CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402282
Explaining Fullerene Dispersion by using Micellar Solutions Marco Dallavalle, Marco Leonzio, Matteo Calvaresi,* and Francesco Zerbetto*[a] An effective computational strategy to describe the dispersion of C60 by surfactants is presented. The influence of parameters such as surfactant concentration and molecular length on the final morphology of the system is explored to explain the experimental results and to understand the incorporation of C60 inside micelles. Both neutral and charged amphiphilic molecules are simulated. The long-discussed problem of the location of fullerenes in micelles is addressed and C60 is found in
the hydrocarbon-chain region of the micelles. If the available hydrophobic space increases, C60 is localized in the inner part of the micellar core. Short, charged amphiphilic stabilizers are more efficient at dispersing fullerenes monomolecularly. Two different phases of C60 are observed as the C60/surfactant ratio varies. In the first, aggregates of C60 are entrapped inside the micelles, whereas, in the second, colloidal nanoC60 is formed with surfactants adsorbed on the surface.
1. Introduction C60 is recognized as a prototypical nanomaterial.[1] Applications in lubricants, superconductors, sensors, solar cells, and, in general, in materials chemistry,[2] nanomedicine, and nanobiotechnology, have been proposed .[3] The extremely poor solubility of fullerene in water has partially hampered its exploitation. In water, the solubility of C60 is estimated to range from 2 10 24 to 1.1 10 11 m and the formation of fullerene aggregates (often termed nanoC60 or nC60) has been reported.[4] The formation of difficult to characterize fullerene aggregates, with a broad size distribution (1–500 nm), is driven by van der Waals interactions.[4] The energy of interaction between C60 molecules is 176 kJ mol 1.[5] Solvent–fullerene interactions are not strong enough to overcome the attraction between fullerene molecules, and clustering occurs both in water and in organic solvents.[4] The formation of aggregates is likely to decrease the molecular-based performance properties. The photophysics and photochemistry of C60 depend on the nature of the dispersion.[6] Toxicity also differs for isolated species and nC60 ; this makes it crucial to know if C60 present in the system is molecularly dispersed or in an aggregated form.[7] For example, the membrane permeability of fullerene depends on its aggregation state and functionalization of the surface.[8] Three approaches have been used to overcome the lack of solubility of fullerene: 1) mechanical dispersion–stabilization of C60,[9] either through ultrasonication[10] or by solvent-exchange methods,[11] 2) synthesis of water-soluble fullerene derivatives by chemical functionalization, with hydrophilic groups, of pris[a] Dr. M. Dallavalle, Dr. M. Leonzio, Dr. M. Calvaresi, Prof. F. Zerbetto Dipartimento di Chimica “G. Ciamician” Alma Mater Studiorum, Universit di Bologna V. F. Selmi 2, 40126 Bologna (Italy) E-mail: [email protected] [email protected] Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402282.
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
tine fullerene,[12] and 3) solvation of C60 by suitable carriers endowed with hydrophobic cores, such as g-cyclodextrins, calixarenes, and other macrocyclic receptors,[13] molecular tweezers,[14] proteins,[15] aqueous micellar media,[16] block copolymers,[17] and liposomes.[18] Method 1 follows a mechanical– physical approach that generates metastable dispersions of fullerenes. They eventually reaggregate, because the method does not provide a way to overcome the strong fullerene–fullerene interactions. Moreover, mechanochemical treatment may often determine the surface chemical modification of C60.[19] Method 2 shows some limitations, because functionalization of C60 leads to alterations of its unique structure that can have a negative influence on its symmetry and electronic properties;[20] thus, restricting the potential for applications. Method 3, that is, the supramolecular approach, seems to be the most effective way to solvate pristine fullerenes, because it retains the physical properties of C60. The micellar environment is almost chemically inert towards entrapped fullerene and screens it from the solvent and from aggressive reagents that may be present in solution. Moreover, micellar solutions may be considered as approximate models of biological systems.[8] Herein, we present a simple but effective computational strategy[21] to describe the dispersion of fullerenes by surfactants. We explore the influence of parameters such as surfactant concentration and molecular length on the final morphology of the system, to explain the experimental results and provide guidelines to understand the incorporation of C60 inside micelles. Both neutral and charged amphiphilic molecules are simulated. The amount of fullerene dispersion and the location of C60 inside micelles are examined. The computational model we selected for the investigation was dissipative particle dynamics (DPD). This model is often used to describe the coupling of the dynamics of fluids to colloidal behavior; a feature shown by some C60 aggregates (see below). DPD has been successfully used and validated for studying interactions and selfChemPhysChem 0000, 00, 1 – 9
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assembly of amphiphilic molecules and carbon nanoparticles.[22] DPD describes accurately the dynamics of aggregate formation. It trades off a lower detail of description for longer timescales and larger system sizes. The momentum-conserving thermostat of DPD, along with the implementation of soft repulsive interactions and coarse graining, makes it possible to simulate 1) the formation of architectures with a morphology resulting from solvophobic interactions (micelles, vesicles, and membranes), and 2) the dynamics of colloidal particles (nanoparticles) and their mutual interactions.[21, 22]
2. Results and Discussion 2.1. Morphology of the Self-Assembly
Figure 1. Snapshots of the equilibrium morphologies of the surfactant assemblies around C60. Top: neutral surfactants (red: hydrophilic, blue: hydrophobic), fullerene (green). Bottom: charged surfactants (pink: hydrophilic, blue: hydrophobic), fullerene (green). Left to right: 15, 30, 60, 120, and 240 surfactants in the simulation box. All water molecules and counter ions are removed for clarity. The box is centered at the fullerene.
Figure 1 shows the equilibrium morphologies of the self-assembly of charged and neutral surfactants around a single fullerene. All analyses were performed after equilibrium was reached (see Figure S1 in the Supporting Information). We space available to hold C60. This behavior explains the greater take, as a representative example, one of the most used and propensity of neutral surfactants to solvate fullerenes in comsimplest surfactants able to solvate carbon nanoparticles, parison to charged surfactants.[16d] [23] A quantitative evaluation of the morphology requires the namely, sodium dodecylsulfate (SDS). All simulations lead to the formation of micelles, which are defined as a group of amanalysis of the radial distributions of the heads of the surfacphiphilic molecules, the tails of which are in contact with each tants with respect to the center of the micelle (Figure 2). other. The case with 15 surfactants in the simulation box, 15 S, Narrow Gaussian distributions indicate spatially ordered and is borderline; the few surfactants adsorbed on the cage of C60 confined micelles. The linear- and step-like trends for neutral and charged surfactants are clearly portrayed in the radial do not encapsulate it properly and the amphiphilic molecules distributions. form a monolayer of surfactants that protect the fullerene cage from contact with water. In all other calculations, C60 is wrapped inside the micelle. The results underscore the ability of micellar solutions to disperse C60 in water. There are, however, differences in the behavior of the two kinds of surfactants. Neutral surfactants always form a single spherical micelle (Figure 1, top). Upon increasing the number of surfactants in the simulation box (i.e. increasing the concentration), the radius, r, of the micelle increases linearly (Figure 2 a). In contrast, charged surfactants prefer to self-assemble into smaller micelles, which minimize electrostatic repulsions between the charged heads. It is also possible to observe the formation of several micellar structures. By increasing the number of surfactants, the average radius of the micelle increases as a step function, because the head–head repulsion governs the thermodynamics of self-assembly.[24] NeuFigure 2. The radial distribution of the heads of a) neutral and b) charged surfactants with respect to the center tral surfactants form micelles of mass of C60 with 15 (white), 30 (light gray), 60 (medium gray), 120 (dark gray), and 240 (black) surfactants in that have a larger hydrophobic the simulation box. The trend of the micelle radius with surfactant concentration is highlighted. 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Figure 3. Evolution of the diffusion coefficient (in DPD dimensionless units) for water (blue), micelle (red) and fullerene in the simulation box with 15 (yellow), 30 (black), 60 (green), 120 (burgundy) and 240 surfactants (purple) as a function of time.
2.2. Diffusion of Fullerene and Micelles Estimation of fullerene diffusion allows the behavior of C60 trapped inside a micelle to be understood. Figure 3 shows that, if there are few surfactants (15 S) adsorbed on the cage of C60, the molecule maintains its characteristic diffusion coefficient. When the micelle is formed and has the correct size to accommodate C60, it diffuses either with the same velocity of the micelle or more slowly, because it is the micelle that drives the global diffusion. 2.3. Location of C60 Inside the Micelles Ever since the incorporation of C60 into micelles was observed for the first time in 1993 by Hungerbuehler et al.,[18a] its location in the micellar environment has been debated. The appearance of a broad band in the UV/Vis spectrum of fullerene at about l 440 nm in the micellar solution is observed. This signal has been explained in two different ways: The first hypothesis is that the band at l = 440 nm is the same band, shifted to lower wavelengths, as the weak band at l = 540 nm observed when C60 is solvated in benzene, toluene, n-hexane, or 1,2-dichloroethane. A similar blueshift of this band is also observed when C60 is dissolved in alcohols. The solvatochromic effect observed in micellar solutions of fullerenes, may be taken as an indication that C60 is located close to the head groups of the surfactants. The blueshift of the fullerene band at l = 540 nm has been explained as the result of the interaction between the polar heads of the surfactant and the p systems of C60.[18a] The implication is that C60 is not located in the inner hydrophobic part of the micelle, but in the neighborhood of the polar head groups. A second hypothesis emerged from subsequent UV/Vis and small-angle neutron scattering (SANS) studies,[16a] which showed that C60 in micellar systems is present in molecular and colloidal states. A transition from molecular to colloidal C60 is induced by increasing the ratio of X = [C60]/[surfactant]. At low values of X (10 4), the UV/Vis spectra are characteristic of monomeric C60, as in conventional hydrocarbon solvents; no aggregates can be detected by SANS. Increasing the value of X 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org up to 2.52 10 3 allows the developing broad band at l 440 nm to be assigned to the presence of colloidal C60 aggregates. Similar spectroscopic behavior has been reported for C60 in water. An increase of fullerene concentration in water leads to aggregation and to a slight shift of the spectral bands into the long-wavelength region together with the appearance of an additional narrow spectral line at l = 450 nm.[4d] Even more accurate analysis of the spectroscopic data[16c] increased the consensus that, when dispersed by micellar solutions, fullerenes are localized in the hydrocarbon chain region, that is, in the inner part of the micelle. Further work confirmed that fullerenes were located preferentially inside the hydrophobic domain.[16d, 19, 25] The results were corroborated by cyclic voltammetry, pyrene fluorescence, and micro-Raman measurements.[19, 25] In the simulations, the position of C60 with respect to the micelle center of mass was recorded, step-by-step, during the dynamics (Figure 4; an alternative presentation of the data is given in Figure S3 in the Supporting Information, in which the radial distribution of the fullerene inside the micelles is shown). C60 molecules explore the entire core of the micelle several times (see Figure S2 in the Supporting Information) by sampling the available space. The region delimited by the sphere corresponds to the maximum probability of finding the hydrophilic heads of the surfactants (Figure 2). C60 is always inside the hydrophobic core of the micelle. When the volume of the available hydrophobic region increases, C60 prefers to localize in the inner part of the micelle. The location of C60 does not depend on the charge of the surfactants. When the radius of the micelle becomes greater than 22 , C60 starts to localize in the micellar core, even if the available hydrophobic space increases. C60 seeks the micellar core to increase the interactions with the surrounding surfactants tails. Atomistic simulations of C60 in a lipid membrane showed that the lipid tails tended to wrap around its surface to maximize the number of contacts.[8l] Figure 5 shows the number of surfactant tail beads that interact with C60 as a function of the micelle radius. The number of enthalpic interactions of C60 increases with increasing radius. In summary, C60 is in the hydrophobic inner region, which is in agreement with the interpretation of the experimental data.[16c, d, 19, 25] The tendency of C60 to localize in the inner part of the micelle may be one of the reasons that explains why C60 also tends to form colloid aggregates inside micelles.[16a]
2.4. Fullerene Aggregation Inside Micelles Molecular dynamics (MD) simulations,[8j] together with differential scanning calorimetry (DSC) and nuclear magnetic resonance (NMR) spectroscopy measurements,[18b] demonstrate that C60 molecules in bilayers are not dispersed. They exist as aggregates, and phase separation between the C60 aggregates and the lipids takes place.[8j, l, 18b] Atomistic simulations reveal that the self-assembly of C70–gallic acid or C70–NOM (NOM = natural organic matter) makes the fullerenes water soluble, but favors aggregation.[8k,l] At high fullerene concentrations, the same behavior is also observed in micellar systems.[16a] ChemPhysChem 0000, 00, 1 – 9
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Figure 4. Fullerene distribution inside the micelle at different surfactant concentrations. The region inside the sphere corresponds to the maximum probability of finding the hydrophilic heads. The center of mass of C60, recorded at different times, is represented by black spots. As the micelle dimension increases, the fullerene moves deeper into the micellar core The charged surfactants show similar behavior that is dependent only on the micelle dimension.
Figure 5. Number of contacts between C60 and the surfactant tail beads. The bars represent standard deviations. Black: neutral surfactants; gray: charged surfactants.
We investigated the effect of the ratio of the number of surfactants and C60 molecules. The number of surfactant molecules was kept constant (240 surfactants in the simulation box), whereas the number of C60 molecules was gradually increased. In all cases, the results in Figure 6 show that increasing the number of C60 molecules leads to aggregation of the fullerenes. The C60 aggregates are spherical, as experimentally determined for small nC60 nanoparticles.[26] Upon increasing the C60 concentration, the system morphology changes from a micelle entrapped C60 to a colloidal aggregate of C60 covered by a surfactant monolayer. Morphological transitions of amphiphilic molecules, induced by nanoparticles clustering at various nanoparticle volume fractions, have been observed experimentally by Park and co-workers.[27] The polymer depletion mecha 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 6. Representative snapshots of the simulation box for increasing fullerene concentrations. The 240 nonionic surfactants always form a single micelle. The fullerenes are encapsulated in the micelle hydrophobic core and undergo aggregation.
nism (owing to increasing surfactant-tail entropy) and the enthalpic van der Waals attraction potential between fullerenes led to clustering of nanoparticles[27] in the core of the micelle. Although both C60 and the alkyl chains of the surfactants are hydrophobic, they are geometrically and chemically different. Fullerenes prefer to interact with other fullerenes and segregate in the micelle core. As before, the diffusion behavior of C60 and surfactants can be used to monitor the effect of increasing concentration (Figure 7). With up to 32 fullerenes in the unit box, we observe fullerenes entrapped inside the micelle. The diffusion coefficient of fullerenes is lower than that of the micelle. with more than 64 fullerenes, the system moves as a single body. SurfacChemPhysChem 0000, 00, 1 – 9
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Figure 7. Diffusion coefficient (in DPD dimensionless units) of fullerene (&), fullerene aggregates (~), and surfactants (*) versus fullerene concentration.
tants and fullerenes have the same diffusion coefficient. The system is a colloidal nanoparticle of C60 with surfactants adsorbed on the surface. The diffusion of the center of mass of the aggregates shows a small variation with concentration. The movement of the aggregate is insensitive to its size. An increase in the concentration of C60 results in an increase of diffusion of the system. Rheological measurements revealed that, micellar systems tended to be more fluid after fullerenes were incorporated into the hydrophobic domains.[28] Enhanced mobility of fullerene nanoparticles has also been observed in the presence of stabilizing agents.[29] Dynamic light scattering experiments showed that an increase in C60 concentration resulted in an increase in the value of the diffusion coefficient for fullerene aggregates,[4c] in accordance with the present simulations. 2.5. Effect of Surfactant Concentration, Chain Length, and Charge on Fullerene Dispersion Figure 8 illustrates how surfactant concentration, chain length, and charge affect the encapsulation of multiple fullerenes in the micellar solutions. Micellization occurs in all simulations. The only exception is for the lowest concentrations of short amphiphilic molecules in which the surfactants simply adsorb on the cages, which screens them from water. Experimentally, when concentrations are below the critical micelle concentration (cmc), the presence of surfactants can still improve the dispersion of C60.[30] Figure 8, top, shows that neutral surfactants preferentially form a single spherical micelle encapsulating the fullerenes. The formation of nC60 aggregates is observed in the majority of the calculations. Fullerenes self-aggregate inside the micelle and it is extremely difficult to obtain fullerenes dispersed monomolecularly.[16a] Figure 8, bottom, depicts the effect of charged surfactants on C60 dispersion. Charged stabilizers tend to form multiple micelles, because of the presence of electrostatic repulsion between the charged heads. In the case of longer surfactants, 7 T and 9 T < (T = tail beads), the presence of multiple micelles improves the dispersion of C60, although the formation of fullerene aggregates is still observed. Shorter surfactants, 5 T and 3 T, are more effective in suppressing aggregate formation. For ex 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 8. Snapshots of equilibrium morphologies of surfactant assemblies around C60. Left to right 15, 30, 60, 120, and 240 surfactants in the simulation box. Top: neutral surfactants. Bottom: charged surfactants. Length of the surfactant in shorthand notation 1T, 3T, 5T, 7T, 9T. Red: hydrophilic neutral beads, blue: hydrophobic neutral beads, sea green: fullerene beads, pink: hydrophilic charged beads. Water molecules and counter ions removed for clarity.
ample, 3 T, with 120 or 240 surfactants in the box, disperses C60 molecularly. The formation of multiple small micelles hinders aggregate formation. If C60 fits the hydrophobic cavity of the micelle and there is no room for another guest, then it is possible to obtain monomeric fullerene dispersion. This encapsulation is similar to that observed in macrocyclic receptors, which are able to disperse pristine C60 in water in monomolecular form[13] or in capsule/clamshell structures with a designed nanoscale cavity for the recognition of fullerenes.[31] This principle can be used for the construction of highly ordered fullerene assemblies characterized by a well-defined tridimensional topology or fullerene sorting.[32] ChemPhysChem 0000, 00, 1 – 9
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CHEMPHYSCHEM ARTICLES The calculations are consistent with experimental observations.[16d, 19] It has been reported that nonionic surfactants disperse a higher amount of C60 in comparison to ionic surfactants,[16d, 19] because of the higher hydrophobic volume available. Nevertheless, the formation of aggregates is observed, because the absorption spectrum displays the characteristic absorption of nC60.[16d, 19] The 1 T amphiphilic molecules are unique in their solvating power, among the stabilizing agents, because they avoid the formation of aggregates inside the micelle. It is known that pyridine and other nitrogen-containing solvents with aromatic rings are able to reduce the extent of aggregation.[4a, 32] In calculations with 1 T amphiphilic molecules, little or no aggregation of C60 is observed. Experimentally, fullerenes, when dissolved in binary solvent mixtures of water/pyridine, exhibit strong solvatochromism and an unusual chemical inertness.[33] This behavior has been associated with the formation of chemically inert, water-soluble C60/pyridine nanocapsules, in which pyridine appears to act as a surfactant around the fullerene molecules to protect them from chemical reagents;[33] this is actually observed in the present simulations. The driving force for self-assembly is provided by hydrophobic interactions between C60 and water.[33] As surfactant behavior in aqueous solutions depends on temperature and/or ionic strength, it is, in principle, possible to control the aggregation of nanoparticles by changing these easily tunable parameters.
3. Conclusions DPD simulations provided a theoretical framework that described the encapsulation of fullerene in micellar solutions. The long-discussed problem of the location of fullerene in micelles was addressed and fullerenes were found to locate themselves in the hydrocarbon-chain region of micelles. When the available hydrophobic space increased, C60 localized in the inner part of the micellar core for enthalpic reasons. A systematic study of the effect of the stabilizer chain length, charge, and concentration on fullerene aggregation was presented. Nonionic surfactants formed larger micelles than charged surfactants. The greater hydrophobic volume available in neutral surfactants micelles explained their greater efficiency in solvating C60. Short, charged amphiphilic stabilizers were more efficient at dispersing fullerenes monomolecularly. The mechanism of the dispersion of fullerenes was concentration dependent; aggregation of C60 molecules was observed inside the micelles as the concentration increased. Two different phases appeared upon varying the C60/surfactant ratio. In the first, aggregates of fullerenes were entrapped inside the micelles; in the second, colloidal nanoC60 was formed with surfactants adsorbed on the surface. Only small micelles with the appropriate hydrophobic cavity entrapped a single C60 particle and led to monomolecular dispersion of fullerenes, without aggregate formation. By tuning the chain length and the charge of the amphiphilic molecules, it was possible to achieve quasi-monomeric fullerene dispersion. Among the stabilizers considered, small amphiphilic molecules, 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org as in the well-known case of nitrogen-containing co-solvents, displayed a unique solvating power.
Computational Details Theory The DPD model used herein was based on the approach introduced by Groot et al.[34] It was a mesoscopic model based on soft beads, each of which represented a fluid element, which entailed a portion of a molecule. The coarse graining of the structure and the soft interactions allowed modeling of larger systems over significantly longer times than those possible with atom-based molecular models (for details, see the Supporting Information). The softcore beads might have carried a charge. This was the situation when we considered anionic surfactants (charge 1 on the head bead) and explicit counter ions (bead with a charge +1). Although the algorithmic approach was conceptually similar to that published by Groot in 2003[35] (both used a particle-mesh method), the Culgi method[36] used the Poisson–Boltzmann equation rather than the Poisson equation. The effect of free ions, that is, salt, was modeled by changing the Debye length, D (which screened charges on the molecules by an appropriate amount). This approach was also appropriate for DPD simulations in which the bead size was relatively large (one bead represented a large amount of material). If, however, as in this situation, the beads were close to the size of hydrated ions, it was more accurate, and more revealing, to model the individual ions explicitly (by using charged beads). In this case, D was set to a large value (100). The Bjerrum length, lb, modeled the shielding effect of the medium. This corresponded to the dielectric permittivity of water at room temperature. As was the case for most parameters in mesoscale modeling, the Debye and Bjerrum lengths were specified in dimensionless units. No general analytical solution existed for the Poisson–Boltzmann model. Therefore, in Culgi, the electrostatics were solved by iterating the Poisson equation on a grid, with the help of particle mesh methods.
Simulation System and Parameters All calculations were performed by using the Culgi 4.0.1 suite of programs.[36] The system consisted of water, surfactants, and one or more fullerenes. Surfactants were described by single chains of soft spheres. A surfactant molecule consisted of one bead, which represented the hydrophilic head group (labeled as h) plus n other beads, which represented the hydrophobic tail group (labeled as t). The water particles were labeled as w. The beads of the fullerenes are labeled as f. The fullerene was modeled as a spherical aggregate of soft-core beads, as originally proposed by Koelman and Hoogerbrugge for colloids.[37] The beads in a single aggregate had fixed relative distances. The distances were frozen and the aggregate moved as a whole. In the algorithm,[38] the equations of motion summed all forces on individual beads. The forces were then split into a translational and a rotational component. These forces were then used to solve the translational and rotational equations of motion for the aggregate as a whole. The interactions between any two particles in the solution were described by the empirical parameters in Table 1. These parameters worked well to reproduce the experimental self-assembly of surfactants with carbon nanotubes[21] and graphene.[22d] In the simulations, the bead density was set at 1 = 3 in DPD units. A cubic simulation box of dimension 20 20 20rc was used and periodic boundary conditions were applied. The total number of ChemPhysChem 0000, 00, 1 – 9
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Table 1. The aij parameters that determine the magnitude of the repulsion force between particles i and j (see Equation 2 in the Supporting Information) for the interactions of beads of water (w), surfactant tail (t), surfactant head (h), and fullerene (f).
w h t f
aij parameters w
h
t
f
25 25 80 80
25 27 40 40
80 40 25 25
80 40 25 25
beads was 24 000. The calculation was run for 100 000 steps by using a time step of 0.05t.
Simulated System, Physical Lengths, and Timescales To transform the dimensionless or DPD units used in the simulations into physical lengths and timescales, it was necessary to link simulations and experimental data. The model system used for the conversions had a tail of nine beads: it represented a SDS molecule. The bead interaction range, rc, was the unit of length of the system and was defined as the side of a cube containing an average number of 1 beads, according to Groot and Warren.[34a] The volume of the C12H15 tail was 350 3 ;[39] hence, each bead was about 39 3. Because the bead density was 3, a cube of rc3 contained 3 beads, and therefore, corresponded to a volume of 117 3. The physical size of the interaction radius, rc, was equal to 4.9 . As proposed by Groot and Rabone,[40] to obtain the physical timescale (see the Supporting Information), we compared the calculated diffusion constant of water beads, Dcalcd, with the experimentally measured values (Dexptl = 2.43 10 5 cm2 s 1).[40] The resulting unit time was 35.4 ps. This meant that the 20 20 20rc box represented a cube of linear dimension of 9.8 nm and that the fullerene had a radius of 4.9 (in agreement with a van der Waals diameter of 10 ). The typical simulation run of 100 000 steps, with a time step of 0.05, corresponded to a total time of 0.18 s.
Keywords: dissipative particle dynamics micelles · self-assembly · surfactants
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fullerenes
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[4] a) N. O. Mchedlov-Petrossyan, Chem. Rev. 2013, 113, 5149 – 5193; b) J. A. Brant, J. Labille, J. Y. Bottero, M. R. Wiesner, Langmuir 2006, 22, 3878 – 3885; c) Y. I. Prylutskyy, A. S. Buchelnikov, D. P. Voronin, V. V. Kostjukov, U. Ritter, J. A. Parkinson, M. P. Evstigneev, Phys. Chem. Chem. Phys. 2013, 15, 9351 – 9360; d) P. Scharff, K. Risch, L. Carta-Abelmann, I. M. Dmytruk, M. M. Bilyi, O. A. Golub, A. V. Khavryuchenko, E. V. Buzaneva, V. L. Aksenov, M. V. Avdeev, Yu. I. Prylutskyy, S. S. Durov, Carbon 2004, 42, 1203 – 1206. [5] P. J. Linstrom, W. G. Mallard, NIST Chemistry WebBook, NIST Standard Reference Database Number 69, July 2001, National Institute of Standards and Technology, Gaithersburg, MD 20899 (http://webbook.nist.gov). [6] B. Zhang, M. Cho, J. B. Hughes, J.-H. Kim, Environ. Sci. Technol. 2009, 43, 9124 – 9129. [7] D. Y. Lyon, L. K. Adams, J. C. Falkner, P. J. J. Alvarez, Environ. Sci. Technol. 2006, 40, 4360 – 4366. [8] a) R. Qiao, A. P. Roberts, A. S. Mount, S. J. Klaine, P. C. Ke, Nano Lett. 2007, 7, 614 – 619; b) L. Li, H. Davande, D. Bedrov, G. D. Smith, J. Phys. Chem. B 2007, 111, 4067 – 4072; c) R. S. G. D’Rozario, C. L. Wee, E. J. Wallace, M. S. P. Sansom, Nanotechnology 2009, 20, 115102; d) J. Wong-Ekkabut, S. Baoukina, W. Triampo, I. Tang, D. P. Tieleman, L. Monticelli, Nat. Nanotechnol. 2008, 3, 363 – 368; e) L. Monticelli, E. Salonen, P. C. Ke, I. Vattulainen, Soft Matter 2009, 5, 4433 – 4445; f) S. Hçfinger, M. MelleFranco, T. Gallo, A. Cantelli, M. Calvaresi, J. A. N. F. Gomes, F. Zerbetto, Biomaterials 2011, 32, 7079 – 7085; g) S. Kraszewski, M. Tarek, C. Ramseyer, ACS Nano 2011, 5, 8571 – 8578; h) M. Bortolus, G. Parisio, A. L. Maniero, A. Ferrarini, Langmuir 2011, 27, 12560 – 12568; i) A. Jusufi, R. H. DeVane, W. Shinodab, M. L. Klein, Soft Matter 2011, 7, 1139 – 1146; j) S. Zhang, Y. Mu, J. Z. H. Zhang, W. Xu, PLoS One 2013, 8, e77436; k) E. Salonen, S. Lin, M. L. Reid, M. Allegood, X. Wang, A. M. Rao, I. Vattulainen, P. C. Ke, Small 2008, 4, 1986 – 1992; l) R. Chen, T. A. Ratnikova, M. B. Stone, S. Lin, M. Lard, G. Huang, J. S. Hudson, P. C. Ke, Small 2010, 6, 612 – 617. [9] S. Deguchi, S. Mukai, M. Tsudome, K. Horikoshi, Adv. Mater. 2006, 18, 729 – 732. [10] G. V. Andrievsky, M. V. Kosevich, O. M. Vovk, V. S. Shelkovsky, L. A. Vashchenko, J. Chem. Soc. Chem. 1995, 1281 – 1282. [11] S. Deguchi, R. G. Alargova, K. Tsujii, Langmuir 2001, 17, 6013 – 6017. [12] a) A. Hirsch, Angew. Chem. Int. Ed. Engl. 1993, 32, 1138 – 1141; Angew. Chem. 1993, 105, 1189 – 1192; b) E. Nakamura, H. Isobe, Acc. Chem. Res. 2003, 36, 807 – 815; c) A. Hirsch, M. Brettreich, Fullerenes—Chemistry and Reactions, Wiley-VCH, Weinheim, 2005. [13] D. Canevet, E. M. Prez, N. Martn, Angew. Chem. Int. Ed. 2011, 50, 9248 – 9259; Angew. Chem. 2011, 123, 9416 – 9427. [14] E. M. Prez, N. Martn, Pure Appl. Chem. 2010, 82, 523 – 533. [15] a) M. Calvaresi, F. Zerbetto, Nanoscale 2011, 3, 2873 – 2881; b) H. Wu, L. Lin, P. Wang, S. Jiang, Z. Dai, X. Zou, Chem. Commun. 2011, 47, 10659 – 10661; c) M. Calvaresi, F. Arnesano, S. Bonacchi, A. Bottoni, V. Cal, S. Conte, G. Falini, S. Fermani, M. Losacco, M. Montalti, G. Natile, L. Prodi, F. Sparla, F. Zerbetto, ACS Nano 2014, 8, 1871 – 1877. [16] a) A. Beeby, J. Eastoe, R. K. Heenan, J. Chem. Soc. Chem. Commun. 1994, 173 – 175; b) J. Eastoe, E. R. Crooks, A. Beeby, R. K. Heenan, Chem. Phys. Lett. 1995, 245, 571 – 577; c) R. Bensasson, E. Bienvenue, M. Dellinger, S. Leach, P. Seta, J. Phys. Chem. 1994, 98, 3492 – 3500; d) V. Milic Torres, M. Posa, B. Srdjenovic, A. L. Simplcio, Colloids Surf. B 2011, 82, 46 – 53. [17] a) S. A. Jenekhe, X. L. Chen, Science 1998, 279, 1903 – 1907; b) X. L. Chen, S. A. Jenekhe, Langmuir 1999, 15, 8007 – 8017. [18] a) H. Hungerbuehler, D. M. Guldi, K. D. Asmus, J. Am. Chem. Soc. 1993, 115, 3386 – 3687; b) A. Ikeda, K. Kiguchi, T. Shigematsu, K. Nobusawa, J. Kikuchi, M. Akiyama, Chem. Commun. 2011, 47, 12095 – 12097; c) Y. Doi, A. Ikeda, M. Akiyama, M. Nagano, T. Shigematsu, T. Ogawa, T. Takeya, T. Nagasaki, Chem. Eur. J. 2008, 14, 8892 – 8897; d) A. Ikeda, M. Mori, K. Kiguchi, K. Yasuhara, J. Kikuchi, K. Nobusawa, M. Akiyama, M. Hashizume, T. Ogawa, T. Takeya, Chem. Asian J. 2012, 7, 605 – 613. [19] B. Todorovic´ Markovic´, V. Jokanovic´, S. Jovanovic´, D. Kleut, M. Dramic´anin, Z. Markovic´, Appl. Surf. Sci. 2009, 255, 7537 – 7541. [20] M. Reiher, A. Hirsch, Chem. Eur. J. 2003, 9, 5442 – 5452. [21] M. Calvaresi, M. Dallavalle, F. Zerbetto, Small 2009, 5, 2191 – 2198. [22] a) D. M ter, H. Bock, J. Phys. Chem. B 2013, 117, 5585 – 5593; b) M. Dutt, O. Kuksenok, A. C. Balazs, Nanoscale 2013, 5, 9773 – 9784; c) P. Angelikopoulos, H. Bock, Phys. Chem. Chem. Phys. 2012, 14, 9546 – 9557; d) S. H.
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ARTICLES Behavior deconstructed: The dispersion of fullerenes by surfactants is described by dissipative particle dynamics simulations. A systematic study of the effect of the chain length, charge, and concentration of the stabilizer on fullerene aggregation is presented to explain the experimental results and to provide guidelines to understand the incorporation of C60 inside micelles.
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M. Dallavalle, M. Leonzio, M. Calvaresi,* F. Zerbetto* && – && Explaining Fullerene Dispersion by using Micellar Solutions
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Explaining Fullerene Dispersion by using Micellar Solutions Marco Dallavalle, Marco Leonzio, Matteo Calvaresi,* and Francesco Zerbetto*[a] An effective computational strategy to describe the dispersion of C60 by surfactants is presented. The influence of parameters such as surfactant concentration and molecular length on the final morphology of the system is explored to explain the experimental results and to understand the incorporation of C60 inside micelles. Both neutral and charged amphiphilic molecules are simulated. The long-discussed problem of the location of fullerenes in micelles is addressed and C60 is found in
the hydrocarbon-chain region of the micelles. If the available hydrophobic space increases, C60 is localized in the inner part of the micellar core. Short, charged amphiphilic stabilizers are more efficient at dispersing fullerenes monomolecularly. Two different phases of C60 are observed as the C60/surfactant ratio varies. In the first, aggregates of C60 are entrapped inside the micelles, whereas, in the second, colloidal nanoC60 is formed with surfactants adsorbed on the surface.
1. Introduction C60 is recognized as a prototypical nanomaterial.[1] Applications in lubricants, superconductors, sensors, solar cells, and, in general, in materials chemistry,[2] nanomedicine, and nanobiotechnology, have been proposed .[3] The extremely poor solubility of fullerene in water has partially hampered its exploitation. In water, the solubility of C60 is estimated to range from 2 10 24 to 1.1 10 11 m and the formation of fullerene aggregates (often termed nanoC60 or nC60) has been reported.[4] The formation of difficult to characterize fullerene aggregates, with a broad size distribution (1–500 nm), is driven by van der Waals interactions.[4] The energy of interaction between C60 molecules is 176 kJ mol 1.[5] Solvent–fullerene interactions are not strong enough to overcome the attraction between fullerene molecules, and clustering occurs both in water and in organic solvents.[4] The formation of aggregates is likely to decrease the molecular-based performance properties. The photophysics and photochemistry of C60 depend on the nature of the dispersion.[6] Toxicity also differs for isolated species and nC60 ; this makes it crucial to know if C60 present in the system is molecularly dispersed or in an aggregated form.[7] For example, the membrane permeability of fullerene depends on its aggregation state and functionalization of the surface.[8] Three approaches have been used to overcome the lack of solubility of fullerene: 1) mechanical dispersion–stabilization of C60,[9] either through ultrasonication[10] or by solvent-exchange methods,[11] 2) synthesis of water-soluble fullerene derivatives by chemical functionalization, with hydrophilic groups, of pris[a] Dr. M. Dallavalle, Dr. M. Leonzio, Dr. M. Calvaresi, Prof. F. Zerbetto Dipartimento di Chimica “G. Ciamician” Alma Mater Studiorum, Universit di Bologna V. F. Selmi 2, 40126 Bologna (Italy) E-mail: [email protected] [email protected] Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402282.
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
tine fullerene,[12] and 3) solvation of C60 by suitable carriers endowed with hydrophobic cores, such as g-cyclodextrins, calixarenes, and other macrocyclic receptors,[13] molecular tweezers,[14] proteins,[15] aqueous micellar media,[16] block copolymers,[17] and liposomes.[18] Method 1 follows a mechanical– physical approach that generates metastable dispersions of fullerenes. They eventually reaggregate, because the method does not provide a way to overcome the strong fullerene–fullerene interactions. Moreover, mechanochemical treatment may often determine the surface chemical modification of C60.[19] Method 2 shows some limitations, because functionalization of C60 leads to alterations of its unique structure that can have a negative influence on its symmetry and electronic properties;[20] thus, restricting the potential for applications. Method 3, that is, the supramolecular approach, seems to be the most effective way to solvate pristine fullerenes, because it retains the physical properties of C60. The micellar environment is almost chemically inert towards entrapped fullerene and screens it from the solvent and from aggressive reagents that may be present in solution. Moreover, micellar solutions may be considered as approximate models of biological systems.[8] Herein, we present a simple but effective computational strategy[21] to describe the dispersion of fullerenes by surfactants. We explore the influence of parameters such as surfactant concentration and molecular length on the final morphology of the system, to explain the experimental results and provide guidelines to understand the incorporation of C60 inside micelles. Both neutral and charged amphiphilic molecules are simulated. The amount of fullerene dispersion and the location of C60 inside micelles are examined. The computational model we selected for the investigation was dissipative particle dynamics (DPD). This model is often used to describe the coupling of the dynamics of fluids to colloidal behavior; a feature shown by some C60 aggregates (see below). DPD has been successfully used and validated for studying interactions and selfChemPhysChem 0000, 00, 1 – 9
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assembly of amphiphilic molecules and carbon nanoparticles.[22] DPD describes accurately the dynamics of aggregate formation. It trades off a lower detail of description for longer timescales and larger system sizes. The momentum-conserving thermostat of DPD, along with the implementation of soft repulsive interactions and coarse graining, makes it possible to simulate 1) the formation of architectures with a morphology resulting from solvophobic interactions (micelles, vesicles, and membranes), and 2) the dynamics of colloidal particles (nanoparticles) and their mutual interactions.[21, 22]
2. Results and Discussion 2.1. Morphology of the Self-Assembly
Figure 1. Snapshots of the equilibrium morphologies of the surfactant assemblies around C60. Top: neutral surfactants (red: hydrophilic, blue: hydrophobic), fullerene (green). Bottom: charged surfactants (pink: hydrophilic, blue: hydrophobic), fullerene (green). Left to right: 15, 30, 60, 120, and 240 surfactants in the simulation box. All water molecules and counter ions are removed for clarity. The box is centered at the fullerene.
Figure 1 shows the equilibrium morphologies of the self-assembly of charged and neutral surfactants around a single fullerene. All analyses were performed after equilibrium was reached (see Figure S1 in the Supporting Information). We space available to hold C60. This behavior explains the greater take, as a representative example, one of the most used and propensity of neutral surfactants to solvate fullerenes in comsimplest surfactants able to solvate carbon nanoparticles, parison to charged surfactants.[16d] [23] A quantitative evaluation of the morphology requires the namely, sodium dodecylsulfate (SDS). All simulations lead to the formation of micelles, which are defined as a group of amanalysis of the radial distributions of the heads of the surfacphiphilic molecules, the tails of which are in contact with each tants with respect to the center of the micelle (Figure 2). other. The case with 15 surfactants in the simulation box, 15 S, Narrow Gaussian distributions indicate spatially ordered and is borderline; the few surfactants adsorbed on the cage of C60 confined micelles. The linear- and step-like trends for neutral and charged surfactants are clearly portrayed in the radial do not encapsulate it properly and the amphiphilic molecules distributions. form a monolayer of surfactants that protect the fullerene cage from contact with water. In all other calculations, C60 is wrapped inside the micelle. The results underscore the ability of micellar solutions to disperse C60 in water. There are, however, differences in the behavior of the two kinds of surfactants. Neutral surfactants always form a single spherical micelle (Figure 1, top). Upon increasing the number of surfactants in the simulation box (i.e. increasing the concentration), the radius, r, of the micelle increases linearly (Figure 2 a). In contrast, charged surfactants prefer to self-assemble into smaller micelles, which minimize electrostatic repulsions between the charged heads. It is also possible to observe the formation of several micellar structures. By increasing the number of surfactants, the average radius of the micelle increases as a step function, because the head–head repulsion governs the thermodynamics of self-assembly.[24] NeuFigure 2. The radial distribution of the heads of a) neutral and b) charged surfactants with respect to the center tral surfactants form micelles of mass of C60 with 15 (white), 30 (light gray), 60 (medium gray), 120 (dark gray), and 240 (black) surfactants in that have a larger hydrophobic the simulation box. The trend of the micelle radius with surfactant concentration is highlighted. 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Figure 3. Evolution of the diffusion coefficient (in DPD dimensionless units) for water (blue), micelle (red) and fullerene in the simulation box with 15 (yellow), 30 (black), 60 (green), 120 (burgundy) and 240 surfactants (purple) as a function of time.
2.2. Diffusion of Fullerene and Micelles Estimation of fullerene diffusion allows the behavior of C60 trapped inside a micelle to be understood. Figure 3 shows that, if there are few surfactants (15 S) adsorbed on the cage of C60, the molecule maintains its characteristic diffusion coefficient. When the micelle is formed and has the correct size to accommodate C60, it diffuses either with the same velocity of the micelle or more slowly, because it is the micelle that drives the global diffusion. 2.3. Location of C60 Inside the Micelles Ever since the incorporation of C60 into micelles was observed for the first time in 1993 by Hungerbuehler et al.,[18a] its location in the micellar environment has been debated. The appearance of a broad band in the UV/Vis spectrum of fullerene at about l 440 nm in the micellar solution is observed. This signal has been explained in two different ways: The first hypothesis is that the band at l = 440 nm is the same band, shifted to lower wavelengths, as the weak band at l = 540 nm observed when C60 is solvated in benzene, toluene, n-hexane, or 1,2-dichloroethane. A similar blueshift of this band is also observed when C60 is dissolved in alcohols. The solvatochromic effect observed in micellar solutions of fullerenes, may be taken as an indication that C60 is located close to the head groups of the surfactants. The blueshift of the fullerene band at l = 540 nm has been explained as the result of the interaction between the polar heads of the surfactant and the p systems of C60.[18a] The implication is that C60 is not located in the inner hydrophobic part of the micelle, but in the neighborhood of the polar head groups. A second hypothesis emerged from subsequent UV/Vis and small-angle neutron scattering (SANS) studies,[16a] which showed that C60 in micellar systems is present in molecular and colloidal states. A transition from molecular to colloidal C60 is induced by increasing the ratio of X = [C60]/[surfactant]. At low values of X (10 4), the UV/Vis spectra are characteristic of monomeric C60, as in conventional hydrocarbon solvents; no aggregates can be detected by SANS. Increasing the value of X 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org up to 2.52 10 3 allows the developing broad band at l 440 nm to be assigned to the presence of colloidal C60 aggregates. Similar spectroscopic behavior has been reported for C60 in water. An increase of fullerene concentration in water leads to aggregation and to a slight shift of the spectral bands into the long-wavelength region together with the appearance of an additional narrow spectral line at l = 450 nm.[4d] Even more accurate analysis of the spectroscopic data[16c] increased the consensus that, when dispersed by micellar solutions, fullerenes are localized in the hydrocarbon chain region, that is, in the inner part of the micelle. Further work confirmed that fullerenes were located preferentially inside the hydrophobic domain.[16d, 19, 25] The results were corroborated by cyclic voltammetry, pyrene fluorescence, and micro-Raman measurements.[19, 25] In the simulations, the position of C60 with respect to the micelle center of mass was recorded, step-by-step, during the dynamics (Figure 4; an alternative presentation of the data is given in Figure S3 in the Supporting Information, in which the radial distribution of the fullerene inside the micelles is shown). C60 molecules explore the entire core of the micelle several times (see Figure S2 in the Supporting Information) by sampling the available space. The region delimited by the sphere corresponds to the maximum probability of finding the hydrophilic heads of the surfactants (Figure 2). C60 is always inside the hydrophobic core of the micelle. When the volume of the available hydrophobic region increases, C60 prefers to localize in the inner part of the micelle. The location of C60 does not depend on the charge of the surfactants. When the radius of the micelle becomes greater than 22 , C60 starts to localize in the micellar core, even if the available hydrophobic space increases. C60 seeks the micellar core to increase the interactions with the surrounding surfactants tails. Atomistic simulations of C60 in a lipid membrane showed that the lipid tails tended to wrap around its surface to maximize the number of contacts.[8l] Figure 5 shows the number of surfactant tail beads that interact with C60 as a function of the micelle radius. The number of enthalpic interactions of C60 increases with increasing radius. In summary, C60 is in the hydrophobic inner region, which is in agreement with the interpretation of the experimental data.[16c, d, 19, 25] The tendency of C60 to localize in the inner part of the micelle may be one of the reasons that explains why C60 also tends to form colloid aggregates inside micelles.[16a]
2.4. Fullerene Aggregation Inside Micelles Molecular dynamics (MD) simulations,[8j] together with differential scanning calorimetry (DSC) and nuclear magnetic resonance (NMR) spectroscopy measurements,[18b] demonstrate that C60 molecules in bilayers are not dispersed. They exist as aggregates, and phase separation between the C60 aggregates and the lipids takes place.[8j, l, 18b] Atomistic simulations reveal that the self-assembly of C70–gallic acid or C70–NOM (NOM = natural organic matter) makes the fullerenes water soluble, but favors aggregation.[8k,l] At high fullerene concentrations, the same behavior is also observed in micellar systems.[16a] ChemPhysChem 0000, 00, 1 – 9
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Figure 4. Fullerene distribution inside the micelle at different surfactant concentrations. The region inside the sphere corresponds to the maximum probability of finding the hydrophilic heads. The center of mass of C60, recorded at different times, is represented by black spots. As the micelle dimension increases, the fullerene moves deeper into the micellar core The charged surfactants show similar behavior that is dependent only on the micelle dimension.
Figure 5. Number of contacts between C60 and the surfactant tail beads. The bars represent standard deviations. Black: neutral surfactants; gray: charged surfactants.
We investigated the effect of the ratio of the number of surfactants and C60 molecules. The number of surfactant molecules was kept constant (240 surfactants in the simulation box), whereas the number of C60 molecules was gradually increased. In all cases, the results in Figure 6 show that increasing the number of C60 molecules leads to aggregation of the fullerenes. The C60 aggregates are spherical, as experimentally determined for small nC60 nanoparticles.[26] Upon increasing the C60 concentration, the system morphology changes from a micelle entrapped C60 to a colloidal aggregate of C60 covered by a surfactant monolayer. Morphological transitions of amphiphilic molecules, induced by nanoparticles clustering at various nanoparticle volume fractions, have been observed experimentally by Park and co-workers.[27] The polymer depletion mecha 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 6. Representative snapshots of the simulation box for increasing fullerene concentrations. The 240 nonionic surfactants always form a single micelle. The fullerenes are encapsulated in the micelle hydrophobic core and undergo aggregation.
nism (owing to increasing surfactant-tail entropy) and the enthalpic van der Waals attraction potential between fullerenes led to clustering of nanoparticles[27] in the core of the micelle. Although both C60 and the alkyl chains of the surfactants are hydrophobic, they are geometrically and chemically different. Fullerenes prefer to interact with other fullerenes and segregate in the micelle core. As before, the diffusion behavior of C60 and surfactants can be used to monitor the effect of increasing concentration (Figure 7). With up to 32 fullerenes in the unit box, we observe fullerenes entrapped inside the micelle. The diffusion coefficient of fullerenes is lower than that of the micelle. with more than 64 fullerenes, the system moves as a single body. SurfacChemPhysChem 0000, 00, 1 – 9
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Figure 7. Diffusion coefficient (in DPD dimensionless units) of fullerene (&), fullerene aggregates (~), and surfactants (*) versus fullerene concentration.
tants and fullerenes have the same diffusion coefficient. The system is a colloidal nanoparticle of C60 with surfactants adsorbed on the surface. The diffusion of the center of mass of the aggregates shows a small variation with concentration. The movement of the aggregate is insensitive to its size. An increase in the concentration of C60 results in an increase of diffusion of the system. Rheological measurements revealed that, micellar systems tended to be more fluid after fullerenes were incorporated into the hydrophobic domains.[28] Enhanced mobility of fullerene nanoparticles has also been observed in the presence of stabilizing agents.[29] Dynamic light scattering experiments showed that an increase in C60 concentration resulted in an increase in the value of the diffusion coefficient for fullerene aggregates,[4c] in accordance with the present simulations. 2.5. Effect of Surfactant Concentration, Chain Length, and Charge on Fullerene Dispersion Figure 8 illustrates how surfactant concentration, chain length, and charge affect the encapsulation of multiple fullerenes in the micellar solutions. Micellization occurs in all simulations. The only exception is for the lowest concentrations of short amphiphilic molecules in which the surfactants simply adsorb on the cages, which screens them from water. Experimentally, when concentrations are below the critical micelle concentration (cmc), the presence of surfactants can still improve the dispersion of C60.[30] Figure 8, top, shows that neutral surfactants preferentially form a single spherical micelle encapsulating the fullerenes. The formation of nC60 aggregates is observed in the majority of the calculations. Fullerenes self-aggregate inside the micelle and it is extremely difficult to obtain fullerenes dispersed monomolecularly.[16a] Figure 8, bottom, depicts the effect of charged surfactants on C60 dispersion. Charged stabilizers tend to form multiple micelles, because of the presence of electrostatic repulsion between the charged heads. In the case of longer surfactants, 7 T and 9 T < (T = tail beads), the presence of multiple micelles improves the dispersion of C60, although the formation of fullerene aggregates is still observed. Shorter surfactants, 5 T and 3 T, are more effective in suppressing aggregate formation. For ex 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 8. Snapshots of equilibrium morphologies of surfactant assemblies around C60. Left to right 15, 30, 60, 120, and 240 surfactants in the simulation box. Top: neutral surfactants. Bottom: charged surfactants. Length of the surfactant in shorthand notation 1T, 3T, 5T, 7T, 9T. Red: hydrophilic neutral beads, blue: hydrophobic neutral beads, sea green: fullerene beads, pink: hydrophilic charged beads. Water molecules and counter ions removed for clarity.
ample, 3 T, with 120 or 240 surfactants in the box, disperses C60 molecularly. The formation of multiple small micelles hinders aggregate formation. If C60 fits the hydrophobic cavity of the micelle and there is no room for another guest, then it is possible to obtain monomeric fullerene dispersion. This encapsulation is similar to that observed in macrocyclic receptors, which are able to disperse pristine C60 in water in monomolecular form[13] or in capsule/clamshell structures with a designed nanoscale cavity for the recognition of fullerenes.[31] This principle can be used for the construction of highly ordered fullerene assemblies characterized by a well-defined tridimensional topology or fullerene sorting.[32] ChemPhysChem 0000, 00, 1 – 9
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CHEMPHYSCHEM ARTICLES The calculations are consistent with experimental observations.[16d, 19] It has been reported that nonionic surfactants disperse a higher amount of C60 in comparison to ionic surfactants,[16d, 19] because of the higher hydrophobic volume available. Nevertheless, the formation of aggregates is observed, because the absorption spectrum displays the characteristic absorption of nC60.[16d, 19] The 1 T amphiphilic molecules are unique in their solvating power, among the stabilizing agents, because they avoid the formation of aggregates inside the micelle. It is known that pyridine and other nitrogen-containing solvents with aromatic rings are able to reduce the extent of aggregation.[4a, 32] In calculations with 1 T amphiphilic molecules, little or no aggregation of C60 is observed. Experimentally, fullerenes, when dissolved in binary solvent mixtures of water/pyridine, exhibit strong solvatochromism and an unusual chemical inertness.[33] This behavior has been associated with the formation of chemically inert, water-soluble C60/pyridine nanocapsules, in which pyridine appears to act as a surfactant around the fullerene molecules to protect them from chemical reagents;[33] this is actually observed in the present simulations. The driving force for self-assembly is provided by hydrophobic interactions between C60 and water.[33] As surfactant behavior in aqueous solutions depends on temperature and/or ionic strength, it is, in principle, possible to control the aggregation of nanoparticles by changing these easily tunable parameters.
3. Conclusions DPD simulations provided a theoretical framework that described the encapsulation of fullerene in micellar solutions. The long-discussed problem of the location of fullerene in micelles was addressed and fullerenes were found to locate themselves in the hydrocarbon-chain region of micelles. When the available hydrophobic space increased, C60 localized in the inner part of the micellar core for enthalpic reasons. A systematic study of the effect of the stabilizer chain length, charge, and concentration on fullerene aggregation was presented. Nonionic surfactants formed larger micelles than charged surfactants. The greater hydrophobic volume available in neutral surfactants micelles explained their greater efficiency in solvating C60. Short, charged amphiphilic stabilizers were more efficient at dispersing fullerenes monomolecularly. The mechanism of the dispersion of fullerenes was concentration dependent; aggregation of C60 molecules was observed inside the micelles as the concentration increased. Two different phases appeared upon varying the C60/surfactant ratio. In the first, aggregates of fullerenes were entrapped inside the micelles; in the second, colloidal nanoC60 was formed with surfactants adsorbed on the surface. Only small micelles with the appropriate hydrophobic cavity entrapped a single C60 particle and led to monomolecular dispersion of fullerenes, without aggregate formation. By tuning the chain length and the charge of the amphiphilic molecules, it was possible to achieve quasi-monomeric fullerene dispersion. Among the stabilizers considered, small amphiphilic molecules, 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org as in the well-known case of nitrogen-containing co-solvents, displayed a unique solvating power.
Computational Details Theory The DPD model used herein was based on the approach introduced by Groot et al.[34] It was a mesoscopic model based on soft beads, each of which represented a fluid element, which entailed a portion of a molecule. The coarse graining of the structure and the soft interactions allowed modeling of larger systems over significantly longer times than those possible with atom-based molecular models (for details, see the Supporting Information). The softcore beads might have carried a charge. This was the situation when we considered anionic surfactants (charge 1 on the head bead) and explicit counter ions (bead with a charge +1). Although the algorithmic approach was conceptually similar to that published by Groot in 2003[35] (both used a particle-mesh method), the Culgi method[36] used the Poisson–Boltzmann equation rather than the Poisson equation. The effect of free ions, that is, salt, was modeled by changing the Debye length, D (which screened charges on the molecules by an appropriate amount). This approach was also appropriate for DPD simulations in which the bead size was relatively large (one bead represented a large amount of material). If, however, as in this situation, the beads were close to the size of hydrated ions, it was more accurate, and more revealing, to model the individual ions explicitly (by using charged beads). In this case, D was set to a large value (100). The Bjerrum length, lb, modeled the shielding effect of the medium. This corresponded to the dielectric permittivity of water at room temperature. As was the case for most parameters in mesoscale modeling, the Debye and Bjerrum lengths were specified in dimensionless units. No general analytical solution existed for the Poisson–Boltzmann model. Therefore, in Culgi, the electrostatics were solved by iterating the Poisson equation on a grid, with the help of particle mesh methods.
Simulation System and Parameters All calculations were performed by using the Culgi 4.0.1 suite of programs.[36] The system consisted of water, surfactants, and one or more fullerenes. Surfactants were described by single chains of soft spheres. A surfactant molecule consisted of one bead, which represented the hydrophilic head group (labeled as h) plus n other beads, which represented the hydrophobic tail group (labeled as t). The water particles were labeled as w. The beads of the fullerenes are labeled as f. The fullerene was modeled as a spherical aggregate of soft-core beads, as originally proposed by Koelman and Hoogerbrugge for colloids.[37] The beads in a single aggregate had fixed relative distances. The distances were frozen and the aggregate moved as a whole. In the algorithm,[38] the equations of motion summed all forces on individual beads. The forces were then split into a translational and a rotational component. These forces were then used to solve the translational and rotational equations of motion for the aggregate as a whole. The interactions between any two particles in the solution were described by the empirical parameters in Table 1. These parameters worked well to reproduce the experimental self-assembly of surfactants with carbon nanotubes[21] and graphene.[22d] In the simulations, the bead density was set at 1 = 3 in DPD units. A cubic simulation box of dimension 20 20 20rc was used and periodic boundary conditions were applied. The total number of ChemPhysChem 0000, 00, 1 – 9
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Table 1. The aij parameters that determine the magnitude of the repulsion force between particles i and j (see Equation 2 in the Supporting Information) for the interactions of beads of water (w), surfactant tail (t), surfactant head (h), and fullerene (f).
w h t f
aij parameters w
h
t
f
25 25 80 80
25 27 40 40
80 40 25 25
80 40 25 25
beads was 24 000. The calculation was run for 100 000 steps by using a time step of 0.05t.
Simulated System, Physical Lengths, and Timescales To transform the dimensionless or DPD units used in the simulations into physical lengths and timescales, it was necessary to link simulations and experimental data. The model system used for the conversions had a tail of nine beads: it represented a SDS molecule. The bead interaction range, rc, was the unit of length of the system and was defined as the side of a cube containing an average number of 1 beads, according to Groot and Warren.[34a] The volume of the C12H15 tail was 350 3 ;[39] hence, each bead was about 39 3. Because the bead density was 3, a cube of rc3 contained 3 beads, and therefore, corresponded to a volume of 117 3. The physical size of the interaction radius, rc, was equal to 4.9 . As proposed by Groot and Rabone,[40] to obtain the physical timescale (see the Supporting Information), we compared the calculated diffusion constant of water beads, Dcalcd, with the experimentally measured values (Dexptl = 2.43 10 5 cm2 s 1).[40] The resulting unit time was 35.4 ps. This meant that the 20 20 20rc box represented a cube of linear dimension of 9.8 nm and that the fullerene had a radius of 4.9 (in agreement with a van der Waals diameter of 10 ). The typical simulation run of 100 000 steps, with a time step of 0.05, corresponded to a total time of 0.18 s.
Keywords: dissipative particle dynamics micelles · self-assembly · surfactants
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fullerenes
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Received: April 29, 2014 Published online on && &&, 2014
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ARTICLES Behavior deconstructed: The dispersion of fullerenes by surfactants is described by dissipative particle dynamics simulations. A systematic study of the effect of the chain length, charge, and concentration of the stabilizer on fullerene aggregation is presented to explain the experimental results and to provide guidelines to understand the incorporation of C60 inside micelles.
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M. Dallavalle, M. Leonzio, M. Calvaresi,* F. Zerbetto* && – && Explaining Fullerene Dispersion by using Micellar Solutions
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