40
2 Experimental Methods for Determination of Nucleation Rates
An alternative approach is to use multiple sample cells and do without any use
of arbitrary cut-off time for the collection of the nucleation data. The constant
subcooling method is suitable for the use of multiple sample cells because the
isothermal nature of the method ensures that all samples are at the same temperature. This is especially useful for homogeneous nucleation, such as freezing of a
liquid droplet suspended in another immiscible liquid, for which one does not need
to worry about the heterogeneity of foreign container walls. The concern here is
the uniformity of the sample size and a potential spatial temperature gradient across
the multiple samples because, albeit constant, maintaining at a constant temperature
generally requires a heating or a cooling device with feedback control that would
induce heat flows across the samples. Another effort directed to shorten the total
experimental time required for the collection of the nucleation data is by Svartaas
and co-workers whose improved analysis method at a constant temperature enabled
to lower the number of required repeat measurements to about 25 [8].
It is rare in reality that one is only interested in the nucleation rate of a given system
at a single subcooling temperature. Nucleation rate depends on the driving force for
nucleation, G driving_force , so a nucleation curve that relates the nucleation rate to
the driving force for a given system is required. Then, one needs to repeat the above
protocol for a number of different subcoolings and use some form of interpolation
to determine the nucleation curve. This is a highly time-consuming and laborious
endeavor.
2.2 Linear Cooling Ramp Method
2.2.1 Introduction
An important recent innovation in the experimental investigations of nucleation rates
was the use of linear cooling ramps that enabled simultaneous determination of an
entire nucleation curve over a whole range of experimentally accessible subcoolings.
An automated lag time apparatus (ALTA) has been used since the middle of the 1990 s
for experimental investigations of ice and other liquids under atmospheric pressure
[1, 2, 9–11]. These studies compiled survival probability distributions as functions
of system subcoolings and used the median of the distribution as the representative
measure of the most probable subcooling. These early studies did not advance so far
as to determine the nucleation rates of the systems. Maeda established a systematic
method that enabled simultaneous determination of an entire nucleation curve over
the whole range of experimentally accessible subcoolings [5, 12]. The details of the
systematic method are summarized in this section and in Sect. 1.2.
A family of high-pressure automated lag time apparatus (HP-ALTA) [13, 14] has
been developed to experimentally determine the survival probability distributions
of clathrate hydrates as functions of system subcoolings, F(T ). Other than an
2 Experimental Methods for Determination of Nucleation Rates
An alternative approach is to use multiple sample cells and do without any use
of arbitrary cut-off time for the collection of the nucleation data. The constant
subcooling method is suitable for the use of multiple sample cells because the
isothermal nature of the method ensures that all samples are at the same temperature. This is especially useful for homogeneous nucleation, such as freezing of a
liquid droplet suspended in another immiscible liquid, for which one does not need
to worry about the heterogeneity of foreign container walls. The concern here is
the uniformity of the sample size and a potential spatial temperature gradient across
the multiple samples because, albeit constant, maintaining at a constant temperature
generally requires a heating or a cooling device with feedback control that would
induce heat flows across the samples. Another effort directed to shorten the total
experimental time required for the collection of the nucleation data is by Svartaas
and co-workers whose improved analysis method at a constant temperature enabled
to lower the number of required repeat measurements to about 25 [8].
It is rare in reality that one is only interested in the nucleation rate of a given system
at a single subcooling temperature. Nucleation rate depends on the driving force for
nucleation, G driving_force , so a nucleation curve that relates the nucleation rate to
the driving force for a given system is required. Then, one needs to repeat the above
protocol for a number of different subcoolings and use some form of interpolation
to determine the nucleation curve. This is a highly time-consuming and laborious
endeavor.
2.2 Linear Cooling Ramp Method
2.2.1 Introduction
An important recent innovation in the experimental investigations of nucleation rates
was the use of linear cooling ramps that enabled simultaneous determination of an
entire nucleation curve over a whole range of experimentally accessible subcoolings.
An automated lag time apparatus (ALTA) has been used since the middle of the 1990 s
for experimental investigations of ice and other liquids under atmospheric pressure
[1, 2, 9–11]. These studies compiled survival probability distributions as functions
of system subcoolings and used the median of the distribution as the representative
measure of the most probable subcooling. These early studies did not advance so far
as to determine the nucleation rates of the systems. Maeda established a systematic
method that enabled simultaneous determination of an entire nucleation curve over
the whole range of experimentally accessible subcoolings [5, 12]. The details of the
systematic method are summarized in this section and in Sect. 1.2.
A family of high-pressure automated lag time apparatus (HP-ALTA) [13, 14] has
been developed to experimentally determine the survival probability distributions
of clathrate hydrates as functions of system subcoolings, F(T ). Other than an