Order–Disorder Tricriticality in Symmetric A n B n Star Polymer Melts

Tricriticality usually requires tuning an additional thermodynamic parameter. Here, we show that, in symmetric AnBn star polymer melts, the arm number n itself plays this role and drives the order–disorder transition (ODT) from second order to first order. By developing a sixth-order free-energy expansion within the random phase approximation and comparing it with self-consistent field theory (SCFT) calculations, we analytically identify a tricritical arm number, ntc ≈ 5.4475. For n < ntc, the lamellar ordering transition remains continuous and occurs at the spinodal point, (χN)s ≈ 10.495. For n > ntc, the transition becomes first order, and (χN)ODT shifts below (χN)s with a quadratic dependence near the tricritical point. SCFT calculations confirm the predicted transition character and phase-boundary shift. The origin of this behavior is traced to inter-arm correlations generated by the common junction. We further show that the noninteger tricritical arm number can be effectively realized in binary mixtures of star polymers. This provides a rare analytically tractable example of architecture-induced tricriticality in a microphase-separating polymer system.