Colloid Chemistry of Fullerene Solutions: Aggregation and Coagulation

Abstract

This review article is devoted to the colloidal properties of fullerene solutions. According to generally accepted understandings, all solvents in relations to fullerenes are divided into “good”, “poor”, and “reactive”. We have consistently considered the state of fullerenes in these systems. In “good”, predominantly non-polar aromatic solvents and CS₂, non-equilibrium dissolution methods lead to the formation of colloidal aggregates, whereas the utilization of equilibrium methods results in the formation of molecular solutions. The latter, however, have some unusual properties; new results considered in this review confirm previously expressed ideas about colloidal properties of these solutions. In “poor” (polar) solvents, lyophobic colloidal systems appear. Both “bottom-up” and “top-down” methods of preparation are well documented in the literature. However, N-methylpyrrolidine-2-one, DMSO, and DMF dissolve fullerenes quite easily and with less energy consumption. These solvents can be considered a subset of “poor” solvents that have some features of being “reactive” at the expense of basic properties. New data confirm that hydrosols of fullerenes are typical hydrophobic colloids that obey the Schulze–Hardy rule and other regularities in the presence of electrolytes. Organosols in acetonitrile and methanol are much less stable with respect to the effects of electrolytes. This allows us to assume a non-DLVO stabilizing factor in the hydrosols. Accordingly, a new estimate of the Hamaker constant of fullerene–fullerene interaction is proposed. In DMSO and DMF, the coagulation of fullerene sols is hindered due to strong solvation with these basic solvents.

1. Introduction

At present, fullerenes C₆₀, C₇₀, etc., belong to the most explored chemical compounds, and their study continues. For example, they are used in solar cells [1,2,3], in creation of nanowhiskers for various areas [4], as additives to the working fluids of refrigerators [5], etc. Their application in various branches of scientific research and technology is often associated with the use of these compounds in solutions. Water-based systems are examined in order to reveal the antioxidant properties of fullerenes [6] and biocompatibility [7,8] to study the environmental impact and related problems [9,10,11]. Therefore, different modifications and improvements of the introduction of fullerenes into water were proposed [12,13,14,15,16]. The peculiar properties of fullerene solutions in various liquid media are the subject of many publications, including reviews [17,18,19,20,21]. There are also several reviews on this topic by one of the authors of this article [22,23,24,25], and therefore we will not repeat much of what is considered in detail in these articles.

The purpose of this review is, on the one hand, to consider the state of the arts. On the other hand, we summarize the results of the work carried out in this laboratory from 1997 to 2022. The focus will be on the colloidal aspect, which is a key to understanding fullerene liquid solutions. We do not consider here either solutions of fullerenes obtained by using surfactants, calixarens, cyclodextrins, etc., or covalently modified fullerenes. We will only discuss the binary systems fullerene–solvent.

2. Solubility of Fullerenes

2.1. “Good”, “Poor”, and “Reactive” Solvents

The first quantitative estimations of C₆₀ solubility in different liquids made by Sivaraman, Matthews and coworkers [26,27], and Ruoff [28] have already shown that these values are very low in any solvent. This was confirmed by other authors [29,30,31,32]. Soon, a significant amount of data was accumulated on the solubility on fullerenes in solvents of various natures, including temperature dependences of solubility [20,33,34,35,36]. The solubility even in solvents called “good”, or “strong” ones, such as 1-chloro-; 1-phenyl-; and 1-methylnaphthalene, 1,2-dichlorobenzene; tetraline; xylenes; toluene; benzene; CS₂, etc., does not reach 0.1 M (hereafter, 1 M = 1 mole dm^–3). These solvents may also be referred to as “high-solubility solvents” [37]. Some authors consider as “good” solvents only those where the molar fraction of fullerenes reaches x₂ = 0.001 [38]. Polar solvents, including alcohols, belong to the so-called “poor” or “weak” ones. The solubility in such media drops down to ~10⁻⁵ M or even ~10⁻⁶ M. Aliphatic hydrocarbons should also be classified as “poor” solvents.

At the same time, typical colloid solutions, i.e., suspensions and organosols, can appear in such solvents as acetonitrile, acetone, N-methyl-pyrrolidine-2-one, ethanol, etc. [17,39,40,41,42,43,44]. Sun and Bunker, who first revealed the formation of C₇₀ aggregates in the toluene–acetonitrile solvent system, considered the new species as clusters, quite different from colloidal ones [45]. However, their next studies [46,47] as well as subsequent research [39,44], make it possible to classify these systems as colloidal. In water, only hydrosols and suspensions are formed [17,20,22,23,24,25].

Many basic solvents form complexes with fullerenes. They are, for example, 1-methylpiperazine, 1-methylpyrrolidone, 1-methylpiperidone, trihexylamine, tetrakis(dimethylamine)ethylene [48]. The interactions can be even stronger and result in the formation of covalent bonds in cases of piperazine, homopiperazine, N,N′-dimethylethylenediamine, and piperazine [49,50]. Therefore these and some other nitrogen-containing compounds, which readily form covalently modified fullerene molecules, are called “reactive” solvents [24].

2.2. Peculiarities of Fullerenes Dissolution

For solutions that were considered as true (molecular) ones, i.e., non-colloidal, a number of correlations were proposed in order to explain the fullerene solubility with the help of various solvent descriptors, including the QSPR (quantitative solvent-property relationship) approach; this problem was considered in a previous review [24]. In such procedures, it is necessary to take into account the formation of crystal solvates of fullerenes with some solvents [51]. This effect was revealed in connection with the detection of an extremum on the dependence of solubility on temperature in some solvents [52]. According to Beck, “there are two problems concerning the molecular states of fullerenes in solution. One should determine the degree of self-association and determine the nature and extent of interaction between the fullerene and the solvent molecules.” [53].

The analysis of the solubility in respect to the Hildebrand constant of the solvents performed by many authors revealed that the optimal ${\delta }_{\mathrm{H}}$ value is within the range of 18 to 20 MPa^1/2 [24]. Ruelle et al. [54] stated that the highest solubility of C₆₀ corresponds to solvents with ${\delta }_{\mathrm{H}}$ = 20.0. As early as 1993, Ruoff et al. [28] stated that a typical “good” solvent for C₆₀ must have a relative permittivity value about ${\epsilon }_r$ = 4, a large refraction index and molecular volume, the ${\delta }_{\mathrm{H}}$ value of 20 MPa^1/2, and tendency to act as a moderate strength nucleophile. The latter indicates that the fullerene is a kind of a Lewis acid. This feature is important for understanding the stability of C₆₀ and C₇₀ colloids in respect of electrolytes in polar solvents; see Section 4.2.

A detailed analysis of 1213 solvents was made using the three-dimensional Hansen solvent parameter [38]. The later allows separately estimate three contributions to the Hildebrand constant of the solvent. Using 15 “good” solvents, Hansen and Smith estimated the corresponding contributions for the C₆₀ solute that are as follows: 19.7 MPa^1/2 for nonpolar dispersion, 2.9 MPa^1/2 for permanent dipole–permanent dipole interactions, and 2.7 MPa^1/2 for hydrogen bonding interactions [38]. The ${\delta }_{\mathrm{H}}$ value for C₆₀ is a square root of the sum of the corresponding squares: 20.1 MPa^1/2. Also, 55 additional earlier not experimentally examined liquids were proposed as “good” solvents for C₆₀, where the solubility reaches molar fraction 0.001 [38]. Cataldo calculated the δ_H values for fullerenes from C₆₀ (19.5 MPa^1/2) to C₉₀ (δ_H = 20.7 MPa^1/2) [55].

In some theoretical studies, the relation between solvation of a fullerene molecule and solubility has been disclosed. For example, Wang et al. [56] used the molecular dynamics simulation of C₆₀ in different solvents to estimate the half-life time of solvent molecules encompassing the fullerene molecule, t_1/2, as well as other parameters of the solvation shell. A pronounced drop of solubility along with decrease in t_1/2 in chlorobenzene, toluene, trichloromethane, ethanol, and water was revealed. Further study on fullerene C₆₀ and its derivative [6,6]-phenyl-C₆₁-butyric acid methyl ester, PC₆₁BM, demonstrated a single time contact characterizing the dynamic stability of angstrom-size solvation shell allows to know the trend of fullerene solubility [57]. Peerless et al. [58] studied the correlation between solvation shell structure, solvate formation, and solubility. Molecular dynamics simulations for C₆₀ and PC₆₁BM in nine aromatic solvents have shown the clear dependence of solubility and solution enthalpy on the degree of order of the solvation shell. Quantum-chemical calculations performed by Zhang et al. [59] for C₆₀ in “good” solvents demonstrated that the solubility is generally proportional to the intermolecular force between solute and solvent.

If “poor” solvents are included in various considerations, it should be taken into account that the very low solubility, determined experimentally, may reflect the (possible) presence of colloidal species. Note that most of the available solubility data were obtained without checking the presence of colloids. This issue is of special importance for fullerene solutions. Non-equilibrium methods of preparation can readily result in formation of oversaturated solutions and colloids even in “good” solvents [60,61,62]. This is likely the main reason of a substantial scatter of the published solubility data. By non-equilibrium methods of preparing solutions, we mean intensive mixing, stirring, sonication, etc. For example, Ruoff et al. determined the solubility of C₆₀ in benzonitrile to be 5.7 × 10⁻⁴ M [28]. Five years later, Nath et al. firmly proved the appearance of ca. 250 nm-sized aggregates at fullerene concentration over 1 × 10⁻⁴ M [63].

Interestingly, the solubility value of fullerenes in dimethylsulfoxide (DMSO) is absent in the available data summaries, though C₆₀ and C₇₀ solutions in DMSO and DMSO–water mixed solvent were already used in 1993 for spreading fullerenes at the water/air surface [64]. Accordingly, DMSO was not included in the correlations between solubility and solvent descriptors. In 2013, Pushkarova and Kholin [65] analyzed the solubility of C₆₀ at 25 °C, basing on Kohonen and probabilistic networks, used a set of nine characteristics of 76 solvents. As a result, they divided the data into eleven solvent groups; DMSO appeared in a group together with N-methylpyrrolidine-2-one (x₂ = 1.2 × 10⁻⁴), benzonitrile (x₂ = 6.3 × 10⁻⁵), nitromethane, and acetonitrile (negligible solubility). As will be demonstrated in Section 4.2, C₆₀ readily forms a colloid solution in DMSO.

As for the targeted preparation of colloidal solutions, there are two ways. Formation of colloidal particles occurs either “top-down” or “bottom-up”. The first approach presumes application of sonication, mechanical impact, grinding, trituration, laser beam, etc. The second one consists of the dilution of a stock molecular solution of fullerene in a “good” solvent with a polar solvent. For this purpose, fullerene solutions in toluene, benzene, or CS₂ are often used.

3. Fullerene Solutions in “Good” Solvents as a Platform for Preparation of Colloids

3.1. Precautions for Preparing Molecular Solutions of Fullerenes in “Good” Solvents

It should be noted that even the preparation of fullerene molecular solutions via the equilibrium procedure in “good” solvents is a nontrivial task [21,24,66,67]. For example, Aksenov et al. revealed a non-monotone change of the total C₆₀ concentration in CS₂ solution over time [67]. They explained it by simultaneous passing of dissolution of the solid phase, aggregation, and sedimentation of large-sized aggregates [67]. Many other examples of such peculiarities of solution preparation can be found in the previous review [24] and references cited therein. After being stored in the dark for at least ten days or, for better results, two weeks, filtering through 220 nm or 450 nm pored filters is necessary, because small pieces of the solid phase can be introduced into the liquid phase. Additional verification of the absence of large-sized species can be made by dynamic light scattering-based methods. Sonication favors clustering of fullerene molecules both in “good” solvents [21,53,60,61] and n-hexane [68]. Checking of the presence of oxidation products is also desirable. These products can appear as result of contact with the atmosphere, illumination, and sonication; the oxidation of fullerene molecules can favor the aggregation processes [69]. The most probable admixture in the commercial samples of C₆₀ is C₆₀O. In general, the biography of the initial solid sample can sometimes influence the results. Recently we have mentioned that if the stock solutions of fullerene C₇₀ in benzene or toluene are kept at low temperatures, the colloid systems obtained by dilution with acetonitrile exhibit somewhat different properties [70]. Note that C₆₀ aggregates were observed by other authors when solutions were prepared in benzene and CS₂ at temperature of solvent freezing [71,72].

As an example of UV-visible spectral data, the molar absorptivities of fullerenes in toluene and benzene are presented in

Table 1. The values of ${\lambda }_{\max }$, nm and (in parenthesis) molar absorptivity, $E_{\max }$ × 10⁻³, M⁻¹ cm⁻¹.

C60 a		C70 b
Benzene	Toluene	Benzene	Toluene
335 (64.30)	336 (58.43)	333 (45.5)	334 (37.9)
407 (2.962)	407 (3.163)	365 (33.3)	365 (28.7)
541 (0.911)	541 (0.908)	382 (44.5)	383 (37.8)
596.5 (0.809)	596.5 (0.798)	472 (24.5)	473 (21.0) c

Note. ^a The values for C₆₀ for 20 °C are taken from ref. [73]. ^b [74] ^c [46,47,75].

. These values can be used for determination of the concentration of a fullerene in a working solution; they obey the Bouguer–Lambert–Beer law within the concentration range of (0.06 to 6.00) × 10⁻⁴ M [73]. We used the molar absorptivities of C₆₀ for determination of the solubility in benzene and toluene, (2.04 ± 0.02) × 10⁻³ and (3.84 ± 0.10) × 10⁻³ M, respectively [73]. Average values of the literature data at 25 °C or room temperature are 2.2 × 10⁻³ and 3.7 × 10⁻³ M [24].

The $E_{\max }$ value of 21.0 × 10³ M⁻¹ cm⁻¹ for C₇₀ in toluene at 473 nm was taken as an average of three publications by Sun, Bunker, and co-authors [46,47,75]. Based on this value, we determined accurate values at 25 °C for other wavelengths [74]. Accordingly, the molar absorptivities of C₇₀ in toluene–benzene mixtures and benzene were estimated. For C₆₀ in benzene and toluene, Gunkin and Loginova [76] reported somewhat lower ${\lambda }_{\max }$ and $E_{\max }$ values as compared with Table 1.

Accurate values for both fullerene solutions in ortho-xylene and ortho-dichlorobenzene were determined by Törpe and Belton [37]. For example, the ${\lambda }_{\max }$, nm ($E_{\max }$ × 10⁻³, M⁻¹ cm⁻¹) values for C₆₀ in ortho-xylene and ortho-dichlorobenzene are 336 (50.63) and 334 (60.37); for C₇₀ they equal 336 (40.61) and 334 (38.83), respectively. In the cited article, an overview of the literature data was presented as well [37]. Data in n-hexane were published by Cataldo et al. [77].

Formation of fullerene aggregates in “good” solvents was reported by different research groups. Some authors state that they can be easily destroyed by hand-shaking [78,79], while others report that the aggregation is irreversible [41]. In the last publication, a radical scavenger is used to prevent the aggregation that may occur thorough the disproportionation process. On the other hand, evidence is given for aggregation and nucleation as a result of fullerene interaction with the surface of the flask [41]. According to Bezmelnitsin et al. [80,81], C₆₀ in carbon disulfide behaves as a “cluster substance”. However, it was shown using the SANS (small-angle neutron scattering) method that equilibrium procedure of preparation leads to a C₆₀ molecular solution in CS₂ [21]. Fullerene solutions in “good” solvents tend to form oversaturated solution, aggregates, and sediment. Based on the SANS method, Avdeev et al. introduced a definition “final quasistationary state of solutions” for low-polarity solvents; small 6 nm-sized clusters can appear near the solubility limit [21]. Using the same method, Török et al. [66] revealed fractal clusters of C₆₀ in toluene at concentrations close to saturation.

3.2. Specific Properties of Molecular Solutions of Fullerenes

Despite the peculiarities mentioned above and some other obstacles, there is a wealth of information on the (unusual) properties of true molecular fullerene solutions in CS₂ and some aromatic solvents. For example, after evaporation of benzene the solid C₆₀ cannot be re-dissolved completely [79]. C₆₀ and C₇₀ in benzene, toluene, and para-xylene within the concentration range of 10⁻⁴ to 0.05 mass % exhibit properties atypical for true solutions [82,83,84]. The concentration dependence of density is nonmonotonous [82], and the same refers to the relative permittivity [85]. Concentration dependence of boiling point was also reported [86]. Structural ordering by X-ray diffraction studies was revealed by Ginzburg, Tuichiev, and their co-authors long ago and confirmed by ebullioscopy and other methods [82,83,84]. These investigations were continued [87,88]. They firmly proved that in the boiling process, the number of the solvent molecules related to one solute molecule in the act of phase transition is within the range of ca. 500 to 1000. Different methods allow concluding that for C₆₀ and C₇₀ in benzene, toluene, bromobenzene, 1,2-dichlorobenzene, and para-xylene, the single fullerene molecule is surrounded by several hundreds of molecules of aromatic compounds; columns of solvent tens of nanometers long are formed. This is in line with their previous data concerning the large solvation shells deduced from the X-ray diffraction patterns [84]. Zhelezny et al. [89] supported these ideas when studying C₆₀ in ortho-xylene. Compressibility studies of C₆₀ solution in toluene allowed deducing that the solvation shell thickness is about 1 nm [90].

A number of important theoretical publications have appeared over the past decade, devoted to the solvation of fullerenes in “good” solvents, including the nature of the solvation shells around the C₆₀ and C₇₀ molecules. These studies confirm in outline the above vision of the fullerene state in “good” solvents [56,91,92]. Fritsch et al. [91] reported the formation of a structured ca. 1 nm-thick toluene layer around a C₆₀ molecule. In another molecular dynamics study, it has been shown that “aromatic solvents are comparatively more structured then the aliphatic ones in close vicinity of C₆₀” [56]. According to quantum-chemical calculations of Li et al., “the π^…π stacking configurations of the complex C₆H₆^…C₆₀ are more strongly bound than the C−H^…π analogues, and the C−H^…π interactions in the C−H^…π configurations of C₆H₆^…C₆₀ are not of the hydrogen bond” [92]. These conclusions are based on the quantitative estimations of the interaction energies [92].

These remarkable results can be consisted with previously published theoretical and experimental studies. So, it was shown that the standard entropy values, $\Delta S^0$, of dissolution and solvation of fullerenes C₆₀ and C₇₀ in “good” solvents are substantially negative [93,94,95,96,97]. For instance, the $\Delta S_{\mathrm{solut}}^0$ values of fullerene C₆₀ dissolution in ortho- and meta-xylene, bromobenzene, 1,2-dichlorobenzene, CCl₄, and toluene are about ≈−100 J mol⁻¹ K⁻¹ [24,94,95]. The solvation entropy for C₆₀ in aromatic solvents, CCl₄, and tetralin is also negative, about $\Delta S_{solv}^0$ ≈ −200 J mole⁻¹ K⁻¹. Such a sharp decrease in entropy indicates an ordering of the solvent structure, similar to what occurs during the well-known hydrophobic hydration of hydrocarbons in aqueous solutions.

The same can be expected for polar (“poor”) solvents, where the solvophobic nature of fullerene colloids is undisputable [23,24,98,99,100,101]. In the recently named systems, it leads to formation of colloidal aggregates owing to solvophobic interactions. Solvophobic properties of solutions of C₆₀ in tetrahydrofurane, benzonitrile, and in other solvents were proved as early as 1992 [102].

The size of the C₆₀, C₇₀, and even more so of higher fullerenes corresponds to the turning point between usual molecules and colloidal particles. They can also be considered as sub-colloidal particles. This allows regarding this kind of nanocarbon as a unique object, which can be a challenge for application of the common principles of solution chemistry. The most important feature is the structure of fullerenes that makes them impenetrable for solvent molecules. This distinguishes them from many much larger molecules, the separate portions of which are solvated individually.

Therefore, the fullerene molecular solution can also be considered as a kind of a colloid system. The solvation layers around the molecules are thick enough to pronouncedly alter the solvent properties. Such systems resemble the so-called periodic colloidal structures [103,104,105] or colloidal crystals [106,107]. In other words, according to the DLVO terminology, it looks like a system that is coagulated in the “distant minimum”. Any external influence readily leads to aggregation or deposition.

This issue should be considered in a more detailed way in future. However, as a preliminary conclusion it may be stated that even molecular solutions of fullerenes in “good” solvents exhibit some colloidal features. From the time of Wolfgang Ostwald [108] and Peter von Weimarn [109], it is known that any chemical compound can be, depending on the nature of the solvent, obtained in a colloidal state. Apparently, due to peculiarities of the molecular structure, in particular, due to the extremely high surface atomic density, fullerenes are compounds that exist in a colloidal state or, at least, exhibit colloidal features, in almost any solvent. (Of course, almost infinite dilutions down to “homeopathic” concentrations in any solvent, “good” and “poor”, will result in a true molecular solution, but this is beyond the scope of our discussion).

In addition to the above considered publications, some other interesting articles are worth to consider. Recently, Garcia-Hernandez et al. [110] isolated the complexes of C₇₀ with three acenes and characterized them by FTIR, TGA, DSC, and electronic absorption spectra. This again gives evidence of strong interaction between fullerenes and aromatics.

On the other hand, Zhang and Li [111] presented a convincing example of governing the shape of fullerene solid species by evaporation of C₆₀ solution in CS₂ under various solvent atmospheres. SEM images demonstrated different architectures of species: belts, sheets, and starfishes depending on the kind of solvent. Twenty different organic liquids were used, which, except for toluene, belong to poor solvents. Previous publications in this direction are also referred to by these authors [111].

3.3. Forced Aggregation of Fullerenes in “Good” Solvents

Until now, we have considered the aggregation of fullerenes rather as a phenomenon that interferes with the preparation of molecular solutions by equilibrium methods. But sometimes prolonged sonication is used consciously to obtain and study aggregates.

Bokare and Patnaik [60,61] purposefully created fullerene aggregates in CS₂ via sonication. Subsequently, Guo et al. [112] prepared C₆₀ solutions in toluene and chlorobenzene via sonication 10 h per day at 50 °C for 4 days. SLS/DLS (static and dynamic light scattering), depolarized DLS, SAXS (small-angle X-ray scattering), and cryo-TEM methods were used in order to characterize thus obtained fullerene aggregates. Though all aggregates have the size of several hundred nm, it was revealed that while aggregate clusters are anisotropic in shape in chlorobenzene, they are basically isotropic in toluene. Solvent-induced differences were disclosed by other methods as well [112].

A series of studies with C₆₀ and C₇₀ fullerenes were performed by Makhmanov et al. [113,114,115,116]. Two methods of preparation of C₆₀ in toluene, non-equilibrium and equilibrium, were compared [113]. Stirring with a magnetic stirrer within 14 days allowed the authors to obtain porous particles with diameter of 380 ± 20 nm and fractal dimension D_f = 2.13. Storing C₆₀ in toluene for the same period results in the formation of particles with size $\le$50 nm, as determined by the TEM and AFM methods. It was revealed that in C₇₀ solutions in xylene–tetrahydrofurane, the changes of the refractive index over time reflect the formation and stabilization of colloidal particles [116].

Makhmanov published interesting results for C₆₀ fullerene in the xylene–hexane binary solvent [115]. In these solutions, prepared using magnetic stirrer and passed through 220 nm pores, the diameter of colloidal particles reaches 60–70 nm. The measurements were accompanied by determination of the refractive index; fullerene concentration was 5 × 10⁻⁵ M. TEM and DLS methods were used in this investigation. Despite the low ${\epsilon }_r$ values, the author managed to determine the electrokinetic potential of −(26.6–28.2) mV; solutions were stable up to 72 h.

Bakhramov et al. [4] developed a method of preparation of C₇₀ nanowhiskers, C₇₀NW, by thermal evaporation of droplets of toluene solutions. The average length of the obtained species was 1.8 $\mathsf{\mu }\mathrm{m}$ with width up to 175 nm; the shape was confirmed by SEM [4]. Solutions of C₆₀ in toluene–tetrahydrofurane were used for fractal coating with thickness up to ca. 1.2 $\mathsf{\mu }\mathrm{m}$ on a flat dielectric glass surface [114].

Jia et al. [1] improved the formation of high quality homogeneous C₆₀ films for preparation of the perovskite solar cells by adding PC₆₁MB in chlorobenzene to C₆₀ solutions in ortho-xylene to suppress the aggregation of fullerene solutions prepared using sonication.

PC₆₁BM and PC₇₁BM are now very popular because of their use in photovoltaic devices. Therefore, their properties in solutions are intensively studied using both theoretical [2,57,58,117,118] and experimental methods [2]. In the last work, agglomeration of both derivatives was examined in trichloromethane, toluene, chlorobenzene, and 1,8-diiodooctane using the Spin-Echo Small Angle Neutron Scattering (SESANS) method. The solutions were prepared by intensive stirring at elevated temperature. As a result, formations of large agglomerates were observed for PC₆₁BM, but not for PC₇₁BM.

3.4. Some Examples of Theoretical Modeling of Fullerene Aggregation

Paliy et al. [118] performed a molecular dynamic study of two C₆₀ molecules with a charge of −5e in a trichloromethane droplet, either with or without 10 and 20 Na⁺ ions. The results clearly illustrate the regulation of the state of C₆₀ molecules with the help of charge. Negatively charged particles, like C₆₀⁵⁻, repel each other, particles neutralized by adsorbed counterions stick together and overcharged and thus positive particles repel each other again. Also, the influence of the nanocarbon species on the state of the nanodroplets is studied. The same simulations were made for a carbon nanotube [119]. This is a good explanation of the overcharging phenomenon, which will be considered by us in Section 5.2.

Somewhat earlier than this study, molecular dynamics modelling was also used by Banerjee [120] for fullerenes C₆₀, C₁₈₀, C₂₄₀, and C₅₄₀ in toluene, acetone, and water. It was shown that the diffusion coefficient of solvent molecules in the solvation shells is much lower than of those in the bulk liquid. Uncharged fullerene molecules agglomerate in water and acetone, but not in toluene. Introducing a negative charge from −0.5e to −3e per molecule, with Na⁺ as counterions, results in repulsion of molecules and significantly reduces agglomeration in polar solvents; in toluene, the sodium ions associate with anions in accordance with the known regularities for electrolytes in non-polar solutions [120]. These theoretical results give a fairly accurate picture of the colloidal properties of fullerenes in solutions.

Mortuza and Banerjee [121] performed a molecular dynamics study of the behavior of PC₆₁BM in toluene, indane, and in mixtures of these two solvents at temperatures between 280 and 320 K with different concentrations of this fullerene derivative. It was demonstrated that large clusters are formed in toluene. Another important work of the same research group was based on the combination of molecular dynamics with kinetic Monte Carlo method [122]. The agglomeration of fullerene species was proved for aqueous NaCl solutions; this article will be considered later in Section 5.1 devoted to coagulation of hydrosols.

4. Formation and Properties of Colloidal Particles in “Good” + “Poor” and “Poor” Solvents

4.1. “Bottom-Up” Procedure of Fullerene Organosols Preparation

The variations of concentration and using different preparation methods, the fullerene spectra in high-solubility solvents stay almost unaffected. Contrary to it, a fundamental change is observed on going to polar solvents, and the DLS method firmly indicates appearance of colloidal species (Figure 1).

Let us consider the “bottom-up” procedure. Dilution of molecular solutions with acetonitrile, ethanol, methanol, and other “poor” solvents leads to formation of colloid solutions. In this case, the formation of colloidal species in solutions can be observed using UV-visible spectra. First it was demonstrated in the pioneering work by Sun and Bunker for fullerene C₇₀ in the toluene–acetonitrile binary solvent system [45]. Since then, a number of such studies with C₆₀ and C₇₀ fullerenes was published; benzene, toluene, carbon disulfide, and some other “good” solvents were used for preparation of the initial fullerene solutions [21,39,40,41,42,43,44,71,72,124,125,126].

Dilution of a fullerene solution in a polar solvent with another polar solvent is a special case [127] that will be considered below. Some studies were performed in this laboratory [70,73,98,99,101,123]. Figure 2 demonstrates the changes in the UV-visible absorption spectra of C₇₀ in toluene–acetonitrile along with the decrease in the CH₃CN concentration [70,99]. At high acetonitrile content, a contribution of light scattering cannot be ruled out [99].

It is well documented that in the toluene–acetonitrile system, the solvent mixing regime is of key importance [44,46]. For example, dropwise or prompt adding of CH₃CN to a toluene solution of C₇₀ results in principally different absorption spectra of fullerene [46]. Molecule–aggregate transitions of fullerenes are accompanied by changes in fluorescence [39,43,46].

It seems natural to reveal the critical composition of the binary solvent where the colloidal particles appear [45]. Nath et al. [42,43] subjected this problem to detailed study. Basing on a number of binary solvent systems and using the ${\epsilon }_r$ value as a characteristic of the solvent, they stated that C₆₀ forms molecular associates already at ${\epsilon }_r$ about 12–13, while C₇₀ only at ${\epsilon }_r$ 27–31. Such differences are explained by a stronger interaction of C₇₀ with “good” solvents [43]. These critical parameters were determined by both electronic absorption spectra and DLS, and the results agree [42,43]. It should be noted that in these works, the ${\epsilon }_r$ values of mixed solvents were calculated using the additive scheme, which can lead to some (slight) errors [73]. Also, it is well known that many properties of solutes can substantially differ in isodielectric solvents [128].

Two remarks should be made on this. First, even when the DLS method demonstrates the formation of colloidal particles and absence of molecular species, the UV-visible spectra retain the features of molecular absorption [70,73,99,101]. In other words, the onset concentration of the polar co-solvent is somewhat lower as determined by light scattering. For example, for the system presented in Figure 3, the critical content of acetonitrile is 62 vol.% and 64–70 vol.% as obtained by DLS and UV-visible spectroscopy, respectively [99]. Such findings can be explained either by hindering of observation of fullerene molecules in the presence of much stronger light scattering colloidal aggregates or by retaining aromatic solvation shells of fullerenes involved into the aggregates. Note that in a toluene–n-hexane solvent system, the absorption spectrum of C₇₀ changes gradually along with rise of the aliphatic component, whereas no sign of colloidal particles is observed. This phenomenon is obviously caused by replacing the toluene molecules in the primary solvation shells of C₇₀ by n-hexane [99] and of C₆₀ by dichloromethane [129].

Second, the fullerene concentration is an important factor. Sun and Bunker [45] mentioned that in a toluene–70% acetonitrile mixture, the absorption spectrum of C₇₀ at concentration $\le$ 8 × 10⁻⁸ M is close to that in neat toluene. We confirmed this early statement using the DLS method: at C₇₀ concentration of 1.2 × 10⁻⁷ M under the same conditions, only species with a size of ca. 1 nm were found [70,99].

A more detailed consideration of the formation of fullerene colloidal species in the toluene–methanol system [73] reveals that the size of the aggregates decreases along with the increase in the polar solvent fraction. This is in accordance with the classical regularity formulated by Volmer [130]: the lower the solubility is, the smaller the colloidal particles are formed. However, if the initial toluene solution of C₆₀ is prepared by a non-equilibrium method and oversaturated, the situation observed for a toluene–acetonitrile solvent system can be reverse [129].

Interestingly, Pille et al. [131] considered the alterations of the C₆₀ UV-visible absorption spectra on adding acetic acid, acetonitrile, methanol, DMSO, and DMF to a 1.3 × 10⁻³ M toluene solution in terms of preferential solvation, not aggregation. The stock solution was prepared using stirring and sonication.

Recently, Kyzyma et al. [129] conducted a detailed study of the C₆₀–toluene–acetonitrile system using the UV-visible absorption spectra, TEM, DLS, SLS, SAXS, SANS, and LDI mass-spectrometry. Two series of experiments were performed, starting with C₆₀ solutions in toluene prepared by equilibrium and non-equilibrium (sonication) methods. The C₆₀ working concentrations were (4.0–6.3) × 10⁻⁶ and (0.23–1.9) × 10⁻³ M, respectively. In all cases, adding of acetonitrile to the toluene solutions of C₆₀ favors aggregation. It is firmly proved that oxidation and illumination display pronounced influence on the aggregation processes. In the cited article [129], the obtained data are compared with the results published by others.

In entire benzonitrile and benzyl alcohol, a threshold concentration of fullerene C₆₀ aggregation was reported [63]. These polar solvents belong to the aromatic ones. For example, in benzonitrile, a solvent with ${\epsilon }_r$ = 26, colloidal ≈250 nm-sized particles appear at 1 × 10⁻⁴ M. Note that ultrasonication was used for preparation; larger particles may be removed by centrifugation and decantation [63]. This critical concentration was estimated by both DLS and visible spectra at λ = 450–700 nm; the nC₆₀ ⇌ (C₆₀)_n equilibrium is reversible [63]. This is typical rather to lyophilic systems, like diphilic surfactants in water, which are characterized by a critical micelle concentration, CMC. However, the fundamental difference consists of the limiting solubility (here, it is 5.7 × 10⁻⁴ M [28,35]), whereas for common surfactants in water, after reaching the CMC, the micellar solubility rises up to gelation. On the other hand, as it was mentioned in Section 3.1, small fullerene aggregates can appear near the solubility limit even in “good” solvents [21]. Obviously, the same takes place for the C₆₀ solutions in benzonitrile.

For C₆₀ in the toluene–acetone binary solvent system, the effects are similar to those observed for toluene or benzene mixtures with acetonitrile [73]. If a benzene solution of C₇₀ is diluted by DMSO, the spectral changes resemble those presented in Figure 2. At DMSO content of 33 vol.%, no sign of colloidal particles is observed (Figure 4). The turning point of molecule–aggregate transition is about 60 vol.% DMSO [74].

It should be noted that, contrary to the mixtures of a “good” solvents with methanol and acetonitrile, the size colloidal particles does not decrease near 100% DMSO. Obviously, DMSO plays another role compared to “poor” solvents, due to good solvation of C₇₀ molecules. The properties of the DMSO-based systems will be considered in the next sections.

4.2. “Top-Down” Preparation of Organosols and Suspensions

Another way is the “top-down” preparation. This means the breaking, grinding, mixing, and stirring of a solid sample in a polar solvent. Sonication and laser beam treatment can be also used. A more practical procedure was developed by Deguchi and Mukai [132]. The “top-down” preparation of C₆₀ colloids in methanol, ethanol, 1-propanol, 2-propanol, 1-octanol, acetonitrile, and acetone was performed using 1–2 min hand-grinding of the solid sample in an agate mortar and sonication in a “poor” solvent [132]. Furthermore, the same research group used this procedure to obtain stable graphite dispersion in aqueous acetone [133].

We have repeated this protocol for C₆₀ in acetonitrile with some modifications [100,129]. The size of particles as determined by DLS is 200–300 nm, in agreement with Deguchi and Murai [131] and with our TEM data. The size distribution by number, scattering volume, and intensity is similar; the repeatability is medium, the polydispersity index, PDI, is 0.3 on average. Dilution with benzene (Figure 5) allowed determination of the initial fullerene concentration in acetonitrile of ca. 3 × 10⁻⁵ M.

Fullerene C₆₀ and C₇₀ solutions in N-methylpyrrolidine-2-one, NMP (${\epsilon }_r$ = 32), are a special case [17,21,125,126,127,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148]. While dilution of fullerene solutions in toluene, benzene, or CS₂ by acetonitrile, acetone, or alcohols is quite understandable from the point of view of colloid chemistry as an example of “bottom-up” preparation, the “top-down” preparation of fullerene colloids in the last “poor” solvents needs sonication. However, sonication is unnecessary in NMP. In earlier studies [125,126], C₆₀ and C₇₀ solutions in toluene were diluted with NMP in order to prepare colloidal solutions. Also, sonication was used for the preparation of fullerene solutions in toluene, toluene–NMP mixtures, and in entire NMP. In other cited papers, the fullerene solutions were prepared directly by stirring the solid sample in NMP. The stirring time varied from 10–15 min [138,140,143,146,147] to 1 h [136,139,144], 6 h [141], 24 h [127] or four days [135]. In some studies, initial solutions for investigation of the NMP–toluene systems were prepared either in toluene or in both polar and “good” nonpolar solvents [140,143,144,145].

Detailed studies of C₆₀ [134,135,136,138,139,140,141,144,147] and C₇₀ [143,145,146] in NMP-based systems made it possible to shed light upon the unusual properties of this solvent in respect to fullerenes. The main specific feature is the strong interaction between the fullerene and solvent molecules. Obviously, it is a kind of donor–acceptor interaction, which results in formation of charge transfer complexes [139,141,144,147] proved by the ¹H NMR spectroscopy, quantum-chemical calculations [139,144], and mass spectra [135,144]. Another property is ageing of fullerene solutions over time, slow increasing in size up to ca. 500 nm as determined by DLS, SANS, and SAXS methods. The UV-visible spectra exhibit some bands characteristic for molecular absorption, but after preparation of solutions, smoothing of the absorption curve begins immediately, and the spectrum strongly resembles that shown in left hand side of Figure 5. Importantly, using some assumptions it was demonstrated that the Mie light scattering makes a negligible contribution it this case [135].

Sun et al. [149] studied the behavior of C₆₀ and C₇₀ in entire triethylamine. The UV-visible spectra of the solutions prepared either by sonication or without it exhibit a smooth curve. UV-visible spectra of freshly prepared solutions exhibit some features of molecular absorption. However, within 2 h, the spectra curve became completely structureless, like in the above mentioned case of NMP. However, the authors assume that the origin of the absorption changes is a chemical reaction, not a complex formation. This point of view is based on the NMR spectra and fluorescence data. This allows classifying triethylamine as a “reactive” solvent.

Returning to the NMP, it should be concluded that, in any case, the reason for the ease of dissolution is the strong interaction of this electron-donor solvent with fullerenes. In toluene–NMP binary solvents, formation of 55–60 nm particles occurs within ca. 1 h [125,126]. A set of works were devoted to absorption spectra of fullerenes in the toluene–NMP system at different sequence of components adding [125,126,140,141,143,144,145,146]. These data demonstrate peculiarities of competition between these two solvents in the solvation shells of fullerene molecules. Because of some information on the irreversible changes of the fullerene solutions [140], the NMP may be (partly) attributed to the “reactive” ones.

Some studies were devoted to kinetics of fullerene aggregation [21,150]. The nucleation process was studied in detail be Tropin, Avdeev, Aksenov, and their colleagues in NMP [21,137,142,151,152]. These authors managed to describe the experimental data using the model of complex formation between fullerene and solvent.

Obviously, the electron-donor properties of solvents are of the crucial role in solvation of fullerenes, which are Lewis acids [74]. While the value of the relative permittivity, ${\epsilon }_r$, is used to characterize the solvent polarity, the Gutmann’s donor number, DN, describes the cationophilic properties [128,153]. In

Table 2. Solvent characterization from ref. [128].

Solvent	${\mathit{\epsilon }}_{\mathit{r}}$	DN
Benzonitrile	25.2	11.9
Acetonitrile	35.9	14.1
Acetone	20.6	17.0
Methanol	32.7	19.1 a
Water	78.4	24.3 a
DMF	36.7	26.6
NMP	32.2	27.3
DMSO	46.4	29.8
Triethylamine	2.42	31.7
Pyridine	12.9	33.1

Note. ^a Approximate estimates.

, both parameters for some selected solvents are given (mainly at 25 °C).

Among the non-hydrogen bond donor solvents, the first three in Table 2 are typical protophobic (cationophobic) ones, while the last five are protophilic (cationophilic). Pyridine dissolves the C₆₀ fullerene, and aggregates were observed via DLS [154]. The preparation of solutions of C₆₀ in DMF was described by at least two research groups [155,156]. However, recently the colloidal solutions in this solvent were obtained even easier [74]. Note that some organic solvents may become unstable over time. For example, DMF can decompose to formic acid and dimethylamine [157]. In our study, we used freshly purified and distilled DMF.

Although solutions of fullerenes in DMSO and DMSO–water solvents were already obtained in 1993 and were used for spreading at the water/air interface [64], these systems were not further considered in more detail. Wang et al. [64] reported no details of the preparation of solutions. For DMSO, the sonication is undesirable (After even several minutes of sonication, substantial amounts of acidic admixtures appear in DMSO; colloidal particles of fullerenes became positively charged and unstable [74].) but fortunately not necessary [74], analogous to the case of NMP. We prepared C₆₀ and C₇₀ colloidal solutions in DMSO and DMF by hand grinding in an agate mortar and 3 h mixing with a magnetic stirrer [74]. The solutions are rather stable over time and contain ≈200–250 nm-sized particles with substantially negative electrokinetic potential. The repeatability of the preparation procedure was good.

UV-visible absorption spectra are typified in Figure 6. Particle sizes and size distribution do not undergo major changes over time. In the freshly prepared solutions of C₇₀ in DMF, the molecular bands are observed with the ${\lambda }_{\max }$, nm ($E_{\max }$ × 10⁻³ M⁻¹cm⁻¹) values of 331 (55.7); 360 (43.2), 380 (56.0), and 467 (31.4). However, smoothing of the spectral curve begins shortly after the preparation of solutions. For the C₆₀ solution in DMF, typical molecular band of 332–333 nm was observed immediately after preparation.

Similar results were obtained in DMSO: C₇₀ exhibits molecular bands of 333, 363, 380, and 470 nm, and smoothing of the curve takes place (Figure 7).

Despite a significant variety of solvent compositions of organosols (suspensions) of fullerenes, they have one important property in common. Namely, colloidal particles are always negatively charged [44]. Now we have a set of electrokinetic potential values in different solvents, calculated using the Henry equation (Ohshima approximation) [158,159]. They are compiled in

Table 3. Values of the electrokinetic potential of organosols, 25 °C.

Fullerene	Solvent	$\mathit{\varsigma }$, mV a	Reference
C60	Methanol	–37	[123]
–“–	CH3CN—0.1 vol.% toluene	–53	[98,129,160]
–“–	CH3CN—0.1 vol.% toluene	–(47–51)	[98,129,160]
–“–	CH3CN—benzene (1:1 by vol.)	–53	[98,101]
–“–	DMSO	–34	[74]
C70	CH3CN—10 vol.% toluene	–55	[70]
–“–	DMSO	–42	[74]
–“–	DMSO—10 vol.% benzene	–45	[74]

Note. ^a The accuracy is normally ±(3–8) mV.

. (The overcharging phenomenon in the presence of electrolytes will be considered in Section 5).

These results are in agreement with the earlier published work by Alargova et al. [44], where the $\varsigma$ = −(32.5–38.5) mV in acetonitrile for colloids if C₆₀, C₇₀, and their mixtures was reported. Their calculations were processed using the Smolukhowski equation; for recalculation to the Henry equation, they are −(48.8–57.8) mV.

The origin of the charge of fullerene colloidal species in polar organic solvents is of special interest. The transfer of electrons from the solvent molecules to fullerenes is obviously the most probable path [44]. Also, disproportionation of the C₆₀ molecules into oppositely charged radicals can also take place [41]. In the latter case, it favors aggregation even in a “good” solvent; this process can be suppressed by introducing a radical scavenger [41]. Indeed, we have demonstrated that if a benzene solution of C₆₀ is mixed with an equal volume of acetonitrile in the presence of 2,6-di-tert-butyl-4-methylphenol, a substantial decrease in the $\varsigma$ value, accompanied by a jump of the particle size, takes place [101]. Within a period of 1 h, the average size reaches 1700 nm, and then the precipitation of fullerene takes place, while $\varsigma$ approaches zero [101]. If, however, the radical scavenger is added at 1.5 h after formation of the colloid, no changes are observed. In a set of C₆₀ colloidal solutions in acetonitrile, prepared by hand-grinding and sonication [100], the $\varsigma$ value was within the range of −(42–63) mV, average value $\varsigma$ = −48 mV. If acetonitrile contains a radical scavenger 2,6-di-tert-butyl-4-methylphenol, the interfacial charge greatly reduces; $\varsigma$ is about −10 mV. This further confirms that free radicals are a source of charge formation. Similar but not expressed changes are observed in acetonitrile with 1 vol.% toluene [101]. For C₇₀ colloids, the above effects were almost imperceptible.

Fullerene solutions in polar basic solvents can readily be mixed with water. This was demonstrated by Mrzel et al. [154] for pyridine. These authors underline the difference between the C₆₀ aggregates in pyridine and nanocapsulates of fullerene in pyridine–water mixtures [154]. DMSO-based organo-hydrosols of C₆₀ and C₇₀ were prepared by Wang et al. [64] and in our study [74]. Chaban et al. [161] studied the C₆₀–water–DMSO system using the molecular dynamics simulations and predicted good solvation of fullerene molecules by DMSO and fullerene aggregation. The same was demonstrated for the DMF–water systems [74]; Yang et al. [156] added water to the C₆₀ deposit after evaporation of DMF, and a hydrosol was obtained. Dilution of fullerene solution in NMP with water also results in organo-hydrosols [135,136,138,146,148]. In all these hybrid sols, the fullerene particles are also negatively charged.

To conclude this section, fullerenes in polar solvents exist as colloidal systems. However, all these solvents exhibit individual features. While methanol, acetonitrile, and acetone are typical “poor” solvents with C₆₀ solubilities of 3.3 × 10⁻⁸, 5.6 × 10⁻⁷, and 1.4 × 10⁻⁶ M, respectively [35], for cationophilic DMF, pyridine, and NMP this key parameter is higher: 3.75 × 10⁻⁵, 8.3 × 10⁻⁴, and 1.2 × 10⁻³ M, respectively [35]. On the other hand, the solubility of C₆₀ in benzonitrile, a polar solvent with the lowest DN value among collected in Table 2, is with 5.7 × 10⁻⁴ M substantial. Obviously, the reason is the aromatic nature of this solvent, which favors solvation of fullerenes. Moreover, just in this solvent single fullerene molecules predominate within a pronounced concentration range, before the aggregation is observed [63]. The same was reported by Nath et al. for the benzyl alcohol [42]; these authors underline the “intermediate” character of polar aromatic solvents. It can be argued that even for the few organic liquids discussed above, it is possible to divide them into three sub-groups of “poor” solvents.

Though NMP should be considered rather as a “poor” solvent, with some features of “reactive” ones, Stuart et al. [127] prepared a C₆₀ solution in acetonitrile by ten-fold dilution of the initial NMP solution with another “poor” solvent CH₃CN. Alargova et al. [44] consider NMP as a polar solvent, which “exhibits good solubility of C₆₀ (comparable to that in toluene), being an exception among the “good” solvents for fullerenes.“ Their experiments showed that dilution of C₆₀ solution in NMP with acetonitrile resulted in the formation of colloidal particles similar to those obtained using aromatic solvents instead of NMP [44]. However, it was firmly proved that, despite relatively easy dissolution of fullerenes in NMP, all solutes within a short interval of time transfer into colloidal state [134,135,136,138,139,140,141,143,144,145,146,147]. The same is true, e.g., for DMSO [74].

So, if such solvents can be classified as “high-solubility” to some extent, they dissolve fullerenes only in the form of colloidal aggregates. On the contrary, aromatic solvents dissolve fullerenes in molecular form under equilibrium conditions.

4.3. Fullerenes in Room Temperature Ionic Liquids, RTIL

Room temperature ionic liquids, RTIL, like fullerenes, have long ceased to be exotic compounds, but their combination has been relatively little studied to date. Theoretical studies on C₆₀ with were performed by Fileti, Chaban, and Maciel [162,163,164,165] and Garcia et al. [166,167], whereas Pádua group performed both experimental [168,169,170] and theoretic studies [168].

In the first article [168], interaction of C₆₀ with four ionic liquids having the same anion, bis(trifluoromethanesulfonyl)amide (Ntf₂⁻), and differing in the lengths of the alkyl chains of the 1-alkyl-3-methylimidazolium cations, from ethyl to n-decyl, was described. Solid fullerene was dissolved in CH₂Cl₂ using 5 min sonication and prolonged stirring. After mixing with the RTIL 1-decyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide and evaporating the molecular solvent, UV-visible spectra at C₆₀ concentrations up to 6.25 × 10⁻⁴ M demonstrated pronounced difference from that in CH₂Cl₂. Some difference in the behavior of the fluorinated fullerene, C₆₀F₄₈, was observed [168]. In the next study, it was shown that the enthalpy of mixing of decylmethylimidazolium bis(trifluoromethanesulfonyl)amide with 1,2-dichlorobenzene is more negative in case the organic solvent contains C₆₀ [169]. More detailed comparison of C₆₀ and C₆₀F₄₈ demonstrated that their solubilities in [bmim]⁺[Ntf₂⁻] are 7 × 10⁻⁵ and 6 × 10⁻⁴ M (here, bmim⁺ means 1-butyl-3-methylimidazolium cation). Whereas colloidal particles of C₆₀ are large, up to 5 × 10⁴ nm and sedimentates even at low concentrations, C₆₀F₄₈ exists as solvated isolated molecules or small aggregates and sedimentates only at concentration of 1.5 g/L. However, the smoothing of absorption curve also takes place for C₆₀F₄₈.

The solubility of C₇₀ in imidazolium-, ammonium-, and phosphonium-based RTIL was found even earlier in the course of fluorescence studies; Cl⁻ and Ntf₂⁻ were used as counter ions [171]. The procedure was as described above. The solubility of C₇₀ varied from 0 in [bmim⁺][BF₄⁻] to 9.5 × 10⁻⁵ M in [methyltrioctylammonium⁺][Ntf₂⁻]. Although the authors exclude the formation of suspensions, this conclusion is probably based on visual observation. In any case, the absorption curve is smooth. Hence, some kinds of aggregates seem to be probable.

Maciel and Fileti [162] used molecular dynamics simulations for estimating the solvation energy of C₆₀ in ethylammonium nitrate and 1-butyl-3-methylimidazolium tetrafluoroborate. The solvation of the fullerene by nitrate is substantially better than by the BF₄⁻ ion. The energy of C₆₀ transfer from the first to the second RTIL was estimated as 235 kJ mole⁻¹ (±1%) [162]. The modeling predicts separation of two C₆₀ by a bmim⁺ cation [163,164]. At the same time, fullerenes are Lewis acids. In the last work, Fileti and Chaban theoretically predicted a jump of the C₆₀ solubility in [bmim⁺][BF₄⁻] at high temperatures, up to 380 K [164]. This interesting conclusion should be verified experimentally.

Garcia et al. [166,167] presented important results on analyzing the interactions of 24 different RTIL with C₆₀ using molecular dynamics and DFT methods. Structural, dynamic, and energetic factors were analyzed to clarify their role on the behavior of the above systems. In particular, the role of the $\pi –\pi$ interactions is important, which is in line with other theoretical considerations [162,163,164]. Useful guidelines are provided for selecting an RTIL suitable for fullerene solvation; rationalization means an adequate cation-anion choice [167].

Recently, Cardoso and Colherinhas [172] published a detailed molecular dynamics investigation of C₆₀ with [bmim⁺][PF₆⁻] and water, using polarization effects. In order to observe the impact of fullerene–solvent electronic interactions, the NMR and electronic absorption spectra were calculated using the GIAO-DFT and TD-DFT methodology [171]. These authors also compared the solvation of C₆₀ in water, DMSO, and DMF and demonstrated a better solvation in the last organic solvents [171].

It can be concluded that in RTIL, also known as “green” solvents due to their negligible vapor pressure, the C₆₀ and C₇₀ fullerenes exist in form of aggregates. As for the permittivity of RTIL, even estimating this value is not an easy task. For [bmim⁺][PF₆⁻] and estimate ${\epsilon }_r$ $\approx$ 10 can be accepted [173,174]. Hence, the RTIL solvents are on the border between polar and non-polar ones; they should be ascribed to “poor” solvents. Also, the large variability of RTIL should be taken into account; in this case, the above mentioned theoretical modeling can be useful for correct choice of solvents.

Campisciano et al. [175] covalently attached imidazolium groups to the C₆₀ molecule and thus obtained a valuable supramolecular system for providing Suzuki and Mizoroki–Heck reactions in aqueous media. The smoothing of the spectral curve in the UV-visible range is pronounced. In any case, such a modification makes it possible to transfer the fullerene to water. Basing on molecular dynamics method, Fileti and Chaban [165] recommended the imidazolium ionic liquid [bmim⁺][BF₄⁻] for dispersion of fullerene in water. In this sense, the RTIL is one of the ionic compounds capable of stabilizing colloidal fullerene particles in hydrosols.

4.4. Hydrosols of Fullerenes: Preparation

In water, fullerenes exist in colloid state. Because the electrophilic properties of C₆₀ and C₇₀ are pronounced, a number of studies were directed to their biological activity and possible application in medicine [6,9,11,12,14,15,176,177]. On the other hand, a plenty of information on cytotoxicity, photocytotoxicity, genotoxicity (DNA damage), etc., is available [24,25]. Many studies are devoted to the behavior of fullerenes in soils, freshwater, etc. [9,10,16,177,178,179,180].

As a result, an impressive number of different procedures and protocols of preparation of fullerene hydrosols and aqueous suspensions is accumulated; see, e.g., recent review papers [15,16,24,25]. This set of methods that have been tried for the preparation of hydrosols and aqueous suspensions of fullerenes can serve as an excellent teaching example for a university course in colloid chemistry.

Some of the colloidal solutions are rather suspensions than sols, first of all those prepared by “top-down” method, whereas hydrosols are first of all prepared by the “bottom-up” way. However, following many authors, we use these terms here mainly as synonyms. For orientation in this dataset, special designations for the most popular preparation methods gradually appeared, such as, e.g., son/nC₆₀. Here “son” and “nC₆₀” denote sonication and aggregate formation, respectively.

First approach was the stepwise solvent exchange going from C₆₀ in benzene to tetrahydrofurane, then to acetone, and finally to water; the final fullerene concentration was 2 × 10⁻⁶ M [181]. If the initial fullerene solution is prepared in toluene and successively diluted with tetrahydrofurane, acetone, and water, the target system is designated as TTA/nC₆₀. In this case, even a C₆₀ concentration of 0.002 M can be reached [182]; the procedure was subsequently reconsidered [183]. Dilution of tetrahydrofurane solution of fullerene with water leads to hydrosols of THF/nC₆₀ type [184,185]. First, a fullerene solution in THF is prepared in inert atmosphere, and after mixing with water the organic solvent is evaporated [184]. Dilution of C₆₀ and C₇₀ solutions in polar solvents N-methylpyrrolidine-2-one and dimethylformamide with water results in NMP/nC_60, NMP/nC₇₀ [186], and DMF/nC₆₀ [155] colloidal systems. New versions of such approaches were developed by the Ausman group [183,187]. These authors proposed a new procedure using C₆₀ solution in hexane, diluted with iso-propanol and water [187]; under such conditions, hexane is evaporated first.

An approach based on the introduction of a surfactant sodium dodecylsulfate (SDS) has been proposed. A fullerene solution in a “good” solvent is added to aqueous acetone containing SDS, and organic solvents are removed by distillation [188,189,190]. Here, SDS stabilizes the final C₆₀ colloidal particles; however, utilization of surfactants, polymers, etc., is beyond the shape of this minireview.

Another “bottom-up” method was already reported as early as 1997. It consists of the introduction of THF solutions of the C₆₀ anion radical into water; oxidation with atmospheric oxygen results in formation of a hydrosol [191]. This procedure was revisited after two decades [192]. Reaction with KOH and oxidation results in formation of fullerenol; the NIR spectra of fullerene anion radical and the properties of hydrosol of fullerenol is recently reported [193].

Preparation of colloid solutions can be performed using sonication. Solutions of C₆₀ were prepared in DMF and THF by stirring and then, instead of mixing with water, the latter was added and accompanied with sonication only after the organic solvents evaporation [156]. The authors of the original article designate thus obtained as DMF/nC₆₀ and THF/nC₆₀ [156]. A versatile analysis of these obtained systems disclosed substantial chemical changes of the fullerene. Not only sonication but the nature of the organic solvent plays a role in these alterations [156].

More popular is the sonication method consisting in ultrasonic extraction from toluene to water [194]. The hydrosols prepared in this “bottom-up” way are designated as son/nC₆₀, or tol/nC₆₀, or SON/nC₆₀. Contrary to the above mentioned procedures this allows to receive much higher fullerene concentrations, up to 0.001 M [195] and particle size down to 20 nm [16].

This method works well not only for C₆₀, but also for C₇₀ [196,197,198] and C₇₆, C₈₄ [196], and is permanently modified [196,199,200,201,202,203]. So, if the pH of the water phase is elevated to 10, the negative charge of the colloidal particles increases, therefore making them more stable [199]. Also, SDS was added in order to stabilize the particles that appear during the ultrasound extraction; the surfactant was removed from the final colloid via dialysis [203]. Some authors added small amounts of ethanol to the aqueous phase [196,200,204]. Slight heating to 40 °C and passing nitrogen to remove toluene traces is proposed [200]. For the same purpose, 15 min boiling of the final hydrosol can be used [201]. Heating the system during the sonication process up to 60 °C allows substantially decrease the size of colloidal particles [202].

The disadvantages of the method include the occurrence of the (possible) fullerene oxidation and other chemical reactions under conditions of sonication. So, reactive oxygen species are readily formed such as superoxide ions, singlet oxygen, etc. [16]. Conversion of toluene into the benzoic acid and benzoate is also reported [205,206].

In 2022, two new approaches to the C₆₀ hydrosols preparation were published [14,15]. Merland et al. modified the extraction/sonication method and developed an emulsification–evaporation process in the presence of an amphiphilic polymer. Instead of toluene, trichloromethane or carbon disulfide was used. Kop et al. [14] proposed a fullerene–curcumin antioxidant system. These authors prepared the C₆₀ hydrosols by 9-fold dilution of a solution in NMP with water, followed by stirring, dialysis, and filtration though a 450 nm-pored filter. The sols were stabilized by Tween-80, polyvinyl pyrrolidone, cyclodextrin, and curcumin with different combinations.

As an example of a hydrosol of C₇₀, the results of our recent study are presented in Figure 8 and Figure 9 [198]. This colloid system of son/nC₇₀ type was prepared by Dr. Vladimir Klochkov using highly pure benzene instead of toluene. At the C₇₀ concentration of 3.3 × 10⁻⁶ M and 25 °C, the size of particles is 97 ± 3 nm (Figure 8) and $\varsigma$ = −40 ± 4 mV [198].

Increase in concentration displays insignificant alterations of the particle size; PDI is always around 0.2 [198]. The above characterization of this C₇₀ hydrosol is in agreement with the results by Aich et al. [196].

The size/$\varsigma$ values for C₇₀ hydrosols, available in the literature, as follows: 92 ± 14 nm/−39 ± 4 mV [196]; 175 ± 5 nm/−34.4 ± 0.7 mV [197]; ≈100 nm/−21.7 mV [177] (in the last paper, the fullerene concentration was 8.9 × 10⁻⁵ M). As a rule, data are published without specifying the type of equation used for $\varsigma$ calculation. As mentioned above, we used the Henry–Ohshima equation, which corresponds to the Hückel equation in the absence of foreign electrolytes.

It is important to note that relatively small variations in this preparation method often lead to formation of hydrosols with significantly different properties. This is a typical sign of hydrophobicity of the colloidal system of interest. Given the widespread use of this method, it is important to try to standardize the synthetic protocol. Such attempts were made by Mikheev et al., who prepared standard samples of fullerene hydrosols [206,207]. Note that in these works as well in the study by Kyzyma et al. [186], sonication was used not only for the toluene–water system, but also during the preparation of the initial toluene solution of fullerenes. Contrary to it, we used to prepare the stock solutions in toluene and benzene without sonication, keeping the solid sample in the “good” solvent within ca. 2 weeks [198].

Finally, the “top-down” methods have been used, first of all, prolonged stirring of the solid samples of fullerene in water. Thus, the obtained colloid systems were designated as aq/nC₆₀, aqu/nC₆₀, stir/nC₆₀, or STI/nC₆₀. Sometimes stirring continued even 1075 days [208]. Murdianti et al. [209] presented experimental evidence that suspension formation does not occur in an inert atmosphere. They attach a key importance to the formation of fullerene oxide C₆₀O for the appearance of colloidal particles [209]. Based on detailed studies, it was concluded that it is impossible to obtain identical results by mixing in water [210].

Mixing and stirring can be performed in the presence of salts of organic acids. For example, if citrate is used, the colloid is named as cit/nC₆₀ [211]. Some authors used sonication in water and named the colloid as aq/SON/nC₆₀ [210], while others crushed a solid fullerene sample in water by a laser beam [212]. The hand-grinding of the solid sample in a mortar followed by transfer to water and sonication was named mechano-assisted reduction of size, or MARS/nC₆₀ [213,214], is preferably carried out on with the addition of SDS [25]. In any case, filtration of the resulting colloid solutions using 220 or 450 nm pore filter is highly recommended.

4.5. Hydrosols of Fullerenes: Key Properties

Briefly summarizing the numerous data accumulated to date, we can give the following characteristics of hydrosols or suspensions of fullerenes. These are typical hydrophobic colloidal nanodispersed systems, with the size of negatively charged particles being between ≈40 and ≈200 nm, and with fullerene concentration, as a rule, below 0.01 mass %. Although it is obvious that the authors of various works sought to obtain the maximum concentration of fullerene, the final concentrations depend to a large extent on the method of preparation used. Other properties of the colloids also strongly depend on the preparation protocol. Such scattering of the properties of the colloidal solutions prepared by different methods or even by the same methods but by different authors gives additional support to the idea of pronounced hydrophobic character of the systems of interest.

Since the initial weight of fullerene usually cannot be completely transferred into water, it is necessary to have a method for determining the fullerene concentration in solution. A common method consists of deposition of fullerene colloidal species by Mg(ClO₄)₂, NaCl, NaNO₃ or/and acetic acid followed by extraction with toluene and absorbance measurements [24,25,183,187]. New method basing on the light scattering has also been developed [210].

As for the determination of particle size and polydispersity of fullerene aqueous dispersions, the dynamic light scattering method is used first of all. However, indirect methods based on UV-visible absorption spectra [213,215,216] may also be used. For example, Deguchi et al. [213] proposed an equation that describes the dependence of the absorption maximum in the region of 340–350 nm on the hydrodynamic diameter of the colloidal particle determined using the DLS method, Equation (1).

$${\lambda }_{\max } = \left(337.1 \pm 1.4\right)+ (0.065 \pm 0.009) d_{\mathrm{H}}$$

(1)

The discussion of applicability of this and other equations can be found in a previous review [25]. A more detailed characterization provides for knowledge about impurities, first of all oxidation products [156,183,187,206,209].

The origin of the negative charge of the colloidal particles is of special interest because it allows to shed additional light on the nature of the fullerene/water interface. Several popular explanations of the charge origin have been considered and discussed in previous reviews [24,25]. The most probable reasons are as follows. (i) Adsorption of the HO⁻ ions, which is typical for many hydrophobic surfaces such as oil droplets [217] and gas bubbles [218]. (ii) Localized hydrolysis caused by electrophilic properties of fullerenes, which are in fact Lewis acids [24,25,219]; it also favors the additional formation of the HO⁻ ions. The role of HO⁻ ions in formation of the surface charge is supported both by additional stabilization at pH above 7 and coagulation at pH 1–2 [25]. (iii) Quantum-chemical calculations made by Choi et al. [220] revealed that the interactions between fullerene and water molecules lead to charge transfer and polarization, thus making a contribution to the negative charging of the fullerene aggregates in water. This explanation is in line with our concept (ii).

In any case, the negative charge is a main factor of the aggregative stability of colloids including fullerene sols and suspensions. Noneman et al. [221] performed a detailed molecular dynamics modeling of mixtures of C₆₀ with C₆₀O in water. The main idea of this and of previous works of this group [183,187,209] consists of stabilization of C₆₀ colloids in water by admixtures of C₆₀O. The latter to some extent plays the role of a diphilic compound, a kind of stabilizing surfactant [221]. This is quite plausible, but the fullerene oxide itself cannot cause the surface charge, and it is the charge screening by electrolytes that leads to coagulation.

According to molecular simulations made by Hinkle and Phelan [222], the Gibbs solvation energy, $\Delta G_{\mathrm{solv}}$, of C₆₀ in water (−50.9 kJ mol⁻¹) is more negative than that reported by Stukalin et al. [93]. However, the energy of transfer from water to methanol and ethanol is −68.1 and −86.5 kJ mol⁻¹, respectively. The $\Delta S_{\mathrm{solv}}$ value of C₆₀ hydration is negative. These parameters, however, refer to the C₆₀ molecule and not to the colloidal particle. Voronin et al. [223] estimated the negative entropic $\Delta S$ value by studying a son/nC₆₀ hydrosol using DLS method at different temperatures, atomic force microscopy, and isothermal titration calorimetry. Based on the combined equation of the first and second laws of thermodynamics, they stated that the C₆₀ fullerene aggregation in aqueous solution is entropically driven, occurring with nearly zero enthalpy change. However, the use of a thermodynamic approach for a hydrophobic colloidal system is clearly inappropriate.

Recently, Godínez-Pastor and González-Melchor [224] published a detailed molecular dynamics study of the behavior of the fullerene/water system under liquid and liquid–vapor conditions. A computational study of fullerene/water systems under liquid phase and liquid-vapor conditions was performed using atomistic model. At 300 K and 1 bar, fullerene aggregates were observed. The aggregation was less defined at 373 K and 10 to 24 kbar [224].

In addition to the hydrosols and aqueous suspensions of fullerenes, the C₆₀ layers on the water/air interface should be mentioned. Kolker and Borovkov [225] used cyclohexane as spreading solvent and prepared a diluted highly homogeneous 2D system C_60—H₂O. They also showed that under compression, instead of true Langmuir monolayers, polylayers up to hexalayers can arise. This system can be considered as an interfacial colloid system; the cited article also provides a review of the relevant literature data [225].

Another interesting issue is the partition of fullerenes between water and nonpolar solvents. Mikheev et al. [226] presented a detailed quantitative study of partition of C₆₀ and C₇₀ between mutually saturated water and toluene. The specificity of their approach consists of using sonication; the ratio of concentration of fullerenes in aqueous and organic phases was relatively similar when the quasi-equilibrium state was reached from both sides. The distribution constants for the two fullerenes were found to be 6 and 2, respectively [226]. Note that Jafvert and Kulkarni [227] determined the partition constants of C₆₀ between toluene or 1-octanol and water, 2.8 × 10⁸ and 4.7 × 10⁶, respectively. These values for mutually saturated solvents were obtained using three different procedures and describe the equilibrium of single C₆₀ molecules in different solvents. The solubility of fullerene in water was estimated as 1 × 10⁻¹¹ M [227]. Such difference of partition constants is understandable because in the first paper [226], fullerene is in colloid state in water and, probably, in toluene under conditions of sonication.

This problem is to some extent connected with the partition of nanoparticles between water and organic solvents, including 1-octanol [228]. The last concept was criticized by Praetorius et al. [229], because, for lyophobic systems, the thermodynamic approach is not correct. Their paper is entitled “The road to nowhere: equilibrium partition coefficients for nanoparticles” [229]. Based on an approach developed by Hill [230], Shchukin et al. [231] mentioned that a disperse system with very small particles can be conditionally regarded as a one-phase colloidal solution containing large “molecules”. However, for the partition of charged particles of a lyophobic system between two liquid phases it can be really misleading.

The colloidal particles, including those of fullerenes in water are charged, which hinders their transfer into the organic phase. However, Mikheev et al. [226] explained their results by transferring of single molecules. They estimated a maximum concentration of C₆₀ in water produced from a toluene solution by the solvent-exchange procedure, i.e., in the son/nC₆₀ sol, as 5.6 × 10⁻⁴ M. Though their results are self-consistent, it would be worthwhile to process the experiments using other parameters of sonication. For example, Scharff et al. managed to prepare a son/nC₆₀ colloid with concentration of 1.9 × 10⁻³ M [232].

5. Coagulation by Electrolytes

5.1. Coagulation of Hydrosols and Aqueous Suspensions

Hydrosols of C₆₀ and C₇₀ are typical lyophobic colloidal systems with negatively charged particles [20,22,23,24,25,198,229,233,234]. They readily coagulate on adding electrolytes, are irreversible (i.e., cannot be spontaneously restored after the complete evaporation of the solvent), and exhibit the so-called coagulation zones, i.e., coagulation—stabilization—coagulation, in the presence of cationic surfactants [16,25,198,233]. The particle size, size distribution, electrokinetic potential, and other properties for fullerene hydrosols and suspensions prepared by different methods and by different authors do not coincide. This is typical for lyophobic (hydrophobic) systems. As a result, a pronounced scatter of the critical coagulation concentrations, CCC, becomes evident after gathering numerous results available in the literature [25]. So, the reported CCC for NaCl vary from 25 mM [203] to 321 [235]. Some representative examples are given in Figure 10 and

Table 4. The critical coagulation concentrations of fullerene hydrosols by electrolytes ^a.

Type of Hydrosol	Fullerene Conc., M	CCC, mM			CCC(NaCl): CCC(CaCl2)	Ref.
		NaCl	CaCl2	LaCl3, La(NO3)3
son/nC60	1 × 10−4	85	4.1	0.056	21	[233]
son/nC60	1.5 × 10−5	140	—	—	—	b
son/nC60	3.9 × 10−5	321	6.7	—	48	[235]
son/nC60	8.2 × 10−6	160	6.1	—	26	[236]
son/nC60	9.2 × 10−7	220	10	—	22	[237]
son/nC70	3.3 × 10−6	250	—	0.070 b	—	[198]
son/nC70	1.7 × 10−5	145	—	—	—	[198]
son/nC70	6.9 × 10−5	130	—	—	—	[198]
son/nC70	7.9 × 10−7	150	12	—	12	[237]
son/nC76	7.3 × 10−6	100	6	—	17	[237]
son/nC84	6.6 × 10−6	70	7.5	—	9	[237]
aqu/nC60	1.1 × 10−5	140	5.3	0.11	26	[238]
aqu/nC60	4.2 × 10−6	295	5.9	—	50	[235]
aqu/nC60	1.5 × 10−6	84	4.25	—	20	[239]
THF/nC60	9.7 × 10−6	104	4.8	—	22	[17]

^a A much larger body of data can be found in ref. [25]. ^b Our data, to be published.

.

A theoretical study by Mortuza et al. [122] sheds additional light on the electrolyte-induced coagulation of fullerene hydrosol. In the first paper [120], it was demonstrated by molecular dynamics simulation that uncharged fullerenes aggregate in water, the charged species avoid it because of electrostatic repulsion. In the second study [122], the increase in the size of the C₆₀ clusters in the 100 mM NaCl solution was described using a combination of molecular dynamics and kinetic Monte Carlo method. The mechanism of cluster growth turns in salt solutions from the reaction limited to the diffusion limited cluster aggregation (RLCA → DLCA) [122].

The most regularities of coagulation were described in outline as early as 1997 [233]. Before that in the same year, it was mentioned that a C₆₀ sol, obtained by oxidation of fullerene anion-radical, can be precipitated using NaOH, HCl, NaCl, and BaCl₂ [191]. Since then, many studies have been performed using more advanced methods for CCC determinations [198,235,236,237,238,239,240,241,242]. Using the DLS method, Meng et al. [242] determined CCC = 98 mM for NaCl at 1.39 × 10⁻⁵ M C₆₀ solutions; Khokhryakov et al. [243] obtained a CCC value of 100 mM for C₆₀ concentration of 4.00 × 10⁻⁴ M using UV-visible spectra. (In Table 5 in ref. [25], for the last two articles the fullerene concentrations were indicated with an error.). In a study by Aich et al., the coagulation parameters of C₆₀, C₇₀, C₇₆, and C₈₄ colloids were determined [237].

For NaCl and KCl, a CCC of 167 mM is average of nineteen values [25]. In these studies performed by different authors, the fullerene concentrations varied from ~10⁻⁶ to ~10⁻⁴ M [25]. For salts with double-charged cations, CaCl₂, MgCl₂, and MgSO₄, an average value of 6.8 mM can be calculated using results of twenty-three studies [25]. This leads to a ratio of the averaged CCC values of single-charged to double-charged cations about 25. Importantly, despite the scatter of the results of different authors, the classical Schulze–Hardy rule is valid in the case of fullerene hydrosols.

For salts with a triple-charged cation, La³⁺, two reports are available for C₆₀ hydrosol. The ratio of reciprocal CCCs for Na⁺, Ca²⁺, and La³⁺ was determined as 1:21:1518 [233]. This result was subsequently confirmed by Zhang et al. [238]: 1:26:1272; such agreement is sufficient for lyophobic colloid systems. The DLVO theory in its classical version predicts the ratio of 1:64:729 (the so-called z⁶ law) for sols with highly charged particles and in the absence of ion adsorption [244]. Since then, a number of modifications of the theory were proposed [245,246,247,248], and this process is ongoing [249,250,251]. Among other problems, the role of the colloidal particles size [252], overcharging, hetero- and mutual coagulation [253,254,255,256], consideration of structural forces [257], and the role of the co-ions (or similiions) influence [258] are discussed in order to refine the theory. For a long ago studied hydrosol As₂S₃, an example of the above ratio for single-, double-, and triple-charged cations is 1:80:725, whereas for AgI hydrosol, it is 1:58:2029. These are averaged values from a fundamental book [259].

For relative to fullerenes nanocarbon systems, single- and multi-walled nanotubes, SWCNT, and MWCNT, respectively, with different degrees of oxidation, twenty-nine CCC values for NaCl, thirty-two CCC values for calcium, magnesium, and barium salts, and five CCC values for cerium, lanthanum, and aluminum salts give an averaged ration of coagulative power: 1:71:2775 [260]. For a sample of SWCNT with 10 mass % oxygen, studied by us, the CCCs for NaCl, Ca(Ba)Cl₂, and La(NO₃)₃ are 150; 1.4; and 0.025 mM, which corresponds to the CCC⁻¹ ratio 1:107:6000 [260]. Specific interactions with oxygen-containing groups, obviously carboxylic, take place for multi-charged metal cations. Either blocking the carboxylic groups by methylation or decarboxylation results in drop of the CCC(NaCl)/CCC(Ca(Ba)Cl₂) ratio by an order of magnitude [260].

Two works connected with the fullerene–electrolyte interaction under unusual conditions should be mentioned. First, the state of C₆₀ layers on the water/air interface is affected by introducing 1% (i.e., 171 mM) of NaCl. The hydrophobic hydration is hindered, and the sub-monolayer structure becomes cross-linked due to direct contacts between fullerene molecules [225]. Note that the above NaCl concentration is around the CCC value of hydrosols. It should be kept in mind that coagulation in the interfacial layers and even the 2D Schulze–Hardy rule is described in the literature [261].

Second, Gigault et al. [178] revealed using in situ DLS, that nC₆₀ aggregation on passing the salinity gradient in a micro-fluid occurs not so expresses as under common bulk conditions at the same NaCl concentrations.

For the same colloidal system, the CCC value sometimes depends on the sol concentration. An increase in the CCC value for a single-charged coagulating ion of the electrolyte along with the dilution of the sol is known as the Burton–Bishop rule [262,263,264], which would be more accurately called the Mukherjee–Sen–Burton–Bishop rule [265]. For some colloidal systems, it was not confirmed [263,264], but it works for fullerene hydrosols. Whereas the particle size of C₇₀ hydrosol stays practically unaffected at the fullerene concentration within the range of 3.3 × 10⁻⁶ to 6.9 × 10⁻⁵ M, the CCC value drops from 250 to 130 mM NaCl [198]. This finding resembles the same effect for C₆₀ [25].

The behavior of fullerene hydrosols in the presence of a cationic surfactant is well within the classical principles of colloid chemistry [264,266]. For the C₇₀ hydrosol at 3.3 × 10⁻⁶ M, the CCC = 0.005 mM value for CTAB is fifty thousand times lower than for NaCl [198]. A jump in size from ca. 100 nm up to ca. 550 nm and substantial decrease in $\left|\varsigma \right|$ is observed. At higher CTAB concentrations, overcharging takes place up to $\varsigma$ = +40 mV at surfactant concentration of 0.02 mM. Both effects occur well below the critical micelle concentration of CTAB, 0.9 mM, and are certainly caused by the surfactant adsorption: first layer of CTA⁺ neutralizes the surface charge and leads to the hydrophobization of the surface of colloid particles, while the second, tail-to-tail layer, results in overcharging and stabilization of the particles. This is in line with the results earlier obtained with C₆₀ [16]. Such “coagulation zones” were observed for the Au, As₂S₃, AgI hydrosols with a number of cationic surfactants [264,266], and SiO₂–CTAB system [267]. The peculiarity of the systems of interest is the extremely low concentration of fullerenes, contrary to much higher concentration of the colloids in the above cited works [259,262,263,264].

The coagulation data can be explained in terms of the universally recognized DLVO theory. However, the exact value of the Hamaker constant for fullerene–fullerene interaction, A_FF, stays unknown. So, an attempt might be done to solve the inverse problem. In this case, an A_FF value corresponding to the CCC value, particle size, and electrical surface potential should be regarded the most reliable. In the classical version, the DLVO approach considers only two contributions to the energy of interaction between two colloidal particles, U, the energies of electrostatic repulsion, U_el, and molecular attraction, U_mol, Equation (2).

$$U = U_{el} + U_{attr}$$

(2)

We used the Dukhin – Derjaguin – Semenikhin version [245] of the DLVO theory, Equation (3).

$$U=U_{el}+U_{attr}=64\pi {\epsilon }_r{\epsilon }_0{\left(\frac{RT}{F}\right)}^2{\mathrm{t}\mathrm{g}\mathrm{h}}^2\left(\frac{{\mathsf{\Psi }}_{\mathrm{d}}F}{4RT}\right)\frac{r \mathrm{e}\mathrm{x}\mathrm{p}(-\kappa h)}{s}-\frac{A_{\mathrm{F}\mathrm{S}\mathrm{F}}^{*}}{6}[\frac{2}{s^2-4}+\frac{2}{s^2}+\mathrm{l}\mathrm{n}\frac{s^2-4}{s^2}]$$

(3)

Here, $h$ stands for the distance between the centers of the particles, s = 2 + h/r, ${\epsilon }_0$ = 8.854 × 10⁻¹² F m⁻¹, κ is the reciprocal Debye length, R, T, F have their usual meanings, ${\mathsf{\Psi }}_{\mathrm{d}}$ is the electrical potential of outer Helmholtz plane; usually, the experimentally available $\varsigma$ value is used instead of ${\mathsf{\Psi }}_{\mathrm{d}}$, which is a kind of a Galvani potential.

The $A_{\mathrm{FSF}}^{*}$ value characterizes the fullerene–solvent–fullerene interaction in solution. It is connected with the $A_{\mathrm{FF}}$ and $A_{\mathrm{SS}}$ values, which characterize the fullerene–fullerene and solvent–solvent interaction in vacuum, through the Hamaker equation:

$$A_{\mathrm{FSF}}^{*} = {(A_{\mathrm{FF}}{}^{1/2} - A_{\mathrm{SS}}^{1/2})}^2$$

(4)

The Hamaker diagrams, i.e., the dependences of U on h, can be constructed. Various $A_{\mathrm{FSF}}^{*}$ values can be used, and those that met the coagulation conditions were selected. Then, Equation (4) should be used to estimate the $A_{\mathrm{FF}}$ value. The systems with $U_{\max }$ ≈ (0–2)k_BT can be considered as unstable and corresponding to the experimentally determined CCC (k_B is the Boltzmann constant).

For C₇₀ hydrosol, Figure 10, such an approach leads to A_FF = 7.0 and 6.2 × 10⁻²⁰ J for U_max = 0 to 1 k_BT, respectively [198]. The results reported by the Elimelech group for the C₆₀ hydrosol lead to an A_FF value of 7.5 × 10⁻² J [240,241]. Our processing of the data of these authors leads to a value of 7.35 × 10⁻²⁰ J, though somewhat different versions of the DLVO theory were used [70]. The utilization of other results of the same research group [242] results in A_FF = 5.25 × 10⁻²⁰ J [70].

Although consideration of C₆₀(or C₇₀)(OH)_x fullerenols in water is beyond the scope of this review, two points should be noted. First, despite excellent solubility, fullerenols as a rule exist in water in form of aggregates [24]. Second, coagulation of fullerenol in water takes place in diluted KCl solutions, despite the substantial initial negative $\varsigma$ value of −60 mV [193]. It is obvious that the energy of molecular attraction is quite high due to the high surface atomic density of the fullerene structure.

5.2. Coagulation of Sols and Suspensions in Polar Organic Solvents (This Section Is Based Entirely on Experimental Results from This Laboratory [70,74,100,101,123,160])

Despite numerous studies devoted to fullerene colloidal solutions in polar and “good” + polar solvents, the stability of these systems in respect to electrolytes was not examined to the best of our knowledge. Accordingly, no information was available concerning the CCC values. On the contrary, many works on coagulation of aqueous colloidal fullerene solutions have been published. Obviously, this is due to the fact that both in biological systems and in environmental objects, the interaction of fullerenes with electrolytes is inevitable. But paradoxically, the study of the aggregative stability of organosols can shed additional light on the nature and properties of hydrosols.

The first experiments made by us have already shown that in polar organic solvents, the C₆₀ aggregates readily coagulate and the CCC in acetonitrile-based solvents are two to three orders of magnitude lower than those in water [101]. For example, in acetonitrile with 1 vol.% toluene, the CCC value for NaClO₄ is 0.15 mM. Some representative values are collected in

Table 5. The CCC values of C₆₀ sols in different solvents, mM.

	In Water a	In Acetonitrile b,c	In Methanol c,d
Na+	85 e	0.15–0.20	0.25–0.30
Ca2+	4.1 f	0.016–0.030	0.04–0.05
La3+	0.056	0.0068	—
H+	0.55–1.2 g	0.14	0.3–1.0 h

Note. ^a From ref. [233]; metal cations were introduced in form of chlorides and nitrates. ^b From ref. [160]. ^c 1 vol.% toluene; metal cations were introduced as perchlorates. ^d From ref. [123]. ^e Average CCC of nineteen literary values is 167 mM (see Section 4.1). ^f Average CCC of twenty three literature values is 6.8 mM (see Section 4.1). ^g HClO₄, HCl, HNO_3. ^h The Fuchs curve for HClO₄ is unusually stretched.

. The accuracy of the CCC values is normally around 15–20%.

The ratio of reciprocal CCC values for NaClO₄, Ca(ClO₄)₂, and La(ClO₄)₃ is 1:9:22. In an acetonitrile–benzene binary solvent, 1:1 by volume, the CCC values are higher due to incomplete dissociation of electrolytes [101]. In this case, the reciprocal CCC values are related as follows: 1 (NaClO₄):1.25 (HClO₄):2 (tetraalkylammonium perchlorates):9.1 {Ca(ClO₄)₂}:62.5 {La(ClO₄)₃}.

Other results obtained with C₆₀ and C₇₀ in methanol and acetonitrile (Figure 11 and Figure 12,

Table 6. The CCC values of fullerene organosols with addition of 10 vol.% toluene, mM ^a.

	C70 in Acetonitrile	CCC(Na+):CCC(Cation)	C60 in Acetonitrile	C70 in Methanol
Na+	0.25	1	0.11	0.13
Li+	0.024	10.4	0.02	0.13
H+ b	0.015	16.7	0.15 c	—
Ca2+	0.001	250	0.016–0.030 d	0.002
La3+	0.0007	357	0.003 c; 0.0068 d	—
Ca2+	1.2 e	0.21	≈1 e	—

Note. ^a From ref. [70]. ^b Acids in organic solvents: perchloric, triflic, p-toluenesulfonic. ^c 6.6 vol.% benzene. ^d 1 vol.% toluene. ^e CCC₂.

) confirm the above conclusions.

Interestingly, in such systems, not only the Schulze–Hardy rule is valid but also the overcharging of colloidal particles by cations and appearance of “coagulation zones” takes place. The overcharging occurs at metal ion concentrations above the CCC and is very pronounced, for example, for C₆₀ sols in acetonitrile with small additives of benzene or toluene, the electrokinetic potential increases from $\varsigma$ = −(47–56) mV to +(30–49) mV in the presence of Ca²⁺, Ba²⁺, and La³⁺ [101,160]. In methanol, the $\varsigma$ = −37 mV value increases up to +37 mV, +26 mV, and +24 mV for La³⁺, Ca²⁺, and Ba²⁺, respectively [123]. The whole dependences of the electrokinetic potential on the electrolyte concentrations are available in the cited papers [123,160].

Such well-documented effects were not observed for the hydrosols [24,25,233]; the sole exception is a study of C₆₀ in water in the presence of Al³⁺ ions [199]. The obvious reason for overcharging in organic solvent is, in addition to enhanced electrostatic interactions, poor solvation of the used cations in acetonitrile and methanol; the introduction of 18-crown-6 and cryptand [2.2.2] substantially weakens the effect due to binding of the metal cations into the macrocyclic ligand [101,123,160]. Even 10 mM N-cetylpyridinium perchlorate causes overcharging (+11 mV) [160]. Acids can also overcharge the colloidal particles in acetonitrile [101].

Such influence of adsorption on the coagulation process is in line with the observed deviation from the z⁶ law. Experiments with C₇₀ sols in acetonitrile were performed in the presence of 10 vol.% toluene; at lower content of the latter, the systems are less stable. The reciprocal CCC values for Na⁺, Ca²⁺, and La³⁺ are given in Table 5. The overcharging of the initial colloidal C₇₀ particles is very pronounced in acetonitrile: the values of $\varsigma$ = −55 mV to +30 mV in the presence La³⁺ and +55 mV for Ca²⁺ cations [70]. Even in LiClO₄ solutions the overcharging of particles reaches +20 mV [70].

The overcharging leads to an interesting phenomenon that is well documented for some colloidal systems studied long ago [253,254]. Namely, the appearance of the coagulation zones allows determining the second CCC value, or CCC₂, corresponding to the coagulation of the modified, i.e., positively charged, fullerene aggregates [70,100,101,123,160]. This CCC₂ value for Ca(ClO₄)₂ is about 1.0 mM for C₆₀ in acetonitrile with 1 vol.% toluene and 1.2 mM for C₇₀ in the presence of 10 vol.% toluene (Table 6). Paradoxically, it is this CCC value that is better suited for estimating the Hamaker constant, which will be discussed below.

Another important issue is the low CCC value for LiClO₄ in acetonitrile, but not in methanol (Table 6). For C₆₀ and C₇₀ colloids, it is 5.5 and 10.4 times lower than that for NaClO₄, respectively [70]. In concert with the pronounced overcharging in the case of Li⁺ this allows deducing that in the last case a typical heterocoagulation or even mutual coagulation takes place [254].

Moreover, the overcharging of colloidal particles by multi-charged counterions gives grounds to assume the effects of hetero- and mutual coagulation, which should affect the ratio of the CCC values [254].

First, the $A_{\mathrm{FF}}$ were estimated using the approach described above for hydrosols. Examples of the corresponding Hamaker diagrams are given in Figure 13. The values (8.7–12.4) × 10⁻²⁰ J and (6.6–13.7) × 10⁻²⁰ J were obtained in methanol [123] and acetonitrile [160], respectively. The first conclusion was as follows: these values are similar to the more precisely determined in water. However, more detailed analysis allowed selecting electrolytes that can be used in such reconstruction of the $A_{\mathrm{FF}}$ value [70]. The systems with pronounced change of the interfacial electrical potential due to adsorption of counterions were ruled out. In this case, higher $A_{\mathrm{FF}}$ values, such as 16 × 10⁻²⁰ J (

Table 7. Examples of the A_FF estimation for C₇₀ organosols ^a.

Salt	CCC, mM	$\mathit{\varsigma }$, mV	AFF × 1020, J
NaClO4	0.25	–6	5.8–8.0
Na[2.2.2]ClO4	5.1	–15	7.7–7.9
Li[2.2.2]ClO4	1.5	–20	11.8–13.2
N(n-C4H9)4ClO4	0.90	–21	14.5–16.0
Ca(ClO4)2	1.2	+40	16.2–16.6

Note. ^a C₇₀ sols in acetonitrile with 10 vol.% toluene, 25 °C; radius of colloid particle: 150–160 nm; in the system with N(n-C₄H₉)₄ClO₄—110 nm.

), are more probable and better agree with the high interfacial atomic density of fullerenes. The corresponding data for C₆₀ are very similar.

As a result, the $A_{\mathrm{FF}}$ value is substantially higher as compared to that estimated basing on coagulation of hydrosols. Accordingly, the construction of a Hamaker diagram for fullerene hydrosol using a higher Hamaker constant $A_{\mathrm{FF}}$ estimated in organosols, predicts the coagulation concentrations of electrolytes well below the experimental CCC (Figure 14).

These findings lead to an idea of some additional “non-DLVO” interactions in the hydrosols. According to the concept proposed long ago by Churaev and Derjaguin [257], a “structural” contribution, $U_s$, to the right hand side of Equation (2). The reason can be the specific interactions, for example described in ref. [220].

The idea of additional interactions “non-DLVO” in water, which are probably absent in acetonitrile, is convincingly supported by data for fullerene sols in DMSO and DMF [74]. In these cationophilic (protophilic) non-hydrogen bond donor solvents, the aggregative stability of fullerene sols increases dramatically. The Gutmann’s Donor Numbers (Table 2) for DMSO and DMF are with 29.8 and 26.6 much higher than those for acetonitrile (14.1) and methanol (19.1, conventional value). The value of the relative permittivity displays (if any) a secondary role; e.g., the ${\epsilon }_r$ values of acetonitrile and DMF is very close. This is clearly illustrated by the data for coagulation of the C₇₀ sols with sodium salts in different solvents (

Table 8. CCC values of NaClO₄ for C₇₀ sols in different solvents ^a.

Solvent:	H2O	CH3OH c	CH3CN c	DMSO
CCC, mM:	130–250 b	0.13	0.25	$\ge$180

Note. ^a In water, NaCl was used. ^b Depending on the sol concentration. ^c With 10 vol.% toluene.

).

For instance, for the colloids of C₇₀ in DMF and C₆₀ in DMSO, the CCCs of NaClO₄ are 40 and 70 mM, respectively. This is ca. 200–300 times higher than in acetonitrile or methanol. For C₇₀ in DMSO, the CCCs of NaClO₄ and LiClO₄ are no less than 180 mM. These abnormal values give evidence of substantial stabilizing factors, which is certainly caused by the basic character of DMSO and DMF and the electrophilic properties of fullerenes, which are Lewis acids. Note that in a basic (cationophilic) solvent, Li⁺ ion is well solvated and displays no anomalous coagulating impact, contrary to the behavior in a cationophobic solvent acetonitrile.

In the case of Ca(ClO₄)₂ in DMSO, the negative charge of the C₇₀ colloidal particles decreases substantially. This gives evidence for the pronounced role of adsorption of cations on the fullerene/DMSO interface. Nevertheless, the CCC value is with 1 mM 1000-fold higher than in acetonitrile.

Interestingly, p-toluenesulfonic acid acts pronouncedly in DMSO: for the sol C₆₀, CCC = 0.1 mM. Moreover, overcharging takes place and CCC₂ = 17 mM [74]. Hence, even in DMSO, like in other solvents (water, acetonitrile, methanol), acidic medium is unfavorable for fullerene stability. The CCC values for acids in water, methanol, acetonitrile, and DMSO range from 1.2 to 0.015 mM (Table 5 and Table 6).

Thus, despite the fact that fullerenes are Lewis acids, the negatively charged centers on the surface of colloidal particles have a basic character and are neutralized by protic acids, as well as by multiply charged metal cations, i.e., Lewis acids. A similar phenomenon was observed for oxidized single walled carbon nanotubes, SWCNT [268]. An aqueous suspension of SWCNT was five-fold diluted with acetonitrile, acetone, and alcohols, which decreases the CCC (NaCl) value by 1–2 orders of magnitude. In contrast, diluting the initial suspension with DMSO and DMF does not lead to a significant change in the CCC [268]. For organohydrosols of detonated nanodiamond, DND, with positive particle charge [269], the CCC values of most inorganic salts are higher than in water, if DMSO is the organic component, whereas in the mixtures of water with acetonitrile a pronounced drop of the CCC is observed. Here, the carbon atoms are in a state of sp³ hybridization, but the strong solvation of DMSO particles is obviously due to the interaction of this cationophilic solvent with cationic centers on the DND surface.

Finally, Figure 15 reflects the pronounced increase in the stability of the C₇₀ organosol with an increase in the DMSO: acetonitrile ratio.

Taking into account Table 2 and the behavior of fullerenes in NMP, considered in Section 4.2, the high stability of the corresponding organosols in respect to electrolytes can be predicted.

6. Conclusions

This review gives the following vision of the state of fullerenes in liquid media at the present time. In so-called “good” solvents, fullerenes exist in molecular form if the solutions are prepared by equilibrium methods. However, despite the molecular nature of such solutions, some of their properties resemble those of colloidal systems. The standard entropy of solvation and dissolution is significantly negative, while experiments prove that each fullerene molecule is surrounded by large solvation shells of an aromatic solvent. This makes the solution similar to systems known as colloidal crystals or periodic colloidal systems.

In polar or ”poor” solvents such as acetonitrile or methanol, fullerenes form typical colloidal solutions with particle sizes up to several hundred nanometers. In binary “good” + “poor” solvent systems, the fullerene aggregates appear at a certain threshold solvent composition. The latter depends to some extent on the concentration of fullerene. It is likely that C₆₀ and C₇₀ molecules are capable of retaining aromatic solvation shells even in colloidal aggregates.

A special group of polar solvents are NMP, DMSO, and DMF. These relatively basic solvents dissolve fullerenes without sonication. The solubility is higher than in other polar solvents, and large aggregates appear spontaneously. Formally, these solvents should be considered as “poor”, but with some features of “reactive” ones. Despite theoretical investigation of fullerenes in room temperature ionic liquids, the corresponding experimental data are few in number.

The interaction of fullerene hydrosols with electrolytes obeys all the classical laws and rules of colloid chemistry. There are known attempts to estimate the Hamaker constant of fullerene–fullerene interaction, A_FF, based on coagulation data. Two features of the behavior of C₆₀ and C₇₀ sols in acetonitrile and methanol fundamentally distinguish them from hydrosols. First, the critical concentrations of coagulations are two to three orders of magnitude lower than in water. Second, the overcharging of colloidal particles readily takes place. These phenomena make it difficult to process the data to estimate the Hamaker constant, A_FF, but after some judicious selection this value was found to be higher than that calculated from the hydrosol data. This allows us to derive some additional, non-DLVO specific interactions in water in accordance with the concept of “structural forces” by Churaev and Derjaguin.

The significance of specific interactions becomes obvious when studying the interaction of fullerenes with electrolytes in DMSO and DMF. In DMSO, the CCC is even higher than in water due to the strong solvation of fullerenes, which can be considered as Lewis acids.

Thus, in solvents of completely different chemical nature and physical properties, fullerenes can be obtained in a colloidal state. The systems discussed in this article provide many new illustrations for modern colloid chemistry.