Mechanical performance of graphene/polymethyl-methacrylate nano-composites under tension loads: A coarse-grained molecular dynamic simulation
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摘要: 高强度是复合材料设计追求的重要目标，自然界中的珍珠层具有优异的力学性能，受其复杂的层次结构的启发，设计了一种石墨烯交错排布增强聚甲基丙烯酸甲酯的纳米复合材料。利用粗粒化分子动力学模拟，系统地研究了拉伸载荷作用下石墨烯的二维几何形状、层数、空间排布对纳米复合材料整体力学性能的影响。结果表明，不同几何形状的石墨烯对复合材料的增强效果有很大的差异，其中，矩形与锯齿形接近，都强于梯形石墨烯；存在最佳的石墨烯层数使复合材料的整体拉伸力学性能最强；减少石墨烯层间距离或增加重叠距离，都可提升其力学性能。总之，现有的研究结果揭示了各个因素的影响规律及微观机制，为设计具有目标性能的纳米复合材料提供了理论指导。
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关键词:
- 粗粒化分子动力学 /
- 石墨烯/聚甲基丙烯酸甲酯纳米复合材料 /
- 拉伸 /
- 几何形状 /
- 力学性能
Abstract: Strength is a important factor to consider when designing high-performance composite materials. Inspired by the excellent mechanical properties and complex hierarchical structure of nacre, a nanocomposite was designed, in which the graphene layers were interlaced in the polymethyl methacrylate matrix. Coarse-grained molecular dynamics simulations were used to investigate the effect of various geometrical variations on the mechanical properties under tension loads, including the two-dimensional geometric shapes of graphene, the number of graphene layers, the interlayer distance of the graphene sheets and the overlap length of the graphene sheets. The simulation results show that the strengthening effects of different geometries of graphenes on composites are very different, among which, the rectangle and sawtooth shapes are close to each other and are stronger than the trapezoidal graphene. There is an optimal number of graphene layers to make the composite have the strongest overall mechanical properties. The mechanical properties of graphene can be improved by reducing the interlayer distance of the graphene sheets or increasing the overlap length of the graphene sheets. Overall, this paper systematically studies the influencing factors of graphene-reinforced polymer composites and reveals the influence rules and microscopic mechanisms of each factor. This study provides a useful guidance for the design of nanocompo-sites with targeted properties. -
图 1 石墨烯/PMMA纳米复合材料分子动力学(MD)模型示意图
Figure 1. Schematic diagram of molecular dynamics (MD) model of graphene/PMMA nanocomposites
H—Distance between graphene layers; N—Number of graphene layers; LOL—Graphene overlap distance; α—Angle of model, 75°
图 2 不同石墨烯几何形状的石墨烯/PMMA纳米复合材料与纯PMMA的拉伸应力-应变曲线(a)和杨氏模量与极限强度(b)
Figure 2. Tensile stress-strain curves (a) and Young's modulus and ultimate strength (b) of graphene/PMMA nanocomposites with different graphene geometries and pure PMMA
图 3 不同石墨烯几何形状的石墨烯/PMMA纳米复合材料的拉伸变形过程((b)和(c)内的插图分别为xy平面应变为0.2和0.24的快照)
Figure 3. Tensile deformation processes of graphene/PMMA nanocomposites with different graphene geometries (Illustrations in (b) and (c) are snapshots of the xy plane when the strains are 0.2 and 0.24)
ε—Strain
图 4 PMMA链与石墨烯的相互作用能变化曲线及聚合物链的构型变化
Figure 4. Variation of the interaction energy between PMMA chain and graphene and the configurational changes of polymer chains
图 5 不同石墨烯层数的石墨烯/PMMA纳米复合材料的应力-应变曲线 (a)、杨氏模量与极限强度 (b)和z方向的密度分布 (c)
Figure 5. Tensile stress-strain curves (a), Young's modulus and ultimate strength (b) and the mass density distribution in the z direction(c) of graphene/PMMA nanocomposites with different number of graphene layers
图 6 不同石墨烯层数的石墨烯/PMMA纳米复合材料的拉伸变形过程
Figure 6. Tensile deformation processes of graphene/PMMA nanocomposites with different number of graphene layers
图 7 不同石墨烯层间距离的石墨烯/PMMA纳米复合材料的应力-应变曲线 (a) 和杨氏模量与极限强度 (b)
Figure 7. Tensile stress-strain curves (a) and Young's modulus and ultimate strength (b) of graphene/PMMA nanocomposites with different interlayer distances between graphene layers
图 8 不同石墨烯层间距离的石墨烯/PMMA纳米复合材料的拉伸变形过程
Figure 8. Tensile deformation processes of graphene/PMMA nanocomposites with different interlayer distances between graphene layers
图 9 不同石墨烯重叠距离的石墨烯/PMMA纳米复合材料的应力-应变曲线 (a)、杨氏模量和极限强度 (b)
Figure 9. Tensile stress-strain curves (a) and Young's modulus and ultimate strength (b) of graphene/PMMA nanocomposites with different overlap distances between graphene layers
图 10 不同石墨烯重叠距离的石墨烯/PMMA纳米复合材料的拉伸变形过程
Figure 10. Tensile deformation processes of graphene/PMMA nanocomposites with different overlap distances between graphene layers
图 11 石墨烯/PMMA纳米复合材料杨氏模量与石墨烯质量分数的关系
Figure 11. Variation of the Young’s modulus with the mass fraction of graphene of graphene/PMMA nanocomposites
表 1 粗粒化石墨烯势函数及参数[41]
Table 1. Functional form and parameters of the force filed for the coarse-grained graphene[41]
Potential Function Parameter Bond ${V_{{\rm{bond}}}} = {k_{\rm{b}}}{(1 - {{\rm{e}}^{ - \partial (d - {d_0})}})^2}$ ${k_{\rm{b}}} = 194.61\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}};\;\;{d_0} = 0.28\;{\rm{nm}};\;\;\partial = 0.155\;{\rm{n}}{{\rm{m}}^{ - 1}}$ Angle ${V_{ {\rm{angle} }} } = {k_{\rm{\theta } } }{(\theta - {\theta _0})^2}$ ${k_{\rm{\theta }}} = 409.40\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}};\;\;{\theta _0} = 120^\circ $ Dihedral ${V_{{\rm{dihedral}}}} = {k_\Phi }(1 - \cos (2\phi ))$ ${k_\Phi } = 4.15\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}$ Non-bonded ${V_{ {\rm{nb} } } } = 4\varepsilon \left[ { { {\left( {\dfrac{\sigma }{r} } \right)}^6} - { {\left( {\dfrac{\sigma }{r} } \right)}^{12} } } \right],\;\;r < {r_{ {\rm{cut} } } }$ $\varepsilon = 0.82\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}};\;\;{r_{{\rm{cut}}}} = 1.2\;{\rm{nm;}}\;\;\sigma = {\rm{0}}{\rm{.346\;nm}}$ Notes: Vbond, Vangle, Vdihedral and Vnb—Sum over the energies of all the bonds, angles, dihedrals, and pair-wise non-bonded interactions of the system respectively; d, θ and ϕ—Bond stretching, bond angle bending and dihedral angle torsion; kb and ∂—Depth and a parameter related to the width of the potential well of the bond respectively; d0—Equilibrium distance of the bond; kθ—Spring constant of the angle interaction; θ0—Equilibrium angle; kΦ—Spring constant of the dihedral interaction; r—Distance between two atoms; ε—Depth of the Lennard-Jones potential well for non-bonded interactions; σ—Lennard-Jones parameter associated with the equilibrium distance between two non-bonded beads; rcut—Cutoff distance of the non-bonded interactions. 
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表 2 粗粒化聚甲基丙烯酸甲酯(PMMA)势函数及参数[42]
Table 2. Functional form and parameters of the force filed for the coarse-grained polymethyl methacrylate (PMMA)[42]
Potential Function Parameters Bond ${V_{{\rm{bond}}}} = \dfrac{{{k_{\rm{d}}}}}{2}{(d - d{}_0)^2}$ ${k_{\rm{d}}} = 19461\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}} \cdot {\rm{n}}{{\rm{m}}^{ - 2}};\;\;{d_0} = 0.402\;{\rm{nm}}$ Angle ${V_{{\rm{angle}}}} = \dfrac{{{k_{\rm{\theta }}}}}{2}{(\theta - {\theta _0})^2}$ ${k_{\rm{\theta }}} = 794.89\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}} \cdot {\rm{ra}}{{\rm{d}}^{{\rm{ - 2}}}};\;\;{\theta _0} = 89.6^\circ $ Dihedral ${V_{{\rm{dihedral}}}} = \dfrac{{{k_\Phi }}}{2}(1 - \cos (2\phi ))$ ${k_\Phi } = 42.05\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}$ Non-bonded ${V_{{\rm{nb}}}} = {D_0}\left[ {{{\left( {\dfrac{{{r_0}}}{r}} \right)}^{12}} - 2{{\left( {\dfrac{{{r_0}}}{r}} \right)}^6}} \right]$ ${D_0} = 1.34\;{\rm{kcal}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}{\rm{;}}\;\;{r_0} = 0.653\;{\rm{nm}}$ Notes: kd—Spring constant of the bond length; D0 and r0—Associated with the equilibrium well depth and the equilibrium distance of the non-bonded interactions.
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