A 2006 paper concerning these substances by Musevic et al showed that separational forces caused by "hedgehog defects" in these substances are important for their self-formation. The order parameter for systems of this type is given as the expectation value of a second-order Legendre polynomial and 
A 2006 paper concerning these substances by Musevic et al showed that separational forces caused by "hedgehog defects" in these substances are important for their self-formation. The order parameter for systems of this type is given as the expectation value of a second-order Legendre polynomial and that use of a quadrupole moment treats a 180-degree rotation as an invariant for this system. When molecules in these substances are modeled with cylindrical shapes, they will align into a parallel formation to minimize orientational entropy while increasing positional entropy according to the Onsager hard-rod model. That phase of these materials, the nematic, contrasts with one in which molecules are positioned into distinct layers, the smectic phase. Often used in screen displays for calculators, for 10 points, identify this class of substances which possess long-range order but still have the ability to flow.
A 2006 paper concerning these substances by Musevic et al showed that separational forces caused by "hedgehog defects" in these substances are important for their self-formation.
liquid crystals