Chemical order-disorder transitions

FIGURE 5.17 Temperature versus G —the shear storage modulus at a frequency of 1.6 Hz for diblock copolymer poly(ethylene propylene)-poly(ethylethylene) (PEP-PEE). The order-disorder transition (ODT) calculated to be 291°C 1°C. (From Rosedale, J.H. and Bates, F.S., Macromolecules, 23, 2329, 1990. With permission of American Chemical Society.)... 

Various types of work in addition to pV work are frequently involved in experimental studies. Research on chemical equilibria for example may involve surfaces or phases at different electric or magnetic potentials [11], We will here look briefly at field-induced transitions, a topic of considerable interest in materials science. Examples are stress-induced formation of piezoelectric phases, electric polarization-induced formation of dielectrica and field-induced order-disorder transitions, such as for environmentally friendly magnetic refrigeration. 

Choice of initial condition. To avoid the slow growth of ordered domains out of disordered initial states and to avoid that the system gets trapped in metastable states ", it is preferable to start the simulation in the appropriate perfectly ordered configuration. The various perfectly ordered states that a model can have are usually found from an analysis of the ground state which may be tedious but in most cases is rather straightforward (for examples, see Refs. 20,22,66). If for the chosen system parameters (temperature T, chemical potential /i) the system is in a disordered phase, the system will relax towards this state smoothly, even if it started out fully ordered, if the order-disorder transition is of second order. In the case of... 

Fig. 18 Order-disorder transition temperature (Todt) as a function of the electric field strength of a 32.5 wt% solution of SI in toluene. The temperatures have been obtained during cooling open circles) and heating cycles (solid circles) of the solution. The dashed line at 53.0°C refers to the constant temperature experiment in Fig. 19. Reprinted with permission from Macromolecules [72]. Copyright 2009 American Chemical Society...

Figure 13.4 Phase diagram of a PS-PI diblock copolymer showing regions of BCC spheres (Im3m), hexagonal cylinders (HEX), laid gyroid, hexagonally perforated lamellae (HPL), lamellar (LAM), and disordered phases /pi is the volume fraction of polyisoprene. The dot-dash line represents the mean-field order-disorder transition based on the formula x = 71.4/T — 0.0857 with reference segment volume v — 144 A. (Reprinted with permission from Khandpur et al.. Macromolecules 28 8796. Copyright 1995, American Chemical Society.)...

Figure 13.15 Reduced storage modulus versus reduced frequency arco for a lamellae-forming polystyrene-polyisoprene diblock copolymer (M = 22,000) at temperatures above the order-disorder transition temperature Todt = 152°C, and quenched to temperatures below it. The disordered samples show terminal behavior, and the ordered (but unoriented) ones show nonterminal behavior. (Reprinted with permission from Patel et al.. Macromolecules 28 4313. Copyright 1995, American Chemical...

Another problem which obscures the analogy between different phase transitions is the fact that one does not always wish to work with the corresponding statistical ensembles. Consider, for example, a first-order transition where from a disordered lattice gas islands of ordered c(2x2) structure form. If we consider a physisorbed layer in full thermal equilibrium with the surrounding gas, then the chemical potential of the gas and the temperature would be the independent control variables. In equilibrium, of course, the chemical potential jx of subsystems is the same, and so the chemical potential of the lattice gas and that of the ordered islands would be the same, while the surface density (or coverage 9) in the islands will differ from that of the lattice gas. The three-dimensional gas acts as a reservoir which supplies adsorbate atoms to maintain the equilibrium value of the coverage in the ordered islands when one cools the adsorbed layer through the order-disorder transition. However, one often considers such a transition at... 

It was shown that VT Si CP/MAS NMR chemical shifts (S), Si-relax-ation times (Ti) and calculated Si-shielding constants (cr) are very useful in studying the solid-state order-disorder transitions in the polysilanes. 

For most BC the phase diagram is characterized by the presence of an upper critical solution temperature, UCST, also known as an order-disorder transition temperature or a microphase separation temperature. Below UCST the block copolymers phase separate, while above it, an isotropic melt is obtained. Owing to the chemical... 

The simplest case of a block copolymer is a diblock consisting of two covalently bonded polymers with chemically distinct repeat units A and B. If A and B are incompatible, below the order-disorder transition at Todt microphase separation is obtained into, for example, a spherical, cylindrical, or lamellar phase. The phase behavior depends on the relative volume fraction of A and B and on the magnitude of the product xabN, where xab is the Flory-Huggins interaction parameter between the two polymers, and N the total degree of polymerization [7]. We can write... 

Li et al. synthesized a PMMA-PEG semi-IPN by radical polymerization and cross-linking of PMMA in the presence of linear PEG, which exhibits two independent shape memory effects at two transition temperatures, the of the PEG crystal and the Tg of the semi-IPN [39]. In the IPN, a single Tg appeared due to the miscibility of the amorphous phase of the two polymers. Based on a reversible order-disorder transition of the crystals below and above the of PEG, and the large difference in storage modulus below and above the Tg of the semi-IPN, the polymer has a recovery ratio of 91 and 99%, respectively For the shape-memory behavior at the of PEG crystals, the fixing phase was the PMMA network and the reversible phase was PEG crystals. For the shape memory behavior at the Tg of the semi-IPNs, the fixing phase was the chemical cross-linked point, while the reversible phase was the PMMA-PEG complex phase. 

Fig. 15 Mean-field phase diagram of supramolecular diblock copolymer model with equivalent block lengths. Labeled phases are Dis (hranogeneous disordered), Lam (lamellar), and 2 phase (coexisting A-rich and B-rich homogtaieons phases). The values of N indicate the diblock copolymer length. Solid dots denote Ltfshitz points (LS). The horizontal dashed line on the l denotes 1//N = 1/4, the macrophase separation transition for a binary blend of polymers. The horizontal dashed line on the right signifies 1//A1 = 0.095, the order-disorder transition for a symmetric diblock copolymer. Reprinted with permission from [97]. Copyright 2007 American Chemical Society...

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