Dissipative structures Benard instability

Bragg peaks with 3.6 nm spacing, that is, well corresponding to the bilayer thickness, observed in the X-ray diffraction pattern of the honeycomb film strongly suggest that the mesoscopic honeycomb patterns are constituted from nanostructured lamella assemblies of the polyion complexes. UV-visible absorption spectra of the patterned films (honeycomb, dots, and stripes) prepared from the polyion complexes of the azobenzene amphiphiles are identical to those of the macroscopically homogeneous cast films described in the previous section. It is concluded that the dissipative structures (Benard cell, fingering instability)... 

Remark. A great deal of attention has been paid in recent years to non-equilibrium stationary processes that are unstable and also extended in space. They can give rise to different phases that exist side by side, so that translation symmetry is broken. The name dissipative structures has been coined for them, and the prime examples are the Benard cells and the Zhabotinski reactions, but they also occur in biology and meteorology. However, these are features of the macroscopic equations. They are only relevant for fluctuation theory inasmuch as the fluctuation becomes very large at the point where the instability sets in. The critical fluctuations in XIII.5 are an example. There are many more varieties, in particular in the case of more variables. 

Dissipative structures arise only in strongly nonequilibrium systems, with the states described by nonhnear equations for internal macro parameters. The emergence of the Benard cells in fluids can be described using non hnear differential equations of hydrodynamics coupled with Lyapunov s analysis of the instability of the respective solutions. It is shown that the solution of hydrodynamic equations related to a resting fluid and normal heat transfer becomes unstable at AT > AT, and a new stable convection mode is established in the fluid. 

Figure 10 Dissipative structures fonned in casting polymer solution (a) Benard cells and lingering instability fonned in chloroform solution of polyion complex of 1 and 11 (b) snapshots of stripe formation from the fingering instability at the three-phase line synchronized with receding front (c) regularly arrayed polymer dots formed by dewetting in the stripes.

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