slow, so we consider each process to fractionate isotopes near equilibrium. Nonetheless, it is currently possible to perform experimental studies of isotopic fractionation to determine how far from equilibrium such processes are. It will be interesting to determine experimentally when the isotopic fractionation data obtained for these equilibria are similar. It could then be possible to experimentally

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confirm when a process has reached equilibrium. The two cases mentioned above are inherently slow transformations, so it is possible that experiments will show that some C-S-H gel is not fully transformed into C2SH, meaning that the isotopic fractionation between the phases can be measured. All these points suggest that the isotopic fractionation of silicon isotopes can be used to trace the evolution of cement as temperature increases, by focusing the measurements on the C-S-H gel present. The isotopic fractionation factor depends on the temperature at which the transformation to C2SH occurs, and accordingly, it could be a new tool for studying the loss of cement durability as temperature increases, to add to the tools already available. 42–44 The isotopic fractionation factor provides information that is complementary to the data provided by standard tools, allowing the nuclear magnetic resonance measurements that are often used to study C-S-H gels to be better understood. 29,45 Besides, the isotopic fractionation properties of the C-S-H gels, with or without substitutions of Ca2+ by H+ , are significantly different. At 300K, the α30 SiCSH−CSH(H) is equal to -1.9% and can be used to trace calcium leaching of C-S-H gels, which is an additional cause of cement strength deterioration. Note that the isotopic properties may vary with the amount of Ca2+ replaced by H+ . Herein, we computed these properties for two extreme cases: one with a Ca/Si ratio of 1.75 which corresponds to common Portland cement and the other with all interlayer Ca2+ replaced by H+ . By changing the charge compensation scheme in the interlayer of the C-S-H gel, the isotopic signature α44/40 Ca varies by 0.8% (see Fig. 6(b)) at 300K. This difference corresponds to the isotopic signature associated with the calcium leaching out of the interlayer space. Further studies should be focused on measurements of the isotopic fractionation factors for the processes described above under experimental conditions. It is noteworthy that studying the formation of C2SH could allow cement with low economic impacts to be produced 31 from cement waste. Besides, the analyze of isotopic fractionation of percolating water could be used to remotely monitor cement aging. We note herein some interesting applications of the isotopic fractionation factors for cement, but isotopic fractionation factors could also be

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used to study other related problems such as for the investigation of interactions of materials with their environment (e.g. storage of CO2 , 46 ).

Conclusions Several minerals composed of calcium silicate hydrates were investigated by determining their isotopic fractionation properties, based on their different thermo-vibrational properties. We found a specific relationship between the polymerization order and the isotopic fractionation properties α of calcium silicates. A linear correlation was revealed between α and d¯Si−O . The fractionation factor is important to the equilibrium between C2SH and the C-S-H gel, which is associated with the loss of durability of cementitious materials. We also found that Ca2+ ion sites play a role in the fractionation properties of calcium silicates. The two mechanisms, polymerization of silicate chains in CSH minerals and Ca2+ leaching in C-S-H gels, leave a footprint also measurable by isotopic fractionation. This study opens the field for developing other tools in order to study the evolution of hydrated cement with temperature. These findings are relevant to the important challenge in reducing the ecological impact of the worldwide cement production.

Calculation details All the phases are computed using density functional theory (DFT) 47 via the SIESTA method. 48 Calculations are performed using the generalized gradient approximation with PBE exchange-correlation functionals. 49 Core electrons are treated using pseudo-potentials, 50 and valence electrons are developed using the DZP basis set. The valence configurations of the pseudopotentials are: Ca(4s2 ), Si(3s2 3p2 ), O(2s2 2p2 ) and H(1s1 ). We used a mesh cutoff of 150 Ry and an energy shift of 10 meV in order to ensure the precision of the method. Vibrational properties are calculated on relaxed structures using a finite-difference method, as implemented in the code. 48 The atomic position and cell shape of the calcium 17



silicates we studied are given in Supplementary Information. Phonon spectra show no negative frequencies, which indicates the stability of those systems. The isotopic properties were calculated at the Γ point of the Brillouin Zone. In these calculations, the uncertainties on the calculation of the β-factor are mostly due to numerical errors on the calculation of the harmonic frequencies. The GGA functional usually underestimate vibrational frequencies by approximatively 5%. 51 This leads to an underestimation of about 5% of the β-factors. For instance, this corresponds to errors of about 3% at 300K on the β-factors presented in Fig. 1. These errors are considered systematic and may partially cancel out when the α-factor is calculated between the studied systems.

Supporting information Details about calculated β-factors and vibrational density of states. Structural information on CSH structures.

Acknowledgements This work was supported by the Spanish Government (FIS2016-76617-P), the Basque Government through the ELKARTEK project(SUPER), and the University of the Basque Country (Grant No. IT-756-13). We also acknowledge the computing resources and time made available by the DIPC.

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Figure 7: For Table of Contents Only

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Tracing Polymerization in Calcium Silicate Hydrates Using Si Isotopic

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