Lipopolymer-containing phospholipid bilayers are important because of their potential as biological membrane models and biosensing platforms. This thesis presents systematic studies of lipopolymer self-diffusion, gradient diffusion, and electrophoresis in solid-supported lipid bilayers (SLBs). A reaction-diffusion fluorescence recovery after photobleaching (FRAP) model was developed to improve accuracy in furnishing the self-diffusion coefficient. Fourier transform post-electrophoresis relaxation (PER) was developed to ascertain the gradient diffusion coefficient, which had not been previously measured in two-dimensional membranes. Finally, a photobleaching technique was adopted to measure the electrophoretic mobility. Hindered self-diffusion and enhanced gradient diffusion with increasing lipopolymer concentration in SLBs were observed. The diffusion data at small but finite concentrations were successfully interpreted using existing theories for transmembrane protein diffusion with a soft lipopolymer interaction potential. Lipopolymer electrophoretic mobility qualitatively correlates with lipopolymer concentration in the same manner as the self-diffusion coefficient. However, the drag force during electrophoresis is larger than derived from the self-diffusion coefficient using the Stokes-Einstein relation. This is attributed to the oppositely directed electro-osmotic flow. A continuum model that calculates the hydrodynamic drag on the polymer chains according to a Brinkman model was developed to quantify lipopolymer electrophoresis. This model furnished excellent agreement with experiments, yielding the polymer segment Stokes radius, and a lipid-tail drag coefficient that increases slightly with lipopolymer concentration.
The goal of this Ph.D. research was to gain a fundamental understanding of polymer adsorption onto colloidal particles using optical tweezers micro-electrophoresis (OTE). The research involved the design and development of an OTE platform, which combines multiple optical tweezers (OT) and electrophoresis to measure the electrical response of single colloidal particles with nm spatial and ms dynamic resolution. This experimental work provided new insights into electro-osmotic flow, and polymer adsorption and desorption from colloidal particles. The results were explained using physical models. The frequency-dependent electrical response of single micro-spheres was measured for various electrolytes in parallel-plate micro-channels. The electrical response is governed by anomalous electro-osmotic flow (EOF) dynamics, which are present in compliant channels, and by particle electrophoresis. At limiting high and low frequencies, the EOF dynamics are those of an open and closed channel, respectively. Polymer adsorption (desorption) dynamics onto single colloidal particles were measured as the solvent (or polymer solution) was rapidly displaced. In OTE, the micro-sphere electrical response is complicated by adsorption onto the channel walls. However, in a symmetric polymer-flow configuration the particle electrophoretic mobility (EP) is accurately resolved. For neutral polymers, EP is a sensitive measure of the hydrodynamic layer thickness (HLT). The relationship between EP, HLT and adsorbed amount is obtained from electrokinetic models and equilibrium polymer layer profiles. The HLT growth reflects polymer reptation and diffusion through initially adsorbed layers, and is limited by polymer reconformation dynamics. Desorption kinetics were faster than expected by local-equilibrium models. The micromechanics of polymer composite nanotubes were investigated using multiple optical tweezers in transverse hydrodynamic flows. Directed assembly of latex beads to a single nanotube was undertaken, and two of these beads were used as handles for the nanotube bending experiments. The calculated nanotube Young's moduli were in agreement with macro-scale continuum models for the bulk materials.
Macroscopic failure (fracture) processes are an ubiquitous phenomenon of immense practical importance. In this work, we use liquid aqueous foam as a soft matter model system to study crack propagation and fracture dynamics on length and time scales that are easily accessible in experiment. The experiment injects air at a given pressure into a single layer of bubbles between the parallel plates of a Hele-Shaw setup (a quasi-two-dimensional foam) and is thus able to track the positions and shapes of individual bubbles, which allows for a complete observation of microstructural processes during fracture. We observe that two very different modes of crack propagation are sustained by the system: a relatively slow propagation of an air finger characterized by plasticity around the crack tip (analogous to ductile failure), and a much faster propagation that breaks successive films without large deformations around the crack (analogous to brittle failure). Being composed of only air, water, and surfactant, the foam system allows for a detailed fluid-mechanical description of these processes, for which we derive quantitative relations of both ductile and brittle crack speed as a function of driving pressure. We show that there is a velocity gap between ductile and brittle speeds, and how the upper limit of ductile propagation speed and the lower limit of brittle propagation speed are determined by viscous dissipation and wave propagation in the foam, respectively. Our system also shows a novel phenomenon of transition between the brittle and ductile modes: a brittle crack can undergo a brittle-to-ductile transition (BDT) spontaneously, i.e., while it is propagating. We describe this process by taking into account the dissipative air flow in the crack opening behind the brittle crack tip, and succeed in predicting the location of the BDT as a function of the applied driving. In a given experiment, the speed, direction, and morphology of the crack is influenced significantly by the microstructure of the foam, i.e., the presence and orientation of defects and other irregularities. Throughout this work, we find that the geometry of foam bubbles and the liquid-carrying structures between them is the main determinant for the rich variety of processes observed. The novel experimental model system we have built therefore extends our knowledge of foam physics to previously unexplored phenomena and serves as a minimal model for failure of a cellular material, in which all physical processes and their relation to the material geometry are observable and quantifiable.