T. V. Tropin

Models of cluster formation in solutions of fullerenes

A review of experimental and theoretical studies of the formation and growth of clusters in solutions of fullerenes is given. General problems of fullerene cluster formation in solutions are considered. The main directions and goals of studies are specified. The experimental data on solutions with various polarities obtained by various methods, including visible and UV spectroscopy, dynamic light scattering, small-angle neutron scattering, mass spectrometry, transmission electron microscopy, etc., are generalized. The conditions of cluster formation and mechanism of cluster stabilization and the role played by clusters in certain effects observed in the corresponding systems are discussed. Cluster growth models are considered on the basis of nucleation theory for solutions of fullerenes with various polarities. It is shown that the description of the observed cluster state requires modification of the kinetic equations of the classic approach using the drop model of clusters. Modified kinetic equations with corrections for the mechanism of cluster stabilization are used to analyze cluster growth and related phenomena.

Dependence of the width of the glass transition interval on cooling and heating rates

In a preceding paper [J. W. P. Schmelzer, J. Chem. Phys. 136, 074512 (2012)], a general kinetic criterion of glass formation has been advanced allowing one to determine theoretically the dependence of the glass transition temperature on cooling and heating rates (or similarly on the rate of change of any appropriate control parameter determining the transition of a stable or metastable equilibrium system into a frozen-in, non-equilibrium state of the system, a glass). In the present paper, this criterion is employed in order to develop analytical expressions for the dependence of the upper and lower boundaries and of the width of the glass transition interval on the rate of change of the external control parameters. It is shown, in addition, that the width of the glass transition range is strongly correlated with the entropy production at the glass transition temperature. The analytical results are supplemented by numerical computations. Analytical results and numerical computations as well as existing experimental data are shown to be in good agreement.

On the theoretical determination of the Prigogine-Defay ratio in glass transition

In a recent analysis [J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511 (2006)] it was shown for the first time that--in contrast to earlier belief arising from the works of Prigogine and Defay [Chemical Thermodynamics (Longman, London, 1954), Chap. 19; The first French edition of this book was published in 1950] and Davies and Jones [Adv. Phys. 2, 370 (1953); and Proc. R. Soc. London, Ser. A 217, 26 (1953)]--a satisfactory theoretical interpretation of the experimentally observed values of the so-called Prigogine-Defay ratio Π, being a combination of jumps of thermodynamic coefficients at glass transition, can be given employing only one structural order parameter. According to this analysis, this ratio has to be, in full agreement with experimental findings, larger than one (Π > 1). Its particular value depends both on the thermodynamic properties of the system under consideration and on cooling and heating rates. Based on above-mentioned analysis, latter dependence on cooling rates has been studied in detail in another own preceding paper [T. V. Tropin, J. W. P. Schmelzer, and C. Schick, J. Non-Cryst. Solids 357, 1303 (2011)]. In the present analysis, an alternative general method of determination of the Prigogine-Defay ratio is outlined, allowing one to determine this ratio having at ones disposal the generalized equation of state of the glass-forming melts under consideration and, in particular, the knowledge of the equilibrium properties of the melts in the glass transformation range. Employing, as an illustration of the method, a particular model for the description of glass-forming melts, theoretical estimates are given for this ratio being, again, in good agreement with experimental data.

On structural features of fullerene C60 dissolved in carbon disulfide: complementary study by small-angle neutron scattering and molecular dynamic simulations.

The parameters of fullerene C(60) dissolved in carbon disulfide CS(2) are analyzed by small-angle neutron scattering (SANS) in a wide interval of momentum transfer. To exclude the influence of nonequilibrium conditions, the solutions are prepared without applying shaking, stirring or ultrasound. No indication of the equilibrium cluster state of C(60) (with the cluster size below 60 nm) in the final solutions is revealed. Molecular dynamic simulations are complementary used to find out the partial volume of C(60) in CS(2) and the scattering contribution of the solvent organization at the interface with the fullerene molecule, which is shown to be small. Among several approaches for describing SANS data the preference is given to the model, which takes into account the presence of stable C(60) dimers (comprising 10% of the total particle number density) in the solution.

Formation of fullerene clusters in carbon disulfide: Data on small-angle neutron scattering and molecular dynamics

Fullerene solutions in carbon disulfide are studied by small-angle neutron scattering (SANS). In addition to earlier experiments on the given system, the range of measured transmitted impulses is extended and the influence of solution preparation methods on C60 cluster formation in these solutions is studied. It is shown that the formation of large C60 clusters (with a size of about 10 nm) is due to nonequilibrium methods of solution preparation. For nonequilibrium dissolution, there is a 10% excess of the observed fullerene size in the solution over the calculated value. It has been established by simulation of the C60/CS2 interface by molecular dymanics methods that inclusion of how solvent molecules are organized on the C60 surface leads to a decrease in the fullerene size in the solution, observed by using SANS. In this paper, the effect of excess Rg is explained by the presence of small clusters in the solution (approximately 10% of dissolved C60 molecules). It is discovered that there is a time variation in the concentration of the saturated solution. The explanation of this effect using a model of formation and sedimentation of large clusters (with a size of 100 nm or more) is proposed.

Aggregation in C60/NMP, C60/NMP/water and C60/NMP/Toluene Mixtures

The solutions of C60 in N‐methyl‐2‐pyrrolidone (NMP) and in the binary mixtures NMP/water and NMP/toluene are investigated using UV‐Vis spectroscopy, small‐angle neutron scattering and mass‐spectroscopy. The decomposition of fullerene clusters after dilution of C60/NMP system with water and the effect of solvent polarity on fullerene aggregation in C60/NMP/toluene solutions are analyzed.

Experimental investigation of C60/NMP/toluene solutions by UV-Vis spectroscopy and small-angle neutron scattering

The transformation of the C60 fullerene cluster state into C60/N-methylpyrrolidone (NMP) solution after the addition of a nonpolar solvent (toluene, electric permittivity ɛ= 2.4) is studied. The results of ultraviolet-visible spectroscopy and small-angle neutron scattering measurements are used for comparison of the C60/NMP/toluene system with C60/NMP mixtures with a high-polar solvent (water, ɛ = 80). As to the observed reorganization of the cluster state, the C60/NMP/toluene system is similar to the C60/NMP/water system. This effect is explained by the formation of charge-transfer complexes in the initial C60/NMP solution. These complexes are thought to be soluble in both binary mixtures. The connection between the cluster-reorganization effect and solvatochromism is discussed.

Formation of C60 fullerene clusters in nitrogen-containing solvents

An approach to the description of the growth of C60 fullerene clusters in nitrogen-containing solvents has been proposed within the framework of the nucleation theory. A temporal solvatochromic effect and reorganization of fullerene clusters have been considered upon addition of water to the C60/N-methyl-2-pyrrolidone (NMP) system. In particular, the reorganization of fullerene clusters manifests itself as a sharp increase in the small-angle neutron scattering intensity for cluster sizes of the order of 10 nm. The conclusion has been drawn that, in order to explain these effects, it is necessary to take into account the formation of new (hypothetically, donor-acceptor) bonds between the C60 and NMP molecules with time after the dissolution of fullerene.

Nonmonotonic Behavior of the Concentration in the Kinetics of Dissolution of Fullerenes

A cluster model for the dissolution of C60 fullerenes in a nonpolar solvent has been proposed. This model provides the explanation of a maximum experimentally observed in the time dependence of the solution concentration during dissolution. The model is based on the kinetic equations of nucleation theory and involves a balance between the flux of fullerene molecules from the solid phase and the sedimentation of large clusters from the solution. The formation of clusters is described using the drop model. Analysis of the numerical solutions of the equations reveals four qualitatively different dissolution regimes depending on the relation between the model parameters.

Absorption Characteristics of Fullerene C 60 in N-Methyl-2-Pirrolidone/Toluene Mixture

UV-Vis spectra of fullerene C60 in various mixtures of polar N-methyl-2-pyrrolidone (NMP), ϵ = 32, and low-polar toluene, ϵ = 2.4, are analyzed. A sharp solvatochromic effect is observed when toluene is added to C60/NMP. The comparison with the effect of water addition, ϵ = 80, to C60/NMP is given.