Short chain diffusion

The mathematical equations that govern the heterogeneous degradation are presented in Chapter 6. A key variable in the equations is the concenlration of the short chains. These short chains diffuse from where their concentration is high to where it is low. This principle can be combined with the requirement for matter conservation and written into a mathanatical equation. Before the computer age, such equations were very difficult to solve for real devices. It is almost impossible to find an analytical function to desalbe how the concentration varies with space and time in a device of sophisticated shape. The finite element method overcomes this difficulty by using two key ideas ... 

Similarly, it is difficult to apply the principle that short chains diffuse from where concentration is high to where it is low to the tetrahedral elements shown in Plate I (a). This is because the elements are of irregular shape and size and connected irregularly with each other. The finite element method resolves this difficulty by using a... 

Equations [2.26] and [2.30] have been widely used in the literature to interpret degradation data for their simplicity. The validity of these equations is often limited to the very early stage of the degradation. For amorphous polymers, the master Equation [2.15] is more generally valid. However, short chain diffusion is ignored, which is the topic of the following chapters. 

Master equation without short chain diffusion... 

The issue of short chain diffusion will be dealt with in Chapter 6. In this chapter, we focus on situations where the short chain diffusion is very slow and can be ignored. In this case we have... 

C i represents the current concentration and can be altered by short chain diffusion. Figure 3.1 illustrates the difference between R i and C i. The short chains are generated at the expense of the long chains which can be expressed as... 

Figure 6.1 Short chain diffusion in a plate showing distributions of short chain concentration over thickness of the plate at different stages of degradation, (a) A representative unit of the plate and (b) change of short chain concentration over time.

For semi-crystalline polymers, the governing equation for chain scission rate and short chain diffusion are... 

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