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_{\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 )}}

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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==