Thermodynamics of Fusion

In the previous sections it was shown that the formation of lamellae with folded chains was essentially a kinetically controlled phenomenon. This section treats the free energy of polymer crystallization and melting point depression. 

The free energy of fusion, AG/, is given by the usual equation, 

Thus a smaller entropy or a larger enthalpy term raises Tf. Thus, the relative changes in AHf and ASf in going from the amorphous state to the crystaUine state determine the melting temperature of the polymer. 

The melting point depression in crystalline substances from the pure state Tf is given by the general equation (143) 

The thermodynamics of melting in polymers was developed by Flory and his co-workers (145-147). To a first approximation, the melting point depression depends on the mole fraction of impurity, Xb, the mole fraction of crys-talUzable polymer being Xa. Substituting Xa for a in equation (6.38), 

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Thermodynamics of fusion of poly-p-propiolactone and poly-e-caprolactone. Comparative analysis of the melting of aliphatic polylactone and polyester chains, Eur. Polym. J.. 8, 449-463, 1972. 

Lifshitz, I.M., 1973. On the statistical thermodynamics of fusion of long heteropolymer chains. Sov. Phys.-JETP 65 1100-1110. 

Thermodynamic Properties. The thermodynamic melting point for pure crystalline isotactic polypropylene obtained by the extrapolation of melting data for isothermally crystallized polymer is 185°C (35). Under normal thermal analysis conditions, commercial homopolymers have melting points in the range of 160—165°C. The heat of fusion of isotactic polypropylene has been reported as 88 J/g (21 cal/g) (36). The value of 165 18 J/g has been reported for a 100% crystalline sample (37). Heats of crystallization have been determined to be in the range of 87—92 J/g (38). 

A study on the thermodynamic properties of the three SO phases is given in Reference 30. Table 1 presents a summary of the thermodynamic properties of pure sulfur trioxide. A signiftcandy lower value has been reported for the heat of fusion of y-SO, 24.05 kj /kg (5.75 kcal/kg) (41) than that in Table 1, as have slightly different critical temperature, pressure, and density values (32). 

Thermodynamic and physical properties of water vapor, Hquid water, and ice I are given ia Tables 3—5. The extremely high heat of vaporization, relatively low heat of fusion, and the unusual values of the other thermodynamic properties, including melting poiat, boiling poiat, and heat capacity, can be explained by the presence of hydrogen bonding (2,7). 

The thermodynamic properties of thiophene,2-methylthiophene, ° and 3-methylthiophene have been computed from careful measurements of the heat capacity of the solid, liquid, and vapor states, the heat of fusion, the heat of vaporization, and the heat of combustion. From the heat of combustion of thiophene and from thermochemical bond energies, the resonance energy of thiophene has been re-estimated to be only 20 kcal/mole. 

Continuous transition of state is possible only between isotropic states it may thus occur between amorphous glass (i.e., supercooled liquid of great viscosity) and liquid ( sealing-wax type of fusion ), or between liquid and vapour, but probably never between anisotropic forms, or between these and isotropic states. This conclusion, derived from purely thermodynamic considerations, is also supported by molecular theory. 

Many enveloped viruses share a common mechanism of fusion, mediated by a virus-encoded glycoprotein that contains heptad repeats in its extraceUnlar domain. Dnring the fnsion process, these domains rearrange to form highly structured and thermodynamically stable coiled-coils. Viruses encoding fusion proteins that have these domains inclnde members of the paramyxovirus family (e.g., respiratory syncytial virus, metapneumovirus, and measles virus), ebola virus, influenza, and members of the retroviridae (e.g., human T cell lenkemia virus type-1 and human immunodeficiency virus type-1, HlV-1). Peptide inhibitors of fusion that disrupt the... 

Percolation in microemulsions and concomitant microstructural changes are the focal points of this review. A complete understanding of percolation phenomena in reverse microemulsions will require an understanding of droplet interactions and the associated thermodynamics of droplet fusion, fission, aggregation to form clusters of varying fractal... 

Thermodynamic measurements such as heat of solution from solution calorimetry [11,12], heat of fusion from differential scanning calorimetry (DSC) [12], and entropy of processing, ASp [12]... 

Cimetidine is known to crystallize in 5 polymorphic forms and 3 hydrated forms [11]. Solubility data is presented in this reference for Forms A, B and C. Form E was not known at the start of the study in reference [11] and Form D could not be crystallized, suggesting that it is less stable than the other forms. This is confirmed by melting point data which indicates the order of thermodynamic stability close to the melting temperature isEmelting point data for the evaluated forms are presented in Table 3. Form A is the commercially available Form and the desired product for this case study. 

Gross, K. D. Williamson, G. Waddington and H. M. Huffman Spiropentane Heat Capacity, Heats of Fusion and Vaporization, Vapor Pressure, Entropy and Thermodynamic Functions. J. Amer. chem. Soc. 72, 4664 (1950). 

Flory, P. J. (1949). Thermodynamics of crystallization in high polymers. IV. A theory of crystalline states and fusion in polymers, copolymers, and their mixtures with diluents. 

Cpra/T VS. T) thereafter. Obtain A// of fusion from Thermodynamics Research Center tables. 

Goursot, P., Girdhar, H.L., and Westrum,E.F.,]r. Thermodynamics of polynuclear aromatic molecnles. III. Heat capacities and enthalpies of fusion of anthracene, J. Phys. Chem., 74 (12) 2538-2541, 1970. 

Pitzer, K.S. and Scott, D.W. Tire thermodynamics of branched-chain paraffins. The heat capacity, heat of fusion and vaporization, and entropy of 2,3,4-trimethylpentane, J. Am. Chem. Soc, 63(9) 2419-2422,1941. 

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