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LIQUID CRYSTALS - DETAILS from Hila and Nadir

  • Lennard Jones model:
    a non-bounded potential between site i and site j, a distance apart
    ,
    where is the separation of the particles when the potential is 0, (also known as the collision diameter) and is the depth of the potential well at its minimum.
  • Gay-Berne potential:
    a generalization for anisotropic particles that includes both attractive and repulsive forces between molecules that have translational and orientational degrees of freedom.
    where is the intermolecular separation at which the attractive and repulsive terms cancel and is given as
    .
    and are the orientation vectors of the two molecules, is the vector joining the two centres and is the unit vector.
    [ GO DIRECT TO LIQUID CRYSTALS with COLLOIDS ]
    and are scaling parameters.
    The shape anisotropy parameter is where . is the separation when the molecules are end to end and when they are side by side. The depth of the well is now expressed as: where and .
    The parameter is related to the anisotropy in the well depth via
    where is the ratio of well-depth for end to end and side by side.