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