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:
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. The spurious results of CDHI illustrate well the danger of using parameter- fitted methods out of the range of molecules that were used in the fitting. Results for logPch–cf are of the same order of magnitude as reference calculations performed with a method by Leo and Hansch
[41]. The atomic partition of SCAP logP for fullerenes shows that the contributions of C70-a–c 6 atoms to normalized logPo–ch–cf are slightly greater than those of d–e are, what can be explained because the distances from the nearest pentagon vary gradually from a to e. By contrast, CDHI does not differentiate atoms a–e. The molecular lipophilicity pattern (MLP) in figure 1b is the
10 normalized logPo map of C70. Lipophilicity monotonically decreases as the distance from the nearest pentagon d increases.
Figure 2 illustrates the variation of normalized logPo vs. the distance from the nearest pentagon d for C70. Normalized logPo correlates quadratically with d:
2 log Po 23.7 0.153d 0.0643d r 0.997 (7)
The aqueous solubility Sw of SWNTs, calculated with AQUAFAC (cf. table 2), shows that
Sw monotonically decreases with n and m. All the values of logSw < –3, meaning that less than
0.1% of SWNT is in solution. Even all the minus logSw values are greater than the Avogadro exponent is, meaning that no solute molecule would be present in solution to allow experiments.
However, all the logSw figures are kept with the only purpose of comparison along the series. The results are consistent with the fact that SWNTs are insoluble in water. The solubility of SWNTs is hindered because SWNTs aggregate in bundles due to large van der Waals interactions. The
2 2 1/2 variation of logSw(n,0) with (n +nm+m ) turn out to be
1 2 log S 4.76 3.53 n2 nm m 2 w n,0 N 10 r 0.999994 s 0.038 F 707859.2 (8)
2 2 1/2 The variation of logSw(n,n) with (n +nm+m ) turn out to be
1 2 log S 5.31 4.09 n2 nm m2 w n,n N 6 r 0.999998 s 0.032 F 836663.0 (9)
The absolute slope of (n,0) is smaller than that of (n,n) is. LogSw(n,0) results greater than logSw(n,n) does, especially for thicker SWNTs. LogSw(10,10) is the smallest for all SWNTs.
The free energies of solvation and partition coefficients, calculated with SCAP (cf. table 2), show that the 1-octanol–water partition coefficient Po increases with n and m. All values of logPo > 3, meaning that more than 99.9% of the solute is in the organic phase. Even all logPo values 7 are greater than the Avogadro exponent is. LogPo results are of the same order of magnitude as reference calculations performed with CDHI. The error of logPo is 30%. The variation of logPo(n,0) with (n2+nm+m2)1/2 turn out to be
1 2 log P 3.17 3.72 n2 nm m2 o n,0 N 10 r 0.9998 s 0.257 F 17257.3 (10)
2 2 1/2 The variation of logPo(n,n) with (n +nm+m ) turn out to be
1 2 log P 4.27 4.28 n2 nm m2 o n,n N 6 r 0.9996 s 0.413 F 5656.5 (11)
The slope of (n,0) is slightly smaller than that of (n,n) is. LogPo(n,0) results smaller than logPo(n,n) does, especially for thicker SWNTs. Pch–cf increase with n and m. Most logP values are greater than the Avogadro exponent is. LogPch–cf results are of the same order of magnitude as reference calculations performed with the method by Leo and Hansch. LogPch–cf error is –28%. The variation
2 2 1/2 of logPch(n,0) vs. (n +nm+m ) turn out to be
1 2 log P 1.08 1.69 n2 nm m2 ch n, 0 N 10 r 0.99992 s 0.068 F 50691.1 (12)
2 2 1/2 The variation of logPch(n,n) with (n +nm+m ) turn out to be
1 2 log P 1.35 1.93 n 2 nm m2 ch n, n N 6 r 0.99993 s 0.082 F 29068.9 (13)
2 2 1/2 The variation of logPcf(n,0) with (n +nm+m ) turn out to be
1 2 log P 1.36 2.80 n2 nm m2 cf n,0 N 10 r 0.99995 s 0.089 F 80850.0 (14)
2 2 1/2 The variation of logPcf(n,n) with (n +nm+m ) turn out to be
1 2 log P 1.87 3.21 n 2 nm m2 cf n,n N 6 r 0.99994 s 0.128 F 33121.7 (15)
LogPo–ch–cf(10,10) are the greatest for all SWNTs. The partition of SCAP logP for (17,0) and (10,10) shows that the contribution of the trivalent atoms a is smaller that that of the divalent atoms b is.
However, CDHI does not differentiate atoms a–b. Figure 3 illustrates MLPs of (17,0)–(10,10).
Divalent atoms b show the greatest lipophilicity. 8 Although the solubility in organic solvents is predicted greater than in water (logP >> 1), absolute solubility in organic solvents is estimated extremely small [e.g. in CHCl3,
53.6 –76.1 –22.5 -1 Scf(10,10) Pcf·Sw = 10 ·10 = 10 mol·L ], which is supported by the fact that there are few solvents for SWNTs. Toluene, ethanol, isopropyl alcohol and acetone do not dissolve SWNTs.
However, CHCl3 and most other chlorinated solvents, e.g., 1,2-dichlorobenzene (DCB), suspend
SWNTs. Solvochromic parameters ( , and *), relative permittivity , AM1 ionization potential
I, electron affinity (EA), TOPO molecular volume V and suggested charge transfer are listed for different solvents in table 3. The solvents can be divided into three groups. Class 1 consists of the best solvents, N-methylpyrrolidone (NMP), N,N-dimethylformamide (DMF), hexamethylphosphoramide (HMPA), cyclopentanone, tetramethylene sulfoxide and -caprolactone, which readily disperse SWNTs, forming light-grey, slightly scattering liquid phases [42]. These solvents are characterized by high electron-pair donicity [43], negligible H-bond donation parameter [44], and high solvochromic parameter * [45]. Lewis basicity without H-donors is key to good solvation of SWNTs. As 33 and EA –29kJ·mol-1, it is suggested that SWNTs in these solvents have a partial negative charge due to the high . Class 2 contains the good solvents, toluene, 1,2-dimethylbenzene (DMB), CS2, 1-methylnaphthalene, iodobenzene, CHCl3, bromobenzene and 1,2-DCB, known to be exceptional for C60–70 [46]. They show 0, high
* , 10 and EA >> 0. CHCl3 and 1,2-DCB have similar –EAs and suspend SWNTs. Other solvents that are co-miscible with 1,2-DCB but that are a poor –EA match, e.g., n-hexane, do not suspend SWNTs. The results are supported by electroplating experiments that showed that SWNTs in 1,2-DCB and 1,2-DCB–CHCl3 are positively charged [47]. SWNTs are not suspended in
1,2-DCB–n-hexane, which is attributed to EA1,2-DCB >> 0 and EAn-hexane < 0. It is suggested that
SWNTs in CHCl3 and other chlorinated solvents with EA >> 0 are positively charged. Controllable aggregation of SWNTs is achieved diluting SWNT–1,2-DCB with CHCl3. Greater aggregation causes complete precipitation of SWNTs. When SWNTs are suspended using non-ionic surfactants, colloids of negatively charged SWNTs are produced. Class 3 entails the bad solvents, n-hexane, 17 Table 3. Solvochromic parameters, relative permittivity, ionization potential, electron affinity, volume and charge transfer for solvents.
Solvent/suspender/co-solvent a b *c d Ie EAf Vg Charge transfer cyclopentanone 0.000 0.537 0.756 16.30h 1041.5 -24.2 80.8 SWNT–/solvent+ hexamethylphosphoramide (HMPA) 0.000 0.990 0.871 29.00 595.7 -44.7 162.9 SWNT–/solvent+ N-methylpyrrolidone (NMP) 0.000 0.754 0.921 32.58 820.8 -29.2 92.6 SWNT–/solvent+ N,N-dimethylformamide (DMF) 0.000 0.710 0.875 37.06 847.0 -44.2 70.9 SWNT–/solvent+ tetramethylene sulfoxide 0.000 0.800 1.000 42.84 832.6 6.6 88.3 SWNT–/solvent+ -caprolactone – – – – – -12.3 103.1 SWNT–/solvent+ mean 0.000 0.758 0.885 31.56 827.5 -24.7 99.8 SWNT–/solvent+ toluene 0.000 0.110 0.535 2.379i 843.0 2.1 95.0 SWNT+/solvent– 1,2-dimethylbenzene (DMB) 0.000 0.120 0.510 2.568 – 6.1 110.4 SWNT+/solvent– + – carbon disulphide (CS2) 0.000 0.070 0.514 2.641 864.4 129.2 55.5 SWNT /solvent 1-methylnaphthalene 0.000 0.100 0.800 2.710 778.0 73.5 146.9 SWNT+/solvent– iodobenzene 0.000 0.050 0.810 4.630 – 63.8 105.9 SWNT+/solvent– + – chloroform (CHCl3) 0.200 0.100 0.760 4.806 1084.8 108.1 72.1 SWNT /solvent bromobenzene 0.000 0.060 0.794 5.400i – 43.4 98.1 SWNT+/solvent– 1,2-dichlorobenzene (DCB) 0.000 0.030 0.800 9.930i 854.9k 71.5 110.3 SWNT+/solvent– mean 0.025 0.080 0.690 4.383 885.0 62.2 99.3 SWNT+/solvent– n-hexane 0.000 0.000 -0.081 1.890 1002.7 -290.9 103.5 SWNT–/solvent+ ethyl isothiocyanate – – – 19.50j 814.6 101.7 80.1 SWNT+/solvent– acrylonitrile – 0.250 0.870 33.01 991.4 44.4 57.1 SWNT+/solvent– dimethyl sulfoxide (DMSO) 0.000 0.752 1.000 46.71 832.8 17.8 66.8 SWNT+/solvent– water 1.017 0.470 1.090 80.37 1150.2 -332.3 23.8 SWNT–/solvent+ 4-chloroanisole – – – – 800.5 4.3 118.1 SWNT+/solvent– mean 0.339 0.368 0.720 36.30 932.0 -75.8 74.9 SWNT+/solvent– 1,2,3,4-tetramethylbenzene – 0.140 0.450 2.59 822.0 9.9 141.0 SWNT+/solvent– 1,2,3,5-tetramethylbenzene – 0.140 0.450 – 794.3 12.1 141.2 SWNT+/solvent– 1,2,4,5-tetramethylbenzene 0.000 0.150 0.430 – 818.2k – 141.3 SWNT+/solvent– mean 0.000 0.143 0.443 2.59 811.5 11.0 141.2 SWNT+/solvent– Table 3 (…/…) 18 Table 3 (…/…)
Solvent/suspender/co-solvent a b *c d Ie EAf Vg Charge transfer – + Triton X-100 – – – – – – 597.7 SWNT /H2O–co-solv – + 12-crown-4 ether – – – – 896.9 -70.6 155.6 SWNT /H2O–co-solv – + 15-crown-5 ether – – – – 879.6 -129.7 194.3 SWNT /H2O–co-solv – + 18-crown-6 ether – – – – 870.0 -81.1 232.9 SWNT /H2O–co-solv – + 21-crown-7 ether – – – – 830.0 -80.5 271.7 SWNT /H2O–co-solv – + 24-crown-8 ether – – – – – – 310.4 SWNT /H2O–co-solv – + 27-crown-9 ether – – – – – – 349.3 SWNT /H2O–co-solv – + 30-crown-10 ether – – – – – – 388.1 SWNT /H2O–co-solv – + 14-crown-4 ether – – – – 852.3 -59.2 186.4 SWNT /H2O–co-solv – + mean – – – – 865.8 -84.2 298.5 SWNT /H2O–co-solv – + ethylenediaminetetraacetic acid (EDTA) – – – – 795.4 28.3 239.2 SWNT /H2O–co-solv – + sodium dodecyl sulphate (SDS) – – – – – 370.5 267.4 SWNT /H2O–co-solv – + mean – – – – 795.4 199.4 253.3 SWNT /H2O–co-solv a Hydrogen-bond donation acidity. b Hydrogen-bond acceptance basicity. c Solvochromic parameter. d Relative permittivity at 20ºC. e Ionization potential (kJ·mol-1) calculated with MOPAC-AM1. f Electron affinity (kJ·mol-1) calculated with MOPAC-AM1. g Molecular volume (Å3). h At –51ºC. i At 25ºC. j At 21ºC. k Calculated with MOPAC-MNDO-d. 9 ethyl isothiocyanate, acrylonitrile, dimethyl sulfoxide (DMSO), water and 4-chloroanisole, with a poor –EA match with either NMP or 1,2-DCB. It is suggested that in these solvents, SWNTs have a partial positive charge provided EA >> 0 and negative charge otherwise, which was shown by electrical resistance for SWNT–water [48]. Although a Lewis basicity without H-donors was suggested experimentally to be an important condition for a good solvent, this may be a necessary but not sufficient condition since DMSO, a bad solvent, is an exception [49]. Triton X-100
[C(CH3)3–CH2–C(CH3)2–C6H4–(O–CH2–CH2)n–OH n = 10 (average)] has been included for comparison. Triton X forms colloids of negatively charged SWNTs in water. Its polyether
(O–CH2–CH2)n moiety suggests to study 12–30-membered cyclic crown ethers as 3n-crown-n cyclo(O–CH2–CH2)n. EAcrown ether > EAwater suggests the formation of colloids of negatively charged
SWNTs in water.
4. Conclusions
The following conclusions can be made from this study.
1. SCAP MLPs 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.
2. (10,10), the most favourite SWNT, presents consistency between a relatively small Sw and great Po–ch–cf.
3. 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.
Acknowledgements
The author acknowledges Dr. N. Mizoguchi for providing with calculation results before publication on the optimum number of inside hydrogen atoms and geometry of C60H60, and 10 financial support from the Spanish MCT (Plan Nacional I+D+I, Project No.
BQU2001-2935-C02-01) and Generalitat Valenciana (DGEUI INF01-051 and INFRA03-047, and
OCYT GRUPOS03-173).
References
[1] Chen J, Hamon M A, Hu H, Chen Y, Rao A M, Eklund PC and Haddon RC 1998 Science
282 95-8.
[2] Hamon M A, Chen J, Hu H, Chen Y, Itkis M E, Rao A M, Eklund P C and Haddon R C 1999
Adv. Mater. (Weinheim, Ger.) 11 834-40.
[3] Riggs J E, Guo Z, Carroll D L and Sun Y-P 2000 J. Am. Chem. Soc. 122 5879-80.
[4] Mickelson E T, Huffman C B, Rinzler A G, Smalley R E, Hauge R H and Margrave J L 1998
Chem. Phys. Lett. 296 188-94.
[5] Mickelson E T, Chiang I W, Zimmerman J L, Boul P J, Lozano J, Liu J, Smalley R E, Hauge
R H and Margrave J L 1999 J. Phys. Chem. B 103 4318-22.
[6] Boul P J, Liu J, Mickelson E T, Huffman C B, Ericson L M, Chiang I W, Smith K A, Colbert
D T, Hauge R H, Margrave J L and Smalley R E 1999 Chem. Phys. Lett. 310 367-72.
[7] McCarthy B, Coleman J N, Czerw R, Dalton A B, Carroll D L and Blau W J 2001 Synth. Met.
121 1225-6.
[8] Monthioux M, Smith B W, Burteaux B, Claye A, Fischer J E and Luzzi DE 2001 Carbon 39
1251-72.
[9] Duesberg G S, Muster J, Krstic V, Burghard M and Roth S 1998 Appl. Phys. A 67 117-9.
[10] Deguchi S, Alargova R G and Tsujii K 2001 Langmuir 17 6013-7.
[11] Thompson D B 2000 Carbohydr. Polym. 43 223-39.
[12] Wenzt G 1994 Angew. Chem., Int. Ed. Engl. 33 803-22.
[13] Torrens F 2004 J. Chem. Inf. Comput. Sci. 44 60-7.
[14] Torrens F in press J. Mol. Struct. (Theochem). 11 [15] Torrens F 2004 Internet Electron. J. Mol. Des. 3 514-27.
[16] Torrens F in press Internet Electron. J. Mol. Des.
[17] Torrens F in press Int. J. Quantum Chem.
[18] Torrens F in press Mol. Simul.
[19] Torrens F submitted for publication J. Chromatogr. A.
[20] Torrens F submitted for publication J. Mol. Struct. (Theochem).
[21] Torrens F submitted for publication Nanotechnology.
[22] Torrens F submitted for publication Probl. Nonlin. Anal. Eng. Syst.
[23] Torrens F, Sánchez-Marín J and Nebot-Gil I 1998 J. Chromatogr. A 827 345-58.
[24] Torrens F 2000 J. Chem. Inf. Comput Sci. 40 236-40.
[25] Torrens F 2001 J. Chromatogr. A 908 215-21.
[26] Torrens F 2001 Chromatographia 53 S199-203.
[27] Torrens F 2002 Polyhedron 21 1357-61.
[28] Hopfinger A J and Battershell R D 1976 J. Med. Chem. 19 569-73.
[29] Born M 1920 Z. Phys. 1 45-8.
[30] Torrens F, Ortí E and Sánchez-Marín J 1991 J. Chim. Phys. Phys.-Chim. Biol. 88 2435-41.
[31] Flower D R 1997 J. Mol. Graphics Mod. 15 238-44.
[32] Maryott A A and Smith E R 1951 Table of Dielectric Constants of Pure Liquids, National
Bureau of Standards Circular No. 514 (Washington: United States Department of Commerce-
National Bureau of Standards).
[33] Eisenberg D, Schwarz E, Komaromy M and Wall R 1984 J. Mol. Biol. 179 125-42.
[34] Torrens F 1999 Toxicol. Environ. Chem. 73 177-89.
[35] Kroto H W, Heath J R, O’Brien S C, Curl R F and Smalley R E 1985 Nature (London) 318
162-3.
[36] Ternansky R J, Balogh D W and Paquette L A 1982 J. Am. Chem. Soc. 104 4503-4. 12 [37] Taylor R, Hare J P, Abdul-Sada A K and Kroto H W 1990 J. Chem. Soc., Chem. Commun.
1423-5.
[38] Heath J R, O’Brien S C, Zhang Q, Liu Y, Curl R F, Kroto H W, Tittel F K and Smalley R E
1985 J. Am. Chem. Soc. 107 7779-80.
[39] Mizoguchi N 1997, VII International Conference on Mathematical Chemistry, Girona.
[40] Kantola A, Villar H O and Loew G H 1991, J. Comput. Chem. 12 681-9.
[41] Leo A and Hansch C 1971 J. Org. Chem. 36 1539-44.
[42] Ausman K D, Piner R, Lourie O, Ruoff R S and Korobov M 2000, J. Phys. Chem. B 104
8911-5.
[43] Kamlet M J and Taft R W 1976, J. Am. Chem. Soc. 98 377-83.
[44] Taft R W and Kamlet M J 1976 J. Am. Chem. Soc. 98 2886-94.
[45] Kamlet M J, Abboud J L and Taft R W 1977 J. Am. Chem. Soc. 99 6027-38.
[46] Korobov M V, Mirakyan A L, Avramenko N V, Olofsson G, Smith A L and Ruoff R S 1999
J. Phys. Chem. B 103 1339-46.
[47] Diehl M R, Yaliraki S N, Beckman R A, Barahona M and Heath J R 2002 Angew. Chem., Int.
Ed. Engl. 41 353-6.
[48] Zahab A, Spina L, Poncharal P and Marlière C 2000 Phys. Rev. B 62 10000-3.
[49] Ausman K D, Piner R, Lourie O, Ruoff R S and Korobov M 2000 J. Phys. Chem. B 104
8911-5.
Figure captions
Figure 1. Flat projection (fragment) of C70-D5h: (a) the five non-equivalent atom types (C5 axis is through the centre of the top and bottom pentagons), and (b) molecular lipophilicity pattern.
Figure 2. Normalized logPo vs. distance to the nearest pentagon for C70-D5h.
Figure 3. (17,0) Nanotube: (a) projection (fragment) showing non-equivalent atoms, and (b) molecular lipophilicity pattern (MLP); (10,10): (c) projection and (d) MLP. 13
a 237
b a a b 235 237 237 235 c a a c 232 237 237 232
c b b c 232 235 235 232
c c 232 232
d d d d 226 226 226 226 e e e e 221 221 221 221
d d d d 226 226 226 226
c c 232 232
c b b c 232 235 235 232 c a a c 232 237 237 232
b a a b 235 237 237 235
a 237
23.5
23 o logP
22.5
22 0 1 2 3 4
Distance from the pentagon ring 14 b b b b a a a a a
a a a a a a a a a a
a a a a a a a a a a
a a a a a b b b b
63 63 63 63 62 62 62 62 62
62 62 62 62 62 62 62 62 62 62
62 62 62 62 62 62 62 62 62 62
62 62 62 62 62 63 63 63 63
b b b b b b
a a a a a a a
a a a a a a
a a a a a a a
a a a a a a
a a a a a a a
b b b b b b
74 74 74 74 74 74
72 72 72 72 72 72 72
72 72 72 72 72 72
72 72 72 72 72 72 72
72 72 72 72 72 72
72 72 72 72 72 72 72
74 74 74 74 74 74