The development of the theoretical treatments described in section 1.4.2 to the gas−liquid interface, would require a significant leap in complexity. The liquid hydrocarbon, with additional degrees of freedom and more atoms than a SAM proxy presents a significant computational challenge. In order for such simulations to be attempted (section 1.4.4), a suitable model for the liquid hydrocarbon structure must be developed to accurately portray the chemical, physical and interfacial properties of liquid hydrocarbons. What follows is a description of the recent developments in the field of molecular dynamics (MD) simulations, as applied to liquid hydrocarbons. Harris was the first to carry out MD simulations of linear liquid hydrocarbons[116] using a UA approach where the methyl (CH3) and methylene (CH2) units were treated
as pseudoatoms (the hydrogen atoms were not explicitly represented). The UA approach was necessary to reduce the associated computational cost but realistic bond
lengths, angles and torsional potentials were included in the simulation. Some 300 decane (C10H22) and eicosane (C20H42) molecules were included in a ‘box’ with periodic
boundary conditions in all directions, assigned random velocities from a Maxwell- Boltzmann distribution and allowed to equilibrate.
The simulations broadly replicated most of the physical and interfacial properties of the liquids; although some physical properties, such as surface tension, were found to be over-estimated with respect to experimental measurements. This was due to the limits of the accuracy of the Lennard-Jones based model and could be corrected for by introducing terms for three-body interactions in the potential. The structural predictions were particularly interesting. It was found that at temperatures well above their melting points the liquids exhibit a significant degree of defined interfacial structure. At 400K (melting points < 300 K) both C10H22 and C20H42 had methyl (CH3) groups
preferentially exposed at the interface. The methyl units were described as tending to protrude from the interface at an angle perpendicular to it and the methylene units were found to lie preferentially, on average, parallel to the interface.
Yamamoto and co-workers, motivated by peculiar structural effects predicted at the gas—liquid interface, carried out similar simulations on n-alkanes[71,72]. The UA method was adopted here also, but a simplified bead-spring system was employed neglecting bond angles and torsional motions, allowing for faster and larger simulations to be carried out. They simulated the gradual heating of a frozen crystalline sample and observed preferential melting in the bulk while the interface remained frozen[72]. This was found to persist over a wide temperature range (385-410 K) around the melting point of the liquids[71]. The surface freezing was described as a monolayer structure and according to the simulations even exhibited the hexagonal packing known for SAMs.
This has important experimental implications as surface freezing was proposed as an explanation for the reduced reactivity of linear hydrocarbons, compared with branched ones, towards O(3P) atoms[68]. McKendrick and co-workers repeated the simulations of Yamamoto, replicating hydrocarbons and experimental conditions used in their experiments and found that the interfacial freezing was observed (figure 1.8). In contrast to the thermally equilibrated simulations of Harris and co-workers[116], the simulations carried out by Yamamoto are more comparable to the experimental conditions used by McKendrick and co-workers. Due to vapour-pressure constraints
the experiments were limited to temperatures just above the melting points making surface freezing a viable explanation for the observed trend in reactivity. Harris’ simulations predict the opposite trend for thermally equilibrated liquid samples; this would be interesting to test experimentally.
Figure 1.8: Molecular dynamics simulations of a C10H21 linear hydrocarbon. Interfaces with
vacuum are located on the top and bottom of the slab. Left view is a snapshot of the thermally equilibrated 400 K simulation and right view follows rapid cooling to 240 K showing the monolayer-type interfacial structure. Reprinted from reference[68].
Mondello and Grest[117] carried out the first MD simulations on the branched liquid hydrocarbon, squalane. It was a development of the UA model used by Harris and the methyl (CH3), methylene (CH2) and methine (CH) units were treated as three distinct
pseudo-atoms. The simulations were designed to test transport properties such as the diffusion coefficients of complex fluids and were a test for the applicability of the potentials to branched hydrocarbons compared with linear ones. The simulations reproduced with reasonable accuracy some experimentally derived properties, but the simulations were regarded as a preliminary study and not fully developed to correctly represent branched hydrocarbons.
This challenge was met by Siepmann who developed a transferable potential for phase equilibria united atom (TraPPE-UA) force field with a Monte Carlo (MC) simulation method to study the liquid-vapour phase behaviour of squalane[118-120]. In Siepmann’s initial work[118,119], the squalane molecules (~200) were given the initial conformation of a layered crystal and cycled through several thousand MC cycles at an
elevated temperature, defining the melt system. The MC cycles represent random selections (from a defined range) of moves such as translation, rotation and conformational change applied to each of the individual molecules. The melt system was then cooled to the desired temperature, equilibrated through a further 25000- 100000 MC cycles[119] and subsequently analysed. The simulations gave excellent agreement with experimentally established properties such as critical and boiling temperatures, reflecting the ability of the model to simulate a branched liquid hydrocarbon.
A subsequent study by Siepmann and co-workers[120] was focussed more on the interfacial structural properties of squalane. The chemical structure of the interface was investigated by plotting Z-density profiles of the individual pseudo-atoms, which reflect the probability of finding a particular pseudo-atom (or corresponding CHx unit) at a
certain distance from the bulk through the interface to the vacuum. They found that the interface was very rough on a molecular level but no individual group was preferentially exposed at the interface, unlike in the linear hydrocarbons[116]. This was of interest to McKendrick and co-workers who set out to use Siepmann’s MC method and (TraPPE-UA) force field to generate Z-density profiles which could in turn be used to predict the probability with which an oxygen atom approaching a squalane surface will hit a particular type of CHx group[121]. The method was extended to 288 squalane
molecules (96 for Siepmann[120]) and the simulations almost exactly replicated experimental surface tension measurements.
McKendrick and co-workers found a modest but clear preference for CH3 primary units
to occupy the interfacial region for the branched hydrocarbon squalane. They argue that this is also the case in the work by Siepmann if their Z-density profiles were scaled to the relative amounts of CH3, CH2 and CH groups present. McKendrick and co-workers
showed that an O atom approaching a squalane surface would be slightly more likely to hit a CH3 unit than predicted by stoichiometry but all three hydrogen environments are
available at the interface for abstraction, corroborating their earlier experimental findings[51].
1.4.4 Inelastic scattering at the gas—liquid interface
To date, there has only been a very limited number of theoretical simulations on inelastic scattering at the gas—liquid interface. Nathanson and co-workers
complemented their experimental work on collisions of Xe atoms at a squalane surface with molecular dynamics simulations. The squalane C30H62 structure was treated
simply as a large soft sphere[16]. This early study, taking into account the obvious structural oversimplifications, was designed to investigate whether simple models could effectively reproduce the experimentally observed scattering behaviour.
The model was accurate at reproducing certain aspects of the experiment, such as a bimodal translational distribution in the scattered products. It was unsuccessful at replicating the energy transferred in the collisions, largely due to the neglect of any internal modes of the liquid. The trapping desorption component was particularly underestimated. TD events are influenced by the projectile-surface intermolecular potential (represented in the model by a Lennard-Jones potential for Xe + CH4). It is
therefore natural that this is where the model was most limited; as a sphere-type model for a liquid hydrocarbon cannot accurately portray these interactions.
Over a decade later, Hase and co-workers carried out classical chemical dynamics simulations of Ne scattering from a squalane surface[122]. The treatment of the squalane molecules remained classical and was developed from a UA approximation. The remainder of the structure was represented by realistic bond lengths, angles, torsion and stretching modes. The interaction potential between the Ne and the CH3 and CH2
units in squalane was developed from high-level electronic-structure calculations similar to those used in simulations of Ne and self-assembled monolayers (section 1.4.1). This gave much better agreement with experiment in terms of energy transfer[8] than Nathanson’s earlier model[16]. The simulations of Hase and co-workers also allowed for the correlation of Ne final energy and number of collisions (kicks) to be investigated. It was found that those trajectories which were thermalised at the surface (TD) had undergone multiple collisions at the surface but were not dissolved in it (as they had relatively short residence times).
There is clearly disparity between the volumes of experimental and theoretical studies of gas—liquid scattering dynamics, favouring experimental work at the present time (section 1.5). The following section will describe recent theoretical advancements towards the accurate simulation of hydrogen abstraction reactions at the gas—liquid interface.