Non-equilibrium processes

D.C. Wallace, Computer Simulation of Non-Equilibrium Processes, in Shock Waves in Condensed Matter (edited by Y.M. Gupta), Plenum, New York, 1986, pp. 37-49. 

Suryanarayana, C. (ed.) (1999) Non-equilibrium Processing of Materials (Pergamon, Oxford). 

Vol. 1 CALPHAD by N. Saunders and A. P. Miodownik Vol. 2 Non-Equilibrium Processing of Materials edited by C. Suryanarayana Vol. 3 Wettability at High Temperatures by N. Eustathopoulos, M. G. Nicholas and B. Drevet... 

The phase distribution observed in the alloys deposited from AlCb-NaCl is very similar to that of Mn-Al alloys electrodeposited from the same chloroaluminate melt [126 129], Such similarity may also be found between the phase structure of Cr-Al and Mn-Al alloys produced by rapid solidification from the liquid [7, 124], These observations are coincident with the resemblance of the phase diagrams for Cr-Al and Mn-Al, which contain several intermetallic compounds with narrow compositional ranges [20], inhibition of the nucleation and growth of ordered, often low symmetry, intermetallic structures is commonly observed in non-equilibrium processing. Phase evolution is the result of a balance between the interface velocity and... 

Hence, when Tk is zero the system is in equilibrium, but for non-zero Tk an irreversible process that takes the system towards equilibrium, occurs. The quantity Tkl which is the difference between intensive parameters in entropy representation, acts as the driving force, or affinity of the non-equilibrium process. 

A reaction in a metabolic pathway is likely to be nonequilibrium if the maximum catalytic activity of the enzyme that catalyses the reaction is low in comparison with those of other enzymes in the pathway. In consequence, the concentration of substrate of this reaction is likely to be high whereas that of the product is likely to be low, since the next enzyme in the sequence readily catalyses its removal. Because the concentration of this product is low, the rate of the reverse component of the reaction is very much less than the rate of the forward component. This situation characterises a non-equilibrium process. Conversely, a reaction is near-equiUbrium if the maximum catalytic activity of the enzyme is high in relation to those of other enzymes in the pathway in this case, the rates of the forward and the reverse components of the reaction are similar and both are much greater than the overall flux... 

Figure 9.26 (a) Near-equUibiium and non-equilibrium reactions in the electron transfer chain. The electron transfer chain is considered to be the Latter part of the physiological Krebs cycle (see above). The non-equilibrium processes are the Krebs cycle and the terminal reaction cytochrome oxidase. All other reactions are near-equilibrium, including the ATP-generating reactions. These are not shown in the figure, (b) The similarity of electron transfer chain and glycolysis in the position of near-equilibrium/non-equilibrium reactions, in the two pathways. In both cases, non-equilibrium reactions are at the beginning and at the end of the processes (see Chapters 2 and 3 for description of these terms and the means by which such reactions can be identified). 

The GPG spin column fractionation step is a non-equilibrium process. During the gel permeation chromatography step, the unbound small molecules in solu-... 

Non-equilibrium Processing of Materials edited by C. Suryanarayana Phase Transformations in Titanium- and Zirconium-based Alloys... 

For a number of applications, particularly those associated with conditions of continuous cooling or heating, equilibrium is clearly never approached and calculations must be modified to take kinetic factors into account. For example, solidification rarely occurs via equilibrium, amorphous phases are formed by a variety of non-equilibrium processing routes and in solid-state transformations in low-alloy steels much work is done to understand time-temperature-transformation diagrams which are non-equilibrium in nature. The next chapter shows how CALPHAD methods can be extended to such cases. 

Because polymer adsorption is effectively irreversible, and because adsorption and floe growth occur simultaneously, flocculation is a non-equilibrium process. As a result, performance is largely determined by the kinetics of adsorption and aggregation. Both of these can be regarded as collision processes involving solid particles and polymer molecules. In each case, collisions can arise due to either Brownian motion or agitation of the suspension. The collision frequency v between particles and polymer molecules can be estimated from °... 

The coefficient C, related to the resistance to mass transfer between the two phases, becomes important when the flow rate is too high for equilibrium to be obtained. Local turbulence within the mobile phase and concentration gradients slow down the equilibrium process (Cs <=> Cm). The diffusion of solute between the phases is not instantaneous, hence the solute will be in a non-equilibrium process. 

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. 

The adsorption of macromolecules is rarely an equilibrium process. Just as the properties of synthetic polymers are often dependent on non-equilibrium processes and relaxation phenomena30), so do the properties of adsorbed proteins depend on time, metastable states, and hysteresis processes. 

The mechanisms that lead to such laser desorption are now believed to be collective, non equilibrium processes in the condensed phase (26). In this respect they are closer to processes that must be assumed to lead to ion generation in SIMS and plasma desorption rather than to the thermal laser induced ion generation discussed above, even though the spectra are often indistinguishable for all different laser techniques. The recently reported observation of metal ion (Cu, Ag, Mg etc.) attachement for desorption with high power, short pulse lasers (10, 11, 12) also points to the similarity with SIMS. 

Poh BT, Ong BT (1984) Dependence of viscosity of polystyrene solutions on molecular weight and concentration. Eur Polym J 20(10) 975-978 Pokrovskii VN (1970) Equations of motion of viscoelastic systems as derived from the conservation laws and the phenomenological theory of non-equilibrium processes. Polym Mech 6(5) 693—702... 

This work has been financially supported, in part, by Grants-in-Aid for Scientific Research on Priority Area Molecular Approaches to Non-equilibrium Processes in Solutions (No. 02245106 and No. 03231105) from the Ministry of Education, Science and... 

One of principal causes of increase of P-conductivity in MF can be magnetosensitive non-equilibrium processes connected with charges carriers transport or change of intensity of capture (or release) by traps of electrons and holes. High times of increase and decrease of P-conductivity confirm the given assumption, indicating the contribution of defect structure to P-conductivity of C6o single crystal in MF. 

The second property expected for non-equilibrium processes is the lack of dependence (Fig. 2.6, curve 1) or weak dependence (curve 2) of the experimental rate constant of ET in both Marcus regions (inverted and non-inverted), compared to that predicted by the classic Marcus expression (curve 3). 

Figure 2.5. Schematic representation of electronic potential energy surfaces 1, consecutive conformational and solvatational equilibrium processes with the essential change in the nuclear coordinates Q and the standard Gibbs energy AG0 2, consecutive non-equilibrium processes with small changes in Q and AG0 3, 4, equilibrium (full line) and non-equilibrium (broken line) processes in the normal and inverted Marcus regions respectively. (Likhtenshtein, 1996) Reproduced in permission.

Figure 2.6. Schematic representation of the dependence of the ET constants logarithm on the equilibrium Gibbs energy AG0 1, non-equilibrium conformational and solvational processes 2, partial non-equilibrium processes, J.n and AGoneq are slightly dependent on AG0 3, equilibrium processes. Arrows a and b are conditions for the maximum X = AGo and A.1 1 = AGonK respectively. (Likhtenshtein, 1996). Reproduced in permission.

It is worth mentioning that a set of the types of the dynamic behavior of the system in the case of copolymerization of m monomers is principally wider in comparison with the distillation process of an m-component liquid mixture as it has already been remarked [13]. The reason for this lies in the fact that copolymerization is a non-equilibrium process in contrast to distillation. In a particular case of three-component copolymerization such a possibility is shown... 

An important parameter for comparison with theory as well as for understanding many properties would be relative binding energies or stabilities. Unfortunately those are hard to assess in the gas phase. One of the few experiments to report thermodynamic binding energies between base pairs is the work by Yanson et al. in 1979, based on field ionization [25], Relative abundances of nucleobase clusters in supersonic beams are an unreliable measure of relative stability for a two reasons First, supersonic cooling is a non-equilibrium process and thus comparison with thermal populations is tenuous at best. Secondly, ionization probabilities may be a function of cluster composition. The latter is certainly the case for multi photon ionization, as will be discussed in detail below. 

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