ethylene molecule is created in a random position of the
simulation box, and its potential energy of interaction UðcÞ
1 with
all the other molecules is calculated. The change of configurational
energy for the reaction step in the backward direction is then given
by the expression:
DUðbÞ
t ¼ UðcÞ
1 þ UðcÞ
2 UðdÞ
3 (7)
By setting z = 1, the product in Eq. (1) takes the form:
YC
i¼1
Ni!
ðNi þ nizÞ!
¼ N3
ðN1 þ 1ÞðN2 þ 1Þ (8)
Substitution of n ¼ 1, z = 1, and Eq. (8) into Eq. (1) leads to
the following expression for the probability of acceptance of a
reaction step in the backward (b) direction:
PðbÞ
rx ¼ min 1;
P0
V
kBT
N3
KeqðN1 þ 1ÞðN2 þ 1Þ
exp DUðbÞ
t
kBT
( !)
(9)
where the change of configurational energy DUðbÞ
t is given by
Eq. (7).
For the simulation of the vapor-phase chemical equilibrium of
the ternary system at given values of temperature T and pressure P,
the following four-stage strategy was implemented. In the first
stage, by specifying the ethylene to water feed mole ratio and
defining an initial number of ethanol molecules in the simulation
box equal to zero, the initial numbers of ethylene and water
molecules were defined from a total number of 900 molecules. In
the second stage, an NVT-ensemble simulation (with
N = 900 molecules) was carried out with an arbitrary vapordensity
value and for a total number of 1 106 moves (molecular
displacements and rotations), 60% of which were used to
equilibrate the configurational energy. In the third stage, starting
from the final configuration obtained after the NVT run, an NPTensemble
simulation was carried out for a total number of 3 106
moves (using a ratio of one volume change to N molecular
displacements and rotations), 60% of which were used to
equilibrate the density and the configurational energy. In the
fourth stage, starting from the final configuration obtained after
Fig
ethylene molecule is created in a random position of thesimulation box, and its potential energy of interaction UðcÞ1 withall the other molecules is calculated. The change of configurationalenergy for the reaction step in the backward direction is then givenby the expression:DUðbÞt ¼ UðcÞ1 þ UðcÞ2 UðdÞ3 (7)By setting z = 1, the product in Eq. (1) takes the form:YCi¼1Ni!ðNi þ nizÞ!¼ N3ðN1 þ 1ÞðN2 þ 1Þ (8)Substitution of n ¼ 1, z = 1, and Eq. (8) into Eq. (1) leads tothe following expression for the probability of acceptance of areaction step in the backward (b) direction:PðbÞrx ¼ min 1;P0VkBTN3KeqðN1 þ 1ÞðN2 þ 1Þexp DUðbÞtkBT( !)(9)where the change of configurational energy DUðbÞt is given byEq. (7).For the simulation of the vapor-phase chemical equilibrium ofthe ternary system at given values of temperature T and pressure P,the following four-stage strategy was implemented. In the firststage, by specifying the ethylene to water feed mole ratio anddefining an initial number of ethanol molecules in the simulationbox equal to zero, the initial numbers of ethylene and watermolecules were defined from a total number of 900 molecules. Inthe second stage, an NVT-ensemble simulation (withN = 900 molecules) was carried out with an arbitrary vapordensityvalue and for a total number of 1 106 moves (moleculardisplacements and rotations), 60% of which were used toequilibrate the configurational energy. In the third stage, startingfrom the final configuration obtained after the NVT run, an NPTensemblesimulation was carried out for a total number of 3 106moves (using a ratio of one volume change to N moleculardisplacements and rotations), 60% of which were used toequilibrate the density and the configurational energy. In thefourth stage, starting from the final configuration obtained afterFig
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