Fabrication Techniques and Properties of Scaffolds - Biodegradable Polymer-Based Scaffolds for Bone Tissue Engineering - page 34

2.6 Diffusion Phenomena

2.6.1 Factors Affecting Diffusion Phenomena

Temperature and composition are the two most important factors which can
affect the diffusion coefficient, D. Between these two factors; temperature has
the more profound influence on the coefficients and diffusion rates. The temper-
ature dependence of diffusion coefficients is related to temperature according to
Arrhenius equation:

Q
RT

D = D 0 exp (2.5)

where T is the absolute temperature (K), Q is the activation energy for diffusion
(J/mol or eV/atom) and D o is a temperature independent constant/pre-exponential
(m 2 is R is the gas constant, 8.314 J/mol-K or 8.62 × 10 − 5 eV/atom. The activa-
tion energy is referred to as the energy required to produce the diffusive motion of
one mole of atoms.
Taking natural logarithms of Eq. (2.6):

Q
R

1
T

ln D = ln D 0 − (2.6)

as D 0 , Q and R are constants, a straight line will be resulted if ln D is plotted
versus the reciprocal of the absolute temperature. The slope and the intercept of
the straight line is ( − Q/R) and ln D 0 respectively. Nevertheless, the quantities D,
D 0 and Q vary with concentration. Diffusion coefficient, D is expected to increase
with increasing lattice irregularity as diffusion is a structure-sensitive property. If
the metals are quenched from high temperature, the excess vacancy concentra-
tion leads to enhanced diffusion at low temperatures where grain boundaries and
dislocations are mostly important to produce enhanced diffusion. In Aluminium
where voids connected to a free surface by dislocations anneal out at appreciably
higher rates than isolated voids and for this reason the enhanced transport of mate-
rial along dislocation channels has been demonstrated (Smallman and Ngan 2007 ).
It was also observed that surface and grain boundary forms of diffusion also obey
Arrhenius equations that possess lower activation energies than for volume diffu-
sion i.e. Q vol ≥ 2Q g.b ≥ 2Q surface . This behaviour could be understandable in con-
sideration of progressively more open atomic structure found at grain boundaries
and external surfaces.
However, the relative importance of the different forms of diffusion does not
solely depend on the relative activation energy or diffusion coefficient values. In
any diffusion process, the amount of material that is transported can be given by
Fick's law and at a given composition gradient it also depends on the effective area