Editing Fused hard sphere chains
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In the '''fused hard sphere chain''' model the ''molecule'' is built up form a string of overlapping [[hard sphere model|hard sphere sites]], each of diameter <math>\sigma</math>. | In the '''fused hard sphere chain''' model the ''molecule'' is built up form a string of overlapping [[hard sphere model|hard sphere sites]], each of diameter <math>\sigma</math>. | ||
An effective number of monomers can be applied to the fused hard sphere chain model by using the relarion (Ref. | 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} | :<math>m_{\rm effective} = \frac{[1+(m-1)L^*]^3}{[1+(m-1)L^*(3-L^{*2}/2)]^2}</math> | ||
where | where ''m'' is the number of monomer units in the model, and <math>L^*=L/\sigma</math> is the reduced bond length. | ||
The volume of the fused hard sphere chain is given by (Ref. | The volume of the fused hard sphere chain is given by (Ref. 5 Eq. 13) | ||
:<math>V_{\rm FHSC} =\frac{\pi \sigma^3 | :<math>V_{\rm FHSC} =\frac{1}{6} \pi \sigma^3 \left( 1 + (m-1)L^* \left(3-L^{*2}/2\right) \right)</math> | ||
</math> | |||
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> | ||
==Equation of state== | ==Equation of state== | ||
The Vörtler and Nezbeda [[Equations of state | equation of state]] is given by | The Vörtler and Nezbeda [[Equations of state | equation of state]] is given by | ||
:<math>Z_{\mathrm{FHSC}}= 1+ (1+3\alpha)\eta_0(P^*) + C_{\rm FHSC}[\eta_0(P^*)]^{1.83}</math> | :<math>Z_{\mathrm{FHSC}}= 1+ (1+3\alpha)\eta_0(P^*) + C_{\rm FHSC}[\eta_0(P^*)]^{1.83}</math> | ||
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:<math>\eta_0(P^*) = \frac{\sqrt{1+4(1+3\alpha)P^*}-1}{2+6\alpha}</math> | :<math>\eta_0(P^*) = \frac{\sqrt{1+4(1+3\alpha)P^*}-1}{2+6\alpha}</math> | ||
#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) | |||
#[http://dx.doi.org/10.1021/ie800755s 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== | ==See also== | ||
*[[Rigid fully flexible fused hard sphere model]] | *[[Rigid fully flexible fused hard sphere model]] | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1080/00268979100100191 M. Whittle and A. J. Masters "Liquid crystal formation in a system of fused hard spheres", Molecular Physics '''72''' pp. 247-265 (1991)] | |||
#[http://dx.doi.org/10.1103/PhysRevE.64.011703 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)] | |||
#[http://dx.doi.org/10.1063/1.1517604 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)] | |||
#[http://dx.doi.org/10.1063/1.470528 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)] | |||
#[http://dx.doi.org/10.1063/1.459523 T. Boublík, C. Vega, and M. Diaz-Peña "Equation of state of chain molecules", Journal of Chemical Physics '''93''' pp. pp. 730-736 (1990)] | |||
#[http://dx.doi.org/10.1080/002689798168989 Antoine Chamoux and Aurelien Perera "On the linear hard sphere chain fluids", Molecular Physics '''93'' pp. 649-661 (1998)] | |||
[[category:liquid crystals]] | [[category:liquid crystals]] | ||
[[category:models]] | [[category:models]] |