The Thermodynamics of Melting

The chain length—as do many mechanical properties of polymers, the glass transition temperature varies according to the empirical relation  

Example 6.3 Measurements such as those described above show that the addition of a small molecular weight chemical known as an external plasticizer (see Chapter 7) softens a polymer by reducing its glass transition temperature. Explain. 

Solution. The plasticizer molecules pry apart the polymer chains, in essence increasing the free volume available to the chains (although not tmly free, the small plasticizer molecules interfere with chain motions much less than would other chains). Also, by forming secondary bonds with the polymer chains themselves, type 1 and type 2 motions are easier. 

The glass transition temperatures for random copolymers vary monotonically with composition between those of the homopolymers. They can be approximated fairly well from knowledge of the Tg values of the homopolymers, Tgj and with the empirical relation  

The crystalline melting point Tm in polymers is a phase change similar to that observed in low molecular weight organic compounds, metals, and ceramics. 

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In this section, the upper temperature limit of the crystalline state is explored on the basis of experimental data on the thermodynamics of melting, extrapolated to equilibrium. The more common nonequilibrium melting will see its final discussion in Sects. 6.2 and 7.2. The other condensed states of macromolecules, the mesophases, glasses, and melts are treated in Sects. 5.5 and 5.6. Much less is known about them than about the crystals. 

This discussion of the thermodynamics of melting reveals a rather simple theory with good predictive capability for the melting parameters. The heat capacities are also well linked to the underlying molecular motion, and various quantitative baselines can be generated. Only with such quantitative information is it possible to analyse the common deviations from equilibrium. Section 2.2 will expand this discussion to non-equilibrium systems. 

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),... 

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). 

Thermodynamic efficiency is hurt by the large ATbetween the temperatures of melting and freezing. In an analogy to distillation, the high a comes at the expense of a big spread in reboiler and condenser temperature. Erom a theoretical standpoint, this penalty is smallest when freezing a high concentration (ca 90%) material. 

In many process design applications like polymerization and plasticization, specific knowledge of the thermodynamics of polymer systems can be very useful. For example, non-ideal solution behavior strongly governs the diffusion phenomena observed for polymer melts and concentrated solutions. Hence, accurate modeling of... 

Molten salt investigation methods can be divided into two classes thermodynamic and kinetic. In some cases, the analysis of melting diagrams and isotherms of physical-chemical properties such as density, surface tension, viscosity and electroconductivity enables the determination of the ionic composition of the melt. Direct investigation of the complex structure is performed using spectral methods [294]. 

In these formulas the letter X stands for the average copolymer composition, while of denotes the dispersion of the SCD quantitatively characterizing its width. The second of these statistical characteristics is extremely significant for the thermodynamics of the melt of a heteropolymer specimen, being in a simple way AHmix = RT jof connected with the specific enthalpy of mixing Affmix per mole of monomeric units. Here T is the absolute temperature, R represents the gas constant, whereas / denotes the Flory /-parameter whose values are available from the literature for many pairs of monomeric units (see, for example, [7]). 

Tables 6.13 and 6.14 list sets of internally consistent thermodynamic data for crystalline and liquid components, for use in equations 6.79 to 81. Although equations 6.80 and 6.81 are simply based on the Clausius-Clapeyron approach, Ghi-orso et al. (1983) use a semiempirical formulation for the volume of melt components. Its development is...

The conducting ion sublattice in FICs is generally considered molten . The molten sublattice model for fast ion conduction was first proposed by Strock (1936) on the basis of structural and thermodynamic data for Agl. In most FICs, the entropy of the phase transition to the FIC state is larger than the entropy of melting. For example, in Agl the entropy of the transition at 420 K from the -form to the a-form (FIC state) is 14.7 J deg mol , whereas the entropy of melting at 861 K is only 11 J deg mol . ... 

In the planetary geochemical literature, there are also extensive discussions about the thermodynamics of crystallizing melts. Sophisticated programs have been developed to model the compositions of the minerals that crystallize from a cooling liquid as well as changes in the residual melt. 

The first thermodynamic expression above states that the intermolecular attraction forces we must overcome to sublime the molecules of a substance are equal to the sum of the forces required to first melt it and then vaporize it. Likewise, the increased randomness obtained as molecules sublime is the same as the sum of entropies associated with the sequence of melting and vaporizing. Consequently, if we can predict such thermodynamic terms for vaporization or melting, we already know the corresponding parameters for sublimation. 

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