CNT

Research Article Cite This: ACS Appl. Mater. Interfaces 2018, 10, 1017−1027

www.acsami.org

Nanoscale Structure−Property Relationships of Polyacrylonitrile/CNT Composites as a Function of Polymer Crystallinity and CNT Diameter Jacob R. Gissinger,† Chandrani Pramanik,† Bradley Newcomb,‡ Satish Kumar,‡ and Hendrik Heinz*,† †

Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, United States School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States

‡

Downloaded via KAOHSIUNG MEDICAL UNIV on July 9, 2018 at 13:28:35 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Polyacrylonitrile (PAN)/carbon nanotube (CNT) composites are used as precursors for ultrastrong and lightweight carbon fibers. However, insights into the structure at the nanoscale and the relationships to mechanical and thermal properties have remained difficult to obtain. In this study, molecular dynamics simulation with accurate potentials and available experimental data were used to describe the influence of different degrees of PAN preorientation and CNT diameter on the atomic-scale structure and properties of the composites. The inclusion of CNTs in the polymer matrix is favored for an intermediate degree of PAN orientation and small CNT diameter whereas high PAN crystallinity and larger CNT diameter disfavor CNT inclusion. The glass transition at the CNT/PAN interface involves the release of rotational degrees of freedom of the polymer backbone and increased mobility of the protruding nitrile side groups in contact with the carbon nanotubes. The glass-transition temperature of the composite increases in correlation with the amount of CNT/polymer interfacial area per unit volume, i.e., in the presence of CNTs, for higher CNT volume fraction, and inversely with CNT diameter. The increase in glass-transition temperature upon CNT addition is larger for PAN of lower crystallinity than for PAN of higher crystallinity. Interfacial shear strengths of the composites are higher for CNTs of smaller diameter and for PAN with preorientation, in correlation with more favorable CNT inclusion energies. The lowest interfacial shear strength was observed in amorphous PAN for the same CNT diameter. PAN with ∼75% crystallinity exhibited hexagonal patterns of nitrile groups near and far from the CNT interface which could influence carbonization into regular graphitic structures. The results illustrate the feasibility of near-quantitative insights into macroscale properties of polymer/CNT composites from simulations of nanometer-scale composite domains. Guidance is most effective when key assumptions in experiment and simulation are closely aligned, such as exfoliation versus bundling of CNTs, size, type, potential defects of CNTs, and precise measures for polymer crystallinity. KEYWORDS: carbon nanotubes, polyacrylonitrile, molecular dynamics simulation, glass transition, composites

1. INTRODUCTION Polyacrylonitrile (PAN)/carbon nanotube (CNT) carbon fibers are among the most promising low-density materials due to their high strength and low weight in comparison to alloys and ceramics. The preparation involves a multistage process that starts with the assembly of precursor solutions consisting of polymers such as polyacrylonitrile (PAN) or poly(methyl methacrylate) (PMMA) with CNTs.1−4 The precursor solutions are then spun into fibers, and the composite fibers are drawn and heated in several stages to achieve oxidation and carbonization.5 The final temperatures exceed 1000 °C to form high-strength graphitic fibers. The theoretical limits for the strength and modulus of the fibers are approximately 100 GPa and 1.0 TPa, respectively, corresponding to carbon nanotubes and graphene, although the currently feasible mechanical characteristics are still far below these limits.6−8 Composite fibers produced at Georgia Tech have recently achieved tensile strengths of up to 12 GPa,9 which is exceptional for PAN-based carbon fiber yet still a small © 2017 American Chemical Society

percentage of the theoretical limit. A modulus of 1 TPa has almost been reached by pitch-based carbon fibers, albeit at a low strength.10,11 PAN/CNT composites currently reach tensile moduli of 300−500 GPa.11−13 A major barrier to approach the theoretical limit of modulus and strength is the limited regularity of graphitic structures formed upon carbonization due to structural defects and lack of alignment.11,14 Among various polymers, polyacrylonitrile (PAN) shows promising fiber and carbonization properties due to the nitrile side chains that can form fused heterocyclic rings and eliminate nitrogen to from continuous graphitic structure.1,2,12,14,15 Understanding the PAN/CNT interface in precursor composites is therefore essential to identify rational controls to improve the mechanical properties. The tedious process required to develop PAN-based carbon fiber of higher Received: July 5, 2017 Accepted: December 12, 2017 Published: December 12, 2017 1017

DOI: 10.1021/acsami.7b09739 ACS Appl. Mater. Interfaces 2018, 10, 1017−1027

Research Article

ACS Applied Materials & Interfaces

Figure 1. Model systems, morphology, and molecular structure of the CNT/polyacrylonitrile composites. (a−d) CNTs of diameters 1−4 nm were equilibrated in a matrix of 100 polyacrylonitrile (PAN) polymer chains of 100 monomers each. The CNT volume fractions are approximately 1.5, 4.5, 9, and 16 vol %, respectively, and several chains are randomly highlighted in each frame to illustrate the dimensions. (e) In addition to amorphous polyacrylonitrile, similar composite systems were created with polymer chains of various degrees of preorientation. Nearby chains are colored similarly to highlight the orientation. (f) Explicit representation of π electrons for the CNT (blue) to correctly capture the multipolar electronic interaction between the graphitic CNT surface and the dipoles of nitrile groups in PAN.

tensile strength and modulus5 has inspired interest in the structure of the materials at smaller length scales. The interaction between matrix and filler, which in this case occurs at the PAN/CNT interface, is also very influential for nanocomposite properties in general.8,16 The advanced mechanical properties of PAN−CNT fibers are attributed to template effects that involve ordering of PAN chains surrounding a CNT and lead to a region of increased crystallinity.2,15 Experimental data suggest that the inclusion of CNTs induces a morphological change in the PAN matrix. Although bulk PAN typically assumes a paracrystalline structure characterized by helical chains, an increase in a planar “zigzag” conformation of the nitrile groups is anticipated in composites. Such changes in conformation are influenced by the draw ratio of the carbon fiber precursor, which is critical to increase the orientation of PAN chains and to promote debundling of CNTs.17,18 High-resolution transmission electron microscopy (HR-TEM) images of carbonized fiber show that ∼10 layers of highly ordered graphitic carbon can form around exfoliated CNTs.13 The PAN precursor morphology is thought to affect these final properties; however, there is currently very limited understanding of this connection on the atomic scale. Therefore, complete understanding of the initial PAN/CNT composite and fiber morphologies is desirable to explain subsequent processes, such as cyclization, carbonization, and graphitization.5 Recent experimental and modeling work indicates that amorphous and crystalline regions exhibit significantly different behavior during these stages,19 and potential breakthrough improvements in PAN-based carbon fiber properties could depend on the specific preparation of the PAN fiber precursor. Prior molecular dynamics (MD) studies have characterized bulk PAN morphologies and interactions with CNTs,19−22 as well as interactions of other polymers with

CNTs.23,24,21,25 The interaction energy of single PAN chains with CNTs in vacuum was found to be attractive,20 and extended conformations of single chains of polyacrylonitrile were reported along the CNT axis.21 Reactive molecular dynamics simulations explored possible pathways of PAN cyclization and carbonization reactions in PAN/CNT composites.19,22 The simulation results indicated that more robust graphitic structures may be formed in the presence of nanotubes than in the presence of graphite, although experimental evidence has not confirmed this trend. No prior simulation studies have yet investigated the effects of polymer orientation and CNT type on composite properties.19 Moreover, earlier force-field based computational studies of gaphitic materials have major limitations. A main reason for uncertainties is the neglect of π electrons and associated multipoles that contribute to interfacial interactions,27,28 as well as missing validation of surface and interfacial energies relative to available experimental data (Table S1). As a result, interfacial properties of graphite using the CVFF20 and DREIDING21 force fields deviate more than 100% from experimental data. Similarly, ReaxFF has not been tested for interfacial properties and involves a large number of parameters.26 These limitations are overcome in this work by using a model that affixes virtual π electrons to each carbon atom of the CNT (Figure S1) and better represents the electronic structure and multipolar nature of the π electron cloud compared to prior models (this is the same model as in the recently published ref 29). The model derivation followed the INTERFACE force field (IFF) protocol,29−34 which enabled quantitative insights into inorganic/organic binding and properties of a diverse range of other nanostructures.35−37 The improvement in the accuracy of computed surface energies, hydration energies, and liquid contact angles of graphite over earlier force fields exceeds one 1018

DOI: 10.1021/acsami.7b09739 ACS Appl. Mater. Interfaces 2018, 10, 1017−1027

Research Article

ACS Applied Materials & Interfaces

Figure 2. Inclusion energy of CNTs in PAN and layer formation according to molecular dynamics simulation. (a) Inclusion energy of CNTs in PAN is seen to increase monotonically with CNT radius for all degrees of polymer preorientation. Strongest binding occurs for SWCNTs and DWCNTs in amorphous or 50% aligned PAN. (b) Average harmonic bond-stretching energy of PAN at the interface between a carbon nanotube and the polymer. (c) Bond energies in top view for 4 nm CNTs with 75% aligned PAN. Binding is unfavorable (a), and bond strain near the surface can be seen. (d) Visualization of pairwise nonbond interaction energies (van der Waals and Coulomb) at the CNT−polymer interface for the same system, showing repulsive pairwise interactions especially in the second molecular layer.

2. METHODS

order of magnitude, leading to typically Tg, enough thermal energy is available to overcome the barrier more frequently. The color code depicts the positions of nitrile groups in the selected chain.

Table 1. Comparison of Glass-Transition Temperatures of Polyacrylonitrile (PAN) and PAN/CNT Composites in Experiment and Simulationa experimental data

simulation results (this work)

system

Tg (°C)

vol % CNT

PAN orientation, % crystallinity

ref

Tg (°C)

PAN PAN PAN PAN−SWCNT

85 100 103 109 114 143 105

0 0 0 4.6b 4.6b 9.2b 4.0d

0% 0.52, 58% 0.58 0.62, 54% 0.68 0.66 0.53, 57%

61, 62 3 42 3 42 42 3

87 ± 5 101 ± 5

0 0

0% ∼50%

124 ± 5 122 ± 5

1.5c 1.5c

∼50% ∼75%

127 ± 5

4.5e

∼50%

PAN−DWCNT

vol % CNT

PAN orientation, % crystallinity

a

Excellent agreement is seen for PAN of different crystallinity. Trends in glass-transition temperatures for the PAN/CNT composites by simulations agree with experiments while absolute computed values are 10−20 °C higher. The difference is in part due to bundling of SWCNTs in experiment vs exfoliation in the simulation, as well as differences in the size of DWCNTs between experiment and simulation. The addition of CNTs to PAN increases Tg, a higher volume fraction of the CNTs increases Tg, and a larger CNT diameter alone has no significant effect on Tg or slightly decreases Tg. bPresent as an SWNCT bundle (5−20 nm thick). cExfoliated SWCNTs. dDiameter, ∼5 nm. eDiameter, 2 nm. thousands of monomers.12 Atactic PAN does not crystallize like syndiotactic PAN, and a periodic model of fully extended chains was found to relax to an axial length of ∼160 Å, although this configuration was still energetically unfavorable. To achieve the desired level of preorientation of the PAN chains, the lengths of the 3D periodic simulation boxes were slowly reduced. Box sizes of 80 and 120 Å correspond to 50 and 75% PAN preorientation, respectively. Accordingly, maximally extended chains correspond to 100% preorientation as was achieved with a syndiotactic crystal. Smaller percentages correspond to less crystallinity and can be qualitatively compared to the Hermans orientation functions of 0.5 and 0.75. The 1 Hermans orientation function is given by F = 2 [3⟨cos2 θ⟩ − 1], whereby θ is the orientation relative to the draw direction (main axis).45 In all prepared configurations, the PAN chains were mobile enough to equilibrate to the experimentally observed density in the NPT ensemble. Subsequent energy minimizations and molecular dynamics simulations utilized the LAMMPS program with a cutoff for Lennard-Jones interactions at 10 Å and the PPPM method for electrostatic interactions with an accuracy of 10−4.44 2.3. Calculation of Properties and Analysis. Inclusion energies of the CNTs in each composite system (Figure 2a) were calculated using a three-box method corresponding to (1) PAN/CNT with the desired preorientation, (2) PAN with the same preorientation, and (3) a corresponding CNT bundle (Figure S2 and Section S2).46 In this way, the interaction energy of a given CNT with a given matrix orientation was computed as the energy of the composite minus the

(DWCNTs) (2.2 nm), and multiwalled carbon nanotubes of 3 and 4 nm diameters, which were combined with the polymer models for a range of three-dimensional (3D) periodic composite systems (Figure 1). The PCFF-IFF force field including the new model for graphitic materials was used to simulate CNTs and their interactions with PAN (Figure S1). The force-field parameters (Table S2), their description (Section S1), and files ready to use for simulations are included in the Supporting Information (identical to the model in ref 29). 2.2. Composite Models with Partial Polymer Crystallinity. The models of amorphous PAN and PAN with partial crystallinity were built using the graphical user interface and the amorphous cell module in the Materials Studio program.43 In addition, we tested manual building protocols using a series of energy minimization, molecular dynamics, annealing, and cooling, which lead to final structures of comparable morphology and energy. A total of 100 chains of bulk amorphous polyacrylonitrile (degree of polymerization (DP) = 100) were used initially. To create composite systems with CNTs, a soft harmonic potential was used to expand appropriately sized void spaces into the amorphous PAN. The insertion of periodic CNTs into these systems was achieved by extending the capabilities of the molecule template feature in the LAMMPS simulation program. The extensions were integrated into the current release.44 For the preoriented systems, PAN chains were defined to be periodic along the CNT axis (Figure 1). Accordingly, there were no chain ends in these systems and the models mirror the average local environment of high-molecular-weight polyacrylonitrile (300 000− 500 000 g/mol) used in experiment, where polymers average 1020

DOI: 10.1021/acsami.7b09739 ACS Appl. Mater. Interfaces 2018, 10, 1017−1027

Research Article

ACS Applied Materials & Interfaces energy of the corresponding pure phases. Due to multiple relaxation modes of polyacrylonitrile at different time scales, it is best to consider the trends rather than the absolute values of the inclusion energies. Potential energy surfaces of bond, torsion, and van der Waals energies (Figures 2b−d and 4b,c) were obtained by recording a breakdown of per-atom energies from molecular dynamics trajectories using the appropriate per-atom LAMMPS compute commands (Figure S3). The per-atom energies were interpolated onto grid points using the function “scatteredInterpolant” in MATLAB. The energy surfaces are the result of averaging 100 planes perpendicular to the CNT axis as well as 125 trajectory frames spanning at least 1 ns. The energy surfaces were visualized using the “surf” command in MATLAB.47 Glass-transition temperatures (Figure 3a and Table 1) were calculated by plotting the specific volume (inverse density) against 11 temperatures ranging from 300 to 460 K (Figure S4). This plot for amorphous materials is known to produce two linear regimes the intersection of which is the material’s Tg.48 Each system was equilibrated and then run for at least 1 ns at each temperature to allow the density to stabilize. Multiple series of simulations were carried out for each system to obtain the reported glass-transition temperatures as an average. Experimental attempts to calculate the interfacial shear strength rely on the pullout test, a technique that was previously adapted in molecular dynamics by removing a periodicity constraint to extract the CNT from the system. However, the majority of the energy difference observed using this technique is then due to the restructuring of the polymeric matrix near the void created by the vacating CNT, rather than frictional interaction between the sliding CNT and matrix.49 Here, Here, instead, we employed steered molecular dynamics to pull the CNT through the polymer to determine the interfacial shear strength (Figure 4a) and retain the periodicity to circumvent erroneous energy contributions (Figure S5a).50 When applying an adequate force in the axial direction to a periodic CNT, it was observed that the CNT reaches a terminal velocity at which it can be assumed that the applied force is in equilibrium with frictional forces exerted by the matrix. Beginning with a sufficiently low applied force, a set of nine forces ranging from 0.015 to 0.515 kcal/(mol Å) was observed to produce two linear regimes of terminal velocity. The transition between these two regimes was used to mark the onset of slippage between the CNT and matrix and corresponds to the interfacial shear strength (Figure S5b,c). The visualization of nitrile group morphologies involved a threedimensional Voronoi analysis using the Voro++ software.51 The results were subsequently converted for visualization with the Visual Molecular Dynamics program.52 Individual molecular dynamics simulations to calculate inclusion energies, glass-transition temperatures, and interfacial shear strengths of the PAN/CNT composites were carried out using multiple replicas of 10 ns duration, totaling at least 50 ns for each system. The analysis of results, including visualizations and energy maps, involved trajectories of at least 10 ns length in local equilibria.

templating upon carbonization, and to initialize covalent bonding with the CNT.55−58 The simulation results show that the inclusion energy of an exfoliated CNT in PAN matrices depends on the PAN crystallinity and CNT diameter (Figures 2a and S2). CNT inclusion tends to be favorable for small diameters of 1 and 2 nm and is unfavorable for larger diamaters of 3 and 4 nm. The inclusion energy mostly represents the large deformation energy of the polymer network to accommodate the CNTs and reaches several joules per square meter (J/m2). The inclusion of larger CNTs is less favorable as they occupy more excluded volume and impose stronger deformations on the entangled polymer network. Local constraints on the polymer− CNT interface may be weaker for larger CNTs due to lower curvature; however, this effect plays a minor role as the local polymer−CNT interaction energy is