Particles at Membranes and Interfaces

Soft surfaces experience morphological changes upon interaction with objects at various length scales. Two important classes of soft surfaces are membranes and interfaces. In presence of particles, through surface-mediated interactions soft surfaces exhibit diverse phenomena in nature. A fluid membrane which acts as a protective periphery enclosing cellular material can be described as a two dimensional mathematical surface characterized by `bending elasticity' and `membrane tension'. Similarly, interfaces at the boundary of two liquid phases or a liquid and a gas phase are characterized by their interface tension. Interestingly, a close interplay of the deformation energy of these soft surfaces and the geometry and form of the particles allows the particles to interact. Thus, the study of interactions of particles with membranes and interfaces forms the basis of this work. The mechanistic aspects of cellular entry via membrane wrapping for particles of various geometries are studied theoretically and numerically. Such systems are characterized by the membrane bending rigidity, the membrane tension, and the adhesion strength. The different wrapping states exhibited are ``non wrapped", ``partially wrapped" (with low and high wrapping fraction), and ``completely wrapped". There are two kinds of phase boundaries: a continuous binding transition and a discontinuous transition either between two partially-wrapped states or from a partially-wrapped to a completely wrapped state. The theoretical analysis predicts stable partially wrapped states for nonspherical particles. Nonspherical particles having flat sides can show preferential initial binding though the decisive factor for encapsulation is the ratio of the width to the length of the particles and the softness of its edges. Wrapping energy contributions of the erythrocyte membrane to the invasion energetics for a malarial merozoite that has an asymmetric ``egg-like'' shape is assessed. Furthermore cell adhesion to nanopatterned substrates is characterized to predict optimal shapes of 3D nanoelectrodes for efficient coupling to cells using deformation energy calculations. For a fluid interface dominated by an interfacial tension, self-assembly via capillary interactions for micron-sized nonspherical particles is reported. A nonspherical particle can induce interface distortion due to an undulating contact line creating excess interfacial area. Neighboring particles interact to minimize the excess area via long-range interface-mediated capillary forces. The particle-induced interface distortion due to single ellipsoidal or cuboidal particles are calculated. The near-field nature of the capillary interactions between a pair of particles in different relative orientations is characterized using power-law fits.