The Silylation Effect of C/SiC Nanofillers on Mechanical Properties of Cellulose Nanocomposite: Insights from Molecular Dynamics Simulations

Abstract

Silylation treatment improves the hydrophobicity of cellulose by reducing the number of hydroxyl groups in the cellulose chains that are available to react with moisture in the surrounding environment. Additionally, silylation increases stress transfer from cellulose to synthetic nanofillers by forming covalent bonds between the hydroxyl groups of cellulose and the oxidized surface of these nanofillers. This study investigates the impact of silane coupling agents on the tensile properties of cellulose nanocomposites. The cellulose nanocomposites are reinforced with four types of C/SiC-based nanofillers: carbon nanotubes, graphene nanoplatelets, silicon carbide nanotubes, and silicon carbide nanoplatelets. Subsequently, the nanofillers are subjected to surface treatment using the silane coupling agent KH550. The mechanical properties of the cellulose nanocomposites are evaluated by molecular dynamics simulations based on the polymer’s consistent forcefield. The results indicate that the reinforcements of silylated silicon carbide nanotubes and carbon nanotubes increase the tensile modulus of cellulose by 18.03% and 24.58%, respectively, compared to their untreated counterparts. Furthermore, the application of silylation treatment on the surface of C/SiC nanofillers increases the yield strength and ultimate tensile strength of cellulose nanocomposites due to enhanced load transfer between cellulose and these reinforcements.

1. Introduction

Globally, there have been alarming ecological concerns about the implementation of synthetic materials in the fabrication of industrial products, especially those used in indispensable structures such as airplane wings and wind turbine blades. Hence, the employment of sustainable materials and their composites, especially novel natural composites, has received considerable attention [1]. Cellulose is a biodegradable, abundant, and freely available polymer with competitive stiffness and strength properties. Therefore, cellulose can be used as a host matrix and reinforcement to fabricate different types of mechanically high-performance nanocomposites. For instance, cellulose nanofibers at 11.70 weight fractions (wt.%) increase the storage modulus of bioepoxy by 70% [2,3]. However, cellulose has lower moisture resistance because of hydroxyl groups in its chemical structure, which restricts its implementation in structural applications. The moisture content of cellulose is critical to the performance of materials reinforced with plant fibers, since it can reduce the interfacial bonding at the fiber–matrix interface and lead to random porosity that affects the overall strength of the cellulose composite [4]. The unwanted effect of moisture absorption in cellulose can be improved by using additives such as coupling agents and hybridization with other hydrophobic nanofillers. The surface functionalization of cellulose-derived reinforcements using chemical treatments such as silylation improves their dispersion in the polymer matrix, leading to a remarkable increase in the tensile strength and modulus of the resulting composite [5].

Graphene oxide (GO) nanofillers interact with raw cellulose at the interface through hydrogen bonds and van der Waals interactions [6]. The stress transfer efficiency at the interface between cellulose and graphene is determined to be 66% [7]. Although the efficiency of stress transfer at the interface is moderate, reinforcing cellulose with GO nanosheets at a 0.27 volume fraction (vol.%) improves tensile strength and elongation at break by 120% and three times, respectively, compared to their corresponding values of neat cellulose [8]. Pristine carbon nanotubes (CNTs) improve the electrical and mechanical properties of crystalline and amorphous cellulose without reducing their tensile strength [9,10,11]. The application of silane coupling agents on the surface of carbon and silicon carbide (C/SiC)-based nanofillers improves their adhesion to cellulose. For instance, vinyltrimethoxysilane is implemented to form covalent bonds between GO nanofillers and cellulose, which significantly improves the hydrophobicity and mechanical properties of the treated composite [12]. SiC reinforcements can be either used alone or combined with graphene-based materials to synthesize nanocomposites suitable for aerospace applications. The biocompatibility of SiC in various forms of composites, particularly those fabricated from cellulose, has rarely been investigated in recently published research, even though there is a broad scope for such studies on SiC [13]. Applying chemical functionalization on the surface of silicon carbide nanotubes (SiCNTs) would further improve the amount of stress transferred from the polymer matrix [14]. Therefore, the silylation of raw cellulose and reinforcement with CNTs and SiCNTs are frequent methods used to improve the mechanical properties of cellulose [15,16,17].

Molecular dynamics (MD) simulations have been used previously to investigate the properties of raw CNTs inserted inside a $I_{\beta }$ cellulose nanocrystal [9]. However, recently published research does not address the mechanical properties of amorphous and semi-crystalline cellulose reinforced with KH550 silane-treated C/SiC nanofillers. In this study, silylated C/SiC nanofillers are used to improve the tensile strength and modulus of amorphous cellulose. Computational models based on MD simulation are developed for silylated single-walled carbon nanotubes (S-SWCNTs), silylated single-layered graphene nanoplatelets (S-SLGNPs), silylated single-walled silicon carbide nanotubes (S-SWSiCNTs), and silylated single-layered silicon carbide nanoplatelets (S-SLSiCNPs) cross-linked with the cellulose chains.

The content of this paper is arranged in four parts. The details of the main elements used to assemble the cellulose-derived composites are provided in Section 2, including the introduction of the methods of molecular modeling performed. Then, the effect of silylated C/SiC nanofillers on improving the tensile properties of cellulose is discussed in Section 3. The main findings of this paper are summarized in Section 4.

2. Materials and Methods

Molecular modeling constitutes a powerful approach to characterizing the impact of silylated C/SiC-derived nanofillers on the tensile properties of cellulose. Details on the type of forcefield and ensembles used for the equilibrium of the MD models and the characterization of stress–strain behavior are discussed in Section 2.1. Then, the details of the silylation process of C/SiC nanofillers are discussed in Section 2.2. After that, the four main forms of C/SiC-derived nanofillers of SWCNTs, SLGNPs, SWSiCNTs, and SLSiCNPs are compared in terms of the highest improvement that can be achieved in the tensile strength and modulus of raw cellulose. The stress–strain behavior for raw cellulose is selected as a baseline to evaluate the improvements in the tensile properties of cellulose attained from using C/SiC nanofillers.

2.1. Molecular Dynamics Simulation

The open-source software of the large-scale atomic/molecular massively parallel simulator (LAMMPS) is used for molecular dynamics simulation [18]. The polymer consistent forcefield (PCFF) and its addendum (PCFF+) retrieved from MedeA software 3.6.1 [19] are implemented to describe the bond and non-bond interactions in cellulose and silylated nanofillers based on parameters evaluated by ab initio calculations. The valence forcefield of PCFF/PCFF+ contains predefined bonds, angles, and torsions for organic and inorganic materials, including silicon. However, the PCFF/PCFF+ can not be used to describe the breaking of nanocovalent bonds between atoms taking place under the tensile load.

Different methods can be used to determine the mechanical properties of molecular systems, such as evaluating the tangent modulus from the stress–strain curve and using the elastic constants. The mechanical properties of the nanocomposites are calculated using the Voigt model based on the elastic constant matrix. The elastic constants can be determined by deforming the unit cell. The deformation of the cell is achieved by changing the Bravais lattice vectors B = (a, b, c) of the reference unit cell to $\stackrel{`}{B}$ = ($\stackrel{`}{a}$, $\stackrel{`}{b}$, $\stackrel{`}{c}$) using the engineering strain matrix:

$$\begin{array}{c}\hfill \stackrel{`}{B}=B\left(\begin{array}{ccc}1+e_{xx}& {\displaystyle \frac{1}{2}}{e}_{xy}& {\displaystyle \frac{1}{2}}{e}_{xz}\\ {\displaystyle \frac{1}{2}}{e}_{yx}& 1+e_{yy}& {\displaystyle \frac{1}{2}}{e}_{yz}\\ {\displaystyle \frac{1}{2}}{e}_{zx}& {\displaystyle \frac{1}{2}}{e}_{zy}& 1+e_{zz}\end{array}\right)\end{array}$$

(1)

The total energy of the lattice is changed due to deformation as follows:

$$\begin{array}{c}\hfill U={\displaystyle \frac{H_{tot}-H_o}{V_o}}={\displaystyle \frac{1}{2}}{\displaystyle \sum _{i=1}^6}{\displaystyle \sum _{j=1}^6}{C}_{ij}{e}_i{e}_j\end{array}$$

(2)

where $H_o$ is the total energy of the unstrained lattice, $V_o$ is the volume of the reference cell, and $C_{ij}$ are the elements of the elastic constant matrix. There are three independent elastic constants for cubic molecular systems: $C_{11}$, $C_{12}$, and $C_{44}$. If the engineering strain is applied along the X direction only, the $C_{11}$ can be determined by Equation (2) as $U=C_{11}{\displaystyle \frac{e^2}{2}}$. If the shear strain field is applied only to the unit cell $e_{zy}$ = $e_{yz}$ = ${\displaystyle \frac{e}{2}}$, while all other strain components are set to zero, the $C_{44}$ can be evaluated as $U=C_{44}{\displaystyle \frac{e^2}{2}}$. The bulk modulus (K) is determined by applying the strain field in all directions ($e_{xx}=e_{yy}=e_{zz}=e$) as $U=K{\displaystyle \frac{e^2}{2}}$. Then, the value of bulk modulus is used to determine the $C_{12}$ as $K={\displaystyle \frac{1}{3}}\left(C_{11}+2C_{12}\right)$. The values of shear modulus, Young’s modulus, and Poisson’s ratio based on the Voigt model can be evaluated using Equations (3)–(5), respectively [20,21].

$$\begin{array}{c}\hfill G={\displaystyle \frac{1}{5}}\left(C_{11}-C_{12}+3C_{44}\right)\end{array}$$

(3)

$$\begin{array}{c}\hfill E={\displaystyle \frac{9K}{1+\frac{3K}{G}}}\end{array}$$

(4)

$$\begin{array}{c}\hfill \nu ={\displaystyle \frac{1}{2}}{\displaystyle \frac{K-\frac{2}{3}G}{2K+\frac{1}{3}G}}\end{array}$$

(5)

The mechanical properties for SWCNTs (12,12), SWSiCNTs (12, 12), raw cellulose, and cellulose/5.40 wt.% SLGNP nanocomposites are evaluated to verify the capability of the PCFF/PCFF+ forcefield in predicting the mechanical properties of cellulose nanocomposites considered in this study. The SWCNTs and SWSiCNTs are not isolated and are placed inside cells with periodic boundary conditions in all directions. Therefore, the evaluated mechanical properties are close to those of carbon and silicon carbide nanoropes. The tensile modulus of SWCNT and SWSiCNT nanofillers in the longitudinal direction are evaluated from their stress–strain responses under tensile load, and the results are listed in

Table 1. The elastic modulus (GPa) values of CNTs and SiCNTs and their corresponding values in the literature.

Material	PCFF	Reference
CNTs (12,12)	535.47	270–950 [22]
SiCNTs (12,12)	399.42	400 [23]

.

The tensile modulus of SWCNTs can be evaluated based on the elastic constants. The cells of standalone CNTs have transversely isotropic properties since the nanotubes are aligned along the longitudinal direction, precisely, $E_2$ = $E_3$<$E_1$. By aligning CNTs along the Z-axis, their Young’s modulus can be evaluated based on the $C_{33}$ elastic constant as follows:

$$\begin{array}{c}\hfill E_{33}={\displaystyle \frac{\left(1+{\nu }_{12}\right)\left(1-{\nu }_{12}-2{\nu }_{13}{\nu }_{31}\right)}{1-{\nu }_{12}^2}}·C_{33}\end{array}$$

(6)

where ${\nu }_{13}={\nu }_{23}$ and ${\nu }_{32}={\nu }_{31}$ are the Poisson’s ratios in the planes of the longitudinal section, i.e., $x_1{x}_2$ and $x_1{x}_3$; ${\nu }_{12}$ is the Poisson’s ratio in the transverse sectional plane ($x_1{x}_2$). Natural materials such as cellulose have anisotropic properties that depend on direction. When the Poisson’s ratio at different planes is unknown, it is valid to assume that the Poisson’s ratio is isotropic [24]. The values of Young’s modulus for CNTs at various chiral indices are evaluated based on the $C_{33}$ elastic constant retrieved from LAMMPS simulations using Equation (6), and the results are compared with previously published results listed in

Table 2. The elastic modulus values of armchair CNTs with their corresponding values in the literature.

Chiral Index (n, m)	Elastic Constant C33 (GPa)	Poisson’s Ratio, $\mathit{\nu }$	Elastic Modulus, E33 (GPa)		Error %
			PCFF	Reference [25]
10, 10	561.71	0.1608	527.10	519	1.56
12, 12	513.04	0.2276	444.22	440	0.96
16, 16	420.68	0.2371	358.68	360	0.37
20, 20	363.70	0.2714	290.16	317	8.47

.

The values of stress–strain for raw cellulose and cellulose/5.4 wt.% SLGNP nanocomposites retrieved from MD simulations are in good agreement with their corresponding values in the published literature, as shown in Figure 1. Based on the results of the MD simulation used to evaluate the mechanical properties of the SWCNT, SWSiCNT, raw cellulose, and raw cellulose reinforced with 5.40 wt.% SLGNP, the PCFF/PCFF+ forcefield can effectively predict the tensile strength and modulus of these materials with good accuracy. Furthermore, PCFF was used to predict the properties of polymer nanocomposites reinforced with SiC nanoparticles [26]. Therefore, PCFF/PCFF+ is combined with the TIP4P/2005 water model [27] to perform MD simulations.

The molecular modeling is conducted using the Schrödinger software 2021-2 [28]. All molecular models have a constant initial density of 0.30 g/cm³ and each molecular model has six replicates. The final density of cellulose molecular models can be attained using the PCFF/PCFF+ forcefield based on the equilibrium protocol clarified in Figure 2. The equilibrium protocol followed in this study contains two stages to eliminate the voids from the simulation cell. At the end of the first stage, the hydrolyzed KH550 silane molecules at the surface of nanofillers are cross-linked with the hydroxyl group (-OH) at the cellulose chains. Then, the voids in the cells of cross-linked models are eliminated using stage II of the equilibrium protocol.

The potential energy of the molecular systems is minimized using the conjugate gradient method [29]. The initial minimization stage’s energy and force tolerances, maximum iterations, and force evaluations are set to 0.0, $1\times {10}^{-4}$, 10,000, and 15,000, respectively. The tensile stress–strain curves are evaluated under volume–conserving uniaxial strain at room temperature (300 K) by running nonequilibrium MD simulations based on PCFF/PCFF+ forcefield in the NVT ensemble using the Nose–Hoover thermostat. The simulation cell is elongated in the longitudinal direction in small increments of $\Delta$${\epsilon }_l$ = 0.002 at every time step. The time duration for each nonequilibrium NVT ensemble is 5.0 picoseconds with a time step size $\Delta$t of 0.5 femtoseconds.

Figure 1. The tensile stress–strain responses of raw cellulose and cellulose/5.40 wt.% SLGNP nanocomposite evaluated based on the PCFF/PCFF+ forcefield (H: white; O: red; C: green for cellulose and black for SLGNP). (a) Raw cellulose; (b) raw cellulose reinforced with 5.40 wt.% of SLGNP; (c) the stress–strain response of raw cellulose and its corresponding response in the literature [30]; (d) the stress–strain response of cellulose/5.40 wt.% SLGNP and its corresponding response in the literature [31].

Figure 1. The tensile stress–strain responses of raw cellulose and cellulose/5.40 wt.% SLGNP nanocomposite evaluated based on the PCFF/PCFF+ forcefield (H: white; O: red; C: green for cellulose and black for SLGNP). (a) Raw cellulose; (b) raw cellulose reinforced with 5.40 wt.% of SLGNP; (c) the stress–strain response of raw cellulose and its corresponding response in the literature [30]; (d) the stress–strain response of cellulose/5.40 wt.% SLGNP and its corresponding response in the literature [31].

Figure 2. Simulation workflow protocol used for the equilibrium of cellulose models.

Figure 2. Simulation workflow protocol used for the equilibrium of cellulose models.

2.2. Reinforcing Cellulose with Silylated C/SiC Nanofillers

There are four critical aspects of nanofillers affecting their capability to improve the tensile properties of cellulose nanocomposites: (a) the atomic weight fraction of the nanofiller in the matrix (affecting stiffness), (b) the interfacial physical interlocking and the number of nanocovalent bonds with cellulose chains (affecting strength), (c) the surface area of the nanofiller that is determined by its dimensions (affecting strength), and (d) the intrinsic material properties of the nanofiller itself, whether it is composed of pure carbon or silicon carbide (affecting strength and stiffness). Based on these characteristics, silylated C/SiC-derived nanofillers with sufficient aspect ratios shown in Figure 3 are designed to improve the tensile properties of cellulose. Both the SWCNT and SWSiCNT have armchair structures. The bond length between two silicon atoms is 1.798 Å, while the bond length for two carbon atoms is 1.418 Å [32].

The KH550 is selected from various silane coupling agents to modify the surface of C/SiC nanofillers since it forms more hydrogen bonds in the molecular systems of cellulose nanocomposites. Particularly, the amino groups in KH550 form many hydrogen bonds with cellulose chains, improving the interaction energy between cellulose and C/SiC nanofillers [33]. The KH550 silane coupling agent, with a total number of 24, is applied to cover the whole surface area of C/SiC-based nanofillers to facilitate the cross-linking process between these reinforcements and neighboring cellulose chains. Two unlinked KH550 silane agents are removed from the surface of C/SiC nanofillers after finishing the cross-linking process to enhance the plasticity of cellulose nanocomposites. The technical specifications for C/SiC nanofillers used to reinforce cellulose, including their size (length (l), width (w), and diameter (d)) and molecular formulas, are listed in

Table 3. The technical specifications of C/SiC nanofillers.

Nanofiller	Molecular Formula	Dimensions (Å)
Raw SWCNT (3,3)	C246H12	l = 50.93
Silylated SWCNT (3,3)	Si24C318N24O72H252	d = 5.02
Raw SLGNP	C264H58	l = 51.84
Silylated SLGNP	Si24C336N24O72H298	w = 14.19
Raw SWSiCNT (3,3)	Si123C123H12	l = 64.09
Silylated SWSiCNT (3,3)	Si147C195N24O72H252	d = 6.10
Raw SLSiCNP	Si132C132H58	l = 65.13
Silylated SLSiCNP	Si156C204N24O72H298	w = 17.48

.

The cellulose used in this study to build the molecular systems is not completely amorphous and includes a large proportion of crystalline regions in its structure. Hence, the cellulose chains are generated with a backbone dihedral of 180° with a polymerization degree of 10. Then, the cellulose chains are packed similarly to the ones shown in Figure 1a. After applying the equilibrium protocol to the packed chains, the cellulose chains include amorphous and crystalline regions. The amorphous region exhibits irregular molecular arrangements with large voids, whereas the crystalline region displays tightly and neatly arranged molecules. There is no clear division between the crystalline and amorphous regions in the cellulose chains, and it is a gradual transition state [34].

Silylation treatment can be applied to a cellulose matrix and C/SiC nanofillers. The silylation process increases the void space in the cellulose matrix. The void space induced by silylation is used to improve the adhesion between natural fibers and petroleum–derived matrices such as epoxy when the synthetic polymer fills these voids at the surface of silylated natural fiber. The hydrolyzed silane coupling agents of KH550 are cross-linked with the hydroxyl groups of the cellulose chains, according to the silylation process clarified in [35], to form silylated cellulose shown in Figure 4.

In this study, the silane coupling agents are used to functionalize the surface of C/SiC nanofillers without altering the chemical structure of cellulose. The silylation treatment at a concentration of 22 silanol molecules is applied to the surface of C/SiC nanofillers to improve the interfacial adhesion of these nanofillers with cellulose. The highly reactive silanols are generated by the hydrolysis of the ethoxy groups of (3-Aminopropyl)tiethoxysilane. Then, the silanols are used to form covalent bonds with the cellulose chains and the oxidized surface of C/SiC nanofillers upon the application of heat [36,37]. The cellulose chains are linked to the silylated C/SiC nanofillers according to the process shown in Figure 4. The total number of cross-linking bonds between cellulose and silylated C/SiC nanofillers is fixed at 22 in all cases of cellulose nanocomposites. The exact molecular formulas of cellulose nanocomposites, the composition of their matrices, and the atomic weight fraction (wt.%) of C/SiC nanofillers that are used to modify these materials are clarified in

Table 4. The technical specifications of cellulose nanomaterials.

Material	Molecular Formula	Matrix Composition	Loading of Nanofiller (wt.%)
Raw cellulose	C1200O1000H2040		-
Raw cellulose/SWCNT	C1446O1000H2052		8.40
Raw cellulose/S-SWCNT	Si22C1512N22O1044H2228		16.10 (7.70 1)
Raw cellulose/SLGNP	C1464O1000H2098		9.00
Raw cellulose/S-SLGNP	Si22C1530N22O1044H2274	Cellulose: 20	16.70 (8.30 1)
Raw cellulose/SWSiCNT	Si123C1323O1000H2052		13.20
Raw cellulose/S-SWSiCNT	Si145C1389N22O1044H2228		20.20 (12.20 1)
Raw cellulose/SLSiCNP	Si132C1332O1000H2098		14.10
Raw cellulose/S-SLSiCNP	Si154C1398N22O1044H2274		21.00 (13.10 1)

¹ These values do not include the weight fractions of KH550.

.

The effect of the silane coupling agent KH550 on the mechanical performance of cellulose nanocomposites reinforced by silylated C/SiC nanofillers can be realized by comparing their tensile strength and modulus properties with their untreated counterparts. Figure 5 and Figure 6 show untreated amorphous cellulose reinforced by raw and silylated C/SiC nanofillers, respectively. The SWCNT has a high aspect ratio and excellent intrinsic material properties compared to other nanofillers.

3. Results and Discussion

Based on the results of the MD simulation, the S-SWCNT has the highest improvement effect on the stiffness and tensile strength of raw and silylated cellulose compared to other C/SiC nanofillers. The S-SLGNP introduces moderate improvements in the tensile strength and modulus since it has a lower aspect ratio compared to the S-SWCNT. The enhancements to the mechanical properties of cellulose attained from implementing the SiC nanofillers of S-SWSiCNT and S-SLSiCNP are lower compared to their carbon-based counterparts since the intrinsic properties of SiC are lower than those of carbon. The strengthening function of the S-SWCNT and other C/SiC nanofillers is analyzed in Section 3.

The Structural Reinforcing Effect of Silylated C/SiC Nanofillers

The currently available treatments to improve the hydrophobicity of cellulose depend on physical and chemical treatments such as oven drying, alkalization, and silylation. However, these methods inherently affect the tensile and stiffness properties as they alter the naturally porous structure of the cellulose. The MD simulation results of this study show that combining chemical treatments such as silylation with C/SiC nanofillers characterized by high mechanical performance can effectively eliminate the undesired impact of moisture on the amorphous cellulose. Some published studies tried to improve the mechanical properties of raw amorphous cellulose by using raw CNTs and stacked GNPs. However, they could not further improve the elastic modulus. The raw CNT increases the void space among the cellulose chains without effectively transferring load between them, whereas the raw multi-layered GNP is agglomerated, acting as a crack initiation site inside the cellulose structure.

Figure 7 and Figure 8 show the pristine and silylated C/SiC nanofillers within the cellulose nanocomposites, respectively, at the fracture point under the tensile load. It can be inferred from Figure 7a that the pristine SWCNT is damaged completely under the tensile load, indicating that there is poor stress transfer at the interfacial region with the cellulose matrix. The tensile failure of cellulose/raw SWCNT starts with sliding of cellulose chains, and then complete failure is noticed after the fracture of the raw SWCNT. The cellulose nanocomposite can effectively withstand the tensile load after the application of the silylation treatment on the surface of the SWCNT, as shown in Figure 8a. The S-SWCNT has a lower amount of damage compared to its pristine counterpart due to the improved level of stress transfer with the cellulose matrix. The results of MD simulation, which are clarified in Figure 7c,d and Figure 8c,d, demonstrate that the SiC-derived nanofillers of the SWSiCNT and SLSiCNP have higher values of failure strain relative to their carbon-derived counterparts of the SWCNT and SLGNP.

When the tensile load is applied to a pure cellulose structure, the amorphous region attenuates the damaging effect of the applied load through the stretching of cellulose chains, specifically, the deformation of bond lengths and bond angles, without breakage of the molecular chains. Cellulose fails under tensile load because some cellulose chains in the crystal structure slide and rearrange [34]. The cellulose nanocomposites reinforced with pristine C/SiC nanofillers have high toughness but low strength (sliding of the cellulose chains is the failure mechanism since the strength is much lower than the ultimate strength of C/SiC nanofillers). The cellulose nanocomposites reinforced with SWCNTs are stiff, strong, and tough. The raw SWCNT has high stiffness and strength but low interfacial strength, and hence, the cellulose/SWCNT nanocomposite has high toughness but low strength. On the contrary, the neat cellulose has higher interfacial strength compared to the SWCNT but lower stiffness and strength. The nanocovalent bonds between cellulose and silylated C/SiC nanofillers change their tensile failure from more ductile to more brittle. This shift can be attributed to the breaking of cellulose chains leads to a considerable reduction in the load-bearing of cellulose. Additionally, the inter-chain hydrogen bonds among the cellulose chains induce lateral pressure on the C/SiC nanofillers, which mitigates the strain to failure of cellulose nanocomposites considerably [38].

The mechanical properties listed in

Table 5. Mechanical properties of cellulose nanocomposites.

Material	Elasticity (GPa)	Shear Modulus (GPa)	Poisson’s Ratio	Density (g/mL)
Raw cellulose	10.1167	4.0050	0.2636	1.3781
Raw cellulose/SWCNT	12.1183	4.7667	0.2706	1.4192
Raw cellulose/SLGNP	11.8017	4.6150	0.2786	1.4221
Raw cellulose/SWSiCNT	11.5917	4.5383	0.2772	1.4144
Raw cellulose/SLSiCNP	11.3083	4.4483	0.2715	1.4168
Raw cellulose/S-SWCNT	15.0967	6.0233	0.2530	1.4257
Raw cellulose/S-SLGNP	14.0367	5.6133	0.2510	1.3933
Raw cellulose/S-SWSiCNT	13.6817	5.4883	0.2472	1.3974
Raw cellulose/S-SLSiCNP	13.0150	5.2117	0.2486	1.3882

show that the silylated C/SiC nanofillers significantly improve the tensile and shear moduli of raw cellulose. The untreated C/SiC nanofillers have a minor effect on the elastic modulus due to poor stress transfer at the interface between these nanofillers and cellulose, which agrees with the findings of previous research proving the poor interaction between synthetic nanofillers and cellulose [39]. The reviewed literature indicates that the hybrid membrane of cellulose cross-linked with GO through vinyltrimethoxysilane exhibits enhanced mechanical properties, excellent hydrophobicity, and good thermal stability. The silylated GO at a concentration of 3 w/w% increases the elastic modulus of the cellulose membrane by 47.38.% [12].

The raw cellulose nanocomposites reinforced with SWCNTs have the highest tensile strength values compared to other nanocomposites, as can be concluded from Figure 9a. This behavior can be justified by the high aspect ratio of the SWCNT compared to that of the SLGNP, in addition to the high intrinsic material properties of the SWCNT relative to those of SiC-derived nanofillers. The silane coupling agent of KH550 improves the stress transfer between cellulose and C/SiC nanofillers. The raw cellulose nanocomposites reinforced with silylated C/SiC nanofillers have higher tensile strength and modulus relative to their counterparts reinforced with untreated nanofillers, as can be inferred from the values listed in Table 5 and the stress–strain responses clarified in Figure 9. Moreover, the elastic modulus of raw cellulose reinforced with SWCNTs increases from 12.1183 GPa to 15.0967 GPa after the application of silylation treatment, while it increases the elasticity of raw cellulose reinforced with SWSiCNTs from 11.5917 GPa to 13.6817 GPa.

The raw C/SiC nanofillers improve the tensile properties of cellulose. The cellulose nanocomposite reinforced with raw C/SiC exhibits higher ductility compared to neat cellulose, leading to enhanced tensile toughness. The fracture mechanism for cellulose nanocomposites reinforced with C/SiC nanofillers changes from only hydrogen bond breakage for neat cellulose to C/SiC nanofiller pulling and hydrogen bond breakage between cellulose and these nanofillers. The significant improvements attained in the tensile modulus, strength, and toughness of cellulose nanocomposites reinforced with the raw SWCNT and SLGNP can be justified because of the uniform dispersion of these nanofillers in the cellulose matrix with minimal possible porosity. In this study, the cellulose is reinforced with a raw SWCNT at 8.40 wt.%, which is well below the critical value determined from previous studies where the CNT agglomerates start to form at the loading range of 10.20–11.60 wt.%. Previously published research reports that reinforcing cellulose with raw 10.20–11.60 wt.% CNTs increases its tensile modulus from 3.89 GPa to 6.26 GPa and its strength from 113.60 MPa to 179.70 MPa. Increasing the content of raw CNTs to 20.10 wt.% decreases the tensile modulus and strength values to 5.46 GPa and 143 MPa, respectively. Untreated CNTs have a high tendency to form more bundles/aggregates at high loadings exceeding 11.60 wt.%, and the voids among the CNTs could not be completely filled by cellulose, leading to an overall reduction in the mechanical properties [40]. Referring to the elastic modulus values listed in Table 5, the pristine SWCNT at 8.40 wt.% introduces the highest improvement on the elasticity of raw cellulose relative to other untreated C/SiC nanofillers, increasing its value from 10.12 GPa to 12.12 GPa. The reported experimental value in the literature for the elasticity of cellulose nanocomposite reinforced with 10 wt.% of SWCNTs is around 11.80 GPa, indicating that the samples of cellulose/SWCNTs prepared for experimental characterization of elasticity contain a small proportion of SWCNT agglomerates and porosity, which adversely affect the stress transfer at the interface between raw SWCNTs and cellulose. The failure strain for cellulose nanocomposites containing raw SWCNTs is in the range between 7 and 8%, which agrees well with the previously reported value in the literature of 7 ± 0.80% [41].

4. Conclusions

Chemical treatments such as silylation are applied to raw cellulose to improve its hydrophobic aspects. We use nanofillers with competitive material properties, such as SWCNTs, SLGNPs, SWSiCNTs, and SLSiCNPs, along with silylation treatment to enhance the elasticity of amorphous cellulose. The improvements attained in the tensile properties of cellulose are primarily affected by the characteristics of nanofillers, such as their intrinsic material properties and the aspect ratios of their shapes. The application of silylation treatment on the surface of a raw SWCNT increases its weight fraction in the raw cellulose matrix from 8.40 wt.% to 16.10 wt.% due to the additional weight fraction attained from the silane coupling agent KH550. The S-SWCNT at 16.10 wt.% can significantly improve the stiffness of raw cellulose by 49.23% since this reinforcement has a high aspect ratio, excellent intrinsic material properties with an adequate atomic weight fraction in the cellulose, and optimum interfacial adhesion with cellulose through the nanocovalent bonds formed by the silane coupling agent KH550. The silylation treatment enhances the elastic modulus of raw cellulose nanocomposites reinforced with SLSiCNPs and SWSiCNTs by 15.09% and 18.03%, respectively, relative to their untreated counterparts.

The published research lacks experimental studies characterizing the relationship between the various concentrations of silane coupling agent (KH550) applied on the surface of C/SiC nanofillers and the mechanical properties of cellulose nanocomposites. The current simulation study can serve as a reference for comparison with outcomes of such future studies.