Chemistry Reference
In-Depth Information
This particular anion is biologically relevant, because it is found in two amino acids
(aspartic acid and glutamic acid) found abundantly on protein surfaces. The smaller
osmotic coefficient of Li
þ
in this system can be explained in terms of small-small
pairing: Li
þ
pairs with the negatively charged, small carboxyl oxygen of the acetate
moiety. Despite these qualitative insights, the law of matching water affinities does
not quantify the effects observed in Fig.
5
and moreover assumes formation of
contact ions pairs, neglecting alternative pairing mechanisms.
Figure
6
shows the potential of mean force (PMF) between a sodium ion and a
chloride ion in water, at infinite dilution of the two ions, obtained from classical
atomistic simulations [
75
]. The first minimum of the potential corresponds to the
contact ion pair (CIP) distance, the second minimum corresponds to the solvent-
shared ion pair (SIP) distance, and the third minimum to the solvent-separated ion
pair (2SIP) distance. Figure
7
a shows an example of a SIP in aqueous NaCl [
75
].
The infinite dilute potential of mean force in Fig.
6
can be used as an effective pair
potential
in implicit solvent simulations. The osmotic coefficient
f
(
r
s
)
¼
P
r
s
the salt number density) can be
obtained through the virial route. For the case of a binary mixture of components
i
and
j
and pairwise additive, density-independent pair potentials, the virial equation
can be expressed as
/2
r
s
k
B
T
(with
P
the osmotic pressure and
ð
1
3
r
s
X
ij
V
eff
ij
d
b
ð
r
Þ
r
3
d
r
fðr
s
Þ¼
1
g
ij
ð
r
; r
s
Þ
:
(1)
d
r
0
This equation involves the infinite-dilute pair force d
V
eff
ij
=
d
r
, while the pair
correlation function
g
ij
(
r
;
r
s
) has to be evaluated at
the density considered.
Fig. 6 Potential of mean force between a sodium ion and a chloride ion at infinite dilution in water
at 298 K obtained from atomistic simulations with the SPC/E water model (
red curve
). (Adapted
from [
75
]). The
dashed curve
shows the Coulomb potential
e
2
/4
pe
e
r
with
e ¼
71 the static
0
dielectric constant of SPC/E water
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