# Difference between revisions of "Fused hard sphere chains"

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The Waziri and Hamad [[Equations of state | equation of state]] for fused hard sphere chain fluids is given by | The Waziri and Hamad [[Equations of state | equation of state]] for fused hard sphere chain fluids is given by | ||

− | :<math>Z_{FHSC} = 1 + 4m_{\mathrm{eff}}P^{*} + \frac{3}{4}m_{\mathrm{eff}}P^{*}\ln\left[\frac{3+P^{*}}{3+25P^{*}}\right] + \frac{216(m_{\mathrm{eff}} - 1)P^{*}}{(3+P^{*})(3+25P^{*})\{16+3\ln[(3+P^{*})/(3+25P^{*})]\}}</math> | + | :<math>Z_{\mathrm{FHSC}} = 1 + 4m_{\mathrm{eff}}P^{*} + \frac{3}{4}m_{\mathrm{eff}}P^{*}\ln\left[\frac{3+P^{*}}{3+25P^{*}}\right] + \frac{216(m_{\mathrm{eff}} - 1)P^{*}}{(3+P^{*})(3+25P^{*})\{16+3\ln[(3+P^{*})/(3+25P^{*})]\}}</math> |

where | where |

## Revision as of 11:35, 18 December 2018

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 for fused hard sphere chain fluids 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)