1) Viscoelasticity: A deformation of cross-linked polymeric microgel particle (Carbopol) is described by the Kelvin-Voigt model (a spring with elastic modulus E and dashpot with viscosity connected in parallel). The elastic response is produced by the polymer skeleton of the particle while the viscous one by the liquid contained in the network. The microgel particle in an AFM experiment is con?ned between two ?at surfaces such that it makes a cylinder with diameter of 2 m. Under constant load of 200 pN, it sags by 5% after 10 seconds while ?nally shrinking by 15% in height. Calculate the elastic modulus E and equivalent viscosity of the Carbopol material. Calculate the time the microgel would require to recover to 99% of its initial height after the stress is removed.
2) Polymer di?usion (5 marks): The ?gure below shows the result of a particle tracking experiment where lateral positions of ?uorescent polystyrene sulphonate (PSS) molecules were recorded. The curve labels on the graph show the polymer concentration in water g/ml.
If the viscosity of the pure water is 1.10-3 Pas and the measurement is done at room temperature, obtain an estimate of
a) size of the molecule (hydrodynamic radius);
b) degree of polymerisation (assuming the Kuhn length for PSS is 3 ° A).
c) viscosity of the concentrated solutions as a function of concentration.
3) Calibration of an optical tweezer: You performed the following calibration experiments at room temp, 25? C for an optically trapped latex bead that is free in solution: x displacements of the trapped bead, in nm, were gathered for some time in stationary water. Fluctuations in position are due to random bombardment of water molecules such as those shown in the ?gure below (black curve). In the second stage of the experiment, the ?uid chamber surrounding the bead was moved along the x direction at a constant velocity of 5.0 m/ms (red curve). Data from an actual experiment, calib no?ow.dat and calib ?ow.dat, can be found on the Black- board/Assignments page. Modeling the optical trap as a Hookean spring, calculate the trap sti?ness using the Boltzmann distribution. Calculate the sphere diameter by comparing the Stokes drag and the tweezer force that balances the drag. Assume the viscosity of water 10-3 Pas.