Thermal Diffusion in Polymer Blends: Criticality and Pattern Formation

Abstract

We discuss the dynamic critical properties of a binary blend of the two polymers poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS), and we have investigated experimentally and theoretically patterning and structure formation processes above and below the spinodal in the case of a spatially varying temperature. Asymptotic critical scaling is found close to T c in the range 6 ×10− 4 ≤ e ≤ 0. 2 of the reduced temperature e and a mean field behavior for large values of e. The thermal diffusion coefficient D T is thermally activated but does not show the critical slowing down of the Fickian diffusion coefficient D, which can be described by crossover functions for D. The Soret coefficient \({S}_{\mathrm{T}} = {D}_{\mathrm{T}}/D\) diverges at the critical point with a critical exponent − 0. 67 and shows a crossover to the exponent − 1 of the structure factor in the classical regime. Thermal activation processes cancel out and do not contribute to S T. The divergence of S T also leads to a very strong coupling of the order parameter to small temperature gradients, which can be utilized for laser patterning of thin polymer films. For a quantitative numerical model all three coefficients D, D T, and S T have been determined within the entire homogeneous phase and are parameterized by a pseudospinodal model. It is shown that equilibrium phase diagrams are no longer globally valid in the presence of a temperature gradient, and systems with an upper critical solution temperature (UCST) can be quenched into phase separation by local heating. Below the spinodal there is competition between the spontaneous spinodal demixing patterns and structures imposed by means of a focused laser beam utilizing the Soret effect. Elongated structures degrade to spherical objects due to surface tension effects leading to pearling instabilities. Grids of parallel lines can be stabilized by enforcing certain boundary conditions. Phase separation phenomena in polymer blends belong to the universality class of pattern forming systems with a conserved order parameter. In such systems, the effects of spatial forcing are rather unexplored and, as described in this work, spatial temperature modulations may cause via the Soret effect (thermal diffusion) a variety of interesting concentration modulations. In the framework of a generalized Cahn–Hilliard model it is shown that coarsening in the two-phase range of phase separating systems can be interrupted by a spatially periodic temperature modulation with a modulation amplitude beyond a critical one, where in addition the concentration modulations are locked to the periodicity of the external forcing. Accordingly, temperature modulations may be a useful future tool for controlled structuring of polymer blends. In the case of a traveling spatially periodic forcing, but with a modulation amplitude below the critical one, the coarsening dynamics can be enhanced. With a model of phase separation, taking into account thermal diffusion, essential features of the spatio-temporal dynamics of phase separation and thermal patterning observed in experiments can be reproduced. With a directional quenching an effective approach is studied to create regular structures during the phase separation process. In addition, it is shown that the wavelength of periodic stripe patterns is uniquely selected by the velocity of a quench interface. With a spatially periodic modulation of the quench interface itself, cellular patterns can also be generated.