Environmental Engineering Reference
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4.2 Adsorption Isotherms
The adsorption of polymers onto different surfaces has been the subject of many
theoretical and experimental studies. Specifically, the adsorption of polyelectrolytes
is a topic of extensive concern because of its practical applications. Many surfactants
and additives are polyelectrolytes, and they must be adsorbed with great selectiv-
ity on different surfaces in order to have a good performance. This phenomenon is
observed in different fields such as water purification where the adsorption of poly-
electrolytes could produce flocculation. Other critical examples are emulsifiers in the
food and pharmaceutical industries, as well as complex polyelectrolytes for medical
science applications, among others. In order to have a good understanding of this
phenomenon, more precise information about the conformation of polyelectrolytes
adsorbed on a surface and living in the surrounding medium is important. Few the-
oretical studies have been developed to describe polyelectrolyte adsorption, while
experimental studies are laborious. For this reason, numerical simulations seem to
be a good alternative. DPD simulations can reproduce the behaviour of this kind of
systems but some considerations must be taken.
By construction, the DPD dynamics keep the number of particles
N
, the cavity
volume
V
, and the temperature
T
constant. For adsorption isotherms one needs the
chemical potential
∂
U
∂
N
i
μ
i
=
N
j
=
i
,
(39)
S
,
V
,
fixed; i.e., one needs to work in a Grand Canonical Ensemble
. This may
be achieved by using a hybrid DPD-Metropolis Criterion (DPD/MC) (Alarcón et al.
2013
). In this, after the usual DPD dynamics, one performs a certain number of cycles
of particle exchange with the virtual bulk that will return the chemical potential to
its initial value
μ(
(μ,
V
,
T
)
, and calculates the final energy of the system: if equal to or
lower than the initial energy, the exchange cycle is accepted; if higher than the initial
energy it is rejected and a new exchange cycle is performed. This is followed by
another iteration of DPD dynamics together with particle exchange cycle, and so
on. By generating separate simulations for different polymer concentrations in this
manner, one may calculate the density profile
ˁ(
t
0
)
z
)
in a box of length
L
z
, and from
it the adsorption
ʓ
as
L
z
ʓ
=
[
ˁ(
z
)
−
ˁ
bulk
]
dz
.
(40)
0
Adsorption isotherms have been calculated performing DPD simulations in this
manner (Alarcón et al.
2013
) and checked to coincide with experimental determi-
nations (Mayoral et al.
2011
; Huldén and Sjöblom
1990
; Esumi et al.
2001
). As
an example, Fig.
5
displays the results for the simulation of the adsorption of poly-
acrylic acid (PAA) on explicit
TiO
2
surfaces. PAA was mapped considering each
DPD bead as one monomeric unit (
COOH
). The repulsive
a
ij
parame-
ters were obtained according to Sect.
3
. The number of independent adsorbed versus
−
CH
2
−
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