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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 ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b09739 • Publication Date (Web): 12 Dec 2017 Downloaded from http://pubs.acs.org on December 14, 2017

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ACS Applied Materials & Interfaces

Nanoscale Structure-Property Relationships of Polyacrylonitrile/CNT Composites as a Function of Polymer Crystallinity and CNT Diameter by Jacob R. Gissinger1, Chandrani Pramanik,1 Bradley Newcomb,2 Satish Kumar,2 Hendrik Heinz1*

1

Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO 80309, USA

2

School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

* Corresponding author: [email protected]

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Abstract Polyacrylonitrile (PAN)/carbon nanotube (CNT) composites are used as a precursor for ultrastrong and lightweight carbon fibers. However, the mechanisms of formation and relationships of the nanoscale structure to mechanical and thermal properties have remained uncertain. This study reports on the impact of different degrees of PAN pre-orientation and CNT diameter on the composite properties using molecular dynamics simulation with accurate potentials and comparisons to experimental data. Relationships between the atomically resolved structure, thermal, and mechanical properties are derived. CNT inclusion in the matrix is favored for a medium degree of PAN orientation and small CNT diameter. The glass transition at the CNT/PAN interface involves the release of rotational degrees of freedom of nitrile side groups in contact with the carbon nanotubes. The glass transition temperature increases sharply in the presence of CNTs and for higher CNT volume fraction, in correlation with the amount of CNT/polymer interfacial area per unit volume of composite rather than with CNT diameter. The increase in glass transition temperature upon CNT addition is larger for PAN of lower crystallinity and smaller for PAN of higher crystallinity. Interfacial shear strengths of the composites are higher for CNTs of smaller diameter and for PAN with pre-orientation, in correlation with more favorable CNT inclusion energies. Amorphous PAN showed the lowest interfacial shear strength for all CNT diameters. Hexagonal patterns of nitrile groups near and far from the CNT interface were identified for PAN of ~75% crystallinity, which could influence carbonization into regular graphitic structures. The results demonstrate the feasibility of reliable predictions of macroscale properties of polymer/CNT composites from simulations of representative composite domains on the nanometer scale. Guidance is most effective when key assumptions in experiment and simulation are closely aligned, such as exfoliation versus

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bundling of CNTs, size, type, potential defects, and precise measures for polymer crystallinity.

Keywords: carbon nanotubes; polyacrylonitrile; molecular dynamics simulation; glass transition; composites



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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

polymethylmethacylate (PMMA) with CNTs.1-4 The precursor solutions are then spun into fibers, and the composite fibers are drawn and heated in 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, corresponding to carbon nanotubes and graphene, respectively, 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 up to 12 GPa,9 which is exceptional for PAN-based carbon fiber yet still a small 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 tensile strength and modulus5 also inspires interest in the structure of the materials at


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smaller length scales. The interaction between matrix and filler, which in this case occurs at the PAN/CNT interface, is also one of the most critical aspects of a nanocomposite in general.8, 16 The advanced materials 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. While 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 electron microscopy (HR-TEM) images of carbonized fiber show that ~10 layers of highly ordered graphitic carbon can form around exfoliated CNTs.19 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 in order to explain subsequent processes such as cyclization, carbonization and graphitization.5 Recent experimental and modelling work indicates that amorphous and crystalline regions exhibit significantly different behavior during these stages,20 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,20-23 as well as interactions of other polymers with CNTs.24,25,22,26 The interaction energy of single PAN chains with CNTs in vacuum was found to be attractive21 and extended conformations of single chains of polyacrylonitrile were reported along the CNT axis.22 Reactive molecular dynamics simulations



explored possible pathways of PAN cyclization and carbonization reactions in PAN/CNT composites.20,

23

The simulation results indicated that more robust graphitic structures may be

formed in the presence of nanotubes than in the presence of graphite,20 although experimental evidence has not confirmed this trend. The effects of polymer orientation and CNT type have not been studied before. The existing computational studies provide mainly qualitative information, however, due to uncertainties in the reproduction of surface energies and interfacial energies of graphite-like structures. For example, the default CVFF21 and DREIDING22 force fields lead to deviations in excess of 100% compared to experimental data (Table S1). ReaxFF involves a large number of parameters and has not been tested for interfacial properties.37 The reason for uncertainties has been 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. These shortcomings are largely eliminated in this work (Table S1). We apply a more realistic approximation of the electron density and validated surface as well as interfacial properties following the Interface force field (IFF) protocol,29-33 which has enabled reliable insights into inorganic/organic binding and properties of a range of other diverse nanostructures.34-36 The IFF protocol has been applied here to graphitic materials for the first time. We analyzed the properties of PAN/CNT composites including several long polymers chains with this new generation of all-atom force field (Figure S1 and Table S1). Using the energy expression of the polymer consistent force field (PCFF),38-39 graphite and CNTs are represented in more detail by incorporation of virtual π electrons and associated internal multipole moments.29,

40

The new models help represent π stacking interactions, surface, and interfacial


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energies up to two orders of magnitude more accurately than existing force fields (Table S1, Table S2 and section S1 for details). We aimed at the elucidation of quantitative structureproperty relationships for PAN/CNTs composites for variable polymer crystallinity and different types of CNTs (Figure 1). The effects of polymer pre-orientation and CNT diameter on inclusion energies, glass transition temperatures (Tg), interfacial shear strength, and domain ordering in the composites are described in atomistic detail, including likely mechanisms and guidance for specific control.

Figure 1. Model systems, morphology, and molecular structure of the CNT/polyacrylonitrile composites. (a-d) CNTs of diameters of 1 to 4 nm were equilibrated in a matrix of 100 polyacrylonitrile (PAN) polymer chains of 100 monomers each. The CNT volume fractions are 7 ACS Paragon Plus Environment


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approximately 1.5 vol%, 4.5 vol%, 9 vol%, and 16 vol%, respectively, and several chains are randomly highlighted in each frame to illustrate the dimensions. (e) In addition to amorphous polymer, similar composite systems were created with polymer chains of various degree of preorientation. Nearby chains are colored similarly to highlight the orientation. (f) Explicit representation of π electrons for the CNT (blue color) to correctly capture the multipolar electronic interaction between the graphitic CNT surface and the dipoles of nitrile groups in PAN.

2. Methods 2.1. Molecular Models of PAN and CNTs. A crystal structure for syndiotactic PAN is known from X-ray diffraction41 to enable validation of the force field. The updated PCFFINTERFACE force field (see Supporting Information) reproduces the lattice parameters and the density (~1.20 g/cm3) of a syndiotactic PAN crystal. Models of amorphous PAN, atactic PAN of different crystallinity, and syndiotactic PAN were employed to explore the full range of polymer matrix preorientation ranging from isotropic, highly entangled bulk PAN (0% crystallinity) to a perfectly aligned crystal (100% crystallinity). The effect of crystallinity of atactic PAN on the composite properties is of high interest as atactic PAN is available at low cost, can be drawn, and has been widely used in laboratory studies to develop carbon fiber. Atactic PAN has a random stereochemical orientation of the nitrile side groups and assumes amorphous morphologies with up to 68% crystallinity depending on the draw ratio in experiment.3,

42

The models with

preorientation from 0% to 100% cover the entire theroretically possible range of crystallinity (Figure 1 and section 2.2). The new model for graphitic materials was used to simulate CNTs and their interactions with


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PAN (Figure S1). The model affixes virtual π electrons to each carbon atom of the CNT and better represents the electronic structure and multipolar nature of the π electron cloud compared to prior models. The improvement in surface energies, hydration energies, and contact angles over earlier force fields is large, reducing deviations from experiment by more than one order of magnitude (Table S1). The force field parameters (Table S2), their description (section S1), and files ready to use for simulations are included in the Supporting Information. We built atomistic models of SWCNTs (1.3 nm), DWCNTs (2.2 nm), and MWCNTs of 3 nm and 4 nm diameter for a range of 3D periodic composite systems (Figure 1). 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 within 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. 100 chains of bulk amorphous polyacrylonitrile (degree of polymerization = 100) were used initially. In order 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, which is integrated into the current release.44 For the pre-oriented 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 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, though this configuration was still energetically unfavorable. In order to achieve the desired level of preorientation of the PAN chains, the lengths of the 3D periodic simulation boxes were slowly reduced. A box size of 80 Å and 120 Å corresponds 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 Hermans orientation function is given by

F=

1 3 cos2 θ − 1 whereby θ is the orientation relative to the draw direction (main axis).45 In 2

[

]

all prepared configurations, the PAN chains were mobile enough to equilibrate to the experimentally observed density in the NPT ensemble. 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 was employed in subsequent energy minimizations and molecular dynamics simulations.44 2.3. Calculation of Properties and Analysis. Inclusion energies of the CNTs in each composite system 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 energy of the corresponding pure phases. Due to multiple relaxation modes of polyacrylonitrile at different time scales it is best to consider the trends and less the absolute values of the inclusion energies. Potential energy surfaces of bond, torsion, and van-der-Waals energy were obtained by recording a breakdown of per-atom energies from molecular dynamics trajectories using the appropriate per-atom LAMMPS compute commands (Figure S3). These were interpolated onto 10 ACS Paragon Plus Environment

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grid points using the function ‘scatteredInterpolant’ in MATLAB. The 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 were calculated by plotting the specific volume (inverse density) against eleven temperatures ranging from 300 to 460 K (Figure S4). This plot for amorphous materials is known to produce two linear regimes whose intersection 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 traditionally adapted in molecular dynamics by removing a periodicity constraint in order 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 Instead, steered molecular dynamics was employed to pull CNTs while retaining their periodicity in order 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 three-dimensional Voronoi analysis using the Voro++ software.51 The results were subsequently converted for visualization with the Visual Molecular Dynamics (VMD) 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.

3. Results and Discussion 3.1. Effect of CNT Diameter and Matrix Alignment on Inclusion Energy. Electrospun PANCNT based precursor fibers are more resistant to structural changes than the neat polymer due to the presence of CNTs and high entanglement density, which greatly restrict the mobility of PAN chains.53-54 The initial morphology likely persists through subsequent stages of processing and may have a critical effect on the final properties of the carbonized fiber. Therefore, much previous work focused on the impact of CNTs on PAN-CNT fiber during late processing stages, and it has been proposed that high surface area and bond strain of smaller-diameter CNTs (~1 nm) are preferable to increase stress transfer, templating upon carbonization, and to possibly initialize covalent bonding with the CNT.55-58 Recent experimental efforts have stressed the importance of characterizing the morphology of the PAN-CNT precursor.12 The simulation results show that the inclusion energy of an exfoliated CNT in PAN matrices depends on the PAN crystallinity and on CNT diameter (Figure 2a and Figure S2). CNT inclusion tends to be favorable for small diameter of 1 and 2 nm and is unfavorable for larger CNTs of 3 nm and 4 nm size. The inclusion energy mostly represents the large deformation 12 ACS Paragon Plus Environment

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energy of the polymer network to accommodate the CNTs and reaches several 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, the local polymerCNT interaction energy is only 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 simulation. 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, in part due to bundling of SWCNTs in experiment versus exfoliation in the simulation and differences in 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.

System

Experimental data

Ref. Simulation results (this work)

Tg

Vol%

PAN orientation,

Tg

Vol%

PAN %

(°C)

CNT

% crystallinity

(°C)

CNT

crystallinity

PAN

85

0

0%

61-62

87±5

0

0%

PAN

100

0

0.52, 58%

3

101±5

0

~50%

PAN

103

0

0.58

42

PAN-SWCNT

109

4.6a

0.62, 54%

3

124±5

1.5b

~50%


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PAN-DWCNT

114

4.6a

0.68

42

143

9.2a

0.66

42

105

4.0c

0.53, 57%

3

122±5

1.5b

~75%

127±5

4.5d

~50%

a

Present as a SWNCT bundle (5 to 20 nm thick). b Exfoliated SWCNTs. c Diameter ~5 nm. d Diameter 2 nm.

3.3. Interfacial Shear Strength. The interfacial shear strength (τi) of CNT composites is an important indicator for failure and challenging to probe in experiment.64-65 Steered molecular dynamics was employed, using the 3D periodic models, to pull a carbon nanotube through the composite in order to selectively capture van der Waals and Coulomb interactions between the matrix and the CNT (Figure S5 and section S2). Shear forces were varied and terminal shear velocities recorded that could reach high final values due to the perfect alignment of the CNTs in the model. The results indicate that pristine CNTs in PAN composites do not have significantly different interfacial shear strengths τi with respect to CNT diameter or matrix orientation (Figure 4a). The computed values in a range of 10.5 to 16.5 MPa agree with recent experimental estimates which suggest a τi of 13.1 MPa for as-spun PAN fibers.18 Somewhat higher interfacial shear strengths are observed in the simulation for SWCNTs in comparison to larger CNTs for all degrees of PAN crystallinity (Figure 4a). This trend correlates with a more favorable inclusion energy for the SWCNTs in the PAN matrix further below zero (Figure 2a). Accordingly, stronger cohesion requires more stress to enable sliding of the CNTs. Amorphous PAN, however, showed the lowest shear strength for all CNT diameters, and higher crystallinity increases the shear strength, at least above a minimum level of 50% crystallinity. The most significant difference in interfacial 21 ACS Paragon Plus Environment


shear strength τi with respect to polymer crystallinity occurs between amorphous and 50% aligned PAN, while subsequent increases in orientation have negligible effects on τi. Conformation strain at the CNT surface was analyzed through a cross-section of the system, and shows much smaller energies in amorphous PAN (Figure 4b) relative to the 75% aligned PAN polymer (Figure 4c), which also indicates more templating and therefore higher τi values (Figure 4a). In fully drawn fibers with highest crystallinity, the shear strength τi was experimentally observed to increase even up to 31 MPa.18 This high experimental value in τi might be due to mechanisms other than increasing van der Waals and Coulomb interactions between the CNT and matrix, such as CNT deformation and changes in composite morphology at length scales beyond those of the simulation. However, the results indicate that ultimately an increase in cohesion (lower inclusion energy) and a certain minimum level of preorder of PAN support higher interfacial shear strength.


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Figure 4. Interfacial shear strength of the composites as a measure of shear stability. (a) The interfacial shear strength increases for smaller CNTs and with increasing PAN orientation. The differences are not significant enough to consider frictional forces as a major contribution to interfacial shear stress. (b) Relative dihedral energies of the amorphous PAN precursor near the CNT surface reveal a small amount of conformation strain energy in the axial direction. (c) Relative dihedral energies of the 75% aligned PAN precursor near the CNT surface reveal higher conformation strain energy and four to five templated polymer layers.

3.4. Relation of Composite Morphology to Cyclization Reactions. Many potential reactions may occur during the cyclization and carbonization stages of carbon fiber production 23 ACS Paragon Plus Environment


using PAN-CNT precursor composites (Figure 5a-c).1,

5, 66, 67

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Due to the high temperatures

required by these processes, desired intra-chain cyclization reactions (Figure 5a)1,

66

can be

complemented by a number of alternative mechanisms such as interchain trimerization (Figure 5b)1, 67 and alternative cyclization reactions (Figure 5c) (see additional references in section S4). Simulations of the composites at 75% alignment at room temperature show the formation of hexagonal arrangements of nitrile groups in the bulk polymer (Figure 5d). The arrangements result from phase segregation of the polar nitrile groups and the nonpolar alkyl backbone of PAN. Analysis by 3D Voronoi cells shows the enclose ed space by individual nitrile groups (Figure 5e, f). Voronoi cell analysis68 was previously employed to understand the local geometry of glass-forming liquids,69 the topology of interpenetrating 3D inorganic networks and polymer nanostructures, as well as to anticipate void formation in polymer nanocomposites (see additional information in section S4).70 The Voronoi analysis in this study helps visualize the orientation of nitrile groups and recognize potential cyclization mechanisms. The likelihood of intrachain cyclization reactions of adjacent nitrile groups is expected to scale with the surface area shared between neighboring Voronoi cells. Regions of PAN further from the CNT have a comparatively low degree of order of adjacent Voronoi cells even though they appear well aligned in a cross-sectional view (Figure 5e). The helical structure of PAN leads to several isolated nitrile groups and neighbor cells often share little common surface area so that only short sequences of intrachain cyclization are likely (Figure 5a). Regular graphitic structures might be more difficult to form and interchain crosslinking could be favored (Figure 5b). PAN chains in the vicinity of the CNT surface exhibit more regular Voronoi cells that share large faces (Figure 5f). These conformations have been termed ‘planar zigzag’ (Figure 5a) and


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could result in longer sequences of intrachain cyclization. For locally syndiotactic sequences, alternating nitrile groups are often in proximity to each other and might undergo alternative intrachain cyclization reactions (not observed in experiment to-date) (Figure 5c,f). These indicators are, however, first estimates at room temperature and higher temperatures for stabilization, cyclization, and carbonization from 200 to 1700 °C would greatly increase the mobility of polymer chains. ReaxFF simulations at high temperatures20,

23

in principle concur

with the proposed mechanisms, however, short fused N-heterocyclic compounds (DP = 10) were analyzed with ReaxFF that differ from infinite periodic polymer chains in this study (DP = 100) to analyze ordered and disordered domains as a function of polymer crystallinity.



Figure 5. Possible carbonization reactions and preferred patterns of nitrile groups in PAN with 75% crystallinity according to molecular dynamics simulation. (a) Intrachain cyclization is a common mechanism and may result in carbon fiber of maximum strength. Reproduced with permission from reference 66. Copyright 1999 Elsevier. (b) Cyclotrimerization could occur between less-ordered chains with isolated nitrile groups (refs. 1, 67). (c) An alternative cyclization mechanism leading to an eight-membered ring could occur in locally syndiotactic sequences. (d) Distinct hexagonal ordering of nitrile groups in 75% aligned PAN at 298 K in a 26 ACS Paragon Plus Environment

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semi-transparent cross-sectional view from molecular dynamics simulation (black highlights). Regions (e) and (f) were selected for further Voronoi analysis. (e) The Voronoi cells indicate the space pertaining to individual nitrile groups. The shared surface area of neighbor cells can be used as an indicator for the propensity of intrachain cyclization reactions. Isolated nitrile groups in less-ordered regions cannot react by this mechanism. (f) Well-ordered regions with the same tacticity appear well-suited for intrachain cyclization while breaks in local tacticity likely affect the carbonization product.

4. Conclusions The inclusion of carbon nanotubes (CNTs) in polyacrylonitrile (PAN) involves significant polymer deformations that can be favorable for single wall and double wall carbon nanotubes in matrices of atactic PAN of 0% to 50% crystallinity due to matching molecular helicity. Conformation strain at the PAN/CNT interface varies as a function of CNT diameter and alignment of the polymer chains. The strain extends up to several molecular layers away from the CNT surface and tunes the inclusion energy from significant attraction to significant repulsion (-3 J/m2 to +5 J/m2) relative to the neat polymer. The local order of neat PAN has noteworthy influence on the glass transition temperature (Tg), which further increases upon addition of CNTs. The major factor to increase the glass transition temperature of the composite appears to be the PAN/CNT interfacial area per unit volume of composite, which correlates with the CNT volume fraction and inversely with the degree of CNT bundling. This ratio tends to decrease for larger diameter of the CNTs at the same volume fraction. Glass transition temperatures can be surprisingly well computed with the new force field in a range of ±5 K, and the molecular mechanism of the glass transition of PAN near the CNT surface involves an



increase in the rotational mobility of the nitrile group. The computed interfacial shear strength ranges from 10.5 to 16.5 MPa, with larger values for better polymer alignment and small diameter (single wall) nanotubes. Distinctive local PAN morphologies were identified based on the relative positions of neighboring nitrile groups using advanced visualization and Voronoi analysis, which could be related to specific mechanisms of carbonization reactions in future work. A remaining limitation are relatively short simulation times of tens of nanoseconds and the representation of associated non-equilibrium states. Similarly, the mechanically drawn PAN/CNT composites in experiment are non-equilibrium structures with a specific degree of polymer crystallinity. The reliability of simulations can be ascertained by implementing closely the same measures for polymer crystallinity, the same features of the CNTs as in experiment, as well as verifying the consistency of results by using advanced sampling techniques and multiple replicas. The correlation of computed glass transition temperatures and interfacial shear strengths with available experimental data is then very good and shows that details of composite properties can be analyzed using the new models and simulations. The reliable analysis of working mechanisms of carbonization and ultimate mechanical properties of carbon fibers by modeling in comparison to experiment has thereby come into closer reach. An essential aspect for future studies may also be the integration of insights at the level of nanoscale domains up to ~1000 nm size into predictive models at the microscopic and macroscopic scales.

Acknowledgements This work was supported by the Air Force Office of Scientific Research AFOSR (FA9550-14-1-


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0194), the National Science Foundation (DMREF 1623947), and the University of Colorado at Boulder. The allocation of computational resources at the CU Biofrontiers Computing Cluster and at the Ohio Supercomputing Center is acknowledged. This work further used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC05-00OR22725, the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357, and the Janus supercomputer, which is supported by the National Science Foundation (award number CNS0821794).

Supporting Information. Movie depicting the glass transition, supporting figures, tables, details of the new models and force field for graphitic materials, additional computational details, additional discussion of glass transition temperatures, molecular models and force field files (extended PCFF) for the CNTs, PAN, and the composites.

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