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

Revision as of 09:33, 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 1:1 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

References