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| Wertheim's first order thermodynamic perturbation theory (TPT1) <ref>[http://dx.doi.org/10.1007/BF01017362 M. S. Wertheim "Fluids with highly directional attractive forces. I. Statistical thermodynamics" Journal of Statistical Physics '''35''' pp. 19-34 (1984)]</ref>
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| <ref>[http://dx.doi.org/10.1007/BF01017363 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)]</ref>
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| <ref>[http://dx.doi.org/10.1007/BF01127721 M. S. Wertheim "Fluids with highly directional attractive forces. III. Multiple attraction sites" Journal of Statistical Physics '''42''' pp. 459-476 (1986)]</ref>
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| <ref>[http://dx.doi.org/10.1007/BF01127722 M. S. Wertheim "Fluids with highly directional attractive forces. IV. Equilibrium polymerization" Journal of Statistical Physics '''42''' pp. 477-492 (1986)]</ref>
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| <ref>[http://dx.doi.org/10.1063/1.453326 M. S. Wertheim "Thermodynamic perturbation theory of polymerization", Journal of Chemical Physics '''87''' pp. 7323-7331 (1987)]</ref>
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| can be expressed as:
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| :<math>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)</math>
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| where <math>Z_{\rm monomer}</math> is the [[equations of state | equation of state]] of the monomer system and ''m'' is the number of monomers in the chains.
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| For example, in the study of the [[Flexible hard sphere chains | flexible hard sphere chain]] model one can use the
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| [[Carnahan-Starling equation of state]] for <math>Z_{\rm monomer}</math>, leading to
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| :<math>
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| 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)}
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| </math>
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| ==See also== | | ==See also== |
| *[[SAFT]] | | *[[SAFT]] |
| ==References== | | ==References== |
| <references/>
| | #[http://dx.doi.org/10.1007/BF01017362 M. S. Wertheim "Fluids with highly directional attractive forces. I. Statistical thermodynamics" Journal of Statistical Physics '''35''' pp. 19-34 (1984)] |
| ;Related reading
| | #[http://dx.doi.org/10.1007/BF01017363 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)] |
| *[http://dx.doi.org/10.1063/1.4947023 Bennett D. Marshall "Dual chain perturbation theory: A new equation of state for polyatomic molecules", Journal of Chemical Physics '''144''' 164104 (2016)]
| | #[http://dx.doi.org/10.1007/BF01127721 M. S. Wertheim "Fluids with highly directional attractive forces. III. Multiple attraction sites" Journal of Statistical Physics '''42''' pp. 459-476 (1986)] |
| | | #[http://dx.doi.org/10.1007/BF01127722 M. S. Wertheim "Fluids with highly directional attractive forces. IV. Equilibrium polymerization" Journal of Statistical Physics '''42''' pp. 477-492 (1986)] |
| | #[http://dx.doi.org/10.1063/1.453326 M. S. Wertheim "Thermodynamic perturbation theory of polymerization", Journal of Chemical Physics '''87''' pp. 7323-7331 (1987)] |
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| [[category:perturbation theory]] | | [[category:perturbation theory]] |