Environmental Engineering Reference
In-Depth Information
Fig. 6
Disjoining pressure isotherms for 20 molecules of short-chain
M
w
=
400, versus 10 mole-
cules of long-chain
M
w
=
800 surfactant molecules of the PEG-type. Taken from Gama Goicochea
et al. (
2009
)
water at room temperature, and promotes polymer adsorption onto the substrate over
solvent adsorption. For the spring constant in the polymer DPD-particles
k
=
100
has been chosen with an equilibrium distance of
r
eq
=
0
.
7. The temperature was
kept constant at
T
300 K.
It could be observed that shorter polymers are better as dispersants when compared
with longer ones at the same monomer concentration. If we multiply the dimension-
less
=
ʠ
∗
r
c
3
depicted in the figure by
k
B
T
/
(cf. Eq.
18
), the disjoining pressure for
10
5
Pa larger than that for the longer chains at cer-
tain wall separations. Stability via surface modification is then much better attained
through the use of monomeric species than through polymer chains. The same behav-
iour is found for grafted polymers (cf. Gama Goicochea et al. (
2009
) for details).
short polymers can be up to 4
.
5
×
4.4 Radius of Gyration
The radius of gyration is a measure of the size of an object of arbitrary shape. For a
polymer chain in solution, however, this is not a very useful definition as it can take
many different configurations. One may calculate a
root mean square end-to-end
distance R
RMS
of the chain as
R
RMS
2
2
=
(
r
N
−
r
0
)
,
(43)
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