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

Abstract

The free energy of the solid and fluid phases of the Girifalco C60 model are determined through extensive Monte Carlo simulations. In this model the molecules interact through a spherical pair potential, characterized by a narrow and attractive well, adjacent to a harshly repulsive core. We have used the Widom test particle method and a mapping from an Einstein crystal, in order to estimate the absolute free energy in the fluid and solid phases, respectively; we have then determined the free energy along several isotherms, and the whole phase diagram, by means of standard thermodynamic integrations. The dependence of the simulation's results on the size of the sample is also monitored in a number of cases.We highlight how the interplay between the liquid-vapor and the liquid-solid coexistence conditions determines the existence of a narrow liquid pocket in the phase diagram, whose stability is assessed and confirmed in agreement with previous studies. In particular, the critical temperature follows closely an extended corresponding-states rule recently outlined by Noro and Frenkel [J. Chem. Phys. 113, 2941 (2000)].We discuss the emerging "energetic" properties of the system, which drive the phase behavior in systems interacting through short-range forces [A. A. Louis, Phil. Trans. R. Soc. A 359, 939 (2001)], in order to explain the discrepancy between the predictions of several structural indicators and the results of full free energy calculations, to locate the fluid phase boundaries.More generally, we aim to provide extended reference data for calculations of the free energy of the C60 fullerite in the low temperature regime, as for the determination of the phase diagram of higher order Cn>60 fullerenes and other fullerene-related materials, whose description is based on the same model adopted in this work.

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

“…It turns out that the triple and critical point temperatures, T tr and T cr , are significantly lower, and much higher, respectively, of their counterparts for a rigid cage model of C 60 . 10,11,13,[15][16][17] We get thus evidence of a huge expansion of the stable liquid phase pocket of C 36 in comparison to that early found in C 60 . 10-12, 14, 16, 17 Moreover, the diffusion coefficient and the structural arrangement at the triple point density of C 36 , maintain liquid-like features over several hundreds degrees below T tr , by thus indicating a substantial extension of the "supercooled" liquid region.…”

“…It follows that the range of existence of a thermodynamically stable liquid phase has an amplitude of ∼600 K, much more indeed than the 80 K interval found for the C 60 case. 10,13,[15][16][17] Since the C-C interaction in the present case has an attractive well depth = 90 K, almost three times greater than the one adopted in C 60 (see Refs. 7 and 16), a certain increase of T cr in C 36 might be expected; the magnitude of the overall expansion of the liquid pocket appears nonetheless remarkable.…”

“…We recall in this instance that attempts to observe experimentally the liquid phase of C 60 by heating its fullerite at high temperature, 22 failed because of the amorphization of the C 60 cage, occurring ∼700 K below the estimated T tr . 10,16,17 The reasons of such an instability of the C 60 molecule in the solid phase have been object of debate in the past (see Ref. 23 and references therein).…”

“…16,17 Therein, however, the fullerene was described in terms of a central potential model, and the extension of those methods to our atomistic C 36 does not appear of immediate feasibility. A similar remark can be made also for the determination of the freezing line in terms of the multiparticle residual entropy behavior, 26 an approach exploited by us in previous works for a central potential model of C 60 and for a simple fluid, respectively.…”

“…A similar remark can be made also for the determination of the freezing line in terms of the multiparticle residual entropy behavior, 26 an approach exploited by us in previous works for a central potential model of C 60 and for a simple fluid, respectively. 16,27 The binodal line could also be derived via direct methods as for instance successive umbrella sampling, grand canonical, or Gibbs ensemble Monte Carlo simulations. 28 On the other hand, the advantage of the present MD study is to provide a full characterization of the fluid phase, including the freezing and melting lines, as well as the dynamical properties of the system.…”