Strong segregation

Strong-segregation theories predict for the domain size D, the interfacial tension F, and the interfacial width A (Helfand and Wasserman 1982 Bates and Fredrickson 1990 Wang 1994)  

The predictions of the strong segregation theories have been verified experimentally for diblocks when x 50. 

In the strong-segregation limit, the phase behavior is controlled mainly by /a, the fraction of component A in the diblock, and, to a lesser extent, by a conformational asymmetry parameter, which is the ratio (Hamley et al. 1994) 

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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... 

Matson M.W. and Bates E.S., Unifying weak- and strong-segregation block copolymer theories. Macromolecules, 29, 1091, 1996. 

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

In the strong segregation phase boundaries were calculated for xN 100 and compared to the experimental results for Pl-arm-PS stars. The results are shown in Fig. 36. 

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. 

A detailed justification of the surfactant parameter approach is still the subject of theoretical investigations, and we will return to several issues below. We mention that the surfactant parameter approach is consistent with the fluid mosaic model of Singer and Nicolson. It tells us that the self-assembly of amphiphiles is driven by the strong segregation of water and hydrocarbon chains, and that packing effects dominate the self-assembly process. 

Strongly segregated systems, Todt > Tc < Tg with hard confinement. A strictly confined crystallization within MDs has been observed for strongly segregated diblock copolymers with a glassy amorphous block [29-42]. 

From this section we can summarize the general behavior of confined crystallizable MDs. These generalizations apply to block copolymers that are in the strong segregation regime and that can crystallize within their specific MD without breakout. When a block copolymer component crystallizes within isolated MD structures like spheres, cylinders or lamellae it may nucleate homogeneously. For homogeneous nucleation to take place, several requirements should be met ... 

Ueda et al. [26] recently investigated a flow-oriented PE-fr-aPP diblock copolymer with Mw = 113 000 (Mn/Mw = 1.1) and a PE volume fraction of 0.48. This diblock copolymer is in the strong segregation regime (i.e., estimated xN = 10.5 and Todt = 290 °C) and has a lamellar morphology in the melt. They found a breakout phenomenon with the formation of spherulites in an intermediate crystallization temperature range 95 < Tc < 101 °C. At crystallization temperatures above 101 °C or below 95 °C spherulites were not formed and the crystallization was confined within the lamellar MD. Ueda et al. report that lamellar MD and spherulites do not co-exist when the material crystallizes from the melt which is separated in lamellar MDs. In other words, in this particular case, breakout or confined crystallization within lamellar MDs depends on the crystallization conditions. 

The combination of careful chemical synthesis with NSE and SANS experiments sheds some light on the fast relaxation processes observed in the collective dynamics of block copolymers melts. The results reveal the existence of an important driving force acting on the junction points at and even well above the ODT. Modelling the surface forces by an expression for the surface tension, it was possible to describe the NSE spectra consistently. The experimental surface tension agrees reasonably well with the Helfand predictions, which are strictly valid only in the strong-segregation hmit. Beyond that, these data are a first example for NSE experiments on the interface dynamics in a bulk polymer system. 

However some Cr rich zones were also observed, formed from the Cr-Al rich phase mentionned. The catalysts contained oxidized chromium (Cr+ ) strongly segregated at the surface. 

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