Polymer crystals chain-direction moduli

Polymers oriented by drawing are of considerable practical importance because they can display up to 50% of the theoretical chain direction modulus of the crystals. This short-fall in modulus is caused by imperfections within the crystals and the presence of folds and non-crystalline material. The value of modulus obtained depends principally upon the crystal structure of the polymer and the extent to which a sample is drawn (i.e. the draw ratio). The maximum draw ratio that can be obtained in turn... 

The crystallization kinetics of commercial polyolefins is to a large extent determined by the chain microstructure [58-60]. The kinetics and the regime [60] of the crystallization process determine not only the crystalline content, but also the structure of the interfaces of the polymer crystals (see also Chapter 7). This has a direct bearing on the mechanical properties like the modulus, toughness, and other end use properties of the polymer in fabricated items such as impact resistance and tear resistance. Such structure-property relationships are particularly important for polymers with high commercial importance in terms of the shear tonnage of polymer produced globally, like polyethylene and polyethylene-based copolymers. It is seen that in the case of LLDPE, which is... 

Here m is the mode order (m — 1,3,5. .., usually 1 for polyethylenes), c the velocity of light, p the density of the vibrating sequence (density of pure crystal) and E the Young s modulus in the chain direction. The LAM band has been observed in many polymers and has been widely used in structural studies of polyethylenes [94—99,266], as well as other semi-crystalline polymers, such as poly (ethylene oxide) [267], poly(methylene oxide) [268,269] and isotactic poly(propylene) [270,271], The distribution of crystalline thickness can be obtained from the width of the LAM mode, corrected by temperature and frequency factors [272,273] as ... 

Creep. One of the most remarkable aspects of the deformation of polydiacetylenes is that it is not possible to measure any time-dependent deformation or creep when crystals are deformed in tension parallel to the chain direction (14,24). This behviour is demonstrated in Figure 3 for a polyDCHD crystal held at constant stress at room temperature and the indications are that creep does not take place at temperatures of up to at least 100 C (24). Creep and time-dependent deformation are normally a serious draw-back in the use of conventional high-modulus polymer fibres such as polyethylenes (28). Defects such as loops and chain-ends allow the translation of molecules parallel to the chain direction in polyethylene fibres. In contrast since polydiacetylene single crystal fibres contain perfectly-aligned long polymer molecules (cf Figure lb) there is no mechanism whereby creep can take place even at high temperatures. 

The heterogeneity of the crystalline polymer solid is accentuated still more in the case of mechanical properties by the enormous mechanical anisotropy of the crystals and the large difference in the elastic moduli of the crystalline and amorphous components. With polyethylene, the elastic modulus of the crystals is 3452 or 2403 X 1010 dynes/cm2 in the chain direction (E ) and 4 X 1010 dynes/cm2 in the lateral direction (E ) (2, 3). The elastic modulus of the amorphous component (Ea) of polyethylene is 109-1010 dynes/cm2 (4). This is significantly less than Eu and Ebut at least 10 times the elastic modulus of a rubber that has about five monomers in the chain segments between the crosslinks. This is quite surprising since room temperature is far above the glass transition temperature of polyethylene (Tg is either —20°C or — 120°C), and therefore one would expect a fully developed rubbery... 

Polymer crystals show very direction-dependent (anisotropic) properties. The Young s modulus of polyethylene at room temperature is approximately 300 GPa in the chain-axis direction and only 3 GPa in the transverse directions (Fig. 1.2). This considerable difference in modulus is due to the presence of two... 

The elastic modulus of a polymer crystal provides us with important information on the molecular conformation in the crystal lattice [24]. The elastic modulus (crystal modulus) of the crystalline regions in the direction parallel to the chain axis has been measured for a variety of polymers by X-ray diffraction [25]. Examination of the data so far accumulated enables us to relate the crystal modulus, namely, the extensivity of a polymer molecule, both to the molecular conformation and the mechanism of deformation in the crystal lattice. Furthermore, knowledge of the crystal modulus is of interest in connection with the mechanical properties of the polymer, because the crystal modulus gives the maximum attainable modulus for the specimen modulus of a polymer. 

A general picture emerges concerning the values of chain direction moduli of polymer crystals. They tend to be high if the molecule is in the form of a planar zig-zag rather than a helix. For example, polyethylene is stiffer than polyoxymethylene or polytetrafluoroethylene which both have molecules in helical conformations (Table 4.1). The helices can be extended more easily than the polyethylene planar zig-zag. Also the presence of large side groups tend to reduce the modulus because they increase the separation of molecules in the crystal. This causes an increase in the area supported by each chain. 

Determine the Young s modulus of the crystals in the polymer in the chain-direction assuming that the stress on the crystals is equal to the stress applied to the specimen as a whole. (The radiation used was CuKa A = 1.542 A.)... 

The majority of research concerned with the relationship between physical structure and mechanical properties of fibres is concerned with the Young s modulus. Theoretical calculations showed that at absolute zero the modulus of polyethylene crystals in the chain direction is between 260 and 320 GPa the value obtained by X-ray measurements assuming homogeneous stress was 240 GPa. The moduli in other directions obtained both by calculation and by the X-ray method are considerably lower. The moduli in the chain direction for other polymers, with essentially extended-chain conformations, are somewhat lower e.g. 110GPa for PET ). For polymer crystals with helical chain conformations, the chain modulus is further reduced e.g. 42 GPa for isotactic polypropyleneThe average transverse moduli obtained by various experimental methods are typically between 2 and 4GPa. ... 

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