Order parameters

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An order parameter is some observable physical quantity that is able to distinguish between two distinct phases. The choice of order parameter is not necessarily unique.

Solid-liquid transition[edit]

Possible choices:

  • Fourier transform of the density
  • Shear modulus

Isotropic-nematic transition[edit]

The uniaxial order parameter is zero for an isotropic fluid and one for a perfectly aligned system. First one calculates a director vector [1]

where is a second rank tensor, is a unit vector along the molecular long axis, and is the Kronecker delta. Diagonalisation of this tensor gives three eigenvalues , and , and is the eigenvector associated with the largest eigenvalue (). From this director vector the nematic order parameter is calculated from [2]

where d is the dimensionality of the system.

i.e. in three dimensions [3]

where is known as the uniaxial order parameter. Here is the second order Legendre polynomial, is the angle between a molecular axes and the director , and the angle brackets indicate an ensemble average.

Tetrahedral order parameter[edit]


See also[edit]


Related reading