Interparticle Force Measurements, Microscopic Dynamics, and the Linear Rheology of Colloidal Depletion Gels

We report an experimental study that relates two-particle force measurement by optical trapping and microscopic dynamics from confocal microscopy to the linear viscoelasticity of a colloidal depletion gel (ϕ = 0.20). Fluorescent poly(methyl methacrylate) spherical particles are dispersed in a mixture of 75 vol% cyclohexane:25 vol% cyclohexyl bromide (Δn = 0.03, Δρ/ρ = 0.12). Non-adsorbing polymer is used as the depleting agent at various concentrations (MW = 900,000 g/mol, c = 5.3 to 15.9 mg/ml) to induce an attractive potential. The optical tweezer measurements show a linear increase in the average rupture force as the attraction strength increases, with possible long-range interactions present at high polymer concentrations. The gels exhibit a linear elastic modulus that increases as a function of the non-adsorbing polymer concentration c. Particle tracking measurements of the single particle mean-squared displacement quantify the localization of particles in the gel.  We discuss the correlation between the interparticle force measurements, the microscopic dynamics, and the linear rheology in light of gelation theory, including results from mode coupling theory.