This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 15065–15072 15065

Observation of two-step nucleation in methane hydratesw

Jenel Vatamanu and Peter G. Kusalik*

Received 13th May 2010, Accepted 17th September 2010

DOI: 10.1039/c0cp00551g

In this work we show that homogeneous nucleation of methane hydrate can, under appropriate

conditions, be a very rapid process, achieved within tens of nanoseconds. In agreement with

recent experimental results on different systems, we find that the nucleation of a gas hydrate

crystal appears as a two-step process. It starts with the formation of disordered solid-like

structures, which will then spontaneously evolve to more recognizable crystalline forms. This

previously elusive first-stage state is confirmed to be post-critical in the nucleation process, and is

characterized as processing reasonable short-range structure but essentially no long-range order.

Its energy, molecular diffusion and local structure reflect a solid-like character, although it does

exhibit mobility over longer (tens of ns) timescales. We provide insights into the controversial

issue of memory effects in methane hydrates. We show that areas locally richer in methane will

nucleate much more readily, and no ‘memory’ of the crystal is required for fast re-crystallization.

We anticipate that much richer polycrystallinity and novel methane hydrate phases could be

possible.

1. Introduction

How ordered phases are nucleated within liquids, which are

characterized by only local stochastic order, is an intriguing

question of fundamental relevance. The simplified image of

classical nucleation theory, which assumes the spontaneous

appearance of a fully ordered crystal nucleus from a disorder

phase under appropriate conditions, has been questioned by

recent theoretical1,2 and experimental3 work. In these studies a

two-step mechanism has been suggested, where the first step is

thought to involve the nucleation of an intermediate ordered

state, referred in ref. 3 as liquid-like clusters, while the

second step involves a structural evolution of these initial

‘‘disordered’’ clusters to regular crystalline structures. Here

we provide, by means of simulations at molecular resolution,

direct evidence of an apparent two-stage mechanism during

homogeneous nucleation of methane-hydrate (MH).

An understanding of the crucial initial stages of hydrate

formation, that is nucleation, has remained elusive and prior

work has focused mostly on the structure generated in water

by methane, either in bulk solution or at interfaces. Rodger

and co-workers4 observed from simulations an increase in

water structure in a supersaturated aqueous methane solution

due to the appearance of pentagonal and hexagonal face

arrangements of water molecules around methane.5

Guo et al.6 showed that water cages around methane have a

relatively long life-time, roughly a hundred picoseconds.

Guo and co-workers found that the local structure of water

around methane involves do-decahedron cage-like arrangements.7

Recently these authors have shown, by means of potential

mean force calculations, an overall affinity of methane for

hydrate-like cages.8

The recent work of Hawtin et al.9 is particularly noteworthy.

They examined a slab system with two solution/methane-gas

interfaces, where the system was initially prepared from a

methane hydrate crystal. This simulation study employed

specific structural order parameters, tuned to detect regular

hydrate cages, to track the appearance of regular hydrate

structural units (512, 51262 and 51264 cages) within their system.

They successfully observed the appearance and growth of

these cages, on timescales of tens of ns, into a phase not

consistent with any common bulk hydrate crystal structure.

They also concluded that the ordering process observed was

preceded by a local spatial organization of methane molecules.

It is notable that the systems under investigation in their study

were prepared by melting a hydrate crystal. Although the

details of the duration of melting were not given, the behavior

of their three systems indicates that these times are important

(i.e. longer melting resulted in delays in the appearance of

regular hydrate cages). Their systems were maintained at a

temperature of 250 K, yet the melting temperature of the water

model being employed is estimated to be 190 K,10 substantially

below that of real water. It is unclear where the point

corresponding to the conditions being employed in their work

is relative to the hydrate melting curve on the phase diagram

of their model system. Although the authors appeared to

monitor the average methane density in their solution slab,

they appear to have not recorded the local density profile of

methane across their solution slab. The slab nature of their

system would suggest that it would de-gas most rapidly near

the interfaces; hence one would expect a significant methane

composition gradient to be present in these systems. The

possibility of an enhanced methane density in the interior

of their slab could have important implications, as we will

see below.

Department of Chemistry, University of Calgary,2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada.E-mail: peter.kusalik@ucalgary.caw Electronic supplementary information (ESI) available: Severalextensive sets of figures, featuring further detailed results togetherwith a description of the simulation setup used in this study. See DOI:10.1039/c0cp00551g

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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15066 Phys. Chem. Chem. Phys., 2010, 12, 15065–15072 This journal is c the Owner Societies 2010

In this paper we provide a detailed account of the homo-

geneous nucleation of a gas hydrates from bulk aqueous

solution. We demonstrate that the mechanism of methane-

hydrate homogeneous nucleation obeys an apparent two-step

mechanism: initially a disordered solid is nucleated, and

subsequently this solid can be observed to evolve into a more

crystalline form. The previously elusive first-stage nucleated

state is examined in detail; based on its energy and molecular

diffusion it has definitive solid-like character, yet we find that

this precursor to crystalline order retains significant disorder

and exhibits rather conspicuous mobility when monitored over

periods of tens of nanoseconds. The intriguing picture of the

mechanism of (MH) crystal nucleation that emerges sugges-

tions that the disordered solid precursor that forms represents

a lower free energy path to crystalline order, as it otherwise

would take too long for complex order to appear completely

in a single step from liquid-like disorder. A surprising con-

sequence of this observed mechanism, where the first-stage

appears to encompass the free energy barrier to nucleation, is

that it implies clear limitations of the applicability of classical

nucleation theory to the formation of ordered (crystalline) phases.

Additionally, we will elucidate the controversial issue of

memory effects11 in MH. We show specifically that it is not

fragments of the crystalline structure that are ‘remembered’ in

liquid phase; rather in a system that has not reached a global

equilibrium state with respect to methane composition (i.e. as

would result after the melting of a methane hydrate crystal) it

is the rapid appearance of solid-like clusters in areas locally

rich in methane that facilitates crystal nucleation. At appro-

priate (supercooled) conditions these solid-like clusters, which

are locally structured and have significantly lower energies and

molecular diffusion constants than in liquid, will then quickly

transform to more recognizable crystalline structures, as

demonstrated in this work.

The remainder of this paper is organized as follows: our

results and discussion will be presented in Section 3, with

concluding remarks given in Section 4.

2. Simulation methods

Simulations were performed within a framework very similar

to our previous work with heterogeneous crystallization of gas

hydrates (see for details ref. 12, and Fig. S1 from ESIw) at

pressure of a 100 atm. The 6-site water model of Nada and van

der Eerden,13 which reproduces the main structural features of

water and has a melting temperature in the range 280–285 K,14

was utilized. For the purpose of the current work, methane

was modeled with a single LJ site.15 Previous simulations have

indicated16 that the results presented here will be essentially

invariant to this choice of potential. The starting configuration

consisted of a periodic two-phase system, where a methane-

hydrate crystal is in contact with an aqueous methane

solution. This starting configuration was prepared by first

equilibrating a methane hydrate crystal in contact with a liquid

water slab for more than 2 ns. It is noteworthy that the initial

aqueous solution in this work was derived from liquid water.

At one of the two interfaces of the system a local tempera-

ture pulse (with a peak of 370 K) was then applied to begin to

melt the hydrate crystal, while the remainder of the system was

thermostated to temperatures (of either 270, 265 or 255 K)

well below the expected melting temperature of the model

hydrate.17 The melting of hydrate crystal at one interface

provides a flux of methane into the solution; if the rate of

methane introduction into the solution is faster than it can be

consumed by crystal growth at the other, then the concentra-

tion of methane in solution will increase. This particular non

steady-state set-up allows us to sample a range of methane

super-saturations within a single simulation, where the rate at

which the methane concentration in solution increased was

controlled by the rate of methane introduction (through the

melting of crystal at the one interface). Optimal rates

(that resulted in nucleation) appeared to correspond to melting

rates (of 3–6 A ns�1) roughly twice the apparent maximum

growth rate for this model hydrate. Systems were further

prepared under these conditions for another 4.2 ns, allowing

them to reach a state where the methane composition in

solution was approaching half that of the hydrate crystal.

In this work we have employed three rather generic

measures to assess and quantify, via predefined thresholds,

the solid- or liquid-like character of molecules or collections of

molecules. These include: (i) a dynamical measure based on

mean-square displacements with respect to the average

molecular position over relatively short (typically 50 ps) times,

which are described in detail in ref. 18, (ii) a structural

criterion based on tetrahedral order parameters19 of water

molecules within molecular configurations, and (iii) an

energetic measure based on potential energies per molecule.

3. Results and discussion

As the level of methane supersaturation of the aqueous

solution gradually increases, two possible events (transformation)

might then occur within a simulation timescale: (i) phase

separation, demixing, of the hydrophobic methane from the

aqueous solution, or (ii) homogeneous nucleation of a gas

hydrate solid. In three independent production runs, with

these supersaturated (metastable) aqueous methane solutions

at deeply supercooled temperatures, we observed a rather

disordered solid homogeneously nucleate within a time-scale

of tens of nanoseconds. Fig. 1 (also see ESIw, Fig. S9) showsthe time evolution of one of these systems. These sequences

of configurations capture the system undergoing ordering/

disordering fluctuations with a final overall trend towards an

increased size of the solid-like region. At an early stage in the

nucleation, pentagonal and hexagonal water ring arrange-

ments around methane were evident as common geometrical

patterns. As the system becomes more ordered, irregular

shaped cages were first apparent. Cages of higher symmetry,

such as those found in sI and sII hydrates, were

identified when the methane concentration reached about

0.0035–0.0037 molecules per A3; at this point the solid

appeared persistent and less susceptible to disordering

fluctuations.

The final result from the simulation performed at 270 K is

shown in Fig. 2. The system configuration in Fig. 2a indicates

that a solid area has formed in the middle of the solution phase

(rather than at either of the interfaces). The methane density

in this solid is at a level comparable to that in crystal,

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0.0046 molecules per A3. The methane density profile and the

molecular configuration both indicate local structuring in the

nucleated solid (see Fig. 2b). The energy profile, also given in

Fig. 2b, shows that the potential energy of this new solid is

roughly 6 kJ mol�1 lower than that of the surrounding

solution at the same temperature, and only about 2 kJ mol�1

higher than the average energy of the ideal MH crystal.

The translational mean-square displacements of molecules

in the nucleated solid are, within the accuracy of our

measure,18 about 30 times smaller than in the liquid phase

(see also Fig. 3c), and are only slightly (about 15%) larger than

those in a hydrate crystal. The angular and radial tetra-

hedral order parameters19 of water molecules in the

newly formed solid have similar values as in a MH crystal

Fig. 1 Images showing the increase of solid-like character during the

nucleation process, for the system nucleated at 270 K. Only the region

of interest is shown (full configurations are shown in the ESIw). Thecorresponding time-index is indicated below each frame. The dark

blue, yellow, light blue and red spheres represent the solid-like

methane, liquid-like methane, solid-like water and liquid-like water

molecules, respectively, where a dynamical measure (the mean square

displacement) has been used to label the molecules.

Fig. 2 (a) A time-average system configuration obtained after 24 ns,

and (b) the profile of the methane density (blue line) and water

potential energy (red line) along the direction of asymmetry. The

temperature was 270 K. The molecules are represented as in Fig. 1.

The areas corresponding to initial crystal and the nucleated solid are

indicated in the plot.

Fig. 3 The time dependence of three order parameters within the

region of the system where homogeneous nucleation is occurring. (a)

Water tetrahedral order parameter from time-averaged configurations,

(b) methane density, and (c) water mean-square displacement (msd)

with respect to average molecular positions. Data points from time

windows of 50 ps are shown. (d) An image snapshot of the final

configuration at 270 K with a shaded area which indicates the region

of the system over which the properties were evaluated (20.2 A in

width). In the area labeled (1), the methane concentration increases

slowly. After the density reaches a critical value, nucleation occurs in

the area labeled (2). In the area labeled (3) the system has become

solid-like, and the changes in measured properties occur on a much

longer time scale. The ordering process within this area rich in

methane results lower potential energy, roughly following the decrease

in water mobility (i.e. the msd value).

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(see also Fig. 3a, region 1), which indicate a high degree of

short-range order, typical of tetrahedral H-bonded water net-

works. All three measures for the nucleated (first-stage) solid

are therefore consistently much closer to hydrate crystal values

than to those of the liquid phase. Based on these criteria, as well

as the short-ranged rather than long-ranged character of the

translational order, we label the initially formed structure as

‘‘solid-like’’ in character. Below we will show that this apparent

solid-like structure retains some liquid-like behavior, including

exhibiting significant mobility on longer (ns) timescales.

The high local concentration of methane is apparently a

critical factor in inducing nucleation. Once the methane

concentration has reached about 0.0027 molecules per A3, as

can seen in Fig. 3, a gradual decrease in potential energy and

molecular mobility concomitant with an increase in water

structure and methane density were recorded. The transition

between liquid- to solid-like behavior appears as a gradual

process over about 10 ns, indicating a time-scale for this

(nucleation) process of tens of ns. The structural fluctuations

clearly observed prior to nucleation and during the early stages

of these trajectories (i.e. in the first 10–12 ns), apparent as

order appearing and disappearing at varying locations in the

region of interest (see ESIw, Fig. S9), confirm this as nucleation

behavior.

The structure within the initial solid-like regions, while

exhibiting some ordered structures involving nearest neighbor

water around methane, also features considerable disorder

over large length scales. Specifically, we can identify methane

in three different water cage environments (see Fig. 4). (i)

Some complete and regular cages (512, 51262, 51264, 435663)

belonging to common methane hydrate structures (sI, sII, sH)

were found; the most common regular cage was the small 512

cage, while the large-sI (51262), large-sII (51264) and HS-I20

(51263) cages were relatively rare (only 1 or 2 such cages were

typically identified). This behavior is consistent with the

observation of Rodger and coworkers.9 (ii) Cages with some

degree of internal symmetry (i.e. C2v) but not belonging to any

known methane hydrate structure were identified (e.g. 425562,

596271, 4151062, 445363). (iii) Irregular cages (i.e. with low or no

internal symmetry), containing mostly tetragonal, pentagonal,

and hexagonal faces and typically 20–24 water molecules, were

frequently observed in the newly formed solid. The presence of

these various cages (also see ESIw) contributes to the apparent

disorder of this solid.

If the first stage of homogeneous nucleation is the formation

of a partially disordered solid structure, then it is important to

understand how it evolves to a more recognizable crystalline

structure and to demonstrate that this annealing does occur.

Although very slow annealing of the structure was apparent,

to probe this aspect more reasonably within the time-scale of

MD simulations, we have studied the evolution of the initially

nucleated solid at somewhat higher temperatures, just slightly

Fig. 4 Images of several types of cages identified in the nucleated solid. (a) Partially formed regular or irregular cages, (b) irregular cages with low

or no internal symmetry, (c) regular and symmetric cages which can be found in common MH structures, and (d) high symmetry cages not

identified yet in the experimentally known hydrate crystals but found in the first-stage nucleated solid. (e) High symmetry cages identified in the

annealed crystal. The blue and grey spheres represent the water and methane molecules identified to behave as solid-like.

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below the melting temperature of a methane hydrate crystal

system.17 Under these conditions we would expect the

first-stage disordered solid either to anneal to a more stable

crystalline structure, or to melt. For temperatures below

290 K, trajectories of 20 ns did not result in any significant

improvement of the solid structure, indicating that at these

temperatures the dynamics are too slow to observe annealing

over the simulation timescale.

Above 290 K, but below the melting temperature, initially

nucleated structures did anneal within 10 ns into more

recognizable crystalline patterns (i.e. when given the chance,

the system always appeared to relax to more ordered

crystalline structures). This is the case in the three annealing

trajectory results shown in Fig. 5 performed at 298, 300 and

302 K from the solid nucleated at 270 K. While the starting

configuration consisted of a relatively disordered solid

(see Fig. 5a), the annealed structures showed a significant

increase in overall crystalline order (see Fig. 5b–d) with far

fewer irregular cages remaining, confirming that indeed the

initial solid was a post-critical (i.e. growing) crystal nucleus.

All three annealed structures are unique, however they share a

common pattern where regular 512, 51262, 51263, 51264, 435663

cages dominate their structure. Presumably these annealed

structures would continue to anneal into a stable hydrate

(presumably either sI or sII) but only on a timescale beyond

the reach of the present simulations. However, a certain subset

of higher symmetry and previously unreported hydrate cages

survived the process of annealing (compare first two snapshots

of Fig. 4d and e). Also, two types of symmetric but previously

unreported cages, made of 20 water molecules, were found in

the annealed crystal (see the last two snapshots of Fig. 4e).

This could possibly signal the potential for much richer

polycrystallinity of hydrate crystals than assumed to-date.

The annealing process we have observed (as in Fig. 5)

clearly implies there must be some degree of mobility in the

first-stage disordered solid. We note that while this first-stage

structure appears solid-like on timescales of a hundred ps, on

longer (ns) timescales we observe considerable mobility

associated with the structural rearrangements of the system.

The extent of the mobility of the molecules during the

annealing process is captured in Fig. 6 where two configura-

tions from before and after the annealing have been super-

imposed. Both configurations were re-centered such that they

share the same Cartesian coordinates for one particular

methane molecule that was identified as remaining trapped

in a solid-like configuration during the entire annealing

process. Out of 128 crystal-like molecules identified within a

region of the annealed (i.e. second-stage) crystal, only 36 of

them were in the same region in the first-stage disordered solid

from which the annealed crystal resulted. Here we use the label

‘‘crystal-like’’ to identify solid-like molecules that are arranged

in a pattern having long-range order. Clearly there was

significant restructuring in the first-stage disordered solid, well

beyond local rearrangements of the H-bond network, during

the formation of the final crystalline phase. One might expect

that experiments probing this aspect to interpret this mobility

during the annealing process as indicative of liquid-like

behavior.3

A rather striking aspect of this work is the short time, only

tens of nanoseconds, over which homogeneous nucleation of

MH occurs. It is important to note that homogeneous

nucleation of ice, as previously observed in simulations, is

apparently an order of magnitude slower than for our

hydrates.21 To confirm that our observation of rapid

nucleation has not been biased by our system setup, the

possible influences of several aspects were explored. To test

the potential impact of the confined geometry of our solution

phase, we have explored the removal of the interfaces from the

system. Starting with our system with the nucleated solid, the

configuration was cropped to give a smaller system containing

only the solution region (including the nucleus). This smaller

system was then heated to 400 K for about 200 ps to melt the

nucleus completely (although not allowing the system to

demix) and then cooled back to 270 K. The nucleus was

observed again to re-form within 20 ns. Hence, the presence

of the crystal interfaces in the original system was apparently

not a significant factor.

The reproducibility of the nucleation events was further

verified by repeating the experiment several more times,

Fig. 6 A comparison of the molecular positions in the second-stage

(i.e. annealed) crystal with the positions of the corresponding first-

stage disordered solid. Red, green, dark blue, and light blue spheres,

respectively, are water molecules in the first-stage solid, methane

molecules in the first-stage solid, methane molecules in the annealed

crystal, and water molecules in the annealed crystal.

Fig. 5 (a) Image of the configuration nucleated at 270 K. The

resulting quenched configurations after further 10 ns simulation at

temperatures of (b) 298 K, (c) 300 K, and (d) 302 K clearly showing an

increase of the crystalline order and the number of cages specific to sI

and sII methane hydrate structures.

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starting from the same initial (full) configuration but with

randomized initial velocities and melting rates between 4 and

6 A ns�1. In three instances a solid clearly nucleated under

these more strongly driven conditions, while the remaining

systems exhibited methane demixing events.

We also confirmed that there was no memory of the crystal

structure transferred into the nucleating solid. An analysis of

the history of individual molecules (see ESIw) within the solid

revealed that each molecule spent at least 3–4 ns in a liquid-

like environment prior to transitioning to solid-like behavior.

The temperature pulse applied at the melting interface has a

maximum that is more than 60 K above the melting point of

the hydrate crystal. At this temperature, the local (regular)

cage structure of the water around methane is destroyed very

rapidly, in less than 50 ps. As additional confirmation, we find

that the methane molecules do not retain knowledge of their

original crystalline positions; rather the relative positions of

methane molecules that were neighbors in the initial crystal

were found to randomize in less than 500 ps after exposure to

the elevated temperatures in the temperature pulse region. The

fact that no collective crystal-like arrangement survives the

temperature pulse is also confirmed by the values of angular

and radial tetrahedral order parameters of water evaluated

within the fresh melt and supersaturated methane solution

regions. The values of these order parameters (0.08 and

1.4 � 10�3, respectively, for the angular and radial measures

as obtained from instantaneous configurations) are typical

for a (disordered) liquid phase rather than crystal, which

would have significantly smaller (i.e. by factors of 10 and 2,

respectively) values.

It is illustrative to consider why previous simulations,7,22

including our own work,16,23 had not observed hydrate

nucleation on similar short timescales. These earlier studies

had used other effective potential models with significantly

lower melting temperatures; for example that of the TIP4P

model is about 50 K below that of the present model.14 Being

able to work at these higher temperatures results in higher

diffusion coefficients, effectively placing the system on an order

of magnitude faster time-scale, at otherwise comparable

thermodynamic conditions. In another test, we verified that

the [001] face of a sI MH crystal can be grown with the 6-site

water model about 3–4 times faster than with TIP4P water at

similar (relative) supercooling and methane supersaturation,

attesting to the inherent ability of the former to form hydrates

more rapidly. Additionally, the high local concentration of

methane, which was being continuously increased in these

simulations, apparently provided the necessary driving force

to help order the system; the methane concentration in the

region where solid initially formed exceeded half of the

methane concentration in the ideal crystal. Given the rapid

formation of solid structure once the necessary level of

methane is achieved (see Fig. 3 and ESIw), it would seem that

primary thermodynamic barrier to hydrate nucleation is the

establishment of this high local methane composition. We

point out that these aqueous methane solutions are metastable

both with respect to demixing and crystallization. Thus, it is

perhaps significant that under appropriate driving conditions

the present system consistently seems more sensitive towards

the latter. This generates a consistent picture where we observe

that, given the presence of highly elevated concentrations of

methane, and otherwise at corresponding conditions of super-

cooling, a methane hydrate crystal will nucleate and grow

faster than ice. The challenge in achieving these nucleation and

growth rates in experiments is maintaining the very high local

levels of methane necessary.

A more explicit comparison with the work of Hawtin et al.,9

in which they observed the appearance and growth of hydrate

structures over a timescale of tens of ns, is now appropriate. In

that study a supersaturated SPC-water/methane system was

examined at a relatively high temperature of 250 K. We might

surmise that the methane composition in the interior of their

slab system remained substantially elevated, allowing for some

disordered hydrate structures, not necessarily detected by their

selective order parameter, to be present. Consequently, the

behavior they report (i.e. the appearance of regular cage

structures coupled with fluctuations and mobility on long

timescales) appears consistent with an interpretation that they

were primarily observing a second stage, annealing, process

associated with methane hydrate nucleation.

A comparison with the very recent results of Walsh et al.24 is

also clearly warranted. This study reports the observation of

nucleation of methane hydrate in simulations on a micro-

second timescale. It is important to point out that both of

their simulation runs started from a fully demixed state

(i.e. separate methane and aqueous phases). Thus, the systems

exhibited rather long (ms) induction times during which the

requisite density fluctuations helped to mix the two phases.

Once substantial mixing was achieved (see Fig. 1 and S1 of

ref. 24) nucleation then proceeded relatively rapidly. Specifi-

cally, it is apparent from Fig. 1 of ref. 24 that between the start

of the simulation and about 1.2 ms, one is primarily waiting for

the mixing of methane into the aqueous phase (presumably via

density fluctuations). Rapid nucleation can be seen to occur at

about 1.3 ms (see frame C), at which time we see that a

majority of the methane is now in the aqueous phase, implying

that the methane density is approaching that of the hydrate

crystal. By 1.4 ms (see frame D) the newly formed crystal has

begun to grow and anneal. In the present work we are able to

induce rapid (i.e. on a ns timescale) nucleation by introducing

a high methane composition directly into our aqueous phase.

It is apparent that Walsh et al.24 also observed a relatively

rapid nucleation event, albeit somewhat slower because of

choice of model and somewhat lower temperature, once the

local methane density in solution had reached a critical

threshold. The structure of the nucleated solid observed by

Walsh et al.24 is in accord with our findings. In particular their

systems exhibit somewhat disordered structures, which

contain expected as well as some ‘‘uncommon’’ water cages,

and where considerable fluctuations are apparent as the

structure evolves.

The short time required for the super-saturated methane/

water liquid system to nucleate has important implications for

helping to explain the ‘memory effect’ in MH.25 Consistent

with the results of others9,24,25 the memory effect does not

appear to be the retention of elements of hydrate crystal

structure in solution phase. Rather it can be seen as arising

from the possibility of having regions in the system of locally

higher methane concentrations, possible when the global

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compositional equilibrium has not yet been achieved

(e.g. a microbubble as in Walsh et al.24). As shown here, upon

supercooling such methane rich regions can quickly nucleate

hydrate solid phases.

Since nucleation does not appear to start as regular sI/sII

crystalline structures, but rather as a partially ordered solid, if

the initial nucleus can be prevented from further transforming

into a crystalline structure (i.e. through rapid cooling), we

conjecture that an amorphous MH structure might be possible

experimentally. Additionally, the observation of several

previously unreported symmetric cages, that either survived

or formed during annealing, raises the possibility of a much

richer polycrystallinity of gas hydrates than previously

assumed. This interesting possibility may explain experi-

mentally prepared hydrate phases not yet fully characterized

structurally.26

4. Concluding remarks

This work has explicitly revealed molecular mechanisms of

methane hydrate homogeneous nucleation. Consistent with

other recent work2,3,27 (experimental and simulations) on

different systems, we find that methane hydrate nucleation

can be characterized as a two-stage process. For the conditions

being examined in this study, nucleation does not appear to

start with immediate formation of small crystals with the usual

sI or sII symmetries, but rather with a somewhat disordered

solid containing a mixture of symmetric and irregular water

cages. The formation of this intermediate solid is apparently

favored because of a far greater likelihood of the appearance

of its somewhat disordered structure. Importantly, this

nucleated structure can be confirmed to be post-critical, that

is it can subsequently be shown to anneal to more regular

crystalline structures. While the initially formed structure has

energy values and short-range structural parameters similar to

those of a hydrate crystal and appears dynamically solid-like

on a ps timescale, on longer (ns) timescales we can still observe

mobility as the disorder in the solid anneals. It would be

expected that any experiment probing the system might

interpret this annealing process as indicating liquid-like

behavior.3 The relationship of the two-stage nucleation

behavior observed here to Oswald’s step rule28 is perhaps

unclear; while the observed mechanism includes the formation

of metastable structures, these structures appear not to define

a macroscopically distinct phase. It is important to note that

the observed two-stage nucleation mechanism would make

an analysis of the nucleation process based upon classical

nucleation theory rather problematic. Prediction of any

barriers, size of critical nuclei, or other quantitative character-

istics of this nucleation process would be inexact due to

incorrect assumptions (i.e. bulk crystalline behaviour) about

the properties of the structures involved. Erdemir et al.27 have

made very similar assertions based on other (experimental)

evidence. In general, the ability of a liquid phase to form

initially a wide variety of solid-like structures may be an

important factor in nucleation of complex order, and may

play a role in selecting among various polymorphs or

determining what final (annealed) crystal may result.

Finally, very recently (while this manuscript was in revision)

Jacobson et al.29 have demonstrated, using coarse grain models

in molecular dynamics simulations, that they also obtain an

amorphous precursor, which transforms into a crystalline

structure, during the nucleation of a gas hydrate system.

We have shown that elevated local concentrations of

methane can dramatically enhance the apparent nucleation

rate of methane hydrates. This offers a straightforward

explanation for memory effects in the melts of methane

hydrates. It also suggests strongly that local methane density

is a critical order parameter in the early stage of methane

hydrate nucleation.

Acknowledgements

We are grateful for the financial support of the Natural

Sciences and Engineering Research Council of Canada. We

also acknowledge computational resources made available via

WestGrid (www.westgrid.ca) and the University of Calgary.

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