MOZ

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

$h_{an}({\mathbf r}) - c_{an}({\mathbf r}) = \int h_{aa} ({\mathbf r'})~\rho_a ~c_{an}(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}~~~~~n=a,2,3,...$

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 $σ$ and energy $ε$ )

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

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

$h_{a2}({\mathbf r}) - c_{a2}({\mathbf r}) = \int h_{aa} ({\mathbf r'})~\rho_a ~c_{a2}(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}$

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

$h_{a3}({\mathbf r}) - c_{a3}({\mathbf r}) = \int h_{aa} ({\mathbf r'})~\rho_a ~c_{a3}(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}$

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MOZ

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