# Molecular field meaning in Liquid Crystal Theory

Given the Frank-De Gennes free energy $F = \int f(\boldsymbol{p},\nabla\boldsymbol{p}, ...)\ d\boldsymbol{x},$ for liquid crystals (see De Gennes-Prost, p. 107, formula 3.21), the vector

$$h_{i}=-\frac{\delta F}{\delta P_{i}}=-\frac{\partial f}{\partial P_{i}}+\partial_{j}\frac{\partial f}{\partial\partial_{j}P_{i}}$$

is usually called molecular field, a "notation derived from magnetism". What is the physical meaning of this vector in this context? Does it have any sense to call it molecular also here?

• "Molecular field is an internal mean effective field resulting from the interaction of dynamic variables in the a system" --Chaikin&Lubensky. I suppose it is the interaction between molecules (or lattice sites) that gives meaning to the "molecular" part. As an example, in the context of the Ising model, this would be $h + zJm$, where $h$ is the external field, $z$ the # of neighbors, $J$ the interaction parameter and $m$ the mean field value of the order parameter. – alarge Jul 27 '14 at 7:45

## 1 Answer

I think the comment from @alarge is correct. Thus, this is the "field" that a molecules feels and tends to align itself.

• This is not an answer. It is a comment. – Bill N Sep 30 '15 at 13:47