Melting temperature relation

To formulate the melting temperature relation we start with the Flory-Huggins expression for the free energy of mixing of a set of chemically identical species with a low molecular weight diluent.(67,68) This expression is given as (7)... 

For monomeric systems the chemical potentials of the species in each of the phases is specified in terms of either composition, or activity. The melting temperature relations are then derived in a straightforward manner.(2) For an ideal mixture of low molecular weight species the free energy of mixing in each phase is determined by a Raoult s law type calculation, i.e. only the combinatorial entropy is considered. The composition is then expressed in terms of mole fraction. The equilibrium melting temperature in terms of the composition of each phase is then specified. 

It can be expected that for kinetic reasons crystallites smaller than predicted from equilibrium theory will usually develop. The appropriate melting temperature relation can be formulated in a straightforward manner by invoking the Gibbs-Thomson equation. The result for an ideal random copolymer is (16)... 

Figure 5.12 represents a compilation of melting temperature relations for rapidly crystallized ethylene copolymers with a set of 1-alkenes and norbomene as comonomers.(74-76,78) The melting temperatures of ethylene copolymers with bulkier side-group comonomers such as 1-decene, 4-methyl-1-pentene, cyclopen-tadiene and dicyclopentadiene follow the same curve as in Fig. 5.12.(78a) The plot clearly indicates that the melting points are independent of co-unit type under these crystallization conditions. Since observed melting temperatures of copolymers are known to depend on chain length the results shown have been limited to molecular weights of about 90000.(21) Studies of ethylene-octene copolymers with much higher comonomer content indicate a continuation of the curve shown in Fig. 5.12...

Similar to homopolymers, the structural parameters of and MWD play a similar role for the properties of the random copolymers, while, the stereospecificity concept changes its meaning. In fact, the introduction of a comonomer into polymeric chain determines a discontinuity that deeply affects the molecule s crystallization behavior. The crystallization speed slows down, forcing lower total crystallinity and a reduction of the melting temperature related to the less perfect structure of the crystals. 

Fig. 4. Relation between crystallization temperature and melting temperature for natural mbber.

Melting temperatures of as-polymerized powders are high, ie, 198—205°C as measured by differential thermal analysis (dta) or hot-stage microscopy (76). Two peaks are usually observed in dta curves a small lower temperature peak and the main melting peak. The small peak seems to be related to polymer crystallized by precipitation rather than during polymerization. 

The IR spectrum obtained at ambient temperature (Fig. 74, curve 1) shows the presence of a strong wide band at 535 cm 1 and a weak shoulder at about 643 cm 1. At the melting temperature (curve 2), the only discemable band observed is shifted slightly toward the higher wave numbers and occurs at 535-540 cm 1. This high frequency shift, which accompanies the melting, is related to changes in the distances between the central atom and the first and second coordination spheres, as illustrated in Fig. 75. 

Time, pressure, and temperature controls indicate whether the performance requirements of a molded product are being met. The time factors include the rate of injection, duration of ram pressure, time of cooling, time of piastication, and screw RPM. Pressure requirement factors relate to injection high and low pressure cycles, back pressure on the extruder screw, and pressure loss before the plastic enters the cavity which can be caused by a variety of restrictions in the mold. The temperature control factors are in the mold (cavity and core), barrel, and nozzle, as well as the melt temperature from back pressure, screw speed, frictional heat, and so on in the plasticator. 

The formation of ECC is not only an extension of a portion of the macromolecule but also a mutual orientational ordering of these portions belonging to different molecules (intermolecular crystallization), as a result of which the structure of ECC is similar to that of a nematic liquid crystal. After the melt is supercooled below the melting temperature, the processes of mutual orientation related to the displacement of molecules virtually cannot occur because the viscosity of the system drastically increases and the chain mobility decreases. Hence, the state of one-dimensional orientational order should be already attained in the melt. During crystallization this ordering ensures the aggregation of extended portions to crystals of the ECC type fixed by intermolecular interactons on cooling. 

We must remember that T in equation (6.161) is the equilibrium melting temperature. Integration of this equation will give an equation that relates melting temperature to activity. Separating variables and integrating... 

In Chapter 6, we derived equation (6.161) shown below, which relates the activity, a, of a component in solution to the equilibrium melting temperature, T, of that substance. 

Equation (8.26) relates the melting temperature, T, of an ideal solution to the mole fraction,, v of the (pure) component that freezes from solution. It can be integrated by separating variables and setting the integration limits between T, the melting temperature where the mole fraction is. y, and 7, the melting temperature of the pure component, /, where. v, = 1. The result is... 

The result is an equation relating Afus//m 2. T,. y2, and the a, parameters. Extrapolate the equation to y2 = 1 a condition where equation (8.26) applies, even if the solution is not ideal to show that AfusHm 2 at the melting temperature of the pure substance is given by... 

The derivation of the quantitative relationship between this equilibrium temperature and the composition of the liquid phase may be carried out according to the well-known thermodynamic procedures for treating the depression of the melting point and for deriving solubility-temperature relations. The condition of equilibrium between crystalline polymer and the polymer unit in the solution may be restated as follows ... 

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