The nine types of flexible polymers considered were PE, PP, poly(acrylonitrile) (PAN), PMMA, PS, poly(ethylene oxide) (PEO), poly(*l*-lactide) (PLLA), poly(caprolactone) (PCL) and nylon 6. The polymers were all built in a head-to-tail and isotactic configuration, and there were 20 monomers in each chain of the polymers. Although the number of atoms of these polymers was <10^{4}, we still considered them as polymers in this paper. They can be regarded as small parts of the corresponding “long” polymers, and their interactions with GNS and with themselves can be exploited to understand the primary behaviors of the long polymers. Because the longest chain was 174.49 Å, we used the GNS, whose length was 178.96 Å. Carbon atoms at the edges of the GNS were saturated with hydrogen atoms to make the whole GNS segment neutral and to enhance the stability of GNS (20).

MD simulations were carried out with the Discover module in Accelrys Materials Studio v. 3.2 (Accelrys Software, Inc., San Diego, CA, USA) and the atomic force field was chosen using the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) (21). The COMPASS force field has been successfully used in the investigation of organic and inorganic materials (22–24). We used the COMPASS forced field to simulate the interactions between PE/PP/PS/PPA/PPV and SWCNTs (8).

The force field potential can be represented as follows (25):

$${E}_{\text{total}}={E}_{\text{valence}}+{E}_{\text{cross-term}}+{E}_{\text{nonbond}}\text{\hspace{1em}(1)}$$(1)

where *E*_{valence} is the valence energy, *E*_{cross-term} is the cross-term interaction and *E*_{nonbond} is the nonbond interaction energy. For the polymer and carbon-based composites, many MD simulations (26, 27) were performed at the 400–500 K range because crystallization behavior occurs in that range. Therefore, we performed MD simulations for 1000 ps at 450 K, where the molecules can change their conformation rapidly. The polymer/graphene systems used the nonperiodic boundary condition. All the simulations were carried out in the NVT ensemble, and the time step was 1 fs. The Andersen algorithm was used for temperature control (28, 29).

The considered interaction energy in the present paper was the nonbond interaction energy including vdW and EI interactions. They can be calculated using the following equation:

$${E}_{\text{vdW}}={\displaystyle \sum _{i>j}\mathrm{(}\frac{{A}_{ij}}{{r}_{ij}{}^{9}}\text{-}\frac{{B}_{ij}}{{r}_{ij}{}^{6}}\mathrm{)}}\text{\hspace{1em}(2)}$$(2)

$${E}_{\text{EI}}={\displaystyle \sum _{i>j}\frac{{q}_{i}{q}_{j}}{\epsilon {r}_{ij}}}\text{\hspace{1em}(3)}$$(3)

where *A*_{ij}*,* and *B*_{ij} are the system-dependent parameters implemented in Accelrys Materials Studio, *r*_{ij} is the *i*–*j* atomic separation distance, *q* is the atomic charge and *ε* is the dielectric constant. The switching function was used to smoothly turn off non-bond interactions over a range of distances to avoid the discontinuities caused by direct cut-offs. The switching function *S*(*r*) can be represented as

$$\text{When}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{r}_{ij}={R}_{\text{S}},\text{\hspace{1em}}S\mathrm{(}r\mathrm{)}=1$$

$$\text{When}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{R}_{\text{S}}\le {r}_{ij}\le {R}_{\text{C}},\text{\hspace{1em}}S\mathrm{(}r\mathrm{)}=\frac{{\mathrm{(}{R}_{\text{C}}\text{-}r\mathrm{)}}^{2}\mathrm{(}{R}_{\text{C}}{}^{2}+2r\text{-}3{R}_{\text{S}}\mathrm{)}}{{\mathrm{(}{R}_{\text{C}}\text{-}{R}_{\text{S}}\mathrm{)}}^{3}}$$

$$\text{When}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{r}_{ij}={R}_{\text{S}},\text{\hspace{1em}}S\mathrm{(}r\mathrm{)}=0,$$

where *R*_{S} is the cut-off distance, *R*_{C} is the sum of the cut-off distance and the spline width, and *r*_{ij} is the *i*–*j* atomic separation distance.

However, the nonbond interaction between two groups cannot be calculated with the Discover module directly because it was for the two groups and excluded the nonbond energy of the atoms in each group itself. Using the parameters in the literature that described the COMPASS forced field in detail (21), we developed a Fortran code to calculate the vdW and EI energies. It should be noted that our code cannot perform dynamics calculation. All the dynamics calculations were carried out with the Discover module, and the coordinates, atomic types and charges used in the code were read from a text-format file, which was transferred from the trajectory file of Accelrys Materials Studio. In the code, our algorithm works by calculating a pair of vdW or EI energy using the information from two atoms, which are from different groups. Therefore, the vdW and EI energy between atoms in one group were not included.

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