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# Fused hard sphere chains

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

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

where *m* is the number of monomer units in the model, and is the reduced bond length.

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

where is the minimal bond angle, and the surface area is given by (Ref. 5 Eq. 12)

## Equation of state

The Vörtler and Nezbeda equation of state is given by

where

and

The Waziri and Hamad equation of state is given by

where

- Horst L. Vörtler and I. Nezbeda "Volume-explicit equation of state and excess volume of mixing of fused hard sphere fluids", Berichte der Bunsen-Gesellschaft
**94**pp. 559- (1990) - Saidu M. Waziri and Esam Z. Hamad "Volume-Explicit Equation of State for Fused Hard Sphere Chain Fluids", Industrial & Engineering Chemistry Research
**47**pp. 9658-9662 (2008)

## See also

## References

- M. Whittle and A. J. Masters "Liquid crystal formation in a system of fused hard spheres", Molecular Physics
**72**pp. 247-265 (1991) - 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) - 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) - 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) - T. Boublík, C. Vega, and M. Diaz-Peña "Equation of state of chain molecules", Journal of Chemical Physics
**93**pp. pp. 730-736 (1990) - Antoine Chamoux and Aurelien Perera "On the linear hard sphere chain fluids", Molecular Physics '
*93*pp. 649-661 (1998)