Polymer crystallinity

11.4 Polymer crystallinity

In most polymers the spaghetti-like chains of various lengths pack together in a random way, forming

a tangled mass in the bulk materials. These polymers are therefore non-crystalline or amorphous. However, in some polymers the chain molecules form regions in which the repeat units are aligned in ordered arrays, in some cases folded backwards and forwards to resemble the ‘jumping jack’ firework. Such crystalline regions are usually quite small ( ∼20 nm) and often associated with amorphous regions, as shown in Figure 11.4 for polyethylene. In this case, crystalline regions nucleate and grow during polymerization, approaching 50% for LDPE and 80% for HDPE. Clearly, the density of a crystalline polymer will be greater than that of an amorphous polymer of the same composition and

554 Physical Metallurgy and Advanced Materials Amorphous

region

Chain branching

Crystalline region

Side groups

Figure 11.4 Semi-amorphous structure of polyethylene ( from Ashby and Jones, 2005).

Specific volume

T m Temperature

Temperature

Temperature

(c) Figure 11.5 Specific volume versus temperature plots for: (a) 100% amorphous polymer,

(a)

(b)

(b) partially crystalline polymer, (c) 100% crystalline polymer.

molecular weight. The degree of crystallinity by weight may be determined from accurate density measurements according to

where ρ is the density of the polymer, ρ c is the density of the fully crystalline polymer and ρ a is the density of an amorphous polymer of the same material. Crystallization is favored by slow cooling rate, since this allows time for the packing and ordering of the chains. Application of stress also aids crystallization. In contrast, crystallization is hindered as molecules become longer and more complex, thereby reducing molecular mobility. Isotactic configurations favor crystallinity compared to atactic configurations. Matching configurations also favor crystallinity and are more likely in copolymers with regular block patterns of constituents than in random copolymers. Thermal degradation increases

with increase in temperature and, above T g , the glass transition temperature, the entangled molecules begin to lose their rigidity until, at T m , the melting point, crystallinity breaks down completely. T m increases with the degree of crystallinity and is 110 ◦

C for LDPE and 135 ◦

C for HDPE. Figure 11.5

Non-metallics II – Polymers, plastics, composites 555 shows the influence of temperature on the specific volume of a polymer with varying degree of

crystallinity. Parameters such as specific volume, heat of fusion and density are influenced by the degree of crystallinity φ according to

p =φp c + (1 − φ) p a ,

where p is the overall experimental value of, for example, specific volume, p c is the value for a crystalline polymer and p a for the amorphous polymer. Differential scanning calorimetry (DSC) can provide the heat of fusion (see Figure 4.61c) and φ is given by

φ = Heat of fusion of sample/Heat of fusion of 100% crystalline polymer.

Worked example

Derive the formulae for % crystallinity by weight and by volume, for evaluation by density measurement of a polymer. High-density polyethylene (HDPE) has a density of 0.95 Mg m −3 . Calculate the degree of crystallinity by weight and by volume if the amorphous PE and fully crystalline PE have densities of 0.84 and 1.01 Mg m −3 respectively.

Solution

Let m, m c and m a be the total mass, mass of the crystalline phase and mass of the amorphous phase respectively of the polymer. Similarly, let V , V c and V a be the total volume, and volumes of

V , i.e. crystallinity by volume, and φ =m c / m, i.e. crystallinity by weight.

the crystalline and amorphous phases. Furthermore, let f =V c /

Since m =m c +m a , ρV =ρ c V c +ρ a V a , or ρ =ρ c f +ρ a (1 − f ).

−ρ a

Hence, f

ρ c −ρ a

a ρ Degree of crystallinity by weight φ

−ρ = c . m = Vρ =f ρ = ρ c −ρ a ρ

Alternatively, since V =V c +V a , m/ρ =m c /ρ c +m a /ρ a , giving

− 1/ρ a

1/ρ = φ/ρ c + (1 − φ)/ρ a .

Thus, φ

, which is the same as the above equation.

For HDPE, f

c −ρ a 1.01

−ρ a c (0.95 − 0.84) × 1.01