MOZ

The Ornstein-Zernike equations for mixtures (MOZ) of monomers with coincident oligomers (coincident dimers, trimers,...,n-mers).

$h_{an}(\mathbf{r})-c_{an}(\mathbf{r})=\int h_{aa}({\mathbf{r}}^{\prime }){\rho }_a{c}_{an}(|\mathbf{r}-{\mathbf{r}}^{\prime }|)\mathrm{d}{\mathbf{r}}^{\prime }n=a,2,3,...$

Since all oligomers are at infinite dilution, the OZ's for all $n>1$ are decoupled. The first member is for the bulk monomer fluid a (with size $\sigma$ and energy $ϵ$)

$h_{aa}(\mathbf{r})-c_{aa}(\mathbf{r})=\int h_{aa}({\mathbf{r}}^{\prime }){\rho }_a{c}_{aa}(|\mathbf{r}-{\mathbf{r}}^{\prime }|)\mathrm{d}{\mathbf{r}}^{\prime }$

For a coincident dimer ($n=2$) of size $\sigma$ and energy $2ϵ$ at infinite dilution in the bulk a-monomers:

$h_{a2}(\mathbf{r})-c_{a2}(\mathbf{r})=\int h_{aa}({\mathbf{r}}^{\prime }){\rho }_a{c}_{a2}(|\mathbf{r}-{\mathbf{r}}^{\prime }|)\mathrm{d}{\mathbf{r}}^{\prime }$

For a coincident trimer ($n=3$) of size $\sigma$ and energy $3ϵ$ at infinite dilution in the bulk a-monomers:

$h_{a3}(\mathbf{r})-c_{a3}(\mathbf{r})=\int h_{aa}({\mathbf{r}}^{\prime }){\rho }_a{c}_{a3}(|\mathbf{r}-{\mathbf{r}}^{\prime }|)\mathrm{d}{\mathbf{r}}^{\prime }$