Fused hard sphere chains

Example of the fused hard sphere chain model, shown here in a linear configuration.

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)

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

See also

• Rigid fully flexible fused hard sphere model

References

1. M. Whittle and A. J. Masters "Liquid crystal formation in a system of fused hard spheres", Molecular Physics 72 pp. 247-265 (1991)
2. Carl McBride, Carlos Vega, and Luis G. MacDowell "Isotropic-nematic phase transition: Influence of intramolecular flexibility using a fused hard sphere model" Physical Review E 64 011703 (2001)
3. Carl McBride and Carlos Vega "A Monte Carlo study of the influence of molecular flexibility on the phase diagram of a fused hard sphere model", Journal of Chemical Physics 117 pp. 10370-10379 (2002)
4. Yaoqi Zhou, Carol K. Hall and George Stell "Thermodynamic perturbation theory for fused hard-sphere and hard-disk chain fluids", Journal of Chemical Physics 103 pp. 2688-2695 (1995)
5. T. Boublík, C. Vega, and M. Diaz-Peña "Equation of state of chain molecules", Journal of Chemical Physics 93 pp. pp. 730-736 (1990)