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Forming an interface between immiscible fluids incurs a free-energy cost that usually favors minimizing the interfacial area. An emulsion droplet of fixed volume therefore tends to form a sphere, and pairs of droplets tend to coalesce. Surfactant molecules adsorbed to the droplets' surfaces stabilize emulsions by providing a kinetic barrier to coalescence. Here, we show that the pressure exerted by bound surfactant molecules also competes with the droplet's intrinsic surface tension and can reverse the sign of the overall surface free energy. The onset of negative surface tension favors maximizing surface area and therefore favors elongation into a wormlike morphology. Analyzing this system in the Gibbs grand canonical ensemble reveals a phase transition between spherical and wormlike emulsions that is governed by the chemical potential of surfactant molecules in solution. Predictions based on this model agree with the observed behavior of an experimental model system composed of lipid-stabilized silicone oil droplets in an aqueous surfactant solution. 

The intensity distribution of a holographically-projected optical trap can be tailored to the physical properties of the particles it is intended to trap. Dynamic optimization is especially desirable for manipulating dark-seeking particles that are repelled by conventional optical tweezers, and even more so when dark-seeking particles coexist in the same system as light-seeking particles. We address the need for dexterous manipulation of dark-seeking particles by introducing a class of “dark” traps created from the superposition of two out-of-phase Gaussian modes with different waist diameters. Interference in the difference-of-Gaussians (DoG) trap creates a dark central core that is completely surrounded by light and therefore can trap dark-seeking particles rigidly in three dimensions. DoG traps can be combined with conventional optical tweezers and other types of traps for use in heterogeneous samples. The ideal hologram for a DoG trap being purely real-valued, we introduce a general method based on the Zernike phase-contrast principle to project real-valued holograms with the phase-only diffractive optical elements used in standard holographic optical trapping systems. We demonstrate the capabilities of DoG traps (and Zernike holograms) through experimental studies on high-index, low-index and absorbing colloidal particles dispersed in fluid media.