Difference between revisions of "Tutorial 2: entropy of mixing of methanol+water"

Revision as of 10:37, 20 April 2017

This tutorial is currently under construction

When two pure liquids are put in contact the new configurations that the molecules can adopt and the new molecular interactions will lead to a change in entropy. Typically, this change is positive because of disorder, although in principle specific molecular interactions can lead to a decrease in entropy in some cases. For ideal gases, the entropy of mixing has an analytical expression, and it depends only on the relative number of molecules of each component in the mixture. The total entropy of a mixture of ideal gases is:

[math]S_\text{mixture}^\text{ideal} = \sum\limits_\Lambda N_\Lambda \bar{S}_\Lambda - k_\text{B} \sum\limits_\Lambda N_\Lambda \ln{\left(\frac{N_\Lambda}{N}\right)},[/math]

where [math]N_\Lambda[/math] is the number of molecules of component [math]\Lambda[/math] and [math]N[/math] is the total number of molecules. [math]\bar{S}_\Lambda[/math] refers to the entropy per molecule in the pure component [math]\Lambda[/math]. For real mixtures, one defines the excess entropy of mixture [math]S_\text{mix}^\text{E}[/math] to account for the deviation of the mixing entropy with respect to what one would expect for ideal systems:

[math]S_\text{mix}^\text{E} = S_\text{mixture}^\text{real} - S_\text{mixture}^\text{ideal}[/math].

In this tutorial we will calculate [math]S_\text{mix}^\text{E}[/math] for a 2:1 mixture of water and methanol. More detailed information can be found in Ref.^[1]

Generating the trajectories

For this tutorial we will use Gromacs to generate the mixture of liquids and the pure liquids. We will use the OPLS force field and the SPCE water model. For methanol we will use the topology available from virtualchemistry.org. We will constrain all bonds with H atoms.

You can skip this section and download the trajectories that we will be analyzing. Then continue with the 2PT analysis section.

Generating the starting configurations

We need the OPLS topology file for methanol (methanol.itp), which we retrieved from virtualchemistry.org. If you reuse this topology file make sure to properly credit the authors.^[2] We also need two sample molecules to generate our liquids, one for water, "water.gro":

One water
  3
    1WAT     OW    1   0.114   0.845   0.401 -0.5236  0.3981  0.1442
    1WAT    HW1    2   0.118   0.886   0.491  1.8112 -1.0518 -0.9491
    1WAT    HW2    3   0.147   0.758   0.425  1.3601  2.0733  3.6058
   1.20000   1.20000   1.20000

and one for methanol, "methanol.gro":

One methanol
6
    1MET    C      1   0.697   0.788   0.843
    1MET    H      2   0.600   0.829   0.873
    1MET    H      3   0.781   0.853   0.870
    1MET    H      4   0.706   0.773   0.736
    1MET    O      5   0.701   0.664   0.911
    1MET    H      6   0.761   0.600   0.875
   1.20000   1.20000   1.20000

We are going to work with 2400 atoms total. This means that our pure water box will contain 800 molecules, our pure methanol box will contain 400 methanol molecules, and our 2:1 mixture will contain 400 water molecules and 200 methanol molecules. We can build our pure water and pure methanol boxes as follows:

gmx insert-molecules -box 3.0 3.0 3.0 -ci water.gro -nmol 800 -try 20 -o pure_water.gro
gmx insert-molecules -box 3.1 3.1 3.1 -ci methanol.gro -nmol 400 -try 20 -o pure_methanol.gro

For the mixture we are going to generate 10 different configurations. This is so that we can obtain statistics. It is important that these initial configurations are completely uncorrelated, and so we will use bash random variables as seed for the generation:

One of the boxes containing a 2:1 water/methanol mixture

for i in `seq 1 1 10`; do
gmx insert-molecules -box 3.1 3.1 3.1 -ci water.gro -nmol 400 -try 20 -o temp1.gro -seed $RANDOM
gmx insert-molecules -f temp1.gro -ci methanol.gro -nmol 200 -try 20 -o temp2.gro -seed $RANDOM
rm temp1.gro; mv temp2.gro mixture_${i}.gro
done

These systems are far away from equilibrium. We need to first optimize the box size (NPT), then equilibrate at constant volume (NVT) and then do the 2PT analysis (again NVT). I will explain it here for "mixture_3.gro" only; the other ones can be equilibrated in the same way. We need the following input files:

"topol.top":

#include "oplsaa.ff/forcefield.itp"
#include "oplsaa.ff/spce.itp"
#include "methanol.itp"

[ system ]
Water+methanol

[ molecules ]
; name  number
WAT       400
MET       200

"em.mdp":

integrator      = steep
nsteps          = 20000
cutoff-scheme   = Verlet
nstlist         = 10
rlist           = 1.0
coulombtype     = pme
rcoulomb        = 1.0
rvdw            = 1.0
nstenergy       = 10
continuation	     =  no
constraints          =  h-bonds
constraint_algorithm =  lincs
lincs_order          =  4

"md.mdp":

constraints = h-bonds
integrator =  md-vv
dt = 0.002
nsteps = 250000
tinit = 0
nstcomm = 1
continuation = no
constraint_algorithm = lincs
lincs_order = 4
nstxout = 1000
nstvout = 1000
nstfout = 0
nstlog = 2500
nstenergy = 1000
nstxtcout = 1000
xtc_precision = 1000
ns_type = grid
nstlist = 10
cutoff-scheme = Verlet
rlist = 1.0
coulombtype = pme
rcoulomb = 1.0
optimize_fft = yes
rvdw = 1.0
Tcoupl = v-rescale
Pcoupl = Berendsen
tau_p = 1.0
compressibility = 4.5e-5
ref_p = 1.0
gen_vel = yes
gen_temp = 298.
gen_seed = 83872
tc-grps = MOL SOL
energygrps = MOL SOL
tau_t = 0.1 0.1
ref_t = 298. 298.

References