Erratum: Phase behavior of C60 by computer simulation using ab-initio interaction potential (original) (raw)
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Phase behavior of C60 by computer simulation using ab-initio interaction potential
International Journal of Quantum Chemistry, 2001
A first-principles intermolecular potential recently proposed by Pacheco and Ramalho [Phys Rev Lett 1997, 79, 3873-3876] has been used with the Gibbs ensemble and Gibbs-Duhem integration Monte Carlo methods to simulate the vapor-liquid and fluid-solid coexistence properties of C 60 . The critical properties were calculated by fitting the results to the laws of rectilinear diameters and order parameter scaling. The triple-point properties were determined from the limiting behavior of the Gibbs ensemble vapor-liquid simulations at the lowest temperature range. A stable liquid phase is predicted for temperatures between 1570 ± 20 and 2006 ± 27 K and densities between 0.444 ± 0.003 and 1.05 ± 0.01 nm −3 . The estimated critical and triple-point pressures are, respectively, 35 ± 6 and 5 ± 16 bars. We show for the first time, to our knowledge, that it is possible, strictly by computer simulation, to estimate a triple point for C 60 in accordance with the predictions of theoretical methods and the basic concepts of thermodynamics. The liquid and fluid radial distribution functions indicate the presence of solid or glasslike features. This may support the suggestion of a more cooperative interaction of clusters in C 60 . A comparison of our results with the data obtained by other authors is presented and discussed.
The Journal of Physical Chemistry B, 2002
A first-principles interaction potential proposed by Pacheco and Ramalho (PRP) and the effective potential of Girifalco (GP) have been used to model the whole phase diagram of C 60 by Gibbs ensemble and Gibbs-Duhem integration Monte Carlo methods. The triple-point properties were determined by a direct method recently proposed by us (Comput. Phys. Commun. 2001, 141, 403). It is based on the behavior of the Gibbs ensemble vapor-liquid simulations at the low-temperature limit, and it does not involve free-energy calculations. A stable liquid phase for temperatures between 1570 ( 20 K and 2006 ( 27 K is predicted with the PRP model and for temperatures between 1529 ( 36 K and 1951 ( 28 K with the GP model. According to these results, the liquid phase for C 60 extends over ∼450 K, a temperature range considerably wider than the ones reported by other authors on the basis of free-energy calculations and density functional approaches. Nonetheless, the present results are in good agreement with the theoretical predictions from the hypernetted mean spherical approximation, the modified hypernetted chain theory, and a correlative self-consistent field method as well as with some molecular dynamics simulations. The reported free-energy data for the fluidsolid region are reproduced here, strictly by computer simulation. According to them, the liquid phase of C 60 extends over ∼100 K. A discussion on the apparent conflicting triple-point data is presented. The calculated enthalpies of sublimation at 700 K (163 ( 9 kJ mol -1 for PRP and 170 ( 12 kJ mol -1 for GP) are in good agreement with the available experimental results. The estimated standard enthalpies are also within the recommended values, and the third-law enthalpies are in excellent agreement with experimental and theoretical data. This suggests that at least the simulated triple-point properties, in the low-temperature limit, should approach that of real C 60 . The radial distribution functions and the self-diffusion coefficients, in the liquid pockets predicted for the two models, are also consistent with a normal liquid state, and no sign of liquid supercooling was observed. On the whole, the differences between the present interaction potentials do not induce significant qualitative changes in the phase behavior of the two models. However, the differences are clearly reflected in the location of the coexistence lines and the critical and triple-point properties as well as in the enthalpies of sublimation. Finally, as a further test of the reliability of our method for the determination of triple-point properties, we also report preliminary results for the triple-point temperature and the standard enthalpy of sublimation of C 70 . They are in excellent agreement with theoretical and experimental data.
Free energy determination of phase coexistence in model C60: A comprehensive Monte Carlo study
The Journal of Chemical Physics, 2003
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.
Phase diagram, structure, and disorder in C60 below 300 K and 1 GPa
Solid State Communications, 1995
Eariier structural studies have shown that the pentagon-to-hexagon orientation ratio in the orientationally ordered simple cubic phase of Cbo decreases under pressure From anomalies observed in the compressibility and thermal conductivity of C60 under pressure we have deduced a pressure-temperature phase diagram for this substance in the range below 300 K and I GPa (10 kbar). We conclude that C6" forms a new, completely "hexagon" ordered structural phase above about 0 G GPa at 150 K (1.2 GPa at 300 K), and that the glass transition shifts upwards in T under pressure by 54 K GPa-' However, above 0 1 GPa, pentagon-to-hexagon orientation relaxation seems to occur on heating at an almost pressure independent temperature near 100 K
Towards a microscopic approach to the intermolecular interaction in solidC60
Physical Review B, 1997
Although the calculation of the ground-state and thermodynamic properties of solid C 60 have been the subject of intense research, our understanding is still based on ad hoc models that treat phenomenologically both the Coulomb and short-range part of the interaction potential between C 60 molecules. These potentials do not predict well those properties not fitted to fix the free parameters of the model, and they also do not properly represent the Coulomb interaction between molecules. To remedy this situation, here we introduce a semiempirical model in which the Coulomb interaction is treated microscopically using the local-density approximation C 60 molecular charge densities, and the short-range part of the potential is modeled phenomenologically via Lennard-Jones (LJ) 12-6 interactions between the centers, delocalized over the surfaces of C 60 molecules. The regular LJ parameters σ and ε as well as multipole moments of the interaction centers distribution were taken to reproduce the details of the observed low-temperature structure. We found that the Coulomb interaction is dominated by the charge overlap between the neighboring C 60 molecules, and is much larger than the interaction calculated using the multipole expansion of the charge densities. Contrary to common belief, this Coulomb interaction by itself does not lead to the observed low-temperature structure. However, combined with the proposed short-range interaction, it stabilizes Pa3 spatial structure with the correct setting angle. We make a comprehensive comparison between the wide range of experimental results and predictions of our, as well as previously proposed models. Our results show that the proposed model has the best overall agreement with the experimental observations in both the low-and hightemperature phases.
Phase Diagram and Sublimation Enthalpies of Model C 60 Revisited
The Journal of Physical Chemistry B, 2004
The objective of the present paper is to reassess our previous results and conclusions on the simulation of model C 60 and other fullerenes, in view of the results recently reported by other authors. We report new sublimation enthalpies in good agreement with the available experimental data and recent theoretical results. Special attention is given to the pressures along the coexistent phases. We also present a comparative study, by NVT and NpT simulations, of supercritical isotherms for Lennard-Jonesium and C 60 , in order to clarify the Gibbs ensemble and Gibbs-Duhem Monte Carlo calculations. It is suggested that even in the case of C 60 the stable fluid-solid transitions can be detected through the visual analysis of the equations of state. Finally, we critically review our previous works on model fullerenes.
Theoretical description of phase coexistence in model C_{60}
Physical Review E, 2003
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.
Model for High Temperature Phase of C70 Solid
2001
Depending on the temperature, the C 70 solid crystallizes in several structures. At high temperature (T > 340K), the ellipsoidal C 70 molecule rotates freely in all directions and may be treated as a uniform thick spherical shell with inner and outer radii as the minimum and the maximum distance of C-atom from the center of the molecule. At lower temperatures the free rotations of molecules freeze out. We have calculated the lattice parameters, energies and bulk modulus at the minimum energy configuration of fcc and hcp phase of pure C 70 solid at high temperature using a simple model based on atom-atom potential.
Stability of different phases of (C60)2 Structures
2006
We investigate the possible binding configurations of pairs of C60 molecules when pushed against each other. Tersoff potential, which represents intramolecular interactions well, has been used to calculate potential energies. We begin relaxation of atomic coordinates at various distances of separation and for all possible mutual orientations of the two molecules. As a result, we have been able to show