Binodal temperature

On the basis of the concept described above, we propose a model for the homogeneous crystallization mechanism of one component polymers, which is schematically shown in Fig. 31. When the crystallization temperature is in the coexistence region above the binodal temperature Tb, crystal nucleation occurs directly from the melt, which is the well-known mechanism of polymer crystal nucleation. However, the rate of crystallization from the coexistence region is considered to be extremely slow, resulting in single crystals in the melt matrix. Crystallization at a greater rate always involves phase separation the quench below Tb causes phase separations. The most popular case... 

The diffusion, thermal diffusion, and Soret coefficients for nine different PDMS concentrations from c = 0.09 to c = 0.9 have been measured between the binodal temperature and approximately 368 K. Figure 8 shows on the left side the diffusion and thermal diffusion coefficients. The temperature dependences of the latter are very well described as thermally activated processes according to (11) with a common activation temperature Ta = 1,395 K, which is very close to the 1,460 K obtained for the critical blend in Sect. 2. 

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... 

SAXS has been mainly used to study morphology of the semi-crystalline blends, affected by composition, crystalhzation rate, compatibihza-tion, additives, etc. However, it can also be used to study local structures in molten polymer blends, for example within the interphasial regions. The method have been used for liquid, glassy or crystalline systems, to determine the spinodal and binodal temperatures, as well as to measure Xj2- A reasonable agreement between the values measured by different methods was obtained... 

The investigation of the Han plots, which is the log-log plot of storage modulus versus loss modulus, is another effective method to determine the onset of phase separation. This method is more sensitive to concentration fluctuations than data obtained from time-temperature superposition. The Han plot of homogeneous phases shows two main features temperature independence and terminal slope of two (Han et al. 1990, 1995). Deviations from these two criteria were reported only for Han plots above the LCST and below the UCST (Kim et al. 1998 Sharma and Clarke 2004). Therefore, it has been suggested to use this method to infer the phase-separation (binodal) temperature rheologicaUy. 

Yu et al. (2011) studied rheology and phase separation of polymer blends with weak dynamic asymmetry ((poly(Me methacrylate)/poly(styrene-co-maleic anhydride)). They showed that the failure of methods, such as the time-temperature superposition principle in isothermal experiments or the deviation of the storage modulus from the apparent extrapolation of modulus in the miscible regime in non-isothermal tests, to predict the binodal temperature is not always applicable in systems with weak dynamic asymmetry. Therefore, they proposed a rheological model, which is an integration of the double reptation model and the selfconcentration model to describe the linear viscoelasticity of miscible blends. Then, the deviatirMi of experimental data from the model predictions for miscible... 

The conditions necessary for the lowering of the critical, spinodal, or binodal temperature of binary mixtures of homopolymers A and B by addition of copolymer AB was also examined analytically by Rigby, Lin, and Roe They showed that under some special conditions, spinodal temperature T can be lowered linearly with the amount of added copolymer AB, so that... 

Figure 7.7 Small-angle neutron scattering data r 0) versus 7 identifying the spinodal and the binodal temperatures, (a) / (O) versus 7 schematically (b) An experimental example of a polymer blend of polystyrene (PS) and...

Fig. 5 Left Inverse susceptibility S O) versus inverse temperature for an off-critical blend. The extrapolated straight line gives the spinodal temperature, while the bend yields the binodal temperature. Below the binodal fluctuations within the domains are visible which decrease with decreasing temperature. Right Phase diagram of three dPB/PS blends of about 2000 molar volume and with different vinyl content of the dPB component. The different miscibilities and positions of the critical point show that the FH parameter depends on the vinyl content...

The spinodal (critical) and binodal temperatures of the three samples are depicted in Fig. 13 versus pressure. In all samples an increase of the phase boundaries with pressure is observed. Such a behavior is expected because of the reduced free volume. The shape of the phase boundary is linear for the blends with the dPB(l,4) and dPB(l,4 l,2) copolymers and is more parabolic for the blend with dPB(l,2). The dPB(l,2) sample was at the critical composition while the other two samples are slightly off critical composition as seen from the deviation between the spinodals and binodals. The worst compatibility is observed for the dPB(l,2)/PS sample, the best one for the dPB, 4)/PS, and for the copolymer sample it lies in between. 

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