Self-Consistent Field Theory and Its Applications by M. W. Matsen
Self-Consistent Field Theory and Its Applications by M. W. Matsen
Self-Consistent Field Theory and Its Applications by M. W. Matsen
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1.7 Polymer Blends 47<br />
-0.92<br />
-0.96<br />
(a) χN = 3<br />
F h<br />
/nk B<br />
T<br />
-1.00<br />
-1.04<br />
F s<br />
φ (1) φ (2)<br />
-1.08<br />
5<br />
4<br />
2-phase<br />
χN<br />
3<br />
2<br />
(b)<br />
1-phase<br />
1<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
φ<br />
Figure 1.10: (a) Free energy, F h , of a homogeneous blend as a function of composition, φ,<br />
calculated for χN =3. The dashed line denotes the free energy, F s, for a macrophase-separated<br />
blend with compositions, φ (1) =0.3 <strong>and</strong> φ (2) =0.6, <strong>and</strong> the dotted line is the double-tangent<br />
construction locating the binodal points denoted <strong>by</strong> triangles. The two diamonds denote spinodal<br />
points, where the curvature of the free energy curve switches sign. (b) Phase diagram showing<br />
the binodal (solid) <strong>and</strong> spinodal (dotted) curves as a function of χN. The triangular <strong>and</strong> diamond<br />
symbols correspond to those in (a), <strong>and</strong> the solid dot denotes a critical point.<br />
1.7.3 Scattering Function for a Homogeneous Blend<br />
A beam of radiation (e.g., x-rays or neutrons) will pass undeflected through a perfectly homogeneous<br />
blend, ˆφ A (r) =φ, assuming the wavelength, λ, is above the atomic resolution <strong>and</strong><br />
that absorption is negligible. However, there are always thermal functuations that disturb the<br />
uniform composition, which in turn scatter the radiation <strong>by</strong> various angles, θ. To predict the