Difference in chemical potential between a given species and an ideal gas
In
thermodynamics, the excess chemical potential is defined as the difference between the
chemical potential of a given
species and that of an
ideal gas under the same conditions (in particular, at the same
pressure,
temperature, and
composition).
[1]
The chemical potential of a particle species is therefore given by an ideal part and an excess part.
Chemical potential of a pure fluid can be estimated by the
Widom insertion method.
Derivation and Measurement
For a system of diameter and volume , at constant temperature , the classical canonical
partition function
with a scaled coordinate, the
free energy is given by:
Combining the above equation with the definition of chemical potential,
we get the chemical potential of a sufficiently large system from (and the fact that the smallest allowed change in the particle number is )
wherein the chemical potential of an ideal gas can be evaluated analytically.
Now let's focus on since the potential energy of an -particle system can be separated into the potential energy of an -particle system and the potential of the excess particle interacting with the -particle system, that is,
and
Thus far we converted the excess chemical potential into an ensemble average, and the integral in the above equation can be sampled by the brute force
Monte Carlo method.
The calculating of excess chemical potential is not limited to homogeneous systems, but has also been extended to inhomogeneous systems by the
Widom insertion method, or other
ensembles such as NPT and
NVE.
See also
Apparent molar property
References