Biomedical Engineering Reference
In-Depth Information
composition and (ii) water uptake. Water adsorption, the first step of degradation is
dependent on polymer hydrophilicity.
The diffusion of water into the polymer bulk and the chain scission reaction com-
pete against each other in the process of polymer erosion. Erosion is caused by degra-
dation and is the process of dissolution or wearing away of degradation byproducts,
resulting in mass loss from the polymer bulk. Erosion is by far much more com-
plex than degradation inasmuch as the number of parameters that potentially might
influence the process is considerably larger. Two main modes of erosion can be sys-
tematized from widely established empirical evidence [7]. If degradation is fast, the
diffusing water is absorbed quickly by hydrolysis and is hindered from penetrating
deep into the polymer bulk. In this case, degradation and consequently erosion are
restricted to the surface of the polymer, a phenomenon referred to as heterogeneous
or surface erosion [45]. This type of erosion changes if degradation is slower than
the rate of diffusion of water through the polymer. In this case, water cannot be
absorbed quickly enough to be hindered from reaching deep into the polymer and
the reaction takes place through its entire swollen bulk, a behaviour which has been
termed homogeneous or bulk erosion [45]. Nevertheless, surface or bulk erosion
modes are two extremes and the erosion of a polymer usually shows characteristics
of both.
Hydrolysis is a very intricate process that occurs at the molecular level, as a vari-
ety of different scission pathways can occur simultaneously and concurrently [48].
Although the reactivity of each bond might be equal when considered individually,
the large number of repeating units and their inherent steric environment, weak links,
and branches may influence locally the rate of reaction. Ultimately, experiments with
gel permeation chromatography provide data to model the mechanism of degradation
[33, 34], and kinetic parameters are obtained from the evolution of experimentally
obtained molecular weight distributions. An approach pioneered by Kuhn [22] and
Montroll and Simha [31] employs combinatorial statistic to derive analytical solu-
tions of the evolution of molecular weight distribution assuming that bond scission
can be described with a known probability density function (e.g. equiprobable ran-
dom scission, central Gaussian, or parabolic) and only for some limited simple initial
conditions. Unfortunately, the applicability of such elegant exact solutions to real
systems is limited essentially due to simplifying assumptions necessary for the ana-
lytical treatment of the problem. A second technique to model polymer degradation
relies on the system of differential equations which describe the depolymerization
rates of individual bonds that upon integration yield the time evolution of the molec-
ular weight distribution [4]. However, the complete kinetic scheme that includes all
the individual rate constents for each reacting bond could represent an enormous
number of coupled differential equations even for modest size macromolecules. A
third common method employs Monte Carlo simulations applied to populations of
polymer chains [6, 9, 21], a versatile approach that can technically overcome the
simplifying assumptions needed on the others, but realistic simulations may require
an excessive amount of computational resources, results are usually subjected to
large statistical errors, and may be in fact unnecessary when compared with simpler
approaches.
