Adjacent crystallites

The shape of nanocrystallites of natural cellulose is a subject of discussion. In several studies the cross-sectional shape of the crystallites was depicted as a square or rectangle. However, recent studies have shown that the most likely cross-sectional shape of the crystallites of natural cellulose is a hexagon (Ding and Himmel, 2006 loelovich, 1991 Yang et al., 2011). Three groups of planes (100), (110), and (110) are located on the surface of crystallites, allowing the co-crystallization process of adjacent crystallites in different lateral directions (loelovich, 1991). The co-crystallization process observed during extraction and hydrolysis of cellulose leads to an increase in lateral sizes of crystallites. 

Campbell and Peterlin and Peterlin concluded from e.s.r. measurements on isotropic and highly drawn nylon 6 and 6.6 fibres that no detectable free radicals were formed in the isotropic state, whereas approximately 1 chain in 250 was fractured in a fibre under high axial tension at failure. These fractured chains were later identified with the tie molecules linking adjacent crystallites together in the fibre direction. Quantitative theories have since been developed by Kausch et and more recently by DeVries et alP which attempt to correlate creep, creep-rupture, and stress-relaxation in fibres in terms of the measured main chain scission. 

The Avrami equationhas been extended to various crystallization models by computer simulation of the process and using a random probe to estimate the degree of overlap between adjacent crystallites. Essentially, the basic concept used was that of Evans in his use of Poisson s solution of the expansion of raindrops on the surface of a pond. Originally the model was limited to expansion of symmetrical entities, such as spheres in three dimensions, circles in two dimensions, and rods in one, for which n = 2,2, and 1, respectively. This has been verified by computer simulation of these systems. However, the method can be extended to consider other systems, more characteristic of crystallizing systems. The effect of (a) mixed nucleation, ib) volume shrinkage, (c) variable density of crystallinity without a crystallite, and (random nucleation were considered. AH these models approximated to the Avrami equation except for (c), which produced markedly fractional but different n values from 3, 2, or I. The value varied according to the time dependence chosen for the density. It was concluded that this was a powerful technique to assess viability of various models chosen to account for the observed value of the exponent, n. 

The picture which emerges from these studies is thus again that of an amorphous phase strongly affected by the limitations for the motion imposed by constraints. These constraints, originating from the adjacent crystallites... 

The number of bonds ( ) in a typical Gaussian amorphous chain sequence, which links the two adjacent crystallites separated by distance (Fig. 13.3), is given by ... 

The relation indicates that a chain that has already been included with one or more sequences in a crystallite will usually not be incorporated into another one adjacent crystallites are then kept at a distance of the order of the coil diameter. 

The model used in these investigations is represented by Figure 5.2. It consists of a tie molecule (t) which forms part of a crystal lamella (c), leaves it perpendicularly to the crystal fold surface, (I), extends straightly through an amorphous region (a) and enters the adjacent crystallite of which it forms a part. The crystal boundaries are assumed to be ideally sharp. No interaction between the tie chain and the amorphous material outside of the crystallite is taken into account. 

Disordered molecular segments in the noncrystalline regions are normally continuous with those in the crystallites. These segments comprise the three types shown in Figure 2. Noncrystalline segments can traverse the intercrystalline zone to connect to an adjacent crystallite, they can double back to attach themselves to the crystallite from which they originated, or they can terminate in a chain end. These three corrfigurations are known respectively as tie chains, loops, ... 

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