Heat of fusion determination

According to this, the heat of evaporation at the melting-point (T = 234 4°) amounts to 14,884, and that for solid mercury to 14,884 + 555 — 15,439 the figure 555 represents the heat of fusion determined by Pollitzer, and confirmed, by a totally different method, by Koref. For the absolute zero, the heat of evaporation of solid mercury is thus... 

The-purity of a /i-pentane sample was determined by a calorimetric method by Clarke et al. (20). The results obtained for pure u-pentane and for a synthetic n-penlane-iso-octane mixture are given in the resistance (temperature) versus time curve in Figure 10.11. For purity determination, these data have been converted to the fraction melted after each equilibration period by allowing for the heat necessary to raise the temperature of the solid and liquid and for the amount of heat leak from radiation and conduction. The heat of fusion determined from this work was 2090 calories per mole, which gave a purity of 99.79 mole-% for the n-pentane. 

Prior to the widespread use of differential scanning calorimetry, DTA analysis was the only method whereby one could obtain heats of transition or fusion. For example, sulfathiazone was found to undergo a transition from Form I to Form II at 161°C, for which the heat of transition was determined to be 1420 cal/mol [80]. The heat of fusion directly obtained for Form II was found to be 5970 cal/mol, which compared favorably with the heat of fusion determined for the material resulting from the conversion of Form I (5960 cal/mol). In another study, heats of fusion were determined for sixteen sulfonamides, some of which exhibited polymorphism and some of which did not [81]. In this work, a fuller understanding of the thermodynamics was provided, where the entropies as well as the enthalpies of the various processes were deduced. 

Next, one may want to calculate the cross-hatched area, A. The calculation is carried out in Fig. 4.72. Area A represents the return to steady state and can be described by using the approach to steady state which was derived in Fig. 4.68. The result represents the first and the last term of the expression for AH as it was given in Fig. 4.71. This means that under the conditions of identical ATi and ATf, one can make use of the simple baseline method for the heat of fusion determination The heat of fusion, AHf, is just the area above the basehne in Fig. 4.71, multiplied with K, the calibration constant. If the baseline deviates substantially from the horizontal, corrections must be made which are discussed in Fig. 4.80, below. 

Finally, if the substance to be dissolved is crystalline at the experimental temperature, experience shows that the heats of fusion of polar compounds are usually rather high. In this case the heat of fusion determines the solubility. Accordingly, the differing solubility of galactose and glucose in water or of silite and inosite in the same solvent must be due to the... 

An alternate means of measuring crystallinity involves comparing the ratio of the heat of cold crystallization, of amorphous polymer to the heat of fusion, Aff of crystalline polymer. This ratio is 0.61 for an amorphous PET and a fully crystalline PET sample should yield a value close to zero.202 After the sample with its initial morphology has been run once in the DSC, the heat of fusion determined in the next run can be considered as Affgg. The lower the Aff /Af ratio, the more crystalline the original sample was. 

Some of the useful information derived from DSC heating scans includes the melting temperature, which is taken as the maximum of the endothermic peak, and the heat of fusion, determined by integrating the area under the endothermic peak. The melting temperature of PP homopolymer is about 160°C, whereas that of usual PP random copolymers is about 145°C. Polypropylene impact copolymers exhibit the same melting temperatures as homopolymers, the rubber constituent not affecting the melting temperature. Impact copolymers do, however, have lower heats of fusion than homopolymers because the heat of fusion is related to the proportion of crystalline polymer present. The rubber portion is essentially noncrystalline and therefore does not melt. 

Once Tf is determined, equations (6.43) and (6.44) permit the calculation of both the Flory interaction parameter and the heat of fusion of the polymer from the slope and intercept of a plot of (1/7/) - (1/7/) versus (1/7/) (146). The heat of fusion determined in this way measures only the crystalline portion. If heat of fusion data are compared with corresponding data obtained by DSC (see Figure 6.3), which measures the heat of fusion for the whole polymer, the percent crystallinity may be obtained. 

The experimental melting points of a series of mixtures can be plotted as (l/Tg-l/Tm)/0i against 0j, whence the intercept equals RVu/AHuVj and the slope equals this quantity multiplied by X, Heats of fusion determined in this manner are generally consistent with the calorimetric values and both are listed in the table. 

Under the conditions of identical ATj and ATf, one can make use of the base-line method for the heat of fusion determination A//f is simply all the area above the base line, multiplied by K, the calibration constant. The cross-hatched area accounts for the sum of the vertically shaded area and the correction term. Even if ATj is not exactly equal to ATf, this method may still be useful as a first approximation. For more accurate determinations, however, Eq. (20) has to be evaluated fully. 

A special problem in heat of fusion determination is presented by linear, flexible macromolecules. They usually crystallize only partially, so that the heat of fusion measured is not the total heat of fusion and cannot be used directly for a discussion of the equilibrium entropy of fusion, for example. Similarly to the heat capacity treatment described in Fig. 5.17, one assumes that the partially crystallized samples can be described by a crystallinity, iv. . A definition of based on density is given in Fig. 5.17. Equation (1) of Fig. 5.25 shows how crystallinity can also be expressed in terms of the heat of fusion. The measured heat of fusion of the semicrystalline sample is A/7f, while Ai/f is the heat of fusion of the perfect crystal. As long as a two-phase model of semicrystalline polymers holds, the two definitions of Wf. give identical values. If perfect crystals are not available for comparison, calibration can in this case be obtained by measuring the heat of fusion of a sample of crystallinity known from some other measurement, such as density measurement. X-ray diffraction, or infrared absorption. In some cases it is possible to plot the change in heat capacity at the glass transition temperature, ACp(Tg), versus the measured heat of fusion A7/f. At the extrapolated value for ACp(Tg) = 0, A//f corresponds to the heat of fusion for the fully crystalline state, A//f. Special difficulties of this method arise from rigid amorphous fractions sometimes found in semicrystalline polymers. In this case the observed AC is lowered, as is discussed in Sect. 5.6. 

It can be seen in Fig. 1.5 that the higher the heats of fusion the broader the width between the liquidus and solidus lines of an ideal system. Furthermore, the difference between the heats of fusion determines the asymmetric shape of the phase diagram. In Section 1.3.1 the consequences of the shape of the solid solution phase diagrams on the segregation behavior in normal freezing growth processes will be discussed. 

The scans of PEG are also much dependent on prior recrystallisation. Craig and Newton [114] demonstrated that ambient cooling conditions altered both the melting point and heat of fusion. Additionally, the heat of fusion, determined as kJmol increased as the molecular weight of PEG increased. 

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). 

In the P-T projection the difference in slopes of the three-phase lines -clathrate-gas and liquid-clathrate-gas at the quadruple point R is determined by the heat of fusion of the number of moles of hydroquinone associated with one mole of argon in the clathrate under the conditions prevailing at R. If we extrapolate the three-phase line liquid-clathrate-gas to lower pressures (where it is no longer stable), the value of yA decreases until it becomes zero when we are dealing with pure / -hydroquinone. Hence, the metastable part of this three-phase line ends in the triple point B of /1-hydro-... 

This equation was deduced by van t Hoff in 1885, and provides a simple method of determining the latent heat of fusion of a... 

Example 1.—If the specific heats of the solid and liquid forms are linear functions of temperature, show that the melting-point is determined by dividing the latent heat of fusion by the difference between the specific heats of the solid and liquid forms at the melting-point (cf. Taramann, Kryst. and Schmelz., p. 42). 

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. 

It has also been inferred that differences found between crystallinities measured by density and those from heat of fusion by DSC area determination, as given for polyethylenes in the example of Figure 4 [72], may be related to baseline uncertainties, or not accounting for the temperature correction of AHc. Given that similar differences in crystallinity from density and heat of fusion were reported for isotactic poly(propylene) [43] and polyfaryl ether ether ketone ketone), PEEKK [73], other features of phase structure that deviate from the two-phase model may be involved in the crystallinity discrepancy. 

Quantitative measurements of the crystallinity content of the block copolymers were made from the determination of the heat of fusion and from the density of the polymer. 

PTT, with three methylene units in its glycol moiety, is called an odd-numbered polyester. It is often compared to the even-numbered polyesters such as PET and PBT for the odd-even effect on their properties. Although this effect is well established for many polycondensation polymers such as polyamides, where the number of methylene units in the chemical structures determines the extent of hydrogen bonding between neighboring chains and thus their polymer properties, neighboring chain interactions in polyesters are weak dispersive, dipole interactions. We have found that many PET, PTT and PBT properties do not follow the odd-even effect. While the PTT heat of fusion and glass transition temperature have values between those of PET and PBT, properties such as modulus... 

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