# Distribution of Conformers in Rotational Isomerism

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This Demonstration shows the effects of rotational energy barriers on the temperature dependence of the mole fractions of trans and gauche conformers in substituted polymethylenes. The complete distribution of conformations at a selected temperature is also shown. Use the sliders to set the parameter values: and .

Contributed by: A. A. Koledenkov (April 2019)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The conformational energy of hindered rotation in classical molecular mechanics simulation is approximated, in the general case, by the equation [1]:

.

The parameters and describe the force field, with torsion angle .

This Demonstration uses a modified version of the potential:

where is the energy barrier (kJ/mol); and are the energy difference gauche(-)/trans and gauche(+)/trans conformers, respectively.

To calculate the full distribution function at temperature , the Boltzmann distribution is used:

where is the universal gas constant, 8.314 J/mol K.

The mole fractions of the trans and gauche , conformers are calculated within ±10° relative to the local energy minima:

,

,

.

Reference

[1] M. Bachmann, *Thermodynamics and Statistical Mechanics of Macromolecular Systems*, Cambridge, UK: Cambridge University Press, 2014.

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