MOZ

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle h_{an}({\mathbf {r} })-c_{an}({\mathbf {r} })=\int h_{aa}({\mathbf {r} '})~\rho _{a}~c_{an}(|{\mathbf {r} }-{\mathbf {r} '}|){\rm {d}}{\mathbf {r} '}~~~~~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 $\epsilon$)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle h_{aa}({\mathbf {r} })-c_{aa}({\mathbf {r} })=\int h_{aa}({\mathbf {r} '})~\rho _{a}~c_{aa}(|{\mathbf {r} }-{\mathbf {r} '}|){\rm {d}}{\mathbf {r} '}}

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle h_{a2}({\mathbf {r} })-c_{a2}({\mathbf {r} })=\int h_{aa}({\mathbf {r} '})~\rho _{a}~c_{a2}(|{\mathbf {r} }-{\mathbf {r} '}|){\rm {d}}{\mathbf {r} '}}

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle h_{a3}({\mathbf {r} })-c_{a3}({\mathbf {r} })=\int h_{aa}({\mathbf {r} '})~\rho _{a}~c_{a3}(|{\mathbf {r} }-{\mathbf {r} '}|){\rm {d}}{\mathbf {r} '}}