Environmental Engineering Reference
In-Depth Information
Fig. 6
The exact DPD wall-fluid force (Eq.
14
)isshownin
blue
, while the full, many-body solvation
force obtained from simulations with the wall force is shown in
red squares
. Both scales on the
y
-axis are shown in reduced DPD units, as is also the
x
-axis. To convert the latter into physical
distances it is necessary to multiply
z
∗
by 6
.
46Å. Adapted from Gama Goicochea and Alarcón
(
2011
)
enon is the result of the collective many—body interactions that carry information
about the boundary conditions of the fluid in the direction of the confinement (Fig.
6
).
By attaching polymer chains to these effective surfaces it is possible to calcu-
late the force between colloidal particles covered with polymer brushes and com-
pare it with other models, like the well-known Alexander-de Gennes (AdG) model
(Alexander
1977
; de Gennes
1980
), which is based on scaling arguments and assumes
that the density profile of the monomers that make up the polymer brushes is a step
function. This is known to be inaccurate. It also assumes that the polymer chains
do not interact with one another, and that they are immersed in a solvent of good
quality (Alexander
1977
; de Gennes
1980
). The AdG force is then the result of short
range repulsion caused by the increased osmotic pressure when the polymer brushes
are brought into close contact, and elastic attraction created by the entanglement
of polymer chains on opposite brushes. In the left panel of Fig.
7
, we present the
density profile of the polymer brushes at a given separation between the walls, which
shows the beads attached to each surface and the structuring in the density profile
of the brushes, which is a consequence of having relatively short chains (
N
5for
the case shown in this figure). Notice how this profile is far from resembling a step
function. Yet, as shown in the right panel of Fig.
7
, the AdG model reproduces fairly
well the trend in the full solvation force obtained with GCMC DPD simulations,
although the latter are more accurate because the interactions between all particles
are accounted for.
The disjoining pressure of a simple monomeric fluid confined by effective linearly
decaying wall forces, as the one shown in Eq. (
13
), has been calculated by means
=
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