Theoretical description of phase coexistence in modelC60

Abstract

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 like the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, or 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 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 Cn>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.

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.…”

Glass Transition Line in C60: A Mode-Coupling/Molecular-Dynamics Study

“…Newly generated fluid-solid coexistence points in the high temperature regime (T = 3500) and in the low temperature solid phase (T ≤ 1200) are displayed as well, in order to elucidate the whole appearance of the coexistence region where all calculations have been done. The coexistence points at high temperature are in particular calculated according to the procedure employed in ref [25]: the free energy of the fluid phase is calculated through thermodynamic integration of the MD pressure at several state points along the isotherm T = 3500 K, whereas for the solid phase we have used a first-order perturbation theory starting from a crystal of hard spheres, whose diameter is chosen according to the Weeks-Chandler-Andersen (WCA) procedure [26]. We have obtained in this way for the coexisting densities: ρ fluid (T = 3500) = 1.02 nm −3 and ρ solid (T = 3500) = 1.24 nm −3 .…”