Crystallinity curve

Fig. 12 Cooling (solid lines) and heating (dotted and dashed lines) crystallinity curves of random copolymers with variable comonomer mole fractions as denoted near the curves. The dashed lines start from the reduced temperature of 2 and meet the dotted curves at high temperatures [52]... 

Figure 2.27. Experimental data (points) and theoretical curves (solid lines) representing changes in temperature (curves 1 and 3) and the degree of crystallinity (curves 2 and 4) during anionic activated polymerization of e-caprolactam in a plate reactor. Width of the reactor is 32 mm Tsur = 150°C (a) 140°C (b) and 130°C (c). Data are shown for the center (curves 1 and 2) and for the wall (curves 3 and 4).

In figure 9, crystalline plots of the same area (two successive photographs) are shown. The fading of the weaker line is visible, but nevertheless, there is only a minor variation of the area under the whole crystalline curve. 

Fig, 16. The combination of the two types of phase equilibrium liquid (curve 1) and liquid-crystalline (curve 2) (according to... 

Fig. 6.1. Free energies of crystalline (curves 1) and non-crystalline (curves 2) nuclei vs the number of atoms in the nucleus for glass-forming (a, b) and nonglass-forming melts (c). N and IV 1 are the critical sizes of embryos...

Fig. 2. Zeolite or zeotype synthesis crystal linear growth plot (solid line) and corresponding bulk growth curve (broken line). The crystallinity curve has here been calculated (by cubing the linear growth values).

Figure 17. The specific enthalpy curve, /i(7) the specific enthalpy curves for the fully amorphous and crystalline states and the percentage crystallinity curve, all based on the specific heat...

Cr,Cl ), and (K, K ) (c) a solid, consisting of crystalline (curve c) and amorphous (curve a) silicon and (d) a solvated polymer, where the pair consists of a polymer segment and a solvent molecule. The plotted function in (c) would be roughly compatible with the others if it were divided by Anr. Curves (b) and (c) are based on neutron-scattering data, while (a) and (d) are the result of MD calculations. [Curve (a) is from Ref. 60 Molecular Simulation), (b) is from Ref. 61 Journal de Physique), (c) is from Ref. 62 (US Atomic Energy Commission), (d) is from Ref. 63 (American Institute of Physics), and they appear by permission of the authors and publishers.]... 

It will be clear that this explanation of the difference between the magnetic moment in crystalline and amorphous materials is not restricted to alloys of 3d metals with rare earth. Its general validity follows for instance from the results shown in fig. 49, where the crystalline curves pertaining to the crystalline states are invariably below those of the amorphous states. Here we wish to stress again that the above explanation of the differences in saturation moment does not mean that band structure effects or charge transfer effects can be completely neglected (Malozemoff et al., 1983). The present analysis only shows that CSRO effects play a rather prominent role in the determination of the magnetic properties. 

The enthalpy-based weight crystallinity curves, (T), as obtained within the two-phase model via numerical integration o% the heat capacity heating curves in combination with the reference enthalpy data for purely amorphous and purely crystalline polyethylene, are given in Figure 2 for the VLDPE studied and its fractions. They illustrate even more clearly that the fractions differ greatly in melting behaviour and crystallinity. 

Figure 12 Temperature-dependent crystallinity is determined for most common polymers by using a simple software package that employs user-defined limits for the calculation on the DSC heat flow curve. The resultant temperature crystallinity curve is produced with the percent crystallinity table.

Figure 15.18 Specific volume versus temperature, upon cooling from the liquid melt, for totally amorphous (curve A), semicrystalltne (curve B), and crystalline (curve C) polymers.

No engineering polymer is 100% crystalline curve C is included in Figure 15.18 to illustrate the extreme behavior that would be displayed by a totally crystalline material. 

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

The reason for the constancy and sharpness of the melting j)oint of a pure crystalline solid can be appreciated upon reference to Fig. 7,10, 1, in which (a) is the vapour pressure curve of the solid and (6) that of the liquid form of the substance. Let us imagine a vessel, maintained at constant temperature, completely filled with a mixture of the above liquid and solid. The molecules of the solid can only pass into the liquid and the molecules of the liquid only into the solid. We may visualise two competitive processes taking place (i) the solid attempting to evaporate but it can only pass into the liquid, and (ii) the liquid attempting to distil but it can only pass into the solid. If process (i) is faster, the solid will melt, whereas if process (ii) proceeds with greater speed the... 

Figure 3.16a shows the storage and loss components of the compliance of crystalline polytetrafluoroethylene at 22.6°C. While not identical to the theoretical curve based on a single Voigt element, the general features are readily recognizable. Note that the range of frequencies over which the feature in Fig. 3.16a develops is much narrower than suggested by the scale in Fig. 3.13. This is because the sample under investigation is crystalline. For amorphous polymers, the observed loss peaks are actually broader than predicted by a...

Remember the units involved here For f they are length time for N, length and for t, time. Therefore the exponent is dimensionless, as required. The form of Eq. (4.24) is such that at small times the exponential equals unity and 6 = 0 at long times the exponential approaches zero and 0 = 1. In between, an S-shaped curve is predicted for the development of crystallinity with time. Experimentally, curves of this shape are indeed observed. We shall see presently, however, that this shape is also consistent with other mechanisms besides the one considered until now. 

The decrease in amorphous content follows an S-shaped curve. The corresponding curve for the growth of crystallinity would show a complementary but increasing plot. This aspect of the Avrami equation was noted in connection with the discussion of Eq. (4.24). 

The significance of these numbers is seen as follows.The average values of A log t are to be added to the log t values at 126 or 130°C to superimpose the latter curves on the one measured at 128°C. Since these values are added to log t values, the effect is equivalent to multiplying the individual t values at 126 and 130°C by the appropriate antilogs to change the time scale in the individual runs to a common time scale. Using the case of 6 = 0.5 as an illustration, we see the following times are required to reach this level of crystallinity ... 

When water activity is low, foods behave more like mbbery polymers than crystalline stmctures having defined domains of carbohydrates, Hpids, or proteins. Water may be trapped in these mbbery stmctures and be more or less active than predicted from equiUbrium measurements. As foods change temperature the mobiUty of the water may change. A plot of chemical activity vs temperature yields a curve having distinct discontinuities indicating phase... 

Fig. 2. Time—temperature—transformation (TTT) diagram where A represents the cooling curve necessary to bypass crystallization. The C-shaped curve separates the amorphous soHd region from the crystalline soHd region. Terms are defined ia text.

Fig. 3. Curve ihustrating the activation energy (barrier) to nucleate a crystalline phase. The critical number of atoms needed to surmount the activation barrier of energy AG is n and takes time equal to the iacubation time. One atom beyond n and the crystahite is ia the growth regime.

Typical stress—strain curves are shown in Figure 3 (181). The stress— strain curve has three regions. At low strains, below about 10%, these materials are considered to be essentially elastic. At strains up to 300%, orientation occurs which degrades the crystalline regions causing substantial permanent set. 

Sohd ammonium nitrate occurs in five different crystalline forms (19) (Table 6) detectable by time—temperature cooling curves. Because all phase changes involve either shrinkage or expansion of the crystals, there can be a considerable effect on the physical condition of the sohd material. This is particularly tme of the 32.3°C transition point which is so close to normal storage temperature during hot weather. 

Master curves can also be constmcted for crystalline polymers, but the shift factor is usually not the same as the one calculated from the WLF equation. An additional vertical shift factor is usually required. This factor is a function of temperature, partly because the modulus changes as the degree of crystaHiuity changes with temperature. Because crystaHiuity is dependent on aging and thermal history, vertical factors and crystalline polymer master curves tend to have poor reproducibiUty. 

Infrared Spectroscopy (ir). Infrared curves are used to identify the chemical functionality of waxes. Petroleum waxes with only hydrocarbon functionality show slight differences based on crystallinity, while vegetable and insect waxes contain hydrocarbons, carboxyflc acids, alcohols, and esters. The ir curves are typically used in combination with other analytical methods such as dsc or gc/gpc to characterize waxes. 

For a fiber immersed in water, the ratio of the slopes of the stress—strain curve in these three regions is about 100 1 10. Whereas the apparent modulus of the fiber in the preyield region is both time- and water-dependent, the equiUbrium modulus (1.4 GPa) is independent of water content and corresponds to the modulus of the crystalline phase (32). The time-, temperature-, and water-dependence can be attributed to the viscoelastic properties of the matrix phase. 

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