1 Calculations on Solvents and Co-Solvents of Single-Wall Carbon Nanotubes: Cyclopyranoses

1 Calculations on solvents and co-solvents of single-wall carbon nanotubes: Cyclopyranoses Francisco Torrens Institut Universitari de Ciència Molecular, Universitat de València, Dr. Moliner 50, E-46100 Burjassot (València), Spain, Tel.: +34.963.543.182, Fax: +34.963.543.156, E-mail: [email protected] Abstract 1-Octanol–, cyclohexane– and chloroform–water partition coefficients (Po, Pch and Pcf) allow calculating molecular lipophilicity patterns, which show that, for a given atom, normalized logPo–ch–cf are sensitive to the presence in the molecule of other atoms–groups, e.g., C70, where logPa–c atomic contributions are greater than logPd–e are. CDHI does not differentiate non-equivalent atoms. (10,10) Single-wall carbon nanotube (SWNT), the most favourite SWNT, presents consistency between a relatively small aqueous solubility and great Po–ch–cf. SWNT solubility is studied in various solvents, finding a class of non-hydrogen-bonding Lewis bases with good solubility. Solvents grouped in three classes. SWNTs in some organic solvents are positively charged, while in water–Triton X are negative. Keywords: Solvation parameter model; Partition coefficient; Electron affinity; Molecular lipophilicity pattern; Hydrophobicity pattern 1. Introduction Single-wall carbon nanotubes (SWNT) have not yet been fully integrated into biosystems, because of the difficulty in rendering them soluble in aqueous solutions. One major problem is the insolubility of SWNTs in all solvents. Although progress has been made on the open-end [1–3] and side-wall [4–6] modifications of SWNTs using covalent chemistry, it has so far not been possible to establish a means of handling SWNTs without risking their partial destruction. Covalent–ionic 2 modifications resulted in a limited success [7]. Often, the band electronic structure of SWNTs was disrupted by these modifications, and in some cases the structure of the individual SWNT was damaged [8]. It seems attractive to explore supramolecular approaches, since (1) they will not disrupt the extended -networks of SWNTs, and (2) they could open the possibilities of being able to organize SWNTs into ordered networks. Progress was made in the use of synthetic polymers to render SWNTs soluble in organic solvents. While some water-soluble polymers and surfactants [9] can bring aqueous solubilities to SWNTs, they may not be biocompatible. It was not possible to extract C60–70 from a solution in toluene to water [10]. However, it was also not possible to extract C60–70 from a dispersion in water to toluene. C60, dissolved in water via complexation with cyclodextrin8 (CD8), was extracted to toluene. C60 incorporated into artificial lipid membranes was not extracted to toluene, but the extraction became possible once the vesicle was destructed adding KCl. Addition of KCl was also required to extract poly(vinylpyrrolidone)-solubilized C60 to toluene. When NaCl was added to the dispersion, C60–70 were extracted into toluene and the toluene phase exhibited faint magenta or orange, characteristic colours for a solution of C60 or C70 in toluene, respectively. It is interesting to explore the possibility of solubilizing SWNTs in aqueous solutions of starch [11]. CD6–10 are cyclic molecules consisting of 6–10, -(1 4)-linked D-glucopyranose (D-Glcp) residues. They are able to form inclusion complexes, even in aqueous solution, with guest molecules ranging in character from purely hydrophobic to purely hydrophilic, provided that the guest molecule be small enough to fit into the annular aperture of CDs [12]. CDs have been valuable model compounds in the study of starch complexes. CD8–9 dissolve fullerenes in water. SWNTs can be classified in three types, viz. zigzag (m = 0), armchair (n = m), and chiral (n,m). In earlier publications, periodic tables of fullerenes [13,14] and SWNTs [15,16] were discussed. A program based on the AQUAFAC model was applied to calculate the aqueous coefficients of SWNTs [17]. A molecular modelling comparative study of linear–cyclic D-Glcpn provided overall conformations, contact surfaces and cavity proportions [18–22]. In the present study, solvation and 3 partition properties of SWNTs are calculated. Section 2 presents the method. Section 3 discusses the results. Section 4 summarizes the conclusions. 2. Experimental The model is an extension to organic solvents [23–27] of the solvent-dependent conformational analysis program (SCAP), which is parametrized for 1-octanol–water solvent pair with solute molecules composed of H, C, N, O, F, S, Cl and Br, and containing a wide variety of functional groups [28]. From Gibbs free energies of solvation, and with equation o o RT ln P Gsolv water Gsolv 1- octanol (1) one can calculate the logarithm logP at a given T, which is taken as 298K. R is the gas constant, and Gsolvº(1-octanol) and Gsolvº(water) are the standard-state free energies of solvation of a solute considered in 1-octanol and water, respectively. For an organic solvent, the maximum number of solvent molecules allowed to fill the solvation sphere is related to the solvent molecular volume as n V log o log s ,o V nw Vs, w n n s ,s s o V s,o (2) where Vs is the solvent molecular volume, and the subscripts o, w and s stand for 1-octanol, water and a general organic solvent, respectively. The variation in the standard Gibbs free energy associated with the extraction of one solvent molecule out of the solvation sphere gsº is calculated using the generalized Born equation [29], 1 1 1 go g o s go o s s o 1 o (3) 1 s o 1 o where o and s are the relative dielectric permittivities. The radius of the solvation sphere is related to the solvent molecular volume as 1 3 V R R s,s v,s v,o V s, o (4) 4 Finally, the free volume available for a solvent molecule in the solvation sphere is related to the solvent molecular volume as V V V s,s f ,s f ,o V s,o (5) The only parameters needed are the relative permittivity and molecular volume Vs of the organic solvent. Vs values have been calculated with a new version of our program TOPO version 2004 [30], which includes an actualized database of van der Waals radii [31]. In the present work, 3 the following values have been used: = 9.862, 2.023 and 4.806 [32]; Vs = 155.0, 93.4 and 72.1Å , for 1-octanol, cyclohexane and chloroform (CHCl3), respectively. The hydrophobic moment calculation is based on the Eisenberg et al. formula [33]: 1 2 M 2 M 2 H hi cos i hi sin i i 1 i 1 (6) where the gyration angle i is the successive angle between an atom and the next, around the z axis. 3. Results and discussion The aqueous solubility of fullerenes C60–70–82, van der Waals dimer (C60)2 and C60H60 has been calculated with our program based on the AQUAFAC model [34]. C60-Ih is especially symmetric, with all atoms occupying equivalent sites in a truncated icosahedron configuration [35]. The molecular structure contains 12 pentagonal and 20 hexagonal rings. The pentagons sit as far as possible from each other, at the vertices of an icosahedron; they may be viewed as defects compared to the un-strained hexagons. Each atom is equivalent to every other atom, and all them occur at the vertex joining a pentagon and two hexagons [36]. C70-D5h is similar to C60, with the 10 extra atoms inserted in a band of hexagons around the middle of the truncated icosahedron, producing a prolate, ellipsoidal structure. A substructure of C70 (cf. figure 1a), where the five non-equivalent atoms are labelled a–e [37,38], shows that atoms a–d join one pentagon with two 5 hexagons while atom e joins three hexagons. On going from a to e the distance from the nearest pentagon increases. One would expect that H atoms introduced by chemical reduction of C 60 would lay in the outside of the cluster. The symmetric structure produced in this way was predicted to be highly strained. Some endohedral C60H60 isomers with one or more C–H bonds pointing inside the cavity were shown to be more stable than their all-out counterparts. The calculations refer to AM1 optimum number of inside H atoms and geometry, which has 10 endohedral H atoms [39]. The solvation descriptors for these fullerenes (cf. table 1) show that the negative Gibbs free energy -1 – Gsolv of hydration slightly increases from C60–82 from 16–21kJ·mol . However, – Gsolv in -1 1-octanol increases from C60–82 from 129–172kJ·mol . 1-Octanol–water partition coefficient Po increases by seven orders of magnitude with the number of atoms. The cyclohexane–water and chloroform–water partition coefficients show the same trend as Po. The results for (C60)2-C5h show a value of logPo 39, indicating that a negligible quantity remains in water. As (C60)2 is only stable in concentrated solutions, the calculation has been repeated imposing the condition that the aqueous phase must be entirely assigned to the monomer form. In this case the organic phase is additionally favoured by 2.7 log units. The effect is similar in the other organic solvents. The results for C60H60 show that no important effect on logP is expected related to the all-exo (Ih) or partially endo (C1) position of H atoms. Both SCAP logP indicate that all C60H60 would remain in the organic phase. Notice the sharp discrepancy in the orders of magnitude predicted by our program CDHI, which is based on a method developed by Kantola et al. [40], for 1-octanol–water (logPo ~ 3–4). CDHI results would indicate a preferential solubility in 1-octanol of only 103 times that in water, a prediction which seems unlikely for a system that can be thought as a fully saturated system of cyclic tertiary C atoms.

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