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Investigation of Pozzolanic Reaction in Nanosilica-Cement Blended Pastes Based on Solid-State Kinetic Models and ^{29}Si MAS NMR

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

^{29}Si nuclear magnetic resonance (NMR) experiments are conducted and conversion fraction of nanosilica is extracted. The results are compared with a solid-state kinetic model. It seems that pozzolanic reaction of nanosilica depends on the concentration of calcium hydroxide.

## 1. Introduction

_{3}S, C

_{2}S, C

_{3}A, and C

_{4}AF for the corresponding chemical composition of 3CaO·SiO

_{2}, 2CaO·SiO

_{2}, 3CaO·Al

_{2}O

_{3}, and 4CaO·Al

_{2}O

_{3}·Fe

_{2}O

_{3}, respectively. Hydrated OPC components include C–S–H and calcium-hydroxide (CH).

_{2}, ZnO

_{2}, fullerenes, carbon nanotubes, silica, alumina, and clays have been examined to improve the strength, stiffness, and ductility characteristics of cementitious materials [17,18]. Some of the nanoparticles were shown to blend with the cement during hydration and create nucleates that enabled further growth of C–S–H [19,20]. The effect of nanosilica on the reduction of calcium leaching in cement were also reported [21,22]. Nanosilica has been investigated by many researchers and has been shown to significantly improve the strength and durability of concrete [13], to soften concrete behavior at relatively high content [23], and to improve the physical properties of oil-well cement was also investigated [24]. Research has shown that the very high surface area of nanoparticles plays a significant role in this process. Other uses for nanoparticles, such as Fe

_{2}O

_{3}and carbon nanotubes as sensors inside the cement matrix and TiO

_{2}for self-cleaning concrete, have also been reported [13,25].

^{29}Si MAS NMR.

## 2. Solid-State Kinetic Models

_{p}is the conversion fraction at time t. The relative diffusion coefficient of k

_{D}is calculated as

_{CSH}and m

_{CH}are the molecular weights of C–S–H and CH, respectively. C

_{w}is the concentration of CH at interface P as shown in Figure 1. ρ

_{CSH}is the density of C–S–H.

_{p}is proportional to the thickness of product l for an infinite flat plane diffusion model, it is only effective for low conversion values (i.e., low x/R values) [28]. Therefore, for the conversion fraction of nanosilica particles, the use of Jander’s model might not be appropriate, as it is known that nanosilica has high conversion fraction values [29].

_{m}is the concentration of CH at the original particle surface, as shown in Figure 2. It is noticeable that the unit for the concentration C

_{w}in Equation (2) and and C

_{m}in Equation (4) is kg/m

^{3}and mol/m

^{3}, respectively.

## 3. Experiments

#### 3.1. Materials

^{®}380, which has an average BET surface area of 380 m

^{2}/g and an average particle diameter of 7 nm. For 1% and 3% nanosilica specimens, 1% and 3% weights of cements are substituted by nanosilica. The procedures for mixing the hydraulic cement pastes followed the ASTM standards [31]. For

^{29}Si MAS NMR of the hardened OPC pastes, a cylinder, ϕ 10 mm × 10 mm height, was prepared for each type of mixture. The specimens were molded in a tube for a day and then cured in water for 7 days of aging. Specimens were cured under tap water with a controlled temperature of 20 °C for ambient curing condition.

Composition | w/w (%) |
---|---|

C_{3}S | 51.0 |

C_{2}S | 24.0 |

C_{3}A | 6.0 |

C_{4}AF | 11.0 |

#### 3.2. ^{29}Si MAS NMR

^{29}Si NMR has been used to examine the polymerization of a silicate tetrahedron in synthetic C–S–H [33,34]. Silicate polymerization represents the number of bonds generated by the silicate tetrahedron. A silicate tetrahedron having the number of n shared oxygen atoms is expressed as Q

^{n}where n is the number of shared oxygen atoms, up to 4. The intensity of the silicate Q connections in hydrated cement can be investigated using

^{29}Si MAS NMR. Q

^{0}is typically observed in hydrated cement due to the remaining tricalcium silicate (C

_{3}S) and dicalcium silicate (C

_{2}S), while Q

^{1}, Q

^{2}, and Q

^{3}are typically detected in silicate due to the layered structure of C–S–H, as shown in Figure 3. Q

^{4}is the polymerization of quartz and can be observed in silica-rich products such as fly ash, silica fume, and nanosilica.

**Figure 3.**Silicate connections detected from the analysis of

^{29}Si magic angle spinning nuclear magnetic resonance (MAS NMR) spectra.

^{29}Si MAS NMR spectra to identify the different chemical shift peaks representing silica polymerization type Q

^{0}to Q

^{4}, and their corresponding intensity representing their existing fraction in C–S–H. From the calculated intensity of Q

^{n}s, the average degree of C–S–H connectivity D

_{c}is calculated [37] as:

_{c}represents high polymerization of C–S–H. From the extensive studies of the structure of C–S–H by

^{29}Si MAS NMR, it is suggested that the polymerization of C–S–H depends on its compositional calcium-silicate (C/S) ratio and the humidity in the interlayer water [38,39]. Furthermore, the degree of hydration h

_{c}of a hydrated OPC paste is defined as the weighted average of the degree of reactivity of the four major OPC components of C

_{3}S, C

_{2}S, C

_{3}A, and C

_{4}AF [11]. The C–S–H chain length is also calculated as:

^{1}and Q

^{2}represent the end-chain and the intermediate silicates, respectively, an l of 3 is the C–S–H silicate chain having three silicate connections. If the value of l is more than 3, it represents a longer chain than the C–S–H silicate chain having three silicate connections, as schematically shown in Figure 4.

^{29}Si chemical shifts are respectively referenced relative to tetramethylsilane Si(CH

_{3})

_{4}(TMS) at 0 ppm, using Si[(CH

_{3})

_{3}]

_{8}Si

_{8}O

_{20}(Q8M8) as a secondary reference (the major peak being at 11.6 ppm relative to TMS).

## 4. Results and Discussion

#### 4.1. Full Reaction Time

_{D}. Considering the value of k

_{D}as 1.269 × 10

^{−17}m

^{2}/s [40], the full reaction time to complete the reaction is calculated as 760 to 2280 days with respect to kinetic models for silica fume particles having a diameter of 100 μm, as shown in Figure 5a. However, the full reaction time of nanosilica particles having a diameter of 100 nm is calculated as 66 to 197 s with respect to kinetic models as shown in Figure 5b.

**Figure 5.**Full reaction time of silicate particles according to particle diameters ranging to (

**a**) 120 μm and (

**b**) 120 nm, JD model and GB model represent Jander’s model in Equation (1) and Ginstling-Broushtein model in Equation (3) respectively.

#### 4.2. The Conversion Fraction from ^{29}Si MAS NMR Results

^{n}intensities were presented in Table 2 with the average degree of C–S–H connectivity D

_{c}in Equation (5) and the C–S–H chain length l in Equation (6). It is noticeable that although some types of nanoparticles show the resonance of Q

^{3}due to the isolated silanol groups and Si–O–Si bond in nanoparticles [41], Q

^{3}was not shown for the nanosilica powder used in this study. The highest degree of polymerization of 1.43 and a chain length of 3.50 were observed with hardened cement paste incorporating 1% nanosilica. Similar chain length for the synthetic C–S–H without nanoparticles and the tendency to increase chain length was also shown by adding nanoparticles [41].

**Table 2.**NMR results and silicate polymerization. D

_{c}: Average degree of C–S–H connectivity; l: C–S–H chain length.

Speciemns | Q^{0} (%) | Q^{1} (%) | Q^{2} (%) | Q^{3} (%) | Q^{4} (%) | D_{c} | l |
---|---|---|---|---|---|---|---|

No nanosilica | 44.0 | 36.0 | 20.0 | – | – | 1.36 | 3.11 |

1% nanosilica | 29.6 | 39.4 | 29.5 | – | 1.5 | 1.43 | 3.50 |

3% nanosilica | 35.5 | 33.2 | 24.0 | – | 7.3 | 1.42 | 3.44 |

^{n}s. We start by evaluating the total number of silicate tetrahedrons, Σ

_{Q}, calculated as

_{A}is the Avogadro constant. ψ

_{C3S}, ψ

_{C2S}, and ψ

_{S}are the molecular weights of C

_{3}S, C

_{2}S, and S, which are 0.228 kg/mol, 0.172 kg/mol, and 0.06 kg/mol, respectively [11]. p is the weight fraction of the subscribed components in the OPC and nanosilica binder. b

_{0}is the initial weight of the binder (in grams) in 1 g of paste calculated as:

_{0}is the initial water to binder ratio of OPC paste incorporated to nanosilica. The conversion fraction of nanosilica α

_{S}, which can be estimated by considering Q

^{4}intensity observations from the de-convoluted NMR spectra as:

_{Q4,S}is the number of silicate tetrahedron in nanosilica as:

_{S}for hardened cement paste specimens incorporating 1% and 3% nanosilica are presented in Table 3. The conversion fraction of hardened cement paste incorporating 1% nanosilica, 66.2%, is higher than that of hardened cement paste incorporating 3% nanosilica, 41.2%.

**Figure 6.**NMR spectra of (

**a**) 0; (

**b**) 1%; and (

**c**) 3% nanosilica (black, red, and dotted lines as spectrum from NMR experiments, total spectrum by summing all Q spectra, and each Q spectrum, respectively).

Equation | 1% Nanosilica | 3% Nanosilica |
---|---|---|

Equation (7) | $\begin{array}{ll}{\mathsf{\Sigma}}_{\text{Q}}& ={b}_{0}\left[(0.99)\left(\frac{0.51}{0.228}+\frac{0.24}{0.172}\right)+\frac{0.01}{0.06}\right]{N}_{A}\\ & =3.763{b}_{0}{N}_{A}\end{array}$ | $\begin{array}{ll}{\mathsf{\Sigma}}_{\text{Q}}& ={b}_{0}\left[(0.97)\left(\frac{0.51}{0.228}+\frac{0.24}{0.172}\right)+\frac{0.03}{0.06}\right]{N}_{A}\\ & =4.023{b}_{0}{N}_{A}\end{array}$ |

Equation (10) | $\begin{array}{ll}{\mathsf{\Sigma}}_{\text{Q}4,\text{S}}& ={b}_{0}\left(\frac{0.01}{0.06}\right){N}_{A}\\ & =0.167{b}_{0}{N}_{A}\end{array}$ | $\begin{array}{ll}{\mathsf{\Sigma}}_{\text{Q}4,\text{S}}& ={b}_{0}\left(\frac{0.03}{0.06}\right){N}_{A}\\ & =0.5{b}_{0}{N}_{A}\end{array}$ |

Equation (9) | ${\text{Q}}^{4}=1.5\%$ | ${\text{Q}}^{4}=7.3\%$ |

$\begin{array}{ll}{\alpha}_{\text{S}}& =1-(0.015)\frac{3.763{b}_{0}{N}_{A}}{0.167{b}_{0}{N}_{A}}\\ & =0.662\end{array}$ | $\begin{array}{ll}{\alpha}_{\text{S}}& =1-(0.073)\frac{4.023{b}_{0}{N}_{A}}{0.5{b}_{0}{N}_{A}}\\ & =0.412\end{array}$ | |

${\alpha}_{\text{S}}=66.2\%$ | ${\alpha}_{\text{S}}=41.2\%$ |

#### 4.3. The Effect of CH Concentration

_{w}and C

_{m}in Equations (2) and (4). If there is enough concentration of CH around nanosilica particles, nanosilica particles will react with CH and be immediately converted to C–S–H. However, if there is not enough concentration of CH around the nanosilica particles, the pozzolanic reaction of nanosilica particles will decrease.

^{−4}kg/m

^{3}(1.185 × 10

^{−2}mol/m

^{3}) for the reference values of k

_{D}[39] and D [42] presented in Table 4. If the CH concentration keeps higher than the minimum value during the time of nanosilica reaction, the nanosilica particles having a diameter of 7 nm will fully react in a second. However, NMR experiments showed that the nanosilica particles did not react fully for 7 days. The average CH concentrations for 7 days can be calculated as 1.027 × 10

^{−10}kg/m

^{3}and 32.836 × 10

^{−10}kg/m

^{3}for hardened cement paste incorporating 1% and 3% nanosilica showing the conversion fractions of 66.2% and 41.2% for 7 days, respectively, from the GB model in Equation (3). Similar values are calculated using the JD model in Equation (1) as 1.288 × 10

^{−10}kg/m

^{3}and 36.818 × 10

^{−10}kg/m

^{3}for hardened cement paste incorporating 1% and 3% nanosilica, respectively. The CH concentrations are much lower than the minimum CH concentration of 8.768 × 10

^{−4}kg/m

^{3}. Such tiny CH concentrations may correspond to a single, isolated, nanoSiO2 particle. It is noticeable that the calculated average CH concentration in this study means the average CH concentration during the reaction of a nanoparticle, not the amount of total CH in the hydrated cement. As a special technique to disperse nanosilica was not used to make specimens in this study, there exists a possibility of nanosilica particle aggregation. The aggregation of nanosilica also occurs as a result of the presence of ions such as Ca

^{2+}or K

^{+}released into the pore solution. Therefore, further research is warranted to confirm the effect of CH concentration for pozzolanic reaction of nanosilica excluding nanosilica particle aggregation.

Reference Values | The Minimum CH Concentration from Equations (2) and (4) |
---|---|

$\begin{array}{l}{k}_{D}=1.269\times {10}^{-17}{m}^{2}/s[39]\\ D=7.42\times {10}^{-12}{m}^{2}/s[42]\\ {m}_{CSH}=0.188kg/mol[8]\\ {\rho}_{CSH}=2604kg/{m}^{3}[8]\\ {m}_{CH}=0.074kg/mol\end{array}$ | $\begin{array}{ll}{C}_{w}& ={\rho}_{CSH}\frac{{k}_{D}}{2D}\left(\frac{{m}_{CH}}{{m}_{CSH}}\right)\\ & =8.768\times {10}^{-4}\text{kg}/{\text{m}}^{3}\end{array}$ |

$\begin{array}{ll}{C}_{m}& ={C}_{w}/{m}_{CH}\\ & =1.185\times {10}^{-2}mol/{\text{m}}^{3}\end{array}$ |

## 5. Conclusions

^{29}Si MAS NMR. The Type II OPC pastes were hydrated for 7 days. The methodology to extract the conversion fraction of nanosilica from the chemical shift spectra of

^{29}Si MAS NMR experiments was presented. The hydrated cement paste incorporating 1% nanosilica showed a higher conversion fraction of 66.2% than the hydrated cement paste incorporating 3% nanosilica, with a conversion fraction of 41.2%. While the full reaction time for nanosilica particles having a diameter of 7 nm is in seconds, the nanosilica particles for both hardened cement pastes incorporating 1% and 3% nanosilica did not fully react for 7 days of curing time. Considering these results, the CH concentration around nanosilica particles might be limited due to some reason such as isolation, even with the amount of CH in the hydrated cement is sufficient. Therefore, it seems that the reaction of nanosilica depends on the concentration of calcium hydroxide (CH) around the particles as well as its particle size. From the solid-state kinetic models, it was shown that the average CH concentrations for 7 days are much lower than the minimum CH concentration of 8.768 × 10

^{−4}kg/m

^{3}.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Moon, J.; Taha, M.M.R.; Youm, K.-S.; Kim, J.J. Investigation of Pozzolanic Reaction in Nanosilica-Cement Blended Pastes Based on Solid-State Kinetic Models and ^{29}Si MAS NMR. *Materials* **2016**, *9*, 99.
https://doi.org/10.3390/ma9020099

**AMA Style**

Moon J, Taha MMR, Youm K-S, Kim JJ. Investigation of Pozzolanic Reaction in Nanosilica-Cement Blended Pastes Based on Solid-State Kinetic Models and ^{29}Si MAS NMR. *Materials*. 2016; 9(2):99.
https://doi.org/10.3390/ma9020099

**Chicago/Turabian Style**

Moon, Jiho, Mahmoud M. Reda Taha, Kwang-Soo Youm, and Jung J. Kim. 2016. "Investigation of Pozzolanic Reaction in Nanosilica-Cement Blended Pastes Based on Solid-State Kinetic Models and ^{29}Si MAS NMR" *Materials* 9, no. 2: 99.
https://doi.org/10.3390/ma9020099