Density of amorphous polymers

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. 

In most cases crystal densities differ from the densities of amorphous polymers. This leads to differences in refractive index, which in turn cause scatter of light at boundaries between amorphous and crystalline zones. Such materials are opaque except in certain instances where the crystal structure can be carefully oriented to prevent such scatter of light. 

The temperature dependence of polymer densities at atmospheric pressure is given in Tables 7.1 and 7.2. Table 7.1 gives densities measured above the glass transition temperature Tg and, for semi-crystalline polymers, above the melting temperature. Table 7.2 lists densities of amorphous polymers below Tg. Volumetric data are presented here in terms of the density p rather than the... 

A) Density of crystalline polymer < density of amorphous polymer... 

Density, mechanical, and thermal properties are significantly affected by the degree of crystallinity. These properties can be used to experimentally estimate the percent crystallinity, although no measure is completely adequate (48). The crystalline density of PET can be calculated theoretically from the crystalline stmcture to be 1.455 g/cm. The density of amorphous PET is estimated to be 1.33 g/cm as determined experimentally using rapidly quenched polymer. Assuming the fiber is composed of only perfect crystals or amorphous material, the percent crystallinity can be estimated and correlated to other properties. 

Unlike other synthetic polymers, PVDF has a wealth of polymorphs at least four chain conformations are known and a fifth has been suggested (119). The four known distinct forms or phases are alpha (II), beta (I), gamma (III), and delta (IV). The most common a-phase is the trans-gauche (tgtg ) chain conformation placing hydrogen and fluorine atoms alternately on each side of the chain (120,121). It forms during polymerization and crystallizes from the melt at all temperatures (122,123). The other forms have also been well characterized (124—128). The density of the a polymorph crystals is 1.92 g/cm and that of the P polymorph crystals 1.97 g/cm (129) the density of amorphous PVDF is 1.68 g/cm (130). 

In principle the heat required to bring the material up to its processing temperature may be calculated in the case of amorphous polymers by multiplying the mass of the material (IP) by the specific heat s) and the difference between the required melt temperature and ambient temperature (AT). In the case of crystalline polymers it is also necessary to add the product of mass times latent heat of melting of crystalline structures (L). Thus if the density of the material is D then the enthalpy or heat required ( ) to raise volume V to its processing temperature will be given by ... 

Examples of crystalline polymers are nylons, cellulose, linear polyesters, and high-density polyethylene. Amorphous polymers are exemplified by poly(methyl methacrylate), polycarbonates, and low-density polyethylene. The student should think about why these structures promote more or less crystallinity in these examples. 

The value of TMWV is dependent on the cohesive energy density (CED) of amorphous polymers, the extent of crystallinity in crystalline polymers, and the effect of reinforcements in polymeric composites. Thus, while a low molecular weight amorphous polymer may be satisfactory for use as a coating or adhesive, a chain length generally above 100 is often required if the polymer is to be used as an elastomer or plastic. 

The degree of crystallinity may be calculated from the density of the polymer if the density is known for the amorphous and crystalline states. Some crystallizable polymers are polymorphic, i.e., they may exist in more than one crystalline form. An unstable crystalline form may change to a more stable form, and crystalline forms may change under stress. For example, hdpe changes from an orthorhombic crystalline polymer to a monoclinic form when subjected to compressive forces. 

Determination of the proportions of crystalline and amorphous material in partially crystalline polymers. Knowledge of the unit cell dimensions in high polymer crystals leads to a knowledge of the density of the crystalline regions. If the density of amorphous regions is also known, either by measurement of the density of an entirely amorphous specimen (if this can be obtained) or by extrapolation of the liquid density/temperature curve, it is possible to calculate, from the measured density of any partially crystalline specimen, the proportions of crystalline and amorphous material. Since the physical properties of polymer specimens are profoundly influenced by the degree of crystallinity, X-ray determinations of crystallinity are much used in such studies (see Bunn, 1957). 

Due to the increase in density upon solidification of semi-crystalline thermoplastics, the thermal conductivity is higher in the solid state than in the melt. In the melt state, however, the thermal conductivity of semi-crystallinepolymers reduces to that of amorphous polymers as can be seen in Fig. 2.2 [40],... 

When we compare this value with the density of amorphous PE (p = 855 kg/m3), then the polymer in the coil appears to be 160 times diluted. If we choose the value for b/b0 as given above, then the result is a dilution factor of 890. Taking into account that the formula/o = 1/Vn holds for the tightest packed centre, then the results are in the same order of magnitude. 

Those amorphous polymers, for which the glass transition temperature is higher than 25 °C, are in the glassy state at room temperature. Table 4.7 gives a survey of the available literature data on the densities of these polymers. For each polymer the molar volume per structural unit has been calculated from the density. 

The density method is very convenient, because the only measurement required is that of the density of a polymer sample. It suffers from some uncertainties in the assignments of crystalline and amorphous density values. An average crystallinity is estimated as if the polymer consisted of a mixture of perfectly crystalline and completely amorphous regions. The weight fraction of material in the crystalline state Wc is estimated assuming that the volumes of the crystalline and amorphous phases are additive ... 

Analysis and Significance. The study of density fluctuations is part of the scattering theory of amorphous materials. In the experiment amorphous polymers exhibit a slow increase of the fluctuation background as a function of increasing s. Only a vague statement is made by existing theory [94,95,131-133] the fluctuation background Ipi ( ) is expanded in even powers of i. In the studies of amorphous polymers the common approximation is... 

The density of a polymer sample can be readily determined by allowing it to float in a density-gradient column, which is a vertical column containing a mixture of liquids with different (known) densities. The density of a small piece of polymer is determined from the position it adopts when it is dropped into the column. The density of the crystalline regions pc can be calculated from a knowledge of the crystal structure [19]. The amorphous density pa can sometimes be measured directly if the polymer can be obtained in a completely amorphous form, for example by rapid cooling of a polymer melt. Otherwise it can be determined by extrapolating either the density of the melt to the temperature of interest or that of a series of semicrystalline samples to zero crystallinity. 

An example of this behavior is shown in Table 11. In the reported experiments, a typical Cr/silica catalyst was tested for ethylene polymerization with small amounts of butene added to the reactor. Three different butene isomers were used in three series of experiments 1-butene, 2-butenes (cis and trans), and isobutylene. In the first series, as 1-butene was added to the reactor, the density of the polymer declined significantly, indicating the presence of ethyl branches on the chains from the incorporation of the comonomer (branching disrupts crystallinity and creates more amorphous polymer, which lowers the average density). The MI values of the polymers in this series went up as 1-butene was added, as would be expected from the greater ease with which a (3-hydride can be abstracted from the tertiary carbon resulting from 1-butene incorporation. This is the behavior typical of all a-olefin comonomers. 

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