Complex non-equilibrium phenomena

The departure from equilibrium occurs primarily on account of appearance of gradients such as temperature and concentration leading to flow of heat or of some species and subsequently leading to a specific non-equilibrium state. Earlier in the first instance, uncoupled flows, e.g. heat conduction, Poisseuille flow and electrical conduction, were the subject of investigation. Discussion of such processes has been given due attention in conventional Physical Chemistry texts. However, complex and exotic phenomena in the non-equilibrium thermodynamics provide a good tool for understanding such phenomena. 

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Part Three deals with complex non-equilibrium phenomena, which occur very far from equilibrium (Chapters 11-13). 

The requirement to specify the polymer density may represent a serious limitation for the practical application of the NELF model. Indeed, the dilation of the polymer matrix at high penetrant pressure could be significant and difficult to estimate without specific experimental data. On the other hand, the use of the non-equilibrium polymer (tensity is actually a powerful tool to represent complex non-equilibrium phenomena. It has been shown, for example, that it allows a description of sorpdon-desorption hysteresis (7) as well as the influence of pretreatments on the solubility isotherms of gases in glassy polymers. For such cases, the different pseudo-equilibrium solubility values at the same prevailing temperature and penetrant fugacity are satisfactorily accounted for by considering die different pseudo-equilibrium polymer densities. 

It may be noted that in real systems, non-equilibrium phenomena are much more complex which involve multi-processes and complex coupling. 

In the non-linear region, exotic non-equilibrium phenomena such as bifurcation from steady state to bistability and oscillations (in time and space) are observed. New mathematical methodology based on non-linear dynamics has been evolved for investigating such phenomena as discussed in Chapter 8. The essential point to note is that such complex phenomena arise when more than three forces are evolved in addition to the occurrence of multi-process as discussed in Parts Two and Three. Bifurcation process... 

How relevant are these phenomena First, many oscillating reactions exist and play an important role in living matter. Biochemical oscillations and also the inorganic oscillatory Belousov-Zhabotinsky system are very complex reaction networks. Oscillating surface reactions though are much simpler and so offer convenient model systems to investigate the realm of non-equilibrium reactions on a fundamental level. Secondly, as mentioned above, the conditions under which nonlinear effects such as those caused by autocatalytic steps lead to uncontrollable situations, which should be avoided in practice. Hence, some knowledge about the subject is desired. Finally, the application of forced oscillations in some reactions may lead to better performance in favorable situations for example, when a catalytic system alternates between conditions where the catalyst deactivates due to carbon deposition and conditions where this deposit is reacted away. 

The phenomena of surface precipitation and isomorphic substitutions described above and in Chapters 3.5, 6.5 and 6.6 are hampered because equilibrium is seldom established. The initial surface reaction, e.g., the surface complex formation on the surface of an oxide or carbonate fulfills many criteria of a reversible equilibrium. If we form on the outer layer of the solid phase a coprecipitate (isomorphic substitutions) we may still ideally have a metastable equilibrium. The extent of incipient adsorption, e.g., of HPOjj on FeOOH(s) or of Cd2+ on caicite is certainly dependent on the surface charge of the sorbing solid, and thus on pH of the solution etc. even the kinetics of the reaction will be influenced by the surface charge but the final solid solution, if it were in equilibrium, would not depend on the surface charge and the solution variables which influence the adsorption process i.e., the extent of isomorphic substitution for the ideal solid solution is given by the equilibrium that describes the formation of the solid solution (and not by the rates by which these compositions are formed). Many surface phenomena that are encountered in laboratory studies and in field observations are characterized by partial, or metastable equilibrium or by non-equilibrium relations. Reversibility of the apparent equilibrium or congruence in dissolution or precipitation can often not be assumed. 

Miodownik et al. 1979, Watkin 1979). Irradiation can cause void-swelling, suppression of a formation in stainless steels and non-equilibrium precipitation of silicides. These phenomena are complex and occur by a combination of thermodynamic and kinetic effects. However, it was shown by Miodownik et al. (1979) that a thermodynamic analysis could be used to good effect to rationalise the effect of radiation on silicide formation. Although the work was done for a simple alloy system, it demonstrates how thermodynamics can be used in unusual cirounstances. 

The development of mixture sorption kinetics becomes increasingly Important since a number of purification and separation processes involves sorption at the condition of thermodynamic non-equilibrium. For their optimization, the kinetics of multicomponent sorption are to be modelled and the rate parameters have to be identified. Especially, in microporous sorbents, due to the high density of the sorption phase and, therefore, the mutual Influences of sorbing species, a knowledge of the matrix of diffusion coefficients is needed [6]. The complexity of the phenomena demands combined experimental and theoretical research. Actual directions of the development in this field are as follows ... 

For example, the standard synergetic approach [52-54] denies the possibility of any self-organization in a system with with two intermediate products if only the mono- and bimolecular reaction stages occur [49] it is known as the Hanusse, Tyson and Light theorem. We will question this conclusion, which in fact comes from the qualitative theory of non-linear differential equations where coefficients (reaction rates) are considered as constant values and show that these simplest reactions turn out to be complex enough to serve as a basic models for future studies of non-equilibrium processes, similar to the famous Ising model in statistical physics. Different kinds of auto-wave processes in the Lotka and Lotka-Volterra models which serve as the two simplest examples of chemical reactions will be analyzed in detail. We demonstrate the universal character of cooperative phenomena in the bimolecular reactions under study and show that it is reaction itself which produces all these effects. 

Finally, the quest to develop mechanistic explanations for these varied and fascinating phenomena can succeed only if more data become available on the component processes. Kinetics studies of the reactions which make up a complex oscillatory system are essential to its understanding. In some cases, traditional techniques may be adequate, though in many others, fast reaction methods will be required. There also appears to be some promise in developing an analysis of the relaxation of flow systems in non-equilibrium steady states as a technique to complement equilibrium relaxation techniques. 

This new theory of the non-equilibrium thermodynamics of multiphase polymer systems offers a better explanation of the conductivity breakthrough in polymer blends than the percolation theory, and the mesoscopic metal concept explains conductivity on the molecular level better than the exciton model based on semiconductors. It can also be used to explain other complex phenomena, such as the improvement in the impact strength of polymers due to dispersion of rubber particles, the increase in the viscosity of filled systems, or the formation of gels in colloids or microemulsions. It is thus possible to draw valuable conclusions and make forecasts for the industrial application of such systems. 

Studies carried out by Yoshida and coworkers have coupled this phenomena with oscillating chemical reactions (such as the Belousov-Zhabotinsky, BZ, reaction) to create conditions where pseudo non-equilibrium systems which maintain rhythmical oscillations can demonstrated, in both quiescent (4) and continuously stirred reactors (5). The ruthenium complex of the BZ reaction was introduced as a functional group into poly(N-isopropyl acrylamide), which is a temperature-sensitive polymer. The ruthenium group plays it s part in the BZ reaction, and the oxidation state of the catalyst changes the collapse temperature of the gel. The result is, at intermediate temperature, a gel whose shape oscillated (by a factor of 2 in volume) in a BZ reaction, providing an elegant demonstration of oscillation in a polymer gel. This system, however, is limited by the concentration of the catalyst which has to remain relatively small, and hence the volume change is small. 

Steady-state thermodynamics in the linear range provides a good glimpse of the non-equilibrium region close to equilibrium. The utility of steady-state thermodynamics is illustrated in the case of electro-kinetic phenomena in Parts Two and Three in the regions more and more distant from equilibrium (non-linear steady state, bistability, oscillations, pattern formation) including complexity and complex phenomena. 

The mechanochemical treatment by ball milling is a very complex process, wherein a number of phenomena (such as plastic deformation, fracture and coalescence of particles, local heating, phase transformation, and chemical reaction) arise simultaneously influencing each other. The mechanochemical treatment is a non-equilibrium solid-state process whereby, the final product retains a very fine, typically nanocrystalline or amorphous structure. At the moment of ball impact, dissipation of mechanical energy is almost instant. Highly excited state of the short lifetime decays rapidly, hence a frozen disordered, metastable strucmre remains. Quantitative description of the mechanochemical processes is extremely difficult, herewith a mechanochemical reaction still lacks clear interpretations and adequate paradigm. 

The new elements are required to describe new interaction phenomena that involve, in an entangled way, the molecular system, the medium (i.e. the solvent) and the external time-dependent perturbing fields. The couplings has two main effects. The first effect is to add a non-linearity in the time-dependent QM problem. More specifically, the time-dependent QM problem requires a proper extension of the time-dependent variation principle. The second effect is to induce a time-dependence in the solute-solvent responsive interaction, which must be described in a non-equilibrium solvation scheme. The PCM response theory face also the complex problem of the connection of the response functions of the molecular solutes... 

In general, the composition of polymer-salt complexes is a result of rather complicated equilibrium and some non-equilibrium, kinetically limited phenomena (Fauteux and Robitaille 1985 Fauteux et al. 1985 Lee and Crist 1986 Minier et al. 1984 Munshi and Owens 1986 Robitaille and Fauteux 1986 Stainer et al. 1984). According to the Gibbs phase rule (Gibbs 1870 Mindel 1962), for all the compositions ranging from pure polymer up to that of the thinnest crystalline complex, two phases should be present pure, crystalline PEO and pure PEO-salt crystalline complex. Nevertheless, polymeric materials are intrinsically impure , for example due to their polydispersity. Additionally, their crystallisation is kinetically limited, therefore in all polymeric materials there are always amorphous domains. Thus PEO-salt complexes usually consist of three phases (Fig. 2.4) - pure crystalline PEO, crystalline PEO-salt complex and amorphous PEO-salt complex the latter is of undefined composition (Wieczorek et al 1989). 

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