Segregation limit

Monte Carlo simulations, which include fluctuations, then yields Simulations of a coarse-grained polymer blend by Wemer et al find = 1 [49] in the strong segregation limit, in rather good... 

A real system must lie somewhere along a vertieal line in Figure 9-5. Performanee is within the upper and lower points on this line namely maximum mixedness and eomplete segregation. Equation 9-10 gives the eomplete segregation limit. The eomplete segregation model with side exits and the maximum mixedness model are diseussed next. 

Here we present only one effect in detail which also is expected to occur in metallic alloys the enrichment of vacancies in the interfacial region (Fig. 4). For the chosen parameters, the density reduction 5p in the center of the interface even is a few percent in the fully segregated limit. However, 5p 0 as T Tc. 

When the residence time distribution is known, the uncertainty about reactor performance is greatly reduced. A real system must lie somewhere along a vertical line in Figure 15.14. The upper point on this line corresponds to maximum mixedness and usually provides one bound limit on reactor performance. Whether it is an upper or lower bound depends on the reaction mechanism. The lower point on the line corresponds to complete segregation and provides the opposite bound on reactor performance. The complete segregation limit can be calculated from Equation (15.48). The maximum mixedness limit is found by solving Zwietering s differential equation. ... 

The limits for part (b) are at the endpoints of a vertical line in Figure 15.14 that corresponds to the residence time distribution for two tanks in series. The maximum mixedness point on this line is 0.287 as calculated in Example 15.14. The complete segregation limit is 0.233 as calculated from Equation (15.48) using/(/) for the tanks-in-series model with N=2 ... 

Recently, Grason and Kamien calculated the phase diagrams in the weak and strong segregation limit for AB miktoarm-star copolymers using both... 

Fig. 36 SCFT results for AB miktoarm stars at strong segregation limit /W = 100. Phase transitions (A) Dis bcc-, (o) bcc Hex-, (0) Hex Lam. All boundaries are computed at /N = 100 with exception of low-0 bcc - Hex and Hex Lam ones for n = 3, 4 and 5. For n = 3 these were computed at /AT = 80, and for n = 4 and 5 these boundaries are computed at /N = 60. Equilibrium results from experiments on Pl-arm-PS melts [219]. From [112]. Copyright 2004 American Chemical Society...

Usually the discussion of the ODT of highly asymmetric block copolymers in the strong segregation limit starts from a body-centred cubic (bcc) array of the minority phase. Phase transitions were calculated using SOFT accounting for both the translational entropy of the micelles in a disordered micelle regime and the intermicelle free energy [129]. Results indicate that the ODT occurs between ordered bcc spheres and disordered micelles. 

The micelle formation is not restricted to solvents for polystyrene but also occurs in very unpolar solvents, where the fluorinated block is expected to dissolve. Comparing the data, we have to consider that the micelle structure is inverted in these cases, i.e., the unpolar polystyrene chain in the core and the very unpolar fluorinated block forming the corona. The micelle size distribution is in the range we regard as typical for block copolymer micelles in the superstrong segregation limit.2,5,6 The size and polydispersity of some of these micelles, measured by DLS, are summarized in Table 10.3. 

Owing to their amphiphilicity and a balanced molecular architecture these molecules from micelles in all solvents for polystyrene as well as in solvents for the fluorinated block. The structure parameters of these micelles have to be regarded as typical for other block copolymers in the superstrong segregation limit.5 6... 

Fig. 2.1 Composition profiles of A and B components in the weak and strong segregation limits, compared to the mean (straight line).

Fig. 2.34 Phase diagram in the strong segregation limit for starblock copolymers with nA A arms and nB B arms as a function of the volume fraction of the B monomer (Milner 1994).

Fig. 2.38 Phase diagram computed using the strong segregation limit theory of Helfand and Wasserman (1982) for the poly(ethylene oxide)-poly(butylene oxide) (PEO-PBO) diblock system. Because the ratio of statistical segment lengths aPB0/ 1, the phase diagram is asymmetric about/= 0.5 (Hamley 1997).

The expressions 2.7-2.12 which define the Leibler structure factor have been widely used to interpret scattering data from block copolymers (Bates and Fredrickson 1990 Mori et al. 1996 Rosedale et al. 1995 Schwahn et al. 1996 Stiihn et al. 1992 Wolff et al. 1993). The structure factor calculated for a diblock with / = 0.25 is shown in Fig. 2.39 for different degrees of segregation JV. Due to the Gaussian conformation assumed for the chains (Leibler 1980), the domain spacing in the weak segregation limit is expected to scale as d Nm. 

Fig. 2.40 Phase diagram for diblock copolymers in the weak segregation limit (Leibler 1980).

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