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Subsections

# Flory Theory

## Approximation

Lattice gas analogy--we have N cells, Np particles A and N-Np particles B. We will use canonical ensemble (Ising model for magnetics corresponds to grand canonical ensemble!). Partition function:
 (1)
Flory idea: substitute (1) by

## Free Energy

The number of terms

Average energy: we have Np As. Each A has z neighbors. About Npz/N of them are A, (N-Np)z/N are B. We have

Free energy:
 (2)

Stirling formula:

New variables:

Free energy:
 (3)

## Critical Point

System is symmetric--critical point is at . We obtain

or

which gives

The system is mixed above critical point and demixed below it

## Binodal & Spinodal

Free energy of Flory system below critical point

On spinodal the second derivative is zero:

On binodal there is local minimum--first derivative is zero:

In critical point binodal & spinodal coincide:

## Problems of Flory Theory

1.
It is not clear how to calculate next approximation(s)
2.
Works because of compensation of errors:
• We overestimate : correlations decrease average energy
• We overestimate : most of states have too small contribution to Q
Flory theory overestimates both energy and entropy--the resulting expression is more or less'' right.

Next: Self-Consistent Field Theory Up: Mean Field Approach Previous: General Idea

© 1997 Boris Veytsman and Michael Kotelyanskii
Tue Oct 14 22:58:59 EDT 1997