Interfacial load transfer mechanisms in carbon nanotube-polymer nanocomposites

Abstract

Carbon nanotubes (CNTs) are highly promising for strength reinforcement in polymer nanocomposites, but conflicting interfacial properties have been reported by single nanotube pull-out experiments. Here, we report the interfacial load transfer mechanisms during pull-out of CNTs from PMMA matrices, using massively- parallel molecular dynamics simulations. We show that the pull-out forces associated with non-bonded interactions between CNT and PMMA are generally small, and are weakly-dependent on the embedment length of the nanotube. These pull-out forces do not significantly increase with the presence of Stone Wales or vacancy defects along the nanotube. In contrast, low-density distribution of cross-links along the CNT-PMMA interface increases the pull-out forces by an order of magnitude. At each cross-linked site, mechanical unfolding and pull-out of single or pair polymer chain(s) attached to the individual cross-link bonds result in substantial interfacial strengthening and toughening, while contributing to interfacial slip between CNT and PMMA. Our interfacial shear-slip model shows that the interfacial loads are evenly-distributed among the finite number of cross-link bonds at low cross-link densities or for nanotubes with short embedment lengths. At higher cross-link densities or for nanotubes with longer embedment lengths, a no-slip zone now develops where shear-lag effects become important. Implications of these results, in the context of recent nanotube pull-out experiments, are discussed.

Keywords: carbon nanotubes; cross-link bonds; molecular dynamics; polymer nanocomposites; shear-slip.

Figure 1.

Model structure of the CNT-PMMA composite. (a) Schematic of the pull-out of a CNT embedded within a PMMA matrix subjected to applied force (F_x). (b) Close-up view of three monomer units of a PMMA polymer chain, with C, H, and O atoms coloured in grey, pink, and red, respectively. (c) Atomic configurations of a SWCNT (blue) with embedment length of L = 500 nm in a PMMA matrix (grey) at the initial stage and the ends of stages I to IV. (d) Evolution of PMMA density through stages I to IV. (Online version in colour.)

Figure 2.

Pull-out of pristine SWCNT from PMMA matrix with initial embedment lengths (L) of 100 nm (a,b) and 500 nm (c,d). Above: displacements of the front and back ends of the SWCNT with increasing pull-out force (F_x). Below: cross-sectional views of SWCNTs during the pull-out process. (Online version in colour.)

Figure 3.

Effects of non-bonded interactions on the critical pull-out forces (F_c) for (a) pristine SWCNTs of varying embedment lengths (L), and (b,c) SWCNTs with varying proportions of Stone–Wales (b) and vacancy (c) defect densities. (Online version in colour.)

Figure 4.

Pull-out of a SWCNT embedded within a PMMA matrix, subjected to F_x = 16 nN, with a single cross-link located near the middle of the L = 100 nm embedment length of the SWCNT. (a) Stretching of the various covalent bonds in the vicinity of the cross-link (bond 1), as defined by the atomic configuration in the inset; C, H, and O atoms representing the cross-linked polymer chain are coloured in grey, pink, and red, while C atoms and associated C─C bonds within the SWCNT are coloured in blue. (b) Axial force distributions along the embedment length of the SWCNT at three time instances. (Online version in colour.)

Figure 5.

Pull-out of SWCNT from PMMA matrix, with three cross-linked bonds located along the L = 300 nm embedment length, subjected to F_x = 30 nN. (a) Bond stretch of the individual cross-links over time. (b) Axial force distributions along the embedment length of the SWCNT at three time instances. (c) Close-up view of the atomic configurations at three time instances, filtered to display only the SWCNT and the cross-linked PMMA chains. (Online version in colour.)

Figure 6.

Pull-out of SWCNT from PMMA matrix, with five cross-linked bonds located along the L = 300 nm embedment length, subjected to F_x = 40 nN. (a) Bond stretch of the individual cross-links over time. (b) Axial force distributions along the embedment length of the SWCNT at three time instances. (c) Close-up view of the atomic configurations at three time instances, filtered to display only the SWCNT and the cross-linked PMMA chains. (Online version in colour.)

Figure 7.

(a) Steady-state axial force distributions along three SWCNTs of L = 500 nm embedment length: (i) five cross-links with F_x = 40 nN, (ii) five cross-links with F_x = 50 nN, and (iii) nine cross-links with F_x = 50 nN. Solid and dashed lines denote results from MD simulations and analytical interfacial shear-slip model predictions, respectively. (b) Axial stress contours within the PMMA matrix for the configurations in (a), with locations of the cross-links as marked. (c,d) Stress–strain response of bulk PMMA under uniaxial tensile deformation (c), and associated atomic configurations (d). (Online version in colour.)

Figure 8.

Interfacial shear-slip model. (a) Schematic of a three-phase shear-lag model accounting for slip along the CNT-PMMA interface. (b) Applied pull-out force (F_b) versus slip length (δ_s) for a cross-link attached to the middle (M) or the unterminated end (E) of a PMMA chain. (c,d) Close-up views of the atomic configurations of the polymer chains attached to the (M)- and (E)-type cross-links, respectively, at various slip-lengths; configurations are filtered to display only the SWCNT and the single polymer chain attached to the cross-linked bond. (Online version in colour.)

Figure 9.

Effects of bond-spacings (b_s) on the axial force (a,b) and shear stress (c,d) distributions along a SWCNT of embedment length L = 800 nm with mid-chain (M) and end-chain (E) bonded cross-links, subjected to F_x = 50 nN. Open symbols in (c,d) denote the transition from interfacial slip (right) to shear-lag behaviour (left).

Figure 10.

Effects of applied pull-out force (F_x) and bond spacing (b_s) on the slip-length (L_s) along a SWCNT of embedment length L = 800 nm with (a) mid-chain (M) and (b) end-chain (E) bonded cross-links.

Figure 11.

(a,b) Critical pull-out force (F_c) versus bond spacing (b_s) for mid-chain (M) and end-chain (E) bonded cross-links along nanotubes of varying embedment lengths (L). (c) Comparison of model predictions for nanotubes with assumed (M)-type cross-link bonds versus experimental pull-out data [2]. (d) Fracture toughness (J_c) along nanotube-PMMA interface versus bond spacing (b_s) for both (M)- and (E)-type cross-links, as denoted by solid curves; slip contribution to J_c denoted by dashed curves. (Online version in colour.)