Amorphous volume fraction

Measurements of the permeability and diffusivity have been undertaken for helium and oxygen for a range of highly oriented polyethylene films The deduced solubilities for both gases are proportional to the amorphous volume fraction showing that the non-crystalline regions are the transport medium in all instances. The solubility obtained for oxygen is about ten times that for helium. This result is consistent with the proposal of Michaels and Bixler which relates the amorphous phase... 

Using D for fiuence (ions/cm ), the amorphous volume fraction is ... 

Figure 8. Amorphous volume fraction, as a function of normalized ion dose for different values of crystallization efficiency, A..

Attempts have also been made to relate the tortuosity factor to the amorphous volume fraction. A power law relationship has been suggested... 

In brief, unlike solubility, the effects of crystallinity on the effective diffusivity intimately involve the details of the polymer morphology. Because of the chain immobilization effect, crystallinity may cause an increase in the activation energy of diffusion. However, observed decreases for the activation energy of diffusion for helium in semicrystalline materials have been attributed to "grain boundary" effects (22.) For a first approximation, some authors have found it sufficient to use the following relationship for the correlation of amorphous volume fraction and effective diffusivity,... 

The mass of crystals in 1 m of polymer is the product of the volume fraction crystallinity, and the crystal density p. The mass of amorphous material is product of the amorphous volume fraction crystallinity (1 — VJ and the amorphous density Pa. Consequently, the polymer density p is linearly related to by... 

For semi-crystalline polymers above Tg, the permeability is proportional to the nth power of the amorphous volume fraction n lies between 1.2 and 2. The gas must diffuse between the lamellar crystals, and the detailed morphology depends on the polymerisation route, thermal history and whether orientation is present. The permeability of gases of molecular weight M is approximately inversely proportional to y/M. However, Table 11.2 shows that the ratio of CO2 to O2 permeability in glassy polymers is higher than in semi-crystalline polymers. 

The rate of change of amorphous volume fraction is given by the equation ... 

FIGURE 17.5 Structural changes during mechanical alloying of A1 17 at.% Mo powder in tumbler ball mill (a) crystallite size, d (b) lattice parameter of aluminum, aai (c) amorphous volume fraction, /am-... 

Therefore, although rather cumbersome, the free-volume theory permits one to prepare theoretical plots of permeability as a function of temperature, penetrant pressure, and amorphous volume fraction in the rubbery polymer. 

It is recognized that the solubility and diffusivity of gas in semicrystalline polymers are a function of the degree of crystallinity because gas does not dissolve in the crystallites [34,59-61]. Increasing the mass fraction of crystallite in the polymer leads to the reduction of the amorphous matrix mass fraction. As a result, the solubility and diffusivity of gas are reduced since the gas does not dissolve in the crystallites, and the crystallites tend to obstruct the movement of gas molecules in the polymer [34]. Since the crystal domains in semicrystalline PLA do not absorb gas, induced crystallinity in PLA by CO2 must have reduced the amount of gas available in the amorphous region due to the lower amorphous volume fraction, thus affecting the morphology developed in the foamed polymer. 

In crystalline polymers, the crystalline areas act as impermeable barriers to permeating molecules and have the same effect as inert fillers, i.e. they force the permeant molecules to diffuse along longer path lengths. " Permeant solubility is proportional to the product of the amorphous volume fraction (f) and the solubility S of the permeant in the amorphous phase. Figure 11 shows the effect of increasing crystallinity, and hence density, on nitrogen permeability. The thermal history of a crystallizable polymer can profoundly affect the permeation properties, since this can affect the number and size of crystallites present. 

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