# spinodal

Spinodal decomposition model

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
scale Scale factor None 1
gamma Exponent None 3
q_0 Correlation peak position -1 0.1

The returned value is scaled to units of cm-1 sr-1, absolute scale.

Definition

This model calculates the SAS signal of a phase separating solution under spinodal decomposition. The scattering intensity $$I(q)$$ is calculated as

$I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B$

where $$x=q/q_0$$ and $$B$$ is a flat background. The characteristic structure length scales with the correlation peak at $$q_0$$. The exponent $$\gamma$$ is equal to $$d+1$$ with d the dimensionality of the off-critical concentration mixtures. A transition to $$\gamma=2d$$ is seen near the percolation threshold into the critical concentration regime.

References

H. Furukawa. Dynamics-scaling theory for phase-separating unmixing mixtures: Growth rates of droplets and scaling properties of autocorrelation functions. Physica A 123,497 (1984).

Authorship and Verification

• Author: Dirk Honecker Date: Oct 7, 2016