Wertheim's first order thermodynamic perturbation theory (TPT1)

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

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 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}} , leadin to

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 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

1. M. S. Wertheim "Fluids with highly directional attractive forces. I. Statistical thermodynamics" Journal of Statistical Physics 35 pp. 19-34 (1984)
2. M. S. Wertheim "Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations" Journal of Statistical Physics 35 pp. 35-47 (1984)
3. M. S. Wertheim "Fluids with highly directional attractive forces. III. Multiple attraction sites" Journal of Statistical Physics 42 pp. 459-476 (1986)
4. M. S. Wertheim "Fluids with highly directional attractive forces. IV. Equilibrium polymerization" Journal of Statistical Physics 42 pp. 477-492 (1986)
5. M. S. Wertheim "Thermodynamic perturbation theory of polymerization", Journal of Chemical Physics 87 pp. 7323-7331 (1987)