Free energy determination of phase coexistence in model C60: A comprehensive Monte Carlo study

Communication: Phase diagram of C₃₆ by atomistic molecular dynamics and thermodynamic integration through coexistence regions

We report an atomistic molecular dynamics determination of the phase diagram of a rigid-cage model of C36. We first show that free energies obtained via thermodynamic integrations along isotherms displaying "van der Waals loops," are fully reproduced by those obtained via isothermal-isochoric integration encompassing only stable states. We find that a similar result also holds for isochoric paths crossing van der Waals regions of the isotherms, and for integrations extending to rather high densities where liquid-solid coexistence can be expected to occur. On such a basis we are able to map the whole phase diagram of C36, with resulting triple point and critical temperatures about 1770 K and 2370 K, respectively. We thus predict a 600 K window of existence of a stable liquid phase. Also, at the triple point density, we find that the structural functions and the diffusion coefficient maintain a liquid-like character down to 1400-1300 K, this indicating a wide region of possible supercooling. We discuss why all these features might render possible the observation of the melting of C36 fullerite and of its liquid state, at variance with what previously experienced for C60.

Reformulation of liquid perturbation theory for low temperatures

A perturbation strategy is proposed which allows liquid perturbation methodology to be applied to extremely low temperature situations for which the available liquid integral equation theory and traditional thermodynamic perturbation theory fail. The possibility of avoiding the low temperature problem of the thermodynamic perturbation theory not only is of relevance to the investigation of complex fluids, but also may be useful for reformulation of other liquid theories to achieve higher accuracy and avoid the respective low temperature problems.

Glass transition line in C60: a mode-coupling/molecular-dynamics study

We report a study of the mode-coupling theory (MCT) glass transition line for the Girifalco model of C60 fullerene. The equilibrium static structure factor of the model, the only required input for the MCT calculations, is provided by molecular dynamics simulations. The glass transition line develops inside the metastable liquid-solid coexistence region and extends down in temperature, terminating on the liquid side of the metastable portion of the liquid-vapor binodal. The vitrification locus does not show re-entrant behavior. A comparison with previous computer simulation estimates of the location of the glass line suggests that the theory accurately reproduces the shape of the arrest line in the density-temperature plane. The theoretical HNC and MHNC structure factors (and consequently the corresponding MCT glass line) compare well with the numerical counterpart. Our results confirm the conclusion drawn in previous works about the existence of a glassy phase for the fullerene model at issue.

Complex phase behaviour from simple potentials

Simple pair potentials, where the term 'simple' denotes potentials that are isotropic and refer to one-component systems, can be used to describe effective interactions among substances with supramolecular architecture. By suitably choosing the functional dependence on the intermolecular distance, through such potentials it is possible to take into account, in an average way, the effect of the internal degrees of freedom of the macromolecules. This may give rise to phase phenomena that are radically different from those characterizing typical monoatomic systems. Here we review a number of simple model potentials presenting unusual, i.e. not argon-like, features and discuss the role of attraction and repulsion in determining their phase behaviour.

Free energy of the solid C60 fullerene orientational order-disorder transition

The free energies of the orientationally ordered crystal phase of C60 at low temperatures and the disordered crystal phase at high temperatures are calculated to an accuracy of +/-0.05 kJ/mol using the expanded ensemble Monte Carlo method with the potential model of Sprik et al. [J. Phys. Chem. 96, 2027 (1992)]. The order-disorder transition temperature at zero pressure is determined directly from these free energies, and is found to be consistent with the abrupt changes in configurational energy and unit cell size also found in simulation. A modification of the potential results in predictions of the transition temperature of 257 K and the entropy change of 18.1 J/mol K at this transition, which are in good agreement with the experimental values of 260 K and 19 J/mol K, respectively. The orientational distinguishability in the ordered phase and the indistinguishability in the disordered phase lead to a contribution to the entropy difference of k ln 60, with 60 being the symmetry number of C60. This quantum mechanical correction is important for the accurate prediction of the phase transition properties of the C60 crystals.

Direct calculation of solid-vapor coexistence points by thermodynamic integration: application to single component and binary systems

We present a new thermodynamic integration method that directly connects the vapor and solid phases by a reversible path. The thermodynamic integration in the isothermal-isobaric ensemble yields the Gibbs free energy difference between the two phases, from which the sublimation temperature can be easily calculated. The method extends to the binary mixture without any modification to the integration path simply by employing the isothermal-isobaric semigrand ensemble. The thermodynamic integration, in this case, yields the chemical potential difference between the solid and vapor phases for one of the components, from which the binary sublimation temperature can be calculated. The coexistence temperatures predicted by our method agree well with those in the literature for single component and binary Lennard-Jones systems.

A general perturbation approach for equation of state development: Applications to simple fluids, ab initio potentials, and fullerenes

A new perturbation scheme based on the Barker-Henderson perturbation theory [J. Chem. Phys. 47, 4714 (1967)] is proposed to predict the thermodynamic properties of spherical molecules. Accurate predictions of second virial coefficients and vapor-liquid coexistence properties are obtained for a large variety of potential functions (square well, Yukawa, Sutherland, Lennard-Jones, Buckingham, Girifalco). New Gibbs ensemble Monte Carlo simulations of the generalized exp-m Buckingham potential are reported. An extension of the perturbation approach to mixtures is proposed, and excellent predictions of vapor-liquid equilibria are obtained for Lennard-Jones mixtures. The perturbation scheme can be applied to complex potential functions fitted to ab initio data to predict the properties of real molecules such as neon. The new approach can also be used as an auxiliary tool in molecular simulation studies, to efficiently optimize an intermolecular potential on macroscopic properties or match force fields based on different potential functions.

Phase and Glass Transitions in Short-Range Central Potential Model Systems: The Case of C60

Extensive molecular dynamics simulations show that a short-range central potential, suited to model C60, undergoes a high temperature transition to a glassy phase characterized by the positional disorder of the constituent particles. Crystallization, melting, and sublimation, which also take place during the simulation runs, are illustrated in detail. It turns out that vitrification and the mentioned phase transitions occur when the packing fraction of the system-defined in terms of an effective hard-core diameter-equals that of hard spheres at their own glass and melting transition, respectively. A close analogy also emerges between our findings and recent mode coupling theory calculations of structural arrest lines in a similar model of protein solutions. We argue that the conclusions of the present study might hold for a wide class of potentials currently employed to mimic interactions in complex fluids (some of which are of biological interest), suggesting how to achieve at least qualitative predictions of vitrification and crystallization in those systems.

A molecular-dynamics simulation study of solvent-induced repulsion between C60 fullerenes in water

Molecular-dynamics simulations of a single C(60) fullerene and pairs of C(60) fullerenes in aqueous solution have been performed for the purpose of obtaining improved understanding of the nature of solvent-induced interactions between C(60) fullerenes in water. Our simulations reveal repulsive solvent-induced interactions between two C(60) fullerenes in aqueous solution in contrast to the associative effects observed for conventional nonpolar solutes. A decomposition of the solvent-induced potential of mean force between fullerenes into entropy and energy (enthalpy) contributions reveals that the water-induced repulsion between fullerenes is energetic in origin, contrasting strongly to entropy-driven association observed for conventional nonpolar solutes. The dominance of energy in the solvent-induced interactions between C(60) fullerenes arises primarily from the high atomic density of the C(60) molecule, resulting in strong C(60)-water van der Waals attraction that is reduced upon association of the fullerenes. The water-induced repulsion is found to decrease with increasing temperature due largely to an increasing contribution from a relatively weak entropy-driven association.

Atomistic versus two-body central potential models of C(60): a comparative molecular dynamics study

We report on an extensive molecular dynamics investigation of two models of C60. The first model is based on an effective pair, central potential obtained by integrating the interaction between two carbon atoms over the fullerene cages [L.A. Girifalco, J. Phys. Chem. 96, 858 (1992)]. The second model explicitly takes into account the discrete, "atomistic" structure of the C60 molecules; we study two different parametrizations of the carbon-carbon interaction, one identical to that employed in the Girifalco approach, the other borrowed from previous studies on graphite [A. Cheng and M.L. Klein, J. Phys. Chem. 95, 6750 (1991)]. We consider a temperature range spanning from 300 to 1900 K, and pressures up to 200 kbar. Results for the lattice spacing and several thermodynamic quantities, as well as for the radial distribution functions, are reported and compared among each other and with experimental data. The central pair model yields only semiquantitative predictions at typical ambient densities, whereas pressures are generally overestimated. Atomistic simulations reproduce to an overall quantitative level of accuracy the experimental C60 properties. A comparison is also made of the central versus the atomistic potential predictions, when using the same potential parameters in the carbon-carbon interaction. We discuss applications of the adopted modelizations to fullerene systems of current interest, as well as different strategies to optimize the values of the potential parameters.

Theoretical description of phase coexistence in model C60

We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely, the modified hypernetted chain (MHNC) implemented under a global thermodynamic consistency constraint, and the self-consistent Ornstein-Zernike approximation (SCOZA), and by a perturbation theory (PT) with various degrees of refinement, for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties such as the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory. We have then selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.