Bifurcation effects in thermodynamics of Markovian copolymers away from the critical point

A. N. Ivanova ; L. I. Manevich

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 696-707

Résumé

Numerical computations of inhomogeneous free-energy extremals on the basis of the thermodynamic model of Markovian copolymers have shown that they exhibit two qualitatively different scenarios of behavior with varying temperature. The first occurs in systems with close points of the trivial and nontrivial spinodals, while the second scenario takes place when the turning point of an extremal is sufficiently far away from the point of the nontrivial spinodal. In this case, as the binodal is approached, the model exhibits a secondary bifurcation point, i.e., the intersection point with the homogeneous nontrivial extremal issuing from the point of the trivial spinodal. At this point, the homogeneous nontrivial extremal becomes unstable with respect to periodic perturbations of frequency $q^*$ corresponding to a bifurcation of inhomogeneous extremals from the trivial state (point of the nontrivial spinodal). This bifurcation is studied for lamellar, hexagonal, and body-centered cubic structures. The evolution of the extremals is numerically computed until an absolutely stable state corresponding to the binodal is reached.