Estimation of Melting Points

Estimation of Melting Points As indicated above, the development of structure-rm relationships is not as straightforward as it is for other properties. In the following sections we discuss briefly the estimation of Tm for homologous series and for other sets of structurally related compounds. A GCM designed to estimate Tm for more diverse sets of compounds is introduced. Although not very accurate, the GCM approach may be applicable for the following tasks  

Both cases are illustrated in Section 10.4 with a variety of examples. 

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It is remarkable that only two descriptors were needed in this method. However, this equation is mostly only of historical interest as it is of little use in modem dmg and combinatorial library design because it requires a knowledge of the compound s experimental melting point which is not available for virtual compounds. Several methods exist for estimating log P [1-14], but only a few inroads have been made into the estimation of melting points. The melting point is a key index of the cohesive interactions in the solid and is still difficult to estimate. 

For the estimation of melting point (K), Joback and Reid give the following equation ... 

Molecular fragments and Their Group Contribution Values for the Estimation of Melting Point (K). 

Tsakinikas, P. and S. Yalkowsky. 1988. Estimation of Melting Point of Flexible Molecules Aliphatic Hydrocarbons. Toxicological and Environmental Chemistry. 17, 19-33. 

Carrera G, Aires-de-Sousa J (2005) Estimation of melting points of pyridinium bromide ionic liquids with decision trees and neural networks. Green Chem 7 20-27... 

Chickos, J.S., Nichols, G. and Ruelle, P. (2002) The estimation of melting points and fusion enthalpies using experimental solubilities, estimated total phase change entropies, and mobile order and disorder theory. /. Chem. Irf. Comput. Sci, 42, 368-374. 

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

At its melting point the heat of fusion for aluminum is 10.04 kJ/mol, and the entropy of fusion is 9.50 J/mol-K. Estimate the melting point of aluminum. 

Combine your information to calculate the thermal diffusivity at 350°C. How does this compare to the value obtained from the plot Can you estimate the melting point of this polycarbonate from these plots ... 

Calculation of the ratio b]d yielded 408° K in very good agreement with the estimated maximum melting point of polyethylene, 409° K. 

Figure 2.45 Extrapolation of melting-point depression data to estimate the melting point of a 0g...

This chapter deals primarily with practical applications of theoretical principles to the estimation of melting enthalpy and entropy in order to estimate melting point. As necessitated by the situations described above, the methods are based entirely upon molecular structure. 

Table 1.1 shows that much of the work has been done on hydrocarbons and, in particular, homologous series. As a result, several very accurate methods are available for estimating the melting points of normal alkanes. For example, Broadhurst (1962) reports errors of less than 0.5°C for paraffins with chain lengths between 44 and 100 carbons. Similarly, Hanson... 

This relationship identifies enthalpy and entropy as the thermodynamic properties that determine the value of the melting point. Because each of these properties shows a different dependence upon structure, attempts to estimate the melting point of a wide variety of organic compounds have been largely unsuccessful. The next two sections seek to correlate AHm and ASm with aspects of molecular structure and present methods for their estimation. 

Hanson, M. and D. Rouvray. 1987. The Use of Topological Indices to Estimate the Melting Points of Organic Molecules. In Graph Theory and Topology in Chemistry, King, R., Rouvray, D., Eds. Elsevier, Amsterdam, 201. 

By reference to Figure 15-8, estimate the melting points and boiling points that hydrogen fluoride, water, and ammonia would be expected to have if these substances did not form hydrogen bonds. What would you expect the relative density of ice and water to be if hydrogen bonds were not formed ... 

The element technetium (Tc) is not found in nature but has been produced artificially through nuclear reactions. Use the data for several neighboring elements in the table below to estimate the melting point, boiling point, and density of technetium. Compare your predictions with the observed values in Appendix F. 

The density-temperature phase diagram for SPC/E water at the pressure of 1 bar has been reported by us earlier [40, 41], The famous density maximum of water, located experimentally at 277 K, is found for this model at the temperature 240 K. Our simulations of two-phase ice/water coexistence for SPC/E model resulted in the melting temperature, which is approximately 50 K below the estimated value of 279 K from the free energy study of melting point for SPC/E water by Arbuckle and Clancy [42], A similar tendency was pointed out by Morris [43], when the melting point from two-phase coexistence simu-... 

Estimate the melting point and heat of fusion of stannic iodide. (The experimental values are 143.5° C and approximately 3,800 cal. mole b)... 

Two important studies have predicted the melting point of sohd materials from first-principles calculations. Sugino and Car (1995) used Car-Parrinello molecular dynamics to estimate the melting point of silicon from first... 

Within a periodic group the physical properties vary more predictably, especially if the elements are in the same physical state. For example, the melting points of argon and xenon are 189.2°C and 111.9°C, respectively. We can estimate the melting point of the intermediate element krypton by taking the average of these two values as follows ... 

Consider the halogens chlorine, bromine, and iodine. The melting point and boiling point of chlorine are — 101.0°C and —34.6°C while those of iodine are 113.5°C and 184.4°C, respectively. Thus chlorine is a gas and iodine is a solid under room conditions. Estimate the melting point and boiling point of bromine. Compare your values with those from a handbook of chemistry. 

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