Date of Award

2012

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Physics & Astronomy

First Advisor

Arjun G. Yodh

Second Advisor

Paul A. Janmey

Abstract

This thesis investigates two soft-matter systems, viz., bio-polymer gels and colloidal dispersions under mechanical deformation, to study non-affinity and jamming. Most materials are assumed to deform affinely, i.e., macroscopic applied deformations are assumed to translate uniformly to the microscopic level. This thesis explores the validity of the affine assumption in model polymer networks under shear. Displacements of micron-sized fluorescent polystyrene tracer beads embedded in polyacrylamide (PA) gels are quantified when the sample is sheared. The experiments confirm that the macroscopic elasticity of PA gels behaves in accordance with traditional flexible polymer network elasticity theory. Microscopically, non-affine deformation is detected, and the observations are in qualitative agreement with many aspects of current theories of polymer network non-affinity. The measured non-affinity in PA gels suggests the presence of structural inhomogeneities resulting from the reaction kinetics, which likely predominates over the effects of thermal fluctuations.

Compared to flexible polymer gels, filamentous biopolymer networks generally have higher shear moduli, exhibit a striking increase in elastic modulus with increasing strain, and show pronounced negative normal stress when deformed under shear. Affine deformation is an essential assumption in the theories of these materials. The validity of this assumption is experimentally tested in fibrin and collagen gels. Measurements demonstrate that non-affine deformation is small for networks of thinner, relatively flexible filaments and decreases even further as strain increases into the non-linear regime. Many observations are consistent with the entropic nonlinear elasticity model for semiflexible polymer networks. However, when filament stiffness and mesh-size increase, then deformations become more non-affine and the observations appear to be consistent with enthalpic bending and stretching models.

A qualitatively different set of studies explores the rheology of monodisperse and bidisperse colloidal suspensions near the jamming transition as a function of packing fraction, steady-state strain rate, and oscillatory shear frequency. The experiments employ soft, temperature-sensitive polymer micro-spheres for easy tuning of sample packing fraction and a rheometer in order to explore scaling behaviors of shear stress versus strain rate, and storage/loss shear moduli versus frequency. Under steady shear, rheometer measurements exhibit predicted scaling behavior for volume fractions above and below the jamming transition that agree with scaling observed in monodisperse particle suspensions by microfluidic rheology; importantly, similar scaling behavior is observed for the first time in bidisperse particle suspensions. At finite frequency, new measurements were performed across the jamming transition for both monodisperse and bidisperse suspensions. The storage and loss moduli of the jammed systems, measured as a function of frequency and volume fraction, could be scaled onto two distinct master curves in agreement with simulation predictions [142]. For unjammed systems, stress-relaxation timescale is found to scale with volume fraction.

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