ファンデルワールス係数の決定 - media.hosei.ac.jp

1 2011 45.. Van der Waals Coefficients Determined by Molecular Dynamics 1) 2). Hiroyuki Ozeki, Yosuke Kataoka, 1).. 2).. Van der Waals coefficients a and b were determined by molecular dynamics simulations . Molar internal energy is a linear function of the inverse of molar volume with the coefficient a. The coefficient b was obtained by the van der Waals equation on pressure. The examined molecular systems were helium, neon, nitrogen and argon. The liquid-gas coexistence points were calculated by Gibbs energy in the case of argon. Keywords : Van der Waals Coefficients, Molecular Dynamics, Coexistence Points 1.. 1) 3.. a, b 2) Materials Explorer V43). 100 . NTV. Rare Gas.

2 2. Dreiding, . Argon Molecular Dynamics . 100,000 steps 1 fs 10 K 298K 90K . 298K.. ~ . NTV( ) ~ ~1g/cm3 . ~ g/cm3 .. 4.. 2011 3 3 . 2011 6 1 . Copyright 2011 hosei University 46. T R +03. Vm Um . +02. 3 a Um RT . Um/(Jmol). y = + +02 R = 2 Vm (1).. +00. 3 +00 +04 +04 +04. RT U m . a . 2 +02. 1/Vm(mol/m3). 1. Molar internal energy of neon vs. inverse of molar Vm (2) volume. Um 1/Vm d) . a +03. 1 4 +03. +03. +03.. Um/(Jmol). a). +02 +03 y = + +03 R = +02 +03. y = + +02. R = Um/(J/mol). +01 +00. +00 +03 +03 +04 +04. 1/Vm/(mol/m3). +01. Molar internal energy of argon vs. inverse of molar +00 volume. +00 +04 +04 +04. +01 1 4 . 1/Vm/(mol/m3). Molar internal energy of helium vs.

3 Inverse of 1. molar volume. 4 . a . b) . +03 . +03 1 . +03. Um/(J/mol). +03 Table 1 Coefficient a compared with the macroscopic y = + +03 R = experimental ). +03.. He Jm3/mol2 Jm3/mol2. +03 3 2. N2 Jm /mol Jm3/mol2. +00. +00 +03 +04 +04 +04. Ne Jm3/mol2 Jm3/mol2. 3 2. 1/Vm/(mol/m3) Ar Jm /mol Jm3/mol2. Molar internal energy of nitrogen vs. inverse of molar volume. p . a . c) b . Copyright 2011 hosei University 47. RT d) . b Vm . a p 2. Vm (3). b d . b/(m3/mol).. a) . y = -6E-07x + 3E-05. R = 0 b/(m3/mol). d/(g/cm3). y = -5E-05x + 2E-05. R = Coefficient b vs. density in the case of argon. 5 8 b . +00 b 0 . d/(g/cm3).. Fig. 5 Coefficient b vs. density in the case of helium.

4 B .. b) .. 1 . Table 2 Coefficient b compared with the macroscopic b/(m3/mol). experimental ).. y = -2E-05x + 4E-05. R = He 10 -2 L/mol 10 -2 L/mol N2 10 -2 L/mol 10 -2 L/mol +00 Ne 10 -2 L/mol 10 -2 L/mol 0 1 Ar 10 -2 L/mol 10 -2 L/mol d/(g/cm3). Fig. 6 Coefficient b vs. density in the case of nitrogen. 5.. c) . 90K 120K.. P Gm . 9 10 T = 90 K. b/(m3/mol). y = -3E-06x + 2E-05. R = T = 120 K . +00. 0 1 d/(g/cm3). Fig. 7 Coefficient b vs. density in the case of neon. Copyright 2011 hosei University 48. a) T = 90 K +06. +02. +05. +07 +07 +02. +06 +00 +06 +07. +04. Vm/(m3/mol). +02. +03. +02 liquid +02 gas +02. Gm/(J/mol). +02 +01. +03 +00. +03 80 90 100 110 120. T/K.

5 +03. P/Pa Molar volume at coexistence points in argon. Fig. 9 Coexistence points in argon at T = 90 K. 11 . b) T = 120 K . +02 . +00 +06 +06 +06 . +02 . 12 15 90 K 120 K . Gm/(J/mol). +02 p . Gm Vm 12 15 . +02.. +02.. +02. P/Pa p(VmL ) p(VmG ). (4). Gm (VmL ) Gm (VmG ). Fig. 10 Coexistence points in argon at T = 120 K.. 12 15 .. a) +06. MPa +00. MPa 1. b) +06. 105 m3/mol, T =90K. P/Pa +06. 105 m3/mol, T=120K. c) +06. 103 m3/mol, T =120K. +06. 104 m3/mol, T =90K. +07. Vm/(m3/mol). Vm 11. Molar volume vs, molar volume of argon at T =. 90 K. Copyright 2011 hosei University 49.. 100 .. -300.. Gm/(J/mol). -500. -700. -900 [1] . -1100 (2000). -1300 [2] . -1500 6 (2001).

6 Vm/(m3/mol). Fig. 13 Molar Gibbs energy vs, molar volume of argon at T = 90 K. +06. +06. +06. P/Pa +06. +06. +05. +00. Vm/(m3/mol). Fig. 14 Molar volume vs, molar volume of argon at T =. 120 K. 100. 0. -100. Gm/(J/mol). -200. -300. -400. -500. -600. Vm/(m3/mol). Fig. 15 Molar Gibbs energy vs, molar volume of argon at T = 120 K. 6.. Copyright 2011 hosei University