Orientational order on axisymmetric interfaces in solid-stabilized emulsions

In emulsions, immiscible oil and water phases are commonly separated by an interface hosting a layer of surfactant molecules, which decreases surface tension and stabilizes the system. Alternatively, in solid-stabilized or Pickering emulsions, nano- or microparticles are embedded in the interface, decreasing interfacial area. Solid-stabilized emulsions are extremely stable and allow for complex non-spherical droplet shapes. Spherical particles embedded in an interface constitute a two-dimensional monolayer in which locally hexagonal packings can be expected. This hexatic arrangement is one type of orientational order, another is nematic order in the alignment of a layer of rod-like interfacial particles. Orientational order interacts with surface shape; hexatic or nematic packing is disrupted by Gaussian curvature. Conversely, droplet shape may adapt to accommodate orientational order. For surfactant-stabilized emulsion systems, the effects of hexatic order on droplet shape have been experimentally and theoretically investigated. I here extend the investigation to solid-stabilized emulsions. On the example of a modulated cylindrical surface shape, I examine the theory of orientational order analytically and using a lattice-based stochastic simulation. With a generic Landau-Ginzburg model, I find that modulations in the amount of order co-occur with well-known defect phenomena. I distinguish type I and type II systems, with zero or up to 4n defects respectively. I deduce that there is a discrete spectrum of modulated tubule shapes. Experiments motivate the adaptation of the generic model to the specific interfacial material of rod-like colloidal nanoparticles. I apply and adapt results from the density functional theory literature to obtain material parameters of a two-dimensional hard-rod gas. The material-specific model reveals that, in the case studied, interfacial mechanics are dominated by surface tension and orientational order conforms to the resulting surface curvature via the defect state.