Exfoliation in ecstasy: liquid crystal formation and concentration-dependent debundling

observed for single-wall nanotubes dispersed in the liquid drug γ-butyrolactone

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IOP PUBLISHING NANOTECHNOLOGY

Nanotechnology 18 (2007) 455705 (10pp) doi:10.1088/0957-4484/18/45/455705

Exfoliation in ecstasy: liquid crystalformation and concentration-dependentdebundling observed for single-wallnanotubes dispersed in the liquid drugγ -butyrolactoneShane D Bergin1, Valeria Nicolosi1, Silvia Giordani1,Antoine de Gromard1, Leslie Carpenter1,2, Werner J Blau1 andJonathan N Coleman1,3

1 School of Physics, Trinity College Dublin, University of Dublin, Dublin 2, Ireland2 Dow Corning Corporation, 3901 S. Saginaw Road, Midland, MI 48640, USA3 Centre for Research on Adaptive Nanostructures and Nanodevices, Trinity College Dublin,University of Dublin, Dublin 2, Ireland

E-mail: colemaj@tcd.ie

Received 18 July 2007, in final form 15 August 2007Published 10 October 2007Online at stacks.iop.org/Nano/18/455705

AbstractLarge-scale debundling of single-walled nanotubes has been demonstrated bydilution of nanotube dispersions in the solvent γ -butyrolactone. This liquid,sometimes referred to as ‘liquid ecstasy’, is well known for its narcoticproperties. At high concentrations the dispersions form an anisotropic, liquidcrystalline phase which can be removed by mild centrifugation. At lowerconcentrations an isotropic phase is observed with a biphasic region atintermediate concentrations. By measuring the absorbance before and aftercentrifugation, as a function of concentration, the relative anisotropic andisotropic nanotube concentrations can be monitored. The upper limit of thepure isotropic phase was CNT ∼ 0.004 mg ml−1, suggesting that this can beconsidered the nanotube dispersion limit in γ -butyrolactone. Aftercentrifugation, the dispersions are stable against sedimentation and furtheraggregation for a period of 8 weeks at least. Atomic-force-microscopystudies on films deposited from the isotropic phase reveal that the bundlediameter distribution decreases dramatically as concentration is decreased.Detailed data analysis suggests the presence of an equilibrium bundle numberdensity. A population of individual nanotubes is always observed whichincreases with decreasing concentration until almost 40% of all dispersedobjects are individual nanotubes at a concentration of 6 × 10−4 mg ml−1.The number density of individual nanotubes peaks at a concentration of∼6 × 10−3 mg ml−1 where almost 10% of the nanotubes by mass areindividualized.

1. Introduction

The study of the dispersion of carbon nanotubes into the liquidphase has been a very active field over the last few years. Many

applications of nanotubes, such as in composites [1] or thinconductive films [2], require the ability to disperse nanotubes,preferentially down to the level of individual tubes. Thisinvolves the exfoliation of tubes from large ropes or bundles.

0957-4484/07/455705+10$30.00 1 © 2007 IOP Publishing Ltd Printed in the UK

Nanotechnology 18 (2007) 455705 S D Bergin et al

However, due to their high surface energy [3], this is less thanstraightforward. In the past, nanotubes have been dispersedwith the aid of acids [4, 5], macromolecules [1, 6–8] andsurfactants [9–12] as well as through covalent functionalizationstrategies [13, 14]. Such systems have been characterized bya range of techniques such as atomic force microscopy [15],infrared photoluminescence spectroscopy [12], viscometry [4]and small-angle neutron scattering [10], to name but a few.However, it has been found that three-phase dispersions,consisting mainly of individual nanotubes, can only beobtained at very low concentration [2, 4], or after intensecentrifugation [12].

However, a number of reports have shown that SWNTcan be dispersed in certain solvents [16–20] without the needfor any third phase dispersant. Such a two-phase systemwould have significant advantages over more complex systems.The focus of most studies has been on amide solvents,with dimethyl-formamide (DMF) and N -methyl-pyrrolidone(NMP) receiving the most attention [18, 19]. Significantly,a recent paper has shown that not only can SWNT be stablydispersed in NMP, but they can be debundled down to thelevel of individual nanotubes with up to 70% yield [21]. Moreimportantly, this process occurs as a function of concentration,allowing the selection of required bundle diameter distributionsor populations of individual nanotubes. Similar behaviour hassubsequently been demonstrated for dispersions of SWNT inDNA/H2O [22] and synthetic peptide/H2O [23].

Now that a small number of solvents have beendiscovered, it is imperative to rapidly expand this cohort todiscover as many good solvents for nanotubes as possible.The expansion of the number of such solvents is necessaryto allow a much greater choice to experimenters who mayrequire certain solvents with certain properties under certaincircumstances. To this end we have undertaken a study ofthe dispersion of nanotubes in a very wide range of solvents,focusing on structural analogues of NMP.

One of the most promising of these solvents is γ -butyrolactone (GBL). This solvent is a pro-drug (in vivoprecursor) of the drug γ -hydroxybutric acid (GHB) [24, 25],but is also a potent narcotic in its own right. Both GBL andGHB are sometimes known as ‘liquid ecstasy’ [26]. WhileGHB has received a great deal of attention in recent years asit is a drug of abuse, GBL is more lipid-soluble than GHB andis considered to be more potent.

In this work we use crossed polarized microscopy,atomic force microscopy, UV–vis–NIR absorption and Ramanspectroscopy to show that single-walled nanotubes can bedispersed effectively in GBL. These dispersions exhibit liquidcrystalline behaviour, allowing us to separate the anisotropicphase from the isotropic phase by centrifugation. TheSWNT can be debundled simply by reducing the isotropicnanotube concentration in GBL dispersions. We findthat the average bundle diameter decreases with decreasingconcentration before saturating at approximately 2.4 nm belowa concentration of ∼10−2 mg ml−1. In addition a populationof individual nanotubes is present at all concentrations. Whilewe attempted to use infrared photoluminescence measurementsas an in situ probe to confirm the AFM measurements, noPL was observed for any concentration. We believe that thestrong nanotube–solvent interaction is responsible for efficientphotoluminescence quenching in these systems.

Figure 1. Raman spectra of the raw HiPCO SWNT powder, thesedimented phase and the supernatant phase. The laser excitationwavelength used was 532 nm. Also shown is the molecular structurefor γ -butyrolactone.

2. Experimental procedure

For this study, purified single-walled carbon nanotubes(HiPCO) were purchased from Carbon Nanotechnologies, Inc.(www.cnanotech.com, lot no. P0288) and used as supplied.Thermogravimetric studies confirmed the residual iron contentto be ∼6 wt%. Microscopy studies showed no evidence ofnon-nanotube carbon. γ -butyrolactone (GBL) (product no.B103608-500ML, batch no. 029H07091) was purchased fromAldrich and also used as supplied. The molecular structure ofGBL is shown as an inset in figure 1. SWNT dispersions inGBL were prepared as follows. A high concentration stockdispersion of SWNT in GBL was prepared at a concentrationof 0.5 mg ml−1. This dispersion was subjected to 2 minhigh power sonication, using an ultrasonic tip processor(Model GEX600; 120 W, 60 kHz). Subsequently, a range ofdispersions was prepared by successive dilution (concentrationrange: 0.5–6 × 10−4 mg ml−1), each subjected to 2 minsonication prior to further dilution. All dispersions were thenmildly sonicated using a low-power ultrasonic bath (ModelNey Ultrasonic) for 4 h followed by a further 1 min high powersonication. In all cases this resulted in a very uniform ‘black’dispersion with varying degrees of darkness, depending on theconcentration. However, for the higher concentrations, largeaggregates were also observed. These large aggregates wereremoved from these dispersions by mild centrifugation (CF)(6000 rpm, ∼3000 g, for a period of 90 min).

Removal of aggregates by CF results in two phases,the sediment and supernatant, which can be separated bydecantation. To quantify the relative amounts of each phase,UV–vis absorbance measurements of each dispersion werecarried out before and after CF. The concentration of thedispersions prior to CF is referred to as Ci , while the trueconcentration of the supernatant after CF and decantation isreferred to as CNT. Sonication is known to damage nanotubesunder certain circumstances. In order to probe the level ofdamage to the SWNTs due to sonication, Raman spectroscopywas employed to compare the raw HiPCO powder with thesediment and supernatant separated after CF. To facilitatethis, the sediment and supernatant were dried on a filter

2

Nanotechnology 18 (2007) 455705 S D Bergin et al

Abs

orba

nce

Wavelength (nm)

Before CF, Ci=0.1 mg/mL

After CF (×8), CNT

=0.011 mg/mL

200 400 600 800 1000 1200 14001

2

3

Figure 2. Absorbance spectra taken before and after centrifugationfor the sample with initial nanotube concentration Ci = 0.1 mg ml−1.For clarity the after-centrifugation spectrum was scaled by a factor of8. The concentration after centrifugation was 0.011 mg ml−1.

paper using a Buchner funnel allowing comparable, solidphase measurements to be made for all three samples. Thenormalized spectra, as shown in figure 1, were virtuallyidentical, indicating minimal damage to the SWNTs aftersonication. This rules out the possibility of any chemicalmodification to the nanotubes during sample preparation.

The biphasic nature of SWNTs dispersions was investi-gated, before and after CF using a cross-polarized microscopeused in transmission mode (Leica Microscope fitted with a JVCcolour video camera). The samples were prepared by droppingthe dispersion on a glass slide and covering it with a cover-slip.The structure of the sedimented phase was investigated usingscanning electron microscopy.

The stability of the supernatant phase was investigated,after CF, by monitoring the optical transmission of a highconcentration dispersion, C = 0.032 mg ml−1, over a periodof 55 d. It should be pointed out that GBL, like NMP, is veryhygroscopic. Exposure to moisture rapidly destabilized thedispersions. As such, efforts were made to avoid exposureto water: however, it was not found necessary to store thedispersions under inert gas.

To investigate possible concentration-dependent aggrega-tion/debundling, a small volume of each supernatant was drop-cast onto cleaned silicon substrates for AFM measurements.Samples were placed in a vacuum oven at 80 ◦C for a periodof 4 h to allow solvent to evaporate. To test the reversibilityof the dilution process, one of the low concentration disper-sions, Ci = 5 × 10−3 mg ml−1, that had been made using theprocedure described above, was allowed to evaporate in a con-trolled manner, thus increasing the SWNT concentration. Sim-ilarly, AFM samples were prepared at set intervals throughoutthe evaporation process.

Raman measurements were made on a Jobin YvonRaman system, fitted with a HeNe 20 mW laser (λ =532 nm). SEM images were taken using a Hitachi S-4300 (operated with an acceleration of 25 kV). UV–visabsorbance measurements were carried out using a Cary6000i. Centrifugation was carried out using a Hettich EBA-12 centrifuge. Tapping mode atomic force microscopy (AFM)was carried out on all these samples, using a DI Multimode

0.01 0.1

C

χ Agg

=(C

I-CF)/

CI

Initial Concentration, CI (mg/ml)

BiphasicC

2C1

B

α 660,

I (m

lmg-1

m-1)

A

Before Centrifuge (CI)

After Centrifuge (CF)

A66

0/l (

m-1)

α = 3426 mL mg-1m-110

100

1000

0

1000

2000

3000

4000

0.0

0.5

1.0

Figure 3. (A) Absorbance per unit length, A/ l (at λ = 660 nm),measured before and after centrifugation. The extinction coefficientshown was calculated from the slope of the low concentrationbefore-centrifuge data (dashed line). (B) Absorption coefficientbefore centrifuge. (C) Fraction of SWNTs that are found to exist aslarge aggregates, as a function of the initial concentration. Thedashed line represents a linear fit for the data in the biphasic region(delineated by the arrows) that can be described by equation (2).

Nanoscope IIIA. Point-probe silicon nitride cantilevers (forceconstant = 42 N m−1, resonant frequency = 330 kHz) wereused for all measurements. High-resolution transmissionelectron microscopy (HR TEM) measurements were carriedout using an FEI Tecnai F20 operated at 200 kV. Samples wereprepared by placing a small drop of the dispersion on holeycarbon grids (mesh size 400).

3. Results and discussion

3.1. Liquid crystal formation

After centrifugation, all dispersions were semi-transparentwith colours ranging from light to dark grey depending onthe concentration. Absorption spectra, taken before and afterCF (Ci = 0.1 mg ml−1), are shown in figure 2. Thesespectra show features typical for dispersions of SWNT. Spectrataken after CF were similar in spectral profile but displayedslightly sharper features. In order to quantify its concentrationdependence, the absorbance, A, measured both before and afterCF (λ = 660 nm) has been plotted as A/ l versus nanotubeconcentration in figure 3(A) (l is the cell length). Beforecentrifugation, the absorbance of the dispersions behaves,at low concentration, according to the Beer–Lambert law:A = αCi l , where α is the extinction coefficient and Ci

is the concentration in mg ml−1. Taking the slope of thiscurve at low concentration, we find the absorption coefficient,α660 nm, to be 3426 ml mg−1 m−1. This value comparesfavourably with the reported values of 3264 ml mg−1 m−1 forSWNTs dispersed in N -methyl-pyrrolidone (NMP) [21] andvalues of α700 nm in the range 3000–3470 ml mg−1 m−1 for

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Nanotechnology 18 (2007) 455705 S D Bergin et al

various other amide solvents [19]. The data in figure 3(A)was then divided by the initial concentration to show theweak variation of α660 nm with concentration (figure 3(B)),probably due to the presence of large aggregates at highconcentration. At high concentrations, α660 nm is relativelylow (∼2400 ml mg−1 m−1). As the dispersions becomeisotropic (see below), α660 nm increases, approaching valuesof ∼3700 ml mg−1 m−1 at low concentration. This value isexpected to reflect the true extinction coefficient for dispersednanotubes.

The absorbance of the supernatants after CF did not scalelinearly with concentration as aggregated material had beenremoved at each concentration by centrifugation. The massfraction of nanotube material removed by centrifugation, χAgg,can be described [21], by

χAgg = A660,Initial − A660,Final

A660,Initial. (1)

This has been calculated and is shown in figure 3(C). Athigh concentration, the fraction of material removed bycentrifugation approaches one, but falls off gradually to closeto zero for the low concentration samples. Visual inspectionconfirmed that CF had removed the aggregates describedpreviously. The fact that χAgg ≈ 0 at low concentrationwould suggest that good dispersions can be obtained at lowconcentration. However, this does not explain why we get aphase separation at high concentration into two phases.

Windle et al [27, 28] have recently shown thatfunctionalized nanotubes form an anisotropic, lyotropic liquidcrystalline phase in a suspension or solution above a criticalconcentration, C2. In addition, an isotropic phase exists wherethe bundles of nanotubes are randomly oriented below anothercritical concentration, C1. The relevant nanotube/solventequilibrium diagram shows these phases to be separated bya biphasic region, classified as the ‘Flory chimney’ [29].Within this biphasic region, both isotropic and anisotropicregions co-exist with the relative amounts of each dependenton the concentration. Windle et al have also shown that theanisotropic phase can be removed by centrifugation [30]. Wesuggest that the aggregates observed in our high concentrationdispersions, and subsequently removed by centrifugation,correspond to an anisotropic liquid crystalline phase. Thus,χAgg corresponds to the fraction of anisotropic phase in thebiphasic region. Figure 3(C), then outlines how our systemmoves through these phases. Low concentrations, whereχAgg is effectively zero, correspond to the isotropic phaseand high concentrations, where χAgg is ≈1, correspond to theanisotropic phase. In between we have the biphasic region. Ingeneral, the concentration dependence of χAgg in the biphasicregion is given by the Lever rule [30]:

χAgg = (Ci − C1)

(C2 − C1). (2)

Fitting equation (2) to the data in figure 3(C), C1 and C2

were found to be ∼0.004 and 0.105 mg ml−1, respectively.The lower value can be considered the dispersion limit ofSWNTs in γ -butyrolactone, i.e. the maximum concentrationbelow which nanotube bundles exist in an isotropic phase.Onsager predicts that the rod–solvent system forms an

anisotropic liquid-crystalline phase at concentrations aboveC2 ≈ 3.3ρd/ l , where ρ is the mass density and d/ l is therod aspect ratio [31]. Applying this to the measured value ofC2 gives a value of l/d ∼ 50 000. This is far too high for thedimensions of the bundles or indeed the nanotubes used in thisstudy (see the following). This means that our measured C2

value lies far below the theoretical value for athermal (zeroenthalpy of mixing) solutions. This strongly suggests thatthe dispersions studied here, unsurprisingly have a positiveenthalpy of mixing [29].

The association of the aggregates with the anisotropicliquid crystalline phase suggests that the aggregates mustconsist of aligned nanotubes. This alignment was examinedby crossed polarized microscopy for a range of concentrationsbefore and after CF. Any anisotropic features will appearbright whereas isotropic features will remain dark. Shownin figure 4 are crossed polarized microscope images for threeof the dispersions before and after CF (Ci = 0.5, 0.1 and0.05 mg ml−1). In all cases, bright regions are observed,indicating the presence of an aligned phase. For the highestconcentration, much of the image is bright. While thissample has a concentration greater than C2, and hence shouldbe all bright, some of the sample remained dark due tocomplete light absorption by the high concentration dispersion.The coverage of the bright areas falls off as the SWNTconcentration decreases. This concurs with the fall in χAgg

with concentration. Sample images before CF for samples withconcentrations <C1 appeared completely black, indicating noaligned aggregates. The corresponding supernatants werealso examined after centrifugation, as shown in the right-hand panels of figure 4. After CF, the coverage of brightregions fell dramatically, indicating that the supernatants werecomprised almost entirely of isotropically arranged carbonnanotube bundles, with the large aligned aggregates havingbeen removed during the CF process. SEM of the sedimentedphase, separated after centrifugation, shown in figure 5,shows highly aligned structures, clearly showing an anisotropicphase. The inset in the bottom left shows a magnified view ofone of these structures, showing an array of aligned bundleseach of order of 100 nm in diameter (including gold coatingfor SEM).

While nematic liquid crystalline phases have beenobserved previously in nanotube dispersions by Windle,Pasquali and others [4, 27, 28, 30, 32–34], all of theseresults were for relatively complex dispersions. In general,these observations have been made for three-phase dispersionswhere nanotubes have been dispersed in a solvent with the aidof a dispersant, i.e. a surfactant [32], an acid [4] or DNA [33].Alternatively, in a number of cases the nanotubes have beenoxidized to introduce polar surface groups to aid interactionwith a polar solvent [27, 28, 30]. We believe that this is the firstexample of liquid crystallinity in a simple, two-phase system ofnominally pristine nanotubes dispersed in a solvent.

3.2. The isotropic phase: stability

A dispersion consisting solely of the isotropic phase ofnanotubes can be prepared by removal of the anisotropic phaseby mild centrifugation followed by decantation. Using themeasured mass fraction, χAgg, the true concentration of the

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Nanotechnology 18 (2007) 455705 S D Bergin et al

Before CF After CF0.5 mg/mL

0.1 mg/mL

0.05 mg/mL

50μm

50μm 50μm

50μm 50μm

50μm

Figure 4. Cross-polarized microscopy of γ -butyrolactone/SWNT dispersions before and after centrifugation. The presence of brightanisotropically aligned bundles is shown to scale with concentration before centrifugation. In all cases, the coverage of bright regionsdramatically decreases after centrifugation.

Figure 5. SEM of SWNT sedimented phase, showing the presenceof anisotropically aligned bundles. Shown in the bottom left corner isa magnified region showing aligned (gold-coated) bundles withdiameters of the order of 100 nm.

supernatants was calculated as CNT = Ci (1 − χAgg). Thestability of the isotropic phase with time was investigated by

taking a high-concentration, CNT = 0.032 mg ml−1, isotropic-phase dispersion and monitoring transmission through it overa period of 55 days. Absorbance (at 650 nm) through thesample as a function of time was monitored using an in-houseapparatus [35]. As illustrated in figure 6(A), the absorbancewas shown to remain stable over this timeframe, showing thatsubsequent sedimentation did not occur. Furthermore, a dropof the dispersion for AFM analysis was taken immediatelyafter CF and again after 55 d. AFM images showed a highpopulation of one-dimensional objects, typically microns longand with heights of a few nanometres. As HiPCO SWNTsnanotubes typically have diameters in the range 0.7–1.4 nm,the majority of objects observed are bundles of nanotubes.By measuring the height profile of many of these objects,statistical analysis of the nanotube bundle diameter can becarried out. The bundle diameter distribution of the sampleprepared immediately after CF is shown, in figure 6, to bestatistically indistinguishable from that of the sample prepared55 d after centrifugation. This shows that no aggregation, orindeed exfoliation, occurs after CF.

5

Nanotechnology 18 (2007) 455705 S D Bergin et al

5

15

25

35

4532 Days<D> = (4.3 ± 0.2)nm

Cou

nts

SWNT Diameter, nm

0

4

8

12

16

20

B 0 Days<D> = (4.1 ± 0.2)nm

C

Time, Days

Abs

orba

nce

660n

m, A

.U.

A

0.7

0.8

0.9

1.0

1.1

0 10 20 30 40 50 60

0 2 4 6 8 10 12 14

0 2 4 6 8 10 12 14

Figure 6. (A) Absorbance (at 650 nm) of a γ -butyrolactone/SWNTdispersion (CNT = 0.032 mg ml−1) demonstrating stability over aperiod of 55 d. (B) and (C) AFM diameter distributions of bundleheights at 0 d and 55 d, respectfully. Statistical analysis shows thediameter distributions to be indistinguishable.

3.3. The isotropic phase: bundle diameter distributions

In order to fully understand the dispersive effect of GBL onSWNTs, AFM studies were made on each of the supernatants.Figures 7(A) and (B) show AFM images of a high (CNT =0.03 mg ml−1) and low (5.8 × 10−4 mg ml−1) concentrationdispersion. Corresponding height profiles (for the black linesin each image) are shown in figures 7(C) and (D). A highcoverage of 1D objects is evident in both images. However,the objects observed at high concentration have much largerheights compared to the objects at low concentrations. Infact, many of the objects observed at low concentration haveheights of ∼1 nm, commensurate with individual nanotubes asobserved previously for NMP-based dispersions [21].

To investigate this further, statistical analysis was carriedon the AFM images for all concentrations. A large set ofbundle heights (approximately 150) was accumulated, fromrandom positions on each sample. It should be noted thatmeasurements were not made near bundle–bundle junctionsto avoid artificially high results. Shown in figure 8 arethe resulting bundle diameter distributions as a function ofconcentration. As the nanotube concentration falls, the

distribution is clearly shifted to bundles of small diameters, ashas been observed previously for SWNT in NMP [21], SWNTin DNA/H2O dispersions [22] and nanowires in various organicsolvents [35, 36].

Plotting the root-mean-square of the bundle diameter,(Drms = √〈D2〉), against SWNT concentration on a log–logplot, as shown in figure 9, clearly demonstrates the decreasein bundle diameter with decreasing SWNT concentration.Root-mean-square bundle diameters are seen to decrease withconcentration, from Drms = 4.8 nm at CNT = 0.03 mg ml−1,to CNT = 0.005 mg ml−1 where the diameter levels off atDrms ≈ 2.4 nm. To illustrate the reversibility of this process, anexisting low concentration dispersion, CNT = 0.006 mg ml−1

was allowed to evaporate in a graduated container. At pre-selected points during the evaporation, drops were taken fromthe dispersion and samples for AFM analysis were taken.Figure 9 shows that, as the SWNT concentration increases,the measured RMS bundle diameter increases, following thesame trend as the initial diluted dispersions. The fact thatDrms follows the same curve for both dilution and evaporationstrongly suggests that a concentration-dependent equilibriumexists. It is interesting that we should reach the sameequilibrium, diluting with sonication as is reached during slowevaporation. This suggests that the main role of sonicationis to affect the kinetics of the debundling process. That thisequilibrium is stable, can be shown by the invariance of thediameter distribution over the course of 55 d after preparation(figure 6). The Drms measured after 55 d falls perfectly onthe equilibrium curve as shown in figure 9, indicating thatrebundling did not occur over this time period. This suggeststhat the bundle diameter reached for each concentration hasreached equilibrium and that only varying the concentration ofSWNTs will affect the bundle diameter.

The average length of all bundles (including individualSWNT) observed in the AFM was found to be approximatelyconcentration-independent with a value of LBun = (2.2 ±1.3) μm. The average length of all individual nanotubes(i.e. those with diameters less than 1.4 nm) was found tobe LNT = (0.9 ± 0.4) μm and was, of course, invariantwith concentration. The difference between these numbersis somewhat surprising. Measurements in SWNT/NMPdispersions show that bundle and individual nanotube lengthswere identical within error, suggesting inter-nanotube slidingto maximize their binding energy [21]. This has also beenobserved for bundles of inorganic nanowires [37]. That wedo not observe this to occur for the GBL-based dispersionssuggests that, for some reason, the nanotubes may besomewhat impeded from relative motion.

It has previously been suggested that the equilibriumdiscussed above can be quantified in terms of an equilibriumbundle number density [21, 36]. This leads to an expression forthe concentration dependence of the root-mean-square bundlediameter

DRMS =√⟨

D2⟩ ≈

[4CNT

ρNTπ 〈LBun〉 (N/V )eqm

]1/2

(3)

where ρNT is the nanotube density, 〈LBun〉 is the mean(concentration-independent) bundle length and (N/V )eqm isthe equilibrium bundle number density. This equation hasbeen fitted to the data set in figure 9. Using this fit and the

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Nanotechnology 18 (2007) 455705 S D Bergin et al

1.8 2.0 2.2 2.4 2.60

2

4

6

8

10

Hei

ght (

nm)

μm

29 30 31 32 330.0

0.2

0.4

0.6

0.8

1.0

Hei

ght (

nm)

nm

C D

A B

Figure 7. AFM images of SWNT dispersions at concentrations of (A) 0.03 mg ml−1 and (B) 6 × 10−4 mg ml−1. Their corresponding crosssections are shown in (C) and (D), respectively. These images are representative of the entire dispersion set.

(This figure is in colour only in the electronic version)

measured values of LBun, from AFM, a value for (N/V )eqm

was found to be (6.0 ± 4.5) × 1017 m−3. Inverting thisterm gives the equilibrium solvent volume per bundle to beV eqm

sol (1.97 ± 1.25) × 10−18 m3. This value compares to thatfor NMP, where V eqm−NMP

sol = (6.7 ± 2.7) × 10−19 m3. Oneexplanation of the difference between these two numbers is thatGBL is not as effective a dispersant of SWNTs as NMP [21].Thus a larger volume of GBL is required to disperse eachbundle at equilibrium when compared with the volume of NMPneeded. It should also be noted that the average saturatedbundle diameter at low concentrations for GBL (2.4 nm) isslightly higher than that for NMP (1.9 nm), again suggestingthat NMP is a slightly better dispersant [21].

3.4. The isotropic phase: population of individual nanotubes

HiPCO nanotubes generally have a diameter range of 0.7 <

D < 1.4 nm. Thus, objects observed by the AFM with heightsof less than 1.4 nm can be classified as individual nanotubes.It should be noted that a population of individual nanotubeswas seen to be present at all concentrations investigated.Shown in figure 10(A) is a HR-TEM image, typical of a lowconcentration (C = 0.002 mg ml−1) dispersion, showing thepresence of large numbers of individual nanotubes. Shown infigure 10(B) is a close up of an individual SWNT.

Using the criterion above, we can deduce the number frac-tion of individual nanotubes, NInd/NT, for each concentrationfrom the AFM data. Figure 11(A) shows that at higher con-centrations (C = 0.032 mg ml−1) only 7% of objects countedcould be classified as individual nanotubes. However, NInd/NT

increases steadily with decreasing concentration, saturating at38% at C = 0.005 mg ml−1. The behaviour of the evapo-rated data set matches that of the diluted data set, further ev-idence of the concentration dependence of bundle size. Thisnumber fraction of individual nanotubes at lower concentra-tions for GBL is not as high as that for NMP at a similarconcentration (C = 0.004 mg ml−1), which corresponded to∼70% individual nanotubes. In the absence of concentration-dependent aggregation, the percentage of individual nanotubeswould remain constant at all concentrations. Thus, deviationfrom the dashed line in figure 11(A) illustrates where the onsetof bundling occurs.

The number fraction of individual tubes can be used togenerate the absolute number of individual nanotubes per unitvolume of solvent using [21]

NInd

V= NInd

NT

NT

V≈ NInd

NT

4CNT

ρNTπ⟨D2

⟩ 〈LBun〉 . (4)

Shown in figure 11(B) is the absolute number ofindividual nanotubes against concentration for both dilution

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Nanotechnology 18 (2007) 455705 S D Bergin et al

02550

Bundle Diameter, (nm)

CNT

=0.00058mg/mL

02550 C

NT=0.0011mg/mL

02550 C

NT=0.0023mg/mL

02550

Cou

nts C

NT=0.0046mg/mL

0

25 CNT

=0.0098mg/mL

02550 C

NT=0.018mg/mL

0

25C

NT=0.032mg/mL

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16

Figure 8. Histograms of bundle diameters for SWNTs dispersed inγ -butyrolactone. The concentration of each dispersion examined isalso shown. Approximately 150 bundle heights per concentrationwere measured.

and evaporation samples. This number density (NInd/V )does not increase linearly with concentration over the wholerange, as would be expected in the absence of rebundling.As the concentration is increased, a maximum number ofindividual nanotubes is reached at C ∼ 0.01 mg ml−1.At higher concentrations NInd/V falls off, clearly indicatingconcentration-dependent re-aggregation. The fact that thispeak is observed for both the dilution and evaporationsamples is further evidence of the presence of a concentration-dependent equilibrium. The presence of a concentration whereNInd/V is maximized immediately suggests that this is theoptimum starting point for fabricating composites/dispersionscontaining large quantities of individual nanotubes.

By averaging over all objects with diameters less than1.4 nm we can estimate the average nanotube diameter in oursample to be 1.0 ± 0.1 nm. Combining this with the averagenanotube length determined above we can calculate the averagenanotube mass, 〈MNT〉, using 〈MNT〉 ≈ π〈DNT〉〈LNT〉M/A,where M/A is the mass per unit area associated with agraphitic sheet (7.7 × 10−7 kg m−2). This works out tobe 〈MNT〉 ≈ 1380 ± 700 kg mol−1, significantly largerthan our previous estimate [21]. We can apply this tothe data in figure 11(b) to work out the concentration ofindividual nanotubes as a function of concentration fromCInd = 〈MNT〉NInd/V . This is shown as the right axisin figure 11(B) demonstrating at the optimum concentrationof ∼0.006 mg ml−1 the population of individual nanotubesapproaches 10% by mass.

It should be pointed out that such AFM measurementsof bundle sizes and individual nanotube populations aregenerally confirmed by infrared photoluminescence (PL)

10-3 10-2 10-12x10-9

3x10-9

4x10-9

5x10-9

6x10-9

Bun

dle

Dia

met

er,

DR

MS (

m)

Nanotube Concentration, CNT

(mg/mL)

Dilution Set Evaporated Set Sedimenting Datum after 32 Days

Drms=2.48*10-8C1/2

Figure 9. SWNT bundle diameter as a function of SWNTconcentration. The black squares represent the initial dilution-baseddispersions. The data saturates at low concentrations, with a meanbundle diameter of 2.4 nm. The circles represent the evaporationdata, where a dispersion, CNT = 0.006 mg ml−1, was allowed toevaporate and the bundle diameter monitored with risingconcentration. The star datum represents a sample,C = 0.032 mg ml−1, allowed to stand for 55 d. The dashed linecorresponds to a fit of equation (3) to the dilution data. The fittedparameters are given in the figure.

spectroscopy [21, 22]. In previous studies, the populationof individual nanotubes has displayed the same concentrationdependence as the PL intensity [21, 22]. This behaviourconfirms that the AFM measurements reflect the state ofthe nanotubes in solution and are not simply due to dryingeffects. Such measurements were attempted as part of thisstudy. However, no PL was observed for SWNT in GBLeven though individual SWNT were unambiguously observedby AFM and HRTEM. However, PL intensities measuredfor nanotubes dispersed in solvents such as NMP have beenextremely weak [21] suggesting that some as-yet unknownquenching process is present. It is likely that, in the caseof SWNT in GBL, the quenching is almost total, resultingin PL intensities below the sensitivity of our instrumentation.It is well known that optical transitions in SWNT are verysensitive to the local environment at the nanotube sidewall. Theoptical transition energies for both emission and absorption areextremely sensitive to both the permittivity [38] and pH [39] ofthe surrounding medium. More seriously, both absorptive andemissive transitions can be quenched by the presence of O2

coupled with a low pH [40]. Thus both physical and chemicalinteractions can affect the nanotube PL. While it is not clearwhat mechanism is at work here, the fact that nanotubesdispersed in both NMP and GBL both display quenching isprobably not coincidental. As we discuss below, successfulsolvents are those which interact strongly with the nanotubesidewall. It is likely that a secondary effect of this interactionis the quenching of the nanotube PL. In any case, as theconcentrations used here are similar to those in previous studieswhere PL has confirmed the validity of the AFM results, webelieve them to be valid in this case also.

3.5. Discussion

The question remains as to why γ -butyrolactone is so effectiveat dispersing nanotubes. It certainly deviates from other

8

Nanotechnology 18 (2007) 455705 S D Bergin et al

BA

Figure 10. High resolution transmission electron microscopy image of (A) individual SWNT and small bundles (C = 0.002 mg ml−1) and(B) an individual SWNT.

10-5

10-4

10-3

10-3 10-2

1016

1017

Dilution Evaporation

Nanotube Concentration, CNT

(mg/ml)

B

Nin

d/V

(m-3)

0.1

A

Nin

d/N

T

MIn

d/V

(m

g/m

l)

Figure 11. (A) Number of individual SWNTs as a fraction of thetotal. (B) Number of individual SWNTs per unit volume. The dashedline in both graphs indicates the low concentration regime wheredebundling has ceased. In (A) and (B) the dashed line is continued,illustrating what would be expected in the system if no concentrationdependent bundling occurred.

successful solvents in that it is not an amide [16, 18, 19, 21, 41]or an amine [42]. In fact, to our knowledge, it is the first non-nitrogen-containing solvent to successfully disperse nanotubes(at least nanotubes without large quantities of functionalgroups). It seems reasonably clear that the major requirementfor a successful solvent is that the energy cost of dispersingthe nanotubes in solvent is not prohibitively high [21]. Thiscost can be expressed as the enthalpy of mixing, �HMix, givenby [29]: �HMix = z�En1φ2, where z is the coordinationnumber, n1 is the number of moles of solvent and φ2 isthe nanotube volume fraction. The parameter �E is themost important contributor here as it describes the balance ofintermolecular interactions in the solvent–solute system. �Eis given by

�E = −(E11 + E22 − 2E12) (5)

where E11 is the solvent–solvent interaction energy, E22 isthe nanotube–nanotube interaction energy and E12 is thenanotube–solvent interaction energy. This means that themore negative E12 becomes the smaller �E and hence �HMix

become. We know from the value of C2 that �HMix > 0. Thismeans that |E12| < (|E11| + |E22|)/2. However for GBL to bea good dispersant, �E must be small, meaning that |E12| mustbe close to its upper limit commensurate with �HMix > 0. Ifthe dominant type of interaction between solvent and nanotubeis the dispersion interaction, then |E12| ∝ α1α2, where α1 andα2 are the polarizabilities of solvent and nanotube, respectively.Thus, it is likely that the success of GBL as a dispersant is dueto the fact that α1 is in just the right range such that |E12| isrelatively large. However, it should be reiterated that |E12| isnot large enough such that �HMix < 0 and hence nanotubesare not truly soluble in GBL.

4. Conclusion

In conclusion, γ -butyrolactone is an excellent dispersant forcarbon nanotubes, rivalling amide solvents such as NMP.At higher concentrations, these dispersions display liquidcrystalline behaviour as shown by absorption spectroscopyand crossed polarized microscopy. The aligned liquidcrystalline phase can be removed by mild centrifugation.SEM measurements show the sediment to consist of alignednanotube bundles. The boundaries between the isotropicand biphasic region and between the biphasic region and theanisotropic region of the phase diagram were determined byfitting absorbance data to the lever rule.

Sedimentation and AFM measurements show that, aftermild centrifugation, the dispersions are stable against bothsedimentation and aggregation. AFM further shows that thebundle diameters tend to decrease with concentration untilvery small bundles are found at low concentration. This canbe explained by an equilibrium characterized by a maximumnumber density of bundles. This allows the calculation of theminimum solvent volume per bundle which is slightly higherthan the equivalent value for NMP dispersions.

In addition, a population of individual nanotubes is presentat all concentrations. The fraction of individual nanotubesincreases as the concentration is decreased, approaching 40%

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Nanotechnology 18 (2007) 455705 S D Bergin et al

at low concentration. We can also calculate the numberdensity of individual nanotubes, which displays a maximum atapproximately CNT ∼ 0.01 mg ml−1. This is then the optimumconcentration for finding individual nanotubes.

The overall performance of γ -butyrolactone as a solventfor carbon nanotubes can be measured using four parameters:dispersion limit, minimum value of Drms, equilibrium volumeof solvent per bundle and number fraction of individualnanotubes at low concentration. These values were (NMPvalues in brackets [21]): 0.004 mg ml−1 (∼0.01 mg ml−1),2.4 nm (1.9 nm), 1.97±1.25×10−18 m3 (6.7±2.7×10−19 m3)and 38% (70%). These values are all reasonable in comparisonwith NMP, which is regarded as the best known solvent fornanotubes. It seems clear that γ -butyrolactone is a usefuladdition to the small but growing band of nanotube solvents.

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