Polyethylene temperature factor

A plot of the orthorhombic unit cell for polyethylene is illustrated in Fig. 4, with the 50% probability density surfaces shown for each atom of the unit cell. The anisotropic dynamics of the polyethylene crystal are immediately apparent. Significantly, the largest contributions to B,- come from the long wavelength acoustic modes, due to the inverse dependence on a/. In experimental studies on polymers, the temperature factor is often... 

The difference between usual (protonated) polymer and deuterated polymer was discussed. 3i ) The crystal structure of polyethylene-d4 is considered to be essentially the same as that of the usual polyethylene, although the temperature factors are somewhat different from the usual polyethylene. 

For the orthoriiombic crystal of polyethylene, the temperature-factor tensors at 100° K and 298° K were calculated by Kitagawa and Miyazawa (1968a), as shown in Table VII.1. The principal axes are nearly parallel or perpendicular to the skeletal plane where the setting angle of the skeletal plane is taken as 45° from the a-axis. From the B tensor, root-mean-squared displacements of carbon atoms at 298° K are calculated as 0.2 A in the c-plane and as 0.1 A along the c-axis. 

Table VII.l. Temperature factor B of the orthorhombic crystd of polyethylene (A ) ...

In the crystallographic analysis of polyethylene at room temperature, Bunn (1939) used the anisotropic temperature factors of B( ) = 5 A and B( )=0. Shearer and Vand (1956) used the isotropic temperature factor of B = 3 A in the x-ray analysis of the monoclinic single crystal of n-CagH,. Rec Uy, Aoki, Chiba, and Kaneko (1969) measured the temperature dependence of the anisotropic temperature factors of polyethylene. The observed values were almost proportional to temperature and the coefficient agreed closely with the temperature coefficient calculated by Kitagawa and Miyazawa (1968a). 

Table VII.2. Contribution of vibrational modes to the temperature factors (A ) cf the orthorhombic crystal of polyethylene...

The way in which these factors operate to produce Type III isotherms is best appreciated by reference to actual examples. Perhaps the most straightforward case is given by organic high polymers (e.g. polytetra-fluoroethylene, polyethylene, polymethylmethacrylate or polyacrylonitrile) which give rise to well defined Type III isotherms with water or with alkanes, in consequence of the weak dispersion interactions (Fig. S.2). In some cases the isotherms have been measured at several temperatures so that (f could be calculated in Fig. 5.2(c) the value is initially somewhat below the molar enthalpy of condensation and rises to qi as adsorption proceeds. In Fig. 5.2(d) the higher initial values of q" are ascribed to surface heterogeneity. 

The power factor of polyethylene which provides the measure of the power loss in the insulated conductor increases slightly with an increase in the temperature of the atmosphere or the electrical equipment, both of which may fluctuate widely. It also increases slightly with an increase in the humidity of the surroundings. 

The insulating properties of polyethylene compare favourably with those of any other dielectric material. As it is a non-polar material, properties such as power factor and dielectric constant are almost independent of temperature and frequency. Dielectric constant is linearly dependent on density and a reduction of density on heating leads to a small reduction in dielectric constant. Some typical data are given in Table 10.6. 

Because the polymer is polar it does not have electrical insulation properties comparable with polyethylene. Since the polar groups are found in a side chain these are not frozen in at the Tg and so the polymer has a rather high dielectric constant and power factor at temperatures well below the Tg (see also Chapter 6). This side chain, however, appears to become relatively immobile at about 20°C, giving a secondary transition point below which electrical insulation properties are significantly improved. The increase in ductility above 40°C has also been associated with this transition, often referred to as the 3-transition. 

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 ... 

Little is known about the variation of the critical stress ", with structure and temperature. For the polyethylene discussed abovedecreased from 620 psi at 22X to 39general trend with all polymers. Turner (84) found that the value of (r(. for polyethylenes increased by a factor of about 5 in going from a polymer with a density of 0.920 to a highly crystalline one with a density of 0.980. Reid (80,81) has suggested that for rigid amorphous polymers. ", should be proportional t° (Tt - T) For brittle polymers, the value of ", may be related to the onset of crazing. 

High density and UHMW polyethylenes are used to make antifriction parts. The coefficients of friction are low but the moduli, hardnesses and softening temperatures are weak, which limits the loads and PV factors. 

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