  Using a simplified microstructural picture we show that interactions between
thermosenstive microgel particles can be described by a polymer brush like
corona decorating the dense core. The softness of the potential is set by the
relative thickness $L_0$ of the compliant corona with respect to the overall
size of the swollen particle $R$. The elastic modulus in quenched solid phases
derived from the potential is found in excellent agreement with diffusing wave
spectroscopy (DWS) data and mechanical rheometry. Our model thus provides
design rules for the microgel architecture and opens a route to tailor
rheological properties of pasty materials.
