Thermodynamic nonequilibrium

TNC.57. P. Glansdorff and I. Prigogine, Thermodynamics, nonequilibrium, in Encyclopaedia of Physics, Addison-Wesley, pp. 1029-1034. 

GIBBS FREE ENERGY ENTHALPY THERMODYNAMICS NONEQUILIBRIUM THERMODYNAMICS A PRIMER... 

The consequence is an inhomogeneous distribution of additives in the individual polymer phases and thermodynamic nonequilibrium after mixing. The latter effect may cause demixing and re agglomeration of additives. A well-known example in this regard is the flocculation or reagglomeration of silica in S-SBR compounds [3]. 

From the pyrrolinium-furanium ion equilibrium (Scheme 62) one can assume, in agreement with CTp values (—1.7 and —0.86 for 2-pyrrolyl and 2-furyl, respectively), that the pyrrole ring stabilizes the adjacent furanium cation better than vice versa. Thus, the selective pyrrole ring protonation at low temperature (—80 C) is most likely a kinetic result leading to the thermodynamically nonequilibrium state with the predominance of pyrrolium ions. 

The evolution of thermodynamically nonequilibrium systems (including the systems with complex stepwise chemical transformations, among them catalytic and biological reactions) occurs with respective changes in thermo dynamic parameters of the whole system or of its parts. Hence, nonequilib rium states are inherent in the nonequilibrium systems (both open and closed), while the relevant parameters and features of those states can be functions of time and/or space. For example, when a system is temperature and pressure isotropic, the Gibbs potential, G, of the entire system may be a function of not only temperature (T) and pressure (p) but also of time (t) ... 

Thus, in the course of any catalytic transformation, the active com ponent exists necessarily in a thermodynamically nonequilibrium state (stationary or other) that is governed by thermodynamic forces that exist in the nonequilibrium system—that is, by current affinities of aU of the involved elementary chemical transformations. 

This covers most hypersonic flow regimes with high thermodynamic nonequilibrium. The statistical uncertainties of the rate constants were below 5% for all cases run. It is found that under reentry flow conditions most of the endothermicity is derived from the N2-O relative translational energy and the NO molecules are formed vibrationally and rotationally very excited. Also, the QCT thermal rate constants showed good agreement with the available experimental data. ... 

A construction makes use of only an insignificant fraction of the Gibbs canonical ensemble and hence is essentially out of equilibrium. This is different from thermodynamic nonequilibrium—it arises because the system is being investigated at time scales much shorter than those required for true statistical equilbrium. Such systems exhibit broken ergodicity [68], as epitomized by a cup of coffee in a closed room to which cream is added and then stirred. The cream and coffee equilibrate within a few seconds (during which vast amounts of microinformation are generated within the whorled patterns) the cup attains room temperature within tens of minutes and days may be required for the water in the cup to saturate the air in the room. 

Data on the fractal forms of macromolecules, the existence of which is predetermined by thermodynamic nonequilibrium and by the presence of deterministic order, are considered. The limitations of the concept of polymer fractal (macromolecular coil), of the Vilgis concept and of the possibility of modelling in terms of the percolation theory and diffusion-limited irreversible aggregation are discussed. It is noted that not only macromolecular coils but also the segments of macromolecules between topological fixing points (crosslinks, entanglements) are stochastic fractals this is confirmed by the model of structure formation in a network polymer. 

Yet another important property of fractals which distinguishes them from traditional Euclidean objects is that at least three dimensions have to be determined, namely, d, the dimension of the enveloping Euclidean space, df, the fractal (Hausdorff) dimension, and d the spectral (fraction) dimension, which characterises the object connectivity. [For Euclidean spaces, d = d = d this allows Euclidean objects to be regarded as a specific ( degenerate ) case of fractal objects. Below we shall repeatedly encounter this statement] [27]. This means that two fractal dimensions, d( and d are needed to describe the structure of a fractal object (for example, a polymer) even when the d value is fixed. This situation corresponds to the statement of non-equilibrium thermodynamics according to which at least two parameters of order are required to describe thermodynamically nonequilibrium solids (polymers), for which the Prigogine-Defay criterion is not met [28, 29]. 

Thus, the density of chemical crosslinking points cannot serve as an index for the cormectivity of the macromolecular skeleton of network polymers. This makes it impossible to use to characterise the structure of network polymers in a computer simulation, which follows from the results presented previously. The d value, which provides determination of elastic properties, may serve as a suitable parameter. However, to estimate other properties, one more parameter is required, which would characterise the degree of thermodynamic nonequilibrium of the structures of vitreous polymers. This role can be played by dfOr the density of the cluster network of physical entanglements [48], or by the proportion of clusters (p [140] For instance, the necessity to take into account d, V i or [Pg.334]

We have illustrated the model predictions by evaluating two-phase ammonia clouds released in dry and moist air. The numerical test cases are identical to those in Kukkonen et al. (1993), which presents a comparison of the model AERCLOUD and the thermodynamical submodel of the heavy cloud dispersion program DRIFT (Webber et al., 1992). DRIFT embodies the homogeneous equilibrium model, while AERCLOUD allows also for thermodynamic nonequilibrium effects. Both models will cope with ammonia interactions with moist air as well as with the simpler dry air problem. 

The thermodynamical nonequilibrium effects in a two-phase cloud have two essential consequences (1) the thermodynamical behavior of the mixture is different, in particular the temperature and density evolution, and (2) the deposition of contaminant liquid may cause... 

Nucleation is the process of initiation of a phase change by the provision of points of thermodynamic nonequilibrium the points are provided by seeding , i.e. the introduction of finely-dispersed nucleating agents. The process has become of great interest to the ceramist since devitrified glass (q.v.) became a commercial product. 

The important argument in favor of fractal approach application is the usage of two order parameter values, which are necessary for correct description of polymer mediums structure and properties features. As it is known, solid phase polymers are thermodynamically nonequilibrium mediums, for which Prigogine-Defay criterion is not fulfilled, and therefore, two order parameters are required, as a minimum, for their structure description. In its turn, one order parameter is required for Euclidean object characterization (its Euclidean dimension d). In general case three parameters (dimensions) are necessary for fractal object correct description dimension of Euclidean space d, fractal (Hausdorff) object dimension d and its spectral (fraction)... 

There are two main physical reasons, which define intercommunication of fractal essence and local order for solid-phase pol miers the thermodynamical nonequilibrium and dimensional periodicity of their structure. In Ref. [9], the simple relationship was obtained between thermod5mamical nonequilibrium characteristic - Gibbs function change at self-assembly (cluster structure formation of pol miers AG - and clusters relative fraction (p jin the form ... 

Similar linear dependences for SP - OPD with various were obtained in Ref. [7] and they testify to molecular mobility level reduction at decrease and extrapolate to various (nonintegral) values at = 1.0. The comparison of these data with the Eq. (1.5) appreciation shows, that reduction is due to local order level enhancement and the condition = 1.0 is realized at values, differing from 2.0 (as it was supposed earlier in Ref [23]). This is defined by pol5miers sfructure quasiequilibrium state achievement, which can be described as follows [24]. Actually, tendency of thermodynamically nonequilibrium solid body, which is a glassy polymer, to equilibrium state is classified within the fimneworks of cluster model as local order level enhancement or (p j increase [24-26], However, this tendency is balanced by entropic essence straightening and tauting effect of polymeric medium macromolecules, that makes impossible the condition (p j= 1.0 attainment. At fully tauted macromolecular chains = 1.0)

polymer structure achieves its quasiequilibrium state at d various values depending on copolymer type, that is defined by their macromolecules different flexibility, characterized by parameter C. ... 

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