Orientational ordering phase diagram

Fig. 9. Two-parameter ordering phase diagram for a system of 500 identical hard spheres (Truskett et ai, 2000 Torquato et ai, 2000). Shown are the coordinates in structural order parameter space (r, ) for the equilibrium fluid (dot-dashed), the equilibrium FCC crystal (dashed), and a set of glasses (circles) produced with varying compression rates. Here, r is the translational order parameter from (26) and is the bond-orientational order parameter Q( from (25) normalized by its value in the perfect FCC crystal ( = Each circle...

The mean-field phase diagram of the anisotropic-rotor model (2.1) + (2.3) as explored by a combination of numerical and analytical methods is presented in Fig. 3. The corresponding orientationally ordered phases are sketched in Fig. 4, and they are shown in Fig. 5 in a more realistic repre-... 

Figure 4.14. Phase diagram, coverage vs. temperature, of N2 physisorbed on graphite. Symbols used fluid without any positional or orientational order (F), reentrant fluid (RF), commensurate orientationally disordered solid (CD), commensurate herringbone ordered solid (HB), uniaxial incommensurate orientation-ally ordered (UlO) and disordered (UID) solid, triangular incommensurate orientationally ordered (lO) and disordered (ID) solid, second-layer liquid (2L), second-layer vapour (2V), second-layer fluid (2F), bilayer orientationally ordered (2SO) and disordered (2SD) solid. Solid lines are based on experimental results whereas the dashed lines are speculative. Adapted from Marx Wiechert, 1996.

From the previous Section it is expected that the application of the flow field will primarily affect the last two order parameters, i.e. the orientation and conformation of the chain. In the discussion of the nucleation dynamics, it is helpful to separate the contributions from the kinetic and thermodynamic processes. The first represents the fundamental timescale to form a nucleus, the prefactor, and the second describes the driving force for the phase transition based on the position of the system in the phase diagram. 

In order to analyze the dependence of the liquid crystalline transition properties on temperature (i.e. on the solvent quality), it is necessary to introduce the attraction of rods parallel to their steric repulsion. This has been done by Rory9 . The classical phase diagram of Rory for the solution of rods (see Fig. 2) agrees well with experimental results from the qualitative point of view1 . However, the Rory theory cannot give adequate answers to all the questions connected with the orientational ordering in the system of rigid rods. Indeed ... 

Figure 12.21 Phase diagram for the surfactants cetylpyridinium chloride and hexanol in 0.2 M NaCl at 30°C. Li is a disordered state of wormy micelles, Nc is the nematic state of oriented micelles, H is a state of hexagonally ordered cylindrical micelles, and L is a lamellar state. The hatched areas are coexistence regions. (Reprinted with permission from Roux et al.. Macromolecules 28 1681. Copyright 1995, American Chemical Society.)...

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