MICROPHASE SEGREGATION IN BRIDGING POLYMERIC BRUSHES - REGULAR AND SINGULAR PHASE-DIAGRAMS

A mean-field theory of deformation-induced microphase segregation in b ridging polymeric brushes anchored to two parallel surfaces is present ed. Models with isotropic and orientation-dependent liquid-crystalline interactions between segments are considered. For the first model, th e problem is similar to that of classical liquid-vapor phase separatio n, and the phase diagram in the P-T plane has a Line of first-order tr ansitions terminating at the critical point. We show that the critical pressure is negative implying that a free brush tethered only to one surface always exists at supercritical conditions and hence cannot und ergo the collapse phase transition. In the second model, the free ener gy density depends on two coupled order parameters, one related to seg ment density and the other to the orientational order, which strongly modifies the phase behavior. Depending on the grafting density the sys tem is described by a phase diagram of a regular or a singular type. I n the regular phase diagram the first-order transition line terminates at the critical point. In a singular diagram, the first-order transit ion line extends to infinity; the critical point corresponds to infini te pressure so that the system undergoes the phase transition at arbit rary external pressures. Regular phase diagrams correspond to dense gr afting, and singular ones to sparse grafting. The change from a regula r phase behavior to another occurs at a certain marginal value of the grafting density. On approaching this Value the critical point on the regular diagram moves to infinity, logarithmically with the deviation from the critical grafting density. We relate the analytical propertie s of the free energy density as a function of the segment concentratio n to the type of the phase diagram and the shape of the coexistence cu rve in the temperature-concentration plane.