Actual chain conformations and crystal structures

If the crystal structure of a polymer is known, it is possible to calculate the expected intensities of all the diffraction spots by using the known scattering powers of its various atoms. If, therefore, it is possible to predict the structure from the measured unit-cell dimensions and some assumed form for the polymer chains within the unit cell, it is possible to compare a predicted set of intensities with the observed diffraction pattern. If the structure assumed is close to the actual one, only minor adjustments will be needed in order to get a more perfect fit between the predicted and observed scattering patterns and thus to determine the structure. Otherwise a new prediction must be made. 

Two important types of polymer chain are the planar zigzag and the helix, but whatever form the chains take in crystallites, they must be straight on a crystallite-size scale and the straight chains must pack side by side parallel to each other in the crystal. The ideas of standard bond lengths, angles and orientations around bonds discussed in chapter 3 can be used to predict likely possible low-energy model chain conformations that exhibit translational symmetry (see example 4.3). As discussed in the 

By assuming the standard bond lengths, angles and preferred orientations around bonds, estimate the most likely chain repeat length for polyethylene. 

The standard C—C bond length / is 0.154 nm, the standard CCC bond angle is tetrahedral, 109.5°, and the planar zigzag structure is the most likely conformation. The 

This value is in fact 2% different from the observed value. The X-ray patterns can be well accounted for by a bond angle of 112° and a C—C bond length of 0.153 nm. 

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