Wertheim's first order thermodynamic perturbation theory (TPT1)

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

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 Z_{\rm TPT1} = \frac{p}{\rho k_BT}= mZ_{\rm monomer}- (m-1)\left( 1 + \rho_{\rm monomer}\frac{\partial \ln {\rm g}(\sigma)}{\partial \rho_{\rm monomer}}\right)}

where 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 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 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 Z_{\rm monomer}} , leading to

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

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)