Environmental Engineering Reference
In-Depth Information
Fig. 7
Density profile for polymer chains with degree of polymerization
N
=
5(
left
). The inset
shows an image from the actual simulations. Full solvation force obtained from GCMC DPD
simulations of polymer brushes (
right
). The
line
represents the AdG model. Axes are shown in
reduced units. Adapted from Gama Goicochea and Alarcón (
2011
)
of GCMC-DPD simulations. This is a quantityof importance when studying the
properties of confined fluids because it is a measure of the stability of complex
fluids under confinement and fixed chemical potential (Gama Goicochea
2007
). It
is defined as the difference between the pressure tensor component in the direction
perpendicular to the confinement (
P
N
) and the pressure of the bulk (unconfined)
fluid,
P
B
.InFig.
7
, we see the disjoining pressure (
) as a function of the distance
between the walls (
L
z
), for a monomeric fluid confined by linearly decaying surface
forces. There appear intercalated maxima with minima whose interpretation is as
follows. The maxima in
ʠ
represent thermodynamic states with maximal force
between colloidal particles (per unit area) represented by the walls, mediated by
the corpuscular nature of the solvent. These maxima are the consequence of an
ordered array of the solvent molecules into layers, whose order gets increasingly lost
as the separation between the surfaces grows, as should be expected. These states
correspond to conditions of optimal stability for the colloidal dispersion. The minima
seen in Fig.
8
represent states where there is an attractive (negative) force between
the surfaces, therefore they are thermodynamically unstable and would lead to the
agglomeration of colloidal particles. It is remarkable that an attractive force can
emerge from a model (DPD) where all particle interactions are repulsive, including
the wall force. It occurs because of the confinement condition and the corpuscular
nature of the solvent, which forces the particles to form orderly layers when the force
is at a maximum (see points labeled
a
,
c
and
e
in Fig.
8
) and be disordered when the
force is minimal (as in states labeled
b
and
d
in Fig.
8
).
The behavior shown in Fig.
8
reproduces very well the trends found in experiments
and with other calculation methods (Israelachvili
2011
), and lends credence to the
usefulness of DPD as a precise predicting tool, not only for polymers in solution,
but also for confined complex fluids. It is advantageous to perform simulations like
these before embarking in laborious, time consuming and expensive experiments,
such as those required to determine adsorption isotherms. In the design of new
colloidal dispersions for the paint industry, for example, or for the improvement and
ʠ
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