Elasticity of Dispersions Based on Carbon Nanotubes Dissolved in a

ARTICLE pubs.acs.org/JPCC

Elasticity of Dispersions Based on Carbon Nanotubes Dissolved in a Lyotropic Nematic Solvent Franco Tardani† and Camillo La Mesa*,†,‡ †

Department of Chemistry and ‡SOFT-INFM Center, La Sapienza University, Rome, Italy ABSTRACT: Single-walled carbon nanotubes were dispersed in a nematic solvent, made of sodium dodecyl sulfate, decanol, and water. Fine and homogeneous dispersions were obtained, depending on the preparation procedures and on the weight percent of carbon nanotubes in that solvent. Modifications in optical textures were compared to those pertinent to the original nematic fluid. According to optical polarizing microscopy and to other methods as well, it is inferred that very tiny amounts of clusters or bundles are present in such composite media. It is stated, accordingly, that the role of single tubes is dominant in the observed optical effects. A systematic investigation on the elastic properties of the above mixtures was performed by rheological methods, as a function of applied frequency, and in moderate shear stress conditions. Up to 0.25 wt % in nanotubes, the nematic dispersions show no, or negligible, elastic components in the corresponding viscoelastic relaxation spectra. Slightly larger amounts of nanotubes increase the system viscosity and give rise to significant elastic contributions in the investigated frequency range. The above findings were interpreted in terms of entanglement between nanotubes dispersed in the nematic matrix. Depending on nanotubes volume fraction, networks are formed and a significant elasticity is ensured to the resulting nematic dispersions.

’ INTRODUCTION The significant interest from the scientific community toward carbon nanotubes, CNTs, has promoted several studies on the fundamental and technologically oriented aspects of the above substances.1
5 In particular, the fine structures of the dispersions they form have got particular attention from the scientific community.6
10 It is currently acquainted now that CNT dispersions almost always contain bundles and clusters, held together by significant π
π interactions.11
15 The status of art in the field and a detailed description of the forces operating in such systems and, more generally, in complex colloid fluids have been recently summarized and discussed by French et al.16 In some cases, percolating networks made of CNTs were observed in water-based17 or polymer-based media.18 Generally, entanglement mediated by micelles or other colloid entities is required to get percolation. CNTs entanglement in fluid matrices is concomitant, very presumably, to the formation of elastic bodies. Conditions for elasticity to occur are the preferred CNTs orientation along the director dictated by applied shear stresses, entanglement, or both. These hypotheses imply that no bundles or clusters should occur, since CNT clustering and macroscopic phase separation do not favor the conditions giving extended and interconnected networks. CNTs are often dispersed in polymer solutions19 and polymer melts20
22 for diverse technological purposes. The results reported to date are promising for practical applications to reinforce fibers and polymer composites.23,24 In such media concentration effects and the chemical affinity between polymers and CNTs play a pivotal role in the formation of clusters and r 2011 American Chemical Society

bundles. However, because of the significant viscosity of polymer-based fluids and because of the poor chemical affinity between the components, the resulting CNT dispersions may be not homogeneous. Clustering, phase separation, and precipitation are usually found in dispersions of CNTs in the presence of significant amounts of polymers, surfactants, and other dispersants. The above dispersions are unstable and contain coarse entities. In addition, little or no elasticity occurs therein. The above phenomena are ascribed to depletion effects,25 which significantly hinder dispersing CNTs in fluid matrices. To avoid the aforementioned drawbacks and ensure, at the same time, significant elastic performances to carbon nanotubes dispersions, new matrices should be used. In this contribution a nonconventional solvent was considered, and the possibility to disperse CNTs in lyotropic nematic matrices was exploited.26
29 In this regard, a recent contribution due to Xin and co-workers is particularly relevant.30 The combination of excluded volume effects, surfactant (or aggregate) adsorption onto nanotubes, and an efficient orientation in the nematic matrices may induce ordering and entanglement as well. CNTs are easily dispersed in lyotropic nematic matrices due to the moderate viscosity of such fluids, to their lipophilic character, to the presence of charges on the nematic domain surfaces, and to the possibility that surfactants (or their aggregates) adsorb onto nanotubes. Received: January 20, 2011 Revised: April 7, 2011 Published: April 25, 2011 9424

dx.doi.org/10.1021/jp2006167 | J. Phys. Chem. C 2011, 115, 9424–9431

The Journal of Physical Chemistry C Lyotropic nematic phases are formed by an ordered allocation of nonisometric micelles (disks or rods) in planar arrangements. The aggregates have rotational degrees of freedom around their main axis.31,32 The location of lyotropic nematic phases in the phase diagrams depends on the solute(s) nature, temperature, and composition. Lyotropic nematic phases can be close to canonical lyotropic ones (as in the CTAB
water system)33,34 or not.35 The peculiar supramolecular organization mode of nematic fluids plays a pivotal role in their viscosity, which is usually moderate.33 It is argued, accordingly, that adding CNTs to ordered fluids may induce elasticity and that the above effect is, presumably, more significant than in polymer melts or solutions. For these reasons, CNTs were dispersed in a nematic phase made of water, sodium dodecyl sulfate, and decanol.36
40 Experiments were performed at fixed temperature, given the limited range of existence for that phase.41 We investigated whether single-walled CNTs play a significant role in the viscosity and elasticity of nematic dispersions. On elementary physical grounds, it is supposed that entanglement and other related mechanisms are responsible for a significant increase in elasticity in such media. To maximize elasticity, single-walled CNTs were used. It is expected that they induce elasticity much more easily than multiwalled carbon nanotubes (MWCNTs) or carbon black. That is the reason why information on the volume fraction contributions due to the dispersed particles, φ, was required and comparison between carbon black and single- and multiwalled CNTs was performed. The aforementioned carbon-based substances significantly differ each from the other in aspect ratios (dictated by the nanotube average section, D, and length, L) and, obviously, in the overlap volume fraction threshold, φC*, which is proportional to the ratio between the above quantities. Very presumably the above threshold plays a significant role as far as the dispersion elasticity is concerned. Viscoelastic relaxation experiments were run in moderate stress conditions, at fixed T values (because the temperature range ensuring the occurrence of nematic order is moderate), and investigated as a function of applied frequency. For the reasons indicated below, studies refer to dilute dispersions. In fact, the maximum amount of CNTs used in the investigation was 1.0 wt % at most.

’ EXPERIMENTAL SECTION Materials. Single-walled CNTs, obtained by the high-pressure CO (HiPCO) process, were from Unydim (Houston, TX). According to the purveyor, CNTs have a uniform diameter, D, of 2 nm; this statement is also confirmed by TEM (which indicates it to be in the range 2
5 nm, with an average value of 3 nm) (Figure 1). According to the purveyor, their nominal molecular mass ranges between 3.4  105 and 5.2  106 uma. This implies a significant polydispersity in length. Home-made multiwalled CNTs (MWCNTs) were kindly offered by Prof. D. Gozzi, Department of Chemistry, at La Sapienza University. The above nanotubes are nominally free from amorphous carbon, metals, and metal oxides but are rather polydisperse in aspect ratios. Some details on the optimal synthetic procedures used to get them, and the related characterization, are reported in the literature.42,43 Carbon black is a commercial Carlo Erba powder, of 550 m2 g
1 nominal surface area. SEM indicates a wide size distribution of the above carbonaceous particles forming spheroidal complex entities.

ARTICLE

Figure 1. TEM image of single-walled CNTs to which a 1.00 wt % phosphotungstic acid solution was added. The original concentration of nanotubes in the dispersion was 0.10 wt %. Resolution on TEM data is 2  105. The size of the objects can be evaluated by comparison with the bar in the lower right-hand side of the figure. In the bottom is reported another TEM picture of CNTs dispersed in 3.0 wt % SDS.

High-purity sodium dodecyl sulfate, SDS, and ultrapure n-decanol, DEC, Sigma, were used. Deionized water was redistilled in presence of alkaline KMnO4. At 25.0
C, its ionic conductivity, χ, is e10
7 S cm
1. Aqueous SDS solutions were prepared by weight. Thereafter, DEC was carefully added by weight to reach a DEC/SDS mole ratio (Md) of 0.40. The final composition of the mixture was 22.70 in SDS and 4.99 wt % in DEC. This concentration corresponds to a discotic nematic phase, ND
.38 In that phase oblate micelles, which orient perpendicular to the magnetic field, are observed. Their axial ratios are 3
4 and approach 6 at the lower phase boundaries.41 In the adjacent calamitic nematic phase, termed NCþ (containing higher amounts of SDS, but lower of DEC), the axial ratios of prolate micelles are close to 3. It is stated that “the shape of micelles in such phase tends to the prolate uniaxial limit, although still being biaxial”.40 A tentative value of the nematic order parameter for that phase, SDA, was estimated to be in the range 0.75
0.85. The resulting SDS/DEC/water mixtures were homogenized by stirring and repeated heating
cooling cycles. The procedure continues until typical Schlieren ND
textures were observed by 9425

dx.doi.org/10.1021/jp2006167 |J. Phys. Chem. C 2011, 115, 9424–9431

The Journal of Physical Chemistry C

ARTICLE

Figure 3. Plot of shear viscosity, η* (Pa s), vs measuring frequency, ω (s
1), for dispersions of nanotubes in the nematic solvent at 25.0
C. Compositions in nanotubes are 0.18 (black circles), 0.32 (black squares), 0.46 (black triangles), 0.52 (gray triangles), and 0.76 wt %.

Figure 2. Optical polarizing microscopy image of a nematic fluid made of 22.70 wt % SDS and 4.99 wt % DEC in water at 25.0
C. Image magnification is 40. The image became fully developed after a few minutes stay.

optical polarizing microscopy44 on the aforementioned samples, at 25.0
C (Figure 2). Preparation of the Dispersions. Single-walled CNTs were dispersed in the nematic fluid by mild sonication and stirring, taking care to avoid heating and subsequent phase separation of the components forming the nematic matrix. The quality of the dispersions was inferred by optical polarizing microscopy and flow birefringence. Good dispersions are birefringent, dark gray in color, and macroscopically homogeneous. They do not show the presence of floating (sinking) objects or significant modifications in optical textures compared to the nematic solvent. Condition for such behavior to occur is a moderate amount of CNTs in the dispersions, which must be quite low. The upper limit used in this contribution is 0.50 wt %. That limit was experimentally determined from the combination of optimal color tone and color intensity of the dispersion, reasonably low turbidity, and absence of sedimented or creaming particles. The upper limit of the volume fraction used to prepare the dispersions depends on the physical properties of interest. In viscoelastic experiments the required concentration limits can be relatively high; in optical analysis high concentrations are not possible because of the reasons mentioned above. The same holds for viscosity measurements. Usually 1.00 wt % CNTs is the upper limit in viscoelastic relaxation studies. For the same reasons, the concentration limits suitable for DLS and viscosity experiments are, usually, e0.05 wt %. This strategy will be clarified in the forthcoming sections, which deal with the properties of the dispersions (optical, DLS, viscometric, and elastic ones). Methods. Optics. Polarizing microscopy was performed by a CETI-Laborlux Topic unit (Antwerp, BE), equipped with a Linkam heating stage, at 25.0
C. Conoscopy was also performed. Details on the experimental setup and sample preparation are given elsewhere.45 Inspection on freshly prepared

dispersions was performed between crossed Polaroids’s in a water circulation bath at 25.0
C. Rheology. The instrument for rheological studies is a TA AR1000 unit, working in the 0.1
100 Hz range in cone
plate geometry. The rotor position is electronically controlled. More details on the apparatus setup are given elsewhere.46,47 The measuring temperature, set at 25.00 ( 0.02
C, is dictated by the region of existence of the nematic phase. The composition of the dispersions was kept constant and dehydration minimized by covering the measuring rotor head and the sample by wet cotton wool tied up in an aluminum cup having a hole in the top, through which the rotating axis was fitted. Samples were investigated as a function of applied shear, θ, by selecting values (e5.0 Pa), ensuring the constancy of both elastic, G0 , and viscous, G00 , components.48 Optimal θ values were determined in oscillatory conditions by stress-sweep measurements. Measurements at fixed θ as a function of frequency, ω, were performed between 0.1 and 100 Hz. To get reliable viscoelastic relaxation spectra, at least 20 properly spaced individual data points were measured in the above frequency range. Data were analyzed by plots of G0 , G00 , and/or η(ω) vs log ω. An example for some selected systems is reported in Figure 3. DLS. The size and aspect ratios of CNTs were determined by a DLS Malvern Zeta Nanosizer, at 632.8 nm and 173
, in backscattering mode. More details on the measuring procedures are given elsewhere.49,50 Measurements were run at least 10 min after introducing dilute dispersions (usually containing less than 0.05 wt % in CNTs) in 1.00 cm quartz cells, thermostated at 25.0 ( 0.1
C. The dispersions were stabilized by addition of 3.00 wt % SDS. The reasons for using dilute systems arise from the absorbance and turbidity of concentrated dispersions, from the need of moderate amounts of added surfactants, and from the necessity to avoid entanglement, in case more concentrated SDS dispersions were used. The hydrodynamic radii of nanotubes, RH, were also measured from the limiting viscosity of their dispersions in aqueous 3.00 wt % SDS. These values are subjected to a significant uncertainty due to the presence of bundles and other aggregates. They are also sensitive to the volume fraction of micellar aggregates, which adsorb onto nanotubes. That is why a moderate amount of 9426

dx.doi.org/10.1021/jp2006167 |J. Phys. Chem. C 2011, 115, 9424–9431

The Journal of Physical Chemistry C

ARTICLE

surfactant was used. RH values were inferred from [ηsp/φ] vs volume fraction (φ) plots. Extrapolation to zero φ gives RH values in the range 600 ( 300 nm. TEM. Drops of the dispersions were adsorbed onto carboncoated copper grids and allowed to adhere therein. Dispersion in excess was removed by filter paper. A drop of 1.00 wt % phosphotungstic acid was added, and the excess liquid was removed. The samples were dried and observed by a ZEISS EM 900 electron microscope, working at 80 kV.51 SEM. Scanning electron microscopy was run by a SEMLEO1450VP unit, equipped with an INCA300 EDS facility.52,53 Dispersions were stratified onto 20  20 mm glass slides, heated at 50
C, properly dried, and transferred in the SEM chamber. AFM. Relevant methods were investigated according to classical procedures, formerly used to determine the optical and structural properties of carbon nanotubes, by using an apparatus elsewhere described in detail.54,55

’ RESULTS AND DISCUSSION The properties of nanotubes that control the mechanical properties of their formulations are related to the aspect ratios, AR, of such entities. Such values are crucial as far as the hydrodynamics and rheology of the dispersions they form are being concerned. Elasticity, in particular, needs ad hoc conditions, related to percolation or entanglement. For such conditions to occur a critical volume fraction of the disperse phase, φC* (related to AR), is required. φC* can be evaluated according to Onsager’s theory on the phase transitions occurring in solutions of macromolecules and in dispersions of anisometric colloid entities as well.56,57 Onsager’s theory refers to anisometric particles in a structureless continuum; i.e., no order or directors for the orientation of particles are accounted for. Accordingly, entanglement is based on φ* values only. To circumvent the limits inherent to the theory, three approaches are possible, namely: (a) Consider the volume fraction not occupied by micelles. Entanglement occurs because a smaller volume is available to nanotubes, and the possibility of junctions increases. In our feeling, this is a crude and nonrealistic approximation. (b) To impose additional constraints to the preferred orientation of nanotubes in the nematic micellar phase. This hypothesis is not realistic because CNT’s do not orient spontaneously in magnetic fields. (c) The positional order of micelles in the available space leaves a substantial possibility to nanotubes to be located in different planes. Thus, CNT’s are not necessarily oriented along the same director as nematic micelles. As a consequence of that, the planes containing micelles are somehow interconnected each with the other during flow. There is a substantial possibility that nanotubes link aggregates, as observed in micellar solutions. The possibility of entanglement between micelles and nanotubes increases in proportion with the amount of CNT’s. The final result is that ordered plains are somehow linked each with the other. Dedicated experimental evidence is required to predict whether CNT formulations may show entanglement and associated elastic effects. Combination of TEM and AFM with, eventually, DLS results is relevant to determine their AR values. The present findings on such values are based on the combination of TEM, AFM, and, in part, of DLS results. We used a back scattering DLS

Figure 4. Normalized autocorrelation intensity vs time (μs) plot relative to a 1.2  10
3φ single-walled carbon nanotube dispersion in a 3.00 wt % SDS aqueous solution at 25.0
C. The surfactant significantly reduces the formation of bundles and phase separation. Data were taken in backscattering DLS mode, about 30 min after centrifugation, and, grossly, 15 min after thermal equilibrium took place.

configuration, since it allow controlling the absorbance and turbidity of the dispersions and determining CNTs sizes. The decay of DLS signals for long rodlike objects is the sum of rotational and translational diffusive contributions.58 The translational term scales with q2, the other no, and plots of ln I vs q2 give only the rotational term. The uncertainty on the rotational contribution, perhaps, is significant. In CNTs dispersions, the behavior of the autocorrelation function, Figure 4, can be interpreted by assuming the occurrence of two decay modes. Proper fitting estimated the average nanotube length, L, and the corresponding minor axis, D. Such values, perhaps, should be considered with due care because a distribution in both quantities is expected to occur. In addition, the operating wavelength is comparable in size with the scattering objects. This implies further drawbacks in data manipulation, mostly when the scatterers are strongly anisotropic in size. Notwithstanding the above problems, fitting was performed by using functions containing two decay modes. Usually, the difference in quality between fits based on two relaxations is negligible. The average D and L values obtained in this way are in the range 5
10 and 500
600 nm, respectively. When the former value is grossly compatible with TEM results, we do not know how much realistic estimates on L values are. Finally, estimates on carbon nanotubes aspect ratios were inferred by a statistical analysis, based on TEM (and AFM). Lengths and diameters refer to single-walled entities: bundles were not considered in the statistics. The diameter, D, of SWNT is close to the nominal one; the experimental values, in fact, span in the range 2
5 nm. Lengths were determined on a population of ≈100 individual nanotubes. Average Ælæ values were calculated by the relation Ælæ = [(∑i=1nili)/N], where ni is the number of nanotubes in a given population. The value obtained is close to 800 nm, with an uncertainty of (400. Length distribution, perhaps, is not Gaussian. Accordingly, CNTs have low aspect ratios and are significantly poly disperse in length. 9427

dx.doi.org/10.1021/jp2006167 |J. Phys. Chem. C 2011, 115, 9424–9431

The Journal of Physical Chemistry C

ARTICLE

The overlap volume fraction threshold, φC*, depends on the aspect ratio of CNTs and can be expressed in terms of Onsager’s theory according to the relation
2 ÆDæ  ð1Þ φC ¼ k ÆLæ where the meaning of symbols is the same as before (and refers to the average D and L values); k is usually set to 3/2. Equation 1 is strictly valid in case of monodisperse rigid rods; values computed accordingly give merely tentative estimates of φC* values if significant length polydispersity and coiling of nanotubes were considered. Within the limits set up by TEM and AFM results (which are more reliable compared to DLS-based ones), φC* values range between 2  10
3 and 5  10
3 in volume fraction units. Estimates based on such methods are realistic. Let us remind that Islam proposed a value of 3  10
3 in CNT formulations dispersed in a nematic gel solvent.58
60 The exact value of φC*, calculated by eq 1, strongly depends on polydispersity of the major axis, L, and on the assumption that D is supposed to be fairly constant. Experimentally based approaches, as the ones dealing with an experimental investigation of the phase diagram of the present system or determined from the rheology of its dispersions, may estimate the overlap volume fraction threshold. It must be pointed out that the determination of φC* values from the phase diagram is subject to a noticeable uncertainty, since CNTs aggregate in bundles when water-based media were used as dispersants. Optics. Classical Schlieren textures were observed in the nematic solvent, termed ND
in common classifications. Additional characterization was performed by NMR deuterium quadrupole splittings (data not shown). There a small, but systematic, dependence of deuterium quadrupolar splitting (a few hertz) on the amount of added nanotubes is observed. Such data confirm and support the predicted optical and magnetic order in the above phase. Dispersions containing CNTs are slightly different compared to the bare system. This is because nanotubes favor the onset of disclinations, along which the nematic domains orient. Orientation was confirmed by comparing polarizing microscopy results in the two cases. Differences are more significant when the dispersions are forced to flow in glass capillaries. The observed differences imply changes in extinction angle. The above behavior gives qualitative indications on the kinetics of orientation for such fluids under flow. It is hardly conceivable, however, to forecast information on elasticity from optical data, and rheological experiments are required to get it. Rheology. Viscoelastic effects on fluids may be induced by the presence of added materials. To ascertain such eventualities, experiments were run on single-walled CNTs, multiwalled ones, and carbon black dispersed in the same nematic solvent. In all such cases, experiments were run at fixed volume fraction in dry matter (0.65 wt %), at concentrations where entanglement may occur or not, depending on the aspect ratio of the disperse particles. As observed in Figure 5, significant differences are met in the above dispersions. The original nematic fluid does not show elastic components. The same holds for multiwalled CNTs or carbon black dispersions. In these mixtures, the volume fraction of the disperse phase does not significantly increase the system viscosity compared to the bare nematic fluid. Only single-walled CNTs ones show significant elastic contributions and shear thinning, too. The observed effect, thus, can be solely ascribed to the high aspect ratio of long anisometric entities

Figure 5. Plot of the dynamic viscosity, η*(ω) (in Pa s), as a function of shear rate (ω), in s
1, for the SDS
DEC nematic phase, black squares, and for the same system dispersing 0.65 wt % carbon black, reverse triangles, 0.65 wt % multiwalled carbon nanotubes, triangles, and 0.65 wt % single-walled carbon nanotubes, circles. Data were taken at 25.00 ( 0.02
C. The uncertainty on η*(ω) values is within the symbol's size.

Figure 6. Plot of G0 (Pa s) versus the volume fraction of CNT dispersed in the nematic phase, expressed as 103φ, at 25.0
C. The critical entanglement volume fraction threshold, φC*, can be inferred from the salient point in the curve.

dispersed therein. Comparison with multiwalled CNTs is diriment, in this regard. A second remarkable effect is the onset of elastic effects only above a well-defined volume fraction, φC* (Figure 6). For very low volume fractions no elastic contribution is observed, and the system response to shear is nearly the same as the original nematic fluid. However, at 0.25
0.30 wt % CNT, a sudden increase in elasticity is observed. The effect is strongly cooperative and levels up slightly above the aforementioned threshold. It is argued from the plot in Figure 6 that a critical volume fraction is required for the onset of elastic contributions. In the subsequent analysis we do not account for moderate elastic terms eventually observed below φC*, being they orders of magnitude lower than the ones above it. The critical volume fraction at which elasticity starts to occur can be evaluated from Figure 6. It is noteworthy that the φC* value from eq 1 is comparable to the experimentally observed one. Very presumably, the experimentally determined φC* is strictly related to the value required for entanglement, that is, to the aspect ratio of CNTs. The location of the entanglement threshold can be inferred by deriving the complex viscosity, η*(ω), and its real, G0 (ω), or 9428

dx.doi.org/10.1021/jp2006167 |J. Phys. Chem. C 2011, 115, 9424–9431

The Journal of Physical Chemistry C

ARTICLE

Figure 7. Plot of the elastic relaxation modulus, G0 , in [Pa s], as a function of applied frequency, ω [s
1]. Data refer to a 5.2  10
3φ in single-walled carbon nanotubes at 25.0
C. Note that G0 is grossly constant above 20 Hz.

imaginary, G00 (ω), components with respect to φ. The former quantity is given by the relation qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  ð2Þ ½G0 ðωÞ2 þ ½G00 ðωÞ2 η ðωÞ ¼ ω where the elastic and viscous contributions are defined, respectively, as ðωτi Þ2  1 þ ðωτi Þ2 i¼1 ðωτi Þ G00 ðωÞ ¼ G
i ½  1 þ ðωτi Þ2 i¼1 G0 ðωÞ ¼

∑ ∑

G
i ½

ð2'Þ ð2''Þ

There τi is the relaxation time associated with a given viscoelastic mode, Gi
the amplitude of the corresponding phenomenon, and ω the measuring frequency. Below or above the entanglement threshold the viscoelastic spectra are largely different from each in both amplitude and relaxation frequency. Obviously, these values depend on the volume fraction of added CNTs. To simplify the data analysis, a dominant contribution is supposed to occur in the summation in eqs 20 and 200 . This hypothesis assigns the observed behavior to a dominant elastic term. A perusal to Figure 7 indicates that plots of the elastic component as a function of the applied frequency approach an upper limit. The effect refers to a point above the percolation threshold. At a given volume fraction, the maximum G0 value in Figure 7 depends on φ
φC*. An analysis based on eq 20 indicates that G0 reaches a maximum when ωτ . 1, i.e., well above the elastic relaxation frequency. Similar conclusions apply when η*(ω) or G00 was chosen. (N.B. In case the analysis were based on η(ω) values, the conditions where ωτ , 1 should be considered.) Provided ω is much higher than ω
, that is G0 ≈ G
, the elastic percolation threshold can be defined in terms of the following constraint: D3 G
¼0 Dφ3

ð3Þ

The salient point inferred by the above plot indicates a sort of phase transition threshold from a purely viscous to an essentially elastic behavior. The experimentally observed behavior is not

strictly coincident with an “all or nothing” approach. That is, polydispersity in size and aspect ratios is, very presumably, significant, as expected. Incidentally, polydispersity comes out also from a comparison of the length of CNT’s inferred from microscopy and viscosity. The latter overestimate the components with higher aspect ratios with respect to that inferred from the other methods. Data indicate that the average φ value required for entanglement to occur, the salient point in the plot in Figure 6, is very close to 3  10
3. φC*, thus, is similar in value to that formerly calculated by Onsager’s relation. Another relevant aspect inferred from Figure 6 is the cooperativeness of the process. On this regard, the volume fraction required for elasticity to occur can be properly defined a “true” critical value, φC*, which fulfils the requirements dictated by eq 3. In the corresponding map, φC* is located at the salient point in Figure 6. As expected, φC* depends on the nature of the dispersing medium. In a nematic solvent it is lower than in net water because of the volume fraction of the surfactant and decanol in the dispersing fluid matrix. It is also possible that anisometric micelles in the fluid interact with CNTs (or adsorb onto them) and act as joints between them. In other words, they may operate according to what formerly observed in SDS-stabilized, or nematic-stabilized, dispersions of CNTs.61
64 This would imply that the onset of entangled networks fulfils a “necklace and pearl” model. More realistically, the interconnections between ordered planes, or between micelles allocated in different planes, could be responsible for the significant elastic contributions pertinent to these nematic dispersions, provided concentrations above φC* are dealt with. The results coming out from the above experimental evidence are promising as far as the volume fraction thresholds are being considered. It is not possible to define in more detail the optimal conditions for the viscoelastic behavior occurring in the nematic system, given the moderate thermal stability of this mixture in the phase diagram. The results could be modulated by the volume fraction of the nematic phase and from the structure (disks or rods) of oriented anisotropic phases in which CNTs are being dispersed.65,66 A systematic investigation on the contributions dictated by the aggregate and phase geometry could be relevant in a complete theoretical analysis of experimental data. Unfortunately, deuterium NMR data we have obtained do not allow to make realistic estimates on modifications in the nematic order of micelles and are, therefore, not reported in this context. The observed increase in the elastic components is, very presumably, related to entanglement. It may occur between nanotubes or between different planes intersected by them. In our opinion the latter is a more realistic hypothesis because not all CNT’s are oriented parallel to the director axis of the phase and since, given their length, they may connect different planes during the flow.

’ CONCLUSIONS Single-walled carbon nanotubes, characterized by high aspect ratios, were dispersed in a lyotropic nematic solvent, made of SDS, decanol, and water. The dispersions obtained in this way are relatively stable. As a rule, several weeks are required to precipitate out nanotubes from the nematic medium. Stabilization is, thus, significant. In addition, the dispersions show marked elastic properties above a critical volume fraction threshold, φC*, whose value is related to the CNTs aspect ratio. 9429

dx.doi.org/10.1021/jp2006167 |J. Phys. Chem. C 2011, 115, 9424–9431

The Journal of Physical Chemistry C The onset of an elastic behavior is quasi critical: this effect is presumably due to the minimum volume fraction required for an effective entanglement between single nanotubes in the dispersing matrix. It is possible that the dispersing matrix somehow participates to entanglement. Perhaps, the above hypothesis is, at the moment, merely tentative and requires use of ad hoc experiments, based on SAXS or SANS methods, to be properly supported. Further developments could be made by extending the analysis to nematic phases differing from the present one in nature of the aggregates, packing density, surface charge, and so forth. The use of nematic fluids reported here and of those made by DNA66 are promising. Perhaps, it is still under debate as to whether such fluids operate as ordering matrices for the mean orientation of CNT’s along a given director or if the latter significantly concur to the observed behavior. From a technologically relevant viewpoint, the possibility to have significant elastic properties could be optimized by choosing ad hoc solvents, presumably also nonaqueous media. Actually, we do not know if a critical increase in elasticity can be also observed in nonorganized media. Anyhow, the large differences observed between nematic fluids and the corresponding solution phases are surely related to the entanglement between nanotubes and ordered matrices. More refined studies along this line will focus on nematic solvents differing each from the other in nature of surfactant (or biopolymer), working composition, and the optimal temperature range where such phases are usually met in the phase diagrams.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Thanks are due to Prof. Marco Rossi, at La Sapienza, and to Dr. Rita Muzzalupo, Calabria University, for help in the characterization by TEM and for relevant discussions. Thanks to Prof. Daniele Gozzi, La Sapienza, for giving us multiwalled carbon nanotubes. Useful suggestions on some aspects of the manuscript, raised from the reviewers, are appreciated. Financial support from La Sapienza University is gratefully acknowledged. ’ REFERENCES (1) Lefrant, S.; Buisson, J. P.; Mevellec, J. Y.; Baibarac, M.; Baltog, I. Mol. Cryst. Liq. Cryst. 2010, 522, 172. (2) Ji, X.; Kadara, R. O.; Krussma, J.; Chen, Q.; Banks, C. E. Electroanalysis 2010, 22, 1148. (3) Peng, M.; Liao, Z.; Qi, J.; Zhou, Z. Langmuir 2010, 26, 13572. (4) Paton, K. R.; Windle, A. H. Carbon 2008, 46, 1935. (5) Cheung, W.; Pontoriero, F.; Taratula, O.; Chen, A. M.; He, H. Adv. Drug Delivery Rev. 2010, 62, 633. (6) Puech, N.; Grelet, E.; Poulin, P.; Blanc, C.; van der Schoot, P. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2010, 82, 020702/ 1–020702/4. (7) Ivanov, E.; Nesheva, D.; Krusteva, E.; Dobreva, T.; Kotsilkova, R. Nanosci. Nanotechnol. 2009, 9, 40. (8) Blanch, A. J.; Lenehan, C. E.; Quinton, J. S. J. Phys. Chem. B 2010, 114, 9805.

ARTICLE

(9) Li, N.; Zhang, F.; Wang, J.; Li, S.; Zhang, S. Polymer 2009, 50, 3600. (10) Datsyuk, V.; Landois, P.; Fitremann, J.; Peigney, A.; Galibert, A. M.; Soula, B.; Flahaut, E. J. Mater. Chem. 2009, 19, 2729. (11) Saito, R.; Dresselhaus, G.; Dresselhaus, M. G. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998; 259 pp. (12) Lin, Y.; Taylor, S.; Li, H.; Fernando, K. A. S.; Qu, L.; Wang, W.; Gu, L.; Zhou, B.; Sun, Y.-P. J. Mater. Chem. 2004, 14, 527. (13) Wang, S.; Humphreys, E. S.; Chung, S.-Y.; Delduco, D. F.; Lustig, S. R.; Wang, H.; Rizzo, N. W.; Subramoney, S.; Chiang, Y.-M.; Jagota, A. Nature Mater. 2003, 2, 196. (14) Baker, S. E.; Cai, W.; Lasseter, T. L.; Weidkamp, K. P.; Hamers, R. J. Nano Lett. 2002, 2, 1413. (15) Huang, W.; Taylor, S.; Fu, K.; Lin, Y.; Zhang, D.; Hanks, T. W.; Rao, A. M.; Sun, Y P. Nano Lett. 2002, 2, 311. (16) French, R. H.; Parsegian, V. A.; Podgornik, R.; Rajter, R. F.; Jagota, A.; Luo, J.; Asthagiri, D.; Chaudhury, M. K.; Chiang, Y.-M.; Granick, S.; Kalinin, S.; Kardar, M.; Kjellander, R.; Langreth, D. C.; Lewis, J.; Lustig, S.; Wesolowski, D.; Wettlaufer, J. S.; Ching, W. Y.; Finnis, M.; Houlihan, F.; von Lilienfeld, O. A.; van Oss, C. J.; Zemb, T. Rev. Mod. Phys. 2010, 82, 1887. (17) Li, J.; Ma, P.-C.; Chow, W.-S-; To, C.-K.; Tang, B.-Z-; Kim, J.-K. Adv. Funct. Mater. 2007, 17, 3207. (18) Pegel, S.; Poetschke, P.; Petzold, G.; Alig, I.; Dudkin, S. M.; Lellinger, D. Polymer 2008, 49, 974. (19) Meuer, S.; Braun, L.; Schilling, T.; Zentel, R. Polymer 2009, 50, 154. (20) Ugur, S.; Yargi, O.; Pekcan, O. Can. J. Chem. 2010, 88, 267. (21) Simoes, R.; Silva, J.; Vaia, R.; Sencadas, V.; Costa, P.; Gomes, J.; Lanceros-Mendez, S. Nanotechnology 2009, 20, 035703/1–8. (22) Zhang, R.; Baxendale, M.; Peijs, T. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 195433/ 1–5. (23) Park, W. K.; Kim, J. H.; Lee, S.-S.; Kim, J.; Lee, G.-W.; Park, M. Macromol. Res. 2005, 13, 206. (24) Lin, T. S.; Cheng, L. Y.; Hsiao, C.-C.; Yang, A. C.-M. Mater. Chem. Phys. 2005, 94, 438. (25) Wang, R.; Sun, J.; Gao, L. J. Phys. Chem. C 2010, 114, 4923. (26) Kuehnast, M.; Tschierske, C.; Lagerwall, J. Chem. Commun. 2010, 46, 6989. (27) Scalia, G.; von Buehler, C.; Haegele, C.; Roth, S.; Giesselmann, F.; Lagerwall, J. P. F. Soft Matter 2008, 4, 570. (28) Lagerwall, J. P. F.; Scalia, G. J. Mater. Chem. 2008, 18, 2890. (29) Dawin, U. C.; Lagerwall, J. P. F.; Giesselmann, F. J. Phys. Chem. B 2009, 113, 11414. (30) Xin, X.; Li, H.; Kalwarczyk, E.; Kelm, A.; Fiazkowski, M.; Gorecka, E.; Pociecha, D.; Hozist, R. Langmuir 2010, 26, 8821. (31) Amaral, L. Q. Liq. Cryst. 2010, 37, 627. (32) Rodriguez, C. R.; Pusiol, D. J.; Figueiredo Neto, A. M.; Martin, C. A. Phys. Rev. E 2004, 69, 041708/1–9. (33) Coppola, L.; Gianferri, R.; Oliviero, C.; Ranieri, G. A. J. Colloid Interface Sci. 2003, 264, 554. (34) Coppola, L.; Gianferri, R.; Nicotera, I.; Oliviero, C.; Ranieri, G. A. Phys. Chem. Chem. Phys. 2004, 6, 2364. (35) Berger, K.; Hiltrop, K. Colloid Polym. Sci. 1996, 274, 269. (36) Yildiz, T.; Kazanci, N. J. Mol. Struct. 2008, 886, 158. (37) Quist, P. O.; Halle, B.; Furo, I. J. Chem. Phys. 1991, 95, 6945. (38) Quist, P. O.; Halle, B.; Furo, I. J. Chem. Phys. 1992, 96, 3875. (39) Quist, P. O.; Halle, B. Mol. Phys. 1988, 65, 547. (40) Quist, P. O. J. Phys. Chem. 1996, 100, 4976. (41) Furo, I.; Halle, B. Phys. Rev. E 1995, 51, 466. (42) Gozzi, D.; Latini, A. PCT Int. Appl. IT 2004-RM50, 2006. (43) Gozzi, D.; Iervolino, M.; Latini, A. J. Am. Chem. Soc. 2007, 129, 10269. (44) Hendrikx, V.; Charvolin, J.; Rawiso, M.; Liebert, L.; Holmes, M. C. J. Phys. Chem. 1983, 87, 3991. (45) Bonicelli, M. G.; Ceccaroni, G. F.; La Mesa, C. Colloid Polym. Sci. 1998, 276, 109. (46) Roversi, M.; La Mesa, C. J. Colloid Interface Sci. 2005, 284, 470. 9430

dx.doi.org/10.1021/jp2006167 |J. Phys. Chem. C 2011, 115, 9424–9431

The Journal of Physical Chemistry C

ARTICLE

(47) Orioni, B.; Roversi, M.; la Mesa, C.; Asaro, F.; Pellizer, G.; D’Errico, G. J. Phys. Chem. B 2006, 110, 12129. (48) Macosko, C. W. Rheology Principles, Measurements and Applications; VCH: New York, 1993; Chapter III, p 109. (49) Sallustio, S.; Galantini, L.; Gente, G.; Masci, G.; La Mesa, C. J. Phys. Chem. B 2004, 108, 18876. (50) Bonincontro, A.; Spigone, E.; Ruiz Pena, M.; Letizia, C.; La Mesa, C.; J. Colloid Interface Sci. 2006, 304, 342. (51) Iemma, F.; Spizzirri, U. G.; Muzzalupo, R.; Puoci, F.; Trombino, S.; Picci, N. Colloid Polym. Sci. 2004, 283, 250. (52) Barbetta, A.; Cameron, N. R. Macromolecules 2004, 37, 3202. (53) Michiotti, P.; La Mesa, C.; Bonicelli, M. G.; Ceccaroni, G. F.; Ferragina, C.; Cifarelli, P. Colloid Polym. Sci. 2003, 281, 431. (54) Rossi, M.; Meo, M. Compos. Sci. Technol. 2009, 69, 1394. (55) Terranova, M. L.; Sessa, V.; Rossi, M. Chem. Vapor Depos. 2006, 12, 315. (56) Malijevsky, A.; Varga, S. J. Phys.: Condens. Matter 2010, 22, 175002/1. (57) Mezzenga, R.; Jung, J.-M.; Adamcik, J. Langmuir 2010, 26, 10401. (58) Varga, S.; Velasco, E. Macromolecules 2010, 43, 3956. (59) Berne, B. J.; Pecora, R. In Dynamic Light Scattering; J. Wiley & Sons: New York, 1976; Chapter VII, p 122. (60) Islam, M. F.; Nobili, M.; Ye, F.; Lubensky, T. C.; Yodh, A. G. Phys. Rev. Lett. 2005, 95, 148301/1. (61) Hough, L. A.; Islam, M. F.; Hammouda, B.; Yodh, A. G.; Heiney, P. A. Nano Lett. 2006, 6, 313. (62) Chen, D. T. N.; Chen, K.; Hough, L. A.; Islam, M. F.; Yodh, A. G. Macromolecules 2010, 43, 2048. (63) Park, J. G.; Smithyman, J.; Lin, C.-Y.; Cooke, A.; Kismarahardja, A. W.; Li, S.; Liang, R.; Brooks, J. S.; Zhang, C.; Wang, B. J. Appl. Phys. 2009, 106, 104310/1. (64) Lee, S. H.; Park, J. S.; Lim, B. K.; Mo, C. B.; Lee, W. J.; Lee, J. M.; Hong, S. H.; Kim, S. O. Soft Matter 2009, 5, 2343. (65) Zamora-Ledezma, C.; Blanc, C.; Maugey, M.; Zakri, C.; Poulin, P.; Anglaret, E. Nano Lett. 2008, 8, 4103. (66) Vigolo, B.; Coulon, C.; Maugey, M.; Zakri, C.; Poulin, P. Science 2005, 309, 920.

9431

dx.doi.org/10.1021/jp2006167 |J. Phys. Chem. C 2011, 115, 9424–9431