60
3 Molecular Liquids
Fig. 3.4 Number of
molecules within a sphere of
radius r . DCHM, solid curve
(red, 130 ◦ C; blue, 65 ◦ C);
TCHM, dashed curve (red,
160 ◦ C; blue, 95 ◦ C); liquid
argon, black dotted curve
calculated using the
literature data [1]
1
2
4
6
8
10
2
4
6
8
100
n
( r)
2.0
1.5
1.0
0.5
r / r fp
<
r
of thermal expansion considering volume expansivities of typical organic liquids
(e.g., 1.3 · 10
−3 K
−1 for cyclohexane and benzene [12], and 1.0 − 1.2 · 10
−3 K
−1
for small primary alcohols [13]). Besides, other peaks of DCHM exhibit compatible
temperature dependences (3.4 · 10
−4 K
−1 on average) with that. In this temperature
range, a substantial portion of DCHM molecules associate through H-bond(s) [9].
Since the radial distribution function is a kind of weighted average of pair distributions (one molecule contributes twice), nearly fixed local geometry contributes
substantially to the first peak. Thus, the weak temperature dependence of the r fp of
DCHM can be interpreted as a reflection of the substantial population of the H-bond
between neighboring molecules.
The number of nearest molecules are, though only slightly, larger in DCHM than
TCHM as seen in Fig. 3.4, which was calculated as
n
v mol
r
0
r
2
g(r )dr
(3.24)
with v mol = (4π/3)(r fp /2)
3 . Reflecting the broadened radial distribution, which is
due to a blurred radius of molecules, the steps are rather broad.
3.2 Molecular Association
Molecular association in hydrogen-bonding (H-bonding) systems is an example of
structural correlation in liquid. The H-bond is stronger than dispersion interactions
and has a more pronounced preference concerning its direction, as discussed in
Sect. 1.2.6.1. Such properties, together with the ubiquitous occurrence, lead to a
general belief that the molecular association through it plays crucial roles in governing the physical properties of the systems. Unique and exceptional properties of
water are one of the best examples [14]. It is thus valuable to consider the molecular
association by the H-bond.
3 Molecular Liquids
Fig. 3.4 Number of
molecules within a sphere of
radius r . DCHM, solid curve
(red, 130 ◦ C; blue, 65 ◦ C);
TCHM, dashed curve (red,
160 ◦ C; blue, 95 ◦ C); liquid
argon, black dotted curve
calculated using the
literature data [1]
1
2
4
6
8
10
2
4
6
8
100
n
( r)
2.0
1.5
1.0
0.5
r / r fp
<
r
of thermal expansion considering volume expansivities of typical organic liquids
(e.g., 1.3 · 10
−3 K
−1 for cyclohexane and benzene [12], and 1.0 − 1.2 · 10
−3 K
−1
for small primary alcohols [13]). Besides, other peaks of DCHM exhibit compatible
temperature dependences (3.4 · 10
−4 K
−1 on average) with that. In this temperature
range, a substantial portion of DCHM molecules associate through H-bond(s) [9].
Since the radial distribution function is a kind of weighted average of pair distributions (one molecule contributes twice), nearly fixed local geometry contributes
substantially to the first peak. Thus, the weak temperature dependence of the r fp of
DCHM can be interpreted as a reflection of the substantial population of the H-bond
between neighboring molecules.
The number of nearest molecules are, though only slightly, larger in DCHM than
TCHM as seen in Fig. 3.4, which was calculated as
n
v mol
r
0
r
2
g(r )dr
(3.24)
with v mol = (4π/3)(r fp /2)
3 . Reflecting the broadened radial distribution, which is
due to a blurred radius of molecules, the steps are rather broad.
3.2 Molecular Association
Molecular association in hydrogen-bonding (H-bonding) systems is an example of
structural correlation in liquid. The H-bond is stronger than dispersion interactions
and has a more pronounced preference concerning its direction, as discussed in
Sect. 1.2.6.1. Such properties, together with the ubiquitous occurrence, lead to a
general belief that the molecular association through it plays crucial roles in governing the physical properties of the systems. Unique and exceptional properties of
water are one of the best examples [14]. It is thus valuable to consider the molecular
association by the H-bond.