Orientation order parameter - Revision history

KevinYager at 12:36, 15 June 2017

2017-06-15T12:36:16Z

KevinYager at 21:49, 29 October 2015

2015-10-29T21:49:08Z

KevinYager: Created page with "The alignment of a system can be characterized by calculating the orientation order parameter, ''S'': : $\begin{alignat}{2} S & = \langle P_2 ( \cos \chi ) \rangle \\ & ..."$

2015-10-29T21:42:52Z

Created page with "The alignment of a system can be characterized by calculating the orientation order parameter, ''S'': :<math> \begin{alignat}{2} S & = \langle P_2 ( \cos \chi ) \rangle \\ & ..."

New page

The alignment of a system can be characterized by calculating the orientation order parameter, ''S'':
:<math>
\begin{alignat}{2}
S & = \langle P_2 ( \cos \chi ) \rangle \\
& = \frac{ 3 \langle \cos^2 \chi \rangle - 1} {2}
\end{alignat}
</math>
Where <math>\scriptstyle \chi</math> is the angle with respect to the director, <math>\scriptstyle P_2</math> is the 2nd [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre polynomial], and the angle-brackets denote averaging over all entities. In scattering, if <math>\scriptstyle \chi</math> is the angle around the scattering pattern, one can compute the order parameter for aligned systems. This quantity is often used in research of intrinsically anisotropic materials, such as liquid crystals.

Note that in two-dimensions, the order parameter has a different definition:
:<math>
\begin{alignat}{2}
S & = 2 \langle \cos ^2 \chi \rangle - 1 \\
& = \langle \cos( 2 \chi) \rangle
\end{alignat}
</math>

@@ Line 12: / Line 12: @@
 * 0 < ''S'' < 1 denotes partial alignment
 * ''S'' = 0 denotes a completely random alignment
-* ''S'' = 1/2 denotes 'anti-alignment' (against the director)
+* ''S'' = -1/2 denotes 'anti-alignment' (against the director)
 Note that in two-dimensions, the order parameter has a different definition:

@@ Line 6: / Line 6: @@
 \end{alignat}
 </math>
-Where <math>\scriptstyle \chi</math> is the angle with respect to the director, <math>\scriptstyle P_2</math> is the 2nd [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre polynomial], and the angle-brackets denote averaging over all entities. In scattering, if <math>\scriptstyle \chi</math> is the angle around the scattering pattern, one can compute the order parameter for aligned systems. This quantity is often used in research of intrinsically anisotropic materials, such as liquid crystals.
+Where <math>\scriptstyle \chi</math> is the angle with respect to the director, <math>\scriptstyle P_2</math> is the 2nd [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre polynomial], and the angle-brackets denote averaging over all entities. In [[scattering]], if <math>\scriptstyle \chi</math> is the angle around the scattering pattern, one can compute the order parameter for aligned systems. This quantity is often used in research of intrinsically anisotropic materials, such as liquid crystals.
 Note that in two-dimensions, the order parameter has a different definition:
@@ Line 15: / Line 21: @@
 \end{alignat}
 </math>

Orientation order parameter - Revision history

KevinYager at 12:36, 15 June 2017

KevinYager at 21:49, 29 October 2015

KevinYager: Created page with "The alignment of a system can be characterized by calculating the orientation order parameter, ''S'': : \begin{alignat}{2} S & = \langle P_2 ( \cos \chi ) \rangle \\ & ..."

KevinYager: Created page with "The alignment of a system can be characterized by calculating the orientation order parameter, ''S'': : $\begin{alignat}{2} S & = \langle P_2 ( \cos \chi ) \rangle \\ & ..."$