Heat-of-fusion rule

The heat of fusion rule of Burger and Ramberger can be used to distinguish each case [9,15] ... 

Table 1 Heat of Fusion Rule of Burger and Ramberger ...

Another empirical rule is the Heat of Fusion Rule, which states that if the higher melting form has a lower heat of fusion relative to the lower melting form, then the two forms bear an enantiotropic relationship. Less well obeyed is the Density Rule, which states that the most dense form will be the most stable at absolute zero. Strictly speaking, the Density Rule is only properly applied to polymorphs of molecular solids where intramolecular hydrogen bonding is not a significant factor. 

Heat of fusion rule If the higher-melting form has the lower heat of fusion, the two forms are usually enantiotropic otherwise they are monotropic. 

To help decide whether two polymorphs are enantiotropes or monotropes. Burger and Ramberger developed four thermodynamic rules [14]. The application of these rules was extended by Yu [15]. The most useful and applicable of the thermodynamic rules of Burger and Ramberger are the heat of transition rule and the heat of fusion rule. Figure 11, which includes the liquid phase as well as the two polymorphs, illustrates the use of these rules. The heat of fusion rule states that, if an endothermic polymorphic transition is observed, the two forms are enantiotropes. Conversely, if an exothermic polymorphic transition is observed, the two forms are monotropes. 

The above conditions, that are implicit in the thermodynamic rules, are summarized in Table 4. The last two rules in Table 4, the infrared rules, and the density rule, were found by Burger and Ramberger [14] to be significantly less reliable than the heat of transition rule and the heat of fusion rule and are therefore not discussed here. 

A// (monotropy Vi. enantiotropy via heat of fusion rule) T, by extrapolation... 

Compton rule phys chem An empirical law stating that the heat of fusion of an element times its atomic weight divided by its melting point in degrees Kelvin equals approximately 2. kam-ton, rul ... 

Of particular interest are changes in enthalpy, such as the heat of fusion, Af us//, and the heat of vaporization, Avap//, as well as the corresponding changes of entropy. A useful observation, discussed in Chapter 3, is Trouton s rule, that entropies of vaporization are often 85 J K mol. 

Application of this method to the heat content of homologous series of organic compounds in the liquid state would result in a non-linear course of the heat content as a function of the number of methylene groups. This is exactly what is found experimentally for the heat of fusion as a function of the number of methylene groups. A second order additivity rule, however, is too complicated for practical application if a large number of structural groups is involved. It would require the compilation of innumerable group pair contributions. 

The relation between melting point and structure is therefore fairly complicated. In many cases both causes counteract each other where we observe a low (high) heat of fusion and at the same time a low (high) entropy of fusion ASf — AHfj T (Table 35). As the crystal structure is nearly always different for isomeric substances, it is not surprising that no exact general rules can be given for the melting point of a substance. 

In Chapter 8, along with tables of measured thermophysical data, we saw some fairly simple techniques for estimating these values when experimental results are not available. Among these techniques were Kopp s Rule for the heat capacity of both liquids and solids, and Trouton s ratio for latent heats of fusion and vaporization, along with Kistiakowski s temperature correction for the latter. 

Estimate the heat capacity of a liquid or solid species using Kopp s rule. Estimate the heat of fusion and heat of vaporization of a species using correlations in Section 8.4b. 

As it follows from Table 4.1, the estimated heats of fusion of Na3pS04 and K3FSO4 are lower than the measured values and the error in the estimation lies within the range 7-13%. This difference is probably due to the limited validity of the Neumann-Kopp s rule, which in most cases, yield higher values of heat capacities of crystalline AB compounds in Eq. (4.19). 

The liquid state in the reaction zone causes, as a rule, little concern from the viewpoint of heat loss, since the latent heat of fusion is small. It can, however, cause a form of convective heat loss that may have unfortunate consequences. In a flare that burns with the flame upward, such as a railroad fusee, a molten slag is sometimes normally permitted to drop off. By faulty formulation, an excessive liquefaction may take place so that not only the burned-out slag but the molten material in the burning zone itself may slide off and prematurely end the burning of the flare. Similar conditions may occur with flame-down burning candles under violent motion. 

Once these empirical rules have been established, it is possible to link the melting temperatures of polymers to chain flexibility, interactions (cohesive energy densities), internal heats of fusion, and the possible presence of mesophases (see Fig. 2.103). Such analyses are of importance for the design of new polymers and of changes in existing polymers when there is a need to alter thermal stabiUty. 

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