The Nanoscale Cinderella Problem: Design of Surfactant Coatings for

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The Nanoscale Cinderella Problem: Design of Surfactant Coatings for Carbon Nanotubes Panagiotis Angelikopoulos and Henry Bock* Department of Chemical Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, U.K.

ABSTRACT We report the design rules for amphiphilic coatings of single-wall carbon nanotubes (SWCNTs) to achieve optimal dispersion. Their knowledge and understanding is critical to exploit the full potential of SWCNTs in structural and functional applications where the tubes need to be individualized and rebundling must be prevented. The required repulsive interactions can be generated by a coating of amphiphilic molecules only if the right structures are achieved. Our article provides understanding of the relationship between the adsorbed structures and the dispersive forces, gives guidance on how these structures can be obtained and demonstrates the transferability of the general concept to other nanostructures. SECTION Nanoparticles and Nanostructures

arbon nanotubes (CNTs) excite us not only because of their set of exceptional properties, which continue to inspire a wealth of structural and functional applications,1,2 but also because of their structural beauty-a highly symmetric hexagonal lattice forming one of the simplest geometrical shapes: a cylinder. Unfortunately, bundling due to intertube van der Waals and solvophobic interactions does not only mar the aesthetics, but impairs many applications as well as further sorting according to radius, metallic/semiconducting electronic properties, and chirality. Consequently, since CNTs became popular almost 20 years ago, there have been intense efforts to individualize them. The most promising route is to ultrasonicate bundles in solution in the presence of amphiphilic molecules. While ultrasonication provides the energy to split the bundles, amphiphilic molecules adsorb with their solvophobic part onto the individualized tubes (Figure 1). This orients the molecules such that the CNT/amphiphilic-molecule complex becomes solvophilic, which should disperse the tubes. In practice, however, many amphiphiles “don't work”. Despite the substantial amount of empirical knowledge gathered by testing many amphiphiles, understanding is still lacking, inhibiting the rational design of effective suspension (and sorting) systems. We can now provide this understanding from computer simulations of mesoscale models (ref 3 and Supporting Information (SI)). These models are ideally suited to approach surface self-assembly problems, as they allow simultaneous access to macroscopic properties and molecular level insight at low computational cost, which currently is not feasible by any other experimental or theoretical method. The prerequisite for understanding dispersion by amphiphiles is appreciation of their adsorption behavior. Three fundamentally different adsorption regimes are possible. Weak amphiphiles do not aggregate and adsorb via a Langmuirtype (Lt) mechanism to form a monolayer (Figure 1A). In

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contrast, adsorption of strong amphiphiles is aggregation dominated, which implies that the adsorbed structures are governed by geometrical restrictions of the molecules rather than the shape of the adsorbent leading to adsorbed spherical micelles (Figure 1B) or encapsulation by a cylindrical micelle (Figure 1C) depending on the shape of bulk aggregates. To resolve a nomenclature confusion in the literature, we propose to call the structure on the small tube (Figure 1D top) “adsorbed spherical micelles” and the structure on the big tube “adsorbed hemi-micelles”. To analyze the dispersion performance of the different adsorbed structures, a relative quality criterion is needed. As the amphiphile coating is intended to prevent rebundling, the best coating has the lowest rebundling rate. Exact determination of the rebundling rate is, however, monumentally difficult, as this nonequilibrium process is influenced by many factors. Here we roughly estimate the relative rebundling rates Rrebundling via the Arrhenius law Rrebundling µ e - WB =kT where k is Boltzmann's constant and T is the temperature. The repulsive barrier WB is the work done by two approaching tubes to overcome the repulsive force F(d) originating from overlap of the solvophilic coronas of the adsorbed structures Z FðdÞDd WB ¼ repulsive region

where d is the tube/tube distance. In Figure 2A, the force distance curves for two Lt monolayers formed by the amphiphile H2T2 (SI) at different concentrations Received Date: December 1, 2010 Accepted Date: December 26, 2010 Published on Web Date: January 07, 2011

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DOI: 10.1021/jz101623t |J. Phys. Chem. Lett. 2011, 2, 139–144

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Figure 1. The three major adsorption regimes: (A) Langmuir-type monolayer, (B) adsorbed spherical micelles, and (C) encapsulation by a cylindrical micelle. Adsorption isotherms are shown as the amount adsorbed per nanotube surface area versus the bulk concentration in reduced units (SI). The cooperativity of aggregation in the adsorbed layer causes the adsorbed amount to increase faster than in the Henry's law limit leading to the S-shaped isotherms in cases B and C. The second increase in C is due to growth and connection of individual aggregates and later to formation of protrusions into the bulk (Figure S4 (SI)). Panel D indicates the difference between adsorbed spherical micelles (top) and adsorbed hemispherical micelles (bottom). In the snapshots, solvophobic tail beads are colored magenta and solvophilic head beads are green.

are presented. Morphologically the adsorbed structures are very similar to grafted polymer brushes. This is interesting, as it allows a theoretical prediction of the upper limit of the tube/ tube repulsion via the Alexander-de Gennes (AG) theory4 using a Derjaguin approximation5 (see also Figure S1 (SI)). On mutual approach of the tubes, the force increases as the overlap volume of the solvophilic coronas of the amphiphilic coatings increases. However, the repulsion falls significantly below the AG prediction right away as, in contrast to a grafted polymer brush, the contact region gets depleted of molecules (Figure 2A). Eventually, the formation of holes in the adsorbed layer of both tubes leads to a decrease of the repulsive force, because molecules in the center of the contact region have a greater impact on the resulting tube/tube force than molecules on its edge (Figure S2).


At even smaller distances, the system can undergo a morphological transition to a structure where the hydrophobic layer now engulfs both tubes simultaneously, i.e., no hydrophilic head groups are located between the tubes. In this situation the surfactant-mediated forces are essentially attractive.6 The transition occurs when the tubes come closer than approximately twice the thickness of the hydrophobic core of the adsorbed structure. Thus the range of this attractive regime is usually much larger than the range of the tube/tube van der Waals attraction.7 As such a transition has been found for all three adsorption regimes, shielding against rebundling must prevent the tubes from entering the attractive regime in all cases. We deduce that there are three ways to increase the repulsive barrier for Lt monolayers: (i) by increasing the

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Figure 2. Force, F, versus distance between the tube axis, d, curves for the three regimes: (A) Lt monolayer (green, C = 0.021; yellow, C = 0.055), (B) spherical micelles (red, C = 5.2 10-5), and (C) encapsulation by a cylindrical micelle (blue, C = 4.1 10-4). Solid lines represent predictions from the AG theory, while dashed lines are a guide to the eye. (A) bottom inset: head-bead density cloud to show the depletion of the contact region, and top inset: tail-bead density isosurfaces to show the formation of holes in both layers. (B) tail-bead density isosurfaces and snapshots to demonstrate pinning of the inner micelles (red) and depletion of the contact region (Figure S3 (SI)). (C) Upon reducing the distance between the tubes, the adsorbed layer on one of the tubes fails, leading to a discontinuous reduction of the force and splitting of the force curve into two branches (filled symbols, both layers intact, and open symbols, one layer has been disrupted). (D) Potentials of mean force (PMF) in kT and repulsive barriers in kT for all systems (same color code as in panels A-C).

concentration, which increases the amount adsorbed and, thus, the repulsive force but, unfortunately, only up to the point where the amount adsorbed levels off (Figure 1A and Figure 2A), (ii) by increasing the interaction between the amphiphile and the tubes, which also increases the amount adsorbed, and (iii) by increasing the range of the repulsive force, e.g., via a longer solvophilic group. Deplorably, the interaction strength is limited by the available “chemistry” of the amphiphiles, and longer ranged repulsion between the solvophilic groups makes the molecules more reluctant to absorb. Thus, to maintain a high density of the adsorbed phase for molecules with longer range repulsion between their solvophilic head groups, an additional driving force is needed. This


driving force is provided by self-assembly. To achieve complete coverage of single-wall CNTs (SWCNTs) by spherical micelles, a concentration just above the steep part of the isotherm is sufficient. Since CNTs are very hydrophobic, this concentration is usually well below the critical micelle concentration (CMC) (ref 8). As expected, the larger headgroup of the (spherical) micelle forming surfactant H5T5 leads to a longer ranged repulsive force (Figure 2B) compared to H2T2. However, although the amount adsorbed is comparable to that of H2T2 at C = 0.055 (Table SII (SI)), the magnitude of the repulsive force is significantly smaller and nowhere near the AG prediction. The reason lies in the morphology of the adsorbed film. When the tubes come close, the micelles at the crossing

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arrange such that they maximize their mutual distance. This pins the local structure with four inner micelles lining the contact point (two on each tube) and the gap between one pair opposing that of the other pair (Figure 2B inset). In this configuration, the center of the contact region is depleted of solvophilic head groups, leading to a low repulsive tube/tube force. At smaller distances, the force remains low because the micelles move away from the contact region increasing the size of the gap between the inner micelles (Figure S3 (SI)). There is relatively little resistance to increasing the gap size because only about half of the emptied tube surface requires desorption of solvophobic tails, as in equilibrium only half of the tube surface is covered by solvophobic groups, whereas the other half is covered by solvophilic groups that do not strongly interact. From these observations above we learn that the adsorbed phase must (i) be strongly bound to the tubes, (ii) have a high density of adsorbed molecules, and (iii) be homogeneous with high resistance to the formation of holes or gaps. These conditions are fulfilled by encapsulation by a cylindrical micelle. The first branch of the force curve, shown in Figure 2C, follows the AG theory perfectly, demonstrating that the maximal force has been reached by this morphology. This also indicates that no depletion of the contact region is occurring until one of the two adsorbed layers eventually fails, which is strikingly different from the behavior of Lt monolayers. The lack of depletion is congruous with the mechanism of failure of the adsorbed layer, which occurs by rupturing the (continuous) adsorbed cylindrical micelle. The result is a gap in the adsorbed layer, which is similar to the gaps between adsorbed spherical or elongated micelles (Figure 1C) and in contrast to the hole formed in the Langmuir-type layers. Rupturing of the adsorbed layer leads to a strong and discontinuous reduction in the force. The force is now dominated by direct repulsion between the solvophobic part of molecules in the unruptured micelle and the bare surface of the other tube. The force increases in magnitude until the morphology changes once again and the mediated tube/ tube interaction becomes attractive. Comparison of the potentials of mean force in Figure 2D shows very clearly the large difference in the performance of the three adsorbed morphologies. The difference becomes even more striking when the rebundling rates are considered. Encapsulation by a cylindrical micelle leads to a more than 5000 times lower rebundling rate compared to the second best system. Thus, rational design of the adsorbed structure is decisive for good dispersion performance. This insight and understanding has immediate practical impact on understanding SWCNT dispersion by surfactants, e.g., by sodium dodecylbenzene sulfonate (NaDDBS), which is well studied experimentally. NaDDBS's adsorption isotherm has two plateaus with a very large step between them (e.g., ref 9). While it is argued that the step and the second plateau are associated with better dispersion, the origin of the effect has remained unclear. To understand this effect, one needs to consider that NaDDBS forms small elongated bulk micelles, which grow in length with increasing concentration.10 Our simulations show


Figure 3. At large concentrations (here C = 9.5 10-4), longrange connections (red) of preferred length form between encapsulated tubes leading to flocculation. Artistic enhancement of a snapshot showing the solvophobic core of tail beads as the surface of an excluded volume (magenta) and the solvophilic heads (green). Tubes are extended for clarity.

that for such a surfactant the adsorbed phase consists of individual elongated micelles in the plateau region of the isotherm (Figure 1C). The gaps between those micelles lead to poor dispersion. Critically, at high enough concentrations, continuous cylindrical encapsulation and therefore good dispersion is achieved. Thus the distinct dispersion behavior and the two plateaus in the adsorption isotherm of NaDDBS are due to a morphological transition of the adsorbed phase from individual adsorbed micelles to uniform encapsulation by a cylindrical micelle. Although dispersion with NaDDBS is good, individualization is not (e.g., ref 11). With a radius of approximately 2.97 nm,12 NaDDBS micelles are big enough to encapsulate small bundles of SWCNTs. Additionally, the adsorption energy is high because of the large surface area of the bundle compared to an individual tube, even one of similar size, and because of potential swelling of the bundle by intercalation of a single layer of hydrophobic tails between the tubes. Thus, the aggregate stabilizes small bundles very well, which is observed experimentally.11,13,14 Interestingly, even higher NaDDBS concentrations lead to the formation of large CNT aggregates.11 Depletion attraction by bulk micelles can, in principle, cause reversible flocculation15 but becomes relevant only for large concentrations of micelles and good alignment of the tubes. We have discovered another mechanism that leads to flocculation. At high enough concentrations, the adsorbed aggregates have protrusions that can connect between the tubes (Figure 3) and keep them at a preferred distance. Such branching is also observed in bulk solutions at concentrations very well above the CMC.16 All three adsorption regimes can be employed for tube separation as they are effected by the adsorption energy, particularly the steep part of the isotherm and the plateauvalue of the amount adsorbed in the case of Lt adsorption. This is consistent with the observed metallic/semiconducting selectivity.17-19 Although Lt adsorption seems more attractive for interaction-selective tube separation by, e.g., density-gradient ultra centrifugation, Lt monolayers are prone for multilayer adsorption and indeed prewetting-like phenomena20 because of their less ordered structure. The faith of the resulting loosely

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(8) Figure 4. Adsorption and encapsulation of spherical particles by the surfactant H5T5 is strongly dependent on the particle size. As in the case of SWCNTs, this leads to weaknesses in the dispersive shielding (bottom right).

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bound outer layers in the strong centrifugal field is unknown and potentially problematic. Although nonaggregative Lt-monolayer adsorption is less size selective than aggregation because it is a priori much less affected by the tubes' curvature, it should be noted that the total molecule/tube interaction also depends on the tube radius, especially for small tubes.21,22 In essence, knowledge and understanding of adsorbed amphiphile structures on SWCNTs is critical as they govern the function of the amphiphile coating. The most critical condition for good dispersion is that the self-assembled aggregates and the nanoparticles must have the same symmetry and are commensurate. This might offer a route to size selectivity - similar in spirit to the concept the prince used to find Cinderella. This concept is relevant for all nanoscale particles well beyond dispersion of SWCNTs as the adsorbed structures in Figure 4 demonstrate.

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SUPPORTING INFORMATION AVAILABLE Description of

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the employed model, force field, the simulation protocol, all respective parameter values, and further illustrative plots. This material is available free of charge via the Internet at http://pubs.acs.org/. (16)

AUTHOR INFORMATION Corresponding Author:

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*E-mail: [email protected].

ACKNOWLEDGMENT We gratefully acknowledge funding from an EPSRC DTA and the Chemical Engineering Endowment Fund. (18)

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Angelikopoulos, P.; Bock, H. The Differences in Surfactant Adsorption on Carbon Nanotubes and Their Bundles. Langmuir 2010, 26, 899–907. De Gennes, P.-G. Scaling Concepts in Polymer Physics, 1st ed.; Cornell University Press: Ithaca, NY, 1980. Derjaguin, B. V. Friction and adhesion. IV. The theory of adhesion of small particles. Colloid Polym. Sci. 1934, 69, 155–164. Angelikopoulos, P.; Al Harthy, S.; Bock, H. Structural Forces from Directed Self-Assembly. J. Phys. Chem. B 2009, 113, 13817–13824. Zhbanov, A. I.; Pogorelov, E. G.; Chang, Y.-C. van der Waals Interaction between Two Crossed Carbon Nanotubes. ACS Nano 2010, 4, 5937–5945. Angelikopoulos, P.; Bock, H. Directed Self-Assembly of Surfactants in Carbon Nanotube Materials. J. Phys. Chem. B 2008, 112, 13793–13801. Utsumi, S.; Kanamaru, M.; Honda, H.; Kanoh, H.; Tanaka, H.; Ohkubo, T.; Sakai, H.; Abe, M.; Kaneko, K RBM Band ShiftEvidenced Dispersion Mechanism of Single-Wall Carbon Nanotube Bundles with NaDDBS. J. Colloid Interface Sci. 2007, 328, 276–284. Cheng, D. C. H.; Gulari, E. Micellization and Intermicellar Interactions in Aqueous Sodium Dodecyl Benzene Sulfonate Solutions. J. Colloid Interface Sci. 1982, 90, 410–423. Cardenas, J. F.; Gromov, A. The Effect of Bundling on the G0 Raman Band of Single-Walled Carbon Nanotubes. Nanotechnology 2009, 20, 465703. Segota, S.; Heimer, S.; Tezak, D. New Catanionic Mixtures of Dodecyldimethylammonium Bromide/Sodium Dodecylbenzenesulphonate/Water: I. Surface Properties of Dispersed Particles. Colloids Surf., A: Phys. Eng. Aspects 2006, 274, 91–99. Angelikoulos, P.; Gromov, A.; Leen, A.; Nerushev, O.; Bock, H.; Campbell, E. E. Dispersing Individual Single-Wall Carbon Nanotubes in Aqueous Surfactant Solutions below the CMC. J. Phys. Chem. C 2010, 114, 2–9. Islam, M. F.; Rojas, E.; Bergey, D. M.; Johnson, A. T.; Yodh, A. G. High Weight Fraction Surfactant Solubilization of SingleWall Carbon Nanotubes in Water. Nano Lett. 2003, 3, 269– 273. Bonard, J.-M.; Stora, T.; Salvetat, J.-P.; Maier, F.; St€ uckl., T; Duschl, C.; Forr, L.; de Heer, W.; Chetelain, A. Purification and Size-Selection of Carbon Nanotubes. Adv. Mater. 1999, 9, 827–831. Bernheim-Groswasser, A.; Wachtel, E.; Talmon, Y. Micellar Growth, Network Formation, and Criticality in Aqueous Solutions of the Nonionic Surfactant C12E5. Langmuir 2000, 16, 4131–4140. Moshammer, K.; Hennrich, F.; Kappes, M. Selective Suspension in Aqueous Sodium Dodecyl Sulfate According to Electronic Structure Type Allows Simple Separation of Metallic from Semiconducting Single-Walled Carbon Nanotubes. Nano Res. 2009, 2, 599–606. Britz, D. A.; Khlobystov, A. N. Noncovalent Interactions of Molecules with Single Walled Carbon Nanotubes. Chem. Soc. Rev. 2006, 35, 637–659. Ju, S.-Y.; Doll, J.; Sharma, I.; Papadimitrakopoulos, F. Selection of Carbon Nanotubes with Specific Chiralities Using Helical Assemblies of Flavin Mononucleotide. Nat. Nanotechnol. 2008, 3, 356–362. Schulz, J.; Bowers, J.; Findenegg, G. H. Crossover from Preferential Adsorption to Depletion: Aqueous Systems of Short-Chain CnEm Amphiphiles at Liquid/Liquid Interfaces. J. Phys. Chem. B 2001, 105, 6956–6964.


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The Nanoscale Cinderella Problem: Design of Surfactant Coatings for

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