# Nanostructure and Fracture Behavior of Carbon Nanofiber-Reinforced Cement Using Nanoscale Depth-Sensing Methods

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials Synthesis

#### 2.2. Methods

#### 2.2.1. Grinding and Polishing

#### 2.2.2. Scanning Electron Microscopy Imaging

#### 2.2.3. Nanoindentation Testing

#### 2.2.4. Scratch Testing

#### 2.2.5. Micromechanical Modeling

## 3. Results

#### 3.1. Microstructural Characteristics

#### 3.2. Probabilistic Description of the Mechanical Behavior

#### 3.3. Influence of CNF Content on Cement Chemo-Mechanical Phases

#### 3.4. Influence of CNF Content on Fracture Resistance

#### 3.5. Influence of CNF Content on Fracture Micromechanisms

## 4. Discussion

#### 4.1. Multiscale Conceptual Model for CNF-Modified Cement

#### 4.2. Influence of CNF on Nanostructure

#### 4.3. Toughening Behavior of CNF-Modified Cement

#### 4.4. Dispersion of CNF

## 5. Conclusions

- The ESEM analysis shows carbon nanofiber bundles filling nanopores. Moreover, carbon nanofiber bundles also emerge from C–S–H grains, suggesting that carbon nanofibers promote the nucleation of C–S–H crystals. Finally, carbon nanofiber bundles can also be seen connecting C–S–H grains, leading to a bridging effect, and facilitating load transfer.
- For cement + 0.1 wt% CNF and cement + 0.5wt% CNF, after seven days of curing, we observe a shift of the histogram of the local packing density towards the high-density area, $\eta $ = 0.7–0.9.
- Carbon nanofibers result in an increase in the fraction of high-density C–S–H: for instance, after seven days of curing, the fraction of C–S–H is increased by 6.7% from plain cement to cement + 0.1 wt% CNF and by 10.7% from plain cement to cement + 0.5 wt% CNF. Moreover, the increase in high-density C–S–H is followed by a decrease in the volume fraction of low-density C–S–H by 6.4% and 5.1% respectively for cement + 0.1 wt% CNF and cement + 0.5 wt% CNF.
- A decrease in the fraction of capillary pores is observed by 6.3% and 4.7% respectively for cement + 0.1 wt% CNF and cement + 0.5 wt% CNF.
- The computed C–S–H gel porosity for plain cement, cement + 0.1 wt% CNF and cement + 0.5 wt% CNF is respectively 15.39%, 18.80%, and 16.35%, after 7 days of curing. The computed total porosity is 26.28% for plain cement, 23.36% for cement + 0.1 wt% CNF and 22.53% for cement + 0.5 wt% CNF. Thus, CNF-modification of cement paste result in a reduction of the total porosity, in a reduction of the capillary porosity, and in an increase in the fraction of small C–S–H gel pores (1.2–2 nm in diameter).
- Adding 0.1 wt% CNF yields a 4.5% increase in fracture toughness and adding 0.5 wt% CNF yields a 7.6% increase in fracture toughness: the fracture toughness of plain Portland cement is 0.66 ± 0.02 MPa$\sqrt{\mathrm{m}}$; the fracture toughness of 0.1 wt% CNF cement is 0.69 ± 0.02 MPa$\sqrt{\mathrm{m}}$ and that of 0.5 wt% CNF cement is 0.71 ± 0.04 MPa$\sqrt{\mathrm{m}}$.
- The use of carbon nanofibers result in a drastic reduction in the crack width in CNF-modified cement nanocomposites.
- A four-level multiscale micromechanical model for CNF-cement predicts an increase of respectively 5.97% and 21.78% in the average Young’s modulus following CNF modification at 0.1 wt% CNF and 0.5 wt% CNF levels. This increase in mechanical performance is due to CNF-induced compositional and microstructural changes at both the micrometer and nanometer length-scale.

## Supplementary Materials

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental protocol employed to synthesize cement nanocomposites reinforced with carbon nanofibers.

**Figure 2.**(

**a**) Environmental backscattered electron microscopy (ESEM) image of CNF cement nanocomposite (0.5 wt% CNF) at a 55× magnification level. The C–S–H matrix is in dark grey, clinker grains are in light grey, and capillary pores are in black. (

**b**) Digital image analysis of ESEM image of CNF-modified cement.

**Figure 3.**Environmental backscattered electron microscopy image of the calcium–silicate hydrate (C–S–H) matrix within the CNF cement nanocomposite (0.5 wt% CNF) at a 20,000× magnification level.

**Figure 4.**Probability distribution functions (PDF) of the local packing density ($\eta $) for plain cement and for CNF-modified cement nanocomposites.

**Figure 5.**PDF of the indentation modulus (M) for plain cement and for CNF-modified cement nanocomposites. The dotted lines represent the probability distribution functions for individual chemo-mechanical phases, whereas the solid line the experimental collective probability distribution function based on 400 indentation tests.

**Figure 6.**Probability distribution functions (PDF) of the indentation hardness (H) for plain cement and for CNF-modified cement nanocomposites. The dotted lines represent the probability distribution functions for individual chemomechanical phases whereas the solid line the experimental collective probability distribution function based on 400 indentation tests.

**Figure 7.**Statistical deconvolution of indentation data for plain cement and for CNF-modified cement nanocomposites. CP = capillary pores. LD CSH = low-density C–S–H. HD CSH = high-density C–S–H. UHD = ultra-high-density C–S–H. M is the indentation modulus and H is the indentation hardness. There were 400 indentation tests conducted per specimen.

**Figure 8.**Phase distribution in both plain cement and CNF-modified cement nanocomposites. CP = capillary pores. LD CSH = low-density C–S–H. HD CSH = high-density C–S–H. UHD = ultra-high-density C–S–H. Cl = unhydrated clinker.

**Figure 9.**Fracture response of CNF cement nanocomposites. ${F}_{T}$ is the horizontal force, X is the scratch path, and $2pA$ is the scratch probe shape function. $N=12$ tests were performed per specimen.

**Figure 10.**Fracture micromechanisms of 5wt% CNF cement nanocomposite compared to plain Portland cement.

**Figure 11.**Multiscale thought-model of CNF-modified cement nanocomposite. CP = capillary pores. LD CSH = low-density C–S–H. HD CSH = high-density C–S–H. UHD = ultra-high-density C–S–H. Cl = unhydrated clinker.

**Figure 12.**Histogram of the predicted macroscopic Young’s modulus, ${E}^{hom}$. (

**a**) Plain Portland cement. (

**b**) Cement + 0.1 wt% CNF. (

**c**) Cement + 0.5 wt% CNF. For each specimen, 50,625 numerical simulations were conducted.

Specimen | Cement | Cement + 0.1 wt% CNF | Cement + 0.5 wt% CNF |
---|---|---|---|

CNF, wt% | 0.0 | 0.1 | 0.5 |

CNF, g | 0.000 | 0.069 | 0.347 |

Cement, g | 69.44 | 69.44 | 69.44 |

DIW, g | 30.56 | 30.56 | 30.56 |

wt% | |
---|---|

Alite Monoclinic $C{a}_{3}Si{O}_{5}$ (C${}_{3}$S) | 73.80 |

Tricalcium Aluminate $C{a}_{3}A{l}_{2}{O}_{6}$ | 12.10 |

Belite $C{a}_{2}Si{O}_{4}$ (C${}_{2}$S) | 9.80 |

Brownmillerite $C{a}_{2}FeAl{O}_{5}$ | 4.30 |

**Table 3.**Computed physical characteristics of chemo-mechanical phases in plain cement and in CNF-modified cement. CP = capillary porosity. LD C–S–H = low-density C–S–H. HD C–S–H = high-density C–S–H. UHD C–S–H = ultrahigh-density C–S–H. For each phase, ${\mu}_{M}$ (respectively ${\mu}_{H}$) is the average value of the indentation modulus (respectively indentation hardness); whereas ${\sigma}_{M}$ (respectively ${\sigma}_{H}$) is the standard deviation of the indentation modulus (respectively indentation hardness).

Vol (%) | (${\mathit{\mu}}_{\mathit{M}}$, ${\mathit{\sigma}}_{\mathit{M}}$), GPa | (${\mathit{\mu}}_{\mathit{H}}$, ${\mathit{\sigma}}_{\mathit{H}}$), GPa | $\mathit{\eta}$ | |
---|---|---|---|---|

Plain Cement | ||||

CP | 2.72 | (0.00,4.73) | (0.02,0.10) | (0.52,0.03) |

CP | 8.17 | (9.39,4.66) | (0.29,0.17) | (0.58,0.04) |

LD C–S–H | 7.26 | (20.74,6.69) | (0.67,0.19) | (0.67,0.05) |

HD C–S–H | 59.89 | (36.98,9.55) | (1.36,0.49) | (0.80,0.07) |

UHD C–S–H | 12.71 | (52.74,6.20) | (2.57,0.72) | (0.92,0.05) |

Clinker | 9.25 | (97.23,35.34) | (4.93,3.31) | N. A. |

Cement + 0.1 wt% CNF | ||||

CP | 3.65 | (0.00,10.27) | (0.26,0.17) | (0.05,0.50) |

CP | 0.91 | (12.49,2.23) | (0.53,0.10) | (0.58,0.03) |

LD C–S–H | 0.91 | (16.89,2.17) | (0.73,0.10) | (0.64,0.02) |

HD C–S–H | 66.61 | (32.37,6.09) | (1.26,0.34) | (0.76,0.05) |

UHD C–S–H | 19.16 | (46.50,5.78) | (2.11,0.51) | (0.87,0.05) |

Clinker | 8.75 | (91.40,21.46) | (4.25,2.41) | N. A. |

Cement + 0.5 wt% CNF | ||||

CP | 2.65 | (0.00,6.32) | (0.07,0.10) | (0.54,0.05) |

CP | 3.53 | (10.65,3.79) | (0.27,0.10) | (0.61,0.02) |

LD C–S–H | 2.65 | (17.60,3.16) | (0.49,0.12) | (0.66,0.02) |

HD C–S–H | 70.60 | (35.58,9.43) | (1.14,0.53) | (0.79,0.07) |

UHD C–S–H | 8.83 | (53.00,5.76) | (2.44,0.77) | (0.93,0.05) |

Clinker | 11.75 | (87.65,24.75) | (4.04,3.43) | N. A. |

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**MDPI and ACS Style**

Akono, A.-T. Nanostructure and Fracture Behavior of Carbon Nanofiber-Reinforced Cement Using Nanoscale Depth-Sensing Methods. *Materials* **2020**, *13*, 3837.
https://doi.org/10.3390/ma13173837

**AMA Style**

Akono A-T. Nanostructure and Fracture Behavior of Carbon Nanofiber-Reinforced Cement Using Nanoscale Depth-Sensing Methods. *Materials*. 2020; 13(17):3837.
https://doi.org/10.3390/ma13173837

**Chicago/Turabian Style**

Akono, Ange-Therese. 2020. "Nanostructure and Fracture Behavior of Carbon Nanofiber-Reinforced Cement Using Nanoscale Depth-Sensing Methods" *Materials* 13, no. 17: 3837.
https://doi.org/10.3390/ma13173837