Environmental Engineering Reference
In-Depth Information
kqq
/
(
)
=
force field are the electrostatic interaction
V
r
r
and a Lennard-Jones type
4
ʵ
(˃/
6
, where the adjustable parameters
12
)
must be obtained by other means (first principles or experimentation). Relevant quan-
tities of the system are computed as time-averages over a macroscopic time interval
(
)
=
)
−
(˃/
)
(ʵ, ˃,
potential
V
r
r
r
k
t
)
dt
(2)
The pieces of information that one can obtain through these simulations are mainly
structural and thermodynamic properties: (i) the density profile
ˁ(
t
0
+
t
A
r
1
(
1
t
t
),
t
), . . . ,
t
)
;
t
),
t
),...,
=
r
2
(
r
N
(
p
1
(
p
2
(
p
N
(
A
lim
t
ₒ∞
t
0
, which in partic-
ular may be used to characterise when two phases (e.g., liquid and vapour) coexist;
(ii) the radial distribution function
g(
r
)
r
)
given by
ˁ
=
ˁ(
r
)g(
r
)
dr
,
(3)
which measures the average number of particles in each coordination shell with
respect to a given centre (and usually obtained through X-ray or neutron scattering
experiments); (iii) the interfacial tension
L
z
P
zz
−
P
yy
2
P
xx
+
1
ʳ
∗
=
,
(4)
obtained from the pressure tensor components
P
ij
within a box of length
L
z
;(iv)the
radius of gyration of a polymer chain, given by
a
f
N
ʽ
,
R
g
=
(5)
where
a
f
3
is the monomer length of the
chain, and
ʽ
is the appropriate scaling exponent; (v) phase diagrams; (vi) adsorp-
tion isotherms; (vii) disjoining pressures; etc. Figure
1
shows descriptively this
methodology.
is proportional to the Flory volume,
N
F
(
r
)=
−∇V
(
r
)=
m
d
2
r
dt
2
N
~10
4
t
t
t
+
t
t
0
+
t
t
A
= lim
tₒ∞
A
(
r
1
(
t
)
, r
2
(
t
)
,...r
N
(
t
)
, p
1
(
t
)
, p
2
(
t
)
,...p
N
(
t
))
dt
t
0
Fig. 1
Descriptive methodology of a
molecular dynamics simulation.
Taken from Gama Goicochea,
private communication (see text for details)
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