Ageing processes of biomedical polymers in the body - Durability and Reliability of Medical Polymers - page 168

into animals (Martin et al. , 2000; Simmons et al. , 2004; Simmons et al. ,
2006; Simmons et al. , 2008). However, necessary approval is required for
this and the period of implantation (usually two years) used in these studies
may not be suffi cient.

8.4.1 A common approach used to express the rate of
ageing of polymers
A method that can be used to determine whether deterioration is likely to
occur over long timescales, is to subject materials to elevated temperatures,
a process known as 'accelerated ageing' (Hemmerich, 1998; Hukins et al. ,
2008; Mahomed et al. , 2010a). This is particularly useful to study the ageing
of materials that are regarded as potential implant material.
A common approach is to assume that the rate of ageing is increased by a
factor of (ASTM-WK4863, 2005; Hemmerich, 1998; Hukins et al. , 2008):

f = 2 DT/10 [8.1]

where D T = T - T ref . T is the elevated temperature used to accelerate the
ageing process and T ref is the reference temperature, at which to study the
effects of ageing. For example, for studies involving materials suitable
to be implanted in the body, T ref is 37 °C (body temperature). Therefore,
maintaining a material at 70 °C for 38 days is the same as ageing it for 38
¥ 2 (70-37)/10 = 380 days, i.e. ageing for ª 13 months, at 37 °C.
Further inspection of equation [8.1], shows that when DT T = 10 °C is
substituted, then f = 2 (Hukins et al. , 2008). This result is a mathematical
expression of the empirical observation that increasing the temperature by
about 10 °C roughly doubles the rate of many polymer reactions, the '10-
degree rule' suggested by Hemmerich (1998). Furthermore, Hukins et al.
(2008), also shows that by using the principles of chemical kinetics, this
is equivalent to assuming that the ageing process is a fi rst-order chemical
reaction with an activation energy of 10 R /log e 2, where R is the universal
gas constant. Hukins et al. (2008) based this on the fact that, for a fi rst-order
chemical reaction:

￿ ￿ ￿ ￿ ￿ ￿

k = K exp (- E act / RT ) [8.2]
where E act is the activation energy for the ageing reaction, R is the universal gas
constant (8.314 J mol -1 ), K is an empirical factor and T the temperature.
If k ref is the value of k when T = T ref , equation [8.2] can be manipulated
to defi ne:

Ê
Ê

ˆ
ˆ

D

R R D

E

k

[8.3] f ¢ = exp =

Ë

k k r k f

act

re

This can be expressed as: