Spinodal temperatures

The osmotic modulus becomes zero at the spinodal point. Therefore, the spinodal temperature, Ts, is obtained by substituting K = 0 into Eq. (220)... 

The scattered intensity increases with increasing temperature as shown in Fig. 10. The scattered intensity diverges at the spinodal temperature, Ts in this particular case Ts = ca. 34.6 °C. Experimentally such a divergence cannot be expected because a macroscopic phase separation occurs and the scattered intensity remains finite. It is worthy to note that the difference in the scattered intensities between at 34.6 °C and at 35.0 °C clearly indicates that the system undergoes a transition. The critical phenomena of the volume phase transition of non-ionic gels with respect to temperature will be discussed in Sect 5.4. 

Fig. 18. Double logarithmic plots of the correlation length, vs. Ts — T, where Ts is the spinodal temperature...

Let us examine the critical dynamics near the bulk spinodal point in isotropic gels, where K + in = A(T — Ts) is very small, Ts being the so-called spinodal temperature [4,51,83-85]. Here, the linear theory indicates that the conventional diffusion constant D = (K + / )/ is proportional to T — Ts. Tanaka proposed that the density fluctuations should be collectively convected by the fluid velocity field as in near-critical binary mixtures and are governed by the renormalized diffusion constant (Kawasaki s formula) [84],... 

In concentrated Al-Zn alloys, the kinetics of precipitation of the equilibrium 0 phase from a are too rapid to allow the study of spinodal decomposition. An Al-22 at. % Zn alloy, however, has decomposition temperatures low enough to permit spinodal decomposition to be studied. For Al-22 at. % Zn, the chemical spinodal temperature is 536 K and the coherent spinodal temperature is 510 K. The early stages of decomposition are described by the diffusion equation... 

The least-squares analysis of the friction according to the above equation yields v = 1/4 and Tf=0 = 33.59 °C. The results are shown in Fig. 11 in which the logarithm of the friction, f/t), is plotted as a function of the logarithm of the distance from the spinodal temperature. The slope of the straight line gives the critical exponent v. 

In contrast to the critical temperature Tc, the spinodal temperature Tsp is well below the binodal temperature for off-critical mixtures and can hardly be reached due to prior phase separation. The diffusion coefficients in the upper left part of Fig. 8 have been fitted by (23) with a fixed activation temperature determined from Dj. The binodal points in Fig. 8 mark the boundary of the homogeneous phase at the binodal. The spinodal temperatures Tsp are obtained as a fit parameter for every concentration and together define the (pseudo)spinodal line plotted in the phase diagram in Fig. 7. The Soret coefficient is obtained from (11) and (23) as... 

To analyze the stability of the ordered microphases, the simplest incompressible random-phase approximation [132] can be employed. Using this approach, the critical value of the Flory-Huggins parameter, x > and the corresponding spinodal temperature, T = l/x > can be determined by the condition that the scattering intensity S(q) reaches its maximum value at a nonzero wave vector q. Within the RPA the scattering intensity is given by [132,142]... 

Moreover, Wu related AGR for miscible polymers to entanglement density 134]. For AG < 0 the entanglement density in the miscible system is reduced compared to additivity behavior which means that the different chain molecules tend to align in the mixture. This is the same effect as stated above. The shift of the spinodal temperature caused by flow can be estimated easily as follows. The spinodal may be given as in the case of a system at rest... 

Expanding AGM around the spinodal temperature T0 for the quiescent blend, it follows that... 

This dependence suggests a spinodal temperature for the PSH/PVME system of I40°C which is in agreement with cloud point measurements. Figure 12 shows that the temperature dependence of Xpsd/pvme and Xpsh/pvme are parallel indicating that deuteration brings about a uniform shift in the spinodal temperature. This result, however, may not hold for other compositions. 

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