Application of Polymer Solubility Theory to Solution Phase Dispersion

May 7, 2009 - Single-walled carbon nanotubes below 1.5 μm in length are effectively rigid rod-like polymers, but polymer solubility theory has not ye...
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J. Phys. Chem. C 2009, 113, 9532–9540

Application of Polymer Solubility Theory to Solution Phase Dispersion of Single-Walled Carbon Nanotubes Monica L. Usrey, Amanda Chaffee, Esther S. Jeng, and Michael S. Strano* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ReceiVed: December 12, 2008; ReVised Manuscript ReceiVed: March 23, 2009

Single-walled carbon nanotubes below 1.5 µm in length are effectively rigid rod-like polymers, but polymer solubility theory has not yet been applied to their solution phase dispersion despite its success in modeling other polymer systems. In this work, we experimentally determine the solubility of arc discharge singlewalled carbon nanotubes (SWNT) covalently functionalized with aryl carboxylic acid or aryl hydroxyl groups in aqueous solution using UV-vis-nIR photoabsorption spectroscopy. Empirically, stable suspension is observed when the optical density at 632 nm is above 0.05. The critical level of functionalization required for surfactant-free aqueous suspension is found to be >1.5 and >5.1 functional groups per 100 carbons for the carboxylic acid and hydroxyl aryl groups, respectively. Solubility parameters are estimated by using established polymer solubility theory (Fedors and Refined Solubility Parameter group additivity models), molecular simulations (Maiti Dissipative Particle Dynamics), or a combination of both (Maiti-RSP and Maiti-Fedors). Flory-Huggins interaction parameters are calculated for suspensions of both chemistries in water and dimethyl formamide (DMF). Comparison of experiment and model indicates that the combined Maiti-RSP model best describes increasing solubility with increasing functionalization. Introduction Suspension of single-walled carbon nanotubes (SWNT) in aqueous solution, organic solvent, or polymer composites is required for many potential applications. For aqueous suspensions, carbon nanotubes are solubilized with the aid of surfactants,1 polymers,2 and proteins3 by using noncovalent functionalization. Individual dispersion can be achieved by using these methods in combination with ultrasonication and ultracentrifugation.1 Other dispersion methods include the covalent modification of the surface via acid purification4 and/or concerted reaction with diazonium salts.5 Organic solvent suspensions have also been investigated for applications where dispersion is desired without chemical modification or suspension agents. N-Methyl-2-pyrrolidinone (NMP), dimethyl formamide (DMF), and other amide solvents have been identified as the best organic solvents.6-9 Suspension capability has been linked to high values of electron pair donicity,9 low values of the hydrogen bond parameter,9 and higher polarity.6 SWNT functionalized with nitric acid reflux purification also demonstrated enhanced solubility in amide solvents.6 Currently, researchers are focused on relating nanotube solubility to a predictive parameter that would allow comparison between nanotube complexes and potential solvents or polymers. Polymer solubility theory describes the behavior of polymers in mixtures and solutions with use of two main parameters: the solubility parameter and the Flory-Huggins interaction parameter. The Hildebrand solubility parameter provides a systemic description of the miscibility behavior of solvents and polymers based on dispersion forces.10 This solubility parameter is defined as the square root of the cohesive energy density, the heat of vaporization normalized to the molar volume.11 An extension of the Hildebrand parameter, named the Hansen parameter, estimates the relative miscibility of polar and hydrogen bonding * To whom correspondence should be addressed. Fax: (617) 258-8224. E-mail: [email protected].

systems by considering three components: dispersion, polar, and hydrogen bonding forces.12 Solvents with similar solubility parameters are miscible in most proportions; dissimilar values yield limited solubility. The Flory-Huggins interaction parameter, χ, directly quantifies this effect. However, the experimental techniques to measure Hildebrand and Hansen solubility parameters, including measuring the heat of vaporization, intrinsic viscosity, and degree of swelling in solvent, can lead to large errors and are prohibitive for larger molecular weight polymers.13 Accurate predictive simulations of these parameters typically require molecular dynamics simulations which can be complex and time intensive. Several efforts have been made to apply polymer solubility theory to carbon nanotube solutions. Hansen solubility parameters of 16 organic solvents were compared to photoabsorption data for six carbon nanotube samples to map the threedimensional Hansen solubility sphere. Successful qualitative predictions regarding an additional four solvents were made based on the results. However, predictions for multiwalled nanotubes functionalized via oxidation were not successful due to limited solubility in the chosen solvents.14 In a similar study, Hansen and Hildebrand solubility parameters were compared to experimental extinction and absorption coefficients for HiPco SWNT suspended in organic solvents. Polar forces and hydrogen bonding correlated better than dispersion forces, although the relationship differed for chlorinated solvents.15 Conversely, the dispersive component of the Hansen parameter offered the best prediction for solubility of heat-treated, washed HiPco SWNT in a variety of solvents, including water. Similarly, the ability of surfactants to promote dispersion also correlated to their calculated Hansen dispersive parameters.16 Carbon nanotubes functionalized with octadecylamine formed the most stable suspensions in organic solvents with a total Hansen parameter similar to that of the functional group. This study concluded that for highly functionalized nanotubes, the predominant interaction governing solubility is that between the

10.1021/jp810992u CCC: $40.75  2009 American Chemical Society Published on Web 05/07/2009

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solvent and functional group, not solvent and nanotube sidewall.17 The Flory-Huggins parameter for pristine HiPco nanotubes in N-methylpyrrolidone (NMP) has been estimated via static light scattering; the negative value indicates that dispersion in NMP is thermodynamically favorable.18 However, only one group has predicted Hildebrand solubility parameters for pristine individual carbon nanotubes.19 A custom software suite, the Accelrys Materials Studio, is utilized to calculate the cohesive energy density of individual bare carbon nanotubes, using dissipative particle dynamics (DPD). The resulting parameters were compared to polymer values to predict the solubility of unmodified SWNT in various polymer composites. Although appropriate questions can be presented regarding the applicability of thermodynamic analysis, which often requires an equilibrium state that is questionable for carbon nanotube solutions, efforts to describe nanotube solubility with polymer theory continue. In this study, arc discharge carbon nanotubes (P2) are functionalized with aryl carboxylic acid and aryl hydroxyl groups by using in situ diazonium chemistry.20 Solubility in aqueous solution is measured by using UV-vis-nIR photoabsorption spectroscopy as a function of the extent of functionalization. After functionalized SWNT capable of stable solubility in aqueous solution are identified, modeling of the effect is conducted by using group additivity polymer solubility theory. Experimental Methods In Situ Covalent Functionalization with Diazonium Salts. P2-SWNT (Carbon Solutions, Inc.) are carbon nanotubes produced via electric arc discharge and purified by oxidation to remove catalyst without appreciable functionalization.21 P2SWNT were suspended in 1,2-orthodichlorobenzene (0.267 mg/ mL) via bath sonication in a sealed flask for 1 h. The in situ reaction, shown in Figure 1a, was carried out according to a published protocol.20 In this reaction, the reactive diazonium salt is synthesized from an aryl aniline compound by using isoamyl nitrite in the carbon nanotube solution, rather than presynthesized separately. 4-Aminobenzoic acid and 4-aminophenol are the aniline compounds used for reaction with the aryl carboxlic acid group (COOH-SWNT) and aryl hydroxyl group (OH-SWNT), respectively. The extent of reaction was controlled by the ratio of aniline added per mole of carbon with a constant excess of isoamyl nitrite. Table 1 lists the reaction extents for the COOH-SWNT and OH-SWNT reaction series. For the OH-SWNT, five reactions were completed with reaction extents (moles of aniline per mole of carbon) as follows: P2-OH1 (0.008), P2-OH2 (0.068), P2OH3 (0.143), P2-OH4 (0.225), and P2-OH5 (1.85). For the COOH-SWNT, seven reactions were completed with reaction extents (moles of aniline per mole of carbon) as follows: P2COOH1 (0.005), P2-COOH2 (0.009), P2-COOH3 (0.050), P2COOH4 (0.102), P2-COOH5 (0.233), P2-COOH6 (0.244), and P2-COOH7 (0.500). The unreacted P2-SWNT was utilized as a control. No SWNT solution was functionalized with both aryl carboxylic and aryl hydroxyl groups. Characterization of the functionalized samples was completed by using Raman spectroscopy at 785 nm excitation. Two key Raman features for carbon nanotubes are the tangential mode (G Peak, ∼1590 cm-1) and the disorder mode (D peak, ∼1300 cm-1), representing sp2 and sp3 hybridized carbons, respectively. Defects in the nanotube sidewall lead to a concomitant increase in the D peak and decrease in the G peak, as carbon bonds in the lattice are broken and reformed with external aryl moieties.22,23 Therefore, the ratio of the D peak area to the G peak area is

Figure 1. (a) Illustration of in situ diazonium reaction with carbon nanotubes. 4-Aminophenol reactant produces aryl hydroxyl functional groups (OH-SWNT). 4-Aminobenzoic acid produces aryl carboxylic acid groups (COOH-SWNT). UV-vis-nIR photoabsorption spectra of 0.085 mg/mL (b) COOH-SWNT and (c) OH-SWNT suspensions in water. The insets show the region where the OD at 632 nm is noted to estimate the SWNT concentration of each sample. Bold lines indicate reactions with successful SWNT suspension.

utilized as a qualitative measure of the extent of functionalization. The D/G ratio for each reaction is normalized to the unreacted control ([D/G]N) to ease comparison. From a previously established correlation between D/G ratio and elemental composition from X-ray photoelectron spectroscopy (XPS),24 the number of functional groups present per 100 carbons (i.e., percent functionalization) can be estimated. This correlation, unlike other characterization methods such as thermogravimetric analysis (TGA), provides a nondestructive technique for analyzing small quantities of nanotube solids and dilute solutions. The D/G ratio and calculated extent for each reaction is listed in Table 1. Solubility Measurement with Use of Photoabsorption Spectroscopy. Aqueous solutions (0.085 mg/mL) for each reaction were prepared via probe tip sonication (15W, 30 min) and benchtop centrifugation (13 000 rpm, 60 min). The solution pH was adjusted to 10, from ∼5, with sodium hydroxide, to deprotonate the functional groups. The supernatant was retained and the pellet discarded. Absorption data (optical density vs. wavelength) were collected with a Shimadzu UV-3100PC instrument from 190 to 1900 nm. The optical density (OD) of carbon nanotube solutions has been correlated to the concentration of dispersed nanotubes.25 The stability of the aqueous

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TABLE 1: Summary of Analysis for COOH-SWNT and OH-SWNT Reactions Raman analysis (785 nm)

photoabsorption

XPS correlation

sample

rxn extent (mol FG/molC)

D peak

G peak

D/G

D/Gn

OD (632 nm)

(OD)N (632 nm)

no. of FG per 100 C’s

P2 P2-COOH1 P2-COOH2 P2-COOH3 P2-COOH4 P2-COOH5 P2-COOH6 P2-OH1 P2-OH2 P2-OH3

0.000 0.005 0.009 0.050 0.102 0.244 0.500 0.068 0.143 0.225

4361 4962 7597 3481 14613 16727 22594 16067 28910 19342

12141 13575 25459 15389 31354 26127 26482 12018 12151 13440

0.023 0.366 0.298 0.226 0.466 0.640 0.853 0.448 2.379 1.439

1.0 15.9 13.0 9.8 20.3 27.8 37.1 19.5 103.4 62.6

0.020 0.017 0.037 0.017 0.142 0.182 0.270 0.043 0.222 0.100

1.0 0.9 1.9 0.9 7.1 9.1 13.5 2.2 11.1 5.0

0 1.22 0.98 0.72 1.58 2.21 2.98 1.52 8.49 5.09

solution was observed qualitatively over time. Successful suspensions (OD at 632 nm >0.05) of COOH-SWNT were stable for several days, while the OH-SWNT solutions were stable for 12-24 h. Results The photoabsorption spectra for all SWNT suspensions are presented in Figure 1. The broad peak in the UV region represents the π plasmon of aromatic systems (λ ≈ 250 nm). For the aqueous SWNT solutions, a peak in this region indicates the presence of carbon nanotubes. The photoabsorption spectra do not contain any of the sharp van Hove singularities associated with individual suspension of carbon nanotubes.26 These singularities represent the valence to conduction band transitions for metallic, semimetallic, and semiconducting nanotube species and typically occur in the 440-1600 nm region depending on the SWNT species present. No peaks are expected due to the diminution of these features following covalent functionalization24 and the limited stability of the suspensions.27 The inset graphs show the 600-700 nm region where the 632 nm OD value is located. This value has been used historically to construct Beer’s law correlations of SWNT concentration. Significant OD values (OD > 0.2 at 250 nm and OD > 0.05 at 632 nm) are observed for three OH-SWNT reactions (P2OH2, P2-OH3, and P2-OH4) and three COOH-SWNT reactions (P2-COOH4, P2-COOH5, and P2-COOH6). This quantitative analysis is supported by visual evidence. Successful suspensions formed gray translucent stable solutions. Unsuccessful reactions formed colorless solutions with large aggregates, similar to the unreacted P2 control. Table 1 summarizes the reaction conditions, Raman spectroscopy analysis, and photoabsorption data for the COOHSWNT and OH-SWNT reactions. All reactions exhibit D/G ratios at least 1 order of magnitude greater than the unreacted P2-SWNT, indicating successful covalent reaction. Stable suspensions exhibit OD values 500-1350% larger than the control compared to 90-220% for other reactions, a clear quantitative difference between soluble and nonsoluble behavior. Soluble COOH-SWNT reactions (P2-COOH4, P2-COOH5, and P2-COOH6) possess aniline concentrations of 0.102, 0.244, and 0.500 and calculated extents of functionalization of 1.6%, 2.2%, and 3.0%, respectively. As expected, increasing reactant concentration provides increasing extent of functionalization. Soluble OH-SWNT reactions (P2-OH2, P2-OH3, and P2-OH4) have aniline concentrations of 0.143, 0.225, and 1.85 and calculated extents of functionalization of 8.5%, 5.1%, and 7.9%, respectively. The calculated extents do not clearly match with the aniline reactant concentrations. P2-OH4’s reactant concentration (1.85) is ∼1300% P2-OH2’s concentration, but both have

similar extents of functionalization (7.9% and 8.5%). Therefore, the in situ OH-SWNT chemistry is not as well controlled. Figure 2 shows the OD values versus the extents of functionalization for the COOH-SWNT and OH-SWNT samples. The minimum OD for stability is consistent for both functionalization schemes. Also, a linear trend of increasing optical density with increasing number of functional groups is apparent for both chemistries. The higher slope for the COOH-SWNT series indicates that the carboxylic acid group requires less functionalization to promote water-phase solubility. This could be attributed to the lower pKa of the carboxylic acid (pKa ≈ 5) than the aryl hydroxyl group (pKa ≈ 10). Therefore, at pH 10, a greater proportion of COOH groups would be deprotonated than OH groups, increasing the dispersion stability related to charge-charge repulsion between functional groups. COOH-SWNT reactions present a clear transition from nonsoluble to soluble behavior between 1.2 and 1.6 aryl carboxylic acid groups, with a corresponding 800% OD increase. The highest extent (3.0%, P2-COOH6) provides the best solubility of any reaction, achieving 13.5× the OD of the control. Successful P2-OH reactions have extents between 5.1% and 8.5% with a corresponding 200% OD increase. These data do not show a clear critical level of functionalization; but g5.0% functionalization appears to be required. Experimental data show the COOH group is more effective for promoting aqueous solubility than the OH group. At a similar extent (1.5%), the COOH group provides a 330% increase in optical density over the OH group. For a similar level of solubility (OD ≈ 0.25), the OH-SWNT requires 7.9% versus 3.0% functionalization for the COOH-SWNT chemistry; therefore each COOH group is as effective as 2.7 OH groups. Model Development. Flory-Huggins theory describes the thermodynamics of a bulk polymer mixture or solution.

Figure 2. Optical density values at 632 nm compared to the calculated extent of functionalization for the COOH-SWNT series (blue diamonds) and the OH-SWNT series (red squares). The solid line at OD ) 0.05 represents the barrier between stable and unstable aqueous SWNT solutions.

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Although this model is not the most sophisticated model available, it is relatively simple and can qualitatively describe mixing in polymer systems.28 The entropy of mixing for two polymers (A, B) with a specified number of monomers (NA and NB) can be described by eq 1. Note that this calculates the entropy of mixing on a monomer basis. The number of monomer units is included as monomers in the same chain cannot be positioned independently.

Sm 1-φ φ ln(φ) + ln(1 - φ) ) k NA NB

(1)

For the energetic portion of the model, a lattice model is assumed, where each lattice site can be occupied only by 1 segment of either polymer or solvent. Interactions between neighboring segments have energies εAA, εBB, and εAB. Using a mean-field assumption and subtracting the energy of the unmixed state from the mixed state results in the free energy of mixing, eq 2.

φB ∆Gm ) φA ln(φA) + ln(φB) + χφAφB kT N

(2)

Here, φ represents the volume fractions of solvent (A) and polymer (B) and N is the number of monomer units in the polymer.29 The only material-specific property is the FloryHuggins interaction parameter, χ, defined in eq 3. In this equation, z is the coordination number of the lattice and k is the Boltzmann constant.

χ)

z(2εAB - εAA - εBB) kT

(3)

Equation 3 shows that χ is the energy change when a segment of A is removed from an area of pure A and replaced with a segment of B from an area of pure B. Positive values of χ indicate that mixing A and B results in an increase in energy; therefore this mixing process is energetically unfavorable from an enthalpic standpoint. Negative values of χ indicate that mixing is energetically favorable. However, two species with positive χ can mix if the entropic gains outweigh the energetic penalty. Traditionally, the Flory-Huggins interaction parameter can be estimated from the Hildebrand solubility parameters of the solvent (δ1) and polymer (δ2) and the solvent molar volume (V1) as shown in eq 4. The solubility parameters for polymers can be determined experimentally via intrinsic viscosity30 or degree of swelling measurements.31

χ12 )

V1(δ2 - δ1)2 RT

(4)

Mutually soluble polymer/solvent pairs possess similar solubility parameters. As the difference between the solubility parameters increases, the tendency toward dissolution decreases.13 The solubility parameters can be estimated by using additive group contribution theory. The definition of the solubility parameter is given in eq 5 in terms of the cohesive energy (Ecoh, J/mol), molar volume (V, cm3/mol), and molar attraction constant (F, J1/2 cm3/2/mol). This equation produces a solubility parameter (δ) with SI units of J1/2/cm3/2.13

δ)

( ) Ecoh V

1/2

)

F V

(5)

The cohesive energy represents the increase in internal energy per mole if all intermolecular forces are eliminated. Cohesive

energies can be calculated from heats of vaporization for low molecular weight substances or from vapor pressure-temperature relationships. Due to difficulties in evaporating polymer materials, methods to predict the cohesive energy have been developed. Small, Van Krevelen, and Hoy developed group contribution values for the molar attraction constant, F, which has additive qualities for low and high molecular weight materials. Fedors catalogued group contribution tables for Ecoh and V. These methods have an average 10% error.13 The Hildebrand solubility parameter considers only dispersion interactions between molecules. For many polymer/solvent pairs, the cohesive energy is also affected by polar group interactions and hydrogen bonding, which led to the development of the Hansen solubility parameter. The refined solubility parameter (RSP) method includes these effects on the cohesive energy, as shown in eq 6.

Ecoh ) Ed + EP + Eh

(6)

In this equation, Ed, EP, and Eh are the energies contributed by dispersion forces, polar group effects, and hydrogen bonding, respectively. This equation can be rewritten in terms of the corresponding solubility parameters, shown below in eq 7. These parameters cannot be directly determined experimentally, but require estimation.

δ2 ) δd2 + δP2 + δh2

(7)

Overall, polar and hydrogen bonding interactions cannot be easily determined for multiple structural groups due to their complex nature. However, rough estimates can be achieved by using eqs 8-10.13

δd )

δP

∑ Fdi

√∑F )

δh )

(8)

V 2

pi

V

∑

Ehi

V

(9)

(10)

The dispersion and polar solubility parameters are calculated from the appropriate molar attraction constants (eqs 8 and 9) as defined by Small.13 The polar attraction constant is multiplied by a symmetry factor if more than one identical polar group is present. The hydrogen bonding solubility parameter cannot be calculated by using a molar attraction constant, but Hansen postulated that the hydrogen bonding energy (Ehi) is constant for structural groups.13 As with polar groups, hydrogen bonding effects can also be negated by multiple planes of symmetry. Van Krevelen summarized the group contributions to Fdi, Fdi, and Ehi for a group of structural units.13 Only a rough estimate of the Hansen solubility parameter is provided, but it allows the effect of polar and hydrogen bonding interactions to be examined. Hildebrand solubility parameters for seven carbon nanotube species have been simulated as a function of diameter with particle-based dissipative particle dynamics theory.19 The cohesive energy of the carbon nanotube was modeled as the debundling energy, the cost of isolating a single nanotube from a bundle. The calculated δ values decreased with the inverse square root of diameter and no relationship with electronic structure was found. Limited experimental evidence from CNTpolymer composites indicated the model could predict the selective affinity for certain CNT/polymer pairs. A power law

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Figure 3. Calculated solubility parameter (δ, J1/2 cm-3/2) for unfunctionalized individual carbon nanotubes and bundles as a function of diameter. Three methods are included for comparison: Maiti (large dashes), Fedors (solid), and refined solubility parameter (small dashes). The horizontal lines at 24.8, 18.7, and 14.4 represent the solubility parameter values for dimethyl formamide, benzene/chloroform, and hexane solvents, respectively.

shows excellent agreement with the simulated data and allows a predicted value for δ for any diameter to be calculated (see the Supporting Information). For these calculations, estimated SWNT volumes was achieved by using a two-step process.32 First, the SWNT volume is calculated by assuming cylindrical geometry with the diameter increased by the carbon van der Waals radius (1.72 Å). The volume of the functional groups is estimated by using an updated group additivity theory based upon 11 000 crystal structures.33 For simplicity, calculations are restricted to three carbon nanotube species: (6,5), (11,3), and (10,10). These three species represent a range of diameters from 0.8 to 1.4 nm. A standard 1000 nm length is assumed. Modeling and Discussion. Solubility parameters for bare SWNT, COOH-SWNT, and OH-SWNT were estimated by using four methods: refined solubility parameter (RSP), Fedors cohesive energy (Fedors), combined Maiti estimate + Fedors cohesive energy (M-F), and combined Maiti estimate + refined solubility parameter (M-RSP). The extent of functionalization was varied from 0% to 10%. This range represents published extents of functionalization for diazonium covalent chemistry.20,24,25 The RSP method is outlined by eqs 6-10. The Fedors method is defined in eq 5. The values of Fdi, Fdi, Ehi, and Ecoh for relevant structural groups are provided in the Supporting Information. The combined Maiti methods use the Maiti solubility parameters for the carbon nanotube and add the effects of functional groups using the Fedors or RSP methods. Solubility parameter predictions for unmodified carbon nanotubes and bundles (d ) 0.75-25 nm) are shown in Figure 3. Three solvents are included for reference: dimethyl formamide (24.8 J1/2/cm3/2), benzene and chloroform (18.7 J1/2/cm3/2), and hexane (14.4 J1/2/cm3/2). Previous studies indicate SWNT can form stable solutions in these solvents. For the Maiti simulations, seven distinct nanotube species with diameters from 0.7 to 3.0 nm were considered.19 The Maiti data set was expanded to include larger diameter species (greater than 3.0 nm) by using the power law previously mentioned. For nanotube bundle calculations, a single cylinder with the bundle diameter is assumed for simplicity. All models predict increasing solubility parameter (δ) with decreasing diameter with the greatest modulation occurring for small bundles and individuals (10 nm), all calculations predict a steady trend

Figure 4. Calculated solubility parameter (δ) as a function of extent of functionalization for (a) OH-SWNT and (b) COOH-SWNT. Four methods are included for comparison: refined solubility parameter (blue, diamonds), Fedors group additivity (red, squares), combined MaitiFedors (green, triangles), and combined Maiti-RSP (black, circles). Data for the (11,3) CNT are shown.

with average values of 9.7, 5.8, and 1.1 J1/2/cm3/2 for the Fedors, Maiti, and RSP methods, respectively. The RSP method predicts the most hydrophobic behavior with a maximum value of 10.9 J1/2/cm3/2, well below the solubility parameters of the reference solvents. Both the Fedors and Maiti methods allow miscibility with the reference solvents. This analysis indicates that the Maiti and Fedors methods better predict the solubility of bare SWNT in organic solvents. Figure 4 presents the estimated solubility parameters for OHSWNT and COOH-SWNT as a function of extent of functionalization for all four methods. To simplify the comparison, only data for the (11,3) SWNT is shown. Total solubility parameters are compared, as the RSP method is the only method to provide estimates for the Hansen components. The Maiti method for estimating solubility parameters of unmodified carbon nanotubes produces only a total parameter; therefore the combined MaitiRSP method cannot provide Hansen component values. Additionally, unlike previous studies with carbon nanotubes functionalized with bulky molecules,17 the OH-SWNT and COOH-SWNT possess relatively low functionalization extents. It is likely that the solvent will interact with the hydrophobic nanotube sidewall as well as the hydrophilic functional groups. Therefore, the total solubility parameter, which considers dispersive forces, hydrogen bonding, and the effects of polar groups, is most applicable for these SWNT complexes. The RSP and Maiti-RSP methods provided the greatest modulation of δ with increasing functionalization for both chemistries. Increases of ∼200% (RSP) and ∼150% (M-RSP) are observed across the 0-10% range. Greater modulation occurs for 0-5 functional groups (RSP: +64-76%, M-R: +38-39%) than for 5-10 functional groups (RSP: +17-19%, M-R: +13-14%). This bodes well for the use of covalent chemistries to increase solubility without requiring extensive sidewall reaction that could diminish other properties. Conversely, the Fedors method showed little to no modulation of δ with functionalization (+3% COOH; -2% OH). The

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Figure 5. Calculated Flory-Huggins interaction parameter (χ) as a function of extent of functionalization for aqueous solutions of (a) OH-SWNT and (b) COOH-SWNT and DMF suspensions of (c, e) OH-SWNT and (d, f) COOH-SWNT. Four methods are included for comparison: refined solubility parameter (blue, diamonds), Fedors group additivity (red, squares), combined Maiti-Fedors (green, triangles), and Combined Maiti-RSP (black, circles). Data for the (11,3) CNT are shown.

Fedors model predicts decreasing solubility parameter with increasing COOH group functionalization (Figure 4b), indicating that adding polar groups decreases aqueous solubility. The MaitiFedors combination predicts slight modulation of δ with functionalization (+12% COOH; +19% OH) with magnitudes similar to Fedors estimates. Calculated Flory-Huggins interaction parameters (χ) for aqueous solutions of OH-SWNT and COOH-SWNT are shown in Figure 5. These values (1.2-10.8) predict that carbon nanotubes, bare or functionalized, are not miscible in water. Due to the hydrophobicity of SWNT, this is not unexpected. However, χ decreases with increasing functionalization indicating that the presence of OH and COOH groups on the nanotube sidewall should improve aqueous solubility. Overall, similar trends are observed for the Flory-Huggins interaction parameter as were shown for the solubility parameter. RSP and MaitiRSP estimates show the greatest variation while the Fedors method shows the smallest variation. Flory-Huggins interaction parameters were also calculated for DMF suspensions of OH-SWNT and COOH-SWNT (Figure 5). Overall, χ is lower for DMF than for water suspensions; this is expected as the solubility parameter of DMF (24.8 J1/2/ cm3/2) is significantly lower than that for water (48.1 J1/2/cm3/2) and closer to SWNT estimates. The RSP and M-RSP models show opposite effects: χ decreases for the RSP model, but increases above 2% functionalization for the Maiti-RSP model. Therefore, if this model is accurate, excessive functionalization with polar aryl groups could reduce solubility in DMF. The

Fedors method predicts χ < 1 for all reactions; however, solubility decreases with COOH functionalization and increases with OH functionalization. The Fedors-Maiti method gives the lowest χ values for both chemistries (all below 0.12). Minima are predicted at 4% and 7% functionalization for OH-SWNT and COOH-SWNT, respectively. To determine if polymer solubility theory can explain the observed stability of COOH-SWNT and OH-SWNT, the calculated δ and χ values were compared to the experimental OD data in Figures 6 and 7. Normalized values are included to show relative changes with functionalization. The stable suspension threshold (OD ) 0.05) is shown with a vertical dashed line. Since the solubility parameter of water is 48.1 (J1/2/cm3/2) and the predicted values for bare SWNT (Figure 3) are considerably lower, increasing solubility parameter is indicative of increasing aqueous solubility. For the OH-SWNT (Figure 6), the Fedors method shows no significant change in δ above the solubility threshold. The remaining methods (RSP, Maiti-RSP, and Maiti-Fedors) each display an upward shift in δ for the soluble reactions (33%, 20%, and 7.5%). A similar analysis is conducted on the Flory-Huggins interaction parameters. Maiti-RSP provides the lowest χ values (1.4-2.1) for successful OH-SWNT reactions and the greatest decrease at the onset of solubility (42%). The remaining methods show decreases of 3.0%, 14%, and 22% for the Fedors, Maiti-Fedors, and RSP models. Figure 7 presents δ and χ values for the COOH-SWNT reaction series. Overall, the magnitudes of the δ values are very

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Figure 6. Estimated solubility parameter (δ, J1/2 cm-3/2) and calculated Flory-Huggins interaction parameter (χ) for aqueous solutions of OHSWNT compared to experimental OD values. The vertical line shows the solution stability cutoff of OD ) 0.05. Four methods are included for comparison: refined solubility parameter (blue, diamonds), Fedors group additivity (red, squares), combined Maiti-Fedors (green, triangles), and the combined Maiti-RSP (black, circles). Data for the (11,3) CNT are shown.

Figure 7. Estimated solubility parameter (δ, J1/2 cm-3/2) and calculated Flory-Huggins interaction parameter (χ) for aqueous solutions of COOHSWNT compared to experimental OD values. The vertical line shows the solution stability cutoff of OD ) 0.05. Four methods are included for comparison: refined solubility parameter (blue, diamonds), Fedors group additivity (red, squares), combined Maiti-Fedors (green, triangles), and the Combined Maiti-RSP (black, circles). Data for the (11,3) CNT are shown.

similar to the OH-SWNT reactions; however, the shift with solubility is more subtle. RSP shows the greatest increase with solubility (+7.9%) followed by the Maiti-RSP method (+5.1%) and the Maiti-Fedors combination (+1.2%). The Fedors method predicts a 0.3% decrease. Flory-Huggins interaction parameters, calculated from the predicted solubility parameters, are presented for COOH-SWNT in Figure 7c,d. Aside from the Fedors method, which shows a 1.1% increase at the onset of solubility, all models predict decreasing χ with increasing functionalization. As with the OH-SWNT, the Maiti-RSP method gives the greatest modulation with a 10.7% decrease, followed by the RSP model (-4.9%) and the Maiti-Fedors method (-2.1%). On the basis of these analyses, the Maiti-RSP method most accurately represents the effect of aryl hydroxyl and aryl carboxylic acid functionalization on nanotube aqueous solubility.

While it does not show the greatest modulation of δ with increasing reaction, the magnitudes are within a reasonable range of 22.5-34.4 J1/2/cm3/2; this range contains δ values for several good nanotube solvents including dimethyl formamide (24.8 J1/2/ cm3/2) and dimethyl sulfoxide (26.4 J1/2/cm3/2). Furthermore, the Maiti-RSP method predicts the smallest Flory-Huggins interaction parameters which represent the most favorable energetic barrier to mixing. The success of the Maiti-RSP model is not surprising. This combination model contains both the complexity of molecular simulations for the bare nanotube (Maiti) and the simple addition of dispersion, hydrogen bonding, and polar group effects of functional groups (RSP). The Maiti model estimates for bare nanotubes are based upon complex dissipative particle dynamics (DPD) simulations with the Accelrys software suite. These

Solution Phase Dispersion of SWNT simulations capture the cohesive energy of nanotubes by using the unique approach of the “debundling” energy. The resulting predictions agree with organic solvent values known for successful SWNT suspension (DMF, DMSO, etc.) and polymers identified as forming stable nanotube composites.19 In contrast, the RSP group additivity model predicts extremely low δ values for bare SWNT ( 0). The predicted Flory-Huggins interaction parameters contain only the enthalpic portion of the free energy and do not include any entropic contributions. Entropy typically increases during mixing and the accepted values for the entropic component of χS are 0.3-0.4 for polymers.19 Therefore an enthalpic barrier in this range can be overcome by entropic gains. This effect was not included in the modeling as the exact value is uncertain for carbon nanotubes.19 Also, the χ values for COOH-SWNT and OH-SWNT in water are predicted to be well above the 0.3-0.4 range. As stated previously, temporal stability differences were observed qualitatively; typically OH-SWNT aqueous solutions were less stable than COOH-SWNT aqueous solutions. This indicates that true thermodynamic equilibrium may not have been reached. To date, only one study has demonstrated a truly thermodynamically stable SWNT dispersion (HiPco in NMP) by tracking the root-mean-square SWNT diameter over ∼200 h.18 In other studies, SWNT solutions are deemed sufficiently stable for solubility analysis following the sonication/centrifugation process.14,17 Thermodynamic equilibrium is not required for the calculation of solubility parameters, which are intrinsic properties of the solvent, nanotube, and functional groups. Only when comparing these parameters by using the energetic analysis presented by Flory-Huggins theory does equilibrium become important. The positive values of χ predicted by the model support the experimental observation of a nonequilibrium state. The relationship between solubility, which is an equilibrium property, and colloidal stability, which is kinetic, is through the interparticle potential. The rate of reaggregation is related to solution thermodynamics around the nanotube and its functional ligands through its influence on the interparticle potential. Future work will develop this relationship for nanotubes more rigorously. Preliminary calculations indicate that approximately 24 to 30 functional groups per 100 carbons (for the (11,3) SWNT) would be required to lower χwater within the potential entropic gain window (assuming χS ) 0.4) for OH-SWNT and COOHSWNT, respectively. Future time-dependent studies can investigate COOH-SWNT and OH-SWNT reactions in this extent range to evaluate if the predicted equilibrium state is achieved. Additionally, model predictions can be used to inform the design of other diazonium chemistries that offer greater solubility benefits. However, the solutions experimentally identified in this study do offer

J. Phys. Chem. C, Vol. 113, No. 22, 2009 9539 surfactant-free dispersion of carbon nanotubes in water with limited functionalization. Conclusion Polymer solubility theory has been applied to the solution phase dispersion of single-walled carbon nanotubes. Experimentally determined solubility data were obtained for SWNT after covalent functionalization with aryl carboxylic acid or aryl hydroxyl groups in aqueous solution by using UV-vis-nIR photoabsorption spectroscopy. The stable suspension threshold was determined to be 0.05 OD at 632 nm. We find that the critical level of functionalization required for surfactant-free aqueous suspension is found to be >1.5 and >5.1 functional groups per 100 carbons for the carboxylic acid and hydroxyl aryl groups, respectively. Solubility parameters are estimated by using established polymer solubility theory (Fedors and refined solubility parameter group additivity models), molecular simulations (Maiti dissipative particle dynamics), or a combination of both (Maiti-RSP and Maiti-Fedors). Flory-Huggins interaction parameters are calculated for suspensions of both chemistries in water and dimethyl formamide (DMF). Comparison of experiment and model indicates that the combined Maiti-RSP model best describes increasing solubility with increasing functionalization. Supporting Information Available: Tables giving a summary of molar volume calculations, summary of group additivity values, calculated solubility parameters, and Flory-Huggins interaction parameters for OH-SWNT and COOH-SWNT. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) O’Connell, M. J.; Bachilo, S. M.; Huffman, C. B.; Moore, V. C.; Strano, M. S.; Haroz, E. H.; Rialon, K. L.; Boul, P. J.; Noon, W. H.; Kittrell, C.; Ma, J. P.; Hauge, R. H.; Weisman, R. B.; Smalley, R. E. Science 2002, 297, 593–596. (2) Barone, P. W.; Strano, M. S. Angew. Chem., Int. Ed. 2006, 45, 8138–8141. (3) Barone, P. W.; Baik, S.; Heller, D. A.; Strano, M. S. Nat. Mater. 2005, 4, 86–U16. (4) Kim, Y.; Lee, D.; Oh, Y.; Choi, J.; Baik, S. Synth. Met. 2006, 156, 999–1003. (5) Dyke, C. A.; Tour, J. M. Nano Lett 2003, 3, 1215–1218. (6) Furtado, C. A.; Kim, U. J.; Gutierrez, H. R.; Pan, L.; Dickey, E. C.; Eklund, P. C. J. Am. Chem. Soc. 2004, 126, 6095–6105. (7) Giordani, S.; Bergin, S.; Nicolosi, V.; Lebedkin, S.; Blau, W. J.; Coleman, J. N. Phys. Status Solidi B 2006, 243, 3058–3062. (8) Giordani, S.; Bergin, S. D.; Nicolosi, V.; Lebedkin, S.; Kappes, M. M.; Blau, W. J.; Coleman, J. N. J. Phys. Chem. B 2006, 110, 15708– 15718. (9) Ausman, K. D.; Piner, R.; Lourie, O.; Ruoff, R. S.; Korobov, M. J. Phys. Chem. B 2000, 104, 8911–8915. (10) Hildebrand, J. H. The Solubility of Non-Electrolytes; Reinhold: New York, 1936. (11) Bicerano, J. Prediction of Polymer Properties; CRC Press: Boca Raton, FL, 2002. (12) Hansen, C. M. J. Paint Technol. 1967, 39, 511. (13) Van Krevelen, D. W. H. P. J. Properties of Polymers; Elsevier Scientific Publishing: New York, 1976. (14) Detriche, S.; Zorzini, G.; Colomer, J.-F.; Fonseca, A.; Nagy, J. B. J. Nanosci. Nanotechnol. 2008, 8, 6082–6092. (15) Cheng, Q. H.; Debnath, S.; Gregan, E.; Byrne, H. J. J. Phys. Chem. C 2008, 112, 20154–20158. (16) Ham, H. T.; Choi, Y. S.; Chung, I. J. J. Colloid Interface Sci. 2005, 286, 216–223. (17) Amiran, J.; Nicolosi, V.; Bergin, S. D.; Khan, U.; Lyons, P. E.; Coleman, J. N. J. Phys. Chem. C 2008, 112, 3519–3524. (18) Bergin, S. D.; Nicolosi, V.; Streich, P. V.; Giordani, S.; Sun, Z. Y.; Windle, A. H.; Ryan, P.; Niraj, N. P. P.; Wang, Z. T. T.; Carpenter, L.; Blau, W. J.; Boland, J. J.; Hamilton, J. P.; Coleman, J. N. AdV. Mater. 2008, 20, 1876–1881. (19) Maiti, A.; Wescott, J.; Kung, P. Mol. Simul. 2005, 31, 143–149.

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