Chapter 2
Experimental Methods
for Determination of Nucleation Rates
2.1 Constant Temperature Method
Nucleation rate is central to nucleation phenomena as we saw in the previous chapter.
The question is: how can one determine the nucleation rate of a given system? It is
important to appreciate that direct detections of nuclei are impossible. There are
several reasons for this: a reason is that one cannot pre-determine where in the
system one should focus his instrument in advance. Another reason is that focusing
of a detection instrument will likely bring about local heating. Such local heating
may be small but, because of the exponential nature of Arrhenius’s law, any small
local heating would lower the nucleation rate at the focused location compared to
the other unheated locations because the subcooling (driving force) would become
lower. These points aside, a primary reason is that nuclei would look like any other
(slightly smaller) clusters that are populating the system which would have a size
distribution of the Boltzmann form. In other words, an experimental technique would
need to have a spatial resolution of a building block of a nucleus to be able to tell
whether the critical size has been reached or not and each building block can be as
small as a single molecule. As such, a nucleation event can only be detected after
the fact, i.e., after a nucleus has surmounted the free energy barrier and completed
an irreversible overgrowth to macroscopically detectable sizes.
There are two basic approaches to this challenge. One is an isothermal method
or a constant temperature (subcooling) method. The other is a linear cooling ramp
(constant cooling rate) method. In this section, we will deal with the former. The
latter will be covered in the next section.
An experimental challenge with the measurements of induction times at a constant
subcooling is that an induction time is often very long and could potentially stretch
to infinity at a shallow subcooling (high temperature), as might be expected from the
exponential distribution of the induction times under a constant driving force. An
introduction of an arbitrary cut-off induction time (maximum waiting time) is thus
common in this type of measurements for practical reasons. A related issue is that the
scatter in induction time data is very large, especially at a shallow subcooling [1–4].
© Springer Nature Switzerland AG 2020
N. Maeda, Nucleation of Gas Hydrates,
https://doi.org/10.1007/978-3-030-51874-5_2
35
Experimental Methods
for Determination of Nucleation Rates
2.1 Constant Temperature Method
Nucleation rate is central to nucleation phenomena as we saw in the previous chapter.
The question is: how can one determine the nucleation rate of a given system? It is
important to appreciate that direct detections of nuclei are impossible. There are
several reasons for this: a reason is that one cannot pre-determine where in the
system one should focus his instrument in advance. Another reason is that focusing
of a detection instrument will likely bring about local heating. Such local heating
may be small but, because of the exponential nature of Arrhenius’s law, any small
local heating would lower the nucleation rate at the focused location compared to
the other unheated locations because the subcooling (driving force) would become
lower. These points aside, a primary reason is that nuclei would look like any other
(slightly smaller) clusters that are populating the system which would have a size
distribution of the Boltzmann form. In other words, an experimental technique would
need to have a spatial resolution of a building block of a nucleus to be able to tell
whether the critical size has been reached or not and each building block can be as
small as a single molecule. As such, a nucleation event can only be detected after
the fact, i.e., after a nucleus has surmounted the free energy barrier and completed
an irreversible overgrowth to macroscopically detectable sizes.
There are two basic approaches to this challenge. One is an isothermal method
or a constant temperature (subcooling) method. The other is a linear cooling ramp
(constant cooling rate) method. In this section, we will deal with the former. The
latter will be covered in the next section.
An experimental challenge with the measurements of induction times at a constant
subcooling is that an induction time is often very long and could potentially stretch
to infinity at a shallow subcooling (high temperature), as might be expected from the
exponential distribution of the induction times under a constant driving force. An
introduction of an arbitrary cut-off induction time (maximum waiting time) is thus
common in this type of measurements for practical reasons. A related issue is that the
scatter in induction time data is very large, especially at a shallow subcooling [1–4].
© Springer Nature Switzerland AG 2020
N. Maeda, Nucleation of Gas Hydrates,
https://doi.org/10.1007/978-3-030-51874-5_2
35