Colloids at liquid interfaces: dynamics and organization

 

This thesis deals with spherical microparticles trapped at liquid interfaces. It focuses on two aspects of their behavior: firstly, the effect of the curvature of a liquid interface on interparticle interactions and their organization; secondly, the mobility of particles at visco-elastic interfaces.

In Chapter 2of this thesis we showed that it is possible to induce capillary interactions between spherical microparticles with homogeneous surface chemistry by tailoring the curvature of the liquid interface. If the interfacial curvature is anisotropic, the constraint of constant contact angle along the contact line can only be satisfied if the interface is deformed locally. These deformations create excess surface area, which changes when two particles approach each other. This leads to a change in the surface free energy, which manifests itself as a capillary interaction between the particles.

To study the effect of curvature on the interactions between particles, we created oil-water interfaces of different shape (ellipsoid, dumbbell, torus and squares) and added spherical negatively charged particles that adsorbed at these interfaces. On all these interfaces, we observed quadrupolar capillary interactions that organized the particles into square lattices. The order of this organization increased with increasing curvature anisotropy, indicating that capillary interactions are stronger as well. By contrast, on flat interfaces or on spherical droplets with homogeneous curvature, no attractive interaction was observed and only at very high surface coverage did the particles order in a hexagonal lattice, as a result of repulsive interactions.

In Chapter 3we studied the interface deformations around particles at curved interfaces and the resulting capillary interactions theoretically. We used the finite element method to solve the Young-Laplace equation for the shape of the interface around a particle and calculated the interaction potential between the particles numerically.

The main finding of these calculations is that for an anisotropically curved interface, with two different local principal curvatures, the particle deforms the interface in two ways simultaneously: concave deformation along one principal direction and convex – along the other, thus creating a deformation field with quadrupolar symmetry. Two particles with such deformations interact favorably only if the overlapping deformations are similar (concave-concave, convex-convex), which occurs when they approach each other along one of the two principal directions. Since the two local principal directions are always perpendicular, particles interacting along them will tend to arrange into a square pattern.

As a consequence of the quadrupolar deformation field, two particles approaching each other along a line forming 45 degrees with the principal axes will repel each other (which is confirmed by our observations), because in this case the deformation fields overlap with four different “petals” (2 pairs of concave-convex), and the excessive surface area doesn’t reduce upon approaching, but increases. A system of two particles oriented at an angle with respect to the principal axis is therefore subjected to a torque rotating the axis of the system so that it gets aligned with one of the two principal directions. The torque magnitude reaches its maximum when the system’s axis is at an angle of 45 degrees with respect to the principal direction and decreases to 0 when the axis is aligned with one of the principal directions.

The family of interaction potentials we obtained allows for calculating the minimum deviatoric curvature needed to initialize capillary interactions strong enough to compete with thermal energy, so that a stable organization can be expected. The calculated value was very close to the deviatoric curvature where ordering was observed experimentally in Chapter 2.

In Chapter 4we studied the mobility of 3 mm polystyrene particles in a monolayer of 1.5 mm core-shell microparticles deposited at flat air-water interfaces; all the particles present in the system were stabilized by negative charges.

In this exploratory chapter we made an attempt to characterize the mechanical properties of such monolayers by analyzing the mobility of the larger tracer particles in the monolayer.  With increasing particle density of the monolayer, we observed that the mean-square displacement of the tracer particles was reduced, which can be interpreted as an increase of the viscosity of the monolayer. At very high densities the motion of the particles became subdiffusive and confined, pointing at elasticity of the monolayer. We also studied correlated movements between neighboring particles in an attempt to do two-point interfacial microrheology. A comparison between the one-point and two-point methods shows clear indications of heterogeneous dynamics of the tracer particles. Our results therefore call for a further development of two-point microrheology at interfaces.

In Chapter 5we used tracer particles to study the properties of thin cross-linked actin networks deposited at the surface of oil droplets. These networks are a model system for the intracellular actin cortex. We used the generalized Stokes-Einstein relation to extract the complex frequency-dependent shear modulus of such networks from the movement of the added tracer particles. We studied the effects of the length of actin filaments and the cross-linker concentration on the mechanical properties of these layers.

The advantage of this system is that actin networks are freely accessible from the water phase, and therefore can be subjected to in-situ addition of cross-linkers, enzymes or other chemicals of interest. Using this, we managed to show strong stiffening after addition of myosin motor proteins and ATP, which we ascribed to contraction of the actin-myosin network.