Analysis of Stability of Nanotube Dispersions Using …walled carbon nanotubes were supplied by...

Published: September 30, 2011

r 2011 American Chemical Society 13451 dx.doi.org/10.1021/la2028466 | Langmuir 2011, 27, 13451–13460

ARTICLE

pubs.acs.org/Langmuir

Analysis of Stability of Nanotube Dispersions Using Surface TensionIsothermsVijoya Sa and Konstantin G. Kornev*

School of Materials Science and Engineering, Clemson University, Clemson, South Carolina 29634, United States

’ INTRODUCTION

Single-walled carbon nanotubes (SWCNT) are typically pro-duced in a powder form where the nanotubes are bundled andclustered owing to strong van der Waals interactions, so thatsingle nanotubes are seldom to find.1 Direct mixing of nanotubeswith most common solvents or polymers results in a dispersionof nanotube clumps, bundles, and ropes.2 Dispersing the nano-tubes in a liquid media, one requires either chemical means toseparate bundles, for example, using surfactants3,4 and chemicalfunctionalization of carbon nanotubes,5�13 or by applying phy-sical methods such as strong sonication or melt mixing.14�16

Aqueous solutions of surfactants are more attractive than dif-ferent toxic solvents (like N-methyl-pyrrolidone, dimethyl-formamide, cyclohexylpyrrolidone, 1-benzyl-2-pyrrolidinone, etc.)used for the preparation of nanotube dispersions;17 hence, theformer received greater attention in recent years. A wide variety ofsurfactants have been used to disperse nanotubes in aqueoussolutions.3,4 Ionic surfactant sodium dodecyl sulfate (SDS) is themost popular stabilizing agent for the preparation of nanotubedispersions in aqueous media.18�20 We used SDS in this study.Preparation of uniform dispersions with a high concentrationof nanotubes is an important step in making multifunctionalSWCNT-based nanocomposites with metallic level of electricconductivity.19,21 However, a homogeneous dispersion of carbonnanotubes is difficult to obtain, especially at high nanotube con-centration: the mechanisms of interactions between surfactantmolecules and nanotubes are poorly understood, and hence, themethodology of nanotube stabilization against aggregationis still under development. A lack of reliable experimental data on

nanotube structuring at different physicochemical conditions hin-ders the progress in this field.

However, none of the available experimental methods providea quantitative way to characterize dispersions in a wide range ofnanotube loading particularly when the dispersion turns black/opaque.22�29 Therefore, there is a need for a characterizationmethod that would be able to assess the state of the nanotubeassembling when other methods fall short. A rheological analysisof nanotube dispersions with high loading appears to be avaluable method.30 On the other hand, the analysis of surfacetension isotherms has been widely used for characterizingsurfactant solutions.31�36 Since this method is not affected bythe color of the liquid, we used this method to investigate theeffect of nanotubes on the surface tension of the dispersion atdifferent levels of nanotube loading.

This paper is organized as follows. We first introduce thehypothesis that, at moderate concentrations, dodecyl sulfateions (DS ions) displaces carbon nanotubes from the air�waterinterface. We then explain the experimental protocol for thestudy of the surface tension isotherm. The analyses of criticalmicelle concentration, phase diagram, and adsorption isothermof DS ions on nanotubes follow next. We conclude with asummary of our findings.Surfactant-Nanotube Positioning at the Air�Water Inter-

face. SDS molecules are electrolytes containing charged hydro-philic heads and lipophilic fatty tails.21 In an aqueous solution,

Received: July 23, 2011Revised: September 29, 2011

ABSTRACT: In this paper, we present the analyses of surface tension ofsurfactant-stabilized dispersions of carbon nanotubes. This method allows oneto study interactions of carbon nanotubes with surfactants at different levels ofnanotube loading when optical methods fall short in quantifying the level ofnanotube separation. Sodium dodecyl sulfate was used as a stabilizing agent touniformly disperse single-walled carbon nanotubes in an aqueous media. Weshow that surface tension is very sensitive to small changes of nanotube andsurfactant concentrations. The experimental data suggest that, at moderateconcentrations, surfactant displaces carbon nanotubes from the air�waterinterface and the nanotubes are mostly moved into the bulk of the liquid. Byanalyzing the surface tension as a function of surfactant concentration, weobtained the dependence of critical micelle concentration on nanotube loading.We then constructed the adsorption isotherm for dodecyl sulfate on carbonnanotubes and bundles of carbon nanotubes. The results of these experiments enabled us to extend the phase diagram of theproduced dispersions to a broader range of surfactant and nanotube concentrations.

13452 dx.doi.org/10.1021/la2028466 |Langmuir 2011, 27, 13451–13460

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SDS dissociates into positively charged sodium ions and nega-tively charged fatty tails of dodecyl sulfate ions. After sonication,the bundles of nanotubes are separated, and then, the negativelycharged hydrophobic fatty tails adsorb on the nanotube. Ideally,when surfactant is in excess, one would expect to have a densecoating on the hydrophobic carbon nanotubes (CNT).21 Con-sequently, the charged surfaces of nanotubes would repel eachother, preventing nanotubes from agglomeration.21 This way,one would make a uniform dispersion of the nanotubes in theaqueous medium.Consider first the case of a SDS�water solution without any

carbon nanotubes. At low surfactant concentrations, the dodecylsulfate ions are rarely distributed at the air�water interface. Theirpolar heads stay dipped in water, while the fatty tails tend toescape from water projecting toward air. Once the solution issaturated with surfactant at the air�water interface, i.e., thesurface is fully occupied by surfactants, the surfactant moleculesin the bulk associate to form clusters in a form of sphericalmicelles or some other more complicated forms. In the micelles,the hydrocarbon chains come together to form spherical clusterswith the polymer chains hidden in the core and polar headspointing outward. The concentration of surfactant at which themicelles start forming is called the critical micelle concentration(CMC). Above the CMC, one observes almost complete cover-age of air�water interface with fatty tails.34 Consequently, thesurface tension stays almost constant above the CMC. The CMCof SDS is reported to be 7�10 mM (millimole/liter).37

With the addition of carbon nanotubes to the SDS�watersolution, the picture of surface coverage by surfactant becomesmore complicated, especially at very low concentrations ofsurfactants. Recent study of the CMC of a dispersion of multi-walled carbon nanotubes has shown that the nanotube disper-sions can be stabilized even below the CMC.22 At low surfactantconcentrations, some nanotubes can be found at the air�waterinterface owing to the nanotube hydrophobicity. However, innanocomposite manufacturing, this range of surfactant concen-trations is of no importance and we do not discuss it in this paper.For nanocomposite manufacturing, the most important range ofsurfactant concentrations is that when all nanotubes and bundlesof nanotubes are partially covered with surfactant, so that thenanotubes are sunk into water or lifted above the air�waterinterface by the surfactant layer. We concentrate our efforts onthe analysis of this level of nanotube dispersion.

Compared to the identical SDS solution without nanotubes, inthe nanotube loaded dispersion, some of the DS ions areadsorbed by the CNTs. Therefore, the surface tension of thenanotube�SDS dispersion should increase due to a reduction inthe number of the DS ions sitting on the air�water interface(Figure 1a). Consequently, to achieve a similar level of surfacecoverage as that of a SDS�water solution, one needs to dissolvemore SDS molecules. As the surfactant concentration increasesfurther, the air�water interface and the nanotube surface willultimately be saturated with the surfactant (Figure 1b). By addingmore surfactants, one would not change the surface coverage, sothat the extra DS ions will subsequently come together and formmicelles (Figure 1c).Therefore, below the CMC of the carbon nanotube loaded

SDS�water solution, the surface tension should not be constantbut should depend on surfactant concentration. This variation ofsurface tension can be quantitatively analyzed as a function ofnanotube loading. In addition, from the surface tension measure-ments, we expect to predict the CMCof the nanotube dispersion.We assume that the nanotubes when added in the SDS solutionare fully absorbed in the dispersion and only DS ions stay at theair�water interface.We examine this assumption experimentally.

’EXPERIMENTAL DETAILS

Preparation of Nanotube Dispersions. High-grade single-walled carbon nanotubes were supplied by Nanoledge S.A., France.Surfactant, sodium dodecyl sulfate, was purchased from MallinckrodtBaker Inc. Three stock solutions of 3.47mM, 34.68mM, and 346.77mMSDS were prepared in 500 mL of distilled water. After preparing thestock solutions, the 3.47 mM SDS solution was diluted to prepare foursolutions in the range 0.347�3.468 mM SDS concentrations. 34.68 mMsolution was diluted to prepare six solutions in the range 5.20�17.34 mM, and the 346.77 mM SDS solution was diluted to preparethe remaining five solutions ranging 52.01�346.77 mM SDS concen-trations. For each solution, six 20 mL vials were filled with 7 mL of thesolution and six dispersions were prepared by adding carbon nanotubesbetween 0 and 6 mg/mL in the solution and then sonicated for 15 minusing a high-power horn sonicator (Branson Sonifier 450). Here, wedefine the nanotube loading as mass of nanotubes per volume of sol-vent (mg/mL). A total of 90 dispersions (6 different nanotube loadingsand for each nanotube loading 15 different SDS concentrations) wereprepared for the analysis.Optical Imaging. The dispersions were transferred to rectangular

capillaries with the length, width, and thickness of 10 cm, 0.5 cm, and

Figure 1. Interaction of SDS�CNT: (a) below the CMCof the dispersion, (b) at the CMC of the dispersion, and (c) above the CMC of the dispersion.


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0.05 cm, respectively. Microscopic images of the samples were takenusing Dalsa Falcon 1.4M100 XDR video camera attached to OlympusMVX10 microscope.Surface Tension Measurements. Surface tension of the pre-

pared samples was measured using pendant drop method by KR€USSDSA10 instrument with a 0.5 mm needle for solutions with SDSconcentration below 17 mM. The 1.25 mm needle was used for thesolutions with SDS concentration between 17 and 87 mM, and the2.5mmneedle was used for the solutions with higher SDS concentrations.Densities of the liquids were calculated assuming that the volume does notchange upon addition of the surfactants and nanotubes as shown inTable 1. The images of pendant drops were captured and analyzed usingKR€USS DSA software. A sequence of droplet shapes when the SDSconcentration was increased is shown in Figure 2. The surface tensionchanged from 68 to 35 mN/m in Figure 2a�e.

’RESULTS AND DISCUSSION

Surface Tension and Adsorption Isotherms. The resultsof surface tension measurements of carbon nanotube dispers-ions are plotted in Figure 3a for up to 17 mM SDS. Theexperimental data for pure SDS solutions were compared withthe data reported in the literature and summarized in Figure 3b.The comparison of our data points with those taken from the

literature shows very good agreement, thus confirming that thismethod provides reliable results. When the SDS concentrationexceeds 17 mM, the surface tension does not change appreciably.We do not show these points of high SDS concentration inFigure 3a and b.The surface tension reaches its limiting value before the SDS

concentration approaches 17 mM. Due to definition, the criticalmicelle concentration is the concentration of surfactant wherethe slope of surface tension versus logarithm of surfactant con-centration changes abruptly. This abrupt change of slope of thesurface tension isotherm cannot be associated with a single SDSconcentration, but with a range of concentrations. In particular,for SDS, the CMC is around 8 mM, which can be seen inFigure 3b.Our hypothesis that the surface tension σ is mostly controlled

by the DS tails at the air�water interface, not by carbon nano-tubes, was validated by the analysis of the surface tensionisotherms. Within the region of SDS concentrations below C <8 mM, the slopes of the surface tension isotherms of SDSsolutions with and without carbon nanotubes were found to bevery close to each other, dσ/dC = �4 ( 0.35 mN/m/mM; seeFigure 4. In the first approximation, we can consider the slopes ofall isotherms identical, and each new isotherm can be obtained

Table 1. Density of Nanotube Dispersion (g/mL) in Aqueous Surfactant (SDS) Solution

SWCNT concentration (mg/mL)

0.00 0.75 1.50 3.00 4.50 6.00

SDS concentration (mM) SDS concentration (mg/mL) dispersion density (g/mL)

0.347 0.10 1.0001 1.0009 1.0016 1.0031 1.0046 1.0061

0.867 0.25 1.0003 1.0010 1.0018 1.0033 1.0048 1.0063

1.734 0.50 1.0005 1.0013 1.0020 1.0035 1.0050 1.0065

3.468 1.00 1.0010 1.0018 1.0025 1.0040 1.0055 1.0070

4.335 1.25 1.0013 1.0020 1.0028 1.0043 1.0058 1.0073

5.202 1.50 1.0015 1.0023 1.0030 1.0045 1.0060 1.0075

6.069 1.75 1.0018 1.0025 1.0033 1.0048 1.0063 1.0078

6.935 2.00 1.0020 1.0028 1.0035 1.0050 1.0065 1.0080

10.403 3.00 1.0030 1.0038 1.0045 1.0060 1.0075 1.0090

17.338 5.00 1.0050 1.0058 1.0065 1.0080 1.0095 1.0110

52.015 15.00 1.0150 1.0158 1.0165 1.0180 1.0195 1.0210

86.691 25.00 1.0250 1.0258 1.0265 1.0280 1.0295 1.0310

173.382 50.00 1.0500 1.0508 1.0515 1.0530 1.0545 1.0560

242.735 70.00 1.0700 1.0708 1.0715 1.0730 1.0745 1.0760

346.765 100.00 1.1000 1.1008 1.1015 1.1030 1.1045 1.1060

Figure 2. Shape of droplets of aqueous solution of SDS at different concentrations: (a) 0.85 mM SDS, (b) 3.4 mM SDS, (c) 17 mM SDS, (d) 52 mMSDS, (e) 242 mM SDS.


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from the isotherm of the SDS solution without nanotubes byshifting it to the right. This finding implies that the surfacetension isotherm is mostly controlled by the adsorption of DS-tails at the air�water interface, but not by carbon nanotubes.Using the obtained isotherms, the amount of surfactant

adsorbed on the nanotubes was determined by comparing thesurface tension of the nanotube dispersions with the surfacetension of SDS solution without nanotubes. The surface tensionof the SDS solution without nanotubes was regarded as areference. Therefore, by drawing the horizontal line correspond-ing to the given surface tension, one can find two points of

intersection of this line with the surface tension isotherms of theSDS solution with and without nanotubes. These intersectionpoints CSDS and C give two different concentrations of SDS(Figure 5). Assuming that the surface tension isotherm iscontrolled solely by the SDS concentration, we can state that,for the same surface tension, the difference between the SDSconcentration in solution without nanotubes (CSDS) and theSDS concentration in the nanotube dispersion (C) gives theamount of SDS (ΔC = C � CSDS) absorbed on the nanotubes.Due to the definition of the surface tension isotherm, thevalue of CSDS corresponds to the amount of SDS in the bulk.

Figure 3. (a) Surface tension isotherms for different nanotube loadings. (b) Comparison of our data points with those found in the literature foraqueous SDS solutions without carbon nanotubes.38,39

Figure 4. Surface tension isotherms for different carbon nanotube loadings.


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Therefore, plotting (ΔC) as a function of CSDS, one can find theadsorption isotherm of SDS on nanotubes for each nanotubedispersion. In Figure 6, we plot this adsorption isotherm ΔC =ΔC(CSDS). As expected, when the nanotube loading is in-creased, the amount of SDS adsorbed on the nanotube aggre-gates is also increased. However, the rate of increase is verydifferent for low and high loadings of carbon nanotubes in thedispersions.For the dispersions with nanotube loading less than ∼1.5

mg/mL, or low loaded dispersions, the amount of DS ad-sorbed on nanotube aggregates stays almost unchanged untilthe SDS concentration reaches the CSDS ≈ 3 mM level. Onlyafter CSDS = 3 mM does the adsorption isotherm of the lowloaded dispersions begin to bend up. This behavior is repro-ducible within the experimental error and it was observedon two different dispersions. The third dispersion with the

nanotube loading of 3 mg/mL has a similar footage with adecrease of derivative dΔC/dCSDS within the 1�3 mM rangeof SDS concentrations. The observed behavior is quite un-usual for colloid science, suggesting that, at this level ofnanotube loading, the air�water interface is a thermodyna-mically more favorable place than the nanotube aggregates.Because of a lack of thermodynamic data and limited informa-tion on the morphology of nanotube agglomerates, it isdifficult to assess whether this behavior is caused by the largersurface area of the air�water interface or because of theenergetic preference. In any case, this very interesting beha-vior of surfactant adsorption has never been reported in theliterature on carbon nanotube dispersions and deserves aspecial theoretical analysis.Within the hypothesis, we can assign CSDS

CMC = 8 mM as thecritical micelle concentration of SDS right underneath the air�water interface in nanotube dispersion. Therefore, drawing thevertical line at CSDS = CSDS

CMC = 8 mM in Figure 6 and obtainingthe amount of SDS adsorbed on nanotube aggregates, ΔCC =ΔC(CSDS

CMC), we can determine the critical micelle concentrationof SDS in the nanotube dispersion as CCNT

CMC = ΔCC + CSDSCMC.

These values CCNTCMC are shown in Table 2 for various nanotube

loadings.Estimates of Surface Area of Nanotube Aggregates.Using

the obtained adsorption isotherms, we can estimate the size ofthe nanotube aggregates in the dispersions. The starting point isthe equation defining the amount of adsorbed DS on thenanotube aggregates. The number of DS tails (which is equal

Figure 5. Illustration of the evaluation of the amount of SDS adsorbedon two surface tension isotherms with almost the same slope that areshifted away from each other by the distanceC�CSDS. Since the surfacetension isotherm does not change shape, it is assumed that the shift C�CSDS corresponds to the amount of DS adsorbed on nanotubes.

Figure 6. Adsorption isotherms of SDS on nanotube agglomerates in the dispersions with different nanotube loadings.

Table 2. Variation of the Critical Micelle Concentration ofSDS with Nanotube Loading

nanotube loading in

dispersion (mg/mL) CCNTCMC (mM)

0.00 8.00

0.75 8.75

1.50 9.00

3.00 10.50

4.50 11.75

6.00 12.25


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to the number of SDS molecules) (NSDS) adsorbed on thenanotubes is calculated from the following equation

NSDS ¼ ΔC 3NAV 3V ð1Þwhere ΔC is the SDS adsorption in millimol/liter (mM) takenfrom Figure 6,NAV is the Avogadro number, and V is the volumeof the solution in liters (here 1/100 L). The surface area ASDS ofthe DS ion tails adsorbed on nanotube aggregates is calculated as

ASDS ¼ NSDS 3 aSDS ð2Þwhere aSDS = 0.436 nm2 is the surface area occupied by a singleDS tail placed perpendicularly to the surface with the polar headpointing toward the liquid.36 Substituting eq 1 into eq 2, we canestimate the surface area of the nanotubes covered by thesurfactant as a function of SDS concentration in the bulk ofliquid. The result of this analysis is plotted in Figure 7.Using these results, we can analyze the level of aggregation

of nanotubes in different dispersions. We model each nano-tube aggregate as a bundle of nanotubes. Thus, the total surfacearea of the nanotube aggregates occupied by surfactants can be

subdivided onto the surface areas of individual nanotubes orbundles of nanotubes. Considering different cases of nanotubepacking shown in Figure 8, one can relate the correspondingsurface areas with the measured ones. As possible configurations,we select a single nanotube, Figure 8a, a hexagonal bundle ofnanotubes, Figure 8b, and a rope of hexagon bundles, Figure 8c.The larger aggregates are modeled by packing the nanotubehexagons into larger ropes keeping the hexagonal symmetry ofthe aggregate.In order to calculate the surface area of these nanotube

bundles, we first calculate the number of nanotubes in the dis-persion NCNT as

NCNT ¼ w 3NAV 3VMWCNT

ð3Þ

where MWCNT is the molecular weight of the nanotubes whichwas estimated from ref 21 to be 6.89 � 106 Da, w is the nano-tube loading in the dispersion in g/L. The average length Land diameterD of the nanotubes were taken as L = 3500 nm andD = 1.33 nm, respectively.21 Assuming that all the bundles are of

Figure 7. Surface area of carbon nanotube aggregates covered with SDS versus SDS concentration in the bulk of the dispersions with different carbonnanotube loadings.

Figure 8. Model shapes of nanotube aggregates in the dispersion: (a) separated nanotubes, (b) hexagonal bundle of nanotubes, (c) a rope ofhexagonally packed nanotubes.


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the same size, the number of nanotube bundles Nb in thedispersion consisting of n nanotubes in the bundle is calculated as

Nb ¼ NCNT=n ð4ÞNow, the surface areas of different bundles can be calculated by

estimating the number of nanotubes forming the outer surface ofthe bundle exposed to the liquid. In the case of hexagon bundles(Figure 8b), the total surface area of the bundle available for thesurfactant corresponds to the surface area of only 3 nanotubesout of 7 nanotubes in the bundle. Similarly, fromFigure 8c we cansee that only the surface area of 12 nanotubes is actually exposedto the liquid out of 49 nanotubes in the bundle. Accordingly, thesurface area of the ropes is calculated in a similar way, accountingfor only outermost surface of hexagons. The surface area ofdifferent bundles and ropes is shown in Table 3 and Figure 9.Figure 9 shows the results of calculations of the surface area of

nanotube aggregates for different nanotube loadings. As ex-pected, separated nanotubes give the largest surface area, butthe area does not change drastically as the size of the nanotubeaggregate decreases.From the comparison of Figure 7 and Figure 9, we can see that,

at all levels of nanotube loadings, the largest nanotube bundleconsists of 2400 nanotubes provided that all bundles are of thesame size. For a constant nanotube loading, when the SDSconcentration increases, the maximum size of the aggregateshould decrease in order to explain an increase of the totalsurface area of the aggregates. Close to the CMC level of the SDSconcentration, the number of nanotubes in the bundle droppedfrom 2400 to 50 for all nanotube loadings, but w = 0.75 mg/mLloading is an exemption. In this exemption case, the number ofnanotubes in the bundle is reduced to 7 at the critical micelle

concentration of SDS. This corresponds to almost 2 to 3 ordersof magnitude decrease in the bundle size of nanotube aggregates.Therefore, the surfactant acts effectively to split the nanotubeaggregates at a low level of nanotube loading. These estimateswere implicitly confirmed by our experiments with carbonnanotube composites.21 We produced fibers using the samedispersion with the nanotube loading of 6 mg/mL. An analysisof the size distribution of nanotube aggregates shows that theaggregates with diameters of a few tens of nanometers werepresent in the material,21 which validates our estimates. There-fore, by analyzing the SDS adsorption isotherms, one canmake reasonable estimate of the degree of exfoliation of nano-tube bundles. It should be noted that the provided estimates werebased on the assumption that the outer surface of the nanotubeaggregates was fully covered with surfactants and all the aggre-gates were of the same size. If the surface of the nanotubeaggregate was not fully covered with surfactants, then the size ofthe aggregate can be even smaller than the estimated one.Optical Analysis of Nanotube Aggregation.The analysis of

surface tension and adsorption isotherms was further validatedby examining optical micrographs of nanotube dispersions atdifferent surfactant concentrations. The dispersion with thenanotube loading of w = 0.75 mg/mL was chosen as the mosttransparent. The sequence of images of internal structure of thenanotube dispersion at different SDS concentrations is shown inFigure 10. With an increase of the SDS concentration, theuniformity of the dispersion is significantly improved. Micro-graphs of dispersions with the SDS concentrations below 6.9mMshowed clusters of nanotubes but after crossing the CMC at8 mM, the dispersion became completely black (Figure 10g).With further increase of the SDS concentration above 87 mM,the clusters appeared again (Figure 10i).This analysis of the nanotube dispersion with 0.75 mg/mL

nanotube loading suggests that the range of SDS concentrationswhere the dispersion is uniform lies between 10 mM and 52 mM.The lowest limit of this SDS concentrations, C = 10 mM,corresponds to the critical micelle concentration extracted fromthe analysis of the surface tension isotherm. Thus, the results ofthe optical microscopy show a direct correlation between thecritical micelle concentration of the SDS in nanotube dispersionand the lowest boundary for the SDS concentration guaranteeingthe dispersion uniformity. Since the surface tension analysis canbe done on solutions with different levels of transparency, it canbe considered a useful technique for the determination of thelevel of dispersion uniformity.Phase Diagram. On the basis of the analysis of the CMC

concentration of SDS in the nanotube dispersions, we haveplotted a phase diagram of the dispersion in terms of the SDSconcentrations versus nanotube loading (Figure 11). As the

Table 3. Surface Area of Nanotube Aggregates in Dispersion of 10 mL Volume

surface area of nanotube aggregates (nm2)

nanotube loading

(mg/mL)

individually separated

CNTs (1 CNT)

hexagonally packed CNTs

(7 CNTs in a bundle)

rope of hexagonally packed CNT

hexagons (49 CNTs in a rope)

large rope of hexagons,

(343 CNTs in a rope)

large rope of hexagons,

(2401 CNTs in a rope)

0.075 9.58 � 1018 4.11 � 1018 1.76 � 1018 7.54 � 1017 3.23 � 1017

0.150 1.92 � 1019 8.22 � 1018 3.52 � 1018 1.51 � 1018 6.47 � 1017

0.300 3.83 � 1019 1.64 � 1019 7.04 � 1018 3.02 � 1018 1.29 � 1018

0.450 5.75 � 1019 2.46 � 1019 1.06 � 1019 4.53 � 1018 1.94 � 1018

0.600 7.67 � 1019 3.29 � 1019 1.41 � 1019 6.04 � 1018 2.59 � 1018

Figure 9. Surface area of nanotube aggregates as a function of nanotubeloading in a 10 mL volume dispersion.


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boundary separating uniform dispersions from nonuniform ones,we used the CMC for SDS found from the adsorption isotherms.The nonshaded region below the straight line in Figure 11corresponds to nonuniform dispersions. This region corre-sponds to the SDS concentrations below the CMC where weobserve nanotube aggregation. All dispersions below the 0.75mg/mL nanotube loading are sufficiently transparent and theirexamination with optical imaging was feasible. Therefore, weprepared a few more nanotube dispersions with nanotubeloading lower than 0.75 mg/mL varying the SDS concentrationfrom 10 mM up to 243 mM. On the basis of the analyses ofimages, the B and C regions were separated. The B regioncorresponds to the region of homogeneous dispersions obtainedin ref 19. In the C region, we observe clusters and clumpsconcluding that this region corresponds to nonuniform disper-sions. We overimpose a phase diagram that is known from theliterature.19 This diagram has been constructed using opticalanalysis as described in the previous section. TheD region on thisphase diagram corresponds to a uniform dispersion.19 The datapoints corresponding to the CMC boundary are close to thelower branch of the boundary that is proposed in ref 19, but theboundary of ref 19 crosses our CMC boundary and goes below it.It appears that the CMC boundary gives the right estimate ofthe stability region below the 0.75 mg/mL nanotube loading.For our dispersions, the upper branch of the boundary of the Dregion moved down: in the experiments, the dispersions werefound nonuniform above the B region. When surfactant con-centration is very large, one expects to see not only micelles, but

columns, lamellas, and so forth.31 These surfactant superstruc-tures are able to engulf many nanotubes and bundles ofnanotubes covering them completely. As a result, the surfac-tant-covered nanotube aggregates are expected to be indistin-guishable from the primary surfactant superstructures. Thenanotube aggregates will therefore follow a somewhat similarthermodynamic pathway to the surfactant, with inevitable phaseseparation. This mechanism explains the hindrance of exfoliationof nanotubes at large SDS concentrations. Since the nanotu-be�surfactant dispersion is a two-component colloidal system,the possible scenarios of phase separations are much richer andnot limited to the scenario associated with a one-componentsystem.We were unable to reproduce the analysis of ref 19 for greater

nanotube loadings: even after increasing the light intensity, theresults were not repeatable. We therefore marked the C region asthe region of nanotube agglomeration; hence, the upper bound-ary of the D region for our nanotubes should bemoved to the lineseparating the B and C regions. Since the nanotube qualitychanges from batch to batch, the phase diagram might change aswell. Hence, we attribute this discrepancy between two phasediagrams to the difference in nanotube powders and, probably,different sonication times. Figure 11 summarizes the results ofthis paper together with those obtained in ref 19. The regionsabove the CMC line mark the composition candidates for thedispersion uniformity as follows from the CMC criterion. Thiscriterion is definitely strict and is limited by the onset ofmicellization

Figure 10. Images of nanotube dispersion with the SWCNT loading at 0.75 mg/mL in DI water with (a) 0.34 mM SDS, (b) 0.85 mM SDS, (c) 1.7 mMSDS, (d) 3.4 mM SDS, (e) 5.1 mM SDS, (f) 6.8 mM SDS, (g) 17 mM SDS, (h) 52 mM SDS, and (i) 87 mM SDS.


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of the dispersion. Yet, it is a helpful guideline for the formulation ofstable uniform dispersions.

’CONCLUSIONS

We have used the surface tension analyses to examine thestability of nanotube dispersions. An aqueous solution of sodiumdodecyl sulfate (SDS) was used as the dispersion carrier. Weshowed that the surface tension isotherms are sensitive to a smallvariation of surfactant and nanotube concentrations. The studyof surface tension isotherm allowed us to put forward andconfirm a hypothesis that the surface tension of nanotubedispersions is mostly controlled by the adsorbed surfactant: thesurface tension isotherms look almost identical for differentdispersion with a broad range of nanotube loadings. This hypo-thesis enabled us to estimate the amount of surfactant adsorbedon the nanotube aggregates. We also examined the efficiency ofexfoliation of nanotube bundles by surfactants: the surface area ofnanotube aggregates were estimated as a function of SDS con-centration. Using the obtained critical micelle concentrations ofSDS in the nanotube dispersions, we estimated the regions ofdispersion stability and drew a phase diagram of the nano-tube dispersion. A part of this diagram has been obtained in theliterature by another method, and we enriched it with new results.

We believe that the proposed method will introduce anopportunity for the examination of different dispersions ofcarbon nanotubes, nanofibers, and grapheme platelets whenother methods fall short.

’AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

’ACKNOWLEDGMENT

The authors are grateful for the financial support from theNational Science Foundation, Grants CMMI 0826067 and EFRI0937985. We also thank Dr. Igor Luzinov, Clemson University,and Dr. Sunil Kumar, Baker Hughes, for fruitful discussionsregarding the adsorption isotherms.

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Figure 11. Phase diagram of the nanotube-loaded dispersions. The CMC criterion forms the boundary separating uniform dispersions fromnonuniform ones. The domain of dispersion uniformity that was obtained from the optical microscopy analyses19 is shown as the D region.


Langmuir ARTICLE

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