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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle n>1} are decoupled. The first member is for the bulk monomer fluid a (with size $\sigma$ and energy $\epsilon$)

$h_{aa}({\mathbf {r} })-c_{aa}({\mathbf {r} })=\int h_{aa}({\mathbf {r} '})~\rho _{a}~c_{aa}(|{\mathbf {r} }-{\mathbf {r} '}|){\rm {d}}{\mathbf {r} '}$

For a coincident dimer ($n=2$) of size Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} and energy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\epsilon} at infinite dilution in the bulk a-monomers:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n=3} ) of size Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} and energy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3\epsilon} at infinite dilution in the bulk a-monomers:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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'}}