A python implementation of the Fundamental Measure Theory for hard-sphere mixture in classical Density Functional Theory
PythonGPL-3.0
PyFMT
A python implementation of the Fundamental Measure Theory for hard-sphere mixture in classical Density Functional Theory
For a fluid composed by hard-spheres with temperature T, total volume V, and chemical potential of each species $\mu_i$ specified, the grand potential, $\Omega$, is written as
where $k_B$, and $\Lambda_i$ is the well-known thermal de Broglie wavelength of each component.
The hard-sphere contribution, $F^{\textrm{hs}}$, represents the hard-sphere exclusion volume correlation described by the fundamental measure theory (FMT) as
$$F^\text{hs}[{\rho_i (\boldsymbol{r})}] = k_B T\int_{V} d \boldsymbol{r}\ \Phi_\textrm{FMT}({ n_\alpha(\boldsymbol{r})})$$
where $ n_\alpha(\boldsymbol{r}) = \sum_i \int_{V} d \boldsymbol{s}\ \rho_i (\boldsymbol{s})\omega^{(\alpha)}_i(\boldsymbol{r}-\boldsymbol{s})$ are the weigthed densities given by the convolution with the weigth function $\omega^{(\alpha)}_i(\boldsymbol{r})$. The function $\Phi$ can be described using different formulations of the fundamental measure theory (FMT) as