The Widom Insertion Method is a statistical thermodynamic approach to the calculation of material and mixture properties. It is named for Benjamin Widom, who derived it in 1963. In general, there are two theoretical approaches to determining the statistical mechanical properties of materials. The first is the direct calculation of the overall Partition Function of the system, which directly yields the system free energy. The second approach, known as the Widom Insertion method, instead derives from calculations centering around one molecule. The Widom Insertion method directly yields the chemical potential of one component rather than the system free energy. This approach is most widely applied in molecular computer simulations but has also been applied in the development of analytical statical mechanical models.
Read more about Widom Insertion Method: Overview, Hard Core Model, Mean Field Approximation
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... The above is simplified further via the application of the mean field approximation, which essentially ignores fluctuations and treats all quantities by their average value ... Within this framework the insertion factor is given as ...
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