Fused hard sphere chains: Difference between revisions

Revision as of 14:59, 18 July 2007

In the fused hard sphere chain model the molecule is built up form a string of overlapping hard sphere sites, each of diameter $\sigma$ .

An effective number of monomers can be applied to the fused hard sphere chain model by using the relarion (Ref. 4 Eq. 2.18)

m_{\rm {effective}}={\frac {[1+(m-1)L^{*}]^{3}}{[1+(m-1)L^{*}(3-L^{*2})/2]^{2}}}

where m is the number of monomer units in the model, and $L^{*}=L/\sigma$ is the reduced bond length.

The volume of the fused hard sphere chain is given by (Ref. 5 Eq. 13)

V_{\rm {FHSC}}={\frac {1}{6}}\pi \sigma ^{3}\left(1+{\frac {m-1}{2}}L^{*}\left(3-L^{*2}\right)\right)

and the surface area is given by (Ref. 5 Eq. 12)

S_{\rm {FHSC}}=\pi \sigma ^{2}\left(1+\left(m-1\right)L^{*}\right)

@@ Line 5: / Line 5: @@
 An effective number of monomers can be applied to the fused hard sphere chain model by using the relarion (Ref. 4 Eq. 2.18)
-<math>m_{\rm effective} = \frac{[1+(m-1)L^*]^3}{[1+(m-1)L^*(3-L^{*2})/2]^2}</math>
+:<math>m_{\rm effective} = \frac{[1+(m-1)L^*]^3}{[1+(m-1)L^*(3-L^{*2})/2]^2}</math>
 where ''m'' is the number of monomer units in the model, and <math>L^*=L/\sigma</math> is the reduced bond length.