Relative crystallinity Repeating units

In a crystalline solid there is a relatively small repeating unit, called a unit cell, that is made up of a unique arrangement of atoms and embodies the structure of the solid. The structure of the crystal can be built by stacking this unit over and over in all three dimensions. Thus, the structure of a crystalline solid is defined by (a) the size and shape of the unit cell and (b) the locations of atoms within the unit cell. 

At such extraordinarily low penetrant concentrations, plasticization of the overall matrix is not anticipated. As noted by Michaels in the previous discussion concerning crystallinity, motions involving relatively few repeat units are believed to give rise to most short-term glassy-state prc rties such as diffusion. In robbery polymers, on the other hand, longer-chain conceited motions occur over relatively short time scales, and one expects plasticization to be easier to induce in these materials. Interestingly, no known... 

As determined from X-ray diffraction measurements, the unit cell of crystalline PET is triclinic with a repeat distance of 1.075 nm along the major axis [5, 6], This corresponds to >98 % of the theoretical extended length of the monomer repeat unit [6], There is very little molecular extensibility remaining in a PET crystal, resulting not only in a high modulus but also a relatively short extension range over which the crystal can be extended and still recover elastically. The density of the crystalline structure is 1.45 g/ml, or about 9% higher than the amorphous structure [3],... 

The chemical potential of the polymer is affected by "impurities" such as solvents or copolymerized units. For an equilibrium condition in the presence of water as the diluent, the melting temperature of starch (Tm) would be lower because p in the presence of diluent is less than pi). For the starch-water system at equilibrium, the difference between the chemical potentials of the crystalline phase and the phase in the standard state (pure polymer at the same temperature and pressure) must be equal to the decrease in chemical potential of the polymer unit in solution relative to the same standard state (Flory, 1953). By considering the free energy of fusion per repeating unit and volume fraction of water (diluent), the... 

The relative molecular mass of the repeat unit on Nylon 6.6 is 226.3 g/mol so that 1.5 times 18 g water in 226.3 g polymer is equal to 12 g water can be absorbed per 100 g polymer. Taking into account the effect of crystallinity using Eq. (9-21a) one gets for the semi-crystalline polymer ... 

In the diffraction pattern from a crystalline solid, the positions of the diffraction maxima depend on the periodicity of the structure (i.e. the dimensions of the unit cell), whereas the relative intensities of the diffraction maxima depend on the distribution of scattering matter (i.e. the atoms, ions or molecules) within the repeating unit. Each diffraction maximum is characterized by a unique set of integers h, k and l (called the Miller indices) and is defined by a scattering vector h in three-dimensional space, given by h=ha +A b +Zc. The three-dimensional space in which the diffraction pattern is measured is called reciprocal space , whereas the three-dimensional space defining the crystal structure is called direct space . The basis vectors a, b and c are called the reciprocal lattice vectors, and they depend on the crystal structure. A given diffraction maximum h is completely defined by the structure factor F(h), which has amplitude F(h) and phase a(h). In the case of X-ray diffraction, F(h) is related to the electron density p(r) within the unit cell by the equation... 

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