Effect of the Onsager coefficient and internal relaxation modes on spinodal decomposition in the high molecular isotopic blend polystyrene/deutero-polystyrene studied with small angle neutron scattering

Abstract

The early state of spinodal decomposition was studied by small angle neutron scattering in the critical mixture of the isotopic blend deutero-polystyrene/polystyrene (d-PS/PS) of equal molecular volume of 1.42×106 cm3/mol in a temperature range 12 K≤‖Tc−T‖≤82 K. This process can be described by the relaxation between two static structure factors, S(Q) representing the equilibrium values of the system in the mixed state and at the temperature where phase separation occurs. The time evolution of the relaxation process is described by the dynamical structure factor, L(Q,t) which depends on the dynamic properties of the mixture. It will be shown that the static structure factor of a mixed system can also be determined in the unstable two-phase region during the early state of spinodal decomposition. Consistent values for the Flory–Huggins parameter were found in comparison with a lower molecular d-PS/PS sample and, therefore, a lower critical temperature which was even smaller than the phase separation temperatures of the present system. The observed time evolution of the fluctuation modes is nonexponential. Therefore, it was originally supposed that internal modes of the coil come into play. The analysis of the data with an ansatz by Akcasu, which takes internal modes into account showed, however, that the phase separation in the experimental range of wave number and time is dominated by the centre of mass diffusion as in the C–H–C case and the nonexponential behavior was attributed to a time dependent increase of the ‘‘range’’ of the Onsager coefficient. A range of the Onsager coefficient larger than the radius of gyration of a single coil is predicted in case of entangled polymers. However, no time dependence was predicted so far. The evaluated diffusion constants follow an Arrhenius behavior and are consistent with earlier studies. They show a D0∝N−2 scaling consistent with reptation. A further result is the observation of a second order peak in the structure factor already in the early times of spinodal decomposition. So far, this was only attributed to the late state of spinodal decomposition.

Gel‐like aspect of a miscible polymer mixture studied by small‐angle neutron scattering

“…q ‐dependent Λ( q ) is due to a reptational molecular motion of polymer chains (Pincus–Binder effect):13, 14 For qR 0 > 1, the molecular motion suppresses the dynamics of the concentration fluctuations according to Λ( q ) ∼ q −2 , whereas Λ( q ) is q ‐independent for qR 0 < 1, where R 0 is the screening length. R 0 ≃ R g has been experimentally established for the polymer components through the observation of the initial stage of spinodal decomposition by SANS 15–17…”

Viscoelastic phase separation in shear flow

“…In our simulations, we shall see that the magnitudes of w 1 and w 2 are both considerably smaller than 1 at most space points. That is, the degree of extension is rather weak, but the network stress can overwhelm the viscous stress ͑ϰ 0 ͒ because of the large factor g⌽ 3 . This justifies the Gaussian form of Q͑W J ͒ in Eq.…”

Nonlinear phase‐separation behavior of poly(methyl methacrylate)/poly(styrene‐co‐maleic anhydride) blends

“…An Arrhenius equation can be applied to describe the temperature dependence of diffusion coefficient, and mobility, the time–temperature relationship of phase separation induced by cure or polymerization, for polymeric materials, the apparent activation energy of phase separation and the relationship between relaxation time and temperature for aqueous polymer solutions . However, to our knowledge, little relevant work has been reported on using an Arrhenius equation to track the whole process (early and late stages) of SD behavior of polymer blends.…”