The endohedral effect

Electron density p r) [au] along the C5 axis in the direction of C atom 

A semiquantitative explanation of these facts is afforded by a simple model [34] involving the statistical Thomas-Fermi theory [35]. In this model, the nuclei of the cage are replaced by an uniform positive charge distributed on a sphere with a radius equal to the radius of the cluster. The charge distribution generates a hollow sphere potential given by 

To find the electron density, one minimizes the respective Thomas-Fermi (TF) functional [36] that reads 

Minimization of the TF energy with respect to p(r) constraint (4) results in the following equation for the electron density [34] 

In the above equation, X is equal to 128Z/9i ) of the reduced cage radius. 

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AC and AEC complexation is also effected efficiently by other macrocyclic ligands such as the spherands 13, cryptospherands 14 [2.9, 2.10], calixarenes [2.38, A.6, A.23], torands [2.39], etc., some of them, for instance the spherands displaying particularly high stabilities. A special case is represented by the endohedral complexes of fullerenes in which the cation (Sr2, Ba2+, lanthanides) is locked inside the closed carbon framework [2.40],... 

Our observation that the series of LiC6o-2n fragment ions terminates sooner than the corresponding Na-Cso -2n series is consistent with the endohedral binding picture. Just as Li can insert into Cm more easily than Na" ", it should be able to escape more readily. The large drop of ion signals toward bigger n clearly shows that Li loss competes effectively with C2 loss ... 

F. DE PROFT, C. VAN ALSENOY and P. GEELINGS, Ab initio study of the endohedral complexes of Ceo, Sieo and Geeo with monoatomic ions influence of electrostatic effects and hardness. J. Phys. Chem., 100, 7440 (1996). 

Besides the substances mentioned so far, functionalized fuUerenes like the simple Bingel adduct can be intercalated into nanotubes as well (Section 2.5.5.2). The formation of peapods has further been described for metallocenes (e.g., ferrocene), porphyrines (e.g., erbium phthalocyanine complex) and small fragments of nanotubes. The most important prerequisite for the feasibility of inclusion is always a suitable proportion of sizes of both the tube and the structure to be embedded. For example, this effect can be observed for the intercalation of different cobaltocene derivatives into SWNT. The endohedral functionalization only takes place at an internal diameter of 0.92nm or above (Figure 3.100). But there is also an upper limit to successful incorporation. When the diameter of the nanotube is too large, the embedded species can easily diffuse away again from the host. Only few molecules are consequently found inside such a wide tube. 

Such findings indicate that even at room temperature a system with two metastable levels exists, and under certain conditions (for example, under the thermal fluctuations or at the expense of a laser pulse), the endohedral atom can migrate from one stable position in the molecular cage to another. This process is similar to the known effect of caging (easy migration) of the impurity atom in the lattice of heavier atoms however in the case of the studied system all atoms are of the one type. 

Metal-free reactions represent a direct way to study the confinement effects induced by the nanotube itself. Few such reactions have been carried out within CNTs, but notable examples include the formation of linear structures, such as fuUerene [151] and fullerene epoxide oligomers [174], formation of DWCNTs from endohedral fiiUerenes encapsulated in SWCNTs [71,155,156], or from encapsulated ferrocene [165], graphene nanoribbons (GNR) [186,187], the transformation of [Fe(C6oMc5)Cp] into encapsulated C70 [157], or the transformation of adamantane [188] and functionalized diamantine [189] in carbon chains. 

The only effective methods for producing endohedral metallofullerenes are laser ablation and DC arc discharge, techniques that are similar to the production of fullerenes. The DC arc method has become more popular because the laser ablation method has low yields and is costly. 

With gram quantities of fullerenes readily available thanks to the Kratschmer-Huffman arc vaporization technique, several properties of the Ceo cluster have been measured lately. Other data has been provided by recent ab initio calculations. In this section, we list the properties that are of relevance to the formation of endohedral complexes. These include molecular geometry (the bond lengths and the cage radius), ionization potential and electron affinity, and electric polarizability. The so-called endohedral effect is also discussed here. 

Since then, a variety of molecular peas were integrated into SWNTs [34, 225] the molecules with three-dimensional structures are endohedral metallofuUerenes [226-229], metallocenes [230,231] and o-carboranes [232, 233]. Molecular and/or atomic motions in the confined space inside the tube were successfully observed by HRTEM due partly to the shielding effect of the carbon cage from electron impact [227-229,232,233]. Two- and one-dimensional conjugated molecules were also encapsulated in SWNTs [234-237]. Relatively small molecules such as tetramethyltetrase-lenafulvalene 63, tetrathiafulvalene 64, tetracyanoquinodimethane 65 and tetrafuluorotetracyanoquinodimethane 66 (Fig. 20) were encapsulated in SWNTs to modify their electronic structures [238]. Ionic liquid l-butyl-3-methylimidazolium hexatiuorophosphate [bmim] [PFe] 67 (Fig. 20) was found to change the physical properties when it was confined in MWNTs [239]. 

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