50 Sara Llamas, Laura Fernández-Peña, Ana Mateos-Maroto et al.
view, the study of the adsorption kinetics is not trivial, especially in the initial
stages. This is easily explained considering the large numbers of factors
involved [29, 109]. In general, the adsorption kinetics appears as a two steps
process: a first fast step in which the adsorption rate is high and a second
slower step in which the adsorption rate decreases until the steady state of the
polymer adsorption is reached. This is due to the temporal coupling of the
time-scales associated with the two first steps, being impossible their
separation from experimental data [13]. Therefore, experimental results show
the adsorption kinetics of polyelectrolytes as a bimodal process [117]. The first
step is fast, and associated with the diffusion process and adsorption through
barriers, thus corresponding to the two first steps predicted by the theoretical
models. This process is not a real diffusion control process because the
attachment of polyelectrolyte chains creates barriers for the adsorption of new
chains [30, 32]. In general, this step has duration from ten second to some
minutes, leading to an adsorbed amount about the 60-80% of the total
adsorbed amount [23, 25, 118]. The second step is related to the reorganization
of polyelectrolyte chains, corresponding to the third step of the theoretical
models. This step is slower than the first one because the adsorbed chains must
be reorganized in order to allow more polymer chains to reach the surface
(densification of the adsorbed layer) [119]. The second step is limited by the
time required for the reorganization of the adsorbed film, being strongly
hindered by steric or electrostatic barriers, being possible that its time-scale
can be span from 10 to 10^5 seconds [109, 118]. According to the above
described model, it is possible to describe the adsorption kinetics of
polyelectrolytes onto surfaces following an Avrami – like expression as
follows [120-123]
/ 12 ( / )12 (1 ) (1 )
ttn A e A e (30)
where Ai(i = 1, 2) corresponds to the amplitudes of each process and τi(i = 1,2)
are the characteristic times of the fast and slow steps, respectively. The second
term is related to the reorganization process, being n an exponent reminiscent
from the Avrami’s theory [124], and assume a value close to 1 for the
adsorption of most of the polyelectrolytes onto solid surfaces [26, 28]. Taking
into account the above discussion, it is possible to define Г∞ as follows
AA (^12) (31)