Proximity to equilibrium

The vividness of our world does not rely on processes that are characterized by linear force-flux relations, rather they rely on the nonlinearity of chemical processes. Let us recapitulate some results for proximity to equilibrium (see also Section VI.2.H.) In equilibrium the entropy production (n) is zero. Out of equilibrium, II = T<5 S/I8f > 0 according to the second law of thermodynamics. In a perturbed system the entropy production decreases while we reestablish equilibrium (II < 0), (Fig. 72). For the cases of interest, the entropy production can be written as a product of fluxes and corresponding forces (see Eq. 108). If some of the external forces are kept constant, equilibrium cannot be achieved, only a steady state occurs. In the linear regime this steady state corresponds to a minimum of entropy production (but nonzero). Again this steady state is stable, since any perturbation corresponds to a higher II-value (<5TI > 0) and n < 0.183 The linear concentration profile in a steady state of a diffusion experiment (described in previous sections) may serve as an example. With... 

The term d jdt is of course the reaction velocity v. The reaction velocity is zero if A = 0, since the system is then in equilibrium. In close proximity to equilibrium we may assume that the velocity is proportional to the affinity... 

The shift of the position of the maximum to lower temperatures with increasing plasticizer content is consistent with the interpretation given above. The smaller decrease at temperatures below the maxima with increasing plasticizer content may reflect increasing proximity to equilibrium, since all samples were prepared by holding at 150°C. for 3 hours. 

In the interval of potentials between equilibrium and about —800 mV, the protective film does not form spontaneously. In this condition, called activity, steel can theoretically corrode. Nevertheless, given the proximity to equilibrium conditions, the rate of the anodic process is still negligible. To emphasize the fact that these conditions of activity are characterized by low corrosion rates because of this proximity to equihbrium, they are also called quasi-immunity conditions. 

These common features suggest that self-assembling process is actually a complex yet organized process mediated by many factors, which in turn should be carefully considered in the manufacture of self-assembled architectures. Specifically, these crucial factors include (but are not limited to) molecular (or component) mobility, proximity to equilibrium, and anisotropy [5]. Mobility refers to the ability of molecules or components to change position and orientation, which is usually... 

If the rate of electron transfer is slow with respect to the time scale of the experiment, then non-Nernstian concentrations will exist at the electrode surface. The qualitative effect is to shift the peak wave to more negative potentials in the case of reduction and to more positive potentials in the case of an oxidation. The proximity to equilibrium is termed reversibility. ... 

Note that this also implies that the proportionality of flux and chemical potential gradient (see Eq. (6.8)) — even though applicable for higher concentrations — is restricted to the proximity to equilibrium (see Eq. (6.10)). 

Fig. 6.74 The stability of stationary states. Entropy production close to equilibrium and distant from equilibrium . In the equilibrium case the statement 11 > 0 is trivial, since II caumot fall below zero. The fact that 60. is positive in proximity to equilibrium is proven by footnote 205. Ear from equilibrium, 5n can become negative, as described in the text.

A system of interest may be macroscopically homogeneous or inliomogeneous. The inliomogeneity may arise on account of interfaces between coexisting phases in a system or due to the system s finite size and proximity to its external surface. Near the surfaces and interfaces, the system s translational synnnetry is broken this has important consequences. The spatial structure of an inliomogeneous system is its average equilibrium property and has to be incorporated in the overall theoretical stnicture, in order to study spatio-temporal correlations due to themial fluctuations around an inliomogeneous spatial profile. This is also illustrated in section A3.3.2. 

The interfacial transfer kinetics were then investigated by perturbing the equilibrium, through the depletion of Cu + in the aqueous phase, by reduction to Cu at an UME located in close proximity to the aqueous-organic interface. This process promoted the transfer of Cu into the aqueous phase, via the transport and decomplexation of the cupric ion-oxime complex, resulting in an enhanced steady-state current at the UME. Approach curve measurements of i/i oo) vs. d allowed the kinetics of the transfer process to be determined unambiguously [9,18]. 

The phase space of the poly(ethylene-aft-propylene)-fr-poly(d, (-lactide) (PEP-fo-PLA) system was recently explored by Schmidt and Hillmyer [63]. All equilibrium symmetries I, C, S, and G were observed. The G morphology, however, existed in only a small region between the L and C in close proximity to the ODT (Fig. 12). 

Two theories exist for the lack of isotope fractionation in chondmles. Both rely on the concept of quasi-statical (i.e., almost equilibrium) exchange of isotopes between liquid and gas followed by permanent loss of rock-forming elements to the escaping gas phase. One model (Alexander 2003) implies that the chondmles formed in such close proximity to one... 

The removal of hydroxyl groups in proximity to the basic center may increase the basicity of imino sugars, whereas the introduction of strongly electronegative substituents, in particular fluorine atoms, may cause the free base to prevail, or at least be present in a comparably higher proportion in the equilibrium at the same pH value. 

For an outer-sphere reaction there are three factors which play a role in determining the rate of electron transfer. The first is the approach of the reactants to be in sufficiently close proximity to create an electronic interaction which provides a basis for the delocalization of the exchanging electron. The second is a barrier to electron transfer that is created by the equilibrium structural differences between reactants and products. The third is an additional barrier that is created in the surrounding solvent by the change in charge distribution associated with the electron transfer act. 

This difference in behavior must reflect the difference in energetic barrier in the different cases, perhaps due to differences in the degree of thickening required in the transition between the different forms, the proximity to the equilibrium melting point and also perhaps to differences in the initial lamellar thickness. 

At one time Taylor considered7 that if adsorption on a solid surface would catalyse the interconversion of ortho and para hydrogen, it was an indication that chemisorption with dissociation into atoms occurred the temperature at which such interconversion took place would (if this were true) have been some indication of the activation energy for chemisorption. No doubt chemisorption does promote this spin isomerization but it is now known that adsorption of the van der Waals type can result in speedy attainment of the equilibrium mixture of ortho and para hydrogen, provided that the surfaces are of some paramagnetic substance the close proximity to a paramagnetic surface can catalyse the interconversion,8 without dissociation of the adsorbed molecules. 

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