Crystallinity invariance

Figures 10.9 to 10.11 illustrate how stretching curves and critical strains vary with temperature, again with results for PEVA12, and with the crystallinity here polyethylenes with different crystallinities are compared. Curves demonstrate a further general property of semicr3 talline pol5oners. While the stresses vary in systematic manner, there is no effect on the critical strains for softening (en 0.1) and hardening (en 0.6) and virtually no change in the elastic-plastic composition of the strains. Hence, tensile deformation of semicrystalline polymers is strain-controlled and changes the mechanism at two critical strains that are temperature and crystallinity invariant.

The inclusion of nonolefinic comonomers such as vinyl acetate, methacrylic acid, and norbomene, or chemical modification with such elements as chlorine and oxygen, destroys the simple relationship linking density and degree of crystallinity. Invariably, polyethylene resins that contain elements other than carbon and hydrogen have an elevated density in eomparison to homopolymers or olefin branched materials with similar degrees of erystallinily. 

Texture. All limestones are crystalline, but there is tremendous variance in the size, uniformity, and arrangement of their crystal lattices. The crystals of the minerals calcite, magnesite, and dolomite are rhombohedral those of aragonite are orthorhombic. The crystals of chalk and of most quick and hydrated limes are so minute that these products appear amorphous, but high powered microscopy proves them to be cryptocrystalline. Hydrated lime is invariably a white, fluffy powder of micrometer and submicrometer particle size. Commercial quicklime is used in lump, pebble, ground, and pulverized forms. 

Mechanical properties of plastics are invariably time-dependent. Rheology of plastics involves plastics in all possible states from the molten state to the glassy or crystalline state (Chapter 6). The rheology of solid plastics within a range of small strains, within the range of linear viscoelasticity, has shown that mechanical behavior has often been successfully related to molecular structure. Studies in this area can have two objectives (1) mechanical characterization of... 

The most characteristic and unique property of crystalline solids is however, neither the shape of their crystals nor the relative size of the crystal faces, but the angle between any pair of crystal facets. For any substance, the angle between the crystal facets is constant and invariable, regardless of the overall shape or size of the crystals. Under some circumstances a substance may form short, wide crystals, while under others, the... 

We can assert outright that a semi-crystalline network in a continuous state of equilibrium might be satisfactorily described by a representative chain of average contour length and average crystallization. This is, after all, the same assumption that is invariably applied to amorphous networks. The results in this instance are exactly the same as those presented herein. 

When the nature of the disorder is spatially invariant EXAFS is a viable technique. Under these circumstances, however, unless the specimens are exceptionally thin (<20 ), HREM is of little value (13, 14), as two-dimensional projected images are difficult to interpret. When, however, there are residual crystalline regions still intact in a growing glassy matrix, or when, conversely, the embryonic stages of crystallization of a glassy precursor have been reached, HREM is particularly powerful (14, 15). 

The first two terms in (4) are relatively small AHS0(RX) = 5-10 kj mol"1 [5, 18, 27] and AHve RX) 20-50 kj mol 1 [5]) and variations in these terms do not warrant discussion. Nevertheless, it should be noted that the sum of AHS0(RX) and AHV6(RX) can be approximated by AHVB (solvent), but the use of the two terms leads to a better analysis, especially for a series of RX, since for a single solvent AHS9(RX) is almost invariant and the AHve RX) is known for many compounds. For those RX which are crystalline at the standard temperature the term required here is AH9sub(RX) and this is considerably larger than Aff e(RX). 

It is pertinent to mention here that in the course of TGA many vital processes, for instance crystallization, crystalline transitions, pure fusion reactions, glass transitions, and solid-state reactions devoid of volatile components might not be indicated as they happen to cause little change in weight of the sample. TGA invariably describes with ample precision the stoichiometry related to chemical changes that are indicated during DTA by an endothermal or exothermal duration from the base-line. 

Many polymer-salt complexes based on PEO can be obtained as crystalline or amorphous phases depending on the composition, temperature and method of preparation. The crystalline polymer-salt complexes invariably exhibit inferior conductivity to the amorphous complexes above their glass transition temperatures, where segments of the polymer are in rapid motion. This indicates the importance of polymer segmental motion in ion transport. The high conductivity of the amorphous phase is vividly seen in the temperature-dependent conductivity of poly(ethylene oxide) complexes of metal salts. Fig. 5.3, for which a metastable amorphous phase can be prepared and compared with the corresponding crystalline material (Stainer, Hardy, Whitmore and Shriver, 1984). For systems where the amorphous and crystalline polymer-salt coexist, NMR also indicates that ion transport occurs predominantly in the amorphous phase. An early observation by Armand and later confirmed by others was that the... 

Absolute asymmetric synthesis refers to the situation in which an asymmetric induction occurs in the absence of an externally imposed source of chirality [5]. Such reactions are invariably carried out in the crystalline state, where the asymmetric influence governing the enantioselectivity derives from the spontaneous crystallization of an achiral compound in a chiral space group. This phenomenon, which is analogous to the spontaneous crystallization of racemates as... 

The Clausius-Clapeyron equation describes the univariant equilibrium between crystal and melt in the P-Tfield. Because molar volumes and molar entropies of molten phases are generally greater than their crystalline counterparts, the two terms and AFfusion both positive and we almost invariably observe an... 

Let us now consider a case in which components 1 and 2 form an intermediate crystalline compound (C) with precise, invariant stoichiometry (e.g., 60% of component 2 and 40% of component 1). If the chemical composition of the intermediate compound is fixed, it behaves as a mechanical mixture with respect to its pure components (i.e., zero miscibility). The presence of the intermediate compound subdivides the compositional join into two fields mechanical mixture 2-C (y") and mechanical mixture C-1 (y ). The resulting crystallization path may assume two distinct geometrical configurations, as shown in figure 7.8. 

Polymers invariably form helical structures, and the helix symmetry is denoted by u, indicating that there are u repeat units in V turns of the helix. The helix pitch is denoted by P and the molecular repeat distance is c = vP. X-ray diffraction patterns from non-crystalline specimens contain diffracted intensities restricted to layer lines that are spaced by 1/c. On a diffraction pattern from a polycrystalline specimen, diffraction signals, or Bragg reflections, occur only at discrete positions on the layer lines, the positions being related to the lateral dimensions of the unit cell of the crystal. The meridian (vertical axis) of the diffraction pattern is devoid of diffracted intensity unless the layer line number J, is a multiple of u, so that u can be determined straightforwardly. The diffracted intensities can be calculated using standard expressions (2), for model structures (i.e. given the atomic coordinates). 

In contrast to the spin-lattice relaxation parameters, which remain invariant, a sijbstantial broadening of the resonant lines occurs upon crystallization. The effect is relatively modest for cis polyisoprene at 0°C and 57.9 MHz, where comparison can be made at the same temperature. Here there is about a 50% increase in the linewidths upon the development of 30% crystallinity. Schaefer (13) reports approximately 3- to 5-fold broader lines (but they are still relatively narrow) for the crystalline trans polyisoprene relative to the completely amorphous cis polyisoprene at 40°C and 22.5 MHz. It is interesting to note in this connection that for carbon black filled cis polyisoprene the line-widths are greater by factors of 5-10 relative to the unfilled polymer. 

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