Thermodynamics melting temperature

Consequently, the thermodynamic melting temperature Tm can be obtained by extrapolation from a plot of the melting temperature Tm against the number of monomeric units per lamella, that is, the lamellar height (Figure 10-13). 

Fig. 2. Thermodynamic stability of a hypothetical dimeric protein with T° = 349 K, = 126 kcal/mol, and ACp = 2138 kcal/(mol K). The dashed line represents the intrinsic free energy AG(H20) as it would have been obtained experimentally. The dotted line shows the function -q [cf. Eq. (10)] corresponding to different protein concentrations as approximately indicated by the concentration scale on the extreme right. If q is added to AC(H20), then AGeft (solid curves) is obtained as own by the arrows. The arrows also indicate the thermodynamic melting temperature Ta corresponding to the total protein concentration Ct expressed in dimer equivalents.

For most polymers the value of 7 was found to be about 2. Consequently, the plot of melting temperature against their crystallization temperature is a straight line. To find the thermodynamic melting temperature T° , an intersection of this line with the line T = has to be drawn. 

Despite the fact that the melting of a semi-crystalline polymer occurs over a finite temperature range, even under equilibrium conditions, as approaches unity dk /dT 0. Therefore, the last traces of crystallinity will appear at a well-defined temperature. Above this temperature dk /dT = 0. Thus the thermodynamic melting temperature can be defined. At Ae = 1, T = Tm,e so that... 

The diffuse nature of the fusion curves given in Fig. 5.1 does not appear to be typical of a first-order phase transition. However, these melting curves are natural consequences of the constitution of random copolymers and the requirement that the B units are restricted to the noncrystalline phase. Theoretically, at the melting temperature Wc and all its derivatives vanish. Hence a true discontinuity exists at this temperature. There is then a true thermodynamic melting temperature that is representative of the disappearance of crystallites composed of very long sequences. Its detection by experimental methods may very well be difficult. 

The onset temperature of the pre-ignition reaction, TpiR, is usually independent of the melting or decomposition temperature of the oxidizer but related to the thermodynamic melting temperature, Tmeit of the metal ... 

While the characterization of the crystallization rates as a function of temperature is important in the evaluation of many processing characteristics, the measurement of the thermodynamic melting temperature is currently very important in the evaluation of the crystallization model. 

Sorrentino et al. [86], using a protocol similar to that proposed by Ho et al. [84], determined the thermodynamic melting temperature for both a and P phases from the Hoffman-Weeks extrapolation. From such a linear extrapolation, the equilibrium melting temperature of the a form was determined as 272 °C, whereas the equilibrium melting temperature of the p form was determined as 282 °C (Table 9.2). 

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