Phase-Boundaries near Critical End points: Applications to Cross-linked Copolymers

Details Phase-Boundaries near Critical End points: Applications to Cross-linked Copolymers Phase-Boundaries near Critical End points: Applications to Cross-linked Copolymers

1997-12-17

arxiv.org/abs/cond-mat/9712211v1

Physics

Condensed Matter

10 pages, Revtex

Scientific paper

The phase behavior of a cross-linked polymer blend made of two incompatible species, $A$ and $B$, of different chemical nature is analyzed. Besides a homogeneous phase, this system also exhibits two microphases and a phase of total segregation. The transition between the homogeneous and the microphase is continuous along a $\lambda$-line; a first-order phase boundaries separate the microphase and the disordered phase from the phase of complete segregation. The critical line meets the first-order phase boundaries at an end point. Scaling arguments indicate that, close to any end point, the equations for the first-order phase boundaries exhibit nonanaliticities associated with the singularities present at the thermodynamic functions near the critical line. Explicit expressions for the phase boundaries near the end point for a cross-linked polymer mixture are obtained and checked for singularities.

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