Chapter 1
Nucleation Theory
1.1 Phase Equilibria and Phase Behavior
1.1.1 Introduction
There are excellent textbooks on phase equilibria and phase diagrams, like [1], so here
we only cover the essence of phase behavior that is necessary for an understanding of
nucleation of gas hydrates or clathrate hydrates. We note at this stage that we regard
the terms “gas hydrates” and “clathrate hydrates” as interchangeable throughout this
book.
A good starting point of the topic would be the Gibbs phase rule [1]. Conditions for
coexistence of macroscopic phases can be set out in terms of intensive thermodynamic
parameters such as pressure, temperature, and composition, in accordance with the
Gibbs phase rule [1].
F = C − P + 2
(1.1.1)
where F is the number of degrees of freedom, C is the number of components,
and P is the number of phases in the system. Therefore, given the pressure and the
temperature (F = 2) of a one-component system (C = 1), the phase state of the
system is completely fixed (P = 1). Below, we consider a one-component system (C
= 1).
The van der Waals equation of state is the first of a series of cubic equations of state
that accounted for phase transitions. There have been a number of variants to the cubic
equations of state since the time of van der Waals, such as Redlich–Kwong equation of
state, Soave–Redlich–Kwong equation of state, Zudkevitch–Joffe–Redlich–Kwong
equation of state, Peng–Robinson equation of state, and so on [1]. The van der Waals
equation of state will suffice for our purpose here.
A remarkable feature of the van der Waals equation of state is that adding the
intermolecular attractions and repulsions to the ideal gas law leads to the presence
of a critical point and phase transitions. It is quite mind-bending that van der Waals
© Springer Nature Switzerland AG 2020
N. Maeda, Nucleation of Gas Hydrates,
https://doi.org/10.1007/978-3-030-51874-5_1
1
Nucleation Theory
1.1 Phase Equilibria and Phase Behavior
1.1.1 Introduction
There are excellent textbooks on phase equilibria and phase diagrams, like [1], so here
we only cover the essence of phase behavior that is necessary for an understanding of
nucleation of gas hydrates or clathrate hydrates. We note at this stage that we regard
the terms “gas hydrates” and “clathrate hydrates” as interchangeable throughout this
book.
A good starting point of the topic would be the Gibbs phase rule [1]. Conditions for
coexistence of macroscopic phases can be set out in terms of intensive thermodynamic
parameters such as pressure, temperature, and composition, in accordance with the
Gibbs phase rule [1].
F = C − P + 2
(1.1.1)
where F is the number of degrees of freedom, C is the number of components,
and P is the number of phases in the system. Therefore, given the pressure and the
temperature (F = 2) of a one-component system (C = 1), the phase state of the
system is completely fixed (P = 1). Below, we consider a one-component system (C
= 1).
The van der Waals equation of state is the first of a series of cubic equations of state
that accounted for phase transitions. There have been a number of variants to the cubic
equations of state since the time of van der Waals, such as Redlich–Kwong equation of
state, Soave–Redlich–Kwong equation of state, Zudkevitch–Joffe–Redlich–Kwong
equation of state, Peng–Robinson equation of state, and so on [1]. The van der Waals
equation of state will suffice for our purpose here.
A remarkable feature of the van der Waals equation of state is that adding the
intermolecular attractions and repulsions to the ideal gas law leads to the presence
of a critical point and phase transitions. It is quite mind-bending that van der Waals
© Springer Nature Switzerland AG 2020
N. Maeda, Nucleation of Gas Hydrates,
https://doi.org/10.1007/978-3-030-51874-5_1
1