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In this Letter we predict the out-of-plane Young’s modulus (perpendicular to the basal plane) and the out-of-plane shear modulus of double-layer graphene using density functional theory calculations with periodic boundary conditions using the G aussian 09 program package. These values are discussed in the context of the corresponding values of graphite.

In this study, the Young’s and flexural moduli of single- and double-layer graphene have been theoretically investigated using periodic boundary condition (PBC) density functional theory (DFT) with the PBE, HSE06H, and M06L functionals in conjunction with the 6-31G* and the 3-21G basis sets. The unit-cell size and shape dependence as well as the directional dependencies of the mechanical properties have also been investigated. Additionally, the calculated stretching and flexural strain–stress curves are reported. Finally, finite-element simulations have been performed so as to find a homogeneous equivalent isotropic transverse material for single-layer graphene, in order to reproduce mechanical behavior in both tensile and bending sollicitations.

Besides chemical functionalisation, the use of surfactants can be applied to debundle and disperse carbon nanotubes before further application in polymer nanocomposites. In this work we present a theoretical analysis of the interaction between single-walled carbon nanotubes and sodium dodecyl sulfate as surfactant and/or polystyrene as polymer matrix using semi-empirical AM1 calculations. Results indicate that the use of short potassium sulfate-terminated polystyrene chains as an extra component can help to remove the surfactant from the nanotube surface within the matrix, resulting in improved electronic properties of the nanocomposite.

The delocalisation that occurs upon deprotonation of a series of hydrofullerenes and substituted hydrofullerenes is analysed. The charges and bond lengths of the acidic and basic forms of each system are considered. We find approximately one electron delocalising from the deprotonated C atom to the rest of the system on deprotonation. The softness of the cage and the bond alternation permit delocalisation of the resulting negative charge over the main part of the fullerene cage, following the pattern of conjugated bonds, showing a clear ‘delocalisation path’. The same paths were found for hydrofullerenes and substituted hydrofullerenes, so that the properties of different functional groups are seen not to influence the delocalisation pattern in a significant way. This delocalisation greatly stabilises the basic form and explains the high acidities of these hydrocarbon systems.The deprotonation energies for the two most stable C60H2 and the two most stable C70H2 isomers have been calculated at the ab initio HF/6-31G* level of theory. 5,6-C70H2 was found to be more acidic than 1,2-C60H2. This inversion as compared to 1H NMR predictions results from the difference in cage structure of C60 and C70. The delocalising charge reaches the equatorial band of six rings present in the C70 structure, giving rise to a better stabilisation of the basic form than for 1,2-C70H2.

Due to its unique mechanical properties, graphene can be applied for reinforcement in nanocomposites. We analyse the Young’s modulus of graphene at the semi-empirical PM6 level of theory. The internal forces are calculated and the Young’s modulus is predicted for a finite graphene sheet when external strain is applied on the system. These results are in a good agreement with theoretical and experimental results from the literature giving values of about 1 TPa for the Young’s modulus. Stress–strain curves are computed for elongation up to 20%. In addition, the influence of the presence of a single vacancy, as well as for oxygenation of a vacancy, on the mechanical properties of graphene has been analysed. Our results indicate that when applying the deformation locally onto the system, higher local stress can be induced, as confirmed by Finite Element Analysis. Also, the presence of structural defects in the system will stiffen the system upon low strain, but reduces the elastic limit from more than 20% strain for pristine graphene to less than 10% strain when defects are present.

Tuning the band gap of graphene nanoribbons by chemical edge functionalisation is a promising approach towards future electronic devices based on graphene. The band gap is closely related to the aromaticity distribution and therefore tailoring the aromaticity patterns is a rational way for controlling the band gap. In the present work, it is shown how the three distinct classes of aromaticity patterns already found for armchair graphene nanoribbons can be rationally tuned by chemical edge functionalisation to modify their electronic arrangement and band gap. The electronic structure and the aromaticity distribution are studied using DFT calculations and through a series of delocalisation and geometry analysis methods, like the six-centre index (SCI) and the mean bond length (MBL) geometry descriptor. Novel aromaticity patterns are found for fluorine and nitrogen functionalisation characterised as inverted incomplete-Clar, and broken-Kekulé classes, while oxygen and nitrogen functionalisation is found to cut and extend the aromatic system, respectively. All these different arrangements of aromatic rings along the structure of graphene nanoribbons are explained using Clar's sextet theory, and a mesomeric effect mechanism for fluorine and nitrogen. In all cases, the changes in the aromaticity patterns are related to changes in the band gap. The energy and stability of the different edge functionalised graphene nanoribbons are also studied. An overall picture of edge effects, aromaticity patterns, and band gap tuning is provided.

Despite its remarkable electronic properties, graphene is a semimetal, or zero-band-gap semiconductor, which limits its potential applications in electronics. Cutting graphene into nanoribbons is one of the most successful approaches to opening the band gap of graphene toward applications. However, whereas armchair graphene nanoribbons exhibit semiconducting behavior, zigzag-edged structures are still semimetals. In this work, we perform periodic density functional theory (DFT) calculations on the electronic structure, together with nonequilibrium Green’s function (NEGF) transport-property calculations, of different tailored-edge zigzag graphene nanoribbons. More precisely, we provide a complete description of the relation between band gap, transport properties, and aromaticity distribution along these materials, based on DFT results and Clar’s sextet theory. The edge design is also shown to be applicable for finite fragments of carbon nanotubes in which the electronic confinement is similar. This ansatz ...

Organic photovoltaics (OPVs) are considered a promising energy source for the future, owing to interesting properties such as easy processing and flexibility. Their main drawback however, is the low efficiencies that can be obtained so far. So far the highest OPV efficiencies have been found for so-called bulk-heterojunction (BHJ) solar cells, where the active layer is a bicontinuous composite of donor and acceptor phases. Due to their high electron affinity and ability to transport charge, fullerene derivatives are the most widespread type of acceptor. As a donor phase a conjugated, light-excitable polymer is required. In this study a poly(3-hexyl thiophene) (P3HT) and [6,6]-phenyl C61 - butyric acid methyl ester (PCBM) blend, the most widespread OPV system, is investigated by both experimental and theoretical means. An important technological challenge for BHJ OPV's is the morphology of the active layer. Due to the limited lifetime of generated excitons, a nm-size phase separated morphology is requiredfor efficient charge generation at the interface between donor and acceptor. A more crystalline material will also lead to more efficient charge transfer, and post-production annealing plays an important role in optimising these two factors. In this work, post production annealing is therefore studied using several fast-scanning calorimetry techniques, such as Rapid Heat-Cool Calorimetry (RHC) and Fast Scanning Differential Chip Calorimetry (FSDCC. By applying the Avrami model on the isothermal crystallisation of a P3HT/PCBM 1:1 blend, it is found that the crystallisation rate goes through 2 maxima, making it possible to improve the annealing procedure. Next to the morphology of the active layer, the mechanism of charge transfer and exciton dissociation at the donor/acceptor interface is just as important. This charge transfer is modelled using ab initio DFT calculations under periodic boundary conditions (PBC).

In this paper, a combined experimental and theoretical study was performed on the P3HT:PCBM system used in organic photovoltaics. Fast-scanning differential chip calorimetry, an advanced thermal analysis technique, was used to simulate the thermal annealing used in the production of P3HT:PCBM solar cells to increase the degree of crystallinity, and thus efficiency. The main advantage of this technique for stuying the thermal annealing are the very high rates of heating and cooling that can be used, up to 10 6 K.s -1 , permitting one to avoid crystallization during cooling. In parallel with the experimental study, the charge transfer between donor (P3HT) and acceptor (PCBM) at the interface is studied using density functional theory. The charge separation between donor and acceptor present for the ground state of the combined system, diminished when the first triplet was investigated. This was explained by the formation of a bridge state, formed after population by the LUMO with one electron. Such a molecular orbital can facilitate charge transfer.

Organic photovoltaics (OPVs) can still only achieve efficiencies below those of conventional silicon photovoltaics. To date the highest OPV efficiencies have been found for so-called bulk-heterojunction (BHJ) solar cells, where the active layer is a bi-continuous composite of donor (a conjugated polymer) and acceptor (a small molecule) phases. As in conventional polymer blend systems, the morphology formed will strongly influence the material characteristics, and post-production annealing has been shown to increase device efficiencies. In this study, the active layer of BHJ devices is analysed using fast-scanning calorimetry techniques in order to investigate the transitions that play a role in stability and morphology development. In particular, Rapid Heat-Cool Calorimetry (RHC) [1], and fast scanning differential chip calorimetry (FSDCC) were used. FSDCC especially shows great potential for these systems due to the very high scanning rates and the ability to study thin layer samples, like in actual BHJ devices.

We analyse the electronic structure and aromaticity of graphene nanoribbons and carbon nanotubes through a series of delocalisation and geometry analysis methods. In particular, the six-centre index (SCI) is found to be in good agreement with the mean bond length (MBL) and ring bond dispersion (RBD) geometry descriptors. Based on DFT periodic calculations, three distinct classes of aromaticity patterns have been found for armchair graphene nanoribbons, appearing periodically as the width of the ribbon is increased. The periodicity in the band gap is found to be related to these aromaticity patterns. Also, the appearance of such distinct aromaticity distribution is explained within the framework of the Clar’s sextet theory. Both delocalisation and geometry analysis methods are shown to be very fast and reliable tools for easily analysing the aromaticity in carbon nanosystems.

Carbon nanotube (CNT) based nanocomposites have attracted much interest, owing to the conductive properties and mechanical reinforcement CNTs may transfer to the complete material. When using CNTs as a filler material for the development of (polymer) nanocomposites, a key element is the dispersion of the CNTs. This will strongly influence at what point a 3D percolating CNT network is formed, also know as the percolation threshold. For various reasons, the percolation threshold should be as low as possible. However, due to the strong interactions between CNTs, achieving good dispersion in the matrix can be problematic. For this purpose, specialized dispersion techniques are used in the preparation of CNT nanocomposites, such as latex technology, where surfactants are used to form aqueous polymer and nanotube emulsions, which are subsequently mixed, freeze-dried and compression-moulded. A complementary approach for lowering the percolation threshold is limiting the volume of the material that is accessible to CNTs. Here a phase separated morphology is desired, with CNTs ideally only found in one of the phases, leading to volume exclusion or double percolation. In this work a polystyrene (PS) / polymethylphenylsiloxane (PMPS) blend system was studied as a matrix for CNT nanocomposites. The study of these polymer blend nanocomposites was performed using thermal analysis techniques, such as DSC, as well as surface characterization and rheology. While an excellent dispersion of CNTs by polydimethylsiloxane (PDMS) was reported before, this is to our knowledge the first study on the related PMPS, which seems to show similar CNT-dispersing properties Unlike the strongly immiscible behaviour known for PS/PDMS blends however, the PS/PMPS system showed partial miscibility. While this means that phase separated morphologies can still be attained, which can be used for volume exclusion, this also makes it possible to develop homogeneous blends where PMPS seems to act more as a CNT compatibiliser. Clear proof of mechanical percolation was found for such systems, and conductivity studies are underway.

International audience; A systematic density functional study of chlorine addition to C(70) up to C(70)Cl(12) confirms experimental observations of regioselectivity and stability of C(70)Cl(10). We show that K@C(70) follows an alternative addition sequence with different isomers and magic numbers to C(70) such as KC(70)Cl(3). This prediction is important for controlling functionalisation behaviour via encapsulation and endofullerene purification.

The potential of polystyrene/polymethylphenylsiloxane (PS/PMPS) blends as a matrix for nanocomposites is investigated. It was proven by dynamic rheometry and conductivity measurements that PMPS effectively disperses carbon nanotubes, as was already known for polydimethylsiloxane (PDMS). The phase behaviour of PS/PMPS blends was investigated using differential scanning calorimetry or modulated temperature differential scanning calorimetry. The blends were found to exhibit partial miscibility, in contrast to the known immiscible behaviour of PS/PDMS blends. A miscibility window exists for PS/PMPS blends containing less than approximately 10 wt% PMPS.

International audience; Via density functional theory calculations, we explore the process of graphene and carbon nanotube fluorination. Contrary to graphene, HF-catalyzed carbon nanotube fluorination adds fluorine pairs at (1,4) spacing, naturally leading to a self-organized C4F coverage, which call subsequently rearrange into dense axial C2F lines by fluorine diffusion upon solubilization or heat treatment. Controlling the fluorination process and subsequent nanotube processing results in fluorinated material types with unexplored electronic and chemical properties.

Although extensive theoretical and experimental research has been conducted on fluorinated fullerenes, little detailed information exists on their solubility in different solvents. However, this solubility is crucial for their processability and possible application. In this work, we predict the solubility of fluorinated C(60) in various polar and non-polar solvents, based on a correlation between experimentally measured solubilities for C(60) from the literature and theoretically predicted solubilisation energies. These solubilisation energies are predicted using the polarizable continuum model (PCM) at the ab initio Hartree-Fock 6-31+G* level of theory. In particular, the solubilities are predicted for C(60)F(2)(n) (n = 1-10) isomers, part of the addition route to saturnene C(60)F(20). An increasing solubility is found for more polar solvents with higher degree of fluorination. With these results, we can determine the minimal fluorination degree necessary for possible solubilisation in a given solvent, and offer new perspectives to separate and purify species with different degrees of fluorination.

We produced large binder-free multi-walled carbon nanotube (MWNT) blocks from fluorinated MWNTs using thermal heating and a compressing method in vacuo. This technique resulted in the formation of covalent MWNT networks generated by the introduction of sp(3)-hybridized carbon atoms that cross-link between nanotubes upon de-fluorination. The resulting carbon nanotube blocks are lighter than graphite, can be machined and polished, and possess average bending strengths of 102.2 MPa, a bending modulus of 15.4 GPa, and an electrical conductivity of 2.1 x 10(2) S/cm. Although each nanotube exhibits a random structure in these blocks, the mechanical properties are 3 times higher than those obtained for commercial graphite. On the basis of theoretical molecular dynamics simulations, a model is presented for the nanotube interconnecting mechanism upon de-fluorination.

Finely tuned: Carbon nanotubes are exposed to a CF(4) radio-frequency plasma (see picture). High-resolution photoelectron spectroscopy shows that the treatment effectively grafts fluorine atoms onto the MWCNTs, altering the valence electronic states. Fluorine surface concentration can be tuned by varying the exposure time.Multi-wall carbon nanotubes (MWCNTs) were exposed to a CF(4) radio-frequency (rf) plasma. High-resolution photoelectron spectroscopy shows that the treatment effectively grafts fluorine atoms onto the MWCNTs, altering the valence electronic states. Fluorine surface concentration can be tuned by varying the exposure time. Evaporation of gold onto MWCNTs is used to mark active site formation. High-resolution transmission electron microscopy coupled with density functional theory (DFT) modelling is used to characterise the surface defects formed, indicating that the plasma treatment does not etch the tube surface. We suggest that this combination of theory and microscopy of thermally evaporated gold atoms onto the CNT surface may be a powerful approach to characterise both surface defect density as well as defect type.

International audience; We explore early stage oxygen addition to C-60 buckminsterfullerene, and compare its oxygenation behavior to that of both pristine and defective metallic carbon nanotubes, using ab initio theoretical modeling. For fullerene oxygen addition up to C60O4, in general oxygenation preferentially occurs at the pentagon-hexagon bonds ([5, 6] type addition), leading to open annulene structures, as opposed to the closed [6, 6] epoxide isomers. For carbon nanotubes the preference for annulene structures is significantly more pronounced as all epoxide addition is endothermic. Higher reaction enthalpies are found for oxidation in the proximity of defects as compared to the pristine sidewalls. In most cases higher reaction enthalpies are found for fullerene oxygenation as compared to carbon nanotubes.

We present a new computer program able to systematically study chemical addition to and growth or evolution of carbon nanostructures. SACHA is a meta-code able to exploit a wide variety of pre-existing molecular structure codes, automating the otherwise onerous task of constructing, running, and analyzing the large number of input files that are required when exploring structural isomers and addition paths. By way of examples we consider fluorination of the fullerene cage C-70 and carbon nanostructure growth through C-2 addition. We discuss the possibilities for extension of this technique to rapidly and efficiently explore structural energy landscapes and application to other areas of chemical and materials research.

Density functional theory (DFT) calculations suggest significantly different oxidation behaviour for phosphorus-doped heterofullerenes compared to their pure and nitrogen-doped counterparts, due to formation of a phosphene oxide. This oxide is not thermally labile, suggesting stable phosphofullerenes are likely to be C(59)POH and (C(59)PO)(2). In contrast, azafullerenes form stable epoxides when oxidised. We calculate the effect of oxidation on radical pairing and hydrogen passivation. Notably while the C(59)N radical behaves as a donor, C(59)PO will be an acceptor.

We present a new computer program able to systematically study chemical addition to and growth or evolution of carbon nanostructures. SACHA is a meta-code able to exploit a wide variety of pre-existing molecular structure codes, automating the otherwise onerous task of constructing, running, and analyzing the large number of input files that are required when exploring structural isomers and addition paths. By way of examples we consider fluorination of the fullerene cage C-70 and carbon nanostructure growth through C-2 addition. We discuss the possibilities for extension of this technique to rapidly and efficiently explore structural energy landscapes and application to other areas of chemical and materials research.

We present a theoretical investigation on the chemical addition patterns governing the fluorination of single wall carbon nanotubes. Monte Carlo calculations based on a Huckel model suggest that fluorination is stabilized in a bandlike pattern due to electronic confinement effects on the tube bond network topology. Ab initio analysis of the fluorination of small nanotubes show that fluorine addition along the nanotube axis direction is favored by a mechanism of carbon framework distortion. The experimentally observed formation of fluorine bands may be thus explained in terms of multiple axial C(2)F rows expanding by contiguous axial addition.

International audience; Calculations of fluorine binding and migration on carbon nanotube surfaces show that fluorine forms varying surface superlattices at increasing temperatures. The ordering transition is controlled by the surface migration barrier for fluorine atoms to pass through next neighbor sites on the nanotube, explaining the transition from semi-ionic low coverage to covalent high coverage fluorination observed experimentally for gas phase fluorination between 200 and 250 °C. The effect of solvents on fluorine binding and surface diffusion is explored.

Here we demonstrate that the incorporation of boron (B) atoms between double-walled carbon nanotubes (DWNTs) during thermal annealing (1400-1600 degrees C) results in covalent nanotube "Y" junctions, DWNT coalescence, and the formation of flattened multiwalled carbon nanotubes (MWNTs). These processes occur via the merging of adjacent tubes, which is triggered by B interstitial atoms. We observe that B atom interstitials between DWNTs are responsible for the rapid establishment of covalent connections between neighboring tubes (polymerization), thereby resulting in the fast annealing of the carbon cylinders with B atoms embedded in the newly created carbon nanotube network. Once B is in the lattice, tube faceting (polygonization) starts to occur, and the electronic properties are expected to change dramatically. Therefore, B atoms indeed act as atomic nanotube fusers (or welders), and this process could now be used in assembling novel electronic nanotube devices, nanotube networks, carbon nanofoams and heterojunctions exhibiting p-type electronic properties.

A systematic study is presented of addition patterns occurring upon fluorination of C60. We use the program SACHA, which increments the number of fluorine addends, tests all available addition sites within a given cutoff radius, and selects the most energetically stable structure for further addition on the basis of full AM1 optimizations for every isomer. The lowest energy structures are optimized at HF/3-21G level of theory. A number of distinct addition routes are predicted, based on octahedral, 'S', and 'T' addition patterns, leading both to experimentally observed C60F(n) isomers and to isomers not previously described in the literature. Furthermore the main addition routes were analyzed for C60F2n isomers, using ab initio global and local aromaticity calculations. For this, magnetizability and NICS calculations have been carried out at HF/3-21G level of theory. We show the possibility of using NICS to predict the next preferential addition site, matching the above-described addition routes.

In the present work a quantum chemical study of a series of substituted hydrofullerenes, C(60)HR, and a series of methanofullerenes, C(60)(CHR), is presented. Their reactivity and geometrical, energetic, electronic, and magnetic properties, as well as the influence of the substituent, are discussed. As a probe of the reactivity, the acidic properties of these fullerene derivatives were predicted, based on the calculated deprotonation energies, with a previously set up scheme. The electronic delocalization upon deprotonation was described, and the global (magnetizabilities) and local aromaticity (nucleus-independent chemical shifts) was analyzed and compared with respect to the group properties for the series of functional groups. The geometries of both acidic and basic forms were fully optimized at the AM1 level, and all property calculations were performed at the HF/3-21G and the B3LYP/6-31G* level of theory.

Current-density maps were calculated by the ipsocentric CTOCD-DZ/6-311G** (CTOCD-DZ=continuous transformation of origin of current density-diamagnetic zero) approach for three sets of inorganic monocycles: S(4) (2+), Se(4) (2+), S(2)N(2), P(5) (-) and As(5) (-) with 6 pi electrons; S(3)N(3) (-), S(4)N(3) (+) and S(4)N(4) (2+) with 10 pi electrons; and S(5)N(5) (+) with 14 pi electrons. Ipsocentric orbital analysis was used to partition the currents into contributions from small groups of active electrons and to interpret the contributions in terms of symmetry- and energy-based selection rules. All nine systems were found to support diatropic pi currents, reinforced by sigma circulations in P(5) (-), As(5) (-), S(3)N(3) (-), S(4)N(3) (+), S(4)N(4) (2+) and S(5)N(5) (+), but opposed by them in S(4) (2+), Se(4) (2+) and S(2)N(2). The opposition of pi and sigma effects in the four-membered rings is compatible with height profiles of calculated NICS (nucleus-independent chemical shifts).

The first all-electron ab initio study of Young's modulus and Poisson ratio for a number of closed single-walled nanotubes is presented. At the Hartree–Fock 6-31G ∗ level, the results obtained compare well with experimental as well as previous theoretical studies, predicting a Young's modulus higher than 1 TPa. The calculated Young's modulus for a graphene layer is found to be smaller than for its (5,5)-nanotube counterpart.

Major advances have been made in density functional theory and linear scaling methods. However, routine application of these methods to larger systems possessing no symmetry still remains difficult. Moreover, no clear standard exists for the use of small basis sets in the calculation of atomic or molecular properties with density functional methods. In this work an evaluation is made of the performance of different density functional methods for small and often used basis sets. Deprotonation energies are calculated for a series of small compounds and compared with high-level quantum chemical calulations. Furthermore, atomic populations calculated with these methods are compared with high-level results. The results show that the use of density functional calculations with smaller basis sets is justified for calculations on larger systems, retaining relatively good accuracies.

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Solvation of Graphene: Thermodynamic Aspects

Out-of-plane shear and out-of plane Yang's modulus of double layer graphene

The main drawback of the organic photovoltaic systems (OPVs) developed to date, is the low efficiencies obtained [1]. So far the highest OPV efficiencies have been found for so-called bulk-heterojunction (BHJ) solar cells, where the active layer is a bicontinuous composite of donor and acceptor phases. A conjugated, light-excitable polymer is used as an electron donor. Fullerene derivatives are the most widespread type of electron acceptor, due to their high electron affinity and ability to transport charge. In this study a poly(3-hexyl thiophene) (P3HT) and [6,6]-phenyl C61 - butyric acid methyl ester (PCBM) blend, one of the most widespread OPV systems, is investigated by both experimental and theoretical means. An important technological challenge for BHJ OPV's is the morphology of the active layer. Due to the limited lifetime of generated excitons, a nm-size phase separated morphology is required for efficient charge generation at the interface between donor and acceptor. A more crystalline material will also lead to more efficient charge transfer. Because the active layer is essentially a blend material, and the ideal morphology is not the thermodynamic equilibrium state, post-production annealing plays an important role in optimising these systems [2-3]. In this work, post production annealing is therefore studied using several fast-scanning calorimetry techniques, such as Rapid Heat-Cool Calorimetry (RHC) [4] and Fast-Scanning Differential Chip Calorimetry (FSDCC) [5]. These techniques make it possible study the effects of annealing for short times. Surface characterisation is also carried out using conducting atomic force microscopy (C-AFM). Next to the morphology of the active layer, the mechanism of charge transfer and exciton dissociation at the donor/acceptor interface is just as important. This charge transfer is modelled using ab initio DFT calculations under periodic boundary conditions (PBC). A possible bridge state, allowing charge transfer, was investigated for the excited triplet state of the combined donor/acceptor system. A similar bridge-state was described earlier in literature [6]. Calculations for the excited singlet state, requiring time-dependent techniques, are underway. 1. Tompson B.C., Fréchet J.M.J., Angew. Chem. Int. Ed., 47, 58-77 (2008). 2. Erb T., Zhokhavets U., Gobsch G., Raleva S., Stuhn B., Schilinsky P., Waldauf C., Brabec C.J., Adv. Funct. Mat., 15, 1193-1196 (2005). 3. Hoppe H., Sariciftci N.S., J. Mater. Chem., 16, 45-61 (2006). 4. Danley R.L., Caulfield P.A., Aubuchon S.R, Am. Lab., 40, 9-11 (2008). 5. Minakov A.A., van Herwaarden A.W., Wien W., Wurm A., Schick C., Thermochim. Acta, 461, 96-106 (2007). 6. Kanaï J., Grossman J.C., Nano Letters, 7, 1967-1972 (2007)

The definition of softness and local softness using the density of states (DOS) and local density of states (LDOS) given by Yang and Parr for metals has been casted into working equations and applied to sequences of finite cylindrical fullerenes modeling the (5,5) and (10,10) single-walled capped carbon nanotubes. The behavior of DOS, LDOS, and global and local softness as functions of length and tube type is investigated in the simplest Huckel approximation. DOS-based calculation of global softness gives results that depend less on the details of the electronic structure than those based on the finite-difference approximation. Armchair single-walled nanotubes with larger diameters are softer than those with smaller diameters at the same tube length. Local softness, after fluctuations in the end-cap region, settles down within the first 20 layers of hexagons of the tube body to a constant (diameter-dependent) value.