1.2 Intermolecular Interaction
23
screened by counterions, which distribute asymmetrically in two sides of membranes,
resulting in the unbalance of osmotic pressures. The effective interaction depends on
the ionic distribution [23].
1.2.6.3 Solvatophobic Effect
Solvatophobic effects, of which the representative is the hydrophobic effect, are often
assumed as a source of some apparent interaction. Micro phase-separation, causing
the formation of various structures in lyotropic liquid crystals, is a notable example.
Although the effect is usually related to entropic effects, it can come from enthalpic
(energetic) effects. The resultant difference in the affinity to the solvent works as
the driving force to the equilibrium distribution of their orientation of chemical
species (molecules or molecular ions). Roughly speaking, the effect appears as a
daily experience that ions and polar molecules favor in polar solvents such as water
and vice versa. In this hydrophobic effect, the breakage/formation of networks of
hydrogen bonds has been believed to be crucially important. General degrees of
effects of ions are organized as the so-called Hofmeister series [24].
1.3 What the Interaction Brings
1.3.1 Equation of State of Gas
If the molecular size and intermolecular interaction are negligible, the equation of
state of classical gas is given by that of the ideal gas (complete gas),
pV = n RT = N k B T
(1.74)
or
p
ρk B T
= Z = 1
(1.75)
with N being the number of molecules and ρ = N /V . Z is often called compressibility factor. Experiments have shown that Eq. 1.74 does not hold exactly though it
is a good approximation at high temperatures. The equation of state of real gases is
often expressed like
p
ρk B T
= 1 + B(T )ρ + C(T )ρ
2
+ D(T )ρ
3
+ · · ·
(1.76)
or
p
ρk B T
= 1 + B p (T ) p + C p (T ) p
2
+ D p (T ) p
3
+ · · ·
(1.77)
using temperature-dependent coefficients, B(T ), etc. These series are called virial
expansions. Coefficients are called virial coefficients, accordingly. The name “expan-
23
screened by counterions, which distribute asymmetrically in two sides of membranes,
resulting in the unbalance of osmotic pressures. The effective interaction depends on
the ionic distribution [23].
1.2.6.3 Solvatophobic Effect
Solvatophobic effects, of which the representative is the hydrophobic effect, are often
assumed as a source of some apparent interaction. Micro phase-separation, causing
the formation of various structures in lyotropic liquid crystals, is a notable example.
Although the effect is usually related to entropic effects, it can come from enthalpic
(energetic) effects. The resultant difference in the affinity to the solvent works as
the driving force to the equilibrium distribution of their orientation of chemical
species (molecules or molecular ions). Roughly speaking, the effect appears as a
daily experience that ions and polar molecules favor in polar solvents such as water
and vice versa. In this hydrophobic effect, the breakage/formation of networks of
hydrogen bonds has been believed to be crucially important. General degrees of
effects of ions are organized as the so-called Hofmeister series [24].
1.3 What the Interaction Brings
1.3.1 Equation of State of Gas
If the molecular size and intermolecular interaction are negligible, the equation of
state of classical gas is given by that of the ideal gas (complete gas),
pV = n RT = N k B T
(1.74)
or
p
ρk B T
= Z = 1
(1.75)
with N being the number of molecules and ρ = N /V . Z is often called compressibility factor. Experiments have shown that Eq. 1.74 does not hold exactly though it
is a good approximation at high temperatures. The equation of state of real gases is
often expressed like
p
ρk B T
= 1 + B(T )ρ + C(T )ρ
2
+ D(T )ρ
3
+ · · ·
(1.76)
or
p
ρk B T
= 1 + B p (T ) p + C p (T ) p
2
+ D p (T ) p
3
+ · · ·
(1.77)
using temperature-dependent coefficients, B(T ), etc. These series are called virial
expansions. Coefficients are called virial coefficients, accordingly. The name “expan-