Soft sphere potential

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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[edit]

The soft-sphere equation of state[2] has recently been studied by Tan, Schultz and Kofke[3] [4] and expressed in terms of Padé approximants. For and one has (Eq. 8):

and for one has (Eq. 9):

Virial coefficients[edit]

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[edit]


pressure Reference
22.66(1) 1.195(6) 1.152(6) Table 1 [5]
23.24(4) 1.2035(6) 1.1602(7) Table 2 [3]


pressure Reference
36.36(10) 1.4406(12) 1.4053(14) Table 3 [3]


pressure Reference
100.1(3) 2.320(2) 2.295(2) Table 4 [3]

Glass transition[edit]


Transport coefficients[edit]


Radial distribution function[edit]



Related reading
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