Thermodynamics carbon clusters

Several proposals have been put forward to account for the formation of C 0F and the other fullerenes. Before reviewing these proposals, it seems appropriate to consider the key observations about fullerene synthesis, the kinds of carbon clusters possible, their energetics, and the thermodynamic and kinetics of carbon clustering. 

In the discussion of the relative acidity of carboxylic acids in Chapter 1, the thermodynamic acidity, expressed as the acid dissociation constant, was taken as the measure of acidity. It is straightforward to determine dissociation constants of such adds in aqueous solution by measurement of the titration curve with a pH-sensitive electrode (pH meter). Determination of the acidity of carbon acids is more difficult. Because most are very weak acids, very strong bases are required to cause deprotonation. Water and alcohols are far more acidic than most hydrocarbons and are unsuitable solvents for generation of hydrocarbon anions. Any strong base will deprotonate the solvent rather than the hydrocarbon. For synthetic purposes, aprotic solvents such as ether, tetrahydrofuran (THF), and dimethoxyethane (DME) are used, but for equilibrium measurements solvents that promote dissociation of ion pairs and ion clusters are preferred. Weakly acidic solvents such as DMSO and cyclohexylamine are used in the preparation of strongly basic carbanions. The high polarity and cation-solvating ability of DMSO facilitate dissociation... 

With respect to the thermodynamic stability of metal clusters, there is a plethora of results which support the spherical Jellium model for the alkalis as well as for other metals, like copper. This appears to be the case for cluster reactivity, at least for etching reactions, where electronic structure dominates reactivity and minor anomalies are attributable to geometric influence. These cases, however, illustrate a situation where significant addition or diminution of valence electron density occurs via loss or gain of metal atoms. A small molecule, like carbon monoxide,... 

It is well known that small particles melt at a lower temperature than the corresponding bulk solid. Buffat and Borel measured a monotonic lowering of melting temperature with decreasing diameter for gold clusters supported on carbon substrates (7). They accounted for their data by means of a thermodynamic model due to Pawlow (16), which states that the melting temperature of small particles is inversely proportional to the particle radius. 

The dominant isomerization pathway for the trimeric allenyl clusters [M3H(CO)9(/Li3-i7, V> 7 I C =C=CHR)] is via a thermal 1,2-hydrogen migration to afford the 1,3-dimetalloallyl clusters [M3H(CO)9(/H3-i7, t7, t7 -RCCHCR)] (53c). Reaction of alkynes and dienes with metal carbonyls M3(C0)2 (M = Ru, Os) often occurs with C-H activation adjacent to the unsaturated carbon-carbon bond (54) however, the final products isolated are often of the 1,3-dimetalloallyl type, the intermediate allenyl complex formed being thermodynamically unstable under the reaction conditions necessary to initiate C-H activation. 

DFT calculations have also demonstrated that in addition to the enhanced capacity to oxidize C atoms and CH fragments, the Sn/Ni surface alloy also lowers the thermodynamic driving force associated with the formation of carbon nucleation centers at low-coordinated Ni sites [16], DFT calculated adsorption energies for various carbon nucleation centers (a carbon atom, a cluster of 8 carbon atoms, and a graphene chain) on monometallic Ni and Sn/Ni surface alloy are shown in Fig. 13.4. The figure shows that for all carbon stractures, the under-coordinated sites on Ni (to model these sites, the Ni(211) surface was used) bind carbon more strongly than the under-coordinated sites on Sn/Ni(211) (in this model systan 1/3 of Ni edge atoms were displaced by Sn atoms). The reason for this is that Sn atoms break the ensembles of... 

In its most general form, the fullerene synthesis could be treated as a complex kinetic scheme described by a huge number of kinetic differential equations. The equilibrium composition comes as the limiting case for infinite time. If we treat the problem from a thermodynamic point of view, we should realize that the conventional standard pressure of 1 atm is considerably different from the actual fullerene synthesis conditions. We should expect lower cluster pressures in the carbon-arc synthesis. The actual entropy and Gibbs free energy change with pressure as can be demonstrated [208-212] on the Cgo and C70 cases based on computed or observed [213] data. For example, the equilibrium constant Xgo/yo for an interconversion between the two clusters, expressed in partial pressures p, offers a deeper insight into the problem [208-212] ... 

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