1. Introduction

2. Solubility of fullerenes

3. Fullerene solutions in “good” solvents as a platform for preparation of colloids

4. Formation and properties of colloidal particles in “good” + “poor” and “poor” solvents

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 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 data set, 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-methylpyrrolidone and dimethylformamide with water results in NMP/nC_60, NMP/nC₇₀ [186], and DMF/nC₆₀ [155] colloidal systems. New versions of such approach 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 basing on 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 in introduction of THF solution 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 colloidal 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 thus 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 thus 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 used addition of small amounts of ethanol to the aqueous phase [196,200,204]. Slight heating to 40 ⁰C 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 ⁰C 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 ion, 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 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 ⁰C, the size of particles is 97±3 nm (Figure 8) and $\varsigma$ = –40±4 mV [198].

Figure 8. Particle size distribution in the son/nC₇₀. From ref. [198] with permission.

Figure 8. Particle size distribution in the son/nC₇₀. From ref. [198] with permission.

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].

Figure 9. UV-visible absorption spectra of C₇₀ in good solvents and in the son/nC₇₀ hydrosol. From ref. [198] with permission. .

Figure 9. UV-visible absorption spectra of C₇₀ in good solvents and in the son/nC₇₀ hydrosol. From ref. [198] with permission. .

The size/$\varsigma$ values for C₇₀ hydrosols, available in the literature, as 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 at preparation of the initial toluene solution of fullerenes. Contrary to it, we use 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 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]. Basing 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]. 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.

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 Table 4.

Figure 8. Determination of the critical coagulation concentration of the C₇₀ hydrosol by NaCl: the results of two independent experiments; asterisks indicate the ς values. From ref. [198] with permission.

Figure 8. Determination of the critical coagulation concentration of the C₇₀ hydrosol by NaCl: the results of two independent experiments; asterisks indicate the ς values. From ref. [198] with permission.

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 solutions 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 were 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 ref. [25], Table 5, for the last two articles the fullerene concentrations were indiated 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. 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 predict 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 and mutual coagulation [253,254,255,256], consideration of structural forces [257], and the role of the co-ions (or simili-ions) 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 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, 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 LaNO₃ 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 size jump 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 [266]. 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).

$$U\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}{U}_{el}\hspace{0.17em}+\hspace{0.17em}{U}_{attr}$$

(2)

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

(3)

Here, $h$ stads for the distance between the centers of the particles, s = 2 + h/r, ${\epsilon }_0$ = 8.854$\times$ 10^–12 F m^–1, k 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:

$$A_{\mathrm{FSF}}^{*}\hspace{0.17em}=\hspace{0.17em}{({A_{\mathrm{FF}}}^{1/2}\hspace{0.17em}-\hspace{0.17em}{A}_{\mathrm{SS}}^{1/2})}^2$$

(3)

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 (8), such 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^–20 J [240,241]. Our processing 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 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 9 and Figure 10, Table 6) confirm the above conclusions.

Figure 9. The reciprocal Fuchs function (= aggregation attachement efficiency) vs. logarithm of the electrolyte concentration (mM) in methanol: NaClO₄ (1); HClO₄ (2); TBAClO₄ (3); Ca(ClO₄)₂ (4). Reprinted from ref. [123] with permission.

Figure 9. The reciprocal Fuchs function (= aggregation attachement efficiency) vs. logarithm of the electrolyte concentration (mM) in methanol: NaClO₄ (1); HClO₄ (2); TBAClO₄ (3); Ca(ClO₄)₂ (4). Reprinted from ref. [123] with permission.

Figure 10. Diameter increase rate and ζ-potential of C₇₀ particles (5×10^–6 M C₇₀) in the presence of NaClO₄ or LiClO₄ in acetonitrile – toluene mixtures (10 vol % toluene). From ref. [70] with permission.

Figure 10. Diameter increase rate and ζ-potential of C₇₀ particles (5×10^–6 M C₇₀) in the presence of NaClO₄ or LiClO₄ in acetonitrile – toluene mixtures (10 vol % toluene). From ref. [70] with permission.

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”. The overcharging occurs at metal ion concentrations above the CCC and is very pronounced. E.g., 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 eletrokinetic 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 is, in addition to enhanced electrostatic interactions, poor solvation of the used cations in acetonitrile and methanol; 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].

Figure 11. The Hamaker diagrams for C₆₀ alcosol in methanol: a – for 0.10 mM ionic strength and A^*×10²⁰ J: 0.9 (1), 1.1 (2), 1.3 (3), 1.6 (4), 2.0 (5), 2.4 (6), 2.8 (7), 3.1 (8); b – for 0.30 mM ionic strength and A^*×10²⁰ J: 0.46 (1), 0.52 (2), 0.6 (3), 0.7 (4), 0.8 (5), 1.0 (6), 1.2 (7), 1.4 (8). The values r = 150 nm and $\varsigma$ = –10 mV are used in the constructing of the presented curves. From ref. [123] with permission.

Figure 11. The Hamaker diagrams for C₆₀ alcosol in methanol: a – for 0.10 mM ionic strength and A^*×10²⁰ J: 0.9 (1), 1.1 (2), 1.3 (3), 1.6 (4), 2.0 (5), 2.4 (6), 2.8 (7), 3.1 (8); b – for 0.30 mM ionic strength and A^*×10²⁰ J: 0.46 (1), 0.52 (2), 0.6 (3), 0.7 (4), 0.8 (5), 1.0 (6), 1.2 (7), 1.4 (8). The values r = 150 nm and $\varsigma$ = –10 mV are used in the constructing of the presented curves. From ref. [123] with permission.

First, the $A_{\mathrm{FF}}$ were estimated using the approach described above for hydrosols. Examples of the corresponding Hamaker diagrams are given in Figure 11. 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. However, more detailed analysis allowed selecting electrolytes that can be used in such reconstruction of the $A_{\mathrm{FF}}$ value [70]. The systems whith 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), 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 12).

Figure 12. Hamaker diagrams for C₆₀ hydrosol in 20 mM NaCl solution, r = 44 nm, $\varsigma$ = –14.3 mV constructed using different $A_{\mathrm{FF}}$ values. The upper (green) curve corresponds to the value $A_{\mathrm{FF}}$ = 6.0×10^–20 J, which was obtained under assumption of the absence of any interactions except electrostatic repulsion and molecular attraction. From ref. [70] with permission.

Figure 12. Hamaker diagrams for C₆₀ hydrosol in 20 mM NaCl solution, r = 44 nm, $\varsigma$ = –14.3 mV constructed using different $A_{\mathrm{FF}}$ values. The upper (green) curve corresponds to the value $A_{\mathrm{FF}}$ = 6.0×10^–20 J, which was obtained under assumption of the absence of any interactions except electrostatic repulsion and molecular attraction. From ref. [70] with permission.

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 described in Section 3.5, 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).

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 factor, 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 is neutralized by protic acids, as well as by multiply charged metal cations, i.e., Lewis acids. 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 iorganic 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 13 reflects the pronounced increase in stability of the C₇₀ organosol on stepwise increase in the DMSO : acetonitrile ratio.

Figure 13. Dependence of the CCC(NaClO₄) values of the C₇₀ organosol on the volume fraction of DMSO in the ternary benzene–acetonitrile–DMSO system. From ref. [74] with permission.

Figure 13. Dependence of the CCC(NaClO₄) values of the C₇₀ organosol on the volume fraction of DMSO in the ternary benzene–acetonitrile–DMSO system. From ref. [74] with permission.

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

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