Phase separation: intermediate-scale

Models of a second type (Sec. IV) restrict themselves to a few very basic ingredients, e.g., the repulsion between oil and water and the orientation of the amphiphiles. They are less versatile than chain models and have to be specified in view of the particular problem one has in mind. On the other hand, they allow an efficient study of structures on intermediate length and time scales, while still establishing a connection with microscopic properties of the materials. Hence, they bridge between the microscopic approaches and the more phenomenological treatments which will be described below. Various microscopic models of this type have been constructed and used to study phase transitions in the bulk of amphiphihc systems, internal phase transitions in monolayers and bilayers, interfacial properties, and dynamical aspects such as the kinetics of phase separation between water and oil in the presence of amphiphiles. 

Figure 35. The scaling relations (4)—(7) do not hold in the intermediate regime of the phase separation. The crossover between early and intermediate regime occurs when the order parameter saturates inside the domains (the order parameter is nonconserved).

Figure 14 Schematic representation of the microphase separation of block copolymers. The left graph shows atomic-scale details of the phase separation at intermediate temperatures, and the right graph shows a lamellar phase formed by block copolymers at low temperatures. The block copolymers have solid-like properties normal to the lamellae, because of a well-defined periodicity. In the other two directions, the system is isotropic and has fluid-like characteristics. From reference 54.

Rgure 8.5 Representative polymer-polymer phase behaviour with different molecular architectures. Microphase separation (a) results when thermodynamically incompatible linear homopolymers are mixed. The covalent bond between blocks in a diblock copolymer leads to microphase segregation (c). A mixed architecture of linear homopolymers and the corresponding diblock copolymer produces a surfactant-like stabilized intermediate-scale phase separation (b). 

Fig. 24a,b. Scaled structure factor F(x) as a function of the reduced scattering vector for A/B/C-fo-D blend containing R22f5 block copolymer with Nbiock= 12 in a the intermediate stage b the late stage of phase separation [71]... 

A number of extreme (critical) situations exist when fluctuations extend to macroscopic scales and exist on all intermediate scales. Temperature phase transitions and percolation processes concern such situations. In these systems a critical point exists which separates two different phase states of the system. 

Several other attempts have been made to model the humidified Nation nano-phase-separated structure and the temperature dependence of proton transport by atomistic MD simulations [53,59-64], It was observed that more filamentous aqueous regions at low humidity change into clusters of more micellar shape at intermediate water content, which connect into channels at high water content [60]. Other studies noted a certain effect of sidechain arrangement (statistical vs. blocks) on the size of the phase-separated regions [59]. These calculations frequently suffer from an ergodicity problem due to the different characteristic time scales of water and polymer. 

A. Macrophase separation into two layers, which commonly arises when two homopolymers are mixed. B. Microphase segregation can arise with diblock copolymers. Here, striated layers appear. C. Mixing homopolymers with the corresponding diblock copolymer gives intermediate-scale phase separation. A surfactant-like mixture occurs. Figure modified from Bates, F. S. "Polymer-Polymer Phase Behavior." Science, 251, 898 (1991). 

The types of polymer blends are quite varied and comprise many diverse combinations of polymeric materials of both academic and industrial interest. The primary differentiation of polymer blends involves their phase behavior specifically, miscibility versus phase separation. Miscibility is related to mixing approaching the molecular dimension scale such that the properties observed are that expected of single phase materials. Miscibility does not imply ideal mixing at the molecular scale. Miscibility was initially believed to be an extremely rare observation and, in fact, most random combinations of binary blends are indeed phase separated. However, many miscible combinations have been noted and the rationale for miscibility is well-established. The primary advantage of miscible versus phase separated polymer blends is the blend property profile, which is generally intermediate between that of the... 

In view of this, some reference state for the cation distribution needs to be defined to serve as a bench mark to which observed low-temperature states can be referred. Summerville (1973) has coined the phrase operational equilibrium to describe the state achieved after a low-temperature anneal when the anion sub-lattice adjusts to a random cation distribution this should be reproducible. Operational equilibrium will be achieved in principle with samples that have been melted initially, or in practice perhaps with those which have been heated above, say, 2000°C. Any tendency for changes in the random cation distribution thus achieved, which might stem from the stable existence below, say, 1600 C of some intermediate compound of defined composition, would only be revealed if the sample were annealed at close to this temperature for sufficient time for the diffusion-controlled reaction to take place. So it is that for the Zr02-Sc203 system, arc-nlelted samples of compositions between those of the y- and S-phases appear optically, to X-rays, but not to electrons as monophasic. However, after a week s annealing at 1600°C and subsequent quenching, phase separation does occur on a sub-microscopic scale, and is clearly shown in X-ray diffraction. 

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