Entropy Transition”

The second or transition entropy is the weight of molecular configurations associated with a transition occurring in time x,... 

When the free enthalpy of reaction AG for the transformation of the structure of a compound to any other structure is positive, then this structure is thermodynamically stable. Since AG depends on the transition enthalpy AH and the transition entropy AS, and AH and AS in turn depend on pressure and temperature, a structure can be stable only within a certain range of pressures and temperatures. By variation of the pressure and/or the temperature, AG will eventually become negative relative to some other structure and a phase transition will occur. This may be a phase transition from a solid to another solid modification, or it may be a transition to another aggregate state. 

The transitional entropy and heat capacity are readily derived by differentiation with respect to temperature. For T < 2 rs... 

The transitional entropy, enthalpy and heat capacity for a tricritical transition is for T < Ttrs ... 

Differences in the Debye temperature, or in other words the vibrational character of the two phases, will modify the transitional entropy to some extent. Still, this entropy change is normally not large for transitions where the coordination number is preserved. 

Table 5.71 Transition energy terms for quartz and cristobalite A5 rans = molar apparent transition entropy at P = 1 bar [J/(mole X K)] = molar...

Note 1 The transitional entropy reflects the change in order, both orientational and translational, at the phase transition. 

We can also write the transition entropy ASa for this phase transition in terms of the associated latent heat AHa and transition temperature T(r as... 

No general rules about the entropy of transitions, as were found for liquid and plastic crystal transitions, can be set up for condis crystals. Two typical examples may illustrate this point. Polytetrafluoroethylene has a relatively small room-temperature transition-entropy on its change to the condis state and a larger transition entropy for final melting. Polyethylene has, in contrast, a higher condis crystal transition entropy than melting entropy (see Sect. 5.3.2). 

Figure 20 shows the phase diagram of polyethylene119). The existence range of the condis crystals increases with pressure and temperature. The enthalpy of the reasonably reversible, first order transition from the orthorhombic to the hexagonal condis phase of polyethylene is 3.71 kJ/mol at about 500 MPa pressure 121) which is about 80 % of the total heat of fusion. The entropy of disordering is 7.2 J/(K mol), which is more than the typical transition entropy of paraffins to their high temperature... 

Spin-crossover phase transition of a manganese(IU) complex [Mn(taa)] was studied by variable-temperature laser Raman spectroscopy and it was found that the vibrational contribution in the transition entropy is not dominant in contrast to the cases of ordinary iron spin-crossover systems. The discovery of a dynamic disorder in the HS phase by means of dielectric measurements provided an alternative entropy source to explain the thermally induced spin-crossover transition. This dynamic disorder was attributed to the reorienting distortion dipoles accompanying the E e Jahn-Teller effect in HS manganese(III) ions. 

Another possibility may be considered if merely a catalytic amount of acetic acid is present in the acetic anhydride medium, something to be expected in fact in any bottle of this reagent that has been opened to the atmosphere just once. If so, one would have the two molecules required for a push-pull tri-molecular process portrayed in VI that would yield the desired product by way of a concerted unraveling reaction. However, such trimolecular couplings require a very large transition entropy, making them unlikely to the point of being experimentally unknown. 

Heat capacities taken over the range 1.3°-20°K. 19) show an extremely narrow peak at 4.58 0.03 °K. at the EuSe ferromagnetic Curie temperature and one at 9.64 0.06 °K. in EuTe identified with the antiferromagnetic transition. The magnetic transition entropy increments are 4 and 3 cal./(mole °K.). 

The thermal and thermodynamic properties of LC polymers make it clear that the flexible spacer has a great influence on both the transition temperatures and transition entropies. This conclusion is again evidence of the vital part played by the flexible spacer in determining the organization and degree of order in the mesophase, and it also points out the critical interplay which occurs between the mesogenic unit and the flexible spacer. 

X-Ray diffraction and transition entropy data for the high-temperature phases of NH4 and K BF4 have been interpreted in terms of an approximate structure for these systems.265 In this the anions are distributed between two sets of statistically equivalent orientations in the skeleton of the positive ions, in a similar manner to that proposed for univalent metal perchlorates. 

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