Spontaneous ordering

Nets with connectivity two exhibit a remarkable collective spontaneous order. As we can see in table 8.9, both the number and size of attractors increases only as /N. a net of size N = 10, for example, settles down into one of only about 100 different attractors, consisting, on average, of about 100 states. The dynamics therefore effectively shrinks the total phase space down to about 10 of the original volume. 

The geometrically optimized model of BD had a roughly linear conformation. This spontaneous ordering was unexpected given the general orientation of dipolar molecules. Azobenzenes that have permanent dipoles parallel to the molecular axis would intuitively be expected to tend to pair with their dipole oriented in the opposite direction. The linear geometry is probably due to the... 

In the other type of self-organization (dynamic self-organization), spontaneous ordering of the systems occurs under thermodynamically non-equilibrium conditions, in which various ordered structures with wavelengths tens to hundreds of thousands times larger than the size of the system components are formed by spatiotemporal synchronization of various factors [10-12]. The spatiotemporal order... 

FIGURE 5.16 Spontaneous ordering of linear polymers in a semicrystalline material. Bundles of dark lines represent crystalline regions. Reprinted from Flory (1953) Paul J. Flory, Principles of Polymer Chemistry, Copyright 1953 Cornell University Press and Copyright 1981 Paul J. Flory. Used by permission of the publisher, Cornell University Press. 

Figure 9.4 Two good reasons for fascination in the field of surfactants (a) spontaneous order out of a chaotic mixture of monomers and (b) the emergence of compartments (microheterogeneous reactions...). (Vesicle and micelle are not to scale.)...

The essential realization in this spontaneous ordering process is the importance of noncovalent bonding interaction between molecules, that is, supramolecular chemistry. These conformation-specific interactions are governed by weak forces including hydrogen bonding, metal coordination, van der Waals forces, pi-pi interactions, and electrostatic Coulombic effects. The cooperative action of multiple noncovalent interaction forces is precisely the path nature takes to produce shape and form. 

As is well-known, the critical point can be found from locating the divergence of the response function ( susceptibility ) S = dm/dH, which signals the onset of symmetry breaking and spontaneous order. The simplest case occurs for Hj=0, and then... 

CB is 4-cyano-4 -pentylbiphenyl. Liquid-crystal phases can also form when amphiphilic molecules associate to form anisotropic structures which, in turn, spontaneously order into liquid-crystalline phases. 

Modern-day interest in LCPs had its origin with the molecular theories of Onsager (5) and Flory (6). They predicted that rod-like molecules would spontaneously order above a critical concentration that depended on the aspect ratio of the molecule. These theories were later expanded to include other effects such as polydispersity (2) and partial rigidity (g). 

Our MC results for the confined dipolar fluids indicate that spontaneous order does indeed occur over a certain range of wall separations. s. This can be seen from Figs. 6.6-6.8 for a system where = 7. Specifically, in Fig. 6.6, we have plotted the global order parameter... 

An important difference between the confined system and the bulk, however, concerns the thermodynamic conditions related to the onset of long-range parallel order. In fact, based on the data plotted in the two parts of Fig. 6.8, we conclude that in the confined system the onset of order occurs at somewhat lower pressures/densities, indicating that the walls promote rather than inhibit spontaneous orientational order. This result is, at least at first sight, rather surprising, because the substrates in the current system do not couple directly to the fluid particle dipole moments. A rationale for this shift of the onset of spontaneous order in the confined relative to the bulk fluid is offered in Ref. 257 where we basically employ entropic arguments. 

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