Hysteresis thermodynamic

Yablonskh, G.S., Lazman, M.Z., 1996. New correlations to analyze isothermal critical phenomena in heterogeneous catalysis reactions ( Critical simplification , hysteresis thermodynamics ). React. Kinet. Catal. Lett. 

The question is not trivial such agreement is not assured in the case of systems showing hysteresis (see Section XVII-16), and it has been difficult to affirm it on rigorous thermodynamic grounds in the case of a heterogeneous surface. 

In calculations of pore size from the Type IV isotherm by use of the Kelvin equation, the region of the isotherm involved is the hysteresis loop, since it is here that capillary condensation is occurring. Consequently there are two values of relative pressure for a given uptake, and the question presents itself as to what is the significance of each of the two values of r which would result from insertion of the two different values of relative pressure into Equation (3.20). Any answer to this question calls for a discussion of the origin of hysteresis, and this must be based on actual models of pore shape, since a purely thermodynamic approach cannot account for two positions of apparent equilibrium. 

Perhaps the most serious limitation, however, arises from the fact neither branch of the hysteresis loop corresponds to thermodynamic reversibility. The value of the integral J Va(p°jp)dn = /, say, differs considerably for the two branches of the loop. In fact... 

When studying heterogeneous equilibria involving clathrates, one is faced with peculiar difficulties owing to the hysteresis effects mentioned in the introduction the solute in a clathrate crystal of hydroquinone, for instance, will not come to thermodynamic equilibrium with the vapor in which it is placed. Consequently it is impossible, or at least very difficult, to measure the equilibrium vapor pressure of the solute in a clathrate by placing some crystals in a tensometer (cf. the experiments of Wynne-Jones and Anderson,58 and those of Leech and Richards reported by Powell33). 

The predicted solids based on thermodynamic measurements and models derived from them depend strongly on chemical composition. However, small aqueous aerosols remain meta-stable with decreasing RH until reaching a crystallization relative humidity(CRH). In contrast, solid aerosols t e up water at the thermodynamically favored deliquescence relative humidity(DRH). This hysteresis causes a dependence of aerosol phase on RH history. 

First-order phase transitions exhibit hysteresis, i.e. the transition takes place some time after the temperature or pressure change giving rise to it. How fast the transformation proceeds also depends on the formation or presence of sites of nucleation. The phase transition can proceed at an extremely slow rate. For this reason many thermodynamically unstable modifications are well known and can be studied in conditions under which they should already have been transformed. 

These assumptions have been expanded upon (Shah and Capps, 1968 Lucassen-Reynders, 1973 Rakshit and Zografi, 1980), especially in regard to the application of the ideal mixing relationship in gaseous films (Pagano and Gershfeld, 1972). It has been pointed out that water may contribute to the energetics of film compression if the molecular structures of the surfactants are sufficiently different (Lucassen-Reynders, 1973). It must be noted that this treatment assumes that the compression process is reversible and the monolayer is truly stable thermodynamically. It must therefore be applied with considerable reservation in view of the hysteresis that is often found for II j A isotherms. 

Hysteresis was generally observed in the compression-expansion cycles of the force-area isotherms, indicating that the timescale for relaxation of the fully compressed film back to its expanded state was slower than the movement of the barrier of the Langmuir trough. Our studies, like many others, imply that monolayers are metastable and that reversible thermodynamics can only be applied to their analysis with caution. 

The two main assumptions underlying the derivation of Eq. (5) are (1) thermodynamic equilibrium and (2) conditions of constant temperature and pressure. These assumptions, especially assumption number 1, however, are often violated in food systems. Most foods are nonequilibrium systems. The complex nature of food systems (i.e., multicomponent and multiphase) lends itself readily to conditions of nonequilibrium. Many food systems, such as baked products, are not in equilibrium because they experience various physical, chemical, and microbiological changes over time. Other food products, such as butter (a water-in-oil emulsion) and mayonnaise (an oil-in-water emulsion), are produced as nonequilibrium systems, stabilized by the use of emulsifying agents. Some food products violate the assumption of equilibrium because they exhibit hysteresis (the final c/w value is dependent on the path taken, e.g., desorption or adsorption) or delayed crystallization (i.e., lactose crystallization in ice cream and powdered milk). In the case of hysteresis, the final c/w value should be independent of the path taken and should only be dependent on temperature, pressure, and composition (i.e.,... 

The states produced by compression of monolayers are not necessarily at thermodynamic equilibrium, but may be metastable. In some cases, this is manifested clearly by different force-area curves being produced at different rates of compression. Slow reorganization of monolayer molecules is also apparent as hysteresis when films are repeatedly compressed and expanded. In chiral monolayers, the rates of molecular reorganization may be stereospecific as well as the thermodynamic behavior. 

The conspicuous separation between the cathodic and anodic peak potentials (hysteresis) was initially interpreted in terms of the simple theory of redox polymers as a kinetic effect of slow heterogeneous charge transfer the thermodynamic redox potential of the whole system was calculated from the mean value between and Epc [5, 7a, 86]. As a simplification it was assumed that the interaction between the charged oligomeric segments was negligible. These redox data correlate... 

Good, R.J, (1952). A thermodynamic derivation of Wenzel s modification of Young s equation contact angles Together with a theory of hysteresis. J. Am. Chem. Soc. 74, 5041-5042. 

The thermodynamics of Reaction 5.43 are comparable to those of other metallic, ionic and covalent hydrides. NaAlH4 exhibits typical low hysteresis and a two-plateau absorption and desorption isotherm. 

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