Critical point blend

Figure 12 shows the effect of mixing plasticizers at a total plasticizer level of 75 p.h.r. Qualitatively the results are as expected in that the transition and critical points for the blends lie between those for the individual components. 

In a blend of immiscible homopolymers, macrophase separation is favoured on decreasing the temperature in a blend with an upper critical solution temperature (UCST) or on increasing the temperature in a blend with a lower critical solution temperature (LCST). Addition of a block copolymer leads to competition between this macrophase separation and microphase separation of the copolymer. From a practical viewpoint, addition of a block copolymer can be used to suppress phase separation or to compatibilize the homopolymers. Indeed, this is one of the main applications of block copolymers. The compatibilization results from the reduction of interfacial tension that accompanies the segregation of block copolymers to the interface. From a more fundamental viewpoint, the competing effects of macrophase and microphase separation lead to a rich critical phenomenology. In addition to the ordinary critical points of macrophase separation, tricritical points exist where critical lines for the ternary system meet. A Lifshitz point is defined along the line of critical transitions, at the crossover between regimes of macrophase separation and microphase separation. This critical behaviour is discussed in more depth in Chapter 6. 

Fig. 6.31 Results from SCFI calculations for diblock/homopolymer blends (Matsen 1995b). (a) The dimensionless Helmholtz free energy Fu() as a function of homopolymer volume fraction at y X = 12, / = 0.45 and /3 = The dashed line shows the double tangent construction used to locate the binodal points denoted with dots. The dotted line is the free energy of non-interacting bilayers, (b) Phase diagram obtained by repeating this construction over a range of %N. The dots are the binodal points obtained in (a), and the diamond indicates a critical point below which two-phase coexistence does not occur. The disordered homopolymer phase is labelled dis, and the lamellar phase lam.

Fig. 6.36 Phase diagram calculated using SCFT for a blend of a symmetric diblock with a homopolymer with fl = 1 (see Fig. 6.32 for a blend with a diblock with / = 0.45) as a function of the copolymer volume fraction

A line of ordinary critical points for macrophase separation is shown as the line CA B in Fig. 6.42 for a ternary blend of two homopolymers with equal degrees of polymerization and a diblock copolymer at high temperature. Four regimes have been identified by Broseta and Fredrickson (1990) and are indicated in... 

The measurements near the critical point have been performed with a PDMS/ PEMS blend with molar masses of Afw = 16.4kgmol 1 (PDMS, Mw/Mn= 1.10) and Afw = 22.8 kg mol 1 (PEMS, Afw/Mn =1.11). The corresponding degrees of polymerization are N = 219 and N = 257, respectively. The phase diagram shows a lower miscibility gap with a critical composition of cc = 0.548 (weight fractions... 

For the system PMMA/PVDF one can estimate the volume of mixing according to Eq. (22). As the key-point, the system exhibits both LCST and UCST. The critical points are reported to be about at 325 and 140 °C for 50/50 blends [11], These data can be used to calculate, from Eqs. (18) and (19), the quantities XAB and p. 

Before discussing theoretical approaches let us review some experimental results on the influence of flow on the phase behavior of polymer solutions and blends. Pioneering work on shear-induced phase changes in polymer solutions was carried out by Silberberg and Kuhn [108] on a polymer mixture of polystyrene (PS) and ethyl cellulose dissolved in benzene a system which displays UCST behavior. They observed shear-dependent depressions of the critical point of as much as 13 K under steady-state shear at rates up to 270 s Similar results on shear-induced homogenization were reported on a 50/50 blend solution of PS and poly(butadiene) (PB) with dioctyl phthalate (DOP) as a solvent under steady-state Couette flow [109, 110], A semi-dilute solution of the mixture containing 3 wt% of total polymer was prepared. The quiescent... 

In the insets of Fig. 15 we show binodal curves for the symmetric blend. Again, we And deviations in the immediate vicinity of the critical point but for larger incompatibilities, xN 2, the mean held predictions provide an adequate description of the phase boundary utilizing the Flory-Huggins parameter extracted from the composition fluctuations in the one-phase region, xN < 2. 

In a binary blend the lowest point on the spinodal curve corresponds to the critical point ... 

Estimate the size of the critical region near the critical point in a symmetric polymer blend by comparing the mean-square composition fluctuations with the square of the difference in volume fractions of the... 

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