AB-INITIO MODELLING AS A TOOL FOR UNDERSTANDING C-S-H GEL

Transcription

1 AB-INITIO MODELLING AS A TOOL FOR UNDERSTANDING C-S-H GEL J. S. Dolado a, I. Campillo a, Y. de Miguel a, E. Erkizia a, A. Porro a, A. Ayuela b, and D. Sánchez-Portal b a. Fundación Labein, C/Geldo, Edif. 700, Parque Tecnológico de Zamudio, Derio, Bizkaia, Spain b. Donostia International Physics Center (DIPC), P.O.Box 1072, San Sebastian/Donostia, Spain Abstract At the nanoscale (from amstrongs to nanometers), nature manifests itself in a discrete way, and its description usually requires an implicit atomistic assumption. It is therefore obvious that both molecular dynamics and ab-initio calculations have presented themselves as the most useful computational tools to describe such a scale. In this work, a general overview on the description of cementitious materials by means of ab-initio calculations will be provided. Especially, it will aim to stress the tremendous capability of these techniques to explain and predict a wide range of parameters and processes which are inaccessible otherwise. In particular, some interesting examples will be discussed, such as the inherent capacity of the ab-initio calculations to describe the condensation reactions that take place during the hydration process and provide crucial information with regards to the stability of the possible species. Keywords: ab-initio calculations, modelling, C-S-H gel 1. Introduction When our description of nature shrinks down to the nanoscale and below, the only existing reliable computational methods are Molecular Dynamics [1] and ab-initio calculations [2]. Molecular Dynamic Calculations are, in a sense, classical since they usually

2 solve Newton s equations to trace back the temporal evolution for as many atoms as the computational capacity allows for. The key point in these calculations consists in finding reliable interatomic potentials which include the underlying quantum effects. These effects, for example, are responsible for either the formation or breakage of bonds, and their spatial arrangement. Thus, the cornerstone of MD calculations is that they can accurately account for these effects in the simplest interatomic potential. The ab-initio calculations can provide great help in such a purpose. As their name implies, ab-initio or first principles calculations stand for a kind of calculations for which no approximations are needed. Obviously this is not actually so, since several general approximations must be called for, but it is the closest image to such a scenario. Historically two different paths have been explored to perform the ab-initio approach: The Hartree-Fock method (HF) [3] and the Density Functional theory (DFT) [4]. There are several text books where these methods are profusely explained, so there is no need to make a detailed explanation of both methods. Detailed information on these approaches can be found for instance in [5, 6]. By the contrary, our purpose is more inclined to advance and highlight practical examples where these methodologies reach all their power in the field of cementitious matrices. We would like to end this section by remarking again that within the Schrödinger equation all the quantum effects are comprised, fact extremely important since several nanometers is the range over which quantum effects become not negligible. 2. Examples This section is devised to provide an overall picture of the capabilities of ab-initio calculations in cementitious materials by the description of different examples we are currently interested in. Silicate chains of C-S-H gel The first example we are going to discuss about is the geometries and formation energies of the silicate chains that make up the C-S-H gel. These chains can be seen as the ultimate components of the cementitious matrix and many of its ulterior properties depend on them. Obviously these chains exhibit an overwhelming importance in the whole cementitious scaffolds, so a thorough and systematic study of them is strongly required. A sound knowledge of the way in which these chains are formed is clearly important if the aim is to manipulate then in order to obtain demanding properties. For instance, it seems quite reasonable that longer chains, or more cross-linked, would bring about more durable structures, with an intrinsic higher (micro)nano-durability. To learn about the way in which these chains polymerise is, therefore, an ineludible prerequisite for such a technological endeavour.

3 But where do these silicate chains come from? To answer this question we would first like to highlight the close parallelism that exists between cementitious hydration and sol-gel chemistry [7]. In fact it could be said that cement hydration is a particular sol-gel process under a highly basic environment. Or more precisely, the hydration of C 3 S and C 2 S phases could be seen as basic catalysed sol-gel processes [7]. Obviously, in the case of truly cementitius processes, there are more processes that take place simultaneously, such as the hydration of C 3 A and C 4 AF phases, so this ideal picture is a bit blurred. Nevertheless, for the following discussion it suffices to say that the Si(OH) 4 (or charged versions of it), as in solgel chemistry, presents itself as the most important element, from which the rest of silicate chains can be derived. In our particular case of cementitious environments, these Si(OH) 4 units come directly from the hydration of silica phases present in cement grains. The point is that from these seed or primary species, larger silicate chains can be formed, as in sol-gel processes, by condensation reactions of the type: Si(OH) 4 + Si(OH) 4 (OH) 3 SiOSi(OH) 3 + H 2 O Moreover, from this dimeric species, longer chains (trimers, tetramers, pentamers and so on) could be formed similarly through ulterior condensation reactions. In fact, if we denote by (m) a silicate chain of length m (i.e. with m Si atoms), the condensation reactions would bring about a growth mechanism of the form: (m) + (1) (m+1) + H 2 0 The energies and geometries for each silicate chain (m) are easily calculated by means of the ab-initio calculations, and hence, the condensation energies can also be evaluated. Note that all the condensation reactions are exothermic, so a priori, the growth is energetically possible. The geometry of the particular case of a silicate chain of length m =5 is depicted in Fig.1. Fig.1 Optimised geometry for m=5

4 One of the most recurring reluctance toward these kind of calculations has to do with the fact that energies and geometries are usually calculated in vacuum and at T= 0 ºK. In fact, the polymerisation of these silicate chains does not occur in a vacuum environment. Moreover, it is well known that the cementitious environment is a highly basic aqueous media (approx. ph 12) in which Ca ions (and its Ca(OH)2 varieties) are certainly playing a pivotal role. Thus, a simple question arises: If Ca is playing such a pivotal role, why is it not explicitly included in the calculation? And, what about the solvation effects? Let us try to justify why these objections, although important, do not impose restrictions to the validity of the ab-initio calculations when dealing with the formation energies of the silicate chains. In view of our results presented in [8], the Calcium is playing a twofold role in the silicate growth: On the one hand it is disturbing the polymerisation (the larger the amount of Calcium ions the slower the growth is). On the other, they are acting somehow as templates onto which the silicate chains can be deposited. In particular, the Calcium ions are constraining the polymerisation of the silicate chains so that these silicate chains follow a dreierketten arrangement [9]. Thus, a simple procedure to account for the effect of the Calcium, but without including it explicitly, is by forcing the silicate chains to follow the dreierketten structure. Fortunately, this trick is easily feasible by the ab-initio methods, and it has been the way in which the mentioned our work [8] proceeded. Doing so, interesting growth properties can be predicted, as will be discussed below in the section devoted to the stability of species, saving much computational time. The applicability of vacuum calculations requires further analysis. Ab-initio calculation can by themselves incorporate sophisticated methods to account for solvation effects. Basically there are two main approaches for such an objective. On the one hand there are discrete solvation approaches, in which each solvent molecule is modelled as a distinct object, and on the other, Continuum solvation methods, which basically form a cavity of some sort containing the solute molecule, while the solvent outside the cavity is thought of as a continuous medium, usually represented by an appropriated dielectric constant. However, it is worth noting that the solvation effects suppose only minor corrections to the values obtained for the silicate formation energies in vacuum calculations. For instance, the formation energies of a monomer that result from sophisticated models such as the COSMO scheme [10] (a standard continuum solvation method), represent corrections lower than the 10-3 % with respect to the values obtained in simpler vacuum calculations. Besides, much lower corrections are found for larger chains. Therefore, we can safely conclude that vacuum calculations present themselves as a cheap and accurate method to describe the formation of the cementitious silicate chains.

5 Stability of species: Definitely one of the most striking points of our work [8] is its ability to predict, from abinitio calculations, the appearance of the experimentally observed m=3n-1 sequence for the silicate chains of C-S-H gel. This sequence, that has been repeatedly confirmed by different experimental techniques [11, 12], states than only certain silicate lengths are detected, namely those which meet the equation m=3n-1, where m stands for the number of Si atoms, and n denotes an integer. Or in other words, only dimers, pentamers, octamers, etc are allowed. Our cited work [8], employing a generalised version of the so called stability index [13], managed to assess the local stability of each specie, and providentially predicted the stability of dimers, pentamers and octamers. Guest ions : Incorporation of Al ions into the C-S-H gel The strength of ab-initio calculations can also be applied to the study of the incorporation of Aluminium ion into the C-S-H gel. From an experimental point of view two important evidences have been concluded at this respect: First, it is observed that the existance of Al ions do not modify the aforementioned m=3n-1 rule [14,15], and secondly, these ions seem to prefer the substitution at the bridging sites [14, 15]. Both facts can be tackled by ab-initio calculations following a scheme as followed to study the stability of the silicate chains. In fact, the only point that one must be aware of is that the existence of Al-ions bring about new [-] growth channels, mainly by means of Al(OH) 4 monomers. And obviously, these new channels must be included in the aforementioned stability index. Once these new growth mechanisms are accounted for, the stability of aluminosilicates can be easily assessed [16]. 4. Conclusions Throughout this overview, several examples have been presented to highlight the tremendous capacity of ab-initio calculations when dealing with cementitious nanophenomena. In particular, the emphasis has been firstly put on the ability of these techniques to describe the condensation processes that govern the growth of silicate chains of C-S-H gel. Special attention has been paid to the prediction of condensation energies, and the possibility of predicting the stability of the formed chains, even when Si for Al substitutions can take place.

6 ACKNOWLEDGEMENTS This work has been supported by the Basque Government through the NANOMAT project under the ETORTEK Program. REFERENCES [1] G. KALINICHEV AND R.J. KIRKPATRICK, Molecular Dynamics Modeling of Chloride Binding to the Surfaces of Ca-hydroxide, Hydrated Ca-aluminate and Ca-silicate Phases, Chemistry of Materials 14, 3359 (2002). [2] M. M. RAHMAN et al. Journal of Nuclear Science and Tecnology, Vol. 38 No. 7, (2001). [3] D. R. HARTREE. Proc. Cambridge Phil. Soc. 24, 89, 111,416 (1929); J. C. SLATER Phys. Rev., (1930); C. C. ROOTHAAN, Rev. Mod. Phys. 23, 69 (1951). [4] P. HOHEMBERG AND W. KOHN; Phys. Rev. 136 B864 (1964); W. Kohn and L. J. Sham; Phys. Rev. 140 A1133 (1965) [5] F. JENSEN. Introduction to Computational Chemistry. John Willey & Sons (2003). [6] C. J. CRAMER. Esentials of Computational Chemistry. John Willey & Sons (2004). [7] C. F. BRINKER AND G. SCHERER. Sol-Gel Science. The Physics and Chemistry of Sol-Gel Processing. Academic Press, Inc (1990). [8] AYUELA et al. An ab-initio study of the silicate chain formation in the nanostructure of silicate based materials. Submitted. [9] H.F.W. TAYLOR. Cement Chemistry. Thomas Telford, 2 nd Ed. (1997). [10] K. KLAMT and G. SCHÜÜRMANN. COSMO: A new approach to Dielectric Screening in Solvents with Explicit Expressions for the Energy and its gradient. Journal of the Chemical Society, Perkin Transation 2 (1993) [11] X. CONG AND R. J. KIRKPATRICK. Adv. Cem. Based Mater (1996). [12] A.R. BROUGH AND C.M. DOBSON, J. Mater. Sci, 29, 3926 (1994) [13] J.A. ALONSO AND M. J. LÓPEZ. Journal of Cluster Science, vol. 14, No. 1 (2003) [14] I. G. RICHARDSON; The nature of C-S-H in hardened cements. Cement and Concrete Resesearch 29 (1999) I. G. RICHARDSON AND G.W. GROVES. The incorporation of minor ad trace elements into calcium silicate hydrate (C-S-H) gel in hardened cement pastes Cement and Concrete Research 23 (1993) I.G. RICHARDSON et al. Location of aluminum in substituted calcium silicate hydrate (C-S-H) gels as determined by 29 Si and 27 Al NMR and EELS J. Am. Ceram. Soc. 76 (1993) [15] M.D. ANDERSEN et al. Characterisation of white Portland cement hydration and the C-S-H structure in the presence of sodium aluminate by 27 Al and 29 Si NMR spectrocopy. Cement and Concrete Research 43 (2004) M. D. ANDERSEN et al.; Incorporation of Aluminium in the Calcium Silicate Hydrate (C-S-H) of Hydrated Portland Cements: A Hight-Field 27 Al and 29 Si MAS NMR investigation. Inorganic Chemistry 42 (2003) [16] H. MANZANO et al. An ab-initio study on the incorporation of Aluminium ions into the C-S-H gel. In preparation.