Aluminum Incorporation to Dreierketten Silicate Chains - The Journal

Feb 10, 2009 - Figure 1. Schematic view of the dreierketten silicate structure as in C−S−H gel. Chains ... In other words, we must investigate if ...
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J. Phys. Chem. B 2009, 113, 2832–2839

Aluminum Incorporation to Dreierketten Silicate Chains H. Manzano,† J. S. Dolado,†,‡ and A. Ayuela*,§ LABEIN-Tecnalia, Parque Tecnolo´gico de Bizkaia, Edificio 700, 49160 Derio, Spain, Nanostructured and Eco-efficient Materials for Construction Unit, Associated Unit LABEIN-Tecnalia/CSIC, Spain, and Departamento de Fı´sica de Materiales, Facultad de Quı´micas, Centro de Fı´sica de Materiales CSIC-UPV/EHU and Donostia Internacional Physics Center, 20018 San Sebastia´n/ Donostia, Spain ReceiVed: June 2, 2008; ReVised Manuscript ReceiVed: December 18, 2008

This work explores, from a theoretical viewpoint, the aluminum incorporation into silicate chains with dreierketten conformation relevant in the cementitious calcium-silicate-hydrate (C-S-H) gel and in other minerals, such as wollastonite and hillebrandite. To this end, we have investigated by means of ab initio calculations both the stability and the formation of aluminosilicate chains. Our results show that only certain aluminosilicate chains are stable, namely, those whose tetrahedra length m obey the m ) 3n - 1 rule with n ) 1, 2, 3,..., in agreement with experiments. Moreover, our detailed analyses explain why Al ions prefer the bridging sites and introduce new insights on the growth process. I. Introduction When cement powder is mixed with water, a complex set of chemical reactions and physical processes occurs. The resulting material is a cement paste, a truly multiphase and heterogeneous material. Within this paste, the C-S-H gel is the most important component. This gel constitutes up to 70% of the fully hydrated paste and is responsible for both the setting and hardening of cements. It is poorly crystalline, although an organized structure exists at the nanoscale. However, the molecular structure of C-S-H gel is still not fully clear, despite the intensive characterization by techniques such as SEM, TEM, XRD, NMR, and so forth (see ref 1 and references therein). Several models have been proposed so far,2-8 which draw structural analogies with its closest crystalline compounds, tobermorite and jennite. In essence, the basic ingredient of these models consists of silicate chains held together by calcium oxide layers. These chains follow the so-called dreierketten arrangement (see Figure 1), in which SiO44 tetrahedra repeat themselves at intervals of three units and have a finite length of 2, 5, 8,... tetrahedra (the 3n - 1 rule with n ) 1, 2, 3,...). The dreierketten arrangement is also common to other minerals such as wollastonite and hillenbrandite; therefore, our results could also be applied to them. Free calcium ions and water molecules are present in the interlayer space. During the growth reactions, guest ions can enter into the silicate chains; among these, aluminum ions are the most common. There are currently several experimental works about the C-S-H gel studying the substitution of Si or Ca ions by Al ions. The 27Al and 29Si NMR experiments in C-S-H gels6,9-18 show that aluminum can be present as tetracoordinated (Al[4]), pentacoordinated (Al[5]), and hexacoordinated (Al[6]). The Al[5] and Al[6] substitutions come from the replacement of Ca2+ by Al3+ in interlayer space.9,14,16,18 The Al[4] originates from the substitution of Si4+ by Al3+ in the chains.6,8-18 This Al * To whom correspondence should be addressed. E-mail: swxayfea@ sw.ehu.es. † LABEIN-Tecnalia. ‡ Nanostructured and Eco-efficient Materials for Construction Unit. § Centro de Fı´sica de Materiales CSIC-UPV/EHU and Donostia Internacional Physics Center.

Figure 1. Schematic view of the dreierketten silicate structure as in C-S-H gel. Chains with eight silicon atoms are shown, held by a calcium layer. Increasing in size, the atoms are hydrogen (gray), oxygen (red), silicon (blue) and calcium (orange). The different positions within the chain are also indicated. In intralayer space, there are water molecules, hydroxyls, Ca2+, and ions of other elements.

substitution should modify the structures. However, the aluminosilicate chains keep the dreierketten arrangement, as well as the 3n - 1 rule, even when there are a significant number of substitutions.6,8-18 When aluminum exists in the chains, their average lengths are larger.9-13,16,17 In addition, aluminum occupies preferentially the bridge sites rather than the pairing ones (Figure 1),19 and it has not been found in end positions. That is why Richardson et al. suggested a merging process; two dimeric silicate chains were linked through a monomer, and they formed pentameric chains.12,13,17 When aluminum is present, it can act as a linker monomer in the bridge positions. Little theoretical research has been done to justify the mechanism of aluminum incorporation into silicate chains. Several works have considered the substitution of Si by Al from a theoretical point of view.20-24 Molecular dynamics (MD) simulations have studied the Al substitutions in tobermoritelike structures20 and the polymerization process of Si(OH)4 with Al(OH)3 in a solution of water with calcium and sodium ions.21 Although these works use pair potentials to describe the atomto-atom interaction, partial success has been obtained. The substitutions of nonbridge silicons have been shown to lead to chain breaks and structural reorganizations.20 With reference to Al-free samples, they have found in the Si-Al polymerization an increase of the average chain length, which means a larger polymerization degree.21 Other authors22 have also performed semiempirical and ab initio calculations with inconclusive

10.1021/jp804867u CCC: $40.75  2009 American Chemical Society Published on Web 02/10/2009

Aluminum Incorporation to Dreierketten Silicate Chains results. They have obtained different stable positions of Al in tobermorite 11 Å depending on the method. Using ab initio methods to calculate the reaction energies, Rahman et al.23 assessed the substitutions of Si by Al. This work concluded that the substitution of Si by Al in isolated chains is always thermodynamically possible at equilibrium. Our idea is to study theoretically the growth of the aluminosilicate chains. In other words, we must investigate if it is energetically favorable to increase the number of monomers n, that is, we have to calculate the first derivative of the energy E(n). Additionally, we must consider the second derivative of E(n) to study the relative stability of certain chains. This is routinely exploited within the framework of cluster physics, where a certain stability index24 is defined as the key parameter to assess the stability of a given cluster size. Recently, a theoretical work25 transferred such a method to study the growth and formation of the silicate chains in the C-S-H gel, and it explained the silicate m ) 3n - 1 rule. However, still no work has been done on substituting Si by Al with a study of the chain growth and checking the possible changes of the 3n - 1 rule. The aim of this work is to study, using ab initio calculations, the formation of aluminosilicate chains in the dreierketten arrangement. After we discuss the computational details in section II, this work is organized as follows. We present our results of the growth via monomers, and we study the chain stability by extending the stability index to the Al-Si reactions in section III. We show that the tetrahedra length m for the most stable aluminosilicate chains obeys the m ) 3n - 1 rule with n ) 1, 2,... When we also analyze the bond and the electronic properties in sections III.1 and III.2, the most stable chains are in correlation with the largest HOMO-LUMO gaps with respect to its neighbors. The merging properties are also studied by gluing aluminosilicate chains to monomers (section IV). We see that the merging process using Al monomers is energetically favorable and produces longer chains. Last, we bring into contact our results with the experiments in section V, discussing the aluminosilicate chain with two tetrahedra and the conformational changes induced by Al guest ions. Aluminum substitution is expected to play an important role in many aspects of the chemical behavior involving cement paste and other minerals, and its control should have practical technological consequences.6

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2833 monomers. Although we have done some work for C-S-H gel in the past, explicitly taking into account the Ca-O layer,30,31 these calculations are made in vacuum. The actual presence of calcium oxide layers is somehow mimicked by taking the dreierketten arrangement as our input silicate structure. The geometries for silicate chains are those from ref 25. In this work, the chains were isolated from the closest crystalline species to the C-S-H gel, tobermorite 14 Å.32 All of the terminal oxygen atoms were saturated with hydrogen in order to have neutral chains. To test the role of the environment, some tests were also made by employing the continuum dielectric model (using a conductor-like screening model),33,34 with no changes in the results; thus, we present our following calculations in vacuum;25 see below. In the silicate chains, we replace one silicon atom with an aluminum atom. When substituting Si by Al, the system gains one electron, and the formed aluminosilicate chains are negatively charged. The Al/Si ratios in Al-rich C-S-H gels range from 0.1 to 0.3.6,10,13,17,18 Therefore, only one Al/Si substitution per chain has been taken into account. III. Condensation Reactions and Chain Stability The local stability of a particular chain of length m (independent of whether it is mSi or mAl) is evaluated by looking at the energies of its neighboring sizes and considering all of the possible pathways to and from m by either the addition or removal of a monomer. To distinguish between pure silicate and aluminosilicate chains, we use the following notation. We denote by mSi a silicate chain of tetrahedra length m (i.e., with m Si atoms), and by mAl, we denote an aluminosilicate of length m (i.e., with m - 1 Si atoms and one Al atom). In this way, the subscripts m - 1 and m + 1 indicate chains with one fewer and one more monomer, respectively. Also, the total charge of the chain is given by a superscript in the previous notation. A neutral silicate chain mSi0 means Si(OH)3O[Si(OH)2)O]m-2Si(OH)3; a negative silicate chain mSi- means Si(OH)3O[Si(OH)2)O]m-2Si(OH)2O-; and an aluminosilicate chain mAl- means Si(OH)3O[Si(OH)2)O]m-2Al(OH)-3 . All of them are following the dreierketten configuration. First, we studied the growth ability of silicate chains by adding different monomers. We give the considered condensation reactions which drive to silicate chains of length (m) with end silicate tetrahedra

II. Computational Procedure We have employed first-principles approaches using density functional theory (DFT). The selected methods for this purpose are implemented in SIESTA26 and Gaussian0327 codes. With the first method (SIESTA), the dreierketten structures have been relaxed to the nearest minimum of energy, where the HOMOLUMO gaps are analyzed. The electron-exchange correlation has been taken into account at the generalized gradient approximation (GGA) level using the Perdew-Burke-Ernzerhof (PBE) functional.28 A transferable double-ζ polarized (DZP) basis set has been used.25 The second method (Gaussian) has been applied to cross-check our results. We performed singlepoint calculations of the previously optimized structures. The calculations were done with the Becke 3-parameter (exchange), Lee, Yang, and Parr (B3LYP) hybrid scheme,29 which includes a mixture of the Hartree-Fock exchange with DFT exchange correlation at the local density approximation (LDA) level. A 6-31G basis set plus an extra polarization d function has been chosen for an improved description of the oxygen polarizability. We have performed our calculations for aluminosilicate chains with lengths ranging from one (orthosilicic acid) to nine

0 0 0 m-1Si + 1Si f mSi + H2O 0 m-1Si + 1Si f mSi + H2O 0 m-1Si + 1Si f mSi + H2O

(1)

where mSi0 and 1Si- are the neutral and charged Si-based monomers ([Si(OH)4] and charged [Si(OH)3O]-), respectively. We now add the reactions involving aluminosilicate chains 0 m-1Si + 1Al 0 m-1Al + 1Si

f mAl- + H2O f mAl- + H2O

(2)

where 1Al- is the Al(OH)4- monomer. These reactions are balanced on the right side by water molecules. Additionally, we must consider the reactions starting with a chain length (m). We show schematically these reactions derived from the existence of Si- and Al-based monomers in Figure 2. The pathways have been represented but without the explicit

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Figure 2. Illustration of possible growth pathways. The chains are denoted as mXq, where m shows the tetrahedra length, q is the charge, and X is Si or Al. X ) Si indicates silicon atoms site in the tetrahedra center, and X ) Al indicates that an Al atom is present in at least one tetrahedra. Water molecules compensate for the missing OHs and protons in the reactions (see eqs 1 and 2 in the text for some examples), but to simplify, they are not written. The horizontal lines represent growth by adding or removing Si(OH)4 monomers. The diagonal dotted lines show the growth by Si(OH)3O-; the diagonal full lines show the growth by Al(OH)4-. In general, the dotted lines represent the pure silicate pathways, while the solid lines represent the aluminum contributions.

Manzano et al. m + 1 on the right one. In this figure, there are Si-based growth pathways (with dashed lines), which were already included in ref 25 by adding Si(OH)4 and Si(OH)3O- monomers to pure silicate chains. The existence of Al monomers offers two more options. First, the growth of silicate chains can incorporate Al monomers. Second, the chains that already contain Al atoms can also grow with Si monomers. These pathways are given in Figure 2 by solid lines. When starting with neutral silicate chains, the condensation energy versus the length of the formed chain is given in Figure 3a. We have found that the silicate chains with a charged aluminum unit [Al(OH)4]- (blue diamonds) are always thermodynamically favorable. Their values are close to those of the charged silicate monomers [Si(OH)3O]- (orange squares), and they are larger than the ones involving the neutral silicate monomers Si(OH)4 (green triangles). Therefore, the condensation reactions involving charged monomers are thermodynamically more favorable. It must be also noted that the most exothermic condensation reactions form (alumino)silicate chains with m ) 2, 5, and 8 tetrahedra. However, we must analyze not only the formation possibility but also the stability of chains with their length. Then, taking into account the reactions in Figure 2, we consider the local stability of chain length m against its neighbors. The stability index gives an idea of the chemical potential of the chains against the addition or removal of monomers. For a pathway with a monomer, it is related to the second derivative of energy versus chain length. Taking into account these pathways, the stability index for a chain with m tetrahedra can be written as a sum of Al and Si contributions

∑ (m) ) ∑ Si (m) + ∑ Al (m)

(3)

were ∑Si(m) stands for the stability index coming from the pure Si-based pathways

∑ Si (m) ) 2E(m-1Si0) + E(m-1Si-) + E(m+1Si0) + 2E(m+1Si-) - 3E(mSi0) - 3E(mSi-) (4) and ∑Al(m) includes the new contributions due to the existence of Al(OH)4- monomers

∑ Al (m) ) E(m-1Al-) + E(m-1Si0) + 2E(m+1Al-) E(mSi0) - 3E(mAl) (5)

Figure 3. (a) Condensation energy of a neutral silicate chain of length m - 1 with an aluminum monomer (blue diamonds with a solid line), with a neutral silicon monomer (green triangles with a dotted line), and with a charged silicon monomer (orange squares with a dashed line). Chain growth occurs because these condensation reactions are exothermic. (b) Stability index as a function of chain length. The contribution of new aluminum pathways is denoted with a thin solid line and diamonds (brown); the contribution of silicon pathways is denoted with a dashed line and squares (magenta); and the total stability index is denoted with a thick solid line and triangles (red). The maxima for the tetrahedra length m ) 2, 5, and 8 indicate chains which are more stable than their neighbors.

chemical reactions involved in these processes. These are similar to eqs 1 and 2 except that they go from m on the left side to

The result of this analysis is clear: when the value is positive, the structure is stable with respect to its neighbors, and when the result is negative, the structure is unstable. Larger values imply more stability. We made this decomposition clearer with a step-by-step demonstration of eqs 3, 4, and 5 in the Supporting Information. As a function of length m in aluminosilicate chains, the total stability of the aluminum pathway (brown thin solid line with diamonds), the silicon pathway (magenta thick solid line with squares), and the sum of them (red solid line with triangles) is represented in Figure 3b. First, we must note that when the global stability index is considered, the maxima occur at m ) 2, 5, and 8. Therefore, our results agree with experiments which show that even when aluminum is incorporated in the C-S-H gel, the m ) 3n - 1 rule is maintained.10-18,20 Additionally, we

Aluminum Incorporation to Dreierketten Silicate Chains

Figure 4. (a) HOMO-LUMO gap in eV versus the length of aluminosilicate chains. The maxima in the HOMO-LUMO gaps indicate chains with large stability. (b) HOMO orbital of several aluminosilicate chain with lengths of m ) 2, 3, 4, 5, and 8. Orbital cuts are at one-tenth of their maximum value. White sticks are hydrogen, and red sticks are oxygen (kinks). When tetrahedrally coordinated, we have silicon (purple sticks), except at the right end of the chain, where aluminum atoms (blue sticks) are sited.

can obtain further insight from Figure 3b by looking at the contributions of the different growth pathways (eq 1). The contribution [∑Al(m)] of the new Al-based pathways follows as well the 3n - 1 rule, and its trend is nearly the same as the Si-driven term [∑Si(m)]. Therefore, the results indicate that the structures of pure silicate chains are similar to those of the aluminosilicate chains, as experimentally described.10-18,20 We note in our results that the presence of dimers containing aluminum is possible. Moreover, both panels in Figure 3 show that Al-Si dimers are as stable as silicate dimers. For aluminosilicate chains, the stability index and the condensation energy are robust and independent of the ab initio model. However, the stability of Al-Si dimers in the monomer-by-monomer growth could not ensure their experimental detection because other processes, such as merging, are taking part in the chain growth. This issue will be discussed in the next section. 1. Origin of Stable Chains by Looking at HOMO-LUMO Gaps. Before we saw that the most stable aluminosilicate chains have 3n - 1 tetrahedra. Now, we analyze the origin of stability in the aluminosilicate chains by looking at the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The structures with a large HOMO-LUMO gap would be kinetically as well as thermodynamically stable. We plot the HOMO-LUMO gap obtained by SIESTA against the chain length of the aluminosilicate structures in Figure 4. It is well-known that the band gap in DFT calculations is smaller than the true band gap by a certain amount, underestimating clearly the experimental values. We compare the gap values calculated within the PBE approach using SIESTA with the B3LYP results of Gaussian. The HOMO-LUMO gaps using SIESTA underestimate systematically by approximately 1 eV the B3LYP values. The gaps are not negligible in both cases, and they are large enough so that the aluminosilicate chains can exist as stable forms. They follow the same pattern with size. We can see in Figure 4 that the

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2835 local maxima of HOMO-LUMO gaps are for m ) 2, 5, and 8. These are certainly correlated with the maxima in the stability index. The structures with larger HOMO-LUMO gaps in comparison with those of their neighbors are those with the larger stability indices, and the 3n - 1 rule is therefore explained in such terms. In Figure 4, we also plot spatially the HOMO for the aluminosilicate chains with lengths of m ) 2, 3, 4, 5, and 8. For silicate chains, it was found that the HOMO delocalization in the bridge oxygen closest to the monomer was a clear hallmark of the less stable structures, whereas the most stable structures are those with a more localized HOMO.25 After visual inspection, it is difficult to see in the Al-Si chains the degree of HOMO localization. The highest occupied molecular orbital is always situated in the OH groups of the [-OAl(OH)3]- unit at the chain end, both for stable lengths (m ) 2, 5, and 8) and unstable lengths (m ) 3 and 4). EnWironmental Role on Reactions InWolWing Charged Chains. Alternatively, one might think about the fact that our calculations are performed in vacuo and not in the presence of water or other environments. One could also wonder about the influence of the environment in the gaps and in the calculated energies. This can be roughly estimated by replacing the surrounding media with an effective dielectric constant to mimic the effects of solvation, as in the so-called conductor-like screening model (COSMO) calculations.33,34 We have carried out calculations within the COSMO method using a dielectric constant appropriate for water. The results lead to the same pattern concerning energy differences as that in the condensation reactions and, in consequence, in the stability index, with or without water. This finding can be described as a compensation effect on both sides of the reactions. Although in gas phase calculations the additional charge hosted by larger species tends to have lower energy, this charge stabilization is reduced in the solvated medium as given in the COSMO method. This electronwithdrawing effect would be large when two different groups are involved on each side of chemical equations. However, we can expect these effects to be rather small because (i) energetic differences are involved, such as in the condensations reactions and in the stability index, and (ii) the electrons are similarly localized in HO-Si and OH-Al bonds on both sides of the reactions. Specifically, they are so localized in the Al-OH bond that it is difficult to get differences by simple eye inspection (as seen in Figure 4). This is why our COSMO results using a dielectric constant lead also to the same pattern for stability indices with or without the environment for charged species. This fact was the reason that lead us to give an in vacuo treatment without loss of generality, although, in principle, it was considered only as a first-order approach. 2. Bond and Charges for End-Terminated Al Chains. In this section, we are interested in taking a closer look at the bond which occurs when aluminum is replacing an end Si atom in the chain structure. We are checking the changes induced by Al replacements in both silanol Si-OH and siloxane Si-O bonds. For the hydroxyl group, the bond lengths (dOH) around the aluminum or the silicon tetrahedra are equal until the second digit, 0.97 Å, and they are not discussed. For the end tetrahedra, the Al-O and Al-OH distances together with the previous Sirelated distances are given versus the chain size in Figure 5a. The Al-O and Al-OH bond distances are between 0.1 and 0.15 Å larger than those of silicon. It can be seen that there is not a clear tendency in the Al-OH nor in the Si-OH bond

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Manzano et al. IV. Merging Processes

Figure 5. (a) Bond distances for the last tetrahedron in chains as a function of their length. Using diamonds (blue), we give the average Al-OH distances, with solid marks, and the Al-OSi distances, with empty symbols. Squares (orange) are used for the average Si-OH distances, with solid marks, and for the Si-OSi distances, with empty marks. (b) Mulliken charges for aluminum (blue diamonds) and silicon (orange squares) located at the end chain positions versus their length. Minima are observed for the most stable chain lengths.

lengths, with mean values around 1.77 and 1.65 Å, respectively. However, there is a clear trend worth noting for the case of Al-O(bridge) and Si-O(bridge) bonds in the end tetrahedra. When the chains are more stable (i.e., 2, 5, and 8 units), the distances are smaller than those for other lengths. We examine the T-O-T and angles, where T stands for Al and/or Si. The idea is to investigate when Al remains strictly tetrahedral. The angles Si-O-Si with silicon in the end chain tetrahedron range from 140 to 123° and show no clear systematics with chain size. For pentamers, the Si-O-Si angles of the bridging positions are about 166°. The replacement of Si by Al changes only slightly the Si-O-Al angles. They decrease less than (8°. Thus, it seems that tetrahedral arrangements remain the standard concerning Si replacement by Al. For an additional description of chemical bonds, we also analyze the Mulliken charges obtained by the SIESTA and the Gaussian methods. Both programs show the same trends. The absolute values of charges are larger by 0.04 e in SIESTA than those in Gaussian. The silicon and aluminum charges in the end tetrahedra are shown against the chain length in Figure 5b. As expected, the charges are larger for silicon than those for aluminum. The interesting point is that the charges follow again the same trend as the bond distances. Although the differences are not large (between 0.03 and 0.05 e), it is clear that the end charges in Al and Si are smaller for the most stable chain lengths. Combining this result with the previous distance analysis, we observe that the most stable chains have shorter bonds and less charge in the end Si-Al positions. These decreases can be explained because the most stable chains have their end position stabilized by stronger bonds, in comparison with other chain sizes.

It would be worth emphasizing that in earlier work about chain condensation, Al is only ever found in a terminal position in these clusters. We are focusing our discussion now on other growth mechanisms of the silicate chains. A first step consists of condensation reactions between two silicate monomers12,13,17,25 (explored in section III). An extra growth mechanism for the silicate chains in the C-S-H gel has been proposed, a merging process. A pentameric chain would be formed by linking two dimeric structures through a monomer. We have explored the energy gain of different growth paths to form pentameric chains via merging reactions. These processes are shown in Figure 6a. The merging process to form pentamers with silicon-based monomers was already studied.25 This process is always thermodynamically favorable, and the charged species lead to higher energy gains. However, for Si monomers, the energy gains of these merging processes are smaller than the condensation energies to produce dimers. Thus, the merging is secondary to the monomer-by-monomer growth. We look now at the merging process to form pentamers when the aluminum unit provides the link between chains. When such an Al monomer is in the bridge position, the merging energy with Al monomer, 1.95 eV, is considerably larger than when silicon (neutral or negative) monomers are the glue (0.12 or 0.32 eV). The preference of aluminum for bridge sites agrees with experiments. The merging process is therefore enhanced by the presence of AlO4-4 groups. This result also explains why the average chain length increases in samples with aluminum.9-13,16,17 Finally, we investigate the merging process not only when aluminum is the linker unit but also when it is part of one of the dimeric chains, which are stable in view of our results. In such a case, the merging is made with a silicon unit linker. In the so-formed pentameric chains, aluminum atoms can occupy two other positions, either pairing or ending. A sketch of these reactions can be seen in Figure 6b. The merging energies for the end and pairing site are 0.23 and 0.97 eV, respectively. Although both processes are thermodynamically favorable, we found a significant difference (0.74 eV) in the energy gain for Al in the pairing position. The end position in chains is always less favorable. We show that aluminum prefers intermediate sites. In fact, our merging results point out that the higher energy gain is for the bridge site, followed by the pairing site. This order also supports experiments that state the presence of Al in bridge sites10-13,15-18 and in pairing ones19 and can be explained by the location of Al in pentamers as in the following paragraphs. 1. Position of Aluminum in Silicate Chains. In seeking the origin for the order of merging energies, we found that they follow the Al location in the pentamer. From the Introduction section, we know that the position of aluminum in the silicate chains is not random. Experimental results show that aluminum has a marked preference for the bridge sites rather than pairing ones,10-13,15-18 and Al has not been found in the end chain positions.10-13,15-18,21 However, Faucon et al.19 found experimentally both bridge and pairing positions. To investigate such site preferences, we now substitute Al by Si in different positions within the chain of a stable structure, such as the pentamer. Due to the symmetry of the pentamer chain, we note that there are only three possible locations of aluminum, the end, pairing, and bridge (Figure 7). First, once the substitution is made, we analyze the differences in total energy with respect to the energetically low-lying structure. These are given below their geometries in Figure 7,

Aluminum Incorporation to Dreierketten Silicate Chains

J. Phys. Chem. B, Vol. 113, No. 9, 2009 2837

Figure 6. Chain merging processes between two dimers and a monomer. (a) Si dimers and monomers. An Al charged monomer (1) has been considered. Also, Si-neutral (2) and Si-charged (3) monomers are given for comparison. The result is two water molecules and the corresponding pentamers. The reactions with the Al monomer are much more exothermic than the ones with Si monomers. For Al substitutions, the merging can involve an aluminosilicate dimer (b). Then, two options are possible, which end with Al in the pairing (4) position and in the end (5) position. These reactions are less exothermic than the previous ones with Al in the bridge site.

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Figure 7. Aluminum in different positions within the pentamer chain. From left to right, we have bridge, pairing, and end positions. The energies with respect to the low-lying structure (Al in the bridge position with E0) are given under the geometries. Aluminum in the bridge site is the most stable. Also, the highest occupied molecular orbital (HOMO) is shown. Atom labeling and orbital cuts follow the previous caption of Figure 4.

TABLE 1: HOMO-LUMO Gap (in eV) for the Pentamer Chain with Al in Different Chain Positionsa position in the pentamer

HOMO-LUMO gap (eV)

charge on Al

charge on Si

end pairing bridge

3.63 4.17 4.22

1.33 1.38 1.40

1.57 1.57 1.58

a The largest gap shown is for the most stable position. Charges for the Al and Si atoms are also given (in e). For Si, they correspond to the end tetrahedron.

where also the HOMO orbital is plotted. We can see that the structure with lower energy has Al in the bridge site. The energetic difference between the structures with aluminum in the end site and aluminum in intermediate positions (bridge and pairing) is larger than 0.7 eV. This result indicates a clear preference of aluminum for the internal sites of silicate chains rather than for the end positions. In Table 1, we also show the HOMO-LUMO gap energies for the pentameric chains with aluminum located in end, pairing, and bridge tetrahedra. The gaps change following a similar pattern, with the Al position fully correlated with the previous energy differences. Both the energies and the HOMO-LUMO gaps indicate a clear preference of aluminum for the inner chain positions, in agreement with experimental data.10-13,15-18,21 Although the differences between the bridge and pairing sites are smaller, the bridge position is already favored from an energetic point of view. We have computed the bond distances and charges for aluminum and silicon located in different positions within the pentameric chain. We have found that the bond lengths are not significantly affected by the atomic position. Changing the position, the Al-O and Al-OH distances have differences smaller than 0.01 Å. The differences for Si-O and Si-OH are slightly higher, less that 0.02 Å, but they are still very small to deduce any conclusion. More important, we have found systematically small changes in the charges. Their values are also given in Table 1. Both SIESTA (in the table) and Gaussian results show that the charge of Al increases approximately by 0.07 e as Al sits deeper into the chain, whereas there are no significant changes in the silicon charge. Although the charge increase is small, this change indicates that the ionic character of the Al-O bond increases slightly, which corresponds to a metallic element when the coordination is increased. As a final note, we would like to discuss the implications of bridge-end differences to the condensation reactions and to the stability index shown in Figure 3. In particular, for neutral or charged silicate chains, the energy differences between positions do not display such large values. During growth, such an energy gain in aluminosilicate chains means conformational changes. We note that when including the energy for the Al-bridge

pentamer in the condensation reactions and in the stability index, we find that the peak for m ) 5 goes beyond the axes of Figure 3, which is, therefore, very stable with respect to the dimer. This is also confirmed by experiments showing Al mainly in bridge positions. In other words, this suggests that the doping could add new characteristics, such as conformational relaxations during growth. V. Further Discussion on Experimental Results Now we would like to comment on two key aspects in order to bring our results into contact with the experimental data. (i) We found that singly charged [Al(OH)3-O-Si(OH)3]dimers are stable. Their condensation energy and their involved stability index are large enough to support their stability. However, dimeric chains with Al have not been found in experiments. Therefore, we must conclude that in solution, such single-charged [(OH)3AlOSi(OH)3]- dimers disappear faster than Si-based ones. In fact, for the aluminum monomers, we found that the condensation energies and the merging energies are larger than those for silicate chains. For aluminosilicate chains, the merging energies are also much larger than the condensation reactions involved in their growth. This is opposite to the comparison between the growth and the merging energies of silicon monomers. This means that once [Al(OH)3O-Si(OH)3]- dimers are formed, the growth of longer chains is more probable than that in the case of Si(OH)3-O-Si(OH)3. We must also consider that the concentration of Al is small in comparison with Si. These reasons explain why no aluminosilicate dimers are found in C-S-H gel. (ii) The energetic differences between pairing and bridge sites are small; in fact, they are starting to compete at room temperature. Within our approach, we cannot rule out the possible presence of other stable species with aluminum located in nonbridge sites, especially in pairing positions. This finding is in agreement with an experiment that identifies Al in pairing and in bridge sites for CSH gels.19 In addition, it has been stated that in real samples where Ca is present, the flexibility of the bridge site might be the main reason for the location of aluminum in that particular position.7,12 Analogously, it has been proposed that for the aluminosilicate chains, aluminum suffers a geometrical reorganization from pairing to bridge sites.20 Although our model does not include specifically those calcium ions, we can imagine already that during the growth process, the aluminum tetrahedra would change conformation toward bridge positions because they lie energetically lower by at least 0.1 eV (Figure 6). Nevertheless, further experimental and theoretical work must be done to clarify these issues. Summing up, we find higher energies for the growth and for the merging of aluminosilicate chains with respect to silicate

Aluminum Incorporation to Dreierketten Silicate Chains ones. Concerning the chain relaxations from end to bridge sites, the energy gain is clearly larger for the Si-Al chains. These findings of Al substitutions in silicate chains imply also that the 3n - 1 rule is automatically fulfilled but with longer tetrahedra lengths. VI. Conclusions We have investigated by ab initio calculations the incorporation of tetracoordinated Al ions in the dreierketten configuration of silicate chains, such as in C-S-H gel. First, to assess the stability of aluminosilicate chains, we have included in our calculations the new growth pathways that come from the Al monomers. Second, we have performed an analysis of the HOMO-LUMO orbitals, bond lengths, and charges of the aluminosilicate chains. Then, we have built a merging model for the growth of aluminosilicate chains in the C-S-H gel, and we have analyzed the energy gains of different merging reactions. Finally, we have researched the position of aluminum within the chain, an issue which is not that crucial in the pure silicate chains. In this way, we have evaluated the thermodynamic stability of silicate chains formed in these processes. The incorporation of aluminum into the silicate chains of C-S-H gel is in accord with the following picture. The tetrahedra lengths of the most stable aluminosilicate chains follow the 3n - 1 rule as in pure silicate chains. The HOMO-LUMO gaps of the studied structures confirm the existence of those “magic numbers”. Moreover, when paying attention to the energies and the HOMO-LUMO gaps, aluminum atoms prefer the bridge chain site rather than the others. In fact, the end sites are very unfavorable. It has also been shown that with aluminum as the linker unit within the dimers, the energy gain of this merging process is much higher than that in pure silicate processes. In fact, these merging energies are also much larger than the condensation energies in the monomer growth processes. This increase indicates that merging reactions would be favored with the presence of aluminum monomers and would give rise clearly to larger chains. Finally, it is worth noting that since the calcium-oxygen part of the material is not taken explicitly into account in this work, the results obtained here should also be relevant for other silicates with the same dreierketten silicate chain structure. Acknowledgment. H. Manzano acknowledges the grant received from the EITE association. Thanks are due to the Basque Government for funding the NANOMATERIALES project, under the ETORTEK program. We also wish to acknowledge the Intramural Special Project (Ref. 20006601242), the Spanish MEC Grants MAT2005-03890 and FIS2007-66711C02-C01, and the European Network of Excellence NANOQUANTA (NM-CT-2004-500198). The computing resources from the Supercomputation Center of Galicia (CESGA) and the Universidad del Pais Vasco (SGIker ARINA) are gratefully acknowledged. Finally, we thank Prof. N. H. March for reading this manuscript. Supporting Information Available: The energy differences of Figure 3a and the local stability index. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Ramachandran, V. S.; Beaudoin, J. J. Handbook of Analytical Techniques in Concret; William Andrew Publishing: New York, 2001.

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