Fused hard sphere chains: Difference between revisions

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


:<math>V_{\rm FHSC} =\frac{\pi \sigma^3}{6}  \left( 1 + (m-1)\frac{3L^*  - L^{*3}}{2} \right)  ~~~~ L^* \leq 1 </math>
:<math>V_{\rm FHSC} =\frac{\pi \sigma^3}{6}  \left( 1 + (m-1)\frac{3L^*  - L^{*3}}{2} \right)  ~~~~  
\scriptstyle{
L^* \leq 1 ~\and~ \left(\gamma=\pi ~ \or ~
L^* \sin{\frac\gamma{2}} \geq \frac{1}{2}\right)
}
</math>


and the surface area is given by (Ref. 5 Eq. 12)
where <math>0<\gamma \leq \pi</math> is the minimal bond angle, and the surface area is given by (Ref. 5 Eq. 12)


:<math>S_{\mathrm FHSC} = \pi \sigma^2 \left( 1+\left( m-1 \right) L^* \right)</math>
:<math>S_{\mathrm FHSC} = \pi \sigma^2 \left( 1+\left( m-1 \right) L^* \right)</math>

Revision as of 13:27, 16 March 2011

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 .

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

  1. 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)
  2. 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

  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)
  6. Antoine Chamoux and Aurelien Perera "On the linear hard sphere chain fluids", Molecular Physics '93 pp. 649-661 (1998)