Wertheim's first order thermodynamic perturbation theory (TPT1): Difference between revisions

Latest revision as of 00:15, 21 July 2016

Wertheim's first order thermodynamic perturbation theory (TPT1) ^[1] ^[2] ^[3] ^[4] ^[5] can be expressed as:

Z_{T P T 1} = \frac{p}{ρ k_{B} T} = m Z_{m o n o m e r} - (m - 1) (1 + ρ_{m o n o m e r} \frac{\partial \ln g (σ)}{\partial ρ_{m o n o m e r}})

where $Z_{m o n o m e r}$ 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 $Z_{m o n o m e r}$ , leading to

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

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 :<math>
-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)}
+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)}
 </math>
 ==See also==