Collin Wick, PhD, Louisiana Tech University
The work carried out in the second year of the PRF grant continued the focus on understanding the alkane/water interface. This is relevant for enhanced oil recovery methods, which often rely on the use of steam injection. Of course alkane/water interfaces form when the steam comes in contact with the oil. One fundamental importance to this is how the alkyl chain length influences the alkane/water interfacial width. X-ray reflectivity experiments (funded previously by PRF according to the citation) has found that increasing alkyl chain length increases the alkane/water interfacial width . We carried out simulations in the first year of the PRF grant to investigate the alkane/water interface, and found a different trend, namely that longer alkyl chain length resulted in a smaller alkane/water interfacial width . This work investigated many aspects of the n-alkane/water interface, including how the interfacial width extracted from the atomic density profile was affected by chain length. To expand on this, we chose two specific n-alkane/water interfaces, n-hexane/water (HEX) and n-nonane/water (NON), and carried out three separate simulations of each of them to make more direct comparisons with x-ray reflectivity experiments.
Figure 1: Electron density across the air-water interface for the systems investigated.
To carry out our goals, we calculated the electron density profile across the alkane/water interface, calculated the structure factor from this, and extracted the scaled x-ray reflectivity from them. We investigated the effect of system size on the x-ray reflectivity, investigating systems that had twice as much alkane (2HEX and 2NON), and systems that were four times larger (4HEX and 4NON), in which the box lengths parallel to the interface was twice as large. The electron density profiles we calculated are shown in figure 1. We found little difference between the interfacial widths of the regular systems and those that had twice as much alkane. However, just as was found with the atomic densities, the interfacial width based on electron density was longer for the HEX systems than the NON systems. We also found that doubling the amount of alkane had little effect on the interfacial width. The systems that were four times larger had a longer interfacial width (4HEX and 4NON), which was due to more capillary wave action due to the larger box length parallel to the interface. It can clearly be seen in figure 1 that the 4HEX and 4NON systems are more smeared out and have less structure than the other systems due to this capillary wave action.
Figure 2: Logarithm of scaled reflectivity as a function of the wave vector squared for systems investigated.
To make more precise comparisons between simulation and experiment, we utilized capillary wave theory to estimate the additional interfacial width that would arise from capillary waves beyond the box length. We then convoluted our electron density profiles with a Gaussian with this estimated width, calculated the structure factor from the electron density, and used this to get the scaled reflectivity. The scaled reflectivity can be directly compared with experiment, and the logarithm of it versus the wave vector squared can be used to estimate the interfacial width. A plot of the logarithm of the scaled reflectivity versus the square of the wave vector extracted from our simulations is given in figure 2. The slope of this line can be used to estimate the interfacial width and compare our computational estimates with experiment. We found that even after correction for capillary waves, the interfacial width was smaller than for the HEX systems than NON systems, in contrast to experiment.
The reason for the discrepancy between simulation and experiment could be due to many reasons. One thing of interest we found is that there is an enhancement of methylene carbons at the interface in comparison with bulk due to the fact that n-alkanes preferred to 'lay flat' at the interface. Also, we found that this region of enhanced methylene concentration was larger for the NON systems than the HEX systems, showing that the NON systems could have a larger interfacial width. We tested this by using ab initio calculations to investigate the electron density surrounding different atoms in n-hexane while in the gas phase. We found that methyl and methylene group atoms had similar electron densities surrounding them, and certainly not enough of a difference to account for the discrepancies the simulation results had with experiment. Finally, since we get the correct trend in interfacial tensions for the increase in chain length , it is unlikely that the simulation results would also give the interfacial width trend incorrect. The only way to make purely direct comparisons between simulation and experiment, though, would be to carry out ab initio molecular dynamics calculations, which would be very computationally expensive, and have not been carried out for the alkane-water interface, to my knowledge, yet. The work described in this report has been submitted to the journal Chemical Physics Letters, and if accepted will be the second paper citing PRF funding.
 D. M. Mitrinović, et al., "Noncapillary-wave structure at the water-alkane interface," Physical Review Letters vol. 85, pp. 582-585, 2000.
 C. D. Wick, et al., "Computational Investigation of the n-Alkane/Water Interface with Many-Body Potentials: The Effect of Chain Length and Ion Distributions," The Journal of Physical Chemistry C, vol. 116, pp. 783-790, 2012/01/12 2011.