problem 1: 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 confined between two flat 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 finally shrinking by 15% in height. find out the elastic modulus E and equivalent viscosity of the Carbopol material. find out the time the microgel would require to recover to 99% of its initial height after the stress is removed.
problem 2: Consider a solution of lysozyme proteins in 1 mmol/L salt buffer with the Debye length of ca. 10 nm. The charge on proteins at these conditions is 10e, the Hamaker constant H = 10kBT. The shape of the molecule can be approximated by a sphere with radius of 1.7 nm. What is the potential barrier for the molecule aggregation? Will the solution be stable at these conditions? Will it be stable at 100 mmol/L salt concentration?