2.1 Crystalline cellulose
Celluloses can be presented in different crystalline phases as \({I}_{\alpha }\), \({I}_{\beta }, II\) and \(II{I}_{I}\). Native plant celluloses are mixture of\({I}_{\alpha }\).and \({I}_{\beta }\). Their ratio of \({I}_{\alpha }\) to \({I}_{\beta }\) depends on original fiber sources. In wood fibers, \({I}_{ \beta }\) is a major component and adapted in this simulation work.
First, \({I}_{\beta }\) crystalline celluloses are built by using Cellulose Builder developed by Gomes and Skaf [8]. One \(\beta\)1–4 linked D-glucose unit is shown in Fig. 1.
The simulated cellulose crystal has thirty-two chains, each chain with five repeated \(\beta\) 1–4 linked D-glucose units as shown in Fig. 2. The total atom number in this crystal is 7620, which are located in a parallelepiped box with a triclinic symmetry. The basis three vectors of the simulation box are a=(x, y, z)= (31.136, 0, 0), b=( -3.7135, 32.593, 0), and c=(0, 0, 51.90), respectively, where length unit is in Angstrom. The cellulose chains are along axial c- or z-direction. During simulations, periodical boundary conditions are imposed in all the three directions.
2.2 Composite of CNT re-enforced cellulose
In order to build a CNT-cellulose composite, one of cellulose chains is removed from the crystalline cellulose solid as shown in Fig. 3 (a) and replaced by a single walled carbon nanotube with (\({n}_{1}, {n}_{2})=\)(3,3) structure as shown in Fig. 3 (b). The single walled carbon nanotube, as shown in Fig. 3. (c), has a diameter of 4.07 Angstrom, which is smaller than the size of space of the removed cellulose chain. The distance between its neighboring cellulose chains is 7.78 Angstrom. The single walled carbon nanotube is built by mapping the atoms of a 2D graphite to the surface of a cylinder. (\({n}_{1}, {n}_{2})\) denotes a particular scheme to build the nanotube from the 2D Bravais lattice of the graphite. The diameter of the carbon nanotube depends on the integer numbers of \({n}_{1}\) and \({n}_{2}\). More details can be found in White et. al. work [9]. Following their work, a carbon nanotube builder software was developed at Western Michigan University [7].
2.3 MD simulations
A open software of molecular dynamics simulation package called Lammps [10] is employed to simulate various physical properties, such as potential energy, total energy, density, hydrogen bond energy etc..
In simulations, the popular Charmm force fields [11] are adopted for cellulose. In Charmm force fields, total energy \({E}_{t}\)in the cellulose system can be presented by
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)
The first term in the right side of the equation represents the bonding energy, the second term is the energy contribution due to vibration of bonded two atoms (only Charmm force field has this term), the third term is the angular energy between two bonds, the fourth term stands for the dihedral energy, the fifth term is improper energy, the sixth term is Van der Waal nonbond potential energy, the last term is electric interaction energy. \({k}_{b}\), \({k}_{UB}\), \({k}_{a}\), \({k}_{d}\), \({k}_{i}\) are the spring coefficients of corresponding terms; \({ϵ}_{ij}\)is the depth of energy well of Lennard-Jones (LJ) potential; \({R}_{min,ij}\)is its minimum energy position; \({q}_{i}\) is the charge of atom i; \({ϵ}_{0}\) is di-electrical constant; \({r}_{0}\), \({s}_{0}\), \({\theta }_{0}\), \({{\psi }}_{0}\), and \({{\psi }}_{0}\) are corresponding equilibrium position or angles. Both the LJ and electric Coulombic forces are cut off at 12 Angstrom. From the gradient of total energy, the forces acting on each atom can be calculated. Then, based on the forces, a leap-frog algorithm is utilized to update velocities and positions of all atoms.
Carbon nanotubes have stable structure due to \(s{p}^{2}\)hydride bonds, resulting in large mechanical strength. It is evident that the Tripos 5.2 force fields [12] are suitable for description of \(s{p}^{2}\)bonds of carbon nanotube. This was verified by our previous work [7]. The Tripos 5.2 force fields are employed again for presenting carbon nanotube motion in this work.
Hydrogen bonds (H-bond) are critically important for stability of cellulose structure. The Dreiding model [13–14] is selected to track the hydrogen bonds. The distance between donor and acceptor is cut off at 4.5 Angstroms and the angle is cut off at 120 degrees in this three-body H-bond model.
In MD simulation, first, an energy minimization is imposed on all atoms, then they run in a NVT ensemble for 40000 time steps at a temperature of 298 \({K}^{0}\). Next, the system runs at a constant pressure of 1atm and at the same temperature for additional 260000 time steps, allowing the system to reach an equilibrium state. During the constant pressure run, 1atm pressure is kept in the x-, y-, and z- directions and a zero pressure is kept in the xy-, yz-, and xz-directions. The volume or density and different type of energies can be measured in the NPT time integration via Nose/Hoover algorithm [15–16]. One step time interval is 0.5 femtoseconds.