Cement and Concrete Research 147 (2021) 106517

Available online 30 June 20210008-8846/© 2021 Elsevier Ltd. All rights reserved.

Role of carbon nanotube in reinforcing cementitious materials: An experimental and coarse-grained molecular dynamics study

Renyuan Qin a,b, Ao Zhou c,1, Zechuan Yu d, Quan Wang e,f, Denvid Lau a,g,*

a Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China b School of Environmental and Civil Engineering, Dongguan University of Technology, Dongguan, China c School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China d School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, China e Department of Civil and Environmental Engineering, Shantou University, Shantou 515063, China f Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China g Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

A R T I C L E I N F O

Keywords: Carbon nanotube (CNT) Cementitious composites Grand canonical Monte Carlo (GCMC) Molecular dynamics

A B S T R A C T

One-dimensional carbon-based nanomaterials, such as carbon nanotube (CNT) or carbon nanofiber (CNF) have been regarded as ideal candidates to form nanocomposites for the fabrication of high-performance cementitious materials. Although CNT, CNF and nanocellulose possess different mechanical properties, the mechanical enhancement of CNT, CNF or nanocellulose reinforced cementitious falls in a similar magnitude compared with plain cement paste, which should be highly related to the interaction between the nanomaterials and cement hydration products. In this study, CNT has been chosen as a representative nanomaterial to investigate the role in reinforcing cementitious materials in the nanocomposite system through an experimental and coarse-grained molecular dynamics approach. The findings suggest that the CNT changes the fracture process in cement ma-trix when the microcracks initiate with the significantly improved fracture energy, leading to the improved global mechanical properties, and a nanoscale interfacial transition zone is found that governs the failure of the nanocomposite system.

1. Introduction

Carbon nanotubes (CNTs) are known for their elegant structure and remarkable mechanical properties, including strength and stiffness and thermal stability, and have been widely considered for the fields of electronic materials, biological technology, chemistry and multifunc-tional composites [1–5]. The theoretical strength and elastic strain ca-pacity of CNTs are 100 and 60 times more than those of steel [6]. Such advantages make CNTs the ideal nano-reinforcement for various kinds of composites. Nowadays, efforts have also been made by researchers to use CNTs as nano-reinforcement for metals, ceramics and cementitious materials [7–11].

Cementitious materials, such as concrete, are heterogeneous mate-rials composed of aggregates and cement matrix, are commonly used due to their low cost and high compressive strength. It can be described as a solid dispersion of hard inclusions into a cohesive matrix, to which

the hydrated cement provides the binding strength. The major cohesive hydration product is calcium silicate hydrate (C-S-H) which is a porous gel-like material generated from the hydration of crystalline mineral particles in ordinary Portland cement powder [12–16]. The pores and cracks, ranging from nanoscale to microscale, often exist in hardened cementitious materials, which make CNTs an ideal reinforcement for the mechanical enhancement of cementitious materials by pores-filling and cracks-bridging. Incorporation of CNTs into concrete is of great potential to improve the overall material properties including stiffness, tensile strength, compressive strength, conductance and functional properties [17–27]. Currently, most experimental works and reviews are based on the fabrication of the multi-walled carbon nanotubes reinforced cement composite and the characterization of the mechanical properties such as compressive strength and flexural strength. It has been shown that depending on their geometrical characteristics, aspect ratio and morphology, low CNT concentration levels in cementitious materials

* Corresponding author at: Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China. E-mail address: denvid@mit.edu (D. Lau).

1 Co-first author.

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https://doi.org/10.1016/j.cemconres.2021.106517 Received 22 December 2020; Received in revised form 30 April 2021; Accepted 11 June 2021

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impart enhanced mechanical properties of the cementitious materials through pore-filling, crack-bridging and pore structure modification. However, the same enhancement in terms of mechanical properties of cementitious materials can also be achieved by the other one- dimensional carbon-based materials, such as carbon nanofiber or cel-lulose nanofiber, although the mechanical properties of these nanofibers are lower than those of CNT. Hence, the enhancement of cementitious materials in terms of mechanical properties by the one-dimensional nanomaterial, such as carbon nanotubes, should depend on the inter-action between the nanomaterial and cement hydration products during the formation and deformation stages at nano to sub-micro scale. The in- site monitoring and characterization of CNTs in cementitious materials during the deformation process using traditional experimental ap-proaches is challenging, as the size of such reinforcement ranges from nano to sub-micro scale. In order to address this issue, molecular dy-namics (MD) simulations provide a powerful tool to investigate the interaction between CNTs and cement hydration products from an atomistic scale to obtain a fundamental understanding on how the CNT reinforces the cementitious materials during deformation.

Recently, several studies have been conducted on the mechanical properties and atomic structure of CNT-reinforced C-S-H by the molec-ular dynamics approach [12,14,16,26,28–31]. The results indicate that the addition of CNT can increase the tensile strength of the composite system and allows for efficient bridging of two sides of the crack [29]. For the compressive behavior, the local-shell buckling mode is domi-nated for the CNT and no significant difference between the compressive behavior of CNT-reinforced C-S-H and normal C-S-H is observed [14,29]. Furthermore, embedding the CNTs in the C-S-H is found to slightly decrease the shear strength of the material in all directions [29]. Moreover, no bonded interaction between CNTs and C-S-H is found at their interface through the molecular dynamics simulations [14,28,29]. Such results reveal some of the reinforcing mechanisms of CNTs in the cement matrix by understanding the interaction between CNT and C-S-H at nanoscale through the MD simulation. However, the compressive and shear properties of the CNT-reinforced C-S-H system are different from the experimental observation of CNT-reinforced cement matrix. This is attributed to that the length of CNTs is usually up to the microscale, and the material morphology of CNTs distributed in the cement matrix at microscale is significantly different from the model of single CNT being embedded in C-S-H matrix at nanoscale. Moreover, the mechanism of CNTs on the pore-filling, crack-bridging and pore structure modification is also related to the material morphology at microscale, which is hard to be captured from full atomistic model due to the geometrical limitation and computational efficiency. Hence, in order to comprehensively investigate the role of CNT in the CNT-reinforced cement matrix, a mesoscale model derived from full atomistic simulation can help to understand the reinforcing mechanism and material morphology change due to the addition of CNTs in the cement matrix. Such mesoscale model can be achieved using coarse-grained (CG) MD simulations.

The objective of this study is to develop an in-depth understanding of the role of CNTs in the deformation process of cementitious nano-composites. In this study, we firstly investigated the effects of CNTs on the global mechanical properties of cement paste using experiments, and microstructure characterization was conducted to study the role of CNTs on the localized microcracks in cement matrix. Furthermore, the inter-action mechanisms between CNTs and cement hydrates have been deeply investigated through a combined molecular dynamic (MD) and a grand canonical Monte Carlo (GCMC) scheme using a coarse-grained CNT-reinforced C-S-H model. The results from this study reveal how the CNT reinforces the cement matrix at the localized cracks by changing the fracture process and failure mode with improved fracture energy, which leads to globally improved mechanical properties. Moreover, it is the first study introducing a mesoscale model of CNT-reinforced C-S-H structures through MD simulations, which is with great potential for evaluation of advanced cementitious through nanomaterials in future studies.

2. Materials and methods

2.1. Materials

The Type I ordinary Portland cement 42.5 R was used in the exper-imental study to prepare the cement pastes, which met all the re-quirements of BS EN 197-1 [32]. The multi-walled CNTs produced by Chengdu Chemicals Co. Ltd., CAS, using chemical vapor deposition (CVD) method, were used in this study, and the physical properties of the CNTs are listed in Table 1. The surfactant employed in this study was TNWDIS, which is a type of non-ionic surfactant for better dispersion of CNTs in aqueous solution.

2.2. Preparation and tests of CNT-reinforced cementitious samples

The CNT suspensions were prepared by mixing CNT powder with surfactant in aqueous solution. Before mixing, the dispersion of CNT in aqueous solution is critical to avoid the aggregation of CNT, which can significantly reduce reinforcement efficiency provided by CNT. Different dispersion methods, including calendaring, ball milling, shear mixing, extrusion and ultrasonication have been adopted to achieve satisfactory dispersion of CNT. Among different methods, ultrasonication combined with surfactant is one of the most used methods in the dispersion of CNT in cementitious composites [5,8,33]. The suspensions were sonicated at room temperature by a 500 W cup-horn ultrasonic processor at cycles of 20 s to prevent the overheating for 30 min. The sonication power and period are set to achieve sufficient sonication energy for the dispersion of CNTs in preparing CNT-reinforced cement pastes [5,8,33]. After sonication, the cement powder was mixed with the prepared CNT sus-pensions using a cement paste mixer in accordance with ASTM C305, with the water to cement ratio of 0.4 for all four batches of samples. The different mixing designs for each batch of sample are summarized in Table 2. After mixing, the CNT-reinforced cement pastes were cast into cubes with the dimensions of 25 × 25 × 25 mm for the compression tests, and beams with the dimensions of 25 × 25 × 120 mm for flexural tests. All the samples were kept in a moist condition for 28 days for curing before conducting the tests. The compressive test was conducted on the cube samples with the displacement control with the loading rate of 0.1 mm/min to determine the compressive strength of plain cement pastes and CNT-reinforced cement pastes with different mix designs, and the elastic modulus was also determined from the compression tests. Moreover, for the prismatic samples, a 12.5 mm pre-crack was intro-duced into the prismatic specimen through a water-cooled saw machine at mid-span, which is shown in Fig. 1. The notched prismatic samples were tested under three-point bending with a support span of 100 mm under the displacement control of 0.01 mm/min to maintain stable crack growth.

The fracture toughness calculated from the three-point bending test on the notched specimens is employed to evaluate the performance of CNT reinforced cementitious composite system using following equa-tions [34,35]:

KIC =PmaxS

th32

f(a

h

)(1)

f(a

h

)= 2.9

(ah

)1/2− 4.6

(ah

)32 + 21.8

(ah

)52 − 37.6

(ah

)72 + 38.7

(ah

)9/2(2)

where KIC is the mode I fracture toughness of the composite; t is the width of the specimen; h is the height of the specimen; a is the depth of

Table 1 Properties of MWCNTs.

Type Diameter (nm)

Length (μm)

Purity (wt %)

Ash (wt %)

Surface area (m2/g)

MWCNTs <80 <10 >98 <1.5 >60

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the notch; S is the span of the beam, and Pmax is the peak load captured during the flexural tests. Moreover, the fracture energy of the composite can be calculated as Gf = KIC

2 (1 − υ2)/E, where E and υ are the Young's Modulus and Poisson's ratio of the composites, considering a plane strain condition.

The morphology and microstructure of the fracture surface of CNT- reinforced cementitious composite were investigated through SEM with the ZEISS Gemini SEM 300. The samples were oven-dried and gold- coated through vapor-deposit process before the examination.

2.3. Coarse-grained molecular dynamics simulation

Coarse-grained models of C-S-H and CNT are proposed based on existing studies on C-S-H at sub-micron scales [36–38]. Among different cement hydration products, such as Ca(OH)2 and ettringites, C-S-H gel has been reported as the major (more than 50% in terms of volume fraction) and most important hydration product to provide cohesion in cement matrix, it has been widely chosen for the investigation of cementitious composites in MD simulations. Moreover, it has been indicated in the previous studies on the growth of cement hydration products on CNT that the C-S-H are the main hydration products around CNT at modeled scale, hence the C-S-H particles have been selected in current study to model the CNT reinforced cementitious composite [14,28–30]. C-S-H is modeled by poly-dispersed spherical particles whose interactions are governed by a modified Lennard-Jones potential, as described by Eq. (3), where σ denotes diameter, ε the potential well depth and is determined by letting the curvature of the potential at its minimum equals stiffness of C-S-H. The interaction parameters can be defined by several steps including (i) calculate the curvature k at r = σ, where k = 288ε

σ2 , (ii) define k the stiffness of the material interface EAσ ,

where A denotes the cross-section area and is set to πσ2

4 (σ = d which is the diameter of the particle) as a result, E denotes the slope of the stress- strain curve obtained at the material interface (68.4 GPa for C-S-H and 14.6 GPa at the C-S-H/CNT interface), (iii) find ε

σ3 and ε can be obtained between particles of the same size (i-i interaction). The inter-action parameter between particles of different sizes (i-j interaction) takes the geometric average of i-type and j-type.

Uij(r, di, dj

)= ε

(di, dj

)∙

[(σ(di, dj

)

r

)24

− 2(σ

(di, dj

)

r

)12 ]

(3)

CNT fiber is modeled by connected beads whose intramolecular in-teractions are governed by harmonic bonding [33] and intermolecular interactions by the Lennard-Jones (LJ) potential. The diameter of C-S-H

particles ranges from 3.9 nm to 9.1 nm, and distribution of the particle diameter is generated within a Monte Carlo scheme. The length of modeled CNT is equal to length of the box, bead-bead distance of CNT is 1.0 nm, and the diameter of bead is 5.0 nm. Nonbonded intramolecular interactions within CNT fiber are not considered. Interaction strength between CNT and C-S-H beads is set to 1/3 of the interaction strength between C-S-H beads, because our preliminary all-atom simulations show that the interfacial strength between C-S-H and CNT is 1/3 of that between C-S-H layers [10,15,39]. The simulation results also reveal that no chemical bond, e.g. covalent bond, electrovalent bond or metallic bond, was formed between C-S-H and CNT, and it has been reported in literature that no such chemical bonds were detected between CNT and C-S-H as well. The frictional forces at nanoscale between C-S-H and CNT are embodied through physical non-bonded interaction, which has been considered in the MD model as well as the CGMD model in current through the LJ potential.

Packing of C-S-H particles is achieved with a Grand Canonical Monte Carlo (GCMC) scheme in a 200 nm × 200 nm × 200 nm box with pre-arranged CNT structures. LAMMPS code is used to implement the method [40]. Corresponding to the water-to-cement ratio (0.4) in ex-periments, packing fraction of the model is set to 0.5 for a reasonable resemblance, as suggested in previous study [36,39]. Four types of models, with 0, 1, 2 and 3 strands of preload CNT fibers, are constructed and used for further simulations. Pore size distributions (PSD) and local density of the modeled composite are calculated using a pixel-based algorithm, which discretizes the box into 1-nm3 pixels and analyzes clustering of pixels identified as solid or pore.

Mechanical test is simulated by applying tensile deformations to equilibrated models of C-S-H and CNT with pre-crack produced by removing coarse-grained particles in a notch, whose thickness is 5 nm and depth is 60 nm. The notch essentially controls the path of crack propagation and makes feasible the calculation of fracture toughness within a theoretical framework. In the tensile test, the strain rate is found a critical parameter in the simulations that determine the me-chanical response of the modeled composite. Results from simulations are fitted against experimental results and a reasonably good strain rate is obtained and employed in all following simulations. Information about stress and strain during the tensile deformation is collected and analyzed.

3. Results and discussion

3.1. Mechanical and fracture properties

The bulk mechanical properties in terms of compressive and flexural strength of CNT-reinforced cement pastes are summarized in Fig. 2(a). For each group of samples, the average value is plotted in the Fig. 2(a). For the compressive strength of cement pastes reinforced by CNT with the weight fraction of 0.05%, 0.1% and 0.15%, it is improved by 11.7%, 22.1% and 5.6%, comparing with the compressive strength of plain cement paste. For the flexural strength of CNT-reinforced cement pastes, it is improved by 8.0%, 23.5% and 9.8%, respectively, for cement pastes

Table 2 Mix proportions of CNT reinforced cementitious composites.

Mix Cement (g) Water (g) MWCNTs (g) CNT/cement (wt%)

P 100 40 – – C5 100 40 0.05 0.05 C10 100 40 0.1 0.1 C15 100 40 0.15 0.15

Fig. 1. Configuration of three-point bending fracture test.

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reinforced by CNT with the weight fraction of 0.05%, 0.1% and 0.15%, comparing with that of plain cement pastes. It is shown that with the addition of CNT in cementitious composite system, most specimens show a significant increase in mechanical performance in terms of both compressive and flexural strength, up to 22.1% for compressive strength and 23.5% for flexural strength, which are found in the samples with addition of 0.1% weight fraction of CNT to cement powder.

The fracture energy and fracture toughness of plain cement pastes and CNT reinforced cement pastes with different addition ratios are plotted in Fig. 2(b). As shown in Fig. 2(b), the fracture toughness and fracture energy of CNT reinforced cement pastes improved significantly compared with those of plain of cement pastes. For the fracture tough-ness of cement pastes reinforced by CNT with the weight fraction of 0.05%, 0.1% and 0.15%, it is improved by 14.5%, 23.6% and 14.7%, comparing with that of plain cement paste. For the fracture energy of CNT-reinforced cement pastes, it is improved by 23.1%, 37.4% and 28.3%, respectively, for cement pastes reinforced by CNT with the weight fraction of 0.05%, 0.1% and 0.15%, comparing with that of plain cement pastes. The same reinforcing trend is found for fracture tough-ness and fracture energy, and the cement pastes with 0.1% of CNT addition show the most improvement in terms of fracture toughness and fracture energy, which is consistent with improvements in terms of compressive and flexural strength. Moreover, it is found that the increasing ratio in terms of fracture toughness and fracture energy is larger than that of compressive and flexural strength for each group of samples, which indicates that the improvement of overall mechanical performance, e.g. compressive and flexural strength, of CNT-reinforced cement pastes could mainly due to the resistance to crack initiation and extension provided by the CNT in the cementitious composite sys-tem. Further, it is found that with the increasing of CNTs dosage, the mechanical and fracture properties of CNT-reinforced cementitious material achieved their maximum at 0.1%, further increasing of CNTs dosage results in a reduction in terms of mechanical and fracture properties. This phenomenon provides the hint that the presence of one- dimensional nanomaterial, such as CNT, can change the failure process of the nanocomposite, which leads to a significant increase in fracture energy. While with further increasing of CNTs dosage, the aggregation of CNTs can occur, and cement hydration products can hardly form within the aggregated CNTs network, which increases pores and reduction in mechanical and fracture properties [8].

3.2. Microstructure characterization

As aforementioned, the mechanical enhancement provided by the CNT in cementitious composites could mainly be due to the resistance to crack initiation and extension. In order to further understand the role of CNT in crack-bridging and its effect on the fracture process, the micro-structure characterizations were conducted using SEM to characterize

the different morphology at the crack region of plain cement pastes and CNT-reinforced cement pastes.

As shown in Fig. 3(a) and (b), the micrograph is captured for a microcrack embedded in the plain cement paste. The fracture line is clear with a smooth fracture surface being observed. By further increasing the magnification at the crack region, a relatively flat fracture surface is observed between the cement hydration products, indicating a brittle failure mode of the material. For the CNT-reinforced cement pastes, due to the high aspect ratio and large surface energy of CNT, the CNTs are well embedded in the cement hydration products. The randomly oriented CNT exhibited a network-like distribution and acted as bridges across pores and cracks, which is confirmed by the SEM im-ages shown in Fig. 3(c). Furthermore, after the CNTs being pulled out from the cement matrix, it is always found that a thin layer of cement hydration products was attached to the surface of CNT, as shown in Fig. 3(d). Moreover, it is found that certain roughness of the fracture surface is observed at the CNT bridging region, which is different from the smooth fracture surface being captured in cracks of the plain cement pastes. In order to further address this finding, another two cracks with bridging or pulled-out CNT were examined, as shown in Fig. 3(e) and (f). Significant roughness at fracture surface between the hydration prod-ucts is observed at the region with CNT reinforcement. By comparing Fig. 3(b) and (f), two distinguished failure modes can be found for the fracture surface in plain cement pastes and CNT-reinforced cement pastes. A schematic diagram indicating the different fracture surfaces for plain pastes and CNT-reinforced cement paste is shown in Fig. 4(a). Moreover, the atomic force microscopy (AFM) results on the fracture surface of plain cement pastes and CNT-reinforced cement paste have demonstrated a similar observation, i.e. the fracture surface of plain cement paste tends to be bulk failure between the large particles, while the significant surface roughness at nano size can be observed for CNT reinforced cementitious composites [41]. Such differences in terms of fracture surface roughness can be observed in the literature on the AFM results of plain cement pastes and similar one-dimensional nanofiller reinforced cementitious composites [42,43]. Furthermore, in order to prove that the observed pull-out or crack-bridging CNT is partially covered by C-S-H, energy dispersive spectrometer (EDS) analysis on the surface of CNT in the SEM observation was performed, and the results are shown in Fig. 4(b), (c), (d) and (e). The cement hydration products can be observed on the CNT surface, and the EDS analysis proved that they were the hydration products of cement, as the main elements were measured as Ca, Si and O, which are the main components of C-S-H gel. Similar observations have been reported in the literature, indicating that in the CNT-reinforced cementitious composites, the CNT is usually partially covered by cement hydration products, which have been re-ported in terms of SEM and EDS measurements [44]. Such observations suggest that apart from the effects of pore filling and crack bridging, the presence of CNT in the cementitious composite system could also lead to

Fig. 2. (a) Bulk and (b) fracture properties of plain cement pastes and cement pastes reinforced by CNTs with the weight fraction of 0.05%, 0.1% and 0.15%.

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a different failure process and failure mode at microscale, which contribute to the improved fracture energy, and hence, improved me-chanical properties of the CNT-reinforced cementitious composite sys-tem. In order to develop a fundamental understanding on the role of CNT on the microstructure of localized regions in the composite system, and its corresponding effects on the fracture process, coarse-grained mo-lecular dynamics simulations were performed.

3.3. Packing of C-S-H and CNT at the sub-micron scale

In this section, coarse-graining scheme, packing, and pore size dis-tribution (PSD) of pristine and CNT-embedded C-S-H are discussed. Fig. 5 demonstrates the coarse-graining scheme, showing that C-S-H is modeled by a collection of poly-dispersed particles, and CNT is modeled by a stand of connected beads. A LJ-style potential is employed to govern interactions between those coarse-grained units. Packing of particles is

implemented via a GCMC approach, which exchanges particles with an idealized reservoir at 300 K. In other words, particles of different sizes are gradually inserted into the simulation box in equilibrium with an imaginary external reservoir. The packing is achieved when the packing fraction reaches 0.5, corresponding to a water-to-cement ratio of around 0.4. The resulted configuration is illustrated in Fig. 5(b).

At the sub-micron scale, cement is a heterogeneous material composed of mesoporous C-S-H, and the distribution of solid content can be influenced by many factors such as water-to-cement ratio, hydration degree and chemical admixtures. The addition of CNT strands would also affect the sub-micron structure of C-S-H, as shown in Fig. 6. The color maps in Fig. 6(c) and (d) show the distribution of local packing fractions in the simulation box. Compared to the pristine C-S-H with stochastic features, the inclusion of CNT creates a region of high-value local packing density around the strand of fiber, which is obvious in Fig. 6(e) and (f). CNT particles strongly attract C-S-H particles at the

Fig. 3. (a) and (b) Microstructure characterization of the fracture surface in plain cement pastes; (c) and (d) fracture surface in CNT reinforced cement pastes; (e) and (f) fracture surface with pulled-outed CNT. Significant roughness in the fracture surface is observed at the region with CNT reinforcement, compared with that in plain cement pastes, indicating a different fracture process.

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interface and creating a dense region. This phenomenon is consistent with an experimental observation, which suggests that by chemical means such as the addition of Ca2+ ions or the addition of nucleating agents, CNT encourages the formation of the reaction products (C-S-H) by providing sites for the reaction to occur [44]. The dense interfacial region suggests a thin layer of cement hydration products attaching to the surface of CNT, with is in good agreement with experimental find-ings in terms of microstructure characterization. Follow by a thin layer

of C-S-H attached, a relatively high free volume area can be observed, which can be the critical region in this nanocomposite system during deformation.

Addition of CNT creates an interfacial region with a dense packing and further alters the overall distribution of C-S-H particles in the simulation box, as shown in Fig. 7(a) and (b). According to the plot of PSD in the 2 cases in Fig. 7(c), pores can be grouped into small pores (<6 nm) and large pores (>6 nm). The addition of CNT reduces number of

Fig. 4. (a) Schematic diagram on the different fracture surface in plain cement paste and CNT-reinforced cement paste; (b) SEM image of CNT in the cement matrix; and (c) EDS spectrum of the cement hydration products on the surface of CNT at point 1; (d) EDS spectrum of the cement hydration products on the surface of CNT at point 2 and (e) EDS spectrum of the cement hydration products on the surface of CNT at point 3.

Fig. 5. (a) Coarse-graining scheme of CNT, (b) sub-micron structure of CNT-embedded C-S-H in the simulation box with dimensions 200 nm × 200 nm × 200 nm, (c) coarse-graining scheme of C-S-H.

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large pores in C-S-H. When the total pore volume is constant, it is thought that the CNT splits large pores into small pores. It should be noted that the zone of influence must be finite, i.e., if the simulation box is much larger than size of CNT, the packing of C-S-H would gradually become similar to pristine C-S-H as it goes further and further away from CNT. Moreover, the findings on the changes of pore size distribution affected by the presence of CNT in simulation agree with the experi-mental finding, which shows reduced pore volume for the pores larger than 10 nm, and increased pore volume of pores smaller than 5 nm. In particular, the simulations results agree well with a recent experimental finding that firstly reported the presence of CNT in cementitious com-posites resulted in an increase of C-S-H gel pores (smaller than 10 nm) by 62.4%, and current simulation showed a 58.8% increase in terms of gel pore volume [45].

3.4. Fracture process

In order to develop a fundamental understanding on the effect of

CNT on the fracture process of cement hydration products, a comparison of the fracture behavior of the single notched composite system between the pure C-S-H matrix and CNT/C-S-H composite is conducted. The J- integral of the composite system during the fracture process has been adopted to evaluate the fracture properties of the pure C-S-H matrix and CNT/C-S-H composites.

The J-integral of a single-edged crack in a finite size structure can be calculated as follows [46,47]:

J = −

∫P

0

[(∂∆∂b

)

P

]

dP∙1B

(4)

where P and Δ are the applied uniaxial tensile load and corresponding tensile deformation of the composite system; B is the thickness of the composite and b is the uncrack length in the structure.

In case of the geometry and loading configuration of the composite system, the J-integral can be further derived as:

Fig. 6. (a) Configurations of coarse-grained models of pristine C-S-H and (b) CNT embedded C-S-H; (c) color maps of local packing density in 3-D space of pristine C- S-H and (d) CNT embedded C-S-H; (e) spatial average of the local packing density along x axis of pristine C-S-H and (f) CNT embedded C-S-H. The global packing density of both systems is 0.5. Packing fraction inside the CNT is not counted. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7. (a) Visualization of pores in pristine C-S-H; (b) Visualization of pores in CNT-embedded C-S-H, and (c) pore size distribution (PSD) in volume vs. equivalent pore diameter plot.

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J = −

∫ P

0

[(∂∆el

∂∆b

)

P+

(∂∆p

∂∆b

)

P

]

dP∙1B

(5)

J =K2

I

E+

1bB

[ ∫ ∆P

0Pd∆P − P∆P

]

(6)

where ∆el and ∆p present the displacements at the elastic and plastic stages of the composite system during the fracture process; E is the elastic modulus of the composite; KI presents the Mode I stress intensity factor, which can be determined as:

KI =P

BW

√

2tan πa

2W

√

cos πa2W

[

0.752+ 2.02( a

W

)+ 0.37

(1 − sin

πa2W

)3]

(7)

where W is the width of the composites. Such method in the determi-nation of J-integral from MD simulations have been widely reported in various literatures with its efficiency.

In current study, four composite systems have been investigated, i.e. pure C-S-H, CNT/C-S-H composite with one to three CNTs. The load- displacement relationships for the different composite systems under the static tensile loading are shown in Fig. 8.

The simulation results reveal that the composite system exhibits a more ductile behavior in the presence of CNT reinforcements, while for pure C-S-H matrix, a brittle failure mode is excepted according to the load-displacement behavior captured from the simulation. The J-inte-gral of the pure C-S-H and CNT/C-S-H composite system determined from the load-displacement curves is listed in Table 3.

From Table 3, the J-integral of a pure C-S-H matrix with a size of 200 × 200 × 200 nm3 and a 60 nm long initial pre-crack is calculated as 0.1276 J/m2. With the presence of CNT reinforcement in the C-S-H matrix, the J-integral of CNT/C-S-H composite increases to 0.2375 J/m2, 0.2712 J/m2, and 0.2994 J/m2, respectively, for the C-S-H matrix reinforced with 1, 2 and 3 CNT. The J-integral increases by 86.2%, 112.5%, and 134.6% for the C-S-H matrix with CNT reinforcement, compared with that of pure C-S-H matrix. The J-integral increases significantly with introducing CNT in the matrix, while by further increasing the content of CNT, a mild increasing trend is observed. Moreover, in order to explore the different failure modes of the com-posite system with the presence of CNT, the failure process of different composite systems is captured, as shown in Fig. 8. The improved effi-ciency of CNT-reinforced cementitious composite calculated from cur-rent simulation varies from 20% to 150% compared to plain cementitious materials. The simulation results in terms of fracture

toughness improvement are within the range of experimental findings on the improved efficiency of CNT-reinforced cementitious composite, which varies from 20% to 150% compared to plain cementitious ma-terials, depending on the content of CNT and calculation methods (using linear elastic fracture mechanics or J-integral) [48–51].

It can be seen from the snapshot during the fracture process of each composite system, after the initiation of the fracture, the stress is mainly distributed at the crack-tip and then the crack prorogates along the fracture line for the pure C-S-H system, which is in agreement of the fracture theory of quasi-brittle material such as cement pastes. However, for the C-S-H matrix with CNT reinforcements, the stress distributes not only on the C-S-H beads at fracture line, but also the CNT and C-S-H beads attached on the CNT inside the bulk material through the adhe-sion between the CNT and C-S-H, as shown in Fig. 9(d), (e) and (f). Eventually, the different failure modes are observed for pure C-S-H matrix and CNT/C-S-H composite system. A clear separation between two bulk C-S-H matrixes is observed in the pure C-S-H system with a relatively flat fracture surface. While for the CNT/C-S-H composite system, due to the load-transfer from the CNT to the C-S-H beads adhered on the CNT, the crack propagates not only along the fracture line, but also into the bulk C-S-H matrix, resulting in a cohesive failure mode with a discrete fracture network and a rough fracture surface, which is shown in Fig. 9(g), (h) and (i).

With the further calculation of local volumetric strain distribution along x-z plane and y-z plane, it can be seen clearly that with the adoption of CNT, the fracture line does not propagate along pre-crack, but shows a zig-zag fracture line with the significant curvature at the location of CNT, which is shown in Fig. 10(d), (e) and (f). Moreover, as shown in Fig. 10(g), (h) and (i), the failure mainly indicates and de-velops at the free volume area at outer ring of CNT within the C-S-H matrix in CNT/C-S-H nanocomposites. While the strain is uniformly distributed along the cross-section of the C-S-H for pure cement matrix.

The finding from the CGMD simulation in terms of J-integral of different composite systems illustrate the sense that the CNT re-inforcements enhance the resistance of the C-S-H matrix to opening a crack, and hence an improved mechanical property, which is consistent with the experimental results. Moreover, the findings in terms of different failure modes of pure C-S-H and CNT/C-S-H composite system observed in the GCMD simulation further explain role of CNT on the different fracture surfaces observed from the microstructure character-ization of plain cement pastes and CNT-reinforced cement pastes. The results from current study suggest that apart from the crack-bridging and pore filling, another effect provided by CNT in the cementitious mate-rials is that it could also change the fracture process and failure modes of the composite system at microscale, leading to the improved mechanical properties of CNT-reinforced cementitious at macroscale. While the free volume area at the outer ring of CNT within the C-S-H matrix is the critical area of the nanocomposite system. After achieving the cohesive failure, further increase of CNT in the system does not improve the fracture energy of the nanocomposite significantly due to this critical region.

Moreover, the CNT aggregation is usually observed in CNT- reinforced cementitious composites due to the high surface areas, which affects the effectiveness of reinforcement at the same amount of CNT addition. The effect of CNT aggregation can be included through the effective span length as span of CNT along x axis in the model. When 0.2 wt% CNT particles are added to C-S-H, they disperse to a full span Fig. 8. Load-displacement relationships for the nanocomposites including pure

C-S-H and CNT/C-S-H with different weight fractions of CNT.

Table 3 J-integral of pure C-S-H and CNT/C-S-H composite system.

Composite system J-integral (J/m2)

C-S-H 0.1276 C-S-H-1CNT 0.2375 C-S-H-2CNT 0.2712 C-S-H-3CNT 0.2994

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along x (long span length), or agglomerate in a mid-span region (short span length). A series of models with the varied length of CNT clusters were simulated under tensile deformation. Normal stress on the CNT cluster along x, which equals total stress minus stress on C-S-H, is useful for indicating the level of reinforcement provided by the CNT. As shown in Table 4, in (90, 110), (80, 120) and (70, 130) cases, CNT particles are placed in the middle of the box such that the x coordinate is within (90, 110), (80, 120) and (70, 130), respectively, to represent highly aggre-gated cases. Here the presentation of (a, b) refers to the case that the coordinates of starting and ending points of CNT are a and b, respec-tively, along the x axis. It is found that in these highly aggregated cases, reinforcement provided by CNT is close to 0. The low level of rein-forcement by the highly aggregated CNT can be explained by insufficient contact, which leads to a relative sliding between the C-S-H and the CNT during the tensile test. As the span length of CNT cluster increases to 180 nm, the reinforcement by CNT gradually increases. In these well- dispersed cases, sufficient contact guarantees stress transfer between the C-S-H and the CNT without relative sliding, and the CNT in turn reinforces the entire composite system effectively.

Furthermore, the reinforcement efficiency is sensitive towards the strength of interaction between CNT and C-S-H. A series of tensile tests on the C-S-H model with 1 CNT reinforcement was performed with the strengths of interaction between CNT and C-S-H ranging from 0% to 90% of the original value. Here, it is defined that the ϵ0 is the depth of potential well used in the original coarse-grained simulations. ϵ/ϵ0 is the ratio between the reduced depth of potential well and its original value, which can describe the different strength of interaction between CNT and C-S-H matrix, and the normal stress on the CNT along the

longitudinal direction for different strength of interaction is shown in Table 5. In the 0% interactive parameter case, the stress on CNT is almost constant during the tensile test, which shows that the deforma-tion of the CNT is independent of the deformation of the system sub-jected to tension, i.e., every step the strain loading is applied, the CNT is forced to elongate and quickly restores because the CNT is not clamped by the C-S-H (relative sliding occurs). In the 10% case and above, the CNT is clamped by the C-S-H and does not immediately restore at each step of the tensile test, and the stress on CNT increases during the tensile process of the composites system with the increases of strength of interaction between CNT and C-S-H. After the deformation of the com-posite system reaches 10 nm, the stress on CNT starts to decrease due to the sliding between the CNT and C-S-H matrix, and this finding agrees with the simulation results on load-displacement response of the com-posites, in which the load decreases at the displacement of 10 nm for the CNT-reinforced C-S-H system. It should be noticed that the early stage of the tensile test, stress on CNT (the reinforcement level) is sensitive to the strength of interaction, and the relatively strong interaction (90%) guarantees a firm clamp to the CNT by the C-S-H.

It should be noticed that no functionalization has been included for the CNT modeled in the current study. Surface modification or func-tionalization of the CNT can add polar functionalized groups such as hydroxyl, carboxyl and carbonyl to the surface of CNT, and the func-tional groups on the surfaces of CNT bring potential chemical interaction between the polar group and the cement hydration products. However, the content and position of the functional groups on the surface of CNT are hardly controllable during surface modification process, and the defects can be generated within the structure of CNT due to that the

Fig. 9. Fracture propagation in (a) pure C-S-H matrix, (b) and (c) CNT/C-S-H composite with 1 and 3 CNT reinforcements at strain of 0.05; (d) pure C-S-H matrix, (e) and (f) CNT/C-S-H composite with 1 and 3 CNT reinforcements at strain of 0.15; and (g) pure C-S-H matrix, (h) and (i) CNT/C-S-H composite with 1 and 3 CNT reinforcements after failure.

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defects can be induced during surface modification process, and such uncertainties significantly affect the model construction and accuracy of simulation results at nano to sub-microscale. In current study, the physical interfacial interaction between CNT and C-S-H has been

included while the chemical interaction induced by surface modification was not included. However, since the interaction parameters in the CGMD model were determined by performing the full atomistic MD simulation, the chemical interaction between the polar group and C-S-H

Fig. 10. (a) Alignment of CNT and C-S-H in the composite shown in (a) pure C-S-H matrix, (b) and (c) CNT/C-S-H composite with 1 and 3 CNT; (d) color maps showing spatial distribution of local volumetric strain at the x-z plane of pure C-S-H matrix; (e) color map showing spatial distribution of local volumetric strain at the x-z plane of CNT/C-S-H composite with 1 CNT; (f) color map showing spatial distribution of local volumetric strain at the x-z plane of CNT/C-S-H composite with 3 CNT; (g) color map showing spatial distribution of local volumetric strain at the y-z plane of pure C-S-H matrix; (h) color map showing spatial distribution of local volumetric strain at the y-z plane of CNT/C-S-H composite with 1 CNT, and (i) color map showing spatial distribution of local volumetric strain at the y-z plane of CNT/C-S-H composite with 3 CNT. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 4 Stress on CNT during tensile tests with varied effective length ranging from 20 nm to 180 nm.

Span length of CNT cluster Stress on CNT cluster at different tensile deformations of composite (MPa)

1 nm 2 nm 3 nm 4 nm 5 nm 10 nm 15 nm 20 nm

(90, 110) 0.063 0.059 0.059 0.073 0.063 0.058 0.042 0.090 (80, 120) 0.041 0.056 0.047 0.053 0.070 0.019 0.053 0.176 (70, 130) 0.060 0.062 0.072 0.087 0.101 0.197 0.248 0.206 (60, 140) 0.260 0.294 0.362 0.415 0.496 0.738 0.771 0.589 (50, 150) 0.568 0.580 0.684 0.664 0.664 0.983 1.063 1.035 (40, 160) 0.879 1.168 1.479 1.575 1.534 1.656 1.121 1.110 (30, 170) 1.090 1.380 1.879 2.180 2.534 3.074 1.942 0.947 (20, 180) 1.812 2.601 3.248 3.686 4.160 3.985 2.571 1.123 (10, 190) 1.969 2.868 3.771 4.510 5.082 4.508 2.627 2.301

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can be efficiently included by performing the full atomistic MD simu-lation using functionalized CNT and C-S-H through reactive forcefields (ReaxFF) in future studies.

Moreover, the proposed CGMD methods can be further developed to various types of nano-size fillers or hybrid fillers. In terms of different types of nanofillers with different mechanical properties, all-atom MD simulations should be firstly conducted to determine the chemical or physical interfacial interaction between the nanofiller and cementitious material (or other material matrices), due to its capability to capture molecular details of the interface between fillers and cementitious ma-terial (including C-S-H, Ca(OH)2 and ettringites, etc.) at the nanoscale. The microstructure formed at the interface, the compatibility between the dissimilar phases at the interface, the adhesion free energy between the two components and the performance of the interface subjected to external loading can be investigated through all-atom MD simulations, providing the input parameters for the interactions between the nano-fillers and matrix for coarse-grained model and use the model in large- scale simulations, so that the different materials properties of nano-fillers and their different interactions with matrix can be included in the coarse-grained model for larger-scale simulations.

4. Conclusions

An experimental and coarse-grained molecular dynamics simulation study is conducted to investigate the role of one-dimensional nano-material, using CNT as a representative, in reinforcing cementitious materials. The experimental results suggest that the mechanical enhancement of CNT-reinforced cementitious composite is a different failure process of the composite system due to the presence of CNT in the cement matrix. The coarse-grained molecular dynamics simulation is conducted to investigate the effect of CNT on the localized material structure in terms of local density distribution and pore size distribution of the cement matrix represented by calcium silicate hydrate. Moreover, the corresponding failure process and properties of CNT-reinforced cement matrix are evaluated through the uniaxial tensile computa-tional test on the single edge notched model for pure C-S-H and CNT/C- S-H system. The results indicate that the J-integral of CNT/C-S-H system improved by 134.6%, compared with that of pure C-S-H system, and a more ductile fracture process can be observed. The findings from current work suggest the improved mechanical properties of CNT-reinforced cementitious material mainly due to the change of fracture process and failure mode in cement matrix when the microcracks initiate with a significantly improved fracture energy. The free volume area at outer ring of CNT becomes the critical region that governs the failure of nanocomposite, which is confirmed by the SEM observation and CGMD simulation results. Hence, after achieving the cohesive failure, further increase of CNT in the system does not improve the fracture energy of the nanocomposite significantly due to this critical region. A higher dosage of CNT can induce the aggregation of CNT easily during the casting of cement pastes, resulting in larger free volume in the composite system and decreased mechanical properties. The developed model and

understanding from this study can be further extended to the design and exploration of cementitious nanocomposites by improving the fracture resistance at multiscale through controlling the corresponding fracture process with nano/micro reinforcements.

CRediT authorship contribution statement

Renyuan Qin: Methodology, Investigation, Analysis, Validation, Visualization, Writing – Original Draft.

Ao Zhou: Conceptualization, Methodology, Investigation, Writing – Original Draft.

Zechuan Yu: Investigation, Analysis, Visualization, Writing – Orig-inal Draft.

Quan Wang: Conceptualization, Writing - Review & Editing. Denvid Lau: Funding acquisition, Project Administration,

Conceptualization, Supervision, Writing - Review & Editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors are grateful for the support from the Research Grants Council (RGC) of the Hong Kong Special Administrative Region, China [Project No. CityU11209418], and the support from Shenzhen Science and Technology Innovation Committee under the grant JCYJ20170818103206501.

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