As-purchased, purified SWNTs show two levels of agglomeration: (i) μm scale aggregates (shown by SEM in Figure 3) and (ii) nm-scale bundles (shown by TEM in Figure 4(a,b)). Even at the low magnification of 18 kX in SEM, SWNT bundles (see arrows) are seen to extend from the larger aggregates. High resolution TEM of aggregate regions (Figure 4(e,f)) shows the μm scale aggregates to be comprised of mechanically interlocked or “tangled” SWNTs whose morphology is unable to be altered with the chemical approaches used here. The binding between bundles comprised of straight parallel SWNTs is, however, chemically addressed by cations and the PSS anions in solution.

TEM shows the PSS anion to adopt spherically collapsed conformations at the SWNT surfaces (Figure 4(b,d–f)). These spherically collapsed PSS morphologies are observed both in regions of aggregates and bundles. Samples prepared without ultrasonication show, on average, larger spherical PSS than those found in the sample ultrasonicated for 20 hours indicating that each sphere is comprised of multiple units of polyelectrolytes which then associate by weak Van der Waals interactions. The spherically collapsed conformation is known to occur as a result of counterion condensation onto monomer units of the PSS polyelectrolyte. Suspensions of PSS and SWNTs contain H⁺ and Na⁺ ions which may adsorb onto PSS. Typically, LbL films comprised of PSS and a polycation (such as polyallylaminehydrochloride, PAH) deposited at the working pH of 3 and with the same abundance of Na⁺ counterions present in solution show a planar polyelectrolyte morphology with each layer having a thickness of 2 nm [14-16]. Spherically coiled polyelectrolyte diameters of 40 nm are predicted by continuum models for molecular chains of 250 nm length [17]. Here, the observed PSS spherically coiled diameter varied between ∼2 nm (the order of the SWNT diameter) and ∼200 nm (for some of the largest PSS coils observed). The size variations in coiled diameter are, perhaps, related to ultrasonication which would inhibit the aggregation of multiple PSS polymeric units. After exposure of the sample to the 120 kV electron beam in TEM for periods of 1 hour, the spherically coiled PSS regions were removed by beam damage (Figure 5). Literature reports beam damage to CNTs at 100 kV [18], but here the electron beam did little to further damage the SWNT wall structures. Due to prolonged ultrasonication, the SWNTs suffered some loss in structural order and the straight parallel walls are buckled in some areas shown in Figure 4(e,f).

The Manning theory of counterion condensation can be used to predict the spacing of counterions adsorbed onto PSS at the onset of spherical coiling by Equation (5). Alternatively, the theory can be used to explore the ranges of local dielectric constants which must exist near PSS in order to cause the onset of spherical coiling. Figure 6 shows dielectric constant (ε_r) as a function of Bjerrum length (ℓ_B) and may be interpreted to yield the spacing, in this case less than 1.3 nm, between counter ions (e.g., Na⁺ or H⁺) adsorbed onto PSS for spherical coiling of PSS to occur in pH neutral water at room temperature. In practice, spherical coiling of PSS is not observed in pH 3 aqueous solutions—and so, the condensation limit of 1.3 nm spacing is not reached by counterions in solutions comprised of Na⁺ (in concentrations found in 2 mg/mL of PSS) and H⁺ (in concentrations at pH 3). In other words, within the bulk solutions containing Na⁺ and H⁺ counter ions, inherent kinetic limitations which control the rate at which counterions enter the coulombic potential of the PSS monomer unit prohibits adsorption of counterions onto the PSS rod-like linear chain backbone with spacing equal to the theoretical Bjerrum length, ℓ_B = 1.3 nm. Because spherically coiled PSS morphologies are observed at the surface of SWNTs, it can be speculated that the counterions attracted to the surface of SWNTs pre-concentrate the solution—giving local dielectric constants (ε_r) greater than 80 and resulting in the condensation counterions at theoretical Bjerrum lengths of 1.3 nm or less. Thus, it may be concluded that dielectric constants, (and cationic concentrations) within the solution near the surface of SWNTs is much different from the bulk solution. Experimental work by Duque et al. [19] report changes in SWNT “immediate environment” as a function of changing pH (toward acidic values) by measured fluorescence data. These changes are not attributable to protonation of the CNT (a covalent interaction)—and can be presumed as an increase in local concentration of H⁺ surrounding the CNT in hydrogen ion rich environments [19]. Furthermore, pH associated confirmation changes of the ionic polymer, PVP, used in that work shows spherically coiled morphologies occur at neutral and high pH while elongated rod-like morphologies occur at low pH. The PVP molecule contains hydrophobic and hydrophilic groups which dictate its conformational structure [19]. Computational research which calculated dielectric constants for biomolecular polyelectrolytes, protein [20] and DNA [18] are useful to discuss here.

That work shows counterion distributions calculated by Poisson-Boltzmann finite-difference models might be more adequately accounted for by assuming a dielectric constant (ε_r) near the surface of polyelectrolytes which is much different from that in the bulk media. Lamm et al. [21]. use an ε_r much lower than 80, a value of 10–30 near the polyelectrolyte surface, which increases to 78.5 in the bulk solution. Contour mapping of the near surface dielectric constant (ε_r), and its associated potential gradient, adequately describes binding sites for ligands and counterions [21]. Although, debate in the literature exists as to whether dielectric constant would adequately describe ligand binding [20]—the argument that near surface dielectric constants may be much different than bulk is validated by the computational study.

Understanding the structure and morphology of polyelectrolytes at the surface of SWNTs is of key relevance because polyelectrolyte self-assembly approaches are currently being used to explore the fabrication of functional coatings containing carbon nanotubes [22-24]. Applications considered are as antimicrobial films [22], electrodes [23], biosensors [24,25], and in the formation of conductive paper [26]. Polyelectrolyte self assembly is presently being used to coat a diverse set of nanomaterials, including biomolecules, proteins, clay platelets, nanorods and nanowires [1,2,26,27]. The surface chemistry of the starting material, in each case, will dictate the propensity for pre-concentration of ions from the working solvent—and hence control polyelectrolyte morphologies. Further studies might consider examining polyelectrolyte morphology and Bjerrum length (ℓ_B) as a measure of ionic preconcentration at near surface regions for a wide set of nanomaterials chemistries.

The ability to form stable suspensions of SWNTs will prove to be key to their use in a variety of new applications. Non-covalent functionalization of SWNTs is an important strategy to generating stable SWNT suspensions because it leaves the intrinsic electronic properties of the SWNT undisturbed [28]. Several non-covalent strategies for SWNT dispersion have included the use of surfactants [29], DNA [30], and peptides [31]. In order to quantatively examine PSS-SWNT dispersion, supernatants of PSS-SWNT suspensions were examined using UV-Vis spectrophotometry.

These supernatants exclude SWNT aggregates which have settled out of suspension. The commercial PABS-CNT samples were measured for comparison. Figure 7(a) shows concentration vs. time profiles for PSS-SWNT and PABS-CNTs. Little change in supernatant concentration is observed over an 8 hour period indicating highly stable suspensions are attained via PSS-overlay. At inset, Figure 7(b) shows a photographic image of an PSS-SWNT dispersion in water after 5 hours of ultrasonication. The photographed dispersions contain 0.36 mg/mL of SWNTs with 2 mg/mL of PSS and the image shows the suspension 2 days after it was prepared.

For assembly of polystyrene sulfonate (PSS) over SWNT surfaces, mixtures comprised of PSS (Sigma-Aldrich) and commercial purified grade single walled carbon nanotubes (MicroTechNano Corp.) were prepared under pH 3 aqueous conditions. The starting materials were mixed in concentrations of 2 mg/mL of PSS and 0.4 mg/mL of SWNTs. Prior to adding PSS and SWNTs, the pH of deionized water was adjusted to 3 using HCl. One mixture was ultrasonicated for 20 hours with the temperature of the ultrasonic bath reaching up to 60 °C. A second mixture underwent no ultrasonication, but was contained in the pH 3 aqueous solution environment for 20 hours.

The absorbance of the solutions was measured using the DU^® 530 UV-Vis spectrophotometer scan wavelength mode. To quantitatively determine SWNT suspension concentration vs. time using the Beer-Lambert law, standard suspensions containing known SWNTs concentrations were prepared at 0.1 mg/mL, 0.05 mg/mL, 0.025 mg/mL and 0.0125 mg/mL. For these standards, the suspensions were prepared using pH 3 deionized water with PSS added in the content of 2 mg/mL. The suspensions were ultrasonicated for 5 hours. A total of six absorption measurements were made at the wavelength of 255 nm and the mean of those measurements was fit to a linear regression curve used as a standard concentration line to evaluate sample suspensions. For comparison, suspensions of commercially available polyaminobenzenesulfonic acid (PABS) functionalized carbon nanotubes (CNTs) (Sigma-Aldrich) were prepared in concentrations of 0.2 mg/mL, 0.1 mg/mL, 0.05 mg/mL, and 0.025 mg/mL. The PABS molecule is covalently bound to the CNTs and these CNTs remain in suspension for long periods. The PABS-CNTs suspensions were ultrasonicated for 5 minutes. Two absorption measurements were made at the 195 nm wavelength and the mean of those measurements were fit to a regression curve.

The UV-Visible absorption from PSS-SWNT mixtures prepared at 2 mg/mL of PSS and 0.4 mg/mL of SWNTs was measured at 1 hour intervals for an 8 hour period using a 255 nm wavelength. The results reported comprise the mean and standard deviation (error bars) for six measurements collected within the first 1 minute of each interval. Similarly, the absorption of PABS-CNT suspensions prepared at 0.2 mg/mL was measured over an 8 hour window at 195 nm wavelength.

Scanning electron microscopy (SEM, HITACHI, model S-4,800) was performed on the as-purchased SWNTs at 30 kV electron energy. Transmission electron microscopy (TEM) was performed using the Zeiss Libra instrument. For as-purchased CNT powders, sample preparation involved transfer of the dry powders to sample holders. For PSS-CNT mixtures, sample preparation involved dropwise addition of as-prepared mixtures, both with and without ultrasonication, to the sample holder grids. A drying period of one to several days was performed in an evacuated chamber.

Surface charge ζ-potential measurements were collected using the ZetaPlus Analyzer (Brookhaven Instruments, Holtsville, NY). ζ-potential measurements were taken for SWNTs at various pH values as a means of determining the counterion H⁺ content around the SWNT surface. For sample preparation, SWNT were added to deionized water having fixed pH values between 3 and 8 at concentrations of 0.1 mg/mL, 0.5 mg/mL and 1 mg/mL. The surface charge was the same for all three SWNT concentrations measured.