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

Revision as of 17:53, 18 July 2007

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 $Z_{\rm {monomer}}$ , leadin 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)}}

@@ Line 1: / Line 1: @@
 :<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>
-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
+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.
-chains.
+For example, in the study of the [[Flexible hard sphere chains | flexible hard sphere chain]] model one can use the
+[[Carnahan-Starling equation of state]] for <math>Z_{\rm monomer}</math>, leadin to
+:<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)}
+</math>
 ==See also==
 *[[SAFT]]