Dissipative structures formation conditions

This will be elaborated in detail in the following section. However, it is of interest that the existence of concentration-dependent (implying a far-from-equilibrium condition) cross-diffusion terms creates a non-linear mechanism between elements of the system, i.e. the flux of one polymer depends not only on its own concentration gradient but also on that of the other polymer component. This is consistent with two of the criteria required for dissipative structure formation. Furthermore, once a density inversion is initiated, by diffusion, it will be acted upon by gravity (as the system is open ) to produce a structured flow. The continued growth, stability and maintenance of the structures once formed may depend on the lateral diffusion processes between neighbouring structures. 

Thus, we know two principles of self-organization self-assembly near equilibrium conditions and dissipative structure formation under conditions far from equilibrium. As summarized in Table 1, these are considerably different in time, scale, order of driving force, existence of potential fiinction, and so on. Because of these thermodynamical differences and their historical backgrounds, they seem to have been studied almost independently in different research fields. 

Although our own research has outlined a complete new theoretical concept, there is still a great need to invest further research into the fundamentals of blend technology, such as dispersion, interfacial phenomena, conductivity breakthrough at the critical concentration, electron transport phenomena in blends, and others. It is not the purpose of this section to review these aspects in greater depth than in Section 1.1 and Section 1.2. In the context of this handbook, it should be sufficient to summarize the basis of any successful OM (PAni) blend with another (insulating and moldable or otherwise process-able) polymer is a dispersion of OM (here PAni, which is present as the dispersed phase) and a complex dissipative structure formation under nonequilibrium thermodynamic conditions (for an overview, see Ref [50] for the thermodynamic theory itself, see Ref [15], for detailed discussions, cf Refs. [63,64]). Dispersion itself leads to the drastic insulator-to-metal transition by changing the crystal structure in the nanoparticles (see Section 1.1). 

In introducing the sense of dissipative structures, Prigogine and Stengers state, In far-from-equilibrium conditions we may have transformation from disorder, from thermal chaos, into order. New dynamic states of matter may originate, states that reflect the interaction of a given system with its surroundings. We have called these new structures dissipative structures to emphasize the constructive role of dissipative processes in their formation. ... 

The presence of reactive ions like CH in the diffuse interstellar medium has been a challenge for interstellar chemistry since CH is easily destroyed by reactions with H2 but slow to form under the known physical conditions of the diffuse interstellar medium. It now appears that a warm chemistry can develop in the tiny dissipative structures of the interstellar turbulence, enabling the formation of transient species like CH and SH [43], The opening up of the sub-millimetre sky by the Herschel telescope has led to the discovery of several new reactive ions, enabling a better characterization of their chemistry. In the future, these tracers should bring interesting constraints on the properties of the interstellar turbulence. 

The minimum entropy production theorem dictates that, for a system near equilibrium to achieve a steady state, the entropy production must attain the least possible value compatible with the boundary conditions. Near equilibrium, if the steady state is perturbed by a small fluctuation (8), the stability of the steady state is assured if the time derivative of entropy production (P) is less than or equal to zero. This may be expressed mathematically as dPIdt 0. When this condition pertains, the system will develop a mechanism to damp the fluctuation and return to the initial state. The minimum entropy production theorem, however, may be viewed as providing an evolution criterion since it implies that a physical system open to fluxes will evolve until it reaches a steady state which is characterized by a minimal rate of dissipation of energy. Because a system on the thermodynamic branch is governed by the Onsager reciprocity relations and the theorem of minimum entropy production, it cannot evolve. Yet as a system is driven further away from equilibrium, an instability of the thermodynamic branch can occur and new structures can arise through the formation of dissipative structures which requires the constant dissipation of energy. 

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