Enthalpy of the transitions

Fig. 30. DSC traces showing the phase transition of the model membrane in its monomeric and polymeric form. Note the difference in the enthalpies of the transition monomer AH = 56 J/g, polymer AH = 26 J/g...

The result is shown in Figure 16.8. From these results, one can directly obtain the enthalpy of the transition. The procedure, like that for the analysis of the optical data, requires the estimation of a pre- and post-transitional baseline. For relatively short temperature intervals, the baselines are often assumed to be linear and are extrapolated to the mid-temperature as shown in Figure 16.8. The area under the curve in Figure 16.8 is the enthalpy of the transition. That is,... 

Figure 16.8 The excess heat capacity, C xcess = Cp (protein + buffer) - C/,(buffer), as a function of temperature, obtained from a differential scanning calorimeter. The shaded area is intergrated to yield the enthalpy of the transition. AtransCp is the difference in the baseline heat capacity at Tm.

According to the Curtin-Hammett principle, the ratio of the distribution between two products depends only on their rates offormation (Figure 9.1). If the two products are conformers, the energy barrier between the two states tends to be small and the ratio between the two products is an indicator of the free enthalpies of the transition states. The Curtin-Hammett principle can be applied when two conformations, tautomers, or isomers of a starting material are in rapid equilibrium compared to the rate of a reaction. In this case, the product ratio provides no information about which conformation, tautomer, or isomer was present in the starting material. 

Y(R Y P) in the case of a left-to-right process with the elementary reaction Y P as the rate-limiting stage. Cases a and b relate to different enthalpies of the transition state formation. 

SO that the integration under the area of the peak directly yields the enthalpy of the transition. 

The enthalpies of the transitions involving vaporization and sublimation are evaluated from equilibrum data by the second- and third-law methods. When reliable calorimetric measurements are available, the adopted enthalpy of transition is usually based on them. 

Since the rate of anti-syn isomerization has been proven to be very rapid in the ligand-free Ci2-allyInickel(II) cation [Ni( / , 7 -Ci2Hi9)], in this case the cis-trans selectivity depends solely on the difference in the free enthalpies of the transition states for the insertion reaction via the anti- or the syn-butenyl complex, independently of the concentrations of the two complexes in the anti-syn equilibrium, according to the Curtin-Hammett principle [26, 61]. 

Gospodinov and Bogdanov [83GOS/BOG] studied the behaviour of a-ZnSe03 on heating. A transition of the a form to the P form occurs at (600 5) K according to measurements with differential scanning calorimetry. The enthalpy of the transition observed was (ZnSeOs, a, 600 K) = (13.22 0.13) kJ-mol. Fusion occurs at (913 5) K... 

When cholesterol is present in dipalmitoylglycerophosphochoUne dispersions in water, the transition temperature between the gel and fluid crystalline phase is lowered and the enthalpy of the transition is reduced [31]. The transition is... 

Fig. 4. In-sample temperature change with elapsed time after the commencement of heating hydrated phosphatidylethanolamine (a, b) and water (c) samples contained in 1 mm diameter capillaries using a temperature-regulated coaxial air stream. The thermal lag in (a) and (b) is due to the diversion of heat away from raising sample temperature and into chain melting which accounts for most of the enthalpy of the transition at 66 °C. T-jumps were from 30 °C to 92 °C (a, c) and 125 °C (b). The inset shows the calculated temperature profile across the capillary diameter in (a) as a function of time in seconds following the T-jump. Adapted from Ref. [31]...

Figure 3 Effect of protein concentration on the heat denaturation of /3-lactoglobulin at pH 3.2 monitored by DSC. Qn apparent calorimetric enthalpy of the transition Tm apparent transition temperature AHvh Van t Hoff enthalpy of the transition. Heating rate 10°C min-1 heating from 20 to 120°C. (Data from Ref. 181.)...

Then from the linear Arrhenius plot of lnA q versus (1/7) the values of (nAH/R) and (nAS/R) are available. When the enthalpy of the transition is known from independent calorimetric measurements, then the average number of molecules per domain can be enumerated. 

The difference between the measured enthalpy contents gave the enthalpy of the transition of thorite to hnttonite, with the assnmption that the heat contents of the two isomorphs are the same. The experimental data (Table 2 of [2005MAZ/USH]) give a value of ((A. 120), 298.15 K) = (7.2 + 7.4) kJ-mol for the reaction ... 

Enthalpies formation of transition states structures are evaluated via the difference between the calculated value of the TS structure and the calculated value of the stable radical adduct(s) (adjacent product and reactant where both are a single species) at the corresponding levels of calculation. The calculation of the enthalpies of the transition state structures are all performed with DFT, which has been demonstrated in the previous chapters to be an accurate and reliable method. We have calculated one transition state structure with the G3 method because the DFT calculations failed. Zero-point energies (ZPVEs) and thermal corrections to 298.15 K are from DFT calculations. The calculation of AfH%g for the transition state structure has been... 

Since the chemical bond is the same in both cases, the enthalpy of the transition should be zero and hence the transformation is determined by entropy factors. The conversion of intermolecular complexes into intramolecular ones is a first-order reaction, the rate constants for which are 5.21 10 s at 303 K and 49.7-10 s at 333 K. The activation energy and the entropy are 63.3 kJ mol and 4.2 J mol K respectively. 

A+H is the difference of the transition state enthalpies of the backward and forward reactions (Fig. 4.1). A+H is the difference between the enthalpy of the transition state and the sum of the enthalpies of the reactants in the ground state. This is called activation enthalpy (Fig. 4.1kThe transition state AB is formed at a maximum energy. ArG is the free reaction enthalpy of the overall process or, in other words, the formation of (C + D). When comparing the right-hand term of Eq. (4.120) with the middle term of Eq. (4.123) and applying Eq. (4.90) to the total process, it follows that ... 

---