Microdomains phase diagram

Fig. 56 Phase diagram of blend of PS-fi-PI with PS. T0dt. o TDMt, Toot- Vertical lines separating microdomain structures are obtained from total volume fraction PS in system. Dashed line results of mean-field calculation for ODT. The OOT line which exists at volume fractions ps 5 ub was obtained during a heating process. From [174]. Copyright 2000 American Chemical Society...

The ability of block copolymers to self-assemble into organized microdomain (MD) structures when the thermodynamic repulsion between the constituents is high enough seems to be fairly well understood. This is particularly true in the case of amorphous diblock copolymers where phase diagrams for particular systems have been successfully predicted and experimentally proven [1-5]. 

All these results support our kinetic interpretations of these supersaturated gelling solutions. We assume that the network growth is described by the growth of individual domains, each one ruled by the autocatalytic model (S). This system behaves like an assembly of microdomains. Sach steroid in a supersaturation state is a potential germ of microdo.main. According to distribution curves of induction times for each microdomain, the typical kinetic curves for each part A and B of the phase diagram are obtained. 

A microemulsion is a thermodynamically stable isotropic dispersion of two relatively immiscible liquids, consisting of microdomains of one or both liquids stabilized by a interfacial film of surface-active molecules. In practice, one often identifies the microemulsion by the formation of a clear isotropic mixture of the two immiscible liquids in the presence of appropriate emulsifiers. In a phase diagram, such region is referred as the microemulsion phase. It has been shown that microemulsion regions consist of different microstructures (1,2), e.g., water-in-oil (W/0), oil-in-water (0/W),... 

Rod—coil block copolymers have both rigid rod and block copolymer characteristics. The formation of liquid crystalline nematic phase is characteristic of rigid rod, and the formation of various nanosized structures is a block copolymer characteristic. A theory for the nematic ordering of rigid rods in a solution has been initiated by Onsager and Flory,28-29 and the fundamentals of liquid crystals have been reviewed in books.30 31 The theoretical study of coil-coil block copolymer was initiated by Meier,32 and the various geometries of microdomains and micro phase transitions are now fully understood. A phase diagram for a structurally symmetric coil—coil block copolymer has been theoretically predicted as a... 

In 2005, Tyler et al. were the first to predict the existence of the orthorhombic Fddd as an equilibrium structure in the phase diagram of diblock copolymers. Using self-consistent field theory, the calculated phase diagram is shown in Fig. 4.3a [13, 16]. Two years later, Takenaka et al. were the first to deliver the experimental proof for the existence of the Fddd microdomain structure, discovered in a PS-ft-PI diblock copolymer melt [17], Thereafter, Kim et al. determined the Fddd phase boundaries in PS- -PI melts, as illustrated in Fig.4.3b [14, 18]. Although it was believed that the latest phase diagram of diblock copolymer was complete. Ho et al. in 2009 reported the discovery of a helical cylinder phase in poly(styrene)-f>-poly (L-lactic acid) melts, see Fig.4.3c [15]. 

Helfand 1975a). The theory was further developed by Hong and Noolandi (1981). Helfand also applied this theoretical method to the study of microdomain structures in block copolymer systems (Helfand 1975b), and tried to make precise computations of the phase diagrams by numerical methods (Helfand and Wasserman 1976). 

There are two distinct differences between the phase diagram of a block copolymer and the one obtained for a mixture of two homopolymers. In block copolymers, owing to the chemical links between blocks, microdomains instead of macroscopic phases are observed. The size of microdomains can be... 

Figure 8.11 Phase diagram for the geometry, stability and microdomains of an AB-type block copolymer.

Fig. 16. Phase diagram of a mixture containing polystyrene (M = 2400) and styrene/butadiene diblock copolymer (27 % styrene, M = 28000). Liquid phases L, and Lj represent mixtures of disordered block copolymer and polystyrene. Mesophase M, consists of ordered microdomains of the block copolymer swollen with polystyrene. Mesophase Mj probably contains aggregates of block copolymer micelles within the medium of polystyrene. The features on the lower right, drawn in broken lines, are more speculative. (From Roe and Zin...

In present study, we employed both SAXS and theological measurements to investigate the order-disorder and order-order transitions in a series of SIS triblock copolymer/low molecular weight PS homopolymer mixtures, which did not show macrophase separation in the whole temperature and composition range covered in this experiment, Phase diagrams obtained from both measurements were compared with the predictions based on the Whitmore-Noolandi theory. The difference between the theory and the experiment was discussed in terms of the change in homopolymer distribution and microdomain morphology by the addition of homopolymer to block copolymer. 

Figure 18.7 TEM images of four types of microdomain morphologies observed in PI-PS-P2VP (a) three-phase four-layer lamellae (squares in the phase diagram), (b) assigned as OTDD first but corrected later as tricontinuous gyroid with PI and P2VP networks (hexagons), (c) tetragonally...

The phase diagrams of solutions of diblock copolymers A-B may be quite complex and depend both on the chemical nature of two blocks and on the solvent. > In a selective solvent, good for the B-block and poor for the A-block, intermolecular aggregates are formed in the dilute regime so that the number of unfavorable contacts A-S is limited. The shape of aggregates (e.g, spherical or wormlike micelles, vesicles), their size and polydispersity depend very much on chain composition and length. In more concentrated solutions, aggregates order in space and form mesophases, i.e., ordered microdomains rich in A (in B) (e.g., lamellar. 

Figure 6.1 shows a schematic representation of the pseudo three-component phase diagram of a typical (surfactant/cosurfactant)-oil-water system. Depending on formulas, fine oil droplets dispersed in the continuous aqueous phase [O/W (or direct) microemulsion] or water droplets in the continuous oily phase [W/O (or inverse) microemulsion] are obtained. Furthermore, the intermediate region between the OAV microemulsion phase and the W/O microemulsion phase is characterized by a bicontinuous microstructure in which the aqueous and oily microdomains are interconnected with each other [13, 14]. The presence of such a middle phase in the colloidal system was verified by literature data [15]. It was shown that the oil-water interfacial layer in the bicontinuous microstructure has a zero mean curvature (i.e., it is flat on the average), and this sponge-like microstructure is completely disor-... 

Figure 8.6 Phase diagrams of AB-type diblock copolymer in terms of xA versus /, which are based on self-consistent mean-field theory, in which S denotes spherical microdomains, C denotes hexagonally packed cylindrical microdomains, G denotes gyroids, and L denotes alternating layers of lamellae. (Reprinted from Matsen and Bates, Macromolecules 29 1091. Copyright 1996, with permission from the American Chemical Society.)...

Fig. 7 Phase diagrams of an AB-type diblock copolymer in terms of vs the volume fraction (/) of block A, predicted from the Leibler theory, in which curve (a) denotes the phase transition from the disordered state to spherical microdomains, curve (b) denotes the phase tiansition from spherical microdomains to cyhndrical microdomains, curve (c) denotes the phase tiansition from cylindrical microdomains to lamellar microdomains, and curve (d) denotes the spinodal curve %N)s. (Reprinted from Han et al. [41], Copyright 1989, with permission from the American Chemical Society)...

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