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Carbon Nanotube Dispersion in Solvents and Polymer Solutions: Mechanisms, Assembly, and Preferences Chandrani Pramanik,† Jacob R. Gissinger,† 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
‡
S Supporting Information *
ABSTRACT: Debundling and dispersion of carbon nanotubes (CNTs) in polymer solutions play a major role in the preparation of carbon nanofibers due to early effects on interfacial ordering and mechanical properties. A roadblock toward ultrastrong fibers is the difficulty to achieve homogeneous dispersions of CNTs in polyacrylonitrile (PAN) and poly(methyl methacrylate) (PMMA) precursor solutions in solvents such as dimethyl sulfoxide (DMSO), N,N-dimethylacetamide (DMAc), and N,N-dimethylformamide (DMF). In this contribution, molecular dynamics simulations with accurate interatomic potentials for graphitic materials that include virtual π electrons are reported to analyze the interaction of pristine single wall CNTs with the solvents and polymer solutions at 25 °C. The results explain the barriers toward dispersion of SWCNTs and quantify CNT-solvent, polymer-solvent, as well as CNT-polymer interactions in atomic detail. Debundling of CNTs is overall endothermic and unfavorable with dispersion energies of +20 to +30 mJ/m2 in the pure solvents, + 20 to +40 mJ/m2 in PAN solutions, and +20 to +60 mJ/m2 in PMMA solutions. Differences arise due to molecular geometry, polar, van der Waals, and CH-π interactions. Among the pure solvents, DMF restricts CNT dispersion less due to the planar geometry and stronger van der Waals interactions. PAN and PMMA interact favorably with the pure solvents with dissolution energies of −0.7 to −1.1 kcal per mole monomer and −1.5 to −2.2 kcal per mole monomer, respectively. Adsorption of PMMA onto CNTs is stronger than that of PAN in all solvents as the molecular geometry enables more van der Waals contacts between alkyl groups and the CNT surface. Polar side groups in both polymers prefer interactions with the polar solvents. Higher polymer concentrations in solution lead to polymer aggregation via alkyl groups and reduce adsorption onto CNTs. PAN and PMMA solutions in DMSO and dilute solutions in DMF support CNT dispersion more than other combinations whereby the polymers significantly adsorb onto CNTs in DMSO solution. The observations by molecular simulations are consistent with available experimental data and solubility parameters and aid in the design of carbon nanofibers. The methods can be applied to other multiphase graphitic materials. KEYWORDS: carbon nanotubes, polyacrylonitrile, poly(methyl methacrylate), molecular dynamics, self-assembly, dispersion, solubility parameters strength,6,10 including commercial polymer-based fibers (e.g., IM7 and IM10)11 and gel-spun carbon fiber at Georgia Tech.1 These properties can still be greatly improved by rational design. The first step in laboratory synthesis of carbon fibers is to prepare precursor solutions that consist of a solvent, a polymer such as PAN or poly(methyl methacrylate) (PMMA), and carbon nanotubes (Scheme 1).2 CNTs are thereby preferred over other sheet-like graphitic materials due to higher directional strength and bending stability. The precursor solutions are spun and drawn into fibers, whereby the solvent evaporates and is
C
arbon nanomaterials have significant advantages as structural materials over metals and alloys due to their low density, high tensile and shear strength, as well as resistance to chemical degradation.1,2 Applications of carbon nanomaterials include load-bearing parts in air and space vehicles, cars, bicycles, and commodity materials such as polymer/graphitic composite panels, carbon nanofibers, and yarns.3,4 The highest theoretically feasible elastic modulus of 1 TPa5 for defect-free graphene has nearly been reached using pitch-based carbon nanofibers,6 however, the tensile strength DMSO. Dispersion energies were calculated relative to the reversibly solvated surface area of the CNTs, which corresponds to one-third of the surface area of the bundle of three CNTs (i.e., the surface area of one CNT) (Figure 2a−d). Two-thirds of the outer surface is exposed to solvent also in the bundled conformation. Poor dispersion of pristine CNTs in polar solvents has been observed in experiment and is consistent with the positive dispersion energies identified in the simulation (Figure 2).61,64,65 The dispersion of pristine CNTs was reported to be better in DMF compared to other solvents,64 sometimes easier than in DMAc after sonication.61 The known experimental propensity of dispersion DMF ≥ DMAc > DMSO agrees with the computational trend (Figure 2e). Pristine small diameter CNTs were also suggested to be more electrophilic and less hydrophobic than larger multiwall CNTs13 and could impart better dispersion in DMF and DMAc related to enhanced CH-π bonding, n-π* donation, and higher solvochromic parameters.13,66 While these relationships are not evaluated here, the simulations agree with better dispersion of SWCNTs in DMF. Spontaneous dispersion would only be expected for negative dispersion energies or small positive values ( DMF (Figure 3d−f and Figures S6−S9). A mixture of PAN and PMMA (ratio 3/1) shows intermediate behavior between neat PAN and neat PMMA solutions (Figure 3g−i and Figures S7 and S8). Polymer chains in the PAN3− PMMA1 mixture do not adsorb onto CNTs in DMF, somewhat in DMAc, and significantly in DMSO. The CNT affinity of the polymers was also analyzed by the average number of adsorbed monomers (Figure 4a). This analysis reveals that higher concentrations of both PAN and PMMA (PAN3 versus PAN2 and PMMA3 versus PMMA2) decrease the adsorbed amount. The reason for the decrease in polymer adsorption to CNTs at higher concentration is favorable aggregation of the polymers in solution rather than contact with the CNT surface. The close contacts of the polymers with the CNT surface involve mainly van der Waals interactions of the alkyl groups with the CNT surface, whereby the polar side groups prefer contact with the polar solvents (Figures S10−S13). This mechanism is similar to globule formation in solution by hydrophobic contacts
Table 2. Energy of Dissolution of Extended PAN and PMMA Oligomers (N = 20) in the Pure Solvents at Room Temperature for Concentrations of 6−14 wt % (50−90 mM)a energy of dissolution ΔEsol (kcal/mol) solvent
PAN20 (6−8 wt %)
PMMA20 (10−14 wt %)
DMF DMAc DMSO
−14 ± 2 −21 ± 2 −18 ± 1
−31 ± 4 −45 ± 2 −41 ± 2
a The affinity to the solvent increases in the order DMF < DMSO < DMAc. The values were obtained as a difference of the average energy of polymer solutions, the pure solvent, and an amorphous oligomer melt, normalized by the number of oligomers present in solution, by NPT molecular dynamics simulation at 101.3 kPa. The uncertainties reflect statistical fluctuations in the simulations.
energies and dissolution enthalpies, which are equal due to negligible volume work, are ∼2.2 times as large for PMMA compared to PAN in all solvents, whereby the mass of PMMA was only 1.9 times that of PAN (2004 g/mol versus 1063 g/mol). Therefore, PMMA was slightly more soluble compared to PAN per unit mass. The order of solubility in the solvents was the same for both polymers, DMAc was a better solvent than DMSO, and DMF was the worst solvent in the series. The associated dissolution energies per monomer are yet comparatively small and equal −0.7 to −1.0 kcal/mol for acrylonitrile (C3H3N) and −1.5 to −2.2 kcal/mol for methyl methacrylate (C5H8O2), respectively. The dissolution energies slightly exceed −1 RT for acrylonitrile, equal to a few favorable van der Waals contacts and a polar interaction related to the nitrile group. Methyl methacrylate can interact through more van der Waals contacts than acrylonitrile due to a larger number of polarizable atoms and through two polar interactions mediated by the ester group (Scheme 1). The dissolution energies reflect these comparatively weak polymer-solvent interactions which, per monomer, are less than half the strength of a hydrogen bond of approximately −4.5 kcal/mol (−4.5 kcal/mol is the strength of a hydrogen bond in liquid water according to a vaporization energy of 9.7 kcal/mol for two hydrogen bonds per molecule and some van der Waals contacts).59
Table 3. Hansen Solubility Parameters for the Components in the Ternary CNT Dispersions and Their Ranges of Uncertaintya s parameter δTb
δD
δP
δH
19.4 ± 0.7 19.9 ± 0.7 22.7
18.5 ± 0.5 19.0 ± 0.5 16.8
5±2 5±2 11.5
3±2 3±2 10.2
PMMA DMF
22.7 (18−23) 24.8
18.6 (16−19) 17.4
10.5 (6.5−10.5) 13.7
7.5 (5.4−7.5) 11.3
11.0 (8.6−11)
PAN DMSO
25.3 (21−26) 26.7
18.2 (15−21) 18.4
16.2 (13−16) 16.4
6.8 (6.8−8) 10.2
10.9 (8−13)
compd a
SWCNT (est) MWCNT (est)a DMAc
R0c
REDd
0.42 (PMMA) 0.59 (PAN) 0.50 (PMMA) 0.49 (PAN) 0.63 (PMMA) 0.31 (PAN)
a From refs 17, 71, and 72,. Solubility parameters for SWCNTs and MWCNTs were estimated from data for large aromatic molecules and molecules with comparable internal polarity. (The estimate of Hansen solubility parameters for CNTs is described in section S4 in the Supporting Information.) Solubility parameters of CNTs show a gap to those of solvents and polymers consistent with poor dispersion. The REDs indicate good solubility of the polymers in all solvents (RED < 1.0). bThe total solubility parameter δT is defined by a sum of squares of dispersion, polar, and hydrogen bond contributions: δ2T = δ2D + δ2P + δ2H. cR0 is the solubility radius (interaction range) of the polymer which is obtained from experiments. Data are taken from refs 69 and 70. dThe RED between a solvent and a solute is used to quantify solubility. It is defined as RED = Ra/R0, where Ra is the distance in Hansen space R2a = 4(δD2 − δD1)2 + (δP2 − δP1)2 + (δH2 − δH1)2 with index 2 for the solvent and index 1 for the solute. RED < 1 signifies the molecules are alike and would dissolve, RED = 1 means the polymer would partially dissolve or swell, and RED > 1 implies the polymer would not dissolve (see ref 69).
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Figure 3. Representative snapshots of SWCNT dispersions in PAN, PMMA, and a PAN3-PMMA1 mixed solutions in the three solvents at 25 °C. The polymer concentrations range from 5 wt % to 11 wt % and CNT concentrations amount to 12−13 wt %. (a−c) PAN shows attraction to CNTs in DMSO and does not bind to CNTs in DMF and in DMAc. (d−f) PMMA shows strongest binding to CNTs in DMSO, consistent binding to CNTs in DMAc, and some binding to CNTs in DMF. (g−i) A mixture of PAN and PMMA shows significant binding to CNTs in DMSO, some binding in DMAc, and no binding to CNTs in DMF. Attraction of both polymers to CNTs in DMSO is related to lower affinity of bare CNTs to DMSO. (j−l) Magnified insets from (g−i) show the local structure and polymer interactions at the CNT surface. Polymer adsorption involves competing van der Waals, polar, and CH-π interactions with the solvent, the CNT surface, and with itself or other polymer chains. Colored numbers refer to the indicated distances in nm. Snapshots are shown for 2 × 2 × 1 supercells containing 20mer polymers after 10 ns NPT molecular dynamics in the dispersed state.
only significant in DMSO. Adsorption of PMMA to CNTs was observed in all three solvents. Effectively, polymer adsorption on the CNT surface helps reduce unfavorable CNT contact with the solvent, especially with DMSO (see subsection on CNT/solvent interactions above). Atomically resolved information can be obtained from radial distribution functions that show the statistical distribution of individual atoms in the solvents and in the polymers from the CNT surface in the different CNT dispersions (Figures S10−S13 and details in section S3 in the Supporting Information). DMF molecules are of intermediate polarity, planar, least repelled from the CNT surface (Figure 2e), and found to diffuse between the CNT surface and the polymer, avoiding direct surface contact of PAN and allowing weak binding of PMMA (Figure 3j and Figures S8−S10 and S13a,b). DMAc molecules are longer than DMF due to the added methyl group, slightly less polar, and sterically less prepared to interact with SWCNTs. As a result, DMAc supports weak binding of PAN and significant binding of PMMA to CNTs (Figure 3k and Figures S8, S9, S11, and S13c,d). DMSO exhibits the least surface interactions with CNTs
among the polymers themselves (see subsection on polymer/ solvent interactions above). The interaction of polymers with the CNT surface can therefore be considered as a partial depletion interaction, whereby the nonpolar backbone binds to the CNT, and polar side groups maintain favorable interactions with the solvent. Smaller contributions to binding also arise from polar-π and CH-π interactions68 in competition with the solvent. The polar nitrile groups in PAN contribute to adsorption onto the CNT surface through polar-π and n-π* interactions,63 and similarly the ester groups in PMMA in some cases. However, equal or better stabilization of the nitrile and C−O dipoles is possible in the solvents that contain polar amide, sulfoxide, and C−S groups. The dominant van der Waals and CH-π interactions between polymers and CNTs are weaker for a PAN 20mer with 62 hydrogen atoms in alkyl groups in comparison to a PMMA 20mer with 162 hydrogen atoms in alkyl groups (Figure 3k,l and Figures S8 and S9). Contacts of hydrogen atoms in alkyl groups of PAN with the CNT surface are also hindered sterically by the elongated CN side groups. Overall, adsorption of PAN to CNTs is weaker than that of PMMA and 12810
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parameters, however, as the parameters and the solubility radius R0 for PAN and PMMA differ somewhat according to source (as indicated by the ranges in Table 3). While we gave preference to more commonly used values and the data in Hansen’s book,69 for example, the RED for PAN in DMAc of 0.59 could also be 0.40. An estimate of solubility parameters for CNTs was made based on large aromatic molecules and molecules with comparable internal polarity (section S4 in the Supporting Information). The δT values of 19.4 ± 0.7 for SWCNTs and 19.9 ± 0.7 for MWCNTs differ somewhat from PMMA (22.7) and strongly from PAN (25.3), consistent with some affinity of PMMA to CNTs and less affinity of PAN to CNTs, which was observed in the simulation (Figures 3 and 4a). The solubility parameters for CNTs are also clearly lower than those for the solvents, indicating poor miscibility with DMF, DMAc, and DMSO (Table 3). This finding also agrees with molecular dynamics simulations and experiment. Experiment64,61 and simulation (Figure 2e) suggest DMF to be a slightly better solvent than DMAc for CNTs, whereas the solubility parameters suggest DMAc to be a better solvent than DMF. DMSO is the most unfavorable solvent for CNT dispersion according to simulations (Figure 2e) and solubility parameters (Table 3). In summary, the main drivers for adsorption versus desorption of polymers on CNTs are the strength of the van der Waals and CH-π interactions between the polymer and the CNT, paired with the relief of unfavorable CNT-solvent interactions and a tendency of the polar polymer side groups to remain in contact with the polar solvent. The nonpolar portion of the polymer may alternatively bind to other polymer chains in solution, including portions of the same chain, and form globule-like structures, especially at higher concentration. Dispersion of CNTs in the Polymer Solutions. The ability of the solvents and polymer solutions to disperse carbon nanotubes was ranked using the average closest distance of carbon nanotubes in the dispersed state in the simulations (Figure 4b) and by dispersion energies (Figure 5). Using solutions of PAN, the dispersion of CNTs is more effective in PAN/DMSO and in PAN/DMF and less effective in PAN/ DMAc solution at high concentration (Figure 4b). Using solutions of PMMA, CNT dispersion is better in PMMA/ DMSO and in dilute PMMA/DMF. Solutions of a PAN3PMMA1 mixture support CNT dispersion in DMSO, less in DMAc, and least in DMF. Overall, CNT dispersion is more favorable in DMSO for all polymers and mixtures. The strength of polymer adsorption on the CNT (Figure 4a) and the extent of CNT dispersion for a given polymer/solvent combination (Figure 4b) show a partial correlation. Good CNT dispersion and strong polymer adsorption are observed with PAN and PMMA at low concentration in DMSO. However, good CNT dispersion without notable polymer adsorption is seen for PAN in DMF. For PAN and for PMMA in all solvents, CNT binding was found to decrease at higher polymer concentration (Figure 4a), while the dispersion of CNTs is only reduced in some cases (Figure 4b). Polymer binding and CNT dispersion therefore may not be directly correlated, however, polymer binding could topologically support CNT separation over an extended period of time (beyond the time scale of the simulations). Much slower diffusion of the adsorbed polymers compared to that of solvent molecules is expected to prevent CNTs agglomeration after barriers of initial separation are overcome, especially at high molecular weight. The propensity for dispersion of carbon nanotubes was also analyzed by dispersion energies (Figure 5). The dispersion
Figure 4. Trends in polymer adsorption and in CNT dispersion as a function of composition and solvent from molecular dynamics simulations at 25 °C. The polymer concentrations range from 5 wt % to 13 wt %. (a) Polymer binding to the CNT surface was characterized by the average number of monomers in contact with the CNT surface, defined as within 4 Å distance. Adsorption is stronger in DMSO than in DMAc and DMF for all polymers. Lower concentration (PAN2, PMMA2) favors adsorption over higher concentration (PAN3, PMMA3, PAN3-PMMA). (b) CNT dispersion was characterized by the average distance between closest CNTs and the corresponding number of solvent layers in between the CNTs. Larger distance equals better dispersion. DMF allows good dispersion of CNTs in the presence of PAN and of PMMA at low concentration (PMMA2). DMAc is moderately suited to disperse CNTs in the presence of PAN and PMMA at low concentration (PAN2, PMMA2). DMSO appears to be most effective to disperse CNTs in the presence of PAN, PMMA, and a PAN-PMMA mixture. Polymer adsorption and CNT dispersion have no direct correlation.
due to pyramidal geometry, fewer surface-accessible polarizable groups, and higher dipole moment relative to DMF and DMAc (Table S2). Therefore, it enables significant binding of PAN and PMMA to the CNT surface (Figure 3l and Figures S8, S9, S12, and S13e,f). The molecular and energy-based insights are in agreement with Hansen solubility parameters17,69−72 and with estimated solubility parameters for CNTs (Table 3). Similar solubility parameters δT for all polymers and solvents (23−27) indicate solubility, which is confirmed by relative energy differences (REDs) < 1. The REDs π* Interaction: A Rapidly Emerging Non-Covalent Interaction. Phys. Chem. Chem. Phys. 2015, 17, 9596− 9612. (64) Lee, G. W.; Kumar, S. Dispersion of Nitric Acid-Treated SWNTs in Organic Solvents and Solvent Mixtures. J. Phys. Chem. B 2005, 109, 17128−17133. (65) Dai, L. Functionalization of Graphene for Efficient Energy Conversion and Storage. Acc. Chem. Res. 2013, 46, 31−42. 12815
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