Orthorhombic polyethylene

Figure 7 Polyethylene orthorhombic crystal habit, (a) Orthogonal view (b) view along the c axis.

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

Fig. 4. Structure of orthorhombic polyethylene unit cell projected on the ab plane. The right-hand pictures define the setting angle .

Regarding mechanical properties of polymers, the efficiency of the Car-Parrinello approach has enabled us to evaluate the ultimate Young s modulus of orthorhombic polyethylene, and demonstrate basis set convergence for that property. 

Also for polyethylene, by increasing the temperature, a first-order reversible transition can occur from the usual orthorhombic form toward a hexagonal disordered form, but only for sufficiently high values of the pressure (above 4 kbar) [70-73, 5],... 

Table 7. Full Set of Compliances for the Oriented Polyethylene Terephthalate Sheet with Orthorhombic Symmetry...

Figure 7.2 Orthorhombic unit cell of polyethylene viewed a) orthogonally and b) parallel to the chain axes...

Figure 18.10 Space filling view of the orthorhombic unit cell of polyethylene...

Attempts were made to include all hydrogen atoms explicitly in the simulations. This computationally demanding explicit-atom model shows (Fig. 1) that the crystal symmetry is orthorhombic, in agreement with the well-known experimental result for polyethylene single crystals, instead of the hexagonal symmetry seen in united-atom model simulations. 

Figure 24. X-ray diffraction pattern (in the inset the 2D image) of the polyethylene sample recovered by the laser-assisted high-pressure reaction in the pure liquid monomer. The two measured sharp lines nicely fit the polymer diffraction pattern having a orthorhombic cell (Pnam) defined by the lattice parameters reported in the figure.

Porat et al. performed TEM (zero-loss bright field) studies of very thin Nation films that were cast from ethanol/water solutions, and some of the conclusions are as follows. It was suggested that the backbone had a planar zigzag conformation in large orthorhombic crystallites as in polyethylene, in contrast with the helical conformation found in poly(tetra-fluoroethylene). This is an interesting result, although there are no other studies that support this view. Sulfur imaging indicated the presence of sulfonate clusters that are 5 nm in size. 

Isomorphism in copolyalkenamers was reported by Dall Asta, Motroni, and Carella (27). These copolymers may be considered as constituted by an unbranched polyethylene chain containing, at irregular intervals, fra s-intemal double bonds. It is known 28) that the crystal structure of the homo-fraws-polyalkenamers depends on the number of methylene groups existing between two subsequent double bonds the odd series crystallizes in an orthorhombic unit cell, similar to that of... 

Figure 20 shows the phase diagram of polyethylene119). The existence range of the condis crystals increases with pressure and temperature. The enthalpy of the reasonably reversible, first order transition from the orthorhombic to the hexagonal condis phase of polyethylene is 3.71 kJ/mol at about 500 MPa pressure 121) which is about 80 % of the total heat of fusion. The entropy of disordering is 7.2 J/(K mol), which is more than the typical transition entropy of paraffins to their high temperature... 

The crystal structures of C2Ht—CO copolymers with QH4/CO ratios of 1, 1.3, 2.2 and 3.5 have been determined49,50). For the 1 1 copolymer an orthorhombic unit cell of dimensions a = 7.97, b = 4.76, c (fiber axis) = 7.57 A was observed 49). The main chain had a planar zigzag form. For copolymers with higher C2Ht contents, the fiber periods were essentially identical with that of polyethylene (c 2.54 A) 50). Also, the higher the C2H content, the shorter the a axis and longer the b axis. 

Fig. 17.6. Maps of in-plane crystallographic orientation of the orthorhombic cell in the crystalline part of the polyethylene structure (a) short-term and (b) longterm implanted acetabular cups (cf. the central photographs). Compare the average direction of c-axis orientation and the motion direction shown on the respective maps and on the photographs of the acetabular cups, respectively...

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