Soft sphere potential
The soft sphere potential is defined as
where is the intermolecular pair potential between two soft spheres separated by a distance , is the interaction strength and is the diameter of the sphere. Frequently the value of is taken to be 12, thus the model effectively becomes the high temperature limit of the Lennard-Jones model [1]. If one has the hard sphere model. For no thermodynamically stable phases are found.
Equation of state
The soft-sphere equation of state[2] has recently been studied by Tan, Schultz and Kofke[3] and expressed in terms of Padé approximants. For and one has (Eq. 8):
and for one has (Eq. 9):
Virial coefficients
Tan, Schultz and Kofke[3] have calculated the virial coefficients at (Table 1):
n=12 n=9 n=6 3.79106644 4.27563423 5.55199919 3.52761(6) 3.43029(7) 1.44261(4) 2.1149(2) 1.08341(7) -1.68834(9) 0.7695(2) -0.21449(11) 1.8935(5) 0.0908(5) -0.0895(7) -1.700(3) -0.074(2) 0.071(4) 0.44(2)
Melting point
For
For
pressure Reference 36.36(10) 1.4406(12) 1.4053(14) Table 3 [3]
For
pressure Reference 100.1(3) 2.320(2) 2.295(2) Table 4 [3]
Glass transition
Transport coefficients
Radial distribution function
References
- ↑ Jean-Pierre Hansen "Phase Transition of the Lennard-Jones System. II. High-Temperature Limit", Physical Review A 2 pp. 221-230 (1970)
- ↑ William G. Hoover, Marvin Ross, Keith W. Johnson, Douglas Henderson, John A. Barker and Bryan C. Brown "Soft-Sphere Equation of State", Journal of Chemical Physics 52 pp. 4931-4941 (1970)
- ↑ 3.0 3.1 3.2 3.3 3.4 Tai Boon Tan, Andrew J. Schultz and David A. Kofke "Virial coefficients, equation of state, and solid-fluid coexistence for the soft sphere model", Molecular Physics 109 pp. 123-132 (2011)
- ↑ Nigel B. Wilding "Freezing parameters of soft spheres", Molecular Physics 107 pp. 295-299 (2009)
- ↑ D. M. Heyes, S. M. Clarke, and A. C. Brańka "Soft-sphere soft glasses", Journal of Chemical Physics 131 204506 (2009)
- ↑ D. M. Heyes and A. C. Branka "Density and pressure dependence of the equation of state and transport coefficients of soft-sphere fluids", Molecular Physics 107 pp. 309-319 (2009)
- ↑ A. C. Brańka and D. M. Heyes "Pair correlation function of soft-sphere fluids", Journal of Chemical Physics 134 064115 (2011)