\textbf{Congruent Lamellar-to-Disorder Phase Transitions in Diblock Copolymer-Homopolymer Ternary Blends }

Symmetric ternary blends of AB diblock copolymers and the corresponding A and B homopolymers are predicted to be characterized by a multicritical Lifshitz point within mean-field theory. Previous studies have shown that fluctuations destroy the predicted Lifshitz point and lead to a bicontinuous microemulsion (B$\mu $E) channel, which separates the lamellar and 2-phase regions in the ternary phase prism. Here, we establish the existence of a line of congruent first-order lamellar-to-disorder transitions when appropriate amounts of poly(cyclohexylethylene) (C) and poly(ethylene) (E) homopolymers are mixed with the corresponding symmetric CE diblock copolymer. We present complimentary optical transmission, small-angle X-ray scattering, transmission electron microscopy (TEM), and rheological results obtained using two experimental protocols: (1) fixing the CE volume fraction and varying the C/E ratio, and (2) setting the C/E ratio at the condition of congruency and varying CE volume fraction from 0 to 1. These results establish a quantitative and facile method for identifying the detailed phase behavior in the vicinity of the B$\mu $E, and provide fresh insight into the nature of such mixtures near the nominal Lifshitz conditions. Surprisingly, well-ordered lamellae are revealed by TEM at compositions within 1{\%} of the B$\mu $E channel, suggesting a remarkably close approach to the predicted, mean-field unbinding transition. Moreover, the width of the B$\mu $E narrows to about 1{\%} under congruent conditions.