Molecular disorder ordering phase diagram

The systematic investigation of order phase diagrams, such as that shown in Fig. 9 but for different molecular interactions, the location of inherent structures in the order plane, and the comparative exploration of order (or disorder) in computer glasses generated by different quenching protocols are, we beheve, fruitful avenues for research into the nature, classification, and quantification of disorder in glasses and other technologically important nonequilibrium materials. 

Each point in the phase diagram in Fig. 8.8 corresponds to a certain value of a and b, i.e., it represents the possible chemical composition of a molecular population. Variable a forms the horizontal axis, (1 +a) being the number of monomer types. The b axis represents the quality factor of the polymer catalysis. The transition region contains those populations which can have both ordered and disordered... 

Fig. 6.10 Phase diagrams for blends of PS homopolymers with PS-PI diblocks of approximately constant molecular weight (average M = 54.3 kgmol"L), annealed at 125 C (Winey et al. 1992ft). (a) Mn (PS) = 5.9kgmor (b) M (PS) = 14kgmol-1, (c) M (PS) = SVkgmor1. Here L, C and S denote lamellar, cylindrical and spherical microstructures respectively, DM indicates disordered micelles, BC a bicontinuous cubic structure and 2

Fig. 6.39 Calculated constant %N (=11) phase diagram for a symmetric diblock blended with low-molecular-weight homopolymers (Janert and Schick 19976). Ordered and disordered phases are indicated. The homopolymers have /3 = 0.1 and fi = 0.3.

Fig. 2. Phase diagram at 340 K, showing the particle concentration p/p0 in the coexisting ordered and disordered phases as a function of the volume fraction of the free polymer for different molecular weights of the free polymer. (I), 36,000 (II), 82,000 (III), 122,000 (IV), 176,000 (V), 490,000. System polyisobutene-stabilized silica particles with polystyrene as the free polymer in cyclohexane, a = 48 nm, 6=5 lim. The lower curves represent the transition boundary from a stable disordered phase to the two-phase region, and the upper curves the two-phase region to the stable ordered phase boundary. x, = 0.47 and xs = 0.10 for polyisobutene—cyclohexane, A/kT = 4.54 and v = 0.10. The value of x for polystyrene—cyclohexane is calculated according to Eqn (16).

In addition to the molecular weight of the free polymer, there axe other variables, such as the nature of the solvent, particle size, temperature, and thickness of adsorbed layer which have a major influence on the amount of polymer required to cause destabilization in mixtures of sterically stabilized dispersions and free polymer in solution. Using the second-order perturbation theory and a simple model for the pair potential, phase diagrams relat mg the compositions of the disordered (dilute) and ordered (concentrated) phases to the concentration of the free polymer in solution have been presented which can be used for dilute as well as concentrated dispersions. Qualitative arguments show that, if the adsorbed and free polymer are chemically different, it is advisable to have a solvent which is good for the adsorbed polymer but is poor for the free polymer, for increased stability of such dispersions. Larger particles, higher temperatures, thinner steric layers and better solvents for the free polymer are shown to lead to decreased stability, i.e. require smaller amounts of free polymer for the onset of phase separation. These trends are in accordance with the experimental observations. 

The self-consistent field theory phase diagram is also likely to be inaccurate at low relative molecular mass, because, like any mean-field theory, it neglects fluctuations. The effect of fluctuations is to stabilise the disordered phase somewhat (Fredrickson and Helfand 1987) in addition the seeond-order transition predicted for the symmetrical diblock is replaced by a first-order transition and, for asymmetrical diblocks, there are first-order transitions directly from the disordered into the hexagonal and lamellar phases. In addition it seems likely that fluctuations tend to stabilise high symmetry states such as the gyroid (Bates et al. 1994). 

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