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1 Molecules and Intermolecular Interactions
mal) chemical bonds. In this respect, the hydrogen bond often plays significant effects
on the aggregation and properties of molecular systems. Anomalous properties of ice
(such as relatively high melting temperature and the decrease in volume upon melting) are understood through considering the effect of the hydrogen bonds between
molecules [18]. The formation and maintenance of DNA duplex via hydrogen bonds
between conjugate pairs of bases is another striking example to demonstrate their
importance. Many monographs are available on the hydrogen bond [19]. Readers are
referred to them to learn more.
1.2.6.2 Entropic Interaction
Thermodynamics says that the equilibrium of any system is characterized by the
minimum of the Gibbs energy, which is given by
G = H − T S,
(1.73)
where G, H , T and S are Gibbs energy, enthalpy, thermodynamic temperature and
entropy, respectively. The statement implies that the enthalpic term (the first term)
and the entropic term (the second term) can be the source of effective interaction. This
kind of interaction is often termed as entropic interaction. The entropic interaction is
a weak interaction comparable to thermal energy (≈ k B T ). The entropic interaction
is generally non-additive owing to its mechanism. It is often the case that a naïve
two-body treatment fails.
Although the entropic interaction is often discussed in multicomponent systems
such as solution, the crystallization of hard spheres (known as Alder transition [20])
can be understood as a result of the entropic interaction in a neat system. By analogy, micro phase-separation in an ensemble of “amphiphilic” molecules may be
understood in terms of the entropic interaction.
One of the well-known examples of entropic interaction is the depletion interaction. In a fluidic system such as a solution containing two types of particles with a
notable difference in size, an effective attraction works between large particles at a
short distance. If their distance is smaller than the size of small particles, the small
particles cannot enter between the large particles resulting in the asymmetry in the
pressure that the small particles exert on the large particle. Since the asymmetry originates in the depletion of the small particles in between, the effect is called depletion
effect or depletion interaction [21].
Another important interaction is the so-called Helfrich interaction [22], which is
the effective interaction between not molecular entities but membranes. The Helfrich
interaction is always repulsive and arises from the entropic penalty of membranes that
independently fluctuate if they are close to each other. The interaction is a crucial
component to govern the intermembrane distance in lamellar phases of lyotropic
liquid crystals.
It is noted that the apparent electrostatic interaction between charged membranes
is, in reality, of entropic origin. The bare charges of the membranes are completely
1 Molecules and Intermolecular Interactions
mal) chemical bonds. In this respect, the hydrogen bond often plays significant effects
on the aggregation and properties of molecular systems. Anomalous properties of ice
(such as relatively high melting temperature and the decrease in volume upon melting) are understood through considering the effect of the hydrogen bonds between
molecules [18]. The formation and maintenance of DNA duplex via hydrogen bonds
between conjugate pairs of bases is another striking example to demonstrate their
importance. Many monographs are available on the hydrogen bond [19]. Readers are
referred to them to learn more.
1.2.6.2 Entropic Interaction
Thermodynamics says that the equilibrium of any system is characterized by the
minimum of the Gibbs energy, which is given by
G = H − T S,
(1.73)
where G, H , T and S are Gibbs energy, enthalpy, thermodynamic temperature and
entropy, respectively. The statement implies that the enthalpic term (the first term)
and the entropic term (the second term) can be the source of effective interaction. This
kind of interaction is often termed as entropic interaction. The entropic interaction is
a weak interaction comparable to thermal energy (≈ k B T ). The entropic interaction
is generally non-additive owing to its mechanism. It is often the case that a naïve
two-body treatment fails.
Although the entropic interaction is often discussed in multicomponent systems
such as solution, the crystallization of hard spheres (known as Alder transition [20])
can be understood as a result of the entropic interaction in a neat system. By analogy, micro phase-separation in an ensemble of “amphiphilic” molecules may be
understood in terms of the entropic interaction.
One of the well-known examples of entropic interaction is the depletion interaction. In a fluidic system such as a solution containing two types of particles with a
notable difference in size, an effective attraction works between large particles at a
short distance. If their distance is smaller than the size of small particles, the small
particles cannot enter between the large particles resulting in the asymmetry in the
pressure that the small particles exert on the large particle. Since the asymmetry originates in the depletion of the small particles in between, the effect is called depletion
effect or depletion interaction [21].
Another important interaction is the so-called Helfrich interaction [22], which is
the effective interaction between not molecular entities but membranes. The Helfrich
interaction is always repulsive and arises from the entropic penalty of membranes that
independently fluctuate if they are close to each other. The interaction is a crucial
component to govern the intermembrane distance in lamellar phases of lyotropic
liquid crystals.
It is noted that the apparent electrostatic interaction between charged membranes
is, in reality, of entropic origin. The bare charges of the membranes are completely