Density, amorphous

Noncrystalline domains in fibers are not stmctureless, but the stmctural organization of the polymer chains or chain segments is difficult to evaluate, just as it is difficult to evaluate the stmcture of Hquids. No direct methods are available, but various combinations of physicochemical methods such as x-ray diffraction, birefringence, density, mechanical response, and thermal behavior, have been used to deduce physical quantities that can be used to describe the stmcture of the noncrystalline domains. Among these quantities are the amorphous orientation function and the amorphous density, which can be related to some of the important physical properties of fibers. 

In the case of crystalline polymers better results are obtained using an amorphous density which can be extrapolated from data above the melting point, or from other sources. In the case of polyethylene the apparent amorphous density is in the range 0.84-0.86 at 25°C. This gives a calculated value of about 8.1 for the solubility parameter which is still slightly higher than observed values obtained by swelling experiments. 

The amorphous and crystalline regions each have different densities, with the crystalline density Pc being higher than the amorphous density Pa due to a more compact structure. The percent crystallinity in a semicrystalline polymer with bulk density Ps... 

Density. Huglin (93) has collected crystalline and amorphous densities from a variety of published and unpublished sources. These values are summarized in Table 21. 

The amorphous density for PET is 1.33 g/cm3 and for PBT is 1.28 g/cm3. It is apparent that only two decimal digits are significant, which must be kept in mind when interpreting the results. 

As obtained by these methods palladium subsulphide is a hard, grey, metallic-looking mass, with a granular fracture. It is amorphous density 7-3 and it is soluble in aqua regia. 

A hydrated arsenate of iron and calcium from Yukon is termed Yukonite. Its composition approximates to13 (Ca3,Fe2)As208.2Fe(0H)3. 5H20. It is brownish black, resinous, and amorphous. Density c.2-65. 

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 ... 

Samples of PET/PEN copolymers with 10, 20, 30, 50, 80 and 100 mol% PEN have been synthesized. Amorphous films of the samples were obtained by melt pressing above the melting point and quenching in ice-water. The samples were then crystallized by annealing the glassy materials at various temperatures. The degree of crystallinity was calculated from the amorphous density measured on quenched samples and from the crystal density derived from the crystal unit cell. 

Qtycogen depletiori Sarcolemmal disruption mitochondrial mitochondrial swelling relaxation amorphous densities of myofibrils... 

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. 

Table 3.5. Experimental amorphous densities p (g/cc) and molar volumes V (cc/mole) at room temperature, "correction index" NMV used in correlation for V, and fitted values of V and p, for 152 polymers. Zeroth-order connectivity indices °x and °xv and first-order connectivity indices X and 1xv- all of which are also used in the correlation, are listed in Table 2.2. The alternative set of °xv and 1 %v values listed in Table 2.3 is used for the silicon-containing polymers. 

Figure 3.6. Comparison between the observed amorphous densities of 152 polymers at room temperature and the densities calculated by using the correlation developed for molar volume. 

The crystalline and amorphous densities of many polymers are listed in Table 3.6. Most of the pa values are from Table 3.5. Most of the pc values are from van Krevelen [1] and... 

Table 3.6. Experimental crystalline and amorphous densities (pc and pa, respectively, in g/cc), and their ratios, for polymers at room temperature. 

Figure 3.8. The (crystalline density)/(amorphous density) ratio has a broad range, from 0.97 to 1.25, for a dataset of 53 polymers. Equation 3.36 provides the best fit to these data.

The trend to higher densities or ciystallinities at higher temperatures and longer residence times. During SSP processing densities rarely exceed 1.42 g/cm, equivalent to a crystallinity of 70 vol% (according to the crystalline and amorphous densities given above). 

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