Stress and crystallization

Another such example is the connection between interface stresses and crystal lattice distortion, and lamellar twisting. The latter phenomenon requires two additional ingredients, in addition to the interface stresses Firstly, the interface stresses must occur asymmetrically at the two opposite lamella surfaces [56,57], which can not be achieved in our simulations by construction of the simulation cell. Reasons for such asymmetries have to be found on different grounds. Secondly, lamellar twisting can only be predicted if also the material properties of the crystalline lamellae are incorporated, either based on experimental [58,59] or simulated data [60]. 

The other form, beta, predominates if stress and crystallization temperatures are low. Therefore, preparation of networks containing a great abundance of beta relative to alpha requires quick cooling to temperatures below U0 C, and this necessarily displaces the specimen away from conditions more conducive for equilibriimi ciystallization. 

Injection molding is one of the most important polymer processing operations. Polymer experiences a complex mechanical and temperature history which cause molecular orientation, residual stresses and crystallization. These process induced microstructures are mainly responsible for mechanical, optical properties, and long-term dimensional stability of molded products[l]. 

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

Most solid surfaces are marred by small cracks, and it appears clear that it is often because of the presence of such surface imperfections that observed tensile strengths fall below the theoretical ones. For sodium chloride, the theoretical tensile strength is about 200 kg/mm [136], while that calculated from the work of cohesion would be 40 kg/mm [137], and actual breaking stresses are a hundreth or a thousandth of this, depending on the surface condition and crystal size. Coating the salt crystals with a saturated solution, causing surface deposition of small crystals to occur, resulted in a much lower tensile strength but not if the solution contained some urea. 

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

Terephthahc acid (TA) or dimethyl terephthalate [120-61 -6] (DMT) reacts with ethyleae glycol (2G) to form bis(2-hydroxyethyl) terephthalate [959-26-2] (BHET) which is coadeasatioa polymerized to PET with the elimination of 2G. Moltea polymer is extmded through a die (spinneret) forming filaments that are solidified by air cooling. Combinations of stress, strain, and thermal treatments are appHed to the filaments to orient and crystallize the molecular chains. These steps develop the fiber properties required for specific uses. The two general physical forms of PET fibers are continuous filament and cut staple. 

More recently, Raman spectroscopy has been used to investigate the vibrational spectroscopy of polymer Hquid crystals (46) (see Liquid crystalline materials), the kinetics of polymerization (47) (see Kinetic measurements), synthetic polymers and mbbers (48), and stress and strain in fibers and composites (49) (see Composite materials). The relationship between Raman spectra and the stmcture of conjugated and conducting polymers has been reviewed (50,51). In addition, a general review of ft-Raman studies of polymers has been pubUshed (52). 

Transformations in the Solid State. From a practical standpoint, the most important soHd-state transformation of PB involves the irreversible conversion of its metastable form II developed during melt crystallization into the stable form I. This transformation is affected by the polymer molecular weight and tacticity as well as by temperature, pressure, mechanical stress, and the presence of impurities and additives (38,39). At room temperature, half-times of the transformation range between 4 and 45 h with an average half-time of 22—25 h (39). The process can be significantly accelerated by annealing articles made of PB at temperatures below 90°C, by ultrasonic or y-ray irradiation, and by utilizing various additives. Conversion of... 

Measurement of Residual Stress and Strain. The displacement of the 2 -value of a particular line in a diffraction pattern from its nominal, nonstressed position gives a measure of the amount of stress retained in the crystaUites during the crystallization process. Thus metals prepared in certain ways (eg, cold rolling) have stress in their polycrystalline form. Strain is a function of peak width, but the peak shape is different than that due to crystaUite size. Usually the two properties, crystaUite size and strain, are deterrnined together by a computer program. 

Polisch, J. and Mersmann, A., 1988. The Influence of Stress and Attrition on Crystal Size Distribution. Chemical Engineering Technology, 11, 40-49. 

It is well established that GGA gives a better description of molecular systems, crystal surfaces and surface-molecule interactions. However, there are cases where the GGA results for solids are in much worse agreement with experiment than the LDA ones (e.g., 3-22 jj has been suggested that the effect of using GGA for solids is roughly equivalent to adding uniform tensile stress, and as a result lattice constants are frequently overestimated. 

It should be noted that the fraction of ECC in samples obtained by other methods described in Sect. 2 is approximately as small as that of the framework in the orientation-ally crystallized samples. These methods differ in details but depend on the mechanical treatment of the crystallizing system and are therefore given the common name stress-induced crystallization . Although the structure of the samples obtained by these methods has some features in common with that of orientationally crystallized samples, the thermodynamics and kinetics of orientational crystallization are fundamentally different from the mechanism of stress-induced crystallization. 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

Both stress-induced crystallization and orientational crystallization can be used for the preparation of polymer materials with mechanical property values (e.g. tenacities and elastic moduli) much higher than those for polymer films and fibers obtained by conventional processing. We believe that the advantage of orientational crystallization over more complex methods consists in the possibility of obtaining samples of elastic moduli and tenacities in a one-step continuous process. 

As in dissolution, a chemical and structural change can occur from hydrolysis as the ions replaced by or OH may be of a different size so that the crystal structure is stressed and weakened. An example of this is the weathering of feldspar or goethite by H ... 

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