Melting point theory

There is still considerable controversy over equilibrium melting point values for polyethylene (414 cf. 419 K) and poly(ethylene oxide) (342 cf. 348 K), which appears to be associated with various melting point theories and crystal structures used in their derivation. 

THEORY OF MELTING AND FREEZING 1,10. Melting point and vapour pressure. The melting point of a... 

The effect of different types of comonomers on varies. VDC—MA copolymers mote closely obey Flory s melting-point depression theory than do copolymers with VC or AN. Studies have shown that, for the copolymers of VDC with MA, Flory s theory needs modification to include both lamella thickness and surface free energy (69). The VDC—VC and VDC—AN copolymers typically have severe composition drift, therefore most of the comonomer units do not belong to crystallizing chains. Hence, they neither enter the crystal as defects nor cause lamellar thickness to decrease, so the depression of the melting temperature is less than expected. 

B.Bg (0.15 mol) of 4-phenylbenzophenoneare dissolved in 200 ml of ethanol and 3 g (0.075 mol) of sodium borohydride are added. After heating for 15 hours under reflux, and allowing to cool, the reaction mixture is hydrolyzed with water containing a little hydrochloric acid. The solid thereby produced is purified by recrystallization from ethanol, 36 g (B9% of theory) of (biphenyl-4-yl)-phenyl-carbinol [alternatively named as diphenyl-phenyl carblnol or a-(biphenyl-4-yl)benzylalcohol] of melting point 72°-73°C are obtained. 

B.7 g (56% of theory) of (blphenyl-4-yl)-imidazol-1-yl-phenylmethane [alternatively named es dIphenyI-ImidazolyI-(1)-phenyl-methane or as 1-(a-biphenyI-4-ylbenzyI) imidazole] of melting point 142°C are obtained. 

The reaction mixture was then dissolved in methylene chloride, the amine was removed by shaking with dilute hydrochloric acid, the reaction product was extracted from the organic phase by means of dilute sodium hydroxide solution and the alkaline solution was acidified with acetic acid to a pH value of 6. The 1 -hvdroxv-4-methyl-6-cvclohexvl-2-pyridone precipitated in crystalline form. It was filtered off with suction, washed with water and dried. The yield was 1.05 g (49% of theory) melting point 143°C. 

The free base can be liberated from the hydrochloride by extracting a butanol solution of the hydrochloride several times with sodium bicarbonate solution. After recrystallization from isopropanol/ligroin, the yield of D-(-f)-1-(3-hydroxyphenyl)-2-aminopropane amounts to 33.0 g, corresponding to 90.1 % of theory relative to the D-form. Melting point = 152°C to 154°C. 

The white precipitate which forms is filtered and dried at 80°C, yielding 45 g of chloro-mercuri acid (= 89% of the theory), MP 106° to 109°C (decomp.). This compound is finally obtained in analytically pure form and with a constant melting point by two recrystallizations from acetone-water giving a MP of 131° to 132°C with decomposition. 

Approximately 25 g (66.2% of theory) of a white crystalline substance were obtained. The melting point of the hydrochloride was 173°C to 174°C. 

After drying of the product on the filter 256 g of 2-p-aminobenzenesulfonamido-4,6-dimethyl-pyrimidine, melting point 196°C to 197°C, purity 99.5% are obtained. The output is 92% of the theory calculated with respect to the sodium acetylacetonate employed. 

The residue is dissolved in ether and the solution is washed with sodium chloride solution and then with a little sodium thiosulfate solution. The ethereal solution is dried over sodium sulfate and ether removed by distillation. A yield of 108 parts of 3,5,5-trimethyl-oxazolidine-2,4-dione is obtained having a melting point of 45° to 46°C with slight softening at 43°C. This represents a 75% theory yield on the ethyl o-hydroxy-iso-butyrate taken. The product may be further purified by dissolving the minimum quantity of dry ether and cooling to -10°C. The product so obtained melts sharply at 45.5° to 46.5°C, according to U.S. Patent 2,559,011. 

Lindemann <8> has made an interesting application of the new theory in the determination of the frequency of atomic vibration, r, from the melting-point. He assumes that at the melting-point, T the atoms perform vibrations of such amplitude that they mutually collide, and then transfer kinetic energy like the molecules of a gas. The mean kinetic energy of the atom will then increase by RT when the liquid is unpolymerised and the fusion occurs at constant volume this is the molecular heat of fusion. 

There is no generally acceptable comprehensive theory of melting. A feature of the fusion process, which is usually regarded as important in theoretical treatments of the subject, is the inability of a solid to superheat, and only a very small number of exceptions to this generalization are known [2], This almost universal onset of liquefaction immediately upon reaching the melting point is in sharp contrast with the reverse process since supercooling of the vast majority of liquids can be demonstrated under appropriate conditions. 

In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4] considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones—Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde s book [3]. 

The theory of melting continues to be the subject of recent publications, including consideration of vacancy concentrations near the melting point [8,9], lattice vibrations and expansions [8,10—12], Meanwhile, the phenomenon also continues to be the subject of experimental investigations Coker et al. [13], from studies of the fusion of tetra-n-amyl ammonium thiocyanate, identify the greatest structural change as that which... 

It is predicted that the dielectric constants of solid HC1, HBr, and HI at temperatures just below the melting points will be very high and dependent on the temperature, the values being given by Debye s theory of the orientation of electric dipole molecules while the low-temperature forms will have low dielectric constants nearly independent of the temperature. 

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