• Insights

Published on August 18, 2021 by Jenny Maat

Surfactants (short for surface-active-agents) are important modulators for the behavior of many chemical products, such as detergents, cosmetics, and paints. They have a dual chemical nature: a hydrophilic part, commonly referred to as the “head”, and a hydrophobic part (“tail”). So, this dual nature lets them facilitate the interaction between hydrophobic and hydrophilic phases in solution by stabilizing the interfacial surface. Through this stabilization, surfactants reduce the aggregation of particles, gasses and fluids in solution leading to the formation of dispersions, foams and emulsions. Surfactants can also add viscosity to a solvent by the formation of larger micelle structures, which we explore here in more detail. 

The phase behavior of C12E6

Linear non-ionic surfactants, such as dodecyl hexaglycol (C12E6 or Laureth-6), form mesoscopic phases in solution. When in a binary mixture with water the surfactants do not disperse other phases, but instead form surfactant aggregates. When a small amount of surfactant molecules come together they will form micelles, which are small globular units of tails coated with a layer of heads. Coalescence of micelles leads to cylindrical structures, forming either cylindrical micelles or hexagonal phases. Hexagonal phases are characterized by the aligned packing of cylinders on a hexagonal lattice. At higher concentrations surfactants can pack laterally into layers forming a lamellar structure. The micellar, hexagonal and lamellar phases can be characterized by their surface curvature. So, micelles have a very high curvature, hexagonally packed cylinders only have curvature in one direction, and lamellar structures have no curvature. 

The existence of such phases influences the rheological behavior of the bulk fluid. Characterizing the phase diagram of surfactants in water is key in understanding rheological behavior in product development. Solubilized micelles do not lead to a significant viscosity increase, but ordered continuous phases will result in a strong shear stress, leading to a high viscosity. The phase-diagram for C12E6 (Figure 2) has already been explored through a variety of methods and is therefore a good reference for the ability to predict phase behavior.2,3 As we can see, C12E6 will form micelles at room temperature at 20%. Increasing the surfactant concentration will cause hexagonal phases to form at 40-60%. Further increasing the concentration will yield lamellar phases. 

Using RheoCube to determine the phase diagram of C12E6

Recently, Coarse-Grained Molecular Dynamics (CGMD) has been added to the Rheocube package to simulate processes at the molecular scale. You can read about this method in more detail in a recent blog from one of our experts.

In CGMD, the molecules are represented by a simple model: one discrete bead represents a small molecule or a group of atoms. This simplification of molecules is called coarse-graining, and makes it possible to run larger simulations, albeit at the cost of losing atomistic detail. These beads are iteratively moved every timestep adhering to Newtonian equations of motion. In the simulations presented here a mixture of water and C12E6 is used, where water is modelled by a single bead and the C12E6 by a chain of 6 hydrophobic and 6 hydrophilic beads. The interactions between these beads are set using Hansen Solubility Parameters (HSPs). These HSPs are a good measure of the cohesive energy of a molecule (or part of a molecule) and are relatively easy to obtain.

The simulations reported here were all carried out for 200 000 beads and a simulated time of 3.37 µs. The temperature was held constant at 293K. To investigate the phase-behavior of the surfactant, four systems were constructed with C12E6 in water at volume percentages of 20%, 30%, 40% and 50% of C12E6. The HSP values used for the C12E6 surfactant are (δD=16.3, δP=7.3, δH=10.9) for the surfactant head and (δD=16.7, δP=0, δH=0) for the surfactant tails. For water the values of (δD=15.5, δP=16.6, δH=42.3) were used. The interaction energies were scaled to correctly represent the interactions between the three components, as it was found that in the HSP model water is generally too incompatible with other chemical species.

Analyzing the simulations

Similar to what was found in experiments, we see that the surfactant forms micelles at 20% and 30%. For example, in the videos below we first see mainly spherical micelles at 20%. However, when we increase the surfactant concentration to 30%, in the second video, we can also see cylindrical micelles. This is the expected behavior. When micelles grow in size, they typically do not extend spherically, but extend to form cylindrical micelles.2

Increasing the surfactant concentration to 40% and 50% causes the cylindrical micelles to elongate further. As a result, the rods fuse to each other due to their close packing, creating network of randomly-oriented connected cylinders, as seen in videos 3 and 4. This phase is very similar to the hexagonal phase when examining the surface curvature. However, the network is very different compared to the densely packed cylinders found in hexagonal phases, it is in fact a disordered hexagonal phase.3,4. This is most likely due to the absence of directionality in the simulation. For example, in an experiment there is always shear present when a surfactant solution is created or poured. This adds a directional stress that will influence how structure is built up. 

Predicting fluid behavior from microscopic phases

Naturally, the rheological properties of the bulk fluid will vary greatly depending on whether the surfactant forms micellar, hexagonal or lamellar phases. Therefore, determining microscopic phase behavior is key in determining the bulk properties of the fluid. Here we have shown that the mesophases of the C12E6 surfactant can be predicted from simple input parameters, namely concentration, HSP, density and molecular weight. This method provides predictive power for other compositions of surfactants and solvents. Rheocube is working to someday incorporate these predictions into a multiscale method – where molecular level insights power the mesoscopic fluid behavior. Stay tuned for the update.

Resources

  1. Israealachvilli, J.N., Intermolecular and Surface Forces, 3rd Edition, Academic Press, 2011
  2. Mitchel, D.J.; Tiddy, G.J.T.; Waring, L. Phase Behavior of Polyoxyethylene Surfactants with Water J. Chem. Soc., Faraday Trans. I. 1983, 79, 975-1000
  3. Guruge, A.G.; Warren, D.B.; Benameur, H.; Pouton, C.W.; Chalmers, D.K. Aqueous phase behavior of the PEO-containing non-ionic surfactant C12E6: A molecular dynamics simulation study J. Colloid Interface Sci. 2021, 588, 257-268

Denham, N.; Holmes, M.C.; Zvelindovsky, A.V. The Phases in a Non-Ionic Surfactant (C12E6)-Water Ternary System: A Coarse-Grained Computer Simulation J. Phys. Chem. B 2011, 115, 1385-1393