Segmental Orientation under Simultaneous Biaxially Stretching Using a Lattice Model and the Application of Oriented Crystallization of Polyethylene Films

Abstract

ABSTRACT:A lattice model proposed before for uniaxial stretching of polyethylene films was applied to estimate the oriented crystallization of ultra-high molecular weight polyethylene (UHMWPE) dry gel films under simultaneous biaxially stretching. In this model system, the preferred axis associated with the preferred orientation of amorphous chain segments was chosen along the direction between two successive cross-linked points and the preferred axis was assumed to deform in an affine fashion with respect to the stretching direction. As the application of the proposed model, the orientation distribution function of crystallites was calculated on the basis of the lattice model and oriented crystallization model. The oriented crystallization model is based on the concept that a kinetically determined distribution of crystal chain axes as the normalized distribution of clusters found at the saddle point corresponding to a non-uniform orientation under conditions of a steady-state nucleation rate. Of course, the crystallites are oriented randomly with respect to the film normal direction. The parameter fitting for the formulated orientation distribution function of crystallites was done for the film which was prepared by the gelation/crystallization from solution with 0.9 g/ 100 mL concentration, the solvent being decalin, since the concentration assured the highest drawability under simultaneous biaxially stretching. The calculated orientation distribution functions 2q j ðcos j Þ of the reciprocal lattice vector of the crystal planes were in good agreement with the observed ones. Thus the numerical calculations indicate that the orientation of the c-axes depends on that of amorphous chain segments and the orientation behavior of crystallites is strongly affected by their rotation around the c-axis. [DOI 10.1295/polymj.37.192] KEY WORDS A Lattice Model / Simultaneous Biaxially Stretching / Preferred Orientation / A Steady-State Nucleation Rate / Orientation Distribution Function of Crystallites / Segmental orientation in uniaxially deformed elastomatic networks has been treated in terms of gas-like theories and liquid-like theories.1-4 In the gas-like theories, the chain vector and segment vector distributions have been estimated theoretically by using idealized models in which the effect of mutual interference between chain segments are neglected. On the other hand, in a liquid-like theory, 3,4 the effect of intermolecular interferences relating to orientation-dependent packing entropy was taken into consideration based on a lattice model. Erman et al. 5,6 have attempted to improve the liquid-like theory by considering the effect of chain stiffness on segmental orientation. For this purpose, they adopted the lattice theory of Flory 7,8 for chains with freely jointed rod-like segments and applied it to a thermotropic system with anisotropic polarizabilities. Namely, Erman et al. pointed out that a segment of polyethylene chains with 1-22 bonds may be viewed as a rod-like object on the basis of the concept of Flor...

Orientation Behavior of Carbon Fiber Axes in Polymer Solutions under Magnetic Field Estimated in Terms of Orientation Distribution Function

“…Accordingly, n must be even, and consequently G l 0 n becomes zero. Thus, eqs and reduce to − F l 0 j = F l 00 P l ( cos Θ j ) + 2 ∑ l = 2 ∞ ( l − n ) ! ( l + n ) ! F l 0 n P l n ( cos Θ j ) cos ( n Φ j ) and 4 π 2 ω ( cos ( θ , η ) ) = 1 2 + 2 ∑ l = 2 ∞ true[ 2 l + 1 2 F l 00 P l false(…”

“…A completely mathematical description for the orientation distribution function of crystallites was proposed by Roe and Krigbaum − using the orientation functions measured for many crystal planes. The description was applied to polyethylene crystallites with orthorhombic unit by Krigbaum et al and Matsuo et al, − to cellulose, poly(vinyl alcohol) (PVA), , and nylon 6 crystallites with monoclinic unit by Matsuo et al, and poly(butylene terephthalate) (PBT) and poly(ethylene terephthalate) (PET) crystallites with a triclinic unit by Matsuo et al The evaluation methods have been developed to obtain the three principle crystallographic axes ( a -, b -, and c -axes) from the predicted orientation distribution function of crystallites. In doing so, the orientation functions of the reciprocal lattice vectors must be measured by X-ray diffraction precisely.…”