Environmental Engineering Reference
In-Depth Information
By its nature, microscopic molecular dynamics simulations require a great deal
of computational resources, the reason being that the integration of the equations of
motion require very small time steps when the interaction potential changes signifi-
cantly over small distances. An alternative that has proven to be very successful is to
do mesoscopic modelling via DPD (Hoogerbrugge and Koelman
1992
), consisting
of carrying out a coarse-graining of the microscopic degrees of freedom. It is highly
dependent on parameters describing the different kinds of force fields, whose para-
metrisation as appears in the literature is not always clear. For this reason, we present
here a revision of DPD parametrisation together with applications and comparison
with experimental results.
In Sect.
2
we give a brief description of the DPD modelling, including
electrostatic
DPD. Section
3
deals with the appropriate parametrisation and how to calculate the
relevant parameters for given realistic systems. The dependence on concentration
and temperature of the interaction parameters is also considered. Section
4
presents
some interesting applications, and we close with some conclusions.
2 Electrostatic Dissipative Particle
Dynamics: A Brief Overview
A good alternative to overcome the difficulties presented by molecular dynamics
simulations is to do a coarse-graining of the microscopic degrees of freedom. When
done carefully, results can be obtained which approximate very well those obtained
through lengthy experimentation (cf. e.g., (Gonzalez-Melchor et al.
2006
;Gama
Goicochea et al.
2009
; Mayoral and Nahmad-Achar
2012
; Mayoral et al.
2011
)
and references therein). DPD as was originally introduced by Hoogerbrugge and
Koelman (
1992
), consists of grouping several molecules, or parts of molecules, into
soft mesoscopic “particles”. As with molecular dynamics simulations, one integrates
the equations of motion to obtain the particle's positions and velocities, but here one
distinguishes only between 3 contributions to the total force:
conservative
,
dissipative
and
random
.
Conservative forces account for local hydrostatic pressure and are of the form
a
ij
ˉ
c
(
r
ij
)
ˆ
e
ij
,(
r
ij
<
r
c
),
F
ij
=
(6)
0
,
(
r
ij
≥
r
c
).
Here,
a
ij
is a parameter which represents the maximum repulsion between particles
i
and
j
,
r
ij
=
r
i
−
r
j
,
r
ij
=|
r
ij
|
, and
ˆ
e
ij
=
r
ij
/
r
ij
where
r
i
denotes the position of
c
particle
i
, and the weight function is given by
ˉ
(
r
ij
)
=
(
−
r
ij
/
r
c
)
.
This force, depicted in Fig.
2
, derives from a soft interaction potential and there is
no hard-core divergence as in the case of the Lennard-Jones potential, which makes
more efficient the scheme of integration since it allows for a large time step. In
the case of macromolecules, such as polymers, the particles (which can consist of
1
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