The unique features of the fullerene molecules enable a number of different routes for tuning their properties by molecular functionalization and formation of complexes. The hollow molecular structure of fullerenes allows, for example, endohedral complex formation, while their polyconjugated electronic structure enables multiple functionalization with covalently attached adducts (up to one adduct per carbon atom in the case of small groups, which for Buckminsterfullerene means up to 60 adducts) (Taylor and Walton, 1993). A third route for “tuning” fullerenes is cocrystal formation with other organic species in the solid state (Sundqvist, 2003; Neretin and Slovokhotov, 2004; Wang, 2015) or supramolecular complex-formation exploiting π stacking interactions (Fernández et al., 2008; Babu et al., 2010). These three modification routes have been termed, in the case of salts of fullerenes with electron donor atoms or molecules such as alkali atoms or ferrocene, “endohedral,” “on-ball,” and “exohedral,” respectively.

Here, I review the physical properties of some solid-state molecular compounds of pristine and functionalized Buckminsterfullerene (C₆₀), namely, cocrystals with small organic molecules including solvates and hydrates. Concerning the latter, while pristine C₆₀ is not water soluble, functionalization with polar groups leads to derivatives with higher water affinity (Wang et al., 2005; Kokubo et al., 2008), which in some cases promotes the formation of hydrates from water solutions (Zachariah et al., 2015).

Fullerenes are quite peculiar molecules. No liquid fullerene phases are known, and binary phases with other molecules cannot be obtained by mixing and cooling from the molten state at arbitrary proportions. Intercalation of gas-phase molecules into solid fullerite can be achieved by application of pressure (and sometimes high temperature) to the molecular gas to aid its diffusion through the interstices of C₆₀ crystals; this method only works, however, for rare gases, methane, or small diatomic gases (Sundqvist, 2003; Galtsov et al., 2007). On the other hand, fullerenes are moderately soluble in a number of organic solvents (Ruoff et al., 1993) and stoichiometric solvates can be obtained by precipitation or slow evaporation. C₆₀ readily forms solvates with a large variety of solvents such as benzene, toluene, chlorobenzene, n-alkanes, halogenated ethane and methane derivatives, hexane, m-xylene, and CS₂. Many solvates are unstable at room temperature; the stable ones decompose upon heating either by incongruent melting or sublimation of the solvent alone. Cocrystals of fullerenes with non-solvent molecules can be obtained from co-solutions in a common (usually aromatic) solvent, either by slow concentration of the solution or by addition of a precipitant (bad solvent). These simple methods not only allow producing a variety of different binary compounds, but can be even employed to obtain quasi-pure fullerene crystals with tailored morphologies and a large variety of forms (Wang et al., 2006; Babu et al., 2010; Shrestha et al., 2013), in some cases with symmetries reminiscent of the quasicrystalline state (Fleming et al., 1991; Céolin et al., 1992; Michaud et al., 1998) and sometimes even with a modified lattice structure (de Boer et al., 1994; Céolin et al., 1999, 2001). In particular, C₆₀ crystals formed from solution may display hexagonal closed packed (hcp) lattice instead of the usual face-centered cubic (fcc) structure of pristine fullerite (Heiney et al., 1991) (the hcp and fcc structures only differ in the stacking alternation of close-packed triangular planes, but in the case of C₆₀, this also entails a different orientational dynamics, see below).

The quasispherical shape of C₆₀ results in crystals with relatively large interfullerene voids that can be occupied by small intercalants, even in the closed-packed (fcc and hcp) structures of pristine fullerite. In compounds of C₆₀ with H₂, NH₄, and CO which is obtained via gas-phase intercalation, for example, the room-temperature symmetry is fcc, with variations of the lattice parameter of less than 0.2% compared to pristine fullerite. Only a minor lattice distortion is observed in N₂-intercalated C₆₀, which is obtained at high pressure (Galtsov et al., 2007), while O₂ can diffuse even at atmospheric pressure through the interstices of C₆₀ (Assink et al., 1992), which rationalizes its observed degradability by photooxidation (Hamed et al., 1993; Katz et al., 1998). These intermolecular interstices, especially the larger octahedral ones, are large enough to accommodate also the heavier alkali ions without distortion nor expansion of the fcc lattice, and cocrystallization of alkali fullerides with ammonia leads to only minor tuning of the lattice spacing.

The fcc structure is also maintained in the 1:1 cocrystal with the cubane C₈H₈ molecule, thanks to the fact that the hydrogen groups at the vertices of the cubic carbon cage of the cubanes result in electronic orbitals with concave surfaces that are complementary to the convex spherical shape of the molecular electronic cloud of the buckyballs (Pekker et al., 2005). The idea of cocrystal formation exploiting the complementarity of the convex fullerene surface with molecules displaying saddle-like, concave surfaces (possibly with aromatic character), was introduced early on (Raston, 1996; Barbour et al., 1998; Hardie and Raston, 1999) and is one of the basic principles for the supramolecular organization of fullerenes, as reviewed in a recent book (Martin and Nierengarten, 2012).

While small, symmetric intercalants can preserve the close-packed structure of the fullerene species, resulting in crystal structures that are often cubic or hexagonal, most fullerene cocrystals display a more open and less symmetric structure (Neretin and Slovokhotov, 2004; Wang, 2015). This is the case of cocrystals with molecules of size comparable to that of the C₆₀ molecule [whose van der Waals diameter is ≈10 Å (Heiney et al., 1991)], but also with smaller aromatic molecules, and even with some tetragonal molecules such as P₄ and CCl₄. In many cases, both for high- and low-symmetry lattices, the crystal structure of fullerene cocrystals can be described as consisting of alternating layers of fullerenes and cocrystallizing species (Spitsina et al., 2002; Neretin and Slovokhotov, 2004; Cui et al., 2012; Mitsari et al., 2016a; Ye et al., 2017).

The interest in molecular fullerene cocrystals started soon after the discovery of a method for bulk production of C₆₀ (Krätschmer et al., 1990) and was driven initially by the discovery of p-electron ferromagnetism in the molecular charge-transfer salt of C₆₀ with tetrakys(dimethylamino)ethylene (Allemand et al., 1991) and further spurred by the quest to increase the critical temperature of fulleride superconductors by tuning their lattice spacing, which could be achieved by ammonia intercalation (Zhou et al., 1993). In some fullerides, lattice expansion via ammoniation leads instead to a metal-insulation transition and antiferromagnetism (Prassides et al., 1999). The appearance of magnetic properties and metal–insulator transitions is associated with the partial filling of the lowest unoccupied molecular orbital of C₆₀, which is accompanied by Jahn–Teller distortions that lift the orbital degeneracy (threefold in fullerite).

Beside these electronic transitions, which are absent in pure C₆₀, an interesting question is whether the orientational transitions of pristine fullerite survive in cocrystals with other organic molecules. At room temperature, fullerite exhibits an fcc rotator phase consisting of rapidly spinning molecules (the lattice symmetry is fcc because all free-rotor molecules are undistinguishable in a diffraction experiment). In hcp fullerite crystals, the molecules only display uniaxial (rather than free) rotation (Céolin et al., 1999). In fcc fullerite, below 260 K the dynamic orientational disorder is replaced by a ratcheting motion between two orientations, and the crystal structure becomes simple cubic (sc) (Tycko et al., 1991). A similar fcc to sc transition is observed in alkali fullerides with 1:1 stoichiometry (Kosaka et al., 1995; Macovez et al., 2008).

Concerning molecular fullerene cocrystals, the prototypical example of a rotator phase is the fullerene-cubane compound. This crystal has been dubbed a “rotor–stator” compound because, at room temperature, the fullerenes exhibit free rotation while the cubane species are static (Pekker et al., 2005). The free-rotator phase is stable down to 140 K, much lower than the transition temperature of pristine C₆₀ and other derivatives (Bortel et al., 2006). Free rotation of the C₆₀ species has been reported or suggested also in other cocrystals, for example, with CHBr₃ (Collins et al., 1999) and with p-bromocalix[4]arene propyl ether, where isotropic reorientations persist down to at least 130 K (Hughes et al., 2000). It is interesting to note that the behavior of simple fullerene derivatives such as C₆₀O and C₆₁H₂ is opposite to that of most cocrystals: these functionalized fullerenes exhibit an orientational ordering transition at higher temperature than that of pristine C₆₀. The increased critical temperature is ascribed to the fact that the entropy of the disordered (high-temperature) phase of the fullerene derivatives is lower than that of C₆₀ because the side adducts must occupy intramolecular voids, so that free rotation is not allowed (Lommen et al., 1994; Meingast et al., 1996).

Solvates with aromatic solvents are usually characterized by stronger intermolecular interactions than other solvates. In the case of the C₆₀ solvate with benzene, at low temperature the fullerenes exist in two distinct orientations (Bürgi et al., 1994), and although a study has suggested the existence of dynamic molecular disorder at room temperature (He et al., 1997), the comparison between solvates with several distinct aromatic solvents indicates that free rotations of the C₆₀ molecules is generally hindered in these systems (Korobov et al., 1999). This leaves open the possibility of a merohedral dynamic disorder, as in pristine C₆₀ below 260 K. The room-temperature crystal structure of the C₆₀ ⋅2C₆H₅Br solvate, for example, was refined assuming two molecular orientations of the fullerenes with occupancy factors of 0.71 and 0.29 (Korobov et al., 1998), which suggests the occurrence of ratcheting motions.

Solvates with halogen-methane or -ethane derivatives generally display orientational disorder of the solvent molecules; this is the case of CBr₂Cl₂ or CBr₂(CH₃)₂, for example, though not for CBr₂H₂ (Ye et al., 2016, 2017). Some cocrystals display simultaneous molecular rotations of both component species, as in the case of the C₆₀ solvate with Fe(C₅H₅)₂ (Espeau et al., 2002; Rozen et al., 2004) and as suggested also for the solvates with some methane derivatives (Collins et al., 2000). An example of molecular dynamics of the intercalant species is shown in Figure 1, which show the results of the characterization of the 1:1 C₆₀ solvate with (1,1,2)trichloroethane. The structure of the solvate, as obtained by refinement of X-ray powder diffraction (XRPD) data, is shown in Figure 1A. Figure 1B exhibits the relaxation times of the trichloroethane species, as measured by dielectric spectroscopy; two distinct relaxation times are observed (Mitsari et al., 2016b) (since this technique is sensitive to changes of the electric dipole moment, it can be used to selectively probe the motion of the polar ethane derivatives).

The presence of two distinct relaxation times has been ascribed to the simultaneous presence in the solvate of two distinct (1,1,2)trichloroethane conformers of different chirality and dipole moment, namely gauche and transoid. The slower dynamics is ascribed to the transoid conformer, whose dipole moment is more than twice that of the gauche conformer, leading to a larger induced polarization of the C₆₀ species [which are highly polarizable due to the large number of π electrons (Pederson and Quong, 1992; Macovez et al., 2011)] and thus to a more pronounced electric hindrance against dipolar reorientation.

As mentioned, decomposition of solvates occurs by the loss of the solvent molecules, leaving behind a quasi-pure C₆₀ solid with numerous defects and faults (Michaud et al., 2000). Enthalpies of desolvation are usually given per mole of solvent, and typical values range between 35 and 60 kJ/mol (Céolin et al., 2001) although, in few cases, they can be as low as 15 or 20 kJ/mol (Jansen and Waidmann, 1995). As a general trend, solvates that are characterized by lower enthalpies of desolvation are characterized by weaker molecular interactions, and thus by lower stability and unhindered fullerene rotation (lower orientational transition temperature). Despite efforts to unveil patterns of common behavior in solvates, however, their variety is such that no simple, universally valid correlations have been found.

Pristine fullerite is a good electron acceptor and usually behaves as an electron-transporting (n-channel) semiconductor. Orientational ordering has an important impact on electron conduction properties. In pristine fullerite, the dc conductivity (σ_dc) decreases by more than one order of magnitude as the temperature is increased through the transition at 260 K (Katz et al., 2003), and orientational ordering plays an important role also in alkali fullerides (Macovez et al., 2008). The electron affinity and n-type conduction are usually preserved by fullerene functionalization, with C₆₀ derivatives exhibiting electron transport properties that are well described by the variable-range hopping model (see also below) (Macovez et al., 2014b; Zachariah et al., 2016; Mitsari et al., 2017) typical of disordered semiconductors. In the case of the brominated C₆₀Br₆ derivative, a deviation from the electronic variable-range hopping behavior has been reported above 215 K, and this conductivity cross-over has been ascribed to a possible onset of orientational dynamics (Zachariah et al., 2016). The electron affinity of fullerene derivatives has spurred a lot of research on fullerene systems aimed at improving the charge transfer and charge transport properties, to achieve, for example, high-efficiency heterojunction solar cells (He et al., 2012; Lai et al., 2014) and air-stable n-channel organic transistors (Jones et al., 2007; Usta et al., 2009). When cocrystals are formed with species that do not significantly alter the crystal packing, the isotropic electron conduction properties of pristine fullerite are retained. This is the case of ammoniated fullerenes, where ammoniation can even preserve superconductivity. In more complex systems, electronic conduction can have a lower effective dimensionality (Idé et al., 2014).

C₆₀ and higher fullerenes are hydrophobic: their solubility in water is extremely poor and no stable hydrates can form. Functionalization with polar groups can be employed to improve the hydrophilic affinity and thus the solubility of fullerenes in water. The most studied hydrophilic fullerene derivatives are polyhydroxilated fullerenes (fullerenol, chemical formula C₆₀(OH)_n with n between 6 and 40). The water solubility increases with increasing number of hydroxyl groups, with relatively poor solubility for n < 12 (Chiang et al., 1994) and good solubility for a higher number of hydroxyl groups (e.g., 16 or 20–24) (Li et al., 1993; Wang et al., 2005). Fullerenols have been suggested to act as proton conductors in water solution and when incorporated inside membranes (Rajagopalan and Oh, 2011; Sardenberg et al., 2011). This is surprising since, as mentioned, in the solid phase of pure derivatives, charge transport occurs via hopping of electronic charge carriers. Recent studies have appeared that address the nature of charge transport in hydrophilic derivatives.

The two related derivatives C₆₀(OH)₂₄ and C₆₀(ONa)₂₄ are particularly interesting in this respect. Both molecules can be synthesized starting from polybrominated fullerene with the maximum possible number of adducts [C₆₀Br₂₄ (Taylor and Walton, 1993)], by substitution and neutralization reactions with sodium hydroxide. Both polyalcohol (–OH) and polyalkoxide (–ONa) derivatives are hydrophilic; the precipitate of the C₆₀(ONa)₂₄ synthesis is a crystalline hydrate with formula C₆₀(ONa)₂₄·16 H₂O, while the C₆₀(OH)₂₄ precipitate is a molecular powder with interstitial water clusters that crystallize into ice upon cooling below 273 K (Macovez et al., 2014a; Zachariah et al., 2015; Mitsari et al., 2017). The XRPD patterns of the pure (water-free) derivatives exhibit Bragg peaks at basically the same angles, as shown in Figure 2A; instead, very different diffraction patterns are observed in the hydrated materials: while hydrated C₆₀(ONa)₂₄ is crystalline (Zachariah et al., 2015), hydrated C₆₀(OH)₂₄ is much more disordered (see Figure 2A). These facts, together with the observation in the fullerenol case of partial crystallization of interstitial water (Mitsari et al., 2017) indicate that although the interfullerene interactions are basically identical in both derivatives, the heterointeractions with water are qualitatively different. This difference is possibly due to the fact while the polyalcoxy derivative can only act as a H-bond acceptor, the polyalcohol derivative can act both as an acceptor and as a H-bond donor, resulting in a more complex (and partially disordered) structure of the H₂O molecules in hydrated fullerenol.

The inset to Figure 2B displays the Arrhenius plot of the dc conductivity of the pure (water-free) C₆₀(OH)₂₄ powder (Mitsari et al., 2017), which follows the Shklovskii-Efros variable-range electron hopping model according to which Log(σ_dc) ~ T^−1/2 (where T is the temperature in kelvin) (Efros and Shklovskii, 1975). Similar results have been obtained for pure C₆₀(ONa)₂₄ (Macovez et al., 2014b), which indicates that also hydrophilic fullerene derivatives are electronic conductors in their pure form. Instead, in hydrated C₆₀(OH)₂₄ and C₆₀(ONa)₂₄, the presence of H₂O molecules results in a dominantly protonic conductivity. This is visible in Figure 2B, where the dc conductivity of the hydrated solid obtained from aqueous solution is observed to be higher than the intrinsic (electronic) conductivity of the pure material by a factor of 10³. In the figure, σ_dc is shown together with the so-called “conductivity relaxation” frequency f_σ, at which the imaginary part of the complex modulus M = ε^–1 (inverse of the complex permittivity) is maximum; f_σ displays the same temperature behavior as σ_dc, and a similar increase in the hydrated sample.

The water-induced conductivity enhancement occurs not only when water is present as a structural component, as in fullerenol (Mitsari et al., 2017), but also when a pure hygroscopic fullerene derivative such as C₆₀(ONa)₂₄ is stored in a humid atmosphere, as the capture of atmospheric water leads to the formation of a proton-conducting surface layer (Zachariah et al., 2015). Also in the latter case the water-induced conductivity enhancement is quite remarkable: the σ_dc value for C₆₀(ONa)₂₄ exposed to humid atmosphere is higher by a factor 10⁴ than the anhydrous material (Zachariah et al., 2015). Such conductivity enhancements are in line with those observed in inorganic hygroscopic systems (Cramer et al., 2011; Aragoneses et al., 2013; Haspel et al., 2013) and exploited in resistive humidity sensors (Farahani et al., 2014).

Water-induced conductivity enhancements are generally due to transport of protons or other small ions. Contrary to the case of water chemisorption, which takes place e.g. in hydrated metal oxides (Egashira et al., 1981), the effects reported in hydrated fullerene derivatives do not arise from water splitting, as the extra surface-conductivity contribution vanishes upon heating to moderate temperatures, indicating that the water molecules maintain their integrity. The rationalization of the conductivity enhancements in hydrated fullerene derivatives is that they are due to proton transport by H-bond shuttling, a mechanism by which O–H bonds are interchanged between adjacent water molecules, which is responsible for the conductivity of water, ice, and some hydrated organic compounds (Charalampopoulos and Papaioannou, 2011; Knight and Voth, 2012; Wojnarowska et al., 2014). Confirmation of the presence of mobile protons in hydrated polyalcohol and polyalcoxide derivatives is obtained from the analysis of dielectric spectra, where two distinct space-charge relaxations are observed, associated with the accumulation of, respectively, electronic and protonic charge carriers at fullerene–water interfaces (Mitsari, 2016c; Mitsari et al., 2017).

In the case of the C₆₀(ONa)₂₄⋅16 H₂O hydrate, σ_dc displays a nonmonotonic behavior across the structural dehydration, which takes place around 365 K (Zachariah et al., 2015). This non-monotonic behavior is due to the structural change associated with dehydration. A σ_dc increase by two orders of magnitude is observed some 10° below the decomposition of the hydrate; this increase appears to be a non-equilibrium contribution, likely due to irreversible changes in the distribution of water around the C₆₀(ONa)₂₄ molecules. Since a similar increase is observed when the pure powder is exposed to humid atmosphere, it is likely that the enhancement is due to a protonic transport mechanism. These studies show that solid C₆₀(OH)₂₄ and C₆₀(ONa)₂₄ only behave as proton conductors in their hydrated forms, and that proton transport takes place through the water network (Zachariah et al., 2015; Mitsari et al., 2017).

Finally, a word is due on the effect of applying pressure on fullerene cocrystals. Just as pure fullerite polymerizes under pressure (Sundqvist, 2004), in the case of cocrystals, application of pressure can result in the formation of non trivial superstructures such as exohedrally intercalated C₆₀ polymers (Cui et al., 2012) or copolymeric structures formed by the reaction of fullerenes with the intercalant (Iwasiewicz-Wabnig et al., 2007). Surprisingly, the application of high pressures leads to the formation of exotic phases with intriguing properties, as discussed in a recent review (Wang, 2015). Compression of C₆₀ cocrystals with m-xylene leads to collapse of the molecular constituents; however, though transformed into amorphous carbon clusters, the fullerene moieties maintain their positions and long-range order is preserved (Wang et al., 2012). The resulting material is incompressible and hard enough to indent diamond anvils (Yao et al., 2013). A recent study has shown that similar “super-hard” materials can be obtained from solvates of Buckminsterfullerene (but also of higher fullerenes such as C₇₀) with several solvents (Yao et al., 2015). It is worth noticing that pristine C₆₀ does not yield a super-hard material after compression at high pressure (Wang, 2015), hence, cocrystal formation is a prerequisite to obtain super-hard materials from fullerene precursors.