A Gibbs ensemble Monte Carlo study of phase coexistence in the solvent primitive model (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.
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.
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.
Studies of the Thermodynamic Conditions for the Existence of a Liquid Phase
2005
The condition under which certain systems may not have a stable liquid phase, instead, sublime from the solid to the vapor phase has been the subject of investigations by many. Until recently, it used to be thought that any amount of attraction added to a short ranged repulsion would give rise to a liquid phase. However, computer simulations, theoretical, as well as experimental studies have showed that this is not the case. By use of Hyper-parallel tempering Monte Carlo (HPTMC) simulation, computer simulations were performed to obtain the liquid-vapor coexistence data for square-well (SW) fluid with variable interaction range with the view of determining the conditions where the liquid state will simply squeeze out. The interaction range (λ) which plays a significant role in giving rise to a liquid phase in the phase diagram was varied from 1.21 to 3.0. The results of the work clearly indicate that the range of temperatures for which the liquid is stable shrinks as the interaction range decreases. And for sufficiently short interaction ranges, the square-well fluid has no stable liquid phase with a threshold value of λ = 1.24.
Liquid-Liquid Phase Transition: Evidence from Simulations
We report, using extensive molecular dynamics simulations of a one-component model system, a firstorder liquid-liquid phase transition. Specifically, by evaluating the pressure-density isotherms above and below a critical temperature, we find the presence of two coexisting phases differing by ϳ15% in density. Moreover, system points in an unstable region decompose into two different spatially separated phases. We identify the two phases, characterized by different local structures and local dynamics, by studying the static structure factor S͑q͒ at small wave vector q. [S0031-9007(97)
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.
Freezing line of the Lennard-Jones fluid: A phase switch Monte Carlo study
The Journal of Chemical Physics, 2006
We report a Phase Switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard sphere freezing, and builds on a previous PSMC study of the LJ system by Errington (J. Chem. Phys. 120, 3130 (2004)). The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results for which we compare to a previous Gibbs-Duhem integration study. Additionally we provide new background regarding the statistical mechanical basis of the PSMC method and extensive implementation details. PACS numbers: 64.70Fx, 68.35.Rh
Phase and Glass Transitions in Short-Range Central Potential Model Systems: The Case of C 60
The Journal of Physical Chemistry B, 2005
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 of biological interest), suggesting how to achieve at least qualitative predictions of vitrification and crystallization in those systems.