Thermodynamic transition

The thermodynamic transition between different forms as the above described is formally discontinuous. The difference between polymorphs is shown in general also by a different metrical description of the corresponding lattices. 

Microdomain stmcture is a consequence of microphase separation. It is associated with processability and performance of block copolymer as TPE, pressure sensitive adhesive, etc. The size of the domain decreases as temperature increases [184,185]. At processing temperature they are in a disordered state, melt viscosity becomes low with great advantage in processability. At service temperamre, they are in ordered state and the dispersed domain of plastic blocks acts as reinforcing filler for the matrix polymer [186]. This transition is a thermodynamic transition and is controlled by counterbalanced physical factors, e.g., energetics and entropy. 

Figure 11.7 shows schematically the resulting calculated variation of H with p for the NaCl-type and the CsCl-type phases of CaO. The NaCl-type structure, which is stable at low pressures, is the rock salt structure in which the Ca and O atoms are 6-coordinate. In the CsCl structure, stable at high pressures, both cation and anion are 8-coordinate. In the static limit where the entropy is set to zero, the thermodynamically most stable phase at any pressure is that with the lowest value of H at the thermodynamic transition pressure, ptrs, the enthalpies of the two phases are equal. For CaO the particular set of potentials used in Figure 11.7 indicates a transition pressure of 75 GPa between the NaCl-type and CsCl-type structures, which compares with experimental values in the range 60-70 GPa. 

W. PoefSnecker. A Theoretical Investigation of the Preconditions for Obtaining the True Thermodynamic Transition Temperature from Only One DSC Measurement. Thermochim. Acta 1993, 219, 325-332. 

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

See Transition-State Theory Transition-State Theory (Thermodynamics) Transition-State Theory in Solutions Entropy of Activation Volume of Activation... 

Paul Ehrenfest suggested a widely used classification of thermodynamic transition phenomena according to the lowest derivative of Gibbs free energy that exhibits a mathematical discontinuity at the phase transition. 

The question of whether the glassy solidification is a purely kinetic process or may be considered as a thermodynamic transition has been frequently discussed4,10. Gibbs and DiMarzio106 10 have assumed that there will be a second-order transition at a temperature, T2, at which the configurational entropy of the system becomes zero. Fewer conformations are available to the macromolecules at lower temperatures and as a result the molecular motion at T2 is slower. 

The glass transition is usually characterized as a second-order thermodynamic transition. It corresponds to a discontinuity on the first derivative of a thermodynamic function such as enthalpy (dH/dT) or volume (dV/dT) (A first-order thermodynamic transition, like melting, involves the discontinuity of a thermodynamic function such as FI or V). However, Tg cannot be considered as a true thermodynamic transition, because the glassy state is out of equilibrium. It may be better regarded as a boundary surface in a tridimensional space defined by temperature, time, and stress, separating the glassy and rubbery (or liquid) domains. 

It thus seems that the glass transition, even with infinitely low cooling rate, is not a real thermodynamic transition, but is only governed by kinetics, as a freezing-in phenomenon. 

There has been a wealth of activity based on the idea that glassy dynamics is due to some underlying thermodynamic transition [1-25], If a glass former shows a jump in some an appropriate order parameter without the evolution of latent heat, then such a system is said to exhibit a random first-order transition [94,95]. Models of this kind, which include the p-spin glasses [110], and the random energy model [111], do not have symmetry between states but do have quenched random long-range interactions and exhibit the so-called Kauzmann entropy crisis. 

In contradiction to the melting point, the glass-rubber transition temperature is not a thermodynamic transition point. It shows some resemblance, however, to a second order transition. For a second-order transition, the following relationships derived by Ehrenfest (1933) hold ... 

Ageing does not affect secondary thermodynamic transitions so the range of ageing falls between Tg and the first secondary transition Tp. 

Recently, microgel-stabilized, size-controlled metal nanoclusters have found promising applications in the field of catalysis. In particular, microgel systems can work as active carriers for the metal nanoparticles, which allows us to modulate the catalytic activity of nanoparticles by a thermodynamic transition that takes place within the carrier system [24, 69], The principle is shown in Fig. 8 Metallic... 

The characteristic temperature, T0, is usually located about 30-70°C below the experimentally measured Tg and in various thermodynamic theories it represents an equilibrium value. We will not discuss these theories, but the existence of such a thermodynamic transition remains in dispute, with some arguing that the T is purely a kinetic phenomenon. Certainly, the experimentally observed quantity is kinetic in character. One manifestation of this is the shift in T... 

If an endothermic phase change is observed at a particular temperature, the transition point hes below that temperature, and the two polymorphs are enantiotropically related. If an exothermic transition is observed, then there is no thermodynamic transition point below that transition temperature. This can occur when the two modifications are monotropicaUy related or when they are enantiotropically related and the thermodynamic transition point is higher than the measured transition temperature. 

Fig. 4.3 (See also colour plate section.) An enantiotropic phase transformation in 2,4,6-trinitro-5-fert-butyl-ra-xylene as observed on the hot stage microscope. Form 11 is stable at room temperature and the thermodynamic transition point is at 84 °C. (a) Room temperature stable Form 11, the coarse crystals at upper right embedded in aggregate of Form 1. (b) On heating Form n grows at the expense of Form 1. (c) At 84 °C the transformation can be halted, (d) Above 84 °C Form 1 is stable and has grown at the expense of Form 11. (From Kuhnert-Brandstatter 1971, with permission.)...

Although the glass transition is a kinetic phenomenon for any attainable cooling rate, it has been argued that a thermodynamic transition could, in principle, occur in the hypothetical limit of an infinitesimal cooling rate. This possibility follows from Kauzman s (1948) observation that the entropy of the equilibrium liquid, when extrapolated to low... 

To keep the liquid at metastable equilibrium while cooling it to T2 Tq, the cooling rate would have to be infinitely slow. It has been argued that in this hypothetical limit a thermodynamic transition of some kind, possibly second order, intervenes to prevent the excess entropy from becoming catastrophically negative. However, another possibility is that the true dependence of excess entropy on temperature deviates from the linear extrapolation to zero, and the excess entropy varies much more slowly with temperature near Tb than it does at higher temperatures. This latter possibility is found in some simple models of the glass transition discussed below. 

There is a third possibility. There could be a purely dynamic transition at or near To, in which ergodicity is broken, but all thermodynamic variables remain continuous, so that no thermodynamic transition occurs. This would mean that below a critical temperature in the vicinity of Tg, the system is kinetically prevented from exploring all microstates that are thermodynamically allowed, but gets permanently locked into a finite subset of these... 

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