Crystalline Fusion

This relationship is sketched in Fig. 4.7a, which emphasizes that P, must vary linearly with 6 and that P, ° must be available, at least by extrapolation. The heat of fusion is an example of a property of the crystalline phase that can be used this way. It could be difficult to show that the value of AH is constant per unit mass at all percentages of crystallinity and to obtain a value for AHj° for a crystal free from defects. Therefore, while conceptually simple, the actual utilization of Eq. (4.37) in precise work may not be easy. 

Lead borate moaohydrate [14720-53-7] (lead metaborate), Pb(B02)2 H20, mol wt 310.82, d = 5.6g/cm (anhydrous) is a white crystalline powder. The metaborate loses water of crystallization at 160°C and melts at 500°C. It is iasoluble ia water and alkaHes, but readily soluble ia nitric and hot acetic acid. Lead metaborate may be produced by a fusion of boric acid with lead carbonate or litharge. It also may be formed as a precipitate when a concentrated solution of lead nitrate is mixed with an excess of borax. The oxides of lead and boron are miscible and form clear lead-borate glasses in the range of 21 to 73 mol % PbO. 

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). 

Other crystallization parameters have been determined for some of the polymers. The dependence of the melting temperature on the crystallization temperature for the orthorhombic form of POX (T = 323K) and both monoclinic (T = 348K) and orthorhombic (T = 329K) modifications of PDMOX has been determined (284). The enthalpy of fusion, Aff, for the same polymers has been determined by the polymer diluent method and by calorimetry at different levels of crystallinity (284). for POX was found to be 150.9 J/g (36.1 cal/g) for the dimethyl derivative, it ranged from 85.6 to 107.0 J/g (20.5—25.6 cal/g). Numerous crystal stmcture studies have been made (285—292). Isothermal crystallization rates of POX from the melt have been determined from 19 to —50 C (293,294). Similar studies have been made for PDMOX from 22 to 44°C (295,296). 

The value for the heat of fusion of PPS, extrapolated to a hypothetical 100% crystalline state, is not agreed upon in the literature. Reported values range from approximately 80 J/g (19 cal/g) (36,96,101) to 146 J/g (35 cal/g) (102), with one intermediate value of 105 J/g (25 cal/g) (20). The lower value, 80 J/g, was originally measured by thermal analysis and then correlated with a measure of crystallinity deterrnined by x-ray diffraction (36). The value of 146 J/g was deterrnined independendy on uniaxiaHy oriented PPS film samples by thermal analysis, density measurement via density-gradient column, and the use of a calculated density for 100% crystalline PPS to arrive at a heat of fusion for 100% crystalline PPS (102). The value of 105 J/g was obtained by measuring the heats of fusion of weU-characterized linear oligomers of PPS and extrapolation to infinite molecular weight. 

Vitreous silica (silica glass) is essentially a supercooled Hquid formed by fusion and subsequent cooling of crystalline silica. It is found ia nature ia fulgerites, ie, fused bodies resulting from lightning striking quart2 sand. 

Chemical methods to determine the crystalline content in silica have been reviewed (6). These are based on the solubility of amorphous silica in a variety of solvents, acids or bases, with respect to relatively inert crystalline silica, and include differences in reactivity in high temperature fusions with strong bases. These methods ate qualitative, however, and fail to satisfy regulatory requirements to determine crystallinity at 0.1% concentration in bulk materials. 

The dye has been degraded by a fusion with caustic potash and the degradation products identified as various o-anilinyl mercaptans. They were identified and characterized by condensation with monochloroacetic acid to give the thioglycohc acids which, on acidification, were converted to well-defined crystalline lactams (2—4) together with a small amount of ji)-aminobenzoic acid. 

The most important of these is the diboride, TiB2, which has a hexagonal stmeture and lattice parameters of a = 302.8 pm and c = 322.8 pm. Titanium diboride is a gray crystalline soUd. It is not attacked by cold concentrated hydrochloric or sulfuric acids, but dissolves slowly at boiling temperatures. It dissolves mote readily in nitric acid/hydrogen peroxide or nitric acid/sulfuric acid mixtures. It also decomposes upon fusion with alkaU hydroxides, carbonates, or bisulfates. 

Crystalline anhydrous borax takes up some water from moist air even at 300°C. It becomes anhydrous near 700°C and melts at 742.5°C. The heat of hydration to borax has been calculated as 161 kJ/mol (38.5 kcal /mol) of Na20 2B202 (73,82). The heat of fusion has been reported as 81.2 kJ/mol (19.4 kcal/mol) (17). 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

Polymer compounds vary considerably in the amount of heat required to bring them up to processing temperatures. These differences arise not so much as a result of differing processing temperatures but because of different specific heats. Crystalline polymers additionally have a latent heat of fusion of the crystalline structure which has to be taken into account. 

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