Wertheim's first order thermodynamic perturbation theory (TPT1)

Wertheim's first order thermodynamic perturbation theory (TPT1) can be expressed as:

$Z_{\mathrm{T}\mathrm{P}\mathrm{T}\mathrm{1}}=\frac{p}{\rho k_{B}T}=m{Z}_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}}-(m-1)(1+{\rho }_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}}\frac{\partial \ln \mathrm{g}(\sigma )}{\partial {\rho }_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}}})$

where $Z_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}}$ is the equation of state of the monomer system and m is the number of monomers in the chains.

For example, in the study of the flexible hard sphere chain model one can use the Carnahan-Starling equation of state for $Z_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{r}}$, leading to

$Z_{\mathrm{F}\mathrm{H}\mathrm{S}\mathrm{C}}=m\frac{1+\eta +{\eta }^2-{\eta }^3}{(1-\eta {)}^3}-(m-1)\frac{1+\eta -({\eta }^2/2)}{(1-\eta )(1-\eta /2)}=1+m\frac{4\eta -2{\eta }^2}{(1-\eta {)}^3}-(m-1)\frac{5\eta -2{\eta }^2}{(1-\eta )(2-\eta )}$

See also

• SAFT

References

Related reading

• Bennett D. Marshall "Dual chain perturbation theory: A new equation of state for polyatomic molecules", Journal of Chemical Physics 144 164104 (2016)