Atomistic Description of Fullerene-Based Membranes - American

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An Atomistic Description of Fullerene Based Membranes Eudes Eterno Fileti J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp507296r • Publication Date (Web): 13 Oct 2014 Downloaded from http://pubs.acs.org on October 18, 2014

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The Journal of Physical Chemistry

An atomistic description of fullerene based membranes Eudes Eterno Fileti ICT, UNIFESP São José dos Campos, São José dos Campos, SP, CEP 12231-280

* Corresponding author. Tel: 55 12 3309 9500. E-mail: [email protected], [email protected]

Abstract We present extensive atomistic molecular dynamics simulations of the structure and stability of fullerene-based membranes. The simulations provides molecular description of the PhK (pentaaryl[60]fullerene anions, C60Ar5–·K+) and C8K (C60Ar5–·K+ with octyl substituents) membranes. Physical chemical properties and molecular organization of PhK and C8K membranes elucidate various aspects related to their formation and potential applications. Our simulations evidence that such membranes are robust and stable. PhK membranes proved very stable and compact. Considering experimental evidence, PhK bilayer is an adequate model for the surface of the PhK vesicle.

Keywords: Fullerene based membranes, ions, atomistic molecular dynamics, molecular interactions.

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1.

Introduction

An important feature of many nanomaterials is their capacity for self-assembly, which allows the production of nanostructures by bottom-up processes. The information for this manufacturing process is contained in their building blocks that self-organize with nanoscopic precision to form complex supramolecular structures.1,2 Fullerene based materials are among the most remarkable self-organizing systems both due to their unique physical chemical properties and a wide horizon of potential applications in diverse areas,3-20 Despite the difficulties related to high hydrophobicity of C60, which hinders the development of direct applications of pure fullerenes, great advances through the techniques of covalent and non-covalent functionalization of its carbonaceous structure have been achieved. These modifications give the fullerenes distinct and desirable characteristics, favoring the production of self-organizing structures and increase their spectrum of applications.3,21-25 In fact, water-soluble fullerene derivatives, which can be dissolved easily in water by introducing proper functional groups, have received much attention.4,26-30 For example, introduction of five phenyl groups around one pentagon of the fullerene molecule leads to the formation of a fascinating cavity structure. The complexation of this structure with potassium ion results in a water-soluble complex (pentaaryl[60]fullerene anions, C60Ar5– K+). The complex self-assembles into nanometer-sized vesicles with the hydrodynamic diameter of ~30 nm, upon dissolution in water.31,32 Such vesicles are much smaller than lipid vesicles and are almost perfectly spherical.32-34 Because of strong intermolecular π–π interactions and the high hydrophobicity of the fullerene core the fullerene based vesicle is very rigid and robust, both in water and in the vacuum, resulting in high stability and very low permeability for water. Those features are completely different from those of the 3 ACS Paragon Plus Environment


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conventional vesicles.33,34 A variety of processes can benefit from the properties of fullerene containing vesicles. Generally, nanocapsules are essential for various applications involving encapsulation and transport of substances,35,36 such as in self-healing systems,37 nanoshells for drug delivery,35 gene delivery process,36 and other processes of interest in biomedicine and engineering of materials.38-40 The study of the fullerene nanovesicles has been done so far only by experimental techniques. Dynamic light scattering was originally employed to determine the average size of the nano-sized vesicles as well as to estimate the critical aggregation concentration and the average aggregation number of the particles.33,34,41 Recently, high-resolution scanning electron microscopy was employed to elucidate the structure of these nanoparticles with subnanometer resolution.32 Despite the accuracy of such experimental technique, the analysis still addresses nanometer scale. Thus, fundamental information regarding molecular interactions inside the vesicle and vesicle-water interface cannot be obtained experimentally. In turn, all above mentioned tentative applications require a molecular description of the properties of these nanostructures.

Hence in this letter, we employ extensive atomistic molecular dynamics simulations to examine structural, dynamical and energetic aspects of the fullerene-based membranes in aqueous solutions. These membranes represent, in qualitative approximation, a small portion of the vesicle surface but still contain all essential information on the physico-chemical behavior of the vesicle as a whole. It is worth mentioning that the atomistic computational study for a whole vesicle in water is still intractable, though more coarse-grained techniques have already been employed to investigate in the systems of submicrometer sizes.42,43


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2.

Methodology

Simulated systems Nakamura and coworkers investigated systematically the behavior of 20 fullerene anions with different substituents, including alkyl groups ranging from methyl to icosanyl groups.33 They found the fullerene anions having a nonpolar/polar/nonpolar motif spontaneously form an interdigitated bilayer vesicle in water. Here, we chose two fullerene anions to represent the set investigated by Nakamura, namely PhK and C8K (octyl substituent) (see Figure 1). The composition of all investigated systems is shown in Table 1.

Figure 1: Optimized geometries of three potassium salts of fullerenes anions at level ωB97XD/6-31G(d) in different representations and perspectives. The three belong to the C5 symmetry group. Potassium cation is showed in gold.

# of fullerenic # K Ions # water molecules Total # of atoms species PhKmonolayer 128 (115) 128 32913 113587 PhKbilayer 128 (115) 128 33060 114028 C8K 128 (235) 128 50319 181165 Table 1: Composition of each membrane investigated here. The number in parentheses refers to the number of atoms in each fullerene anion. The total number of atoms in the last column includes all ions in the system, which was necessary to compensate the net charge of the membrane. System



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Experimental studies suggest that PhK membrane can be organized in two different configurations: monolayer or bilayer. Therefore, in this study we investigate these two possible formations for this type of membrane and check which one is best suited to represent the surface of a vesicle fullerenes.

Interaction potential models A key aspect of the modeling of a new material is the use of appropriate force field, which is crucial to obtain physically meaningful results. In this regard we propose here a carefully elaborated model based on the CHARMM36 force field44 with partial charges obtained quantum mechanically. The CHARMM36 force field was chosen to describe excellently the lipid membranes properties,45-47 which also has long alkyl hydrophobic chains and polar and/or charged groups. We note here that unlike what occurs to lipid membranes where long apolar tails are well compacted and practically define the structural order of the membrane, here the tails are relatively shorter and separated from each other (as can be seen in Figure 1) and their packaging, although important has only secondary role in stabilization of the fullerene membranes. The most important role is played by fullerenic heads, which have a high cohesive energy. Therefore the van der Waals parameters used for the carbon cage description taken from a prior model for the interaction between fullerenes and has already been successfully tested on various media such as water,

26,48

organic solvents,49,50; ionic liquids51,52 and supercritical

liquids.48 Electronic structure description of each fullerene anion was carried out using omega ωB97XD53 hybrid density functional theory (DFT) functional. This functional, allegedly, exhibits improved performance for electronic energy levels, non-covalent interactions (importantly) and thermochemistry. Therefore, ωB97XD was preferred over more traditional 6 ACS Paragon Plus Environment

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functionals. The wave function was expanded using the gaussian basis functions provided in the 6-31G(d) basis set. Additionally, the polarization and diffuse functions have been centered on each heavy atom to provide an improved description of the ions containing high-energy valence electrons (as opposed to neutral molecules). The number of basis functions per system varied with respect to the total number of electrons. No pseudopotentials were used for core electrons. The selected basis set is considered to provide a trustworthy approximation of the real wave function when applied to carbon nanostructures.15,54 Hence the ChelpG scheme55 with a default grid size in Gaussian 0956 was employed to perform a charge assignment for the fullerene anions. Finally, to maintain compatibility with the CHARMM force field, the TIP3P potential was used for the water molecule.57 This procedure for the generation of the potential molecular model has proven effective in describing the properties of different molecular systems both as hydrophilic hydrophobic nature.3,26,58

Computational details The pre-assembled systems were equilibrated for 10 ns and for the production stage we have performed a sampling for 100 ns, both in the NPT ensemble with periodic boundary condition employing the minimum image convention. Properties were calculated from simulations considering a time-step of 2 fs with coordinates collected every 20 ps, which gives a total of 5000 frames for statistical analysis. The system was kept at the appropriate temperature and pressure via velocity rescaling59 and semiisotropic ParrinelloRahman60 schemes, with coupling constants of 0.1 and 2.0 ps, respectively. All bond lengths were constrained via the LINCS algorithm.61 A cutoff distance of 1.0 nm for LJ interaction was employed, whereas the Coulomb interactions were treated by using the PME algorithm.62 All molecular dynamics simulations have been performed with the GROMACS 4.6 program.63,64



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Image rendering and visual analysis were performed with the VMD.65 Thickness maps were calculated using GridMat66 and plotted using Gnuplot.67

3.

Results and discussions

Vesicle and membrane formation is a non-equilibrium process that involves structural changes towards the equilibrium state; the latter is achieved when the free energy minimum is found by the self-assembling system.42,43,68,69 The structural details of the self-assembly process are crucial to elucidate experimental and computational issues, such as driving forces for self-assembly, the relationship between the fullerene anions and the properties of the vesicles. The forces that promote self-organization of fullerene based membranes are of hydrophobic nature, as occurs for lipids, detergents and polymers. The difference however is in strength. Whereas the interaction between hydrocarbon chains is relatively weak, the cohesive forces between fullerene molecules are extremely high keeping its carbon cage stick together very tightly.70 The time of the membrane self-assembly of the membrane from the fullerene anions aqueous solution is relatively long from the computational point of view. To circumvent the problem related to sampling, we started from pre-assembled configurations for structures inspired on experimental structural data available. The starting energy-minimized (steepest descent plus short run NPT) configurations for the investigated systems are presented ate Figure 2.


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Figure 2: Top and front view of the starting energy-minimized (steepest descent plus short run NPT) configurations for the investigated systems. Note that the boxes are relatively large to ensure that the ions stay sufficiently dispersed. Potassium cation is showed in gold. For clarity, hydrogen atoms are omitted.

Figure 3 shows the equilibrated configuration after 100ns simulation for each of the membranes investigated. It is possible to observe that the potassium ions adsorb on the membrane surface despite having started the trajectory fully hydrated. Furthermore, it is possible to visually distinguish certain structural characteristics of each membrane such as greater organization and packing of the PhK monolayer and the irregularities of the C8K bilayer.



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Figure 3: Equilibrated configuration of each investigated system. The PhK membrane was found stable in two possible morphological conformations, monolayer and bilayer, while C8K membrane was stable only in bilayer configurations. Potassium cation is showed in gold. For clarity hydrogen are omitted and only a narrow slice of water is depicted.

Planar (lateral plane) radial distributions of the centers of mass of the fullerene anions are presented in Figure 4. These distributions provide a description idea of the degree of ordering in terms of the probability of finding fullerene anions neighbors from a reference fullerene anion. As can be seen, for all membranes there is a structural order at long distances (> 4.5 nm) that extends beyond the dimensions of the simulation box. Both PhK membranes are highly ordered, in particular, their monolayer implementations. We can observe that their peaks are repetitive and well defined. This membrane, therefore, behaves like a solid wall between two liquid media. For C8K membrane, we observed similar structural pattern, with organization and periodicity that extends over long distances. The heights of the peaks are lower though.


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Figure 4: Planar radial distribution functions (RDFs) calculated between the centers-of-mass of the fullerene anions. RDFs suggest solid-like structures.

The average mass distribution across the simulation box contains important information on the membrane structure and also on the interfacial distribution of the aqueous solution on its surface. The mass density profiles for the PhK membranes along the membrane normal axis are shown in Figure 5 (left). We see that PhK monolayer contains no water inside. Furthermore, all potassium cations are adsorbed at the polar moiety of the monolayer. Here it is important to note that the zeta potentials for these systems indicate that the ions are actually dispersed.33 However, we observed that, even starting from an initial configuration in which the ions were fully hydrated and placed far from the surface of the membrane. 11 ACS Paragon Plus Environment


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However, within a few nanoseconds of dynamics, they formed ionic pairs with the fullerene anions. The peak corresponding to the fullerene anions is practically symmetrical and its width is about 1.3 nm.

Figure 5: (Left), mass density distribution (kg m−3) along the z direction (normal) computed for the components of the PhK membrane at two possible morphological conformations, monolayer and bilayer. Blue, green and red colors stand for fullerene anions, water and potassium, respectively. (Right) Membrane thickness is presented as a function of two12 ACS Paragon Plus Environment

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dimensional position along the PhK membrane. Color bar represents the thickness from 0.5 nm (blue) to 2.0 nm (red).

For the bilayer, we observed a broader peak for the fullerene (~2.0nm), as expected. This makes it possible to observe a larger amount of water at the membrane surface. Unlike what occurs for the monolayer, where the fullerenes are tightly packed, at the bilayer a certain rotational mobility is allowed and thus the fullerene anions can be re-oriented and foster interactions among the aromatic rings and the carbon cage of the adjacent anions. In this case, the potassium cations, despite being paired with their respective anions, are no longer distributed evenly over the membrane surface. The distribution of mass in the C8K membrane is also highly symmetric and its width is approximately 2.6 nm. Although there is no water inside the membrane, it is possible to find a volume of water in the grooves formed between fullerene anions. As in the case of bilayer, PhK ions are dispersed over the surface and the reorientation of fullerene anions are even more pronounced.

Membranes investigated here feature local inhomogeneities. Therefore, we employed a gridbased method to determine the variations of membrane thickness.66 In practice, the bidimensional grid of 20×20 points was created over the membrane and for each fullerene anion was assigned the number of grid points. The grid points in the xy-plane form polygons corresponding to a 1:1 mapping, where each polygon represents a specific anion. Twodimensional maps shown at right of Figure 5 allow an analysis of the membrane thickness variation along its extension. From these maps, it is possible to visualize both the membrane average thickness as the pattern of distribution of fullerene anions according to the regions of maximum and minimum thickness. In the case of bilayer, for example, the minimum 13 ACS Paragon Plus Environment


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thickness regions corresponding to groove at the membrane surface that can accommodate both the potassium ions as certain amount of water. For C8K membrane we observed pattern and average thickness similar to that obtained for PhK bilayer, with extensive inhomogeneity. It is interesting to note that the octyl aliphatic chains contribute to increasing membrane thickness, on average, only by 0.6 nm.

Some properties of these membranes, averaged over 100ns, are shown in Table 1. The thickness, as we have seen, ranges from 1.29 to 2.62 nm. Both values are much lower than those found for conventional lipid membranes, which are of the order of 3.5-4.0 nm58 (SI from that reference presents some data for lipid bilayers for comparison). The area per fullerene was found to be 0.95 and 0.66 nm2 for PhK membrane in the monolayer and bilayer conformations respectively. This last value is consistent with the value of 0.59 nm2, inferred by Nakamura et. al.33 For C8K membrane the estimated value for the area was 0.93 nm2. Although the C8K membrane also exists in a bilayer conformation, its value is greater than the value for PhK bilayer. This is due to octyl aliphatic chains that interact expanding the total area of the membrane.

(nm) PhKmonolayer PhKbilayer C8K

1.29 2.07 2.62

(nm2) 0.95 0.66 0.93

(kJ mol-1)

(kJ mol-1)

(µm2 s-1)

-3 -13 58

-399 -406 -639

0.2 0.4 1.4

Table 2: Properties of the fullerene anions based membranes. and are the area per anion and thickness of the membrane, respectively.

is the lateral diffusion coefficient for the anion motion along the membrane plane. and

are the Coulomb and LJ

contributions to non-bonded interaction potential energy between anions, per anion. 14 ACS Paragon Plus Environment

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The stability of these membranes can be partially estimated by the energy of interaction between the fullerene anions. The interaction total energy was calculated and decomposed into electrostatics and van der Waals components. Overall, we see that the stability of the membranes is governed by van der Waals interactions, whose interaction component to from about -400 t -640 kJ mol-1 per fullerene anion. This energy is very large, making the electrostatic component (ranging from -13 to -58 kJ mol-1) negligible. For a comparison, these energies for the lipid POPC membranes are -209 and -4 kJ mol-1, respectively. The lateral diffusion coefficient of fullerenes in this membrane is an order of magnitude smaller than that found for the lipid membranes. The diffusion occurs at a rate of 0.2 to 1.4 µm2s-1, corroborating the high structural order observed for these membranes. This data (the energetics and diffusion) are further evidence of how the fullerene-based membranes are more robust than lipid membranes.

4.

Conclusions

This study sheds light on the structure and stability of fullerene-based membranes at atomistic resolution. In agreement with recent experiments on the characterization of the self-assembled fullerene anions vesicles, our simulations show that such membranes are indeed very robust and stable. Membranes PhK proved very stable and compact, considering the experimental evidence of the bilayer PhK is an adequate model to represent the surface of the PhK vesicle with favorable energetics, although an analysis of entropy component of the aggregation free energy should still be taken into consideration for a more accurate conclusion.



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The development of applications of fullerene-based nanoscale vesicles is promoted by an accurate description of their organization and interaction with the aqueous environment. The rigidity of these membranes makes them potentially useful for certain applications while hinders possible applications in other areas. An important area for application where it is desirable that such membranes were looser is the transport of substances. In this case the study of the interaction of these membranes with other systems such as surfactants, detergents, and lipid probes become desirable. This work opens new possibilities to investigate at the molecular level the behavior of these membranes in interaction with different media or systems.

Acknowledgment This work has been partially supported by the Brazilian agencies FAPESP and CNPq.

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