Cluster nucleation hypothesis

A different model presented by Christiansen and Sloan is based on the fact that water molecules form labile water clusters around dissolved gas molecules. The number of water molecules in each water cluster shell depends on the size of the dissolved gas molecules, e.g. 20 for methane and 24 for ethane or 28 for propane. The clusters of the dissolved species combine to form unit cells. The formation rate of a particular hydrate structure depends on the availability of labile clusters with required coordination numbers. With a mixture of methane and propane dissolved in the liquid water phase, hydrates should form more rapidly than if either methane or propane alone are dissolved in the water phase. This cluster nucleation hypothesis is based on the assumption that the guest molecule has to be dissolved in the liquid phase before getting encased into a hydrate lattice. 

Molecular simulation methods have been applied to investigate the nucleation mechanism of gas hydrates in the bulk water phase (Baez and Clancy, 1994), and more recently at the water-hydrocarbon interface (Radhakrishnan and Trout, 2002 Moon et al., 2003). The recent simulations performed at the water-hydrocarbon interface provide support for a local structuring nucleation hypothesis, rather than the previously described labile cluster model. 

Becker-Doiing nucleation hypothesis indicates a much larger number, of the order of 100, for the critical cluster. Klein and Driy, in nucleation studies combining the drop method and homogeneous precipitation, found the rate of nucleation of strontium sulfate to depend on the 27th power of the concentration, indicating a nucleus containing 52 ions. 

The hypothesis was extended to nucleation of hydrates from liquid water. An alternative hypothesis was proposed by Rodger [1516]. The main difference between these two sets of theories is that Rodger s hypothesis relates the initial formation process to the surface of the water, whereas the theory of Sloan and coworkers considers clusters related to soluted hydrate formers in liquid water as the primary start for joining, agglomeration, and crystal growth. The theories of Sloan and coworkers have been discussed and related to elements of the hypothesis proposed by Rodger [1043]. 

In the hypothesis, Points 5 and 8 above (alternative structures) have come under criticism, first by Skovborg et al. (1992) and then by Natarajan et al. (1994). However, Skovborg noted that alternating structures may account for some of his nucleation data. A further criticism of the labile cluster hypothesis is that the energy barrier for agglomeration of clusters is far larger than cluster disintegration (Radhakrishnan and Trout, 2002). 

A hypothesis picture of hydrate growth at a crystal is shown in Figure 3.21, modified from Elwell and Scheel (1975). This conceptual picture for crystal growth may be combined with either the labile cluster or local structuring hypotheses for nucleation. 

The extensive series of studies on in vitro core formation reported by Harrison and co-workers (32, 63, 82, 140) and others (133) has led to the development of a three-step hypothesis for iron uptake. In the first step, iron entry through the channels, Fe + passes from the outside of the protein through the channels in the apoferritin coat to the interior cavity. The second step, nucleation, involves iron binding to groups on the inner surface of the protein in such a way that a small cluster of coupled Fe ions is formed. The final step, formation of the core, involves the extension of a small nucleating cluster by the addition and oxidation of Fe +. This stage is characterized by an initial catalytic phase, during which the small cluster rapidly expands, followed by a reduced rate of expansion once the core has attained a particular size (—1000-1500 iron atoms per molecule). 

We find that the nucleation proceeds via "the local structuring mechanism/ " i.e., a thermal fluctuation causing the local ordering of CO2 molecules leads to the nucleation of the clathrate, and not by the labile cluster hypothesis, one current conceptual picture. The local ordering of the guest molecules induces ordering of the host molecules at the nearest- and next-to-nearest-neighbor shells, which are captured by a three-body host-host order parameter, f these thermodynamic fluctuations lead to the formation of the critical nucleus. 

Similar MC calculations were used by Trout s group to study the carbon dioxide-liquid water interface at 220 K and 4 MPa near the phase boundary of a carbon dioxide hydrate (273 K and 4MPa). Nucleation was achieved by seeding the system with a cluster of carbon dioxide hydrate. It was found that a small cluster with diameter <9.6 A dissolved into the solution readily. A hydrate crystal started to grow, however, when a hydrate cluster twice that size (19.3 A) was implanted into the system. The crystal eventually spanned the whole system (Figure 22). Thus the critical nucleus size for hydrate nucleation is estimated to be about 19 A consisting of approximately 200 water molecules. This is a considerably smaller number than that estimated from the local harmonic model of around 600 molecules. The theoretical results refuted the labile cluster hypothesis.This hypothesis speculates the agglomeration... 

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