(406a) On the Origin of the Interfacial Phase Transition Causing the Stabilization of Water/Oil Emulsions By Asphaltenes: Accounting for Excluded Area Effects through a Lattice Gas Equation of State

Authors: 
Pauchard, V., City College of New York
Koplik, J., City College of New York and Graduate Center,City University of New York
Darjani, S., The City College of New York
Stabilization of water in oil emulsions by asphaltenes (a solubility class of crude oil comprising polyaromatic and heterocyclic molecules) has for a long time been attributed to the formation of a cohesive â??gelâ? at the interface, as revealed by the formation of wrinkles upon contraction of water droplets aged in asphaltenes solutions. This interpretation however suffers from many shortcomings, the most obvious one being the timescale discrepancy between emulsion stabilization (fast) and transition from fluid to solid rheological properties of adsorbed asphaltenes layers (slow). An alternative paradigm recently emerged from the systematic study of surface pressure-interfacial area and surface pressure-dilatational elasticity curves which proved independent from adsorption conditions and in particular adsorption time. This demonstrated that asphaltenes follow an equation of state, which could be approximated by a Langmuir model. The corresponding surface excess coverage (the reciprocal of molecular area) was found particularly consistent with the observed conformation of asphaltenes at the water surface (with the aromatic core flat on water) and their average core size. From this starting point, droplet contraction experiments could be reanalyzed quantitatively: deviations of the surface pressure isotherm from the Langmuir equation of state and of the droplet from the Laplacian shape appeared to occur when surface coverage approached maximum packing. In other words transition to a solid like interface would be driven by steric effects as it is the case for the jamming of particle laden interfaces. The parallel with particles was further extended to the analysis of emulsion stability. The critical mass of asphaltenes per unit interfacial area for preventing droplets coalescence was actually found to be very close to the ratio of molar weight to molar area. This indicates that asphaltenes block coalescence when approaching packing at water surface just like particles. As in Pickering emulsions, this condition can be reached much faster in an emulsion which is stirred and undergoes limited coalescence than in a rheometer where interfacial area remains constant and mass transport is diffusion limited. On a theoretical point of view it is however troublesome that molecules following a Langmuir equation of state would exhibit a fluid to solid transition due to steric interactions like particles do. The localized adsorption assumption of the Langmuir model should actually rule out any hard core repulsion between adsorbed molecules as it imposes that their size is smaller than that of adsorption sites. Reversely this restriction with respect to the relative size of adsorbates and adsorption sites should preclude the use of the Langmuir equation of state for molecules that are bigger than water molecules (3 to 4 times for asphaltenes). These inconsistencies are largely alleviated when considering lattice gas equations of state in which an adsorbate covers several adsorption sites. Such models actually predict a phase transition at high coverage due to excluded area effects. On the other hand when plotted similarly to experimental data, lattice gas equations of state (below their phase transition) can fairly be approximated by the Langmuir equation of state. In particular the limiting elasticity versus surface pressure relationship seems to be primarily dependent upon molecular area. This means that molecular area can be first evaluated from experimental data with the Langmuir equation of state, then used to calculate the number of water molecules covered by each adsorbed molecule. Proper lattice gas models can then be identified from the literature and compared with more details to experimental data. For asphaltenes the selection is further refined based upon the geometry of their aromatic cores which are roughly hexagonal. The corresponding equation of state (hexagons covering three sites on a triangular lattice) is extensively described in the literature and is found to match experimental observations up to a surprising level of detail. In particular the predicted phase transition domain exactly matches the onset and final steep increase of the error to the Laplacian shape during droplet contraction. Furthermore, the predicted relationship between limiting elasticity and surface pressure exhibits the same inflexion point as experimental data. At low coverage both first and second derivative of elasticity with respect to pressure are positive, but at high coverage the second derivative becomes null: elasticity is somewhat proportional to pressure. This peculiar feature is verified for all lattice gas equations of state tested so far, with a proportionality constant ranging from 2 for small adsorbates to 5 for large ones. Interestingly similar observations were repeatedly reported for dilatational rheology experiments on surfactants (with a proportionality constant circa 2-3) and proteins (with a proportionality constant circa 4-5).