Polyethylene elastic moduli

The highest reported experimental values of polyethylene elastic modulus attained to date have been in the range of 230-264 GPa [23]. This equals or exceeds some of the values calculated for perfectly aligned polyethylene mole-... 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

Fig. 6. Variation of elasticity modulus (E) under tension and yield strain (es) of the polymer matrix (I, I ) and polyethylene-based composites polymerization filled with kaolin (2,20 in function of polymer MM [320], Kaolin content 30% by mass. The specimens were pressed 0.3-0.4mm thick blates stretching rate e = 0.67 min-1...

Although the amount of ECC in polyethylene samples is not large, the mechanical properties of the material are markedly affected the tenacity and elastic modulus are higher. 

Figure 3 Chemometric calibration of the elastic modulus (left) and the yield stress (right) of a series of polyethylenes. Reproduced from Gabriel et al. [23], Copyright 2003, with permission from Wiley-VCH Verlag GmbH.

Three common methods of measuring crosslinking (swelling, elastic modulus, and gel point measurements) have recently been critically appraised by Dole (14). A fourth method using a plot of sol + sol against the reciprocal dose has also been used extensively. However, Lyons (23) has pointed out that this relation, even for polyethylenes of closely random distribution, does not have the rectilinear form required by the statistical theory of crosslinking. Flory (19) pointed out many years ago that the extensibility of a crosslinked elastomer should vary as the square root of the distance between crosslinks. More recently Case (4, 5) has calculated that the extensibility of an elastomer is given by ... 

Division of the total tensile strain under conditions of F = const into several components 25,6R,69) produced interesting results (see Fig. 8). It has been found that the behavior of molten low-density polyethylene (Fig. 8a) is qualitatively different from polyisobutylene (Fig. 8 b) the extension of which was performed under temperature conditions where the high-elasticity modulus, relaxation time, and initial Newtonian viscosity practically coincided (in the linear range) in the compared polymers. Flow curves in the investigated range of strain velocities were also very close to one another (Fig. 21). It can be seen from the comparison of dependencies given in Fig. 8a,... 

The associated elastic modulus of polyethylene is E = 290 GPa. However, the critical test of eq 2 is in the /s —1- °o region. The results for long extended-chain alkanes up to C2g4H5go were at variance with eq 2 and obeyed the simple V —1- 1 In law, with v — 0 as ls —... 

Good models are needed because information on important properties such as heat capacity and elastic modulus can be derived from the force constants, The elastic modulus data is particularly useful since it allows the ultimate tensile strength of polyethylene to be determined. Based on present estimates of this, it is apparent that it is still possible to improve existing materials. 

The mechanical properties of most polymers are modified by irradiation. They usually deteriorate in polymers undergoing predominant chain scission. In crosslinked polymers, the mechanical properties strongly depend on the temperature at which the measurements are performed and improvements are often obtained, especially above the melting point. Crosslinked polyethylene, for instance, is a rubbery solid above its crystalline melting point instead of being a viscous liquid if not irradiated. At room temperature, the elastic modulus and tensile strength are often increased by irradiation. Results on individual polymers will be discussed in section 5. 

The mechanical properties of irradiated polyethylene depend strongly on the temperature as shown in Figs. 41—43. Figure 41 reproduces the stress—strain curve for low-density samples subjected to 15 Mrad irradiation [427]. Figure 42 gives the value of the elastic modulus, E, as a function of temperature [428]. 

Stress—strain curves at room temperature are also given in Fig. 41 for irradiated low-density polyethylene [427]. The change in elastic modulus... 

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... 

In the special case of branched polyethylene, the elastic modulus at 45° to the fiber axis is exceptionally small this means that shear compliance along the fiber axis is very high (16). Such deformation involves reversible shearing displacement of adjacent fibrils. Since a similarly high shear compliance does not occur with linear polyethylene and isotactic polypropylene, the difference may be attributable to the substantial difference in draw ratio (4.5 in branched, 20 in linear polyethylene and propylene) which results in proportionately shorter microfibrils and fibrils in the former. The shorter the microfibril, the shorter the fibril and the smaller the surface-to-cross section ratio and hence the smaller the resistance to shear displacement. 

A plate of high-density polyethylene has a surface crack 7.5 pm in one face. The plate fractures in a brittle fashion when a force of 6 X 10 N m is apphed in a direction perpendicular to the crack. The elastic modulus of the polyethylene is 0.95 GPa. Estimate the surface energy of the material. 

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