Wertheim's first order thermodynamic perturbation theory (TPT1)

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

$Z_{\rm {TPT1}}={\frac {p}{\rho k_{B}T}}=mZ_{\rm {monomer}}-(m-1)\left(1+\rho _{\rm {monomer}}{\frac {\partial \ln {\rm {g}}(\sigma )}{\partial \rho _{\rm {monomer}}}}\right)$

where $Z_{\rm {monomer}}$ 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 $Z_{\rm {monomer}}$, leading to

$Z_{\rm {FHSC}}=m{\frac {1+\eta +\eta ^{2}-\eta ^{3}}{(1-\eta )^{3}}}-(m-1){\frac {1+\eta -(\eta ^{2}/2)}{(1-\eta )(1-\eta /2)}}=1+m{\frac {4\eta -2\eta ^{2}}{(1-\eta )^{3}}}-(m-1){\frac {5\eta -2\eta ^{2}}{(1-\eta )(2-\eta )}}$

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)