Pull-Out of Pristine and Functionalized Carbon Nanotubes from Cement: A Molecular Modelling Study

: Carbon nanotubes (CNTs) are widely used as reinforcements in cement-based composites. The improvement in the mechanical properties of the resulting materials depends on the characteristics of the interface formed between CNTs and the cement matrix. The experimental characterization of the interfacial properties of these composites is still limited and hard to achieve with currently available technologies. In this work, molecular dynamics and molecular mechanics pull-out simulations of pristine and functionalized CNTs, taken from a tobermorite crystal, were carried out to study interfacial shear strength (ISS) from an atomic perspective. ISS was calculated from the potential energy of the systems. The effects of the CNT diameter and the degree of functionalization on the pull-out process were analyzed according to the ISS and non-bonded energy results. The inﬂuence of H-bonding and electrostatic interactions between the CNT and the matrix were also studied. The results show that ISS decreases with increasing CNT radius for pristine CNTs and depends upon the number of H-bonds for functionalized CNTs. ISS values are positively correlated to E non-bonded energy , which is related to the number of carboxyl groups on the CNT surface. A high degree of functionalization increases both the number of H-bonds and the number of Ca 2+ -O interactions between the CNT and the tobermorite surface. This results in a stronger interfacial interaction and, therefore, an elevated ISS value.


Introduction
Cementitious composites are widely used materials with high compressive strength and simple production methods.However, they also have many disadvantages such as low tensile strength, high permeability to water and other harmful substances, and high cracking tendency.Reinforcements are used to overcome these drawbacks.Due to their remarkable mechanical properties, carbon nanotubes (CNTs) are promising candidates as reinforcing materials.During the last few years, there have been an increasing number of research studies on composites made of cement and CNTs [1][2][3][4][5].Mechanical testing has shown that CNTs have elastic moduli greater than 1 TPa and tensile strengths as high as 63 GPa [6,7].When appropriate dispersion of CNTs within the cement matrix is achieved, the resulting composites show denser structures [8], reduced water permeability [9], improved mechanical properties [10] and good durability [11].The improved mechanical properties are attributed to the crack-bridging effect of CNTs.The addition of CNTs to a cement matrix results in a delay in cracks propagation.A recent study [12] shows that the use of functionalized CNTs improves compressive strength of cement pastes without the need for ultrasonication.Thus, good dispersion of the reinforcement into the matrix and improved interfacial interactions, enhanced by the functional groups, are the key factors in obtaining materials with better properties.CNTs have also been used as additives to enhance the bonding strength between concrete-and carbon fiber-reinforced polymers [13], C 2022, 8, 80 2 of 13 which in turn increased the bond strength, ultimate slip, and interfacial fracture energy of the composites.
It is well known that the interface between CNTs and the cement matrix plays a critical role in determining the effectiveness of mechanical reinforcement, as the interface is usually the weakest part in a composite and determines its fracture behavior [14].Apart from diverse experimental results, recent coarse-grained and all-atoms molecular dynamics studies [15,16] suggest that the addition of CNT to a cement matrix changes the way of fracturing and significantly improves the fracture energy and other mechanical properties.
Interfacial bond strength can be tailored in many ways, one of which is functionalizing the CNT surface [17,18].The functionalization processes can be classified into two broad groups depending on the nature of the interactions established between the CNTs and the molecules linked to them [19]: covalent functionalization, which implies the formation of strong chemical bonds between the CNTs and the functional groups, and non-covalent functionalization, which is based on different adsorption forces (hydrogen bonds, van der Waals forces, electrostatic forces or π-stacking interactions) and does not modify the properties of CNTs [20].Non-covalent functionalization is weaker than covalent functionalization, which may result in low efficiency of the load transfer in composites [21].Acid treatment of the CNTs allows for covalent modification and is commonly used to introduce carboxyl groups to the sidewalls of CNTs [22], thereby facilitating dispersion as well as improving the bonding between CNTs and the cement matrix [23,24].
A direct measure of the interfacial bond strength can be estimated from the interfacial shear strength (ISS), which can be obtained from micromechanical and macromechanical tests, such as fragmentation, pull-out, microdroplet, push-out and push-in tests [25][26][27][28][29][30].A consensus is yet to emerge on the best experimental technique to measure the ISS, and most experimental studies have focused on CNTs-reinforced polymer composites.
Due to the difficulties in obtaining experimental results to study the CNT-cement interface, the interfacial properties of CNTs-reinforced cementitious composites have mainly been studied by molecular mechanics (MM) and molecular dynamics (MD) simulations.It is important to note that this kind of simulations can take advantage of providing atomic information of the interface between CNTs and matrices, which is unattainable with experimental methods.Many authors have calculated ISS using a pull-out model [31].This is because the CNT-matrix interface strength is essentially related to the pulling-out behavior, which determines how strongly the CNT is bonded to the matrix, and how effective the reinforcement is.As in the case of experimental results, ISS of CNTs-reinforced polymer composites has been extensively studied by molecular modelling [32][33][34][35][36], and only several results on carbonaceous nanomaterials-cement matrices have been reported in the literature, most of which related to graphene [37][38][39][40].As the interface between CNTs and matrices play a critical role in enhancing the mechanical properties of the composites, the influence of the functionalization of the CNT surface on the pull-out process has also been studied by many authors [40][41][42][43][44][45].Both simulation and experimental results show that cement composites, containing functionalized CNTs, result in improved mechanical properties due to a better adhesion at the interface.However, technical difficulties associated with the manipulation of the nanotubes in cement matrices, hinder the measurement of ISS of these composites.
After carrying out a review of the existing literature, we noticed that there are many experimental results on ISS of CNT-containing composites, but most of them have focused on polymeric matrices, as ISS of CNT-cement composites are difficult to measure experimentally.On the other hand, simulation studies of cementitious composites are more numerous, especially those that contain graphene and graphene-derived reinforcements.There are some MD calculations of mechanical properties of CNT-cement composites, but almost none focuses on ISS of functionalized CNTs.Therefore, in this work, the ISS of CNT/tobermorite nanocomposites was systematically studied by using a series of CNT pull-out simulations based on MD and MM approaches.The results are explained as a function of non-bonded energies, which in turn, are influenced by the chemical interactions established between the CNTs and the matrix at the composite interface.Pristine and functionalized armchair CNTs, with a radius in the range of 2.70 to 4.74 Å and a length of 19.68 Å, were inserted into a tobermorite matrix.The effect of CNT diameter and degree of functionalization with carboxyl groups on ISS was assessed and related to non-bonded interactions between the CNT and the matrix.To the best of our knowledge, molecular simulations of a CNT pull-out from a cement matrix, unlike in the case of polymer matrices or graphene, are scarce.With this work, we are aiming to get more insight into the atomic interactions existing at CNT-cement interfaces, which are primarily responsible for the enhancements and failures of the mechanical properties of these composites.

Model Systems
A simulation cell, with a periodic boundary condition in the y-z plane (29.54 × 67.46 Å 2 ), was used for the pull-out calculations.The size of this cell was large enough (500 Å) in the axial direction of the CNT (x direction), and included a vacuum layer to eliminate the interaction between periodic images in neighboring cells and leave space for pulling out the CNT (Figure 1).
C 2022, 8, x FOR PEER REVIEW 3 of 13 function of non-bonded energies, which in turn, are influenced by the chemical interactions established between the CNTs and the matrix at the composite interface.Pristine and functionalized armchair CNTs, with a radius in the range of 2.70 to 4.74 Å and a length of 19.68 Å , were inserted into a tobermorite matrix.The effect of CNT diameter and degree of functionalization with carboxyl groups on ISS was assessed and related to non-bonded interactions between the CNT and the matrix.To the best of our knowledge, molecular simulations of a CNT pull-out from a cement matrix, unlike in the case of polymer matrices or graphene, are scarce.With this work, we are aiming to get more insight into the atomic interactions existing at CNT-cement interfaces, which are primarily responsible for the enhancements and failures of the mechanical properties of these composites.

Model Systems
A simulation cell, with a periodic boundary condition in the y-z plane (29.54 × 67.46 Å 2 ), was used for the pull-out calculations.The size of this cell was large enough (500 Å ) in the axial direction of the CNT (x direction), and included a vacuum layer to eliminate the interaction between periodic images in neighboring cells and leave space for pulling out the CNT (Figure 1).To represent the cement matrix, a tobermorite 11 Å structure was used (left side of Figure 2).This structure contained double silicon oxide chains interspersed with calcium oxide sheets and hydration water molecules; 11 Å indicates the basal spacing of the calcium oxide layers.Although it is well known that real cementitious systems present poor crystalline order with variable stoichiometry [46], tobermorite has been regarded as a good model of cement structures by many different authors [47][48][49].To represent the cement matrix, a tobermorite 11 Å structure was used (left side of Figure 2).This structure contained double silicon oxide chains interspersed with calcium oxide sheets and hydration water molecules; 11 Å indicates the basal spacing of the calcium oxide layers.Although it is well known that real cementitious systems present poor crystalline order with variable stoichiometry [46], tobermorite has been regarded as a good model of cement structures by many different authors [47][48][49].Since the interface between the tobermorite and the CNT is the focus of this research, we think this model is reasonable and can work well for our purposes.
The composite material was built by inserting a CNT into the tobermorite matrix (right side of Figure 2).CNTs with radius ranging from 2.71 to 4.   Since the interface between the tobermorite and the CNT is the focus of this research, we think this model is reasonable and can work well for our purposes.
The composite material was built by inserting a CNT into the tobermorite matrix (right side of Figure 2).CNTs with radius ranging from 2.71 to 4.   Since the interface between the tobermorite and the CNT is the focus of this research, we think this model is reasonable and can work well for our purposes.
The composite material was built by inserting a CNT into the tobermorite matrix (right side of Figure 2).CNTs with radius ranging from 2.71 to 4.

Calculation Method
Initially, a 100 ps calculation in the NPT ensemble at 298 K and atmospheric pressure was performed to optimize the parameters of the simulation lattice and relax the system.The temperature was controlled by a Nose-Hoover thermostat [50], and a Berendsen barostat [51] was used to maintain the pressure at 1 atm.A time step of 1 fs was used during the entire relaxation.Then, the resulting relaxed structures were used as inputs to simulate the pull-out process.This was done after increasing the size of the cell in the axial direction of the CNT (x direction) and including a vacuum layer, while keeping the lattice parameters in the other two directions unchanged.These new models were further optimized by molecular mechanics (MM) before the pull-out process.The models used to simulate the pull-out process were created by displacing the CNT along the x axis in increments of 10 Å. Snapshots of the models for one of the CNT/tobermorite systems during the CNT pull-out process are shown in Figure 4.After each pull-out step, the energy of the resulting molecular structure was calculated by MM. Materials Studio 9.0 software [52] was used to perform the simulations.

Calculation Method
Initially, a 100 ps calculation in the NPT ensemble at 298 K and atmospheric pressure was performed to optimize the parameters of the simulation lattice and relax the system.The temperature was controlled by a Nose-Hoover thermostat [50], and a Berendsen barostat [51] was used to maintain the pressure at 1 atm.A time step of 1 fs was used during the entire relaxation.Then, the resulting relaxed structures were used as inputs to simulate the pull-out process.This was done after increasing the size of the cell in the axial direction of the CNT (x direction) and including a vacuum layer, while keeping the lattice parameters in the other two directions unchanged.These new models were further optimized by molecular mechanics (MM) before the pull-out process.The models used to simulate the pull-out process were created by displacing the CNT along the x axis in increments of 10 Å .Snapshots of the models for one of the CNT/tobermorite systems during the CNT pull-out process are shown in Figure 4.After each pull-out step, the energy of the resulting molecular structure was calculated by MM. Materials Studio 9.0 software [52] was used to perform the simulations.The COMPASSII force field was used to calculate the interactions between the tobermorite and the CNT [53].COMPASSII has been successfully applied in the simulation of systems containing CNTs and different materials derived from cement [38,[54][55][56][57]. Coulomb interactions were calculated by the Ewald summation method, and an atom-based The COMPASSII force field was used to calculate the interactions between the tobermorite and the CNT [53].COMPASSII has been successfully applied in the simulation of systems containing CNTs and different materials derived from cement [38,[54][55][56][57]. Coulomb interactions were calculated by the Ewald summation method, and an atom-based cut-C 2022, 8, 80 6 of 13 off method was applied for the calculation of van der Waal interactions [58].The cutoff distance for both kind of interactions was set to 12.5 Å.
The interfacial shear strength (ISS = τ) was calculated based on the total pull-out energy, and is given by [59]: τ, r, and L are the interfacial shear strength, CNT radius and CNT length.E pull-out is the energy difference between the fully embedded configuration of the CNT and the complete pull-out configuration (see Figure 5).It should be noted that this formula gives the average ISS.
C 2022, 8, x FOR PEER REVIEW 6 of 13 cutoff method was applied for the calculation of van der Waal interactions [58].The cutoff distance for both kind of interactions was set to 12.5 Å .
The interfacial shear strength (ISS = τ) was calculated based on the total pull-out energy, and is given by [59]: τ, r, and L are the interfacial shear strength, CNT radius and CNT length.Epull-out is the energy difference between the fully embedded configuration of the CNT and the complete pull-out configuration (see Figure 5).It should be noted that this formula gives the average ISS.

Interfacial Shear Strength
Figure 5 shows the variation in total potential energy of the composite, with pull-out displacement for one of the models.As the CNT was pull out from the tobermorite matrix, the total potential energy increased toward a constant value, which indicated that there was no interaction between the CNT and the matrix beyond a certain pull-out distance.Thus, in all cases studied in this work, the energy of the fully embedded configuration was lower than the energy of the complete pull-out configuration.As indicated in Figure 5, Epull-out is the energy difference between the fully embedded configuration of the CNT and the complete pull-out configuration.A similar trend was also observed in previous studies [33,[36][37][38].Increasing the pull-out displacement, the total potential energy decreased since the interfacial interaction between the CNT and the matrix progressively reduced to zero.
The ISS was calculated from Equation (1), and the results are presented in Figure 6 for all systems.The figures above each column correspond to the number of H-bonds existing at the interface between the CNT and the matrix, and the mean distance (Å ) between both structures.The geometrical criteria for the existence of an H-bond are the following: the distance between the H of the donor group (D) and the O of the acceptor group (A) is less than 2.5 Å and the DHA angle is greater than 90°.

Interfacial Shear Strength
Figure 5 shows the variation in total potential energy of the composite, with pull-out displacement for one of the models.As the CNT was pull out from the tobermorite matrix, the total potential energy increased toward a constant value, which indicated that there was no interaction between the CNT and the matrix beyond a certain pull-out distance.Thus, in all cases studied in this work, the energy of the fully embedded configuration was lower than the energy of the complete pull-out configuration.As indicated in Figure 5, E pull-out is the energy difference between the fully embedded configuration of the CNT and the complete pull-out configuration.A similar trend was also observed in previous studies [33,[36][37][38].Increasing the pull-out displacement, the total potential energy decreased since the interfacial interaction between the CNT and the matrix progressively reduced to zero.
The ISS was calculated from Equation (1), and the results are presented in Figure 6 for all systems.The figures above each column correspond to the number of H-bonds existing at the interface between the CNT and the matrix, and the mean distance (Å) between both structures.The geometrical criteria for the existence of an H-bond are the following: the distance between the H of the donor group (D) and the O of the acceptor group (A) is less than 2.5 Å and the DHA angle is greater than 90 • .It can be seen that ISS values decrease with increasing CNT radius for pristine CNTs.Li et al. [34] found similar results the pull-out of pristine CNTs from a polyethylene matrix.However, functionalized CNTs do not follow the same trend, and ISS values for these systems seem to be correlated to the number of H-bonds established between the carboxyl groups of the CNT and the tobermorite structure.In general, the higher the numof carboxyl groups, the higher the ISS value.This is because more H-bonds can be formed at the interface, a phenomenon which reinforces the interaction between the CNT and the tobermorite matrix.Some exceptions can be observed.For example, the ISS value for the CNT (4, 4)-4COOH system (392.56MPa), which presents six H-bonds, is higher than that calculated for the CNT (5, 5)-4COOH system, with eight H-bonds (325.27MPa).This may be because the mean distance for H-bonds in the CNT (4, 4) system is somewhat smaller (1.60 Å ) than that found for the CNT (5, 5) system (1.70 Å ), which weakens the interaction.
Some authors analyzed the influence of groups, capable of forming H-bonds with the matrix, on the mechanical properties of graphene-reinforced cementitious composites [37,40,48,60,61].In all cases, the surface functionalization led to composites with enhanced strength and good binding affinity between the graphene and the cement matrix compared to that of the non-functionalized graphene.In a previous work [62], we also found that the calculated binding energies and experimental results of the mechanical properties of functionalized CNTs are better than those of pristine CNTs.Additionally, other authors found that the functionalized C atoms move out of the nanostructure surface (the hybridization of the functionalized C atom changes from sp 2 to sp 3 ).The result is that the flat carbon structures turn into wrinkled structures, which mechanically interlock with the matrix, contributing to the enhancement of the mechanical strength [63].
In this work, the calculated ISS values range from 170 to 586 MPa, depending upon the CNT diameter and the number of carboxyl groups bonded to the CNT surface.Other authors found values ranging from 2 to 940 MPa using MD studies of CNT/polymer matrices [64] and references therein].It would be useful to compare our results with experimental data of single-CNT pull-outs from cement matrices tests.To the best of our knowledge, none are currently available.This may be due to the technical difficulties in It can be seen that ISS values decrease with increasing CNT radius for pristine CNTs.Li et al. [34] found similar results for the pull-out of pristine CNTs from a polyethylene matrix.However, functionalized CNTs do not follow the same trend, and ISS values for these systems seem to be correlated to the number of H-bonds established between the carboxyl groups of the CNT and the tobermorite structure.In general, the higher the number of carboxyl groups, the higher the ISS value.This is because more H-bonds can be formed at the interface, a phenomenon which reinforces the interaction between the CNT and the tobermorite matrix.Some exceptions can be observed.For example, the ISS value for the CNT (4, 4)-4COOH system (392.56MPa), which presents six H-bonds, is higher than that calculated for the CNT (5, 5)-4COOH system, with eight H-bonds (325.27MPa).This may be because the mean distance for H-bonds in the CNT (4, 4) system is somewhat smaller (1.60 Å) than that found for the CNT (5, 5) system (1.70 Å), which weakens the interaction.Some authors analyzed the influence of groups, capable of forming H-bonds with the matrix, on the mechanical properties of graphene-reinforced cementitious composites [37,40,48,60,61].In all cases, the surface functionalization led to composites with enhanced strength and good binding affinity between the graphene and the cement matrix compared to that of the non-functionalized graphene.In a previous work [62], we also found that the calculated binding energies and experimental results of the mechanical properties of functionalized CNTs are better than those of pristine CNTs.Additionally, other authors found that the functionalized C atoms move out of the nanostructure surface (the hybridization of the functionalized C atom changes from sp 2 to sp 3 ).The result is that the flat carbon structures turn into wrinkled structures, which mechanically interlock with the matrix, contributing to the enhancement of the mechanical strength [63].
In this work, the calculated ISS values range from 170 to 586 MPa, depending upon the CNT diameter and the number of carboxyl groups bonded to the CNT surface.Other authors found values ranging from 2 to 940 MPa using MD studies of CNT/polymer matrices [64] and references therein].It would be useful to compare our results with experimental data of single-CNT pull-outs from cement matrices tests.To the best of our knowledge, none are currently available.This may be due to the technical difficulties in designing the experiments and characterizing the interface at the nanoscale.Fan et al. [37] modeled the pull-out of graphene and graphene oxide sheets from a tobermorite crystal, finding ISS values as high as 647 MPa.Their results are comparable to ours.The ISS values calculated by et al. [38] for pulling-out graphene functionalized with hydroxyl, amine and carboxyl groups varied between 1.2 and 13.5 GPa.

Non-Bonded Energy
As our models do not include chemical bonds between the CNT and the tobermorite, ISS values can be mainly correlated to changes in non-bonded energy (Van Waals and electrostatic energies) as the CNT is pulled out from the tobermorite matrix.Figure 7 shows ∆E non-bonded energy = E non-bonded energy pulled-out − E non-bonded fully embedded (non- bonded energy difference between the complete pull-out and the fully embedded configuration of the CNT) for all systems.The higher the value, the the interaction between the CNT and the matrix.Again, the figures above each column correspond the number of H-bonds existing at the interface between the CNT and the matrix, and the mean distance (Å) between both structures.∆E non-bonded energy follows the same trend as that of ISS.High ∆E non-bonded energy values correlate well with the number of H-bonds, indicating a strong interfacial interaction and, therefore, an elevated ISS.The positive correlation between ∆E non-bonded energy and ISS is clearly seen in Figure 8.Using MD simulations, Lushnikova et al. [65] inserted a functionalized CNT into a tobermorite structure and found improved bulk modulus, shear modulus, plane stress, and Young's modulus.They attributed the results to the interactions established between the O atoms of the tobermorite and the CNT surface, that is to say, to high non-bonded energy values.
C 2022, 8, x FOR PEER REVIEW 8 of 13 designing the and characterizing the interface at the nanoscale.Fan et al. [37] modeled the pull-out of graphene and graphene oxide sheets from a tobermorite crystal, finding ISS values as high as 647 MPa.Their results are comparable to ours.The ISS values calculated by Alkhateb et al. [38] for pulling-out graphene functionalized with hydroxyl, amine and carboxyl groups varied between 1.2 and 13.5 GPa.

Non-Bonded Energy
As our models do not include chemical bonds between the CNT and the tobermorite, ISS values can be mainly correlated to changes in non-bonded energy (Van der Waals and electrostatic energies) as the CNT is pulled out from the tobermorite matrix.Figure 7 shows ΔEnon-bonded energy = Enon-bonded energy pulled-out − Enon-bonded energy fully embedded (non-bonded energy difference between the complete pull-out configuration and the fully embedded configuration of the CNT) for all systems.The higher the value, the stronger the interaction bethe CNT and the matrix.Again, the figures above each column correspond to the number of H-bonds existing at the interface between the CNT and the matrix, and the mean distance (Å ) between both structures.ΔEnon-bonded energy follows the same trend as that of ISS.High ΔEnon-bonded energy values correlate well with the number of H-bonds, indicating a strong interfacial interaction and, therefore, an elevated ISS.The positive correlation between ΔEnon-bonded energy and ISS is clearly seen in Figure 8.Using MD simulations, Lushnikova et al. [65] inserted a functionalized CNT into a tobermorite structure and found improved bulk modulus, shear modulus, plane stress, and Young's modulus.They attributed the results to the interactions established between the O atoms of the tobermorite and the CNT surface, that is to say, to high non-bonded energy values.

Ca 2+ -O Interactions
Ca 2+ ions in the tobermorite structure can interact with the functional groups of the CNT, acting as bridges that connect the O atoms of the carboxyl groups with the O of the tobermorite structure.Thus, as in the case of H-bonds, this kind of interaction, mediated by 2+ ions, improves the adhesion between the CNT and the tobermorite surface.Hou et al. [48] studied the strengthening mechanisms of calcium silicate hydrate (C-S-H) and graphene oxide (GO) using reactive force field molecular dynamics and found that Ca 2+ ions could bridge O atoms in silicate chains and hydroxyl groups in GO, which resulted in the construction of a reinforcing silicate-carbon skeleton in the interface region.Kai et al. [40] found that the Young's modulus and strength of C-S-H were enhanced by 52.6% and 23.3%, respectively, by the incorporation of hydroxyl groups into the GO.This came because of Ca 2+ coordination and the formation of hydrogen bonds with the hydroxyl groups of GO.The abovementioned value of 647 MPa, found by Fan et al. [35], is attributed to the strong interactions established between the O atoms of a functionalized GO sheet and the Ca 2+ ions in the tobermorite structure.
The mean coordination number of Ca 2+ ions at the interfacial region, the number of Ca 2+ -carboxylic O close contacts for each CNT, and the mean distance between Ca 2+ ions and O atoms (either in the carboxyl groups or in the silicate chains) are shown in Table 2 for all systems.As can be seen in Table 2, coordination numbers vary from 5 to 6, with the latter being the preferred one in most structures.It is well known that Ca 2+ ions in crystal structures generally bind to O atoms in ligands, with coordination numbers mostly ranging from 6 to 8 [66].Bond lengths are similar to those found in compounds with 6-fold oxygen coordination [67].In all cases, one or two of the O ligands coordinating a Ca 2+ ion belong to a carboxyl group of the CNT surface.Furthermore, the number of Ca 2+ ions that are coordinated by a carboxylic O increases with the number of carboxyl groups, as expected (right column of Table 2).This electrostatic interaction contributes, together with the H-bonds, to the strengthening of the composite interface.The structure of a 6-fold coordinated Ca 2+ at the interface between the CNT and the tobermorite matrix is shown

Ca 2+ -O Interactions
Ca 2+ ions in the tobermorite structure can interact with the functional groups of the CNT, acting as bridges that connect the O atoms of the carboxyl groups with the O atoms of the tobermorite structure.Thus, as in the case of H-bonds, this kind of interaction, mediated by Ca 2+ ions, improves the adhesion between the CNT and the tobermorite surface.Hou et al. [48] studied the strengthening mechanisms of calcium silicate hydrate (C-S-H) and graphene oxide (GO) using reactive force field molecular dynamics and found that Ca 2+ ions could bridge O atoms in silicate chains and hydroxyl groups in GO, which resulted in the construction of a reinforcing silicate-carbon skeleton in the interface region.Kai et al. [40] found that the Young's modulus and strength of C-S-H were enhanced by 52.6% and 23.3%, respectively, by the incorporation of hydroxyl groups into the GO.This came because of Ca 2+ coordination and the formation of hydrogen bonds with the hydroxyl groups of GO.The abovementioned value of 647 MPa, found by Fan et al. [35], is attributed to the strong interactions established between the O atoms of a functionalized GO sheet and the Ca 2+ ions in the tobermorite structure.
The mean coordination number of Ca 2+ ions at the interfacial region, the number of Ca 2+ -carboxylic O close contacts for each CNT, and the mean distance between Ca 2+ ions and O atoms (either in the carboxyl groups or in the silicate chains) are shown in Table 2 for all systems.As can be seen in Table 2, coordination numbers vary from 5 to 6, with the latter being the preferred one in most structures.It is well known that Ca 2+ ions in crystal structures generally bind to O atoms in ligands, with coordination numbers mostly ranging from 6 to 8 [66].Bond lengths are similar to those found in compounds with 6-fold oxygen coordination [67].In all cases, one or two of the O ligands coordinating a Ca 2+ ion belong to a carboxyl group of the CNT surface.Furthermore, the number of Ca 2+ ions that are coordinated by a carboxylic O increases with the number of carboxyl groups, as expected (right column of Table 2).This electrostatic interaction contributes, together with the H-bonds, to the strengthening of the composite interface.The structure of a 6-fold coordinated Ca 2+ at the interface between the CNT and the tobermorite matrix is shown in Figure 9 for one of the models.For the sake of clarity, some of the atoms of the structure have been removed.in Figure 9 one of the models.For the sake of clarity, some of the atoms of the structure have been removed.

Conclusions
A series of pull-out simulations of pristine and functionalized CNTs, taken from a tobermorite matrix, were carried out to study the interfacial characteristics of the resulting composites.Only non-bonded interactions were considered.The results allow for the following conclusions:

Conclusions
A series of pull-out simulations of pristine and functionalized CNTs, taken from a tobermorite matrix, were carried out to study the interfacial characteristics of the resulting composites.Only non-bonded interactions were considered.The results allow for the following conclusions:

•
ISS decreased with increasing CNT radius for pristine CNTs and depended upon the number of H-bonds for functionalized CNTs.

•
In the absence of chemical bonds between the CNT and the matrix, ISS values were positively correlated to ∆E non-bonded energy .

•
High, positive ∆E non-bonded energy values were mainly derived from the destruction of H-bonds and electrostatic Ca 2+ -O interactions, as the CNT was pulled out from the matrix.Specifically, the complete pull-out configuration was less stable than the fully embedded configuration.

•
The higher the number of carboxyl groups, the higher the ISS value, as the functionalization of CNTs with these polar groups resulted in both more H-bonds and more Ca 2+ -O interactions.

Figure 1 .
Figure 1.Schematic cell for the pull-out simulations.

Figure 1 .
Figure 1.Schematic cell for the pull-out simulations.

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Figure 4 .
Figure 4. Snapshots of the pull-out process in the CNT/tobermorite composites.

Figure 4 .
Figure 4. Snapshots of the pull-out process in the CNT/tobermorite composites.

Figure 5 .
Figure 5. Variation of total potential energy pull-out displacement.

Figure 5 .
Figure 5. of total potential energy with pull-out displacement.

Figure 6 .
Figure 6.ISS as a function of CNT diameter and number of COOH groups.

Figure 6 .
Figure 6.ISS as a function of CNT diameter and number of COOH groups.

Figure 7 .
Figure 7. ΔEnon-bonded energy as a function of CNT diameter and number of COOH groups.Figure 7. ∆E non-bonded energy as a function of CNT diameter and number of COOH groups.

Figure 7 . 13 Figure 8 .
Figure 7. ΔEnon-bonded energy as a function of CNT diameter and number of COOH groups.Figure 7. ∆E non-bonded energy as a function of CNT diameter and number of COOH groups.

Table 1 .
Geometrical characteristics of the CNTs used in the simulations.

Table 1 .
Geometrical characteristics of the CNTs used in the simulations.

2 .
Coordination number of Ca 2+ ions, mean Ca 2+ -O distance and number of Ca 2+ -carboxylic O close contacts.

Table 2 .
Coordination number of Ca 2+ ions, mean Ca 2+ -O distance and number of Ca 2+ -carboxylic O close contacts.