Adsorption of F127 onto Single-Walled Carbon Nanotubes Characterized Using Small-Angle Neutron Scattering.

Aqueous single-walled carbon nanotube dispersions are often made using polymers from the Pluronic family of amphiphilic block copolymers, however relatively few studies have been made using small-angle neutron scattering techniques to discover the mechanism by which they act. SANS results reported here show that a relatively simple core-shell cylinder model can be used to ﬁt data successfully at diﬀerent contrasts. The results across all contrasts showed that the best ﬁt gave an inner nanotube radius of 10 ˚A, corresponding to small nanotube bundles with a small amount of water present (20%), and a polydisperse adsorbed layer thickness of 61 ˚A, with a water content of 94% in the adsorbed layer. The data ﬁtting is thus consistent with a small SWCNT bundle surrounded by an extended and water-swollen F127 adsorbed layer. Compar-ing the scattering from F127/SWCNT at diﬀerent contrasts, it has been found that the polymer-decorated SWCNTs are contrast matched at a D 2 O/H 2 O volume ratio of 0.36:0.64, corresponding to a scattering length density of 1.92 × 10 − 6 ˚A − 2 .


Introduction
Carbon nanotubes have been of great interest since their discovery by Iijima in 1991, due to their unique properties such as their high aspect ratio, mechanical strength and electrical conductivity. 1 Single-walled carbon nanotubes (SWCNTs) can be thought of conceptually as a rolled-up sheet of atomically-thin carbon, with both the angle used when rolling up this cylinder and the diameter of the resulting nanotube being key parameters in determining its electronic properties. Syntheses of SWCNTs result in a third of the nanotubes being metallic, with two thirds being semiconducting. 2 There has been a surge in research interest in recent years looking into possible separation methods for these two species of nanotube in order to make SWCNTs of a single electronic type for future electronic applications.
A major challenge in utilising the properties of SWCNTs is the difficulty encountered on attempting to form a nanotube dispersion in either aqueous or organic media, due to the propensity of SWCNTs to bundle together. Methods which have been investigated to overcome this problem include both covalent and non-covalent approaches, with noncovalent methods generally being favoured as they do not affect the intrinsic properties of the SWCNTs. that the adsorption of SDS molecules on the SWCNT surface was unstructured, with no preferential adsorption of either the headgroup or the tail of the molecule onto the SWCNT wall. 3 Theoretical calculations have shown that in dilute solution, the adsorption of surfactant on the tube is random in nature, while at high surfactant concentration hemispherical micelles are preferentially formed. 4 The stabilisation of carbon black and SWCNTs has been reported to be more effective with the use of surfactants possessing aromatic groups, due to π-π stacking interactions between the surfactant and the graphitic carbon surface. 5,6 Work published by Granite et al. looked into using SANS to probe the interactions between SWCNTs and Pluronic block copolymers (F127 and F108) below the polymers' critical micellisation temperature (CMT). 7 They observed minimum scattering at 70% D 2 O, rather than the 17% D 2 O, which is where the Pluronic polymers would be expected to be "matched out" based on their chemical structure. Both a cylindrical core-adsorbed chains model and a cylindrical core-shell-chains model were reported as fitting the data well, however corrections had to be made as to why the data at 70% D 2 O scattered less than the data at 40% D 2 O, a value which is closer to the match point of F127.
We have studied the adsorption of F127 onto SWCNTs using SANS, and have found our data to show a different scattering vector (Q) dependency to previous data. Our data show minimal scattering at a D 2 O/H 2 O composition consistent with a model in which the SWCNT has a high scattering length density, and is surrounded by a diffuse F127 adsorbed layer. We have found it possible to obtain good fits to our F127/SWCNT data using a relatively simple core-shell cylinder model.

Preparation of dispersions
Sample preparation involved dissolving the polymer in water (either hydrogenated or deuterated) overnight whilst on a roller-mixer. All samples were made by addition of the required mass of SWCNTs to 2 ml of a polymer solution of the correct concentration to obtain a dispersion which was 0.3% wt SWCNTs, and 1% wt F127. This was followed by sonication (QSonica Q125) in pulsed mode at 57% max power for 1 hr. The samples were then centrifuged for 40 min at 20800 g, and the top ∼1.5 ml of the resulting supernatant was removed for use in scattering experiments. It is important to note that the SWCNT concentration of 0.3% wt quoted is not the final concentration, but rather is the concentration calculated before purification by ultracentrifugation. It is estimated from absorption measurements that ∼ 1/3 of the SWCNTs remain dispersed after purification, a relatively high concentration thought to be a consequence of the high purity of SWCNTs used.

Absorption Spectroscopy
Absorption spectroscopy was performed on a HP/Agilent 8453 spectrophotometer over the range 400-1100 nm. Samples were diluted by a factor 30 with deionised water and run in square quartz cells with a 10 mm path length. Background water absorption was subtracted from all data. Each raw scattering data set was corrected for the detector efficiencies, sample transmission and background scattering and converted to scattering cross-section data (δΣ/δΩ vs. Q) using instrument-specific software. 8 These data were placed on an absolute scale (cm −1 ) using the scattering from a standard sample (a solid blend of hydrogenous and perdeuterated polystyrene), in accordance with established procedures. 9 Samples were studied in 2 mm or 1 mm square quartz cells depending on the D 2 O/H 2 O content. All samples were studied below the critical micellisation temperature (CMT) to minimise scattering from the bare polymer. For an F127 concentration of 1% w/v, as used here, the CMT is 24 • C. 10 Therefore, samples were studied at 15 • C. All data sets had background solvent scattering subtracted.
In order to ensure the F127/SWCNT samples contained the same amount of carbon as each other (to simplify the SANS data analysis), the samples were made from F127/SWCNT/D 2 O and F127/SWCNT/H 2 O stock solutions which were mixed together in the correct proportions. The stock solutions were made as described previously, to give a total volume for the stock solution of over 1 mL. The concentrations of the two stock solutions were then compared using absorption spectroscopy, and the more concentrated D 2 O solution was diluted to the same concentration as the H 2 O stock solution dilution with a 1% F127 solution until the absorption spectra of the two stock solutions matched.
The scattering patterns from dispersions of F127 polymer along with the F127/SWCNT data at the contrasts studied are given in fig. 1. As all dispersions were studied below the CMT of the polymer, the F127 did not form micelles and was instead present as free polymer chains, and thus the scattering contribution from the F127 itself was relatively small. At low Q values, the data for the F127/SWCNTs has a higher scattering intensity than the F127, however at high Q the curves have a very similar shape, suggesting that the scattering at high Q is dominated by the free F127 molecules. The curves for F127/SWCNTs tend to be at a lower intensity than the F127 alone at higher Q, suggesting that some of the F127 has adsorbed onto the SWCNT surface, which is thus affecting the scattering intensity at this Q range. The scattering data shows the highest intensity scattering at 100% D 2 O, as expected, with 80% and 70% D 2 O data both showing scattering of lower intensity than the full contrast data. The minimal scattering for our samples is seen at 40% D 2 O, with some scattering seen at the lowest Q values for the 17% D 2 O data (the match point of the F127), corresponding to the scattering of the nanotubes themselves with the F127 adsorbed layer matched to the solvent.
Data for F127 data were fit to a Debye-Guinier model for free polymers, which was then subtracted from the F127/SWCNT data. Detail about the fitting procedure is given in the supporting information to this paper. Data for SWCNT/F127 showed lower intensity scattering at high Q, so only 75% of the F127 Debye-Guinier fit was subtracted from the F127/SWCNT data to account for F127 adsorption onto SWCNTs, and the resulting scattering curves are shown in fig. 2.   an intensity above that of the 40% D 2 O data. Ideally, two separate lines would be drawn (above and below the match point) in order to find the x-intercept and thus the contrast match point, however in this case only one of the contrasts studied was at a D 2 O composition below the match point. Thus, the intensity value at 17% D 2 O was multiplied by a factor of -1 to enable one straight line to be drawn. The data shows a good fit to a straight line, and it can be concluded that a volume fraction of 36% D 2 O would be required in order to obtain the minimal scattering from this system. This is in contrast to results reported by  SWCNTs and a wide range of SWCNT sizes. It is thus possible that dispersions made here have a lower degree of SWCNT branching, and are thus more amenable to being fit to a core-shell cylinder model. 7,11,12 Judging from previous experiments looking at the dispersions using TEM (shown in the supporting information to this paper) it is unlikely that the SWCNTs will be present as individual tubes, although some of them may be. Rather, the majority of the nanotubes will be present in small bundles. TEM images also show that residual catalyst particles are present in the dispersions, however this is not thought to affect the SANS results, as explained further in the supporting information to this paper.
It has been reported that the degree of bundling in a sample can be detected by UV-vis-NIR spectrophotometry. 13 SWCNT bundling causes broadening and red-shifting of the peaks in the UV-vis-NIR spectra. 14 The absorption spectra obtained from our samples, shown in  The model used to fit the data presented here is a core-shell cylinder model, simpler than models previously used to fit such data and the scattering length densities (of the core and shell) are averaged with the relative amount of water thought to be present, as explained in the supporting information.
We have used a core-shell cylinder model to fit the scattering data of the decorated SWCNT cylinders at all contrasts studied, using the SasView fitting programme, developed at NIST. 15 This model consists of a core (with an SLD calculated as a mixure of the SLD of graphene (calculated to be 7.4 ×10 −6Å−2 ) and the scattering length density of the appropriate solvent mixture, and a homogeneous shell consisting of a diffuse F127 layer. In order to simulate the inhomogeneity of the F127 adsorbed layer in this simple model, a log-normal polydispersity for thickness has been introduced into the scattering of the shell.
The polydispersity function used also serves to account for the instrument resolution, as the Q-dependency of the data is weak and smearing due to polydispersity is much greater than the effect of the instrument resolution. It is therefore expected that the adsorbed F127 layer will have a relatively low volume fraction, however the thickness could be anywhere in a wide range of reported values. 17,18 The adsorbed layer thickness must be less than the extended chain length of one of the PEO blocks (350Å based on a monomer chain length of 3.5Å 19 ).
The fitting procedure used here consists of several stages: 1. The thickness of the adsorbed layer can be approximated using the scattering data obtained at 100% D 2 O. We have assumed that the core has a high SLD (as we think it mainly consists of carbon, with some solvent present from the opening of the tubes during ultrasonication) and a relatively small radius. The shell is composed of a diffuse layer which has a high solvent composition. Therefore, at the highest D 2 O content, the scattering length density of the shell will nearly match the scattering length density of the core, and fitting the shape of this data will depend mainly on the thickness of the adsorbed layer.
Rather than using a model in which the adsorbed layer is 'fuzzy', it was decided to use a simple model in order to keep the number of parameters at a minimum. Adding polydispersity to the thickness of the adsorbed layer has a similar effect to using a fuzzy layer model, and decreases the polymer segment density away from the core. This can be seen in fig. 5. Thus a value of 61Å was obtained for the F127 adsorbed layer, with a log-normal polydispersity of 0.4, the distribution of which is given in the supporting information. By integrating over the log-normal distribution, a mean thickness (taking into account the polydispersity) of 65Å was obtained. 3. Lastly, fig. 3 shows that the contrast match point for the F127/SWCNT scattering occurs at 36% D 2 O. The thickness and the volume fraction of the adsorbed layer is known, therefore the scattering length density of the SWCNT can be calculated so that the scattering from the core and the shell cancel each other out at this D 2 O composition. Preliminary data fitting shows that the best fits are obtained with a relatively small core radius and a low volume fraction of water in the SWCNT core.
We can use the relationship between the scattering of the core and shell to fit the data at different core radii and core SLDs (assuming different amounts of solvent are present in the core each time), in order to find the best fit across all contrasts studied. At the contrast match point, shown in fig. 3 to be 36% D 2 O, must satisfy the condition given in eq. (1).
ρ core a core + ρ shell a shell = 0 (1) We have calculated the contribution to the overall scattering from the inner SWCNT core and the outer adsorbed layer, based on the fitting parameters given in table 1.
With Fitting the data to a core-shell cylinder model gives reasonable fits across all contrasts studied, as shown in fig. 6. The fits show the core to be a small SWCNT bundle surrounded by a diffuse, polydisperse layer of F127, with a thickness of 61Å. The parameters used in fitting the data to a core-shell cylinder model are given in table 1. The data at 17% D 2 O could be fit by including a small amount of scattering in the shell (i.e. the shell was slightly off contrast), to account for imperfect contrast matching of the F127. Polydispersity was added to the thickness of the adsorbed layer, in order to approximate the effect of the PEO and PPO blocks of the polymer. The data for the system at 40% D 2 O has a very low scattering intensity and large error bars associated with it, and thus fitting this data is difficult. However, this is a key piece of evidence to support the core-shell cylinder model, as it shows that the system is close to the match point at this D 2 O content.

Conclusions
Dispersions of SWCNTs dispersed with F127 Pluronic block copolymer were investigated using small-angle neutron scattering. In this work we have shown that our data agreed with predicted scattering for a SWCNT core surrounded by a diffuse polymer layer, with minimal scattering being seen at a D 2 O composition of 40%, as expected for core-shell cylinders of this type. The SANS data fitting is consistent with small SWCNT bundles in dispersion, stabilised with an adsorbed F127 layer which is extended (with a 61Å thickness) and waterswollen (with a water content of 94% in the adsorbed layer).
Absorption spectra of the samples studied with SANS shows no differences between the peaks of the samples made in D 2 O compared to those made in H 2 O. The peaks seen in these spectra are consistent with a high degree of debundling, although we believe they are too broad for single tubes, consistent with the parameters obtained when fitting the SANS data using the core-shell cylinder model.
The adsorbed layer fit the core-shell cylinder model well, with the adsorbed layer having a thickness and volume fraction of F127 which fits with previous literature values.
SWCNT/F127 samples were stable for many months after initial dispersion, hence F127 is a suitable steric stabiliser for SWCNTs. These results show that the analysis of F127 adsorption onto SWCNTs can be simplified by using a core-shell cylinder model to characterise the adsorbed layer, which could have wider applications for the analysis of other adsorbed molecules onto carbon nanotubes.

Supporting Information Available
This material is available free of charge via the Internet at http://pubs.acs.org/.