Model Potentials

These EOS for model potentials are useful for understanding theory, and capture some (but perhaps not all) of the physics of “real” fluids.

import teqp
teqp.__version__

'0.19.1'

Square-well

The potential is defined by

\[\begin{split}V(r) = \left\lbrace \begin{array}{cc} \infty & r < \sigma \\ -\varepsilon & \sigma < r < \lambda\sigma \\ 0 & r > \lambda \sigma \end{array}\right.\end{split}\]

from which an EOS can be developed by correlating results from molecular simulation. The EOS is from:

Rodolfo Espíndola-Heredia, Fernando del Río and Anatol Malijevsky Optimized equation of the state of the square-well fluid of variable range based on a fourth-order free-energy expansion J. Chem. Phys. 130, 024509 (2009); https://doi.org/10.1063/1.3054361

model = teqp.make_model({
  "kind": "SW_EspindolaHeredia2009",
  "model": {
      "lambda": 1.3
  }
})

EXP-6

model = teqp.make_model({
  "kind": "EXP6_Kataoka1992",
  "model": {
      "alpha": 12
  }
})

Lennard-Jones Fluid

The Lennard-Jones potential is given by

\[V(r) = 4\varepsilon\left((\sigma/r)^{12}-(\sigma/r)^{6}\right)\]

and EOS are available from many authors. teqp includes the EOS from Thol, Kolafa-Nezbeda, and Johnson.

for kind, crit in [
    ["LJ126_TholJPCRD2016", (1.32, 0.31)], # Note the true critical point was not used
    ["LJ126_KolafaNezbeda1994", (1.3396, 0.3108)],
    ["LJ126_Johnson1993", (1.313, 0.310)]]:

    j = { "kind": kind, "model": {} }
    model = teqp.make_model(j)
    print(kind, model.solve_pure_critical(1.3, 0.3), crit)

LJ126_TholJPCRD2016 (1.3035125549100017, 0.3103860327864468) (1.32, 0.31)
LJ126_KolafaNezbeda1994 (1.3396478193468193, 0.3108038977722935) (1.3396, 0.3108)
LJ126_Johnson1993 (1.3130000571792173, 0.3099999768607838) (1.313, 0.31)

Two-Center Lennard-Jones Fluid

model = teqp.make_model({
  'kind': '2CLJF-Dipole',
  'model': {
      "author": "2CLJF_Lisal",
      'L^*': 0.5,
      '(mu^*)^2': 0.1
  }
})
print(model.solve_pure_critical(1.3, 0.3))

model = teqp.make_model({
  'kind': '2CLJF-Quadrupole',
  'model': {
      "author": "2CLJF_Lisal",
      'L^*': 0.5,
      '(Q^*)^2': 0.1
  }
})
print(model.solve_pure_critical(1.3, 0.3))

(2.8282972062188056, 0.2005046666634018)
(2.832574303561834, 0.2003194655463274)