Isotropic Lifshitz critical behavior

Fig. 23 Phase diagram in the temperature-diblock copolymer plane for the (dPB PS) mixture below the Lifshitz line separating blend like from diblock-like phase behavior. The full dots and the solid line represent the critical points of a two-phase region. The hatched area indicates a crossover from Ising to isotropic Lifshitz critical behavior, and a double critical point DCP is at 7% diblock concentration. The Lifshitz line separates at high and low temperatures the disordered phases and droplet and bicontinuous microemulsion phases ( xE). Its non-monotonic shape near the DCP is caused by the strong thermal fluctuations...

In the (PB PS) mixture a crossover from Ising to isotropic critical Lifshitz behavior was observed at about 4.8% diblock concentration as indicated by the dashed area in the phase diagram of Fig. 23. On the other hand, a crossover to a renormalized Lifshitz critical behavior was not observed in this system. The susceptibility critical exponent y of both systems has been depicted in Fig. 26 versus diblock concentration. A crossover of the exponent y at about 4.8% and 6.2% from the Ising 1.24 to larger values is visible for the (PB PS) and (PEE PDMS), respectively. A constant y = (1.62 0.01) and... 

A first systematic study of such system was performed on the relatively large-molar-mass symmetric polyolefins PE and PEP and the corresponding diblock copolymer PE-PEP PE being polyethylene and PEP being poly(ethylene propylene). A mean-field Lifshitz like behavior was observed near the predicted isotropic Lifshitz critical point with the critical exponents y=l and v=0.25 of the susceptibility and correlation length, and the stmcture factor following the characteristic mean-field Lifshitz behavior according to S(Q)ocQ". Thermal composition fluctuations were apparently not so relevant as indicated by the observation of mean-field critical exponents. On the other hand, no Lifshitz critical point was observed and instead a one-phase channel of a polymeric bicontinuous miaoemulsion phase appeared. Equivalent one-phase channels were also observed in other systems. 

Mean field theory predicts that the critical lines of blend like and diblock like behavior meet at the isotropic critical lifshitz point and the lifshitz line (LL) which is defined when Q becomes zero. The isotropic critical Lifshitz point represents a new imiversahty class [54-56]. Under special conditions even a tricritical Lifshitz point is predicted [55]. In this article we will discuss in some detail SANS experiments on a mixture of a critical binary (A/B) polymer blend with different concentrations of a symmetric (A-B) diblock copolymer of roughly five times larger molar volume. Under such conditions an isotropic critical Lifshitz point is predicted [55]. 

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