Distinguishing Spinodal and Nucleation Phase Separation in Dewetting Polymer Films

摘要

It is a common experience that liquid films on non-wetting surfaces may dewet and break up into liquid droplets. Despite of its ordinariness, the physics of this phenomenon is not fully understood. Specifically, it cannot be resolved whether these thin films rupture by a spinodal mechanism or heterogeneous nucleation. According to Cahn (1965), if the second derivative of a system's free energy as a function of the order parameter is less than zero (i.e. G"(h) < 0), the system is unstable against spinodal decomposition. Under this circumstance, spontaneous fluctuations in the system order parameter may grow exponentially with time (Cahn, 1965). In particular, the fluctuation mode with wavevector, q, equals q_m = [G"(h)/γ]~(1/2) will grow the fastest, resulting in a characteristic wavevector = q_m in the morphology incurred in the initial stage of phase separation, though in the later stage coarsening of the morphology may occur (Chaikin and Lubensky, 1995) whereupon the characteristic wavevector will shift to smaller q. In apolar liquid films on a substrate, if the film thickness is less than ～100 nm, the free energy is mainly due to non-retarded van der Waals interactions (deGenees, 1985) so is of the form -A/12πh~2 per unit area, where A is the Hamaker constant and h, i.e. the system order parameter, is the film thickness. It follows that those liquid films with A < 0 are unstable against spinodal decomposition. From the foregoing, spinodal rupturing proceeds by exponential growth of the amplitude of the surface undulations in these films and the initial phase-separated state is a distribution of ridges and valleys before the dewetting film ripens into liquid beads. However, if G"h) is positive, the spinodal process will be suppressed. Nonetheless, so long as G'(h) is negative, the film will still undergo phase separation though by heterogeneous nucleation.