172
H. Sun et al.
The temperature and pressure were controlled using the Nose–Hoover thermostat
and barostat [83, 84] respectively.
The isobaric-isothermal condition (NPT) molecular dynamics (MD) simulations
were carried out to calculate the P–V-T curves using the. The HOV was computed
by the following formula:
H v = −
E liquid,inter
+ RT
(30)
The constant volume and temperature (NVT) MD simulations were performed to
predict the surface tension (γ ) of a vacuum–liquid benzene interface using the slab
model:
γ =
L z
2
P zz −
P xx +
P yy
2
(31)
where the factor of 1/2 is included to account for the two surfaces in the slab model,
P ii are the diagonal terms of the averaged pressure tensor, and L z is the length of
z-direction of the simulation box, which is normal to the surface. The slab model was
created by extending a cubic simulation box along the z-direction to add a vacuum
space. The simulation box length in L z was approximately three times larger than L x
or L y , to ensure the separation between the images is at least twice longer than the
LJ cutoff. The PPPM method was used to evaluate the electrostatic energy without
the 2D correction [85] that requires calculation of the total dipole moment of the slab
but our system slab does not have a sharp boundary.
Vapor–liquid equilibria (VLE) is obtained directly from MD simulations. From
the VLE curves, the extrapolated critical temperatures and densities, which were
derived using the laws of density scaling [86] and rectilinear diameters [40] are very
close.
ρ liq − ρ vap = B|T − T c |
0.325
(32)
1
2
ρ liq + ρ vap
= ρ c + A(T − T c )
(33)
Additional thermodynamic properties, compressibility (κ T ), thermal expansion
coefficients (α), isobaric heat capacity (C P ) and isochoric heat capacity (C V ) were
calculated. By analyzing the trajectories of NPT simulations at 298 K, the former
three properties are estimated by calculating the averages of the fluctuations of the
volume V, as well as the combinations of enthalpy H
conf and volume and the enthalpy.
For the constant volume heat capacity, it can be derived using the similar method
by calculating the fluctuations on the configurational energy U
conf with an NPT
simulation at 298 K:
H. Sun et al.
The temperature and pressure were controlled using the Nose–Hoover thermostat
and barostat [83, 84] respectively.
The isobaric-isothermal condition (NPT) molecular dynamics (MD) simulations
were carried out to calculate the P–V-T curves using the. The HOV was computed
by the following formula:
H v = −
E liquid,inter
+ RT
(30)
The constant volume and temperature (NVT) MD simulations were performed to
predict the surface tension (γ ) of a vacuum–liquid benzene interface using the slab
model:
γ =
L z
2
P zz −
P xx +
P yy
2
(31)
where the factor of 1/2 is included to account for the two surfaces in the slab model,
P ii are the diagonal terms of the averaged pressure tensor, and L z is the length of
z-direction of the simulation box, which is normal to the surface. The slab model was
created by extending a cubic simulation box along the z-direction to add a vacuum
space. The simulation box length in L z was approximately three times larger than L x
or L y , to ensure the separation between the images is at least twice longer than the
LJ cutoff. The PPPM method was used to evaluate the electrostatic energy without
the 2D correction [85] that requires calculation of the total dipole moment of the slab
but our system slab does not have a sharp boundary.
Vapor–liquid equilibria (VLE) is obtained directly from MD simulations. From
the VLE curves, the extrapolated critical temperatures and densities, which were
derived using the laws of density scaling [86] and rectilinear diameters [40] are very
close.
ρ liq − ρ vap = B|T − T c |
0.325
(32)
1
2
ρ liq + ρ vap
= ρ c + A(T − T c )
(33)
Additional thermodynamic properties, compressibility (κ T ), thermal expansion
coefficients (α), isobaric heat capacity (C P ) and isochoric heat capacity (C V ) were
calculated. By analyzing the trajectories of NPT simulations at 298 K, the former
three properties are estimated by calculating the averages of the fluctuations of the
volume V, as well as the combinations of enthalpy H
conf and volume and the enthalpy.
For the constant volume heat capacity, it can be derived using the similar method
by calculating the fluctuations on the configurational energy U
conf with an NPT
simulation at 298 K: