- #1
Liam79
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Hi everyone,
I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter S is often used:
S=\left\langle\frac{1}{2}\left(3\cos^{2}\theta-1\right)\right\rangle
with \theta the angle of the molecule with a "director" (the magnetic field in NMR, the normal to a membrane for lipids, the global direction in a nematic phase etc). S corresponds to a second-order Legendre polynomial.
I have often read that in an isotropic environment, S=0 whereas when all the molecules are well aligned with the reference vector (director), S=1. I understand why S=1 as \theta=0° but I can't find why S=0 when all the orientations are random.
Can anyone help me?
Liam
I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter S is often used:
S=\left\langle\frac{1}{2}\left(3\cos^{2}\theta-1\right)\right\rangle
with \theta the angle of the molecule with a "director" (the magnetic field in NMR, the normal to a membrane for lipids, the global direction in a nematic phase etc). S corresponds to a second-order Legendre polynomial.
I have often read that in an isotropic environment, S=0 whereas when all the molecules are well aligned with the reference vector (director), S=1. I understand why S=1 as \theta=0° but I can't find why S=0 when all the orientations are random.
Can anyone help me?
Liam
