Ginzburg Number of a Homopolymer–Diblock Copolymer Mixture Covering the 3D-Ising, Isotropic Lifshitz, and Brasovskiĭ Classes of Critical Universality

The Ginzburg number Gi of deuterated poly(butadiene) (dPB) and poly(styrene) (PS) homopolymer blend of critical composition mixed with a dPB-PS symmetric diblock copolymer was determined from small angle neutron scattering. A 3 orders of magnitude change of Gi was determined between binary polymer blend and diblock copolymer melt. The strongest change of Gi is observed within the isotropic Lifshitz regime of critical universality occurring over a 3% range of diblock concentration and interpolates the corresponding Gi of the 3D-Ising and Brasovskiĭ regimes. A Lifshitz critical point was not observed consistent with the proposed lower critical dimension $d_{\mathrm{LCP}}=4$.

Figure 1

Temperature-diblock concentration plane of the phase diagram of the three component blend PS/dPB/PS-dPB of fixed critical blend composition. The inset depicts the Lifshitz critical region in more detail.

Figure 2

Structure factor measured around 96 °C in the disordered regime above the two-phase, microemulsion, and lamellar ordered regimes.

Figure 3

Susceptibility versus inverse temperature for three diblock concentrations. The empty and full dots represent $S(0)$ and $S(Q^{*})$, respectively.

Figure 4

Ginzburg number versus diblock concentration. The different symbols represent Gi within the different universality classes and the crossover between them as indicated.